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IL-10 constrains sphingolipid metabolism to limit inflammation

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Nature, Published online: 21 February 2024; doi:10.1038/s41586-024-07098-5

IL-10 exerts its anti-inflammatory activity in macrophages by increasing the expression of enzymes that promote fatty acid desaturation and downstream regulation of the transcription factor REL.

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Light can restore a heart’s rhythm

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Directive giant upconversion by supercritical bound states in the continuum

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Theory

In the section ‘TCMT: critical coupling for an isolated mode’, the local field enhancement at critical coupling for an isolated resonant mode is demonstrated. In the section ‘Open-resonator TCMT’, the non-Hermitian Hamiltonian formalism of TCMT for FW-BIC formation is used. It will be shown that, as the asymptotic condition of BIC cannot be ideally reached, the FW quasi-BIC originates from non-orthogonal modes. This understanding will then be used in the section ‘Supercritical coupling’ to evaluate the coupling between the dark FW quasi-BIC and the bright leaky partner, demonstrating the analogy to EIT and the equation for supercritical local field enhancement. In the section ‘RCWA validation’, we validate the TCMT results using RCWA.

TCMT: critical coupling for an isolated mode

The basic equation describing the evolution of the mode amplitude A₁ (oscillator 1) in a resonating system with a characteristic angular frequency ω₁ = 2πc/λ₁, is

$$\frac{{\rm{d}}{A}_{1}}{{\rm{d}}t}=\,j{\omega }_{1}{A}_{1}-\left(\frac{1}{{\tau }_{{\rm{a}}}}+\frac{1}{{\tau }_{{\rm{r}}}}\right){A}_{1},$$

(2)

in which energy can be lost through absorption (or other additive non-radiative channels, such as scattering by dielectric fluctuations or in-plane leakage) with decay rate γ_a = 1/τ_a, as well as through direct far-field coupling with external radiation in the outer space with a decay rate γ_r = 1/τ_r. The amplitude is normalized such that |A₁|² represents the energy of the mode¹⁵. When adding the driving field of power |s₊|² and monochromatic time dependence exp(jω_int), associated with the external excitation and coupled with the resonator with coefficient κ_i, the equation becomes

$$\frac{{\rm{d}}{A}_{1}}{{\rm{d}}t}=\,j{\omega }_{1}{A}_{1}-\left(\frac{1}{{\tau }_{{\rm{a}}}}+\frac{1}{{\tau }_{{\rm{r}}}}\right){A}_{1}+{\kappa }_{{\rm{i}}}\,{s}_{+}.$$

(3)

The solution is

$${A}_{1}({\omega }_{{\rm{in}}})=\frac{{\kappa }_{{\rm{i}}}\,{s}_{+}}{j({\omega }_{{\rm{in}}}-{\omega }_{1})+\left(\frac{1}{{\tau }_{{\rm{a}}}}+\frac{1}{{\tau }_{{\rm{r}}}}\right)}.$$

(4)

It is possible to demonstrate that the input power coupling must be related to the radiation decay as ${\kappa }_{{\rm{i}}}=\sqrt{2/{\tau }_{{\rm{r}}}}$ by invoking energy conservation and time-reversal symmetry of Maxwell’s equations. On resonance, that is, when the input frequency 2πc/λ_in = ω_in is set at the peak ω₁, it follows that

$${A}_{1}({\omega }_{1})=\frac{\sqrt{2/{\tau }_{{\rm{r}}}}{s}_{+}}{1/{\tau }_{{\rm{a}}}+1/{\tau }_{{\rm{r}}}}.$$

(5)

Now let us consider that the quality factor Q of a resonator is defined as the ratio between the stored (W) and the lost energy fractions. Indeed, for the absorption-related power loss P_abs (or, more generally, all non-radiative losses) and the radiation loss P_rad, the following holds true

$$\frac{1}{Q}=\frac{1}{{Q}_{{\rm{a}}}}+\frac{1}{{Q}_{{\rm{r}}}}=\frac{{P}_{{\rm{abs}}}}{{\omega }_{1}W}+\frac{{P}_{{\rm{rad}}}}{{\omega }_{1}W}=\frac{2}{{\omega }_{1}}\left(\frac{1}{{\tau }_{{\rm{a}}}}+\frac{1}{{\tau }_{{\rm{r}}}}\right)=\frac{2}{{\omega }_{1}}\left({\gamma }_{{\rm{a}}}+{\gamma }_{{\rm{r}}}\right).$$

(6)

The driving field has amplitude E_i = s₊/A_c, in which A_c is a normalized cross-section, which we define as A_c = 1, for simplicity. The local field of the resonant mode has amplitude given by ${E}_{{\rm{loc}}}={A}_{1}/\sqrt{{V}_{{\rm{eff}}}}$, with V_eff the normalized effective mode volume. Thus, from equation (5), it follows that the local field enhancement G is given by

$$G=\frac{| {E}_{{\rm{loc}}}{| }^{2}}{| {E}_{{\rm{i}}}{| }^{2}}\simeq \frac{{Q}^{2}}{{Q}_{{\rm{r}}}{V}_{{\rm{eff}}}}=\frac{{Q}_{{\rm{a}}}^{2}{Q}_{{\rm{r}}}^{2}}{{Q}_{{\rm{r}}}{({Q}_{{\rm{r}}}+{Q}_{{\rm{a}}})}^{2}{V}_{{\rm{eff}}}},$$

(7)

and depends on the ratio between the total quality factor Q = 1/(1/Q_a + 1/Q_r) = Q_aQ_r/(Q_a + Q_r) and the radiation quality factor Q_r. Clearly, if Q_r ≫ Q_a as for the ideal BIC with Q_r → ∞, then asymptotically $G\approx {Q}_{{\rm{a}}}^{2}/{Q}_{{\rm{r}}}\to 0$. The maximum enhancement G_cr is reached when Q_r = Q_a, at the critical coupling condition, for which

$${G}_{{\rm{cr}}}\approx \frac{{Q}_{{\rm{a}}}^{4}}{{Q}_{{\rm{a}}}^{3}{V}_{{\rm{eff}}}}=\frac{{Q}_{{\rm{a}}}}{{V}_{{\rm{eff}}}}.$$

(8)

The above result has been applied to BICs in several papers¹³ and its origin dates to the general theory of optical and electrical resonators discussed in textbooks¹⁵. Supposing a nearly ideal resonator with Q_r = Q_a, the maximum field enhancement would reach the physical capacity limit imposed by the unavoidable system losses represented by Q_a. In dielectric resonators sustaining quasi-BICs, the critical coupling point can be approached by breaking the in-plane symmetry of the system to tune the radiation quality factor that scales quadratically with the asymmetry parameter⁵, which requires precise nanostructure engineering and knowledge of the system losses.

Open-resonator TCMT

The theory of FW-BIC formation owing to coupling of two leaky modes has been reviewed in ref. ⁴⁷. The demonstration based on the non-Hermitian Hamiltonian of temporal coupled modes can be found in recent papers¹⁹. The formation of FW-BICs has gained attention particularly in the context of photonic-crystal slabs with vertical asymmetry, in which TM-like and TE-like modes couple and interfere^48,49. However, it is worth noting that the existence of non-radiating modes arising from the interference of vector TE-like and TM-like eigenmodes was first discussed in ref. ¹⁷. It was found that, in 2D holey textured slabs, TE and TM modes can couple at virtually any point in the first Brillouin zone, leading to anticrossing of their dispersion and formation of a mode with zero imaginary part of its eigenfrequency, known as an FW-BIC². In this study, a photonic-crystal slab placed over a dielectric waveguide substrate with air cladding was considered, breaking vertical symmetry and favouring the coupling of vector TE-like and TM-like modes. The same system was used in our previous work¹⁰, in which we experimentally observed and applied the FW quasi-BIC, and it is also used in the present study.

To develop what we term the ‘supercritical enhancement equation’, we start from the non-Hermitian Hamiltonian of coupled waves^25,48. By generalizing equation (3), the dynamic equations for resonance amplitudes can be written in the following form

$$\frac{{\rm{d}}{\bf{A}}}{{\rm{d}}t}=(\,j\hat{\varOmega }-{\hat{\varGamma }}_{{\rm{r}}}-{\hat{\varGamma }}_{{\rm{a}}}){\bf{A}}+{\hat{K}}_{{\rm{i}}}^{{\rm{T}}}{{\bf{s}}}^{+},$$

(9)

$${{\bf{s}}}^{-}=\hat{C}{{\bf{s}}}^{+}+\hat{D}{\bf{A}},$$

(10)

in which both $\hat{\varOmega }$ and ${\hat{\varGamma }}_{{\rm{r}}}$ matrices are Hermitian matrices representing the resonance frequencies and the radiation decay, respectively. On the other hand, ${\hat{\varGamma }}_{{\rm{a}}}$ represents non-radiative losses and is initially set to zero ${\hat{\varGamma }}_{{\rm{a}}}=0$ to isolate the radiative rate associated with an ideal BIC. The resonant mode is excited by the incoming far-field waves s⁺ coupled to the resonator with coefficients denoted by ${\hat{K}}_{{\rm{i}}}$. The outgoing waves s⁻ depend on the direct scattering channel $\hat{C}$ and the resonant modes A by means of the decay port coefficients in $\hat{D}$. Energy conservation and time-reversal symmetry imply that ${\hat{K}}_{{\rm{i}}}=\hat{D}$ and that the coupling with the port is linked with radiation loss, implying that ${\hat{D}}^{\dagger }\hat{D}=2{\hat{\varGamma }}_{{\rm{r}}}$. These relationships determine the elements of ${\hat{K}}_{{\rm{i}}}^{{\rm{T}}}$ and imply that ${\rm{r}}{\rm{a}}{\rm{n}}{\rm{k}}({\hat{\varGamma }}_{{\rm{r}}})={\rm{r}}{\rm{a}}{\rm{n}}{\rm{k}}({\hat{D}}^{\dagger }\hat{D})={\rm{r}}{\rm{a}}{\rm{n}}{\rm{k}}(\hat{D})$. Also, $\hat{D}=-\,\hat{C}\,{\hat{D}}^{\star }$. Let us consider a system denoted by A = (A₁, A₂)^T, in which A₁ and A₂ represent the amplitudes of two modes with frequencies ω₁ and ω₂, respectively. These resonances have radiative lifetimes τ_r1 = 1/γ_r1 and τ_r2 = 1/γ_r2. Moreover, both resonances may experience absorption loss, characterized by 1/τ_a = γ_a. It is important to note that, for the specific case of the avoided crossing point, the absorption terms for both modes are the same, as we demonstrate below. Then, in general, γ_1,2 = γ_r1,r2 + γ_a, but for now, let’s turn γ_a = 0.

Recall that the modes of the resonator are defined as the eigenmodes of the non-Hermitian Hamiltonian operator $\hat{H}=j\hat{\varOmega }-{\hat{\varGamma }}_{{\rm{r}}}$ (neglecting non-radiative loss). Only Hermitian matrices allow for a diagonal representation with orthogonal eigenvectors, whereas non-Hermitian matrices may have linearly dependent or linearly independent but non-orthogonal eigenvectors, or they may have orthogonal eigenvectors depending on specific properties such as parity–time symmetry. The Hamiltonian and its eigenvalues are functions of the in-plane momentum k = k_o(sinθcosϕ, sinθsinϕ). A previous study demonstrated that the eigenvectors of the non-Hermitian Hamiltonian are always non-orthogonal when the total number of independent decay ports is less than the number of optical modes and both modes are coupled to the decay ports²⁵. The crucial concept here is that of independent decay ports, which are related to the sharing of the vertical symmetry of the modes. In the case of evolving TE-like and TM-like modes, the inversion of their character at the avoided crossing can occur at any point in energy–momentum space. We know that the eigenmodes of a matrix form an orthogonal basis if and only if ${\hat{H}}^{\dagger }\hat{H}=\hat{H}{\hat{H}}^{\dagger }$. Because both $\hat{\varOmega }$ and ${\hat{\varGamma }}_{{\rm{r}}}$ are Hermitian, this is equivalent to the relation $\hat{\varOmega }\,{\hat{\varGamma }}_{{\rm{r}}}={\hat{\varGamma }}_{{\rm{r}}}\,\hat{\varOmega }$, which implies that $\hat{\varOmega }$ and ${\hat{\varGamma }}_{{\rm{r}}}$ can be simultaneously diagonalized. When considering two eigenmodes and a single independent radiation channel, in which ${\rm{r}}{\rm{a}}{\rm{n}}{\rm{k}}({\hat{\varGamma }}_{{\rm{r}}})=1$, one of the orthogonal eigenmodes of the matrix will have a pure imaginary eigenvalue. This indicates that one of the two modes has an infinite lifetime (BIC) and does not couple to the decay port. As a non-zero coupling with the single decay port exists, the two eigenvectors in the resonator system will always be non-orthogonal²⁵. Therefore, the modes are generally non-orthogonal if a single radiation channel is involved. However, they can satisfy the orthogonality condition at a specific point in momentum space. This point is referred to as an ideal FW-BIC point k_BIC when the Hamiltonian ($\hat{H}=j\hat{\varOmega }-{\hat{\varGamma }}_{{\rm{r}}}$, defined below) has a purely imaginary eigenvalue (or, equivalently, $\hat{\varOmega }+j{\hat{\varGamma }}_{{\rm{r}}}$ has a purely real eigenvalue). This allows for the simultaneous diagonalization of the Hermitian matrices $\hat{\varOmega }$ and ${\hat{\varGamma }}_{{\rm{r}}}$.

FW condition

The Hamiltonian of a two-waves-two-ports system is represented as:

$$\hat{H}=j(\begin{array}{cc}{\omega }_{1} & \kappa \\ \kappa & {\omega }_{2}\end{array})-(\begin{array}{cc}{\gamma }_{{\rm{r}}1} & X\\ {X}^{\star } & {\gamma }_{{\rm{r}}2}\end{array})=j(\begin{array}{cc}{\omega }_{1}+j{\gamma }_{{\rm{r}}1} & \kappa +jX\\ \kappa +j{X}^{\star } & {\omega }_{2}+j{\gamma }_{{\rm{r}}2}\end{array})\equiv j(\begin{array}{cc}{\mathop{\omega }\limits^{ \sim }}_{1} & {\mathop{\omega }\limits^{ \sim }}_{12}\\ {\mathop{\omega }\limits^{ \sim }}_{21} & {\mathop{\omega }\limits^{ \sim }}_{2}\end{array}),$$

(11)

in which κ measures the near-field coupling and X represents the coupling mediated by the continuum between the two closed, uncoupled channel resonances of frequencies ω₁ and ω₂. Following the calculation in refs. ^19,25, X can be expressed as

$$X=\sqrt{{\gamma }_{{\rm{r1}}}{\gamma }_{{\rm{r2}}}}{{\rm{e}}}^{j\psi },$$

(12)

in which the phase angle ψ describes the relative phase of the coupling with the open channel and in general with the two ports (up and down). The eigenvalues of the two diagonal frequency and decay matrices of the Hamiltonian at the BIC point, defined by

$$\hat{{H}^{{\rm{r}}}}({{\bf{k}}}_{{\rm{B}}{\rm{I}}{\rm{C}}})=\hat{\varOmega }+j{\hat{\varGamma }}_{{\rm{r}}}=(\begin{array}{cc}{\mathop{\omega }\limits^{ \sim }}_{+} & 0\\ 0 & {\mathop{\omega }\limits^{ \sim }}_{-}\end{array})+j(\begin{array}{cc}{\mathop{\gamma }\limits^{ \sim }}_{+} & 0\\ 0 & {\mathop{\gamma }\limits^{ \sim }}_{-}\end{array}),$$

(13)

and associated with the collective modes ${\widetilde{A}}_{+},{\widetilde{{\rm{A}}}}_{-}$, are related to the uncoupled mode frequency and decay rates by

$${\mathop{\omega }\limits^{ \sim }}_{\pm }+{j\mathop{\gamma }\limits^{ \sim }}_{\pm }=({\omega }_{1}+{\omega }_{2})/2+j({\gamma }_{{\rm{r}}1}+{\gamma }_{{\rm{r}}2})/2\,+$$

(14)

$$\pm \frac{1}{2}\sqrt{{\left[({\omega }_{1}-{\omega }_{2})+j({\gamma }_{{\rm{r}}1}-{\gamma }_{{\rm{r}}2})\right]}^{2}+4{\left(\kappa +j\sqrt{{\gamma }_{{\rm{r}}1}{\gamma }_{{\rm{r}}2}}{{\rm{e}}}^{j\psi }\right)}^{2}}.$$

(15)

This relation allows us to determine the asymptotic FW condition as a function of the uncoupled mode frequency, the decay rate and the coupling rate among closed channel modes κ

$$\kappa ({\gamma }_{{\rm{r}}1}-{\gamma }_{{\rm{r}}2})=\sqrt{{\gamma }_{{\rm{r}}1}{\gamma }_{{\rm{r}}2}}{{\rm{e}}}^{j\psi }({\omega }_{1}-{\omega }_{2}),$$

(16)

$$\psi =m{\rm{\pi }},\,m\in {\mathscr{Z}}$$

(17)

Substituting (γ_r1 − γ_r2) from equation (16) into equation (15), it is possible to find that the third term with the square root is exactly equal to the second term in equation (14) and cancels, or adds with it, depending on the sign ±. The dark mode acquires ideally zero radiation loss (say, ${\widetilde{\omega }}_{-}$ without loss of generality). At this condition, the eigenvalues are

$${\mathop{\omega }\limits^{ \sim }}_{+}{+j\mathop{\gamma }\limits^{ \sim }}_{+}=\frac{{\omega }_{1}+{\omega }_{2}}{2}+\frac{\kappa ({\gamma }_{{\rm{r}}1}+{\gamma }_{{\rm{r}}2})}{2\sqrt{{\gamma }_{{\rm{r}}1}{\gamma }_{{\rm{r}}2}}{{\rm{e}}}^{j\psi }}+\,j({\gamma }_{{\rm{r}}1}+{\gamma }_{{\rm{r}}2}),$$

(18)

$${\mathop{\omega }\limits^{ \sim }}_{-}+\,j{\mathop{\gamma }\limits^{ \sim }}_{-}=\frac{{\omega }_{1}+{\omega }_{2}}{2}-\frac{\kappa ({\gamma }_{{\rm{r}}1}+{\gamma }_{{\rm{r}}2})}{2\sqrt{{\gamma }_{{\rm{r}}1}{\gamma }_{{\rm{r}}2}}{{\rm{e}}}^{j\psi }},\,\,\,{\rm{w}}{\rm{i}}{\rm{t}}{\rm{h}}\,{\mathop{\gamma }\limits^{ \sim }}_{-}=0,$$

(19)

in which the wave of amplitude ${\widetilde{A}}_{-}$ has no radiative loss and becomes the ideal FW-BIC (ideally dark mode), whereas all radiative loss is transferred to the bright mode ${\widetilde{A}}_{+}$. At this point in momentum space (k = k_BIC), $\hat{\varOmega }$ and ${\hat{\varGamma }}_{{\rm{r}}}$ are both diagonal, and because ${\rm{r}}{\rm{a}}{\rm{n}}{\rm{k}}({\hat{\varGamma }}_{{\rm{r}}})=1$ (only a single independent decay port exists), the resonant states interfere to annihilate the coupling with the radiation channel of the BIC mode, which guarantees energy conservation, as any coupling among the final orthogonal modes asymptotically vanishes⁴⁷.

However, arbitrarily close to the BIC point in the momentum, both modes experience non-zero radiative loss. The modes are coupled with a single independent radiation channel and, thus, are non-orthogonal because their coupling guarantees energy conservation. This behaviour holds true in any real system, particularly with momentum close to ideal FW-BICs, referred to as FW quasi-BICs. It is worth mentioning that, in the presence of non-negligible absorption loss, the modes are always non-orthogonal. If we perturb the ideal FW-BIC condition by moving in momentum space, in the representation in which $\hat{\varOmega }$ is diagonal, in general, ${\hat{\Gamma }}_{r}$ must have non-zero off-diagonal terms to ensure energy conservation, or similarly, in the representation in which ${\hat{\varGamma }}_{{\rm{r}}}$ is diagonal, $\hat{\varOmega }$ must have non-zero off-diagonal terms, κ_12,21, which represent the near-field coupling. This is a key concept that implies that $\forall {\bf{k}}:{\bf{k}}\simeq {{\bf{k}}}_{{\rm{BIC}}}$, the new perturbed Hamiltonian $\hat{{H}^{{\rm{r}}}}({\bf{k}}\simeq {{\bf{k}}}_{{\rm{B}}{\rm{I}}{\rm{C}}})$ for the final coupled modes, the FW quasi-BIC ${A}_{-}({\bf{k}}\simeq {{\bf{k}}}_{{\rm{B}}{\rm{I}}{\rm{C}}})$ and bright ${A}_{+}({\bf{k}}\simeq {{\bf{k}}}_{{\rm{B}}{\rm{I}}{\rm{C}}})$ modes, can be represented with non-zero off-diagonal terms in $\hat{\varOmega }({\bf{k}}\simeq {{\bf{k}}}_{{\rm{B}}{\rm{I}}{\rm{C}}})$, when ${\hat{\varGamma }}_{{\rm{r}}}$ is diagonal because of energy conservation, as described below (Extended Data Fig. 1a).

The same non-Hermitian Hamiltonian can also describe the effect of coupled-resonance-induced transparency resulting from the interference of non-orthogonal eigenvectors, that is, at a wavevector different from the ideal FW-BIC condition. Hsu et al. demonstrated that, when several resonances (two or more) are connected to a single independent decay port, a transparency window, known as coupled-resonance-induced transparency, always occurs regardless of the radiation loss values of the resonances because of the off-diagonal terms²¹. Therefore, this coupling, also necessary for any FW quasi-BIC point, can give rise to coupled-resonance-induced transparency in special cases. The condition for EIT can, in principle, also occur with momentum near the ideal FW-BIC point, for example, when k_EIT = k_BIC + δk (Extended Data Fig. 1a). At the EIT point, the slow light condition increases the photon–matter interaction time, enhancing emission properties.

Supercritical coupling

Coupled-resonance-induced transparency in far-field representation

We first describe the occurrence of the transparency condition in the far-field representation and its link with the near-field representation. We then consider the perturbation of the Hamiltonian close to the FW-BIC to explicitly demonstrate that the FW quasi-BIC, despite being a quasi-dark mode, can reach the maximum physical limit of the local field enhancement under the supercritical coupling condition, thanks to the near-field coupling with its bright partner. The calculations presented here follow refs. ^21,25 for clarity of description, but with harmonic time dependence convention exp(jω_int). Let us first restate the TCMT problem by writing the dynamical equations for the two modes that are non-orthogonal in the representation in which $\hat{\varOmega }({\bf{k}})$ is diagonal, with a single radiation channel. Because the representation is changed with respect to equation (11), we consider different symbols for elements in the matrices and we adopt this representation only because the condition for EIT emergence is rather simple to show:

$$\frac{{\rm{d}}}{{\rm{d}}t}\left(\begin{array}{c}{A}_{1}\\ {A}_{2}\end{array}\right)=\left[j\left(\begin{array}{cc}{\bar{\omega }}_{1} & 0\\ 0 & {\bar{\omega }}_{2}\end{array}\right)-\left(\begin{array}{cc}{\bar{\gamma }}_{{\rm{r}}1} & {\gamma }_{12}\\ {\gamma }_{12} & {\bar{\gamma }}_{{\rm{r}}2}\end{array}\right)-\left(\begin{array}{cc}{\gamma }_{{\rm{a}}} & 0\\ 0 & {\gamma }_{{\rm{a}}}\end{array}\right)\right]\left(\begin{array}{c}{A}_{1}\\ {A}_{2}\end{array}\right)+\left(\begin{array}{c}{d}_{1}\\ {d}_{2}\end{array}\right){s}^{+},$$

(20)

$${s}^{-}={c}_{21}{s}^{+}+{d}_{1}{A}_{1}+{d}_{2}{A}_{2}.$$

(21)

In equation (20), the off-diagonal terms γ₁₂ in the radiative decay matrix must be non-zero for energy conservation if both modes decay in the channel, meaning that the decay matrix and the frequency matrix cannot have diagonal forms simultaneously^21,25. In equation (21), s⁻ is the transmitted wave and we have, owing to the presence of the substrate-breaking vertical symmetry, that the direct scattering matrix elements are c₁₁ = −c₂₂ = (1 − n)/(1 + n), with n index of the substrate and ${c}_{12}={c}_{21}=2\sqrt{n}/(1+n)$. Equation (21) simplifies when the system is mirror symmetric because n = 1 (ref. ²¹). Invoking again energy conservation and time-reversal symmetry and using the relations between ${\hat{\varGamma }}_{{\rm{r}}}$, $\hat{C}$ and $\hat{D}$:

$${d}_{1,2}=j\sqrt{2{\bar{\gamma }}_{{\rm{r}}1,{\rm{r}}2}/(n+1)},$$

(22)

$${\gamma }_{12}=\sqrt{{\bar{\gamma }}_{{\rm{r}}1}{\bar{\gamma }}_{{\rm{r}}2}}.$$

(23)

Let us keep using a mirror-symmetric system to determine the condition of induced transparency. The experimental case is then calculated with RCWA, showing that the condition for induced transparency also holds for vertical asymmetry. The complex transmission coefficient at regime is²⁵

$$t={{\rm{c}}}_{21}\mp \frac{({c}_{11}\pm {c}_{12})[\,j({\omega }_{{\rm{in}}}-{\bar{\omega }}_{2})+{\gamma }_{{\rm{a}}}]{\bar{\gamma }}_{{\rm{r}}1}+[\,j({\omega }_{{\rm{in}}}-{\bar{\omega }}_{1})+{\gamma }_{{\rm{a}}}]{\bar{\gamma }}_{{\rm{r}}2}}{[\,j({\omega }_{{\rm{in}}}-{\bar{\omega }}_{1})+{\gamma }_{{\rm{a}}}+{\bar{\gamma }}_{{\rm{r}}1}][\,j({\omega }_{{\rm{in}}}-{\bar{\omega }}_{2})+{\gamma }_{{\rm{a}}}+{\bar{\gamma }}_{{\rm{r}}2}]-{\bar{\gamma }}_{{\rm{r}}1}{\bar{\gamma }}_{{\rm{r}}2}},$$

(24)

in which |c₁₁ + c₁₂| = |c₂₂ − c₁₂| and we have already established that absorption is the same for both modes and given by γ_a. The top (bottom) signs are used when both modes are even (odd) with respect to vertical symmetry. In the limit ${\gamma }_{{\rm{a}}}\ll {({\bar{\omega }}_{1}-{\bar{\omega }}_{2})}^{2}/\max ({\bar{\gamma }}_{{\rm{r}}1},{\bar{\gamma }}_{{\rm{r}}2})$, the absorptive decay rate is sufficiently small that the transmission coefficient approaches 1 (EIT condition) when the numerator of the second term becomes zero at the transparency frequency ω_t, given by

$${\omega }_{{\rm{in}}}=\frac{{\bar{\omega }}_{1}{\bar{\gamma }}_{{\rm{r}}2}+{\bar{\omega }}_{2}{\bar{\gamma }}_{{\rm{r}}1}}{{\bar{\gamma }}_{{\rm{r}}1}+{\bar{\gamma }}_{{\rm{r}}2}}\doteq {\omega }_{{\rm{t}}}.$$

(25)

This condition is always fulfilled when ${\bar{\omega }}_{1} < {\omega }_{{\rm{in}}} < {\bar{\omega }}_{2}$ provided that the resonances are sufficiently close, regardless of their radiative damping. In a real system for γ_a ≠ 0, the approximation to this condition is a consequence of the optical theorem, for which t cannot reach ideally 1. Nonetheless, the fast dispersion induced at the transparency frequency leads to an enhancement of the local optical field^50,51,52. Indeed, when the EIT is approached, light is substantially slowed down, which favours light–matter interactions and enhances the optical-emission process. With this simple demonstration, we have proved that FW-BIC and EIT can be close in principle in the momentum space. Indeed, the induced transparency arises from the coupling of two optical modes to the same radiation channel, which is also the same framework near FW-BIC.

Near-field representation

Although the diagonal frequency matrix representation is useful for finding the transparency condition, the next one will provide more insight into the mode coupling. Let us now rewrite the dynamic equations (20) in the representation in which the radiative decay is diagonal. We will indicate the final eigenvector waves at k = k_EIT with amplitudes A′₊ and A′₋ (not to be confused with the amplitudes ${\widetilde{A}}_{+},{\widetilde{{\rm{A}}}}_{-}$ at the FW-BIC wavevector k = k_BIC in equation (13). As mentioned earlier, ${\rm{r}}{\rm{a}}{\rm{n}}{\rm{k}}({\hat{\varGamma }}_{{\rm{r}}})={\rm{r}}{\rm{a}}{\rm{n}}{\rm{k}}(\hat{D})=1$. Thus, in its diagonal representation, ${\hat{\varGamma }}_{{\rm{r}}}$ has only one non-trivial element because the determinant must be zero. It is straightforward to demonstrate that, in this equivalent representation (with c₂₁ = 1),

$$\frac{{\rm{d}}}{{\rm{d}}t}\left(\begin{array}{c}{{A}^{{\prime} }}_{+}\\ {{A}^{{\prime} }}_{-}\end{array}\right)=\left[j\left(\begin{array}{cc}{{\omega }^{{\prime} }}_{+} & {{\kappa }^{{\prime} }}_{12}\\ {{\kappa }^{{\prime} }}_{12} & {{\omega }^{{\prime} }}_{-}\end{array}\right)-\left(\begin{array}{cc}{{\gamma }^{{\prime} }}_{+} & 0\\ 0 & 0\end{array}\right)-\left(\begin{array}{cc}{{\gamma }^{{\prime} }}_{{\rm{a}}} & {{\zeta }^{{\prime} }}_{12}\\ {{\zeta }^{{\prime} }}_{21} & {{\gamma }^{{\prime} }}_{{\rm{a}}}\end{array}\right)\right]\left(\begin{array}{c}{{A}^{{\prime} }}_{+}\\ {{A}^{{\prime} }}_{-}\end{array}\right)+\left(\begin{array}{c}{{d}^{{\prime} }}_{1}\\ 0\end{array}\right){s}^{+},$$

(26)

$${s}^{-}={s}^{+}+{{d}^{{\prime} }}_{1}\,{{A}^{{\prime} }}_{+},$$

(27)

in which the connection with the previous representation of the diagonal frequency matrix is given by:

$${{\omega }^{{\prime} }}_{+}=\frac{{\bar{\omega }}_{1}{\bar{\gamma }}_{{\rm{r}}1}+{\bar{\omega }}_{2}{\bar{\gamma }}_{{\rm{r}}2}}{{\bar{\gamma }}_{{\rm{r}}1}+{\bar{\gamma }}_{{\rm{r}}2}},$$

(28)

$${{\omega }^{{\prime} }}_{-}=\frac{{\bar{\omega }}_{1}{\bar{\gamma }}_{{\rm{r}}2}+{\bar{\omega }}_{2}{\bar{\gamma }}_{{\rm{r}}1}}{{\bar{\gamma }}_{{\rm{r}}1}+{\bar{\gamma }}_{{\rm{r}}2}},$$

(29)

$${{\kappa }^{{\prime} }}_{12}=\frac{({\bar{\omega }}_{2}-{\bar{\omega }}_{1})\sqrt{{\bar{\gamma }}_{{\rm{r}}1}{\bar{\gamma }}_{{\rm{r}}2}}}{{\bar{\gamma }}_{{\rm{r}}1}+{\bar{\gamma }}_{{\rm{r}}2}},$$

(30)

$${{\gamma }^{{\prime} }}_{+}={\bar{\gamma }}_{{\rm{r}}1}+{\bar{\gamma }}_{{\rm{r}}2},$$

(31)

$${{\gamma }^{{\prime} }}_{-}=0,$$

(32)

$${d}_{1}^{{\prime} }=\sqrt{{d}_{1}^{2}+{d}_{2}^{2}}.$$

(33)

The above relations are useful because they directly state that the transparency frequency ω_t = ω′₋, that is, it corresponds to the final dark mode. This link is important: at the transparency frequency, the fast dispersion slows down the light and enhances the local field, which corresponds to the dark mode. Although in the previous representation we were dealing with non-orthogonal modes in which their coupling was expressed in the far field, in this second representation, we can see that a non-radiative dark mode with γ′₋ = 0 is coupled by means of a non-zero near-field constant κ′₁₂ to a bright leaky wave with a decay rate ${{\gamma }^{{\prime} }}_{+}={\bar{\gamma }}_{{\rm{r}}1}+{\bar{\gamma }}_{{\rm{r}}2}$. These identities must not be confused with equations (18) and (19) that express the relations between the diagonal dark and bright modes at the FW-BIC point k = k_BIC with the original uncoupled modes. Instead, the above equations refer to two different representations of the same modes at fixed and same wavevector k = k_EIT ≠ k_BIC. Here, when the drive field is turned off, the dark-mode amplitude decays to zero. In the linear regime, exchange energy occurs between the modes. We see below that, while the drive field is on, energy flows from the bright mode to the dark mode. As the drive field is turned off, energy flows from the dark mode to the bright mode. Consequently, the dark mode undergoes decay in the far field owing to its nearly zero direct coupling with the radiation channel and its non-zero near-field coupling with the bright mode⁵³. In this alternative representation, it is the near-field coupling between a dark mode and the bright mode that gives rise to the transparency condition. This formulation aligns with the general framework used in the subradiant–superradiant model, which illustrates the analogue of EIT in photonic and plasmonic systems^50,51,52.

Maximum enhancement at the FW quasi-BIC

The FW-BIC and classical analogue of EIT formalisms are derived from the same original framework of modes coupled to a single radiation channel: the EIT with non-zero off-diagonal terms, whereas the ideal FW-BIC is a limit of this framework with zero off-diagonal terms. Because the EIT occurs at the avoided crossing, FW-BIC must not be at the avoided crossing, which implies that the radiative decay rates of the closed channel modes in equation (16) differ, γ_r1 ≠ γ_r2. Thus, the ideal FW-BIC is not at the avoided crossing (ω₁ = ω₂) but is shifted in its vicinity. Both conditions can be fulfilled, in principle, for close wavevectors when, for example, γ_r1 ≃ 5γ_r2 (see the simulated linewidths when the modes do not cross each other in Extended Data Fig. 3; orientation angle of the photonic crystal ϕ = 45°). This also means that the realization of EIT is possible when the involved dark mode is a perturbation of the FW-BIC mode, that is, it exhibits characteristics of an FW quasi-BIC. Although this will be shown using RCWA in our system, let us now explore the consequences for enhancing the local optical field.

As shown in the scheme of Extended Data Fig. 1a, let us write explicitly the dynamical equations (13) and add the perturbation of the diagonal representation (FW-BIC point) of the Hamiltonian as we move away from the ideal BIC wavevector towards the EIT point. Because the radiative Q factor of a BIC scales as |k − k_BIC|^−α with α ≥ 2, for any wavevector close to the BIC point, k = k_BIC + Δq ≃ k_BIC, it is necessary to admit a finite non-zero decay rate of the dark mode A₋, that is, 1/γ₋ = τ_R1 with γ₋ → ε ≳ 0 and, as such, it is necessary to include a non-zero mode coupling κ₁₂ ≠ 0 to guarantee energy conservation, as both modes are coupled to a single independent radiation channel. The perturbed Hamiltonian is $\hat{{H}^{{\rm{r}}}}({{\bf{k}}\simeq {\bf{k}}}_{{\rm{B}}{\rm{I}}{\rm{C}}})=(\begin{array}{cc}{\omega }_{+} & {\kappa }_{12}\\ {\kappa }_{12} & {\omega }_{-}\end{array})+j(\begin{array}{cc}{\gamma }_{+} & 0\\ 0 & {\gamma }_{-}\end{array})$. It is important to note that the modes are the final coupled modes: their frequencies are considered shifted with respect to the exact frequencies of bright and dark modes of the FW point k = k_BIC in equation (14). The finite decay rate of the dark mode turns it into a quasi-dark mode (FW quasi–BIC), and this non-zero coupling to the radiation channel $(\sqrt{2{\gamma }_{-}}=\sqrt{2/{\tau }_{{\rm{R}}1}})$ will imply non-zero near-field (κ₁₂) or far-field (γ₁₂) coupling with the shifted bright partner, depending on the representation used. The bright mode has amplitude A₊, with a decay rate 1/γ₊ = τ_R2 ≪ τ_R1. Generally, the off-diagonal terms can be kept complex to include both near-field and far-field coupling, but we have verified by RCWA that the coupling is real with good approximation in the next section. Here we assume the representation with near-field coupling κ₁₂. Considering the general dynamical equations with both modes having the same losses included all in γ_a = 1/τ_a, it is possible to write, $\forall {\bf{k}}:{\bf{k}}\simeq {{\bf{k}}}_{{\rm{BIC}}}$ that

$$\frac{{\rm{d}}{A}_{-}}{{\rm{d}}t}=j{\omega }_{-}\,{A}_{-}-\left(\frac{1}{{\tau }_{{\rm{a}}}}+\frac{1}{{\tau }_{{\rm{R}}1}}\right){A}_{-}+j{\kappa }_{12}{A}_{+}+\sqrt{\frac{2}{{\tau }_{{\rm{R}}1}}}{s}_{+},$$

(34)

$$\frac{{\rm{d}}{A}_{+}}{{\rm{d}}t}=j{\omega }_{+}\,{A}_{+}-\left(\frac{1}{{\tau }_{{\rm{a}}}}+\frac{1}{{\tau }_{{\rm{R}}2}}\right){A}_{+}+j{\kappa }_{12}A\_+\sqrt{\frac{2}{{\tau }_{{\rm{R}}2}}}{s}_{+}.$$

(35)

This set of equations is valid for any system (for example, plasmonic modes, whispering-gallery modes, guided modes, defect modes). Considering $\frac{{\rm{d}}}{{\rm{d}}t}\to j{\omega }_{{\rm{in}}}$ and solving for A₋ in equation (34), substituting it in equation (35) and then substituting the resulting A₊ again in equation (34), we find, at the steady state, that

$$\begin{array}{l}\frac{{A}_{-}({\omega }_{{\rm{in}}})}{{s}_{+}}=\frac{\sqrt{\frac{2}{{\tau }_{{\rm{R}}1}}}}{j({\omega }_{{\rm{in}}}-{\omega }_{-})+\frac{1}{{\tau }_{{\rm{a}}}}+\frac{1}{{\tau }_{{\rm{R}}1}}}+\\ +\frac{j/{\tau }_{\kappa }\sqrt{\frac{2}{{\tau }_{{\rm{R}}2}}}}{\left[j({\omega }_{{\rm{in}}}-{\omega }_{-})+\frac{1}{{\tau }_{{\rm{a}}}}+\frac{1}{{\tau }_{{\rm{R}}1}}\right]\left[j({\omega }_{{\rm{in}}}-{\omega }_{+})+\frac{1}{{\tau }_{{\rm{a}}}}+\frac{1}{{\tau }_{{\rm{R}}2}}+\frac{1/{\tau }_{\kappa }^{2}}{j({\omega }_{{\rm{in}}}-{\omega }_{-})+1/{{\rm{\tau }}}_{a}+1/{{\rm{\tau }}}_{R1}}\right]}+\\ -\frac{1/{{\rm{\tau }}}_{{\rm{\kappa }}}^{2}\sqrt{\frac{2}{{{\rm{\tau }}}_{R1}}}}{{\left[j({\omega }_{{\rm{in}}}-{\omega }_{-})+\frac{1}{{\tau }_{{\rm{a}}}}+\frac{1}{{\tau }_{{\rm{R}}1}}\right]}^{2}\left[j({\omega }_{{\rm{in}}}-{\omega }_{+})+\frac{1}{{\tau }_{{\rm{a}}}}+\frac{1}{{\tau }_{{\rm{R}}2}}+\frac{1/{\tau }_{\kappa }^{2}}{j({\omega }_{{\rm{in}}}-{\omega }_{-})+1/{\tau }_{{\rm{a}}}+1/{\tau }_{{\rm{R}}1}}\right]},\end{array}$$

(36)

$$\begin{array}{l}\frac{{A}_{+}({\omega }_{{\rm{in}}})}{{s}_{+}}=\frac{\sqrt{\frac{2}{{\tau }_{{\rm{R}}2}}}}{j({\omega }_{{\rm{in}}}-{\omega }_{+})+\frac{1}{{\tau }_{{\rm{a}}}}+\frac{1}{{\tau }_{{\rm{R}}2}}+\frac{1/{\tau }_{\kappa }^{2}}{j({\omega }_{{\rm{in}}}-{\omega }_{-})+1/{\tau }_{{\rm{a}}}+1/{\tau }_{{\rm{R}}1}}}+\\ +\frac{j/{\tau }_{\kappa }\sqrt{\frac{2}{{\tau }_{{\rm{R}}1}}}}{\left[j({\omega }_{{\rm{in}}}-{\omega }_{-})+\frac{1}{{\tau }_{a}}+\frac{1}{{\tau }_{{\rm{R}}1}}\right]\left[j({\omega }_{{\rm{in}}}-{\omega }_{+})+\frac{1}{{\tau }_{{\rm{a}}}}+\frac{1}{{\tau }_{{\rm{R}}2}}+\frac{1/{\tau }_{\kappa }^{2}}{j({\omega }_{{\rm{in}}}-{\omega }_{-})+1/{\tau }_{{\rm{a}}}+1/{\tau }_{{\rm{R}}1}}\right]}.\end{array}$$

(37)

Above, we have explicitly defined the near-field coupling lifetime ${{\rm{\tau }}}_{{\rm{\kappa }}}=\frac{1}{{{\rm{\kappa }}}_{12}}$ and the associated quality factor τ_κ = 2Q_κ/ω. We can see that the quasi-dark mode A₋ can be excited by means of internal coupling κ₁₂ more than what is expected from the isolated resonance response of the dark mode, represented by the first term in equation (36) (in Supplementary Information section 1.2 and Supplementary Fig. 4, the mediated drive term is also made explicit in the original quantum model)². In Extended Data Fig. 1b–d, the behaviour for both mode intensities for a specific set of informative values, Q_R1 = 5 × 10⁹, Q_R2 = 200, Q_a = 5,000 is plotted to capture the main insight. In Extended Data Fig. 1b, the intensity field enhancement

$$G=\frac{{\left|{A}_{\pm }\right|}^{2}}{{\left|{s}_{+}/\sqrt{{\omega }_{{\rm{in}}}}\right|}^{2}{V}_{{\rm{eff}}}}$$

(38)

is plotted for both modes (solid red line for the dark A₋ and blue line for the bright A₊), showing that the dark mode on resonance (ω_in = ω₋) reaches the maximum limit of field enhancement possible in a real-world resonator with non-radiative loss, G_max = Q_a/V_eff, even if

$${Q}_{{\rm{R}}1}\gg {Q}_{{\rm{a}}},$$

(39)

which would be impossible in case of a single dark resonance, that is, not coupled to another wave (dashed red line). This condition occurs at the supercritical coupling point defined by

$${\bar{\tau }}_{\kappa }=\sqrt{{\tau }_{{\rm{R}}2}{\tau }_{{\rm{a}}}},$$

(40)

$${\bar{Q}}_{\kappa }=\sqrt{{{Q}_{{\rm{R}}2}Q}_{{\rm{a}}}}.$$

(41)

Indeed, assuming τ_R1 ≫ τ_a, τ_R2, τ_κ and τ_R2 < τ_a in equation (36) and considering ω_in = ω₋ (on resonance with the dark mode) and |ω_in − ω₊| ≃ 2κ₁₂ = 2/τ_κ (the coupling affects the split in frequencies, thus the pump is shifted from the bright mode when on resonance with the dark one), the relation simplifies as

$$\frac{{A}_{-}\left({\omega }_{{\rm{in}}}={\omega }_{-}\right)}{{s}_{+}}\to {\left[\frac{j/{\tau }_{\kappa }\sqrt{\frac{2}{{\tau }_{{\rm{R}}2}}}}{j/\left({\tau }_{\kappa }{\tau }_{{\rm{a}}}\right)+1/{\tau }_{{\rm{a}}}^{2}+1/\left({\tau }_{{\rm{R}}2}{\tau }_{{\rm{a}}}\right)+1/{\tau }_{\kappa }^{2}}\right]}_{{\bar{{\rm{\tau }}}}_{\kappa }=\sqrt{{\tau }_{{\rm{R}}2}{\tau }_{{\rm{a}}}}}\to j\sqrt{{\tau }_{{\rm{a}}}/2},$$

(42)

in which the first two terms in the denominator were neglected, as they are smaller when τ_R2 < τ_a. The above relation proves that the dark-mode intensity enhancement $G={| \frac{{A}_{-}\left({\omega }_{{\rm{in}}}={\omega }_{-}\right)}{{s}_{+}/\sqrt{{\omega }_{{\rm{in}}}}}| }^{2}\frac{1}{{V}_{{\rm{eff}}}}={Q}_{{\rm{a}}}/{V}_{{\rm{eff}}}={G}_{\max }$, that is, it can reach the maximum imposed by non-radiative losses even in extreme situations with mismatched quality factors. It is worth mentioning that, when Q_κ → ∞ (κ₁₂ → 0), we again obtain the correct case of uncoupled resonances and the dark-mode field goes to the level it could gain if it were isolated (dashed red line). Indeed, in the plot, we have specified that the near-field coupling rate affects the spectral separation among resonances, as it is proportional to their distance: ω_± = ω_o ± κ₁₂ = ω_o[1 ± 1/(2Q_κ)] Thus, for Q_κ → ∞, the resonant frequencies coincide and cross. Even when out of perfect spectral tuning, the maximum gain achieved by the quasi-dark mode A₋ is orders of magnitudes larger than what possible in a single dark mode, as shown in Extended Data Fig. 1c,d. In case ω_in = ω_o = 1/2(ω₊ + ω₋), the optimum shifts to larger Q*_κ ≃ Q_a. When Q_R2 → Q_a and ω_in = ω₋, the bright mode is critically coupled with the pump, but there is still energy going into the dark mode up to 0.3G_max at a certain ${{Q}^{* }}_{\kappa }\lesssim {\bar{Q}}_{\kappa }={Q}_{{\rm{a}}}$. Furthermore, by inspecting the ratio between the solid red line and the dashed red line, it is possible to appreciate how, even if Q_κ does not reach the optimum, the intensity of the coupled dark resonance is orders of magnitude larger than that of the single resonance.

Further discussion

The supercritical coupling mechanism guarantees the possibility of achieving the maximum level of local field enhancement when the coupling (Q_κ) is optimally tuned, and always in the highest Q-factor mode, even under the conditions of coupling, for both bright and dark modes, which would be unfavourable in the case of single isolated modes. To give an example, let Q_R2 = 10³ ≪ Q_a = 10⁶ ≪ Q_R1 = 10¹⁰, thus none of the modes matches Q_a; by contrast, they have completely unmatched quality factors. If ${Q}_{\kappa }=\sqrt{{10}^{3}\times {10}^{6}}\simeq 3\times {10}^{4}$ (say, V_eff = 1 for brevity), the dark mode reaches the maximum intensity enhancement G_max = 10⁶, although the intensity enhancement of the single dark resonance would be only 10², that is, four orders of magnitude less, as shown in Fig. 1e. Also, the supercritical coupling condition is independent of the highest Q-factor resonance, unlike the critical coupling condition (Q_R1 = Q_a); the model converges to the critical-coupling result if Q_R1 → Q_a and can ensure a higher level of enhancement in the dark mode, with a considerable advantage over the single-dark-resonance case, even when Q_R2 and Q_κ vary over a considerably large range of values. This is shown for fixed ${\bar{Q}}_{\kappa }=\sqrt{{{Q}_{{\rm{R2}}}Q}_{{\rm{a}}}}$ in Extended Data Fig. 1e.

This mechanism holds true for all wavevectors that span the range from an FW quasi-BIC to the EIT point (if this is also present in the system), with correspondingly varied values of the parameters involved (coupled mode frequencies, decay rates and near-field coupling). Far from this momentum region, the mode coupling becomes progressively negligible (as it can be easily calculated numerically) and the isolated single mode response is restored.

Turning to the parallel with coupled-resonance-induced transparency, we understand that, at the dark mode frequency ω_t = ω′₋ (equations (25) and (29)), in which the transparency window occurs, the fast dispersion leads to slow light and an enhanced field that, with suitable coupling between modes, could reach the maximum field enhancement of the system, as indicated by supercritical coupling. We recall that EIT is not a necessary condition for the FW mechanism, although it may widen, if present, the wavevector span of an enhanced field.

RCWA validation

The validity of TCMT is confirmed through numerical simulations using full 3D RCWA. RCWA simulations are performed using the Fourier modal expansion method (Ansys Lumerical, RCWA module). Validation is performed by evaluating the exact transmittance spectra, the 3D-vector-field distribution of the interfering modes, their complex coupling constant, their evolution with momentum, the near-field coupling at EIT, FW quasi-BIC and FW-BIC points in momentum space. The modes belonging to the dispersion curves are a linear combination of tens to hundreds of Fourier plane waves in each xy-periodic, z-homogeneous layer satisfying the continuity boundary conditions in each z layer of the structure (with forward and backward propagating factors along the z axis), providing the exact solution of the problem, including material dispersion, matching the experimental transmittance spectrum measured to reconstruct the energy–momentum band diagrams for both s-polarized (vector TE-like character) and p-polarized (vector TM-like character) excitation. RCWA is indeed used as a benchmark for validating other numerical techniques such as resonant-state expansion, quasi-normal modes and other methods. It provides the 3D vector fields and the exact solution, which can be analytically approximated by the leaky TE-like and TM-like modes of the effective waveguide, or TCMT. Further details are in Supplementary Information with measured refractive index dispersion (Supplementary Fig. 1) and details on fitting, giving imaginary refractive index used for simulations n_I = 10⁻⁴ over the spectral range 700–1,200 nm.

Extended Data Fig. 2a shows the theoretical TE bands expected for a uniform film of upconversion nanoparticles (UCNPs) with a refractive index of 1.45, matching the experimental absorption band of UCNPs in Extended Data Fig. 2b. Extended Data Fig. 2c shows the mode distribution, whereas Extended Data Fig. 2d evaluates the mode energy fraction superimposed on the nonlinear material as a function of refractive index, for one layer (1L), two layers (2L) and with a cladding of air or silicone oil. The silicone oil promotes vertical symmetry, which means that it increases the field overlap with the UCNPs and helps minimize scattering losses, but it cannot affect the vertical symmetry of the TE-like and TM-like modes, which is determined mainly by the different refractive index of the glass substrate, silicon nitride and UCNPs index. Indeed, the energy fraction with silicone oil only changes from 8% to 9% (Extended Data Fig. 2d). Nonetheless, silicone oil was often useful to better observe the side emission, as the silicone layer acted as a partially opaque screen crossing the outcoupled light (as shown in Fig. 3b). Note that the silicone oil layer was not used in Fig. 4b.

Extended Data Fig. 3 shows the evolution of the transmittance spectra by changing the azimuthal angle of incidence ϕ. The avoided crossing stops only when the two modes no longer intersect, as shown clearly in Extended Data Fig. 3b at ϕ = 45°, at which it is also possible to observe that the uncoupled mode 1 has linewidth larger than mode 2, that is, γ_r1 ≫ γ_r2. Extended Data Fig. 3c,d shows the details of FW quasi-BIC and avoided crossing.

Extended Data Fig. 4 shows that vector TE-like and TM-like modes evolve and change symmetry along the momentum; they are, in general, non-orthogonal and nearly coincident at the avoided crossing (and approximately even with respect to the z-mirror symmetry). Because the modes are nearly coincident, the approximation γ_a = 1/τ_a in the above model, that is, the same for both modes, is correct. Also, because the input intensity is I_input = 1, the resonance field intensity is much larger than what would be expected on the basis of critical coupling (material absorption loss, n_I = 10⁻⁴ is included in the simulation), providing an estimate of the field enhancement (I₁ > 3 × 10⁴I_input).

Extended Data Fig. 5a shows the spectral coincidence of the coupled-resonance-induced transparency (EIT) frequency (for θ = 2.7° at the avoided crossing) with the FW quasi-BIC frequency at θ = 3.15° for the angle mismatch <0.5° (mismatched momentum k_EIT = k_BIC + δk). The existence of coupled-resonance-induced transparency can only occur for non-orthogonal modes²⁵, and the proximity in momentum space to the BIC point proves that FW-BIC is an ideal condition originating from the evolution of non-orthogonal modes. Extended Data Fig. 5b shows the near-field coupling constant normalized to ω′₋ = 2πc/λ_model calculated using the formula in ref. ⁵⁴ (equation (4.13), page 162, including material distribution), for θ from 2.7° (EIT) to 3.24° (nearly ideal FW-BIC). The phase mismatch is minimal, thus the two modes also exchange energy along the propagation (Pendellösung effect), as it commonly occurs between two modes of the same waveguide coupled by a periodic modulation^15,54. The near-field coupling was calculated as

$${\kappa }_{12}=\frac{1}{4}\sqrt{\frac{{\varepsilon }_{{\rm{o}}}}{{\mu }_{{\rm{o}}}}}\frac{{k}_{{\rm{o}}}}{\sqrt{{N}_{1}{N}_{2}}}\int \left(\varepsilon -{\varepsilon }_{{\rm{o}}}\right){{{\bf{E}}}_{1}}^{\star }\cdot {{\bf{E}}}_{2}{\rm{d}}A,$$

in which ${N}_{{\rm{1,2}}}=\frac{1}{2}| \int ({{{\bf{E}}}^{* }}_{1,2}\times {{\bf{H}}}_{1,2}+{\bf{c}}.{\bf{c}}.)\cdot \widehat{z}{\rm{d}}A| $ are optical power normalizations. The integral is over the unitary cell area A. Note that the calculation provides the complex κ₁₂, in which the imaginary part of κ₁₂ is to be understood as a representation of ζ′₁₂ in equation (26) above. We estimated that ζ′₁₂ < 10⁻⁴κ₁₂ for all modes in the range θ ∈ (0°, 5°), thus ζ′₁₂ ≃ 0. Also, we found that κ₁₂ ≃ κ₂₁, as expected. The near-field coupling is stronger at the EIT point, whereas it decreases at the ideal FW-BIC, in agreement with the behaviour expected from the temporally coupled mode theory. As the incidence angle varies from the EIT point (2.7°) to the ideal position of the BIC (3.24°), Q_κ = τ_κ ω/2 varies accordingly and is characterized by a ${Q}_{\kappa }\approx ({10}^{3},{10}^{4})\approx \sqrt{{Q}_{{\rm{R2}}}{Q}_{{\rm{a}}}}$ at the FW quasi-BIC mode (dashed black line, 3.15°). As the near-field coupling is modulated, the fulfilment of the supercritical coupling condition can be tuned.

Supplementary Fig. 2 shows the evolution of the interference process as a function of κ₁₂ and describes how the coupling changes at the edge. The effect of the finite boundary on resonance was investigated using near-field scanning optical microscopy (Witec Alpha RAS 300) and shown in Supplementary Fig. 3.

Supplementary Fig. 4 shows theoretical linewidths calculated with the original FW quantum model², revealing that the open-channel wave acts as a drive field in the coupled BIC equation, for representative near-field coupling values.

Fabrication

Extended Data Fig. 6 shows the energy-level scheme of the produced UCNPs. All materials and synthesis details of NPs, NP characterization, PCNS fabrication and characterization are in Supplementary Information sections 2–4 and Supplementary Figs. 5 and 6.

Optical characterization

Dispersion-band-diagram measurements, experimental interrogation and detection scheme of upconversion are provided, respectively, in Supplementary Information sections 5 and 6 and Supplementary Figs. 7–10. For upconversion, the pulsed (150-fs) Ti:Sa oscillator, with central wavelength λ_in = 810 nm and full-width at half-maximum of 6 nm, is tuned to the FW quasi-BIC and focused to a 6-µm spot on the PCNS. The power coupled with NPs was 5%, corresponding to 48 kW cm⁻² at a pulse energy of 6.25 nJ (10³ kW cm⁻²).

Photoluminescence, enhancement-factor and radiance-enhancement estimation

Enhancement-factor estimation, spectral emission datasets from samples and radiance-enhancement-factor estimation are provided, respectively, in Supplementary Information section 7 and Supplementary Figs. 11 and 12.

FDTD simulations

The radiation properties of the PCNS were evaluated using the FDTD method in Ansys Lumerical. A single dipole source was used to compute the isofrequency map using the Z-transform of the local optical field retrieved within the finite-structure domain with the 3D full-field monitor. The intensity of the Z-transform determines the strength of radiation in the momentum space and better represents the radiation properties associated with the PCNS. To validate the results found with this approach, we first simulated a literature case discussed in ref. ⁴⁴, that is, supercollimation resulting from flat-band dispersion in the momentum space, which is shown in Supplementary Fig. 13. The isofrequency far-field intensity map in momentum space showed, in our case, non-trivial vanishing strips along orthogonal arms (cross of zeros; Fig. 3 and Extended Data Fig. 7). The near-field intensity map showed self-collimation as occurring when flat dispersion is involved. In Extended Data Fig. 7e, the experimental proof is reported using a rescaled geometry of the PCNS (using the fit in Extended Data Fig. 2e) to move the FW-BIC at 532 nm and make the beam easily visible. At this stage, the radiation properties were examined by placing an array of dipole sources (18 × 18) at the boundary of the finite PCNS with a uniform slab covering an area of several microns squared. The results are shown in Fig. 3c and Extended Data Fig. 8. The sources collectively add up their field and coherently emit radiation in the plane of the slab, as shown in Extended Data Fig. 8a, in which the field propagates along the direction (+1, 0) with intensity enhancement as large as 1.5 × 10⁴ (normalized to the number of emitters). The emission was always pointing towards the non-textured slab, thus—on the opposite edge—the propagation was along the direction (−1, 0). It was found that, at shorter wavelengths, other preferential directions of propagation were also possible, such as (1, ±1). The divergence was evaluated along 1 mm of propagation from the edge, as shown in Extended Data Fig. 8b, which showed a divergence of 0.02° (Extended Data Fig. 8c), which is even lower than the experimental values. Analysis of the whole visible and near-infrared spectrum revealed that the typical value of the divergence is less than 0.5° (Extended Data Fig. 8d), demonstrating that this regime of narrow radiation is expected to be common in this type of photonic structure. Indeed, as shown in Extended Data Fig. 8e, the full width at half maximum of the beam periodically contracts and expands along the propagation, which is because of a mechanism of self-healing that compensates for diffraction.

Directivity measurements

Extended Data Fig. 9a shows the microscopy inspection of light propagation near the edge. Extended Data Fig. 9b shows the experimental results on the divergence of the side beam (directed along the outer edge versor), with a polar plot of the edge emission in Extended Data Fig. 9c, in agreement with simulation in Extended Data Fig. 8 in the upconverted emission.

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Twisted-layer boron nitride ceramic with high deformability and strength

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Sample preparation

The oBN nanoprecursors were prepared by the chemical vapour deposition method^16,20,29; the raw materials used in the current work were trimethyl borate and ammonia. The oBN particle size ranged from 50 to 500 nm, with an average size of around 180 nm (Supplementary Fig. 1). A DR.SINTER SPS system and HIGH MULTI 10000 hot-pressing sintering device were used to sinter the precursors, respectively. For SPS sintering, a pressure of 50 MPa was applied first, followed by rapid heating to the target temperature at a rate 100 °C per min. Temperature was monitored with an on-line infrared thermometer during sintering. After 5–10 min at the target temperature, the power was cut off, and the pressure was released. The as-sintered specimens were left in the SPS until they had cooled to room temperature; then, they were taken out and polished. TS-BN ceramics can be synthesized between 1,600 and 1,800 °C by SPS. The ceramic synthesized at 1,500 °C was a composite consisting of TS-BN and residual untransformed oBN (Supplementary Fig. 5). For hot-pressing sintering, the same sintering pressure of 50 MPa was applied first, followed by gradual heating to the target temperature at a rate of 10 °C per min. The holding time was set to 5 min, and then the heating was stopped, and the pressure was released. Densities of the as-sintered specimens were measured according to the Archimedes principle.

XRD and Raman spectroscopy

XRD was used to characterize both the oBN nanoprecursors and the as-sintered BN ceramics, using a Rigaku diffractometer (SmartLab, Rigaku) with Cu Kα radiation (λ = 0.15418 nm). The applied voltage and current were 40 kV and 40 mA, respectively, with a step size of 0.02° at a scanning rate of 1° per min. Raman spectra were also collected at room temperature using a Horiba Jobin Yvon LabRAM system with a laser wavelength of 473 nm. The size of the laser spot was approximately 1 μm.

TEM sample preparation

oBN nanoparticles were dispersed in ethanol solution by ultrasonic treatment, drop-casted on to a carbon-coated copper grid and then dried before TEM observation. Sintered BN ceramics were first crushed and ground in an agate mortar; then, small nanoplates from ceramics were used to prepare TEM samples in the same way as above for oBN. In addition, thin foils were cut from as-sintered bulk samples for TEM observation using a focused ion beam (Helios 5 CX DualBeam, ThermoFisher). The foils were further milled to less than 100 nm and polished by Ar-ion milling (NanoMill; Model 1040, Fischione) to remove surface damage.

Microstructure characterization

We used scanning electron microscopy (Verios, ThermoFisher) to characterize the oBN nanoparticles and fracture morphology of BN ceramics. More detailed microstructure was characterized with a scanning transmission electron microscope (Talos F200X, ThermoFisher) operated at an accelerating voltage of 200 kV and a spherical-aberration-corrected scanning transmission electron microscope (Themis Z, ThermoFisher) operated at an accelerating voltage of 300 kV. HAADF images were collected by combining 20 frames from acquired series with drift correction (DCFI in Velox software, Thermo Fisher). The probe convergence angle was set to 25 mrad, and the collecting angle for HAADF was set to 65–200 mrad to eliminate the coherent scattering effect.

First-principles calculations

We constructed twist-layer BN structures using the Materials Visualizer module of the Materials Studio software³⁰. Calculations were performed on the basis of DFT as implemented in the CASTEP code³¹. Ultrasoft pseudopotentials were used^32,33. We used the local density approximation exchange-correlation functional of Ceperley and Alder parameterized by Perdew and Zunger^34,35 to perform structural optimization and calculations of total energies and elastic properties. A k-point sampling³⁶ of 0.04 × 2π Å⁻¹ and a plane-wave cutoff of 570 eV were applied. The Broyden–Fletcher–Goldfarb–Shanno³⁷ minimization scheme was used for geometry optimization. Structural relaxation was stopped when the total energy changes, maximum ionic displacement, stress and ionic Hellmann–Feynman force were less than 5.0 × 10⁻⁶ eV per atom, 5.0 × 10⁻⁴ Å, 0.02 GPa and 0.01 eV Å⁻¹, respectively. The elastic moduli of the investigated structures were calculated in the linear elastic strain range. Selected calculation parameters were tested to ensure that energy convergence was less than 1 meV per atom. To validate our computational scheme, benchmark calculations were conducted for the hBN structure. The calculated lattice parameters of a = 2.49 Å and c = 6.48 Å were in good agreement with experimental values of a = 2.50 Å and c = 6.66 Å (ref. ³⁸). The calculated bulk modulus (27.9 GPa) of hBN was in agreement with the experimental value (25.6 GPa)³⁹.

Deformability factor calculation

The ability of layered vdW materials to deform without fracture can be characterized by the deformability factor Ξ = (E_c/E_s)(1/Y) (in units of GPa⁻¹)¹⁸, where E_c and E_s are the cleavage energy and slipping energy, respectively, and Y is the in-plane Young’s modulus along the slip direction. The E_c/E_s ratio quantifies the plasticity of the material that conforms to the criterion proposed by Rice et al.^40,41. Interlayer interactions and the relative glide of the twist-stacked BN structures were simulated on the basis of DFT calculations. The slipping step was kept at 0.3 Å during the simulation. For each step, the energy of the most stable configuration was obtained by geometrically optimizing only the interlayer distance. The (001) plane uniformly slipped along the [210] direction, which is considered to be the lowest-energy sliding direction in hBN⁴². We obtained the energy as a function of the slip distance over the range of periodic distances. The energy difference between the slip distance at maximum energy (E_max) and no slip (E₀) was used to represent the energy barrier to overcome resistance to slip, that is, E_s = E_max − E₀ (ref. ¹⁸). The energy difference between the infinite interlayer distance (E_inf) and E_max was considered to represent the cleavage energy, E_c = E_inf − E_max (ref. ¹⁸). An interlayer distance of 10 Å was used to calculate E_inf, which safely ensured that there was no interlayer interaction.

Molecular dynamics simulation

The phase transition process from oBN to a twisted-layer structure was simulated by molecular dynamics with the large-scale atomic/molecular massively parallel simulator code⁴³. An extended Tersoff potential was chosen to describe the interatomic interaction⁴⁴; this has been widely used to investigate the microstructural evolution of hBN^45,46. In this work, a 10 × 10 × 4 nm³ supercell containing a two-shell BN nano-onion at the centre was constructed. The two-shell BN nano-onion structure was constructed using the method reported in our previous work²¹. The outer (inner) shell corresponded to B₇₅₀N₇₅₀ (B₄₆₀N₄₆₀), and the diameter of the BN onion was 3.61 nm. Periodic boundary conditions and isothermal–isobaric (NPT) ensemble were applied in the simulations. Each supercell was first optimized with the conjugate gradient algorithm and then relaxed for 20 ps at room temperature. Following the relaxation, the supercell was compressed uniaxially along the z direction to a given pressure (6 GPa) within 200 ps and finally heated to the target temperature (1,500 K) within 2 ns. Atomic configurations were visualized and analysed with the help of the Open Visualization Tool package⁴⁷. The local structural environment of the atoms was identified using the polyhedral template matching algorithm⁴⁸.

Mechanical property characterization

Uniaxial compression tests were performed in the MTI mechanical property testing system (MTII/Fullman SEMtester 2000) at room temperature with a strain rate of 1 × 10⁻⁴ s⁻¹. Ceramic specimens were machined into cylinders with diameter of 2.7 mm and length of 4.0 mm (length to diameter ratio: approximately 1.5). Both ends of the cylinders were polished with diamond powder of around 0.5 μm. Parallelism between the two ends was within 0.01 mm. A thin copper foil was placed between the sample and the tester to reduce stress concentration on the contact area. Thin nickel (Ni) film was deposited on the sample surface to form markers. Each compression process was recorded in situ with a digital video recorder. Sample strain was estimated by measuring the change in distances between Ni markers. We conducted at least five tests for uniaxial compressive properties on bulk samples obtained from SPS and hot-pressing sintering.

Tensile tests were carried out at a strain rate of 1 × 10⁻⁴ s⁻¹. The specimens were processed into I-shape with an effective tensile length of 6 mm and a rectangular cross section of 1 mm × 1.5 mm. Flexural strength was measured using the three-point bending method. The specimens were processed into cuboids with a size of 1 mm × 2 mm × 12 mm. The span length was 11 mm, and the loading rate of the indenter was set to 0.1 mm min⁻¹. Flexural strength (σ_f) was calculated as follows:

$${{\sigma }}_{{\rm{f}}}=\frac{3FL}{{2bh}^{2}},$$

(1)

where F is the maximum load until the specimen fractured, L is the span length, and b and h are the width and height of the specimen, respectively.

Fracture toughness of the specimens was determined using the single-edge V-notched beam method. The specimens were processed into cuboids with a size of 1 mm × 1.5 mm × 5 mm. A straight-through V-notch with a depth of approximately 0.5 mm was cut in the specimen using a femtosecond laser (Astrella-1K-USP). The radius of the notch tip was less than 10 μm, the span length was 4 mm and the crosshead loading rate was 0.1 mm min⁻¹. Fracture toughness (K_IC) was calculated using the following equations:

$${K}_{{\rm{I}}{\rm{C}}}=\left(\frac{FL}{B{W}^{1.5}}\right)\left\{1.5{\left(\frac{a}{W}\right)}^{0.5}Y(\frac{a}{W})\right\},$$

(2)

$$Y\left(\frac{a}{W}\right)=1.964-2.837\left(\frac{a}{W}\right)+13.711{\left(\frac{a}{W}\right)}^{2}-23.25{\left(\frac{a}{W}\right)}^{3}+24.129{\left(\frac{a}{W}\right)}^{4},$$

(3)

where F is the maximum load until the specimen fractured, L is the span length, B is the specimen width, W is the specimen height and a is the notch depth. Tests for tensile strength, flexural strength, Young’s modulus and fracture toughness were repeated at least five times.

In situ synchrotron radiation XRD measurements

In situ triaxial compression tests were performed using a deformation-DIA apparatus coupled with synchrotron X-rays, at the GSECARS 13-BM-D beamline of the Advanced Photon Source at the Argonne National Laboratory, USA. Details of the deformation-DIA module and the sample assembly can be found elsewhere^28,49. The specimens were cylinders of 2.5 mm in diameter and 3.5 mm in length. The specimen was first compressed to a hydrostatic pressure of around 1.5 GPa; then, the differential rams were advanced to shorten the sample at a constant speed (strain rate = 1 × 10⁻⁵ s⁻¹) at room temperature.

The incident monochromatic beam (45 keV) was collimated to tungsten carbide (WC) slits of 200 mm × 200 mm. Detector tilt and rotation relative to the incident beam were calibrated with a CeO₂ standard using the Dioptas program⁵⁰. XRD patterns and radiographs of the sample were collected automatically during deformation. Exposure times for XRD and radiographs were 300 s and 10 s, respectively.

The strain of specimen was defined as ε = (l−l_ε)/l, where l and l_ε are the sample lengths at the initial state and under compression, respectively. Lattice strain of the (002) and (100) reflections was defined as

$$\frac{{d}_{{\rm{hkl}}}(\varphi ){-d}_{{\rm{P}}({\rm{hkl}})}}{{d}_{{\rm{P}}({\rm{hkl}})}}{=Q}_{{\rm{hkl}}}({1-{\rm{3cos}}}^{2}\varphi ),$$

(4)

where d_P(hkl) is the hydrostatic pressure d-spacing, for which the right-hand side of equation (4) is zero. For each plane (hkl), d_(hkl) and φ were measured from the two-dimensional diffraction pattern (with cosφ = cosθcosδ), δ being the true azimuth angle. Q_(hkl) and d_P(hkl) were extracted by fitting d_(hkl) versus φ according to equation (4). Differential stresses σ_(hkl) were calculated for planes from lattice strains Q_(hkl) according to:

$${\Delta \sigma }_{{\rm{hkl}}}{=6Q}_{{\rm{hkl}}}{G}_{{\rm{hkl}}},$$

(5)

where the ‘effective moduli’ G_hkl were calculated with elastic compliances S_ij from inversion of the stiffness tensor (C_ij) for hBN. In the current work, elastic constants of c₃₃ = 27 GPa and c₁₁ = 811 GPa (ref. ³⁹) were used to calculate σ₍₀₀₂₎ and σ₍₁₀₀₎ of layered BN structures, respectively, without considering pressure effects on these moduli.

In situ TEM nanopillar compression

Nanopillars with diameter of around 200 nm and aspect ratio of around 2:1 from the sintered bulk ceramic were fabricated using a Ga ion beam at a voltage of 30 kV in a FEI Helios focused ion beam instrument. Initially, the samples were processed into pillars with a cross-sectional width of approximately 5 μm using relatively large currents from 21 nA to 7 nA. Subsequently, the pillars were milled to cylinders with diameter of 1 μm using low currents from 5 nA to 1 nA. Finally, the pillars were polished to the desired size of approximately 200 nm using small currents from 500 pA to 7.7 pA to minimize the damage layer.

In situ uniaxial compression tests were performed with a Hysitron Picoindenter instrument inside a transmission electron microscope (FEI Titan ETEM G2) operated with an accelerating voltage of 300 kV. The Hysitron PI-95 holder was equipped with a diamond punch joined to a MEMS transducer. In situ compression experiments were carried out in a displacement control mode, which has been proved to be more sensitive to transient phenomena. The displacement rate was kept at 10 nm s⁻¹ during compression, corresponding to a strain rate of 1 × 10⁻² s⁻¹. The whole process was recorded using a digital video recorder for observation of the evolution of the microstructure.

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Genomic data in the All of Us Research Program

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The All of Us cohort

All of Us aims to engage a longitudinal cohort of one million or more US participants, with a focus on including populations that have historically been under-represented in biomedical research. Details of the All of Us cohort have been described previously⁵. Briefly, the primary objective is to build a robust research resource that can facilitate the exploration of biological, clinical, social and environmental determinants of health and disease. The programme will collect and curate health-related data and biospecimens, and these data and biospecimens will be made broadly available for research uses. Health data are obtained through the electronic medical record and through participant surveys. Survey templates can be found on our public website: https://www.researchallofus.org/data-tools/survey-explorer/. Adults 18 years and older who have the capacity to consent and reside in the USA or a US territory at present are eligible. Informed consent for all participants is conducted in person or through an eConsent platform that includes primary consent, HIPAA Authorization for Research use of EHRs and other external health data, and Consent for Return of Genomic Results. The protocol was reviewed by the Institutional Review Board (IRB) of the All of Us Research Program. The All of Us IRB follows the regulations and guidance of the NIH Office for Human Research Protections for all studies, ensuring that the rights and welfare of research participants are overseen and protected uniformly.

Data accessibility through a ‘data passport’

Authorization for access to participant-level data in All of Us is based on a ‘data passport’ model, through which authorized researchers do not need IRB review for each research project. The data passport is required for gaining data access to the Researcher Workbench and for creating workspaces to carry out research projects using All of Us data. At present, data passports are authorized through a six-step process that includes affiliation with an institution that has signed a Data Use and Registration Agreement, account creation, identity verification, completion of ethics training, and attestation to a data user code of conduct. Results reported follow the All of Us Data and Statistics Dissemination Policy disallowing disclosure of group counts under 20 to protect participant privacy without seeking prior approval⁴⁰.

EHR data

At present, All of Us gathers EHR data from about 50 health care organizations that are funded to recruit and enrol participants as well as transfer EHR data for those participants who have consented to provide them. Data stewards at each provider organization harmonize their local data to the Observational Medical Outcomes Partnership (OMOP) Common Data Model, and then submit it to the All of Us Data and Research Center (DRC) so that it can be linked with other participant data and further curated for research use. OMOP is a common data model standardizing health information from disparate EHRs to common vocabularies and organized into tables according to data domains. EHR data are updated from the recruitment sites and sent to the DRC quarterly. Updated data releases to the research community occur approximately once a year. Supplementary Table 6 outlines the OMOP concepts collected by the DRC quarterly from the recruitment sites.

Biospecimen collection and processing

Participants who consented to participate in All of Us donated fresh whole blood (4 ml EDTA and 10 ml EDTA) as a primary source of DNA. The All of Us Biobank managed by the Mayo Clinic extracted DNA from 4 ml EDTA whole blood, and DNA was stored at −80 °C at an average concentration of 150 ng µl⁻¹. The buffy coat isolated from 10 ml EDTA whole blood has been used for extracting DNA in the case of initial extraction failure or absence of 4 ml EDTA whole blood. The Biobank plated 2.4 µg DNA with a concentration of 60 ng µl⁻¹ in duplicate for array and WGS samples. The samples are distributed to All of Us Genome Centers weekly, and a negative (empty well) control and National Institute of Standards and Technology controls are incorporated every two months for QC purposes.

Genome sequencing

Genome Center sample receipt, accession and QC

On receipt of DNA sample shipments, the All of Us Genome Centers carry out an inspection of the packaging and sample containers to ensure that sample integrity has not been compromised during transport and to verify that the sample containers correspond to the shipping manifest. QC of the submitted samples also includes DNA quantification, using routine procedures to confirm volume and concentration (Supplementary Table 7). Any issues or discrepancies are recorded, and affected samples are put on hold until resolved. Samples that meet quality thresholds are accessioned in the Laboratory Information Management System, and sample aliquots are prepared for library construction processing (for example, normalized with respect to concentration and volume).

WGS library construction, sequencing and primary data QC

The DNA sample is first sheared using a Covaris sonicator and is then size-selected using AMPure XP beads to restrict the range of library insert sizes. Using the PCR Free Kapa HyperPrep library construction kit, enzymatic steps are completed to repair the jagged ends of DNA fragments, add proper A-base segments, and ligate indexed adapter barcode sequences onto samples. Excess adaptors are removed using AMPure XP beads for a final clean-up. Libraries are quantified using quantitative PCR with the Illumina Kapa DNA Quantification Kit and then normalized and pooled for sequencing (Supplementary Table 7).

Pooled libraries are loaded on the Illumina NovaSeq 6000 instrument. The data from the initial sequencing run are used to QC individual libraries and to remove non-conforming samples from the pipeline. The data are also used to calibrate the pooling volume of each individual library and re-pool the libraries for additional NovaSeq sequencing to reach an average coverage of 30×.

After demultiplexing, WGS analysis occurs on the Illumina DRAGEN platform. The DRAGEN pipeline consists of highly optimized algorithms for mapping, aligning, sorting, duplicate marking and haplotype variant calling and makes use of platform features such as compression and BCL conversion. Alignment uses the GRCh38dh reference genome. QC data are collected at every stage of the analysis protocol, providing high-resolution metrics required to ensure data consistency for large-scale multiplexing. The DRAGEN pipeline produces a large number of metrics that cover lane, library, flow cell, barcode and sample-level metrics for all runs as well as assessing contamination and mapping quality. The All of Us Genome Centers use these metrics to determine pass or fail for each sample before submitting the CRAM files to the All of Us DRC. For mapping and variant calling, all Genome Centers have harmonized on a set of DRAGEN parameters, which ensures consistency in processing (Supplementary Table 2).

Every step through the WGS procedure is rigorously controlled by predefined QC measures. Various control mechanisms and acceptance criteria were established during WGS assay validation. Specific metrics for reviewing and releasing genome data are: mean coverage (threshold of ≥30×), genome coverage (threshold of ≥90% at 20×), coverage of hereditary disease risk genes (threshold of ≥95% at 20×), aligned Q30 bases (threshold of ≥8 × 10¹⁰), contamination (threshold of ≤1%) and concordance to independently processed array data.

Array genotyping

Samples are processed for genotyping at three All of Us Genome Centers (Broad, Johns Hopkins University and University of Washington). DNA samples are received from the Biobank and the process is facilitated by the All of Us genomics workflow described above. All three centres used an identical array product, scanners, resource files and genotype calling software for array processing to reduce batch effects. Each centre has its own Laboratory Information Management System that manages workflow control, sample and reagent tracking, and centre-specific liquid handling robotics.

Samples are processed using the Illumina Global Diversity Array (GDA) with Illumina Infinium LCG chemistry using the automated protocol and scanned on Illumina iSCANs with Automated Array Loaders. Illumina IAAP software converts raw data (IDAT files; 2 per sample) into a single GTC file per sample using the BPM file (defines strand, probe sequences and illumicode address) and the EGT file (defines the relationship between intensities and genotype calls). Files used for this data release are: GDA-8v1-0_A5.bpm, GDA-8v1-0_A1_ClusterFile.egt, gentrain v3, reference hg19 and gencall cutoff 0.15. The GDA array assays a total of 1,914,935 variant positions including 1,790,654 single-nucleotide variants, 44,172 indels, 9,935 intensity-only probes for CNV calling, and 70,174 duplicates (same position, different probes). Picard GtcToVcf is used to convert the GTC files to VCF format. Resulting VCF and IDAT files are submitted to the DRC for ingestion and further processing. The VCF file contains assay name, chromosome, position, genotype calls, quality score, raw and normalized intensities, B allele frequency and log R ratio values. Each genome centre is running the GDA array under Clinical Laboratory Improvement Amendments-compliant protocols. The GTC files are parsed and metrics are uploaded to in-house Laboratory Information Management System systems for QC review.

At batch level (each set of 96-well plates run together in the laboratory at one time), each genome centre includes positive control samples that are required to have >98% call rate and >99% concordance to existing data to approve release of the batch of data. At the sample level, the call rate and sex are the key QC determinants⁴¹. Contamination is also measured using BAFRegress⁴² and reported out as metadata. Any sample with a call rate below 98% is repeated one time in the laboratory. Genotyped sex is determined by plotting normalized x versus normalized y intensity values for a batch of samples. Any sample discordant with ‘sex at birth’ reported by the All of Us participant is flagged for further detailed review and repeated one time in the laboratory. If several sex-discordant samples are clustered on an array or on a 96-well plate, the entire array or plate will have data production repeated. Samples identified with sex chromosome aneuploidies are also reported back as metadata (XXX, XXY, XYY and so on). A final processing status of ‘pass’, ‘fail’ or ‘abandon’ is determined before release of data to the All of Us DRC. An array sample will pass if the call rate is >98% and the genotyped sex and sex at birth are concordant (or the sex at birth is not applicable). An array sample will fail if the genotyped sex and the sex at birth are discordant. An array sample will have the status of abandon if the call rate is <98% after at least two attempts at the genome centre.

Data from the arrays are used for participant return of genetic ancestry and non-health-related traits for those who consent, and they are also used to facilitate additional QC of the matched WGS data. Contamination is assessed in the array data to determine whether DNA re-extraction is required before WGS. Re-extraction is prompted by level of contamination combined with consent status for return of results. The arrays are also used to confirm sample identity between the WGS data and the matched array data by assessing concordance at 100 unique sites. To establish concordance, a fingerprint file of these 100 sites is provided to the Genome Centers to assess concordance with the same sites in the WGS data before CRAM submission.

Genomic data curation

As seen in Extended Data Fig. 2, we generate a joint call set for all WGS samples and make these data available in their entirety and by sample subsets to researchers. A breakdown of the frequencies, stratified by computed ancestries for which we had more than 10,000 participants can be found in Extended Data Fig. 3. The joint call set process allows us to leverage information across samples to improve QC and increase accuracy.

Single-sample QC

If a sample fails single-sample QC, it is excluded from the release and is not reported in this document. These tests detect sample swaps, cross-individual contamination and sample preparation errors. In some cases, we carry out these tests twice (at both the Genome Center and the DRC), for two reasons: to confirm internal consistency between sites; and to mark samples as passing (or failing) QC on the basis of the research pipeline criteria. The single-sample QC process accepts a higher contamination rate than the clinical pipeline (0.03 for the research pipeline versus 0.01 for the clinical pipeline), but otherwise uses identical thresholds. The list of specific QC processes, passing criteria, error modes addressed and an overview of the results can be found in Supplementary Table 3.

Joint call set QC

During joint calling, we carry out additional QC steps using information that is available across samples including hard thresholds, population outliers, allele-specific filters, and sensitivity and precision evaluation. Supplementary Table 4 summarizes both the steps that we took and the results obtained for the WGS data. More detailed information about the methods and specific parameters can be found in the All of Us Genomic Research Data Quality Report³⁶.

Batch effect analysis

We analysed cross-sequencing centre batch effects in the joint call set. To quantify the batch effect, we calculated Cohen’s d (ref. ⁴³) for four metrics (insertion/deletion ratio, single-nucleotide polymorphism count, indel count and single-nucleotide polymorphism transition/transversion ratio) across the three genome sequencing centres (Baylor College of Medicine, Broad Institute and University of Washington), stratified by computed ancestry and seven regions of the genome (whole genome, high-confidence calling, repetitive, GC content of >0.85, GC content of <0.15, low mappability, the ACMG59 genes and regions of large duplications (>1 kb)). Using random batches as a control set, all comparisons had a Cohen’s d of <0.35. Here we report any Cohen’s d results >0.5, which we chose before this analysis and is conventionally the threshold of a medium effect size⁴⁴.

We found that there was an effect size in indel counts (Cohen’s d of 0.53) in the entire genome, between Broad Institute and University of Washington, but this was being driven by repetitive and low-mappability regions. We found no batch effects with Cohen’s d of >0.5 in the ratio metrics or in any metrics in the high-confidence calling, low or high GC content, or ACMG59 regions. A complete list of the batch effects with Cohen’s d of >0.5 are found in Supplementary Table 8.

Sensitivity and precision evaluation

To determine sensitivity and precision, we included four well-characterized control samples (four National Institute of Standards and Technology Genome in a Bottle samples (HG-001, HG-003, HG-004 and HG-005). The samples were sequenced with the same protocol as All of Us. Of note, these samples were not included in data released to researchers. We used the corresponding published set of variant calls for each sample as the ground truth in our sensitivity and precision calculations. We use the high-confidence calling region, defined by Genome in a Bottle v4.2.1, as the source of ground truth. To be called a true positive, a variant must match the chromosome, position, reference allele, alternate allele and zygosity. In cases of sites with multiple alternative alleles, each alternative allele is considered separately. Sensitivity and precision results are reported in Supplementary Table 5.

Genetic ancestry inference

We computed categorical ancestry for all WGS samples in All of Us and made these available to researchers. These predictions are also the basis for population allele frequency calculations in the Genomic Variants section of the public Data Browser. We used the high-quality set of sites to determine an ancestry label for each sample. The ancestry categories are based on the same labels used in gnomAD¹⁸, the Human Genome Diversity Project (HGDP)⁴⁵ and 1000 Genomes¹: African (AFR); Latino/admixed American (AMR); East Asian (EAS); Middle Eastern (MID); European (EUR), composed of Finnish (FIN) and Non-Finnish European (NFE); Other (OTH), not belonging to one of the other ancestries or is an admixture; South Asian (SAS).

We trained a random forest classifier⁴⁶ on a training set of the HGDP and 1000 Genomes samples variants on the autosome, obtained from gnomAD¹¹. We generated the first 16 principal components (PCs) of the training sample genotypes (using the hwe_normalized_pca in Hail) at the high-quality variant sites for use as the feature vector for each training sample. We used the truth labels from the sample metadata, which can be found alongside the VCFs. Note that we do not train the classifier on the samples labelled as Other. We use the label probabilities (‘confidence’) of the classifier on the other ancestries to determine ancestry of Other.

To determine the ancestry of All of Us samples, we project the All of Us samples into the PCA space of the training data and apply the classifier. As a proxy for the accuracy of our All of Us predictions, we look at the concordance between the survey results and the predicted ancestry. The concordance between self-reported ethnicity and the ancestry predictions was 87.7%.

PC data from All of Us samples and the HGDP and 1000 Genomes samples were used to compute individual participant genetic ancestry fractions for All of Us samples using the Rye program. Rye uses PC data to carry out rapid and accurate genetic ancestry inference on biobank-scale datasets⁴⁷. HGDP and 1000 Genomes reference samples were used to define a set of six distinct and coherent ancestry groups—African, East Asian, European, Middle Eastern, Latino/admixed American and South Asian—corresponding to participant self-identified race and ethnicity groups. Rye was run on the first 16 PCs, using the defined reference ancestry groups to assign ancestry group fractions to individual All of Us participant samples.

Relatedness

We calculated the kinship score using the Hail pc_relate function and reported any pairs with a kinship score above 0.1. The kinship score is half of the fraction of the genetic material shared (ranges from 0.0 to 0.5). We determined the maximal independent set⁴¹ for related samples. We identified a maximally unrelated set of 231,442 samples (94%) for kinship scored greater than 0.1.

LDL-C common variant GWAS

The phenotypic data were extracted from the Curated Data Repository (CDR, Control Tier Dataset v7) in the All of Us Researcher Workbench. The All of Us Cohort Builder and Dataset Builder were used to extract all LDL cholesterol measurements from the Lab and Measurements criteria in EHR data for all participants who have WGS data. The most recent measurements were selected as the phenotype and adjusted for statin use¹⁹, age and sex. A rank-based inverse normal transformation was applied for this continuous trait to increase power and deflate type I error. Analysis was carried out on the Hail MatrixTable representation of the All of Us WGS joint-called data including removing monomorphic variants, variants with a call rate of <95% and variants with extreme Hardy–Weinberg equilibrium values (P < 10⁻¹⁵). A linear regression was carried out with REGENIE⁴⁸ on variants with a minor allele frequency >5%, further adjusting for relatedness to the first five ancestry PCs. The final analysis included 34,924 participants and 8,589,520 variants.

Genotype-by-phenotype replication

We tested replication rates of known phenotype–genotype associations in three of the four largest populations: EUR, AFR and EAS. The AMR population was not included because they have no registered GWAS. This method is a conceptual extension of the original GWAS × phenome-wide association study, which replicated 66% of powered associations in a single EHR-linked biobank⁴⁹. The PGRM is an expansion of this work by Bastarache et al., based on associations in the GWAS catalogue⁵⁰ in June 2020 (ref. ⁵¹). After directly matching the Experimental Factor Ontology terms to phecodes, the authors identified 8,085 unique loci and 170 unique phecodes that compose the PGRM. They showed replication rates in several EHR-linked biobanks ranging from 76% to 85%. For this analysis, we used the EUR-, and AFR-based maps, considering only catalogue associations that were P < 5 × 10⁻⁸ significant.

The main tools used were the Python package Hail for data extraction, plink for genomic associations, and the R packages PheWAS and pgrm for further analysis and visualization. The phenotypes, participant-reported sex at birth, and year of birth were extracted from the All of Us CDR (Controlled Tier Dataset v7). These phenotypes were then loaded into a plink-compatible format using the PheWAS package, and related samples were removed by sub-setting to the maximally unrelated dataset (n = 231,442). Only samples with EHR data were kept, filtered by selected loci, annotated with demographic and phenotypic information extracted from the CDR and ancestry prediction information provided by All of Us, ultimately resulting in 181,345 participants for downstream analysis. The variants in the PGRM were filtered by a minimum population-specific allele frequency of >1% or population-specific allele count of >100, leaving 4,986 variants. Results for which there were at least 20 cases in the ancestry group were included. Then, a series of Firth logistic regression tests with phecodes as the outcome and variants as the predictor were carried out, adjusting for age, sex (for non-sex-specific phenotypes) and the first three genomic PC features as covariates. The PGRM was annotated with power calculations based on the case counts and reported allele frequencies. Power of 80% or greater was considered powered for this analysis.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

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Autonomous transposons tune their sequences to ensure somatic suppression

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Cell culture and generation of stable cell lines

Flp-In T-REx HEK293 (Thermo Fisher Scientific, catalogue no. R78007) cells were maintained according to the manufacturer’s recommendations. Cells were cultured in DMEM with glutamax supplemented by Na-Pyruvate and High Glucose (Thermo Fisher Scientific, catalogue no. 31966-021) in the presence of 10% fetal bovine serum (FBS; Thermo Fisher Scientific, catalogue no. 10270106) and penicillin/streptomycin (Thermo Fisher Scientific, catalogue no. 15140-122). Before their introduction, transgene cells were cultured at a final concentration of 100 µg ml⁻¹ zeocin (Thermo Fisher Scientific, catalogue no. R250-01) and 15 µg ml⁻¹ blasticidin (Thermo Fisher Scientific, catalogue no. A1113903). For generation of stable cell lines, pOG44 (Thermo Fisher Scientific, catalogue no. V600520) was cotransfected with pcDNA5/FRT/TO (Thermo Fisher Scientific, catalogue no. V652020) containing the gene of interest at a 9:1 ratio. Cells were transfected with Lipofectamine 2000 (Thermo Fisher Scientific, catalogue no. 11668019) on a six-well-plate format with 1 µg of DNA (that is, 900 ng of pOG44 and 100 ng of pcDNA5/FRT/TO + GOI) according to the transfection protocol provided by the manufacturer. All transgenes were cloned with an N-terminal His₆-biotinylation sequence-His₆ tandem (HBH) tag that allows rapid and ultraclean purification without the use of antibodies. We also added a 3× FLAG tag immediately before the HBH tag to increase the versatility of the construct, which we refer to as the 3FHBH tag. Twenty-four hours following transfection, cells were split among three wells of a six-well plate at dilution ratios of 1:6, 2:6 and 3:6 to allow efficient selection of hygromycin B (Thermo Fisher Scientific, catalogue no. 10687010). Hygromycin selection was started 48 h following the transfection time point, with a final concentration of 150 µg ml⁻¹, and refreshed every 3–4 days until control, non-transfected cells on a separate plate were totally dead. Induction of the transgene was performed overnight at a final concentration of 0.1 µg ml⁻¹ doxycycline (DOX). Cells were validated by immunoblotting of whole-cell lysates.

An endogenous biotin acceptor peptide affinity tag and a FLAG tag were inserted into the Safb gene locus for mouse and fly cell lines using CRISPaint. The mouse Flp-In 3T3 cell line was purchased from Thermo Fisher Scientific (catalogue no. R76107) and cultured according to the manufacturer’s instructions. Vells were cultured in DMEM (Thermo Fisher Scientific, catalogue no. 31966-021) in the presence of 10% FBS (Thermo Fisher Scientific, catalogue no. 10270106) and penicillin/streptomycin (Thermo Fisher Scientific, catalogue no. 15140-122). The Drosophila S2R+ -MT::Cas9 cell line was purchased from DGRC (DGRC stock no. 268) and cultured in S2 medium (Thermo Fisher Scientific, catalogue no. 21720024) in the presence of 10% FBS (Thermo Fisher Scientific, catalogue no. 10270106). For CRISPaint⁵⁶ constructs (see Supplementary Table 2 for a list of single-guide RNAs), cells were cotransfected with three plasmids according to the CRISPaint protocol on the six-well-plate format using FuGene HD (Promega, catalogue no. E2311). Twenty-four hours following transfection, cells were expanded on 10 cm culture plates to facilitate efficient selection of puromycin (Thermo Fisher Scientific, catalogue no. A1113803). Puromycin selection is provided in the tag construct and is driven by expression from the gene locus (in this case, either the mouse or fly Safb1 gene locus). Puromycin selection was started 48 h following transfection, at 1 µg ml⁻¹ final concentration, and was refreshed every 2 days and, in total, was maintained until all untransfected 3T3 or S2 cells were dead. Cells were validated by immunoblotting of whole-cell lysates.

The HeLa cell line (ACC57) was purchased from Deutsche Sammlung von Mikroorganismen und Zellkulturen and maintained in the same medium as the Flp-In 3T3 cell line, but with the addition of non-essential amino acids (Thermo Fisher Scientific, catalogue no. 11140050).

Mouse N2A cells were maintained in DMEM, and stably expressing 3× FLAG-Cas9 or 3× FLAG-SAFB1 (Extended Data Fig. 10g) was created by cotransfection of cells with plasmids expressing the protein of interest (Cas9, SAFB1 or control) under the EF1alpha promoter flanked by PiggyBack inverted repeats, together with a plasmid expressing PiggyBac transposase. In this design, because neomycin resistance was coupled to transgene expression via an IRES element, cells were selected with 1 mg ml⁻¹ geneticin until none remained in control transfected cells.

Cell lines (human Flp-In T-REx HEK293, human HeLa, human HCT116, mouse Flp-In 3T3, mouse N2A and fly S2R+) were all purchased from vendors or repositories or provided by colleagues (as described above), and no further authentication of cell lines was performed following purchase. Routine mycoplasma contamination tests were performed on all cell lines using the Jena Biosciences Mycoplasma (PCR-based) detection kit (Jena Biosciences, no. PP-401).

FLASH

Cells on 15 cm dishes were washed with 6 ml of ice-cold PBS and UV-crosslinked with 0.199 mJ cm⁻² UV-C light, after which they were pelleted, snap-frozen in liquid nitrogen and stored at −80 °C until use. Pellets were resuspended in 600 µl of 1× native lysis buffer (NLB) with protease inhibitors and briefly sonicated in a Bioruptor water bath sonicator (30 s on, 30 s off, five cycles at 4 °C). Lysates were then centrifuged at 20,000 relative centrifugal force (rcf) for 10 min at 4 °C to remove insoluble material. Supernatant was transferred to a fresh tube with 25 µl of MyONE C1 streptavidin beads (Thermo) and incubated in a cold room with end-to-end rotation for 1 h. Beads were washed once with high-salt buffer (HSB), once with non-denaturing buffer (NDB), treated with 0.02 U µl⁻¹ RNase I (Thermo) in 100 µl of NDB for 3 min at 37 °C and immediately placed on ice to stop the reaction. Beads were then washed once each with HSB and NDB. RNA ends were repaired with T4 polynucleotide kinase, after which barcoded s-oligos were ligated with T4 RNA ligase 1 for 90 min at 25 °C. The 3′ phosphate at the 3′ end of each s-oligo was removed with recombinant shrimp alkaline phosphatase (NEB, M0371) and beads were washed once each with lithium dodecyl sulfate buffer, protein lysis buffer and HSB, and finally with NDB. RNA was released by treatment with proteinase K and purified using Oligo Clean and Concentrator columns (Zymo). Reverse transcription was carried out with SuperScript III and samples then treated with RNase H (NEB) to phosphorylate the 5′-end of the cDNA molecule. Following a final round of purification with Oligo Clean and Concentrator columns (Zymo), cDNA was circularized with CircLigaseII (Lucigen) and amplified with Q5 polymerase (NEB). PCR products were purified with solid-phase reversible immobilization beads, quality controlled with Bioanalyzer and subjected to high-throughput sequencing.

FLASH data processing

Paired-end reads were merged with bbmerge.sh v. 38.72 using the following command: bbmerge.sh in1 = {R1.fastq.gz} in2 = {R2.fastq.gz} out = {merged.fastq.gz} outu1 = {unmerged.R1.fastq.gz} outu2 = {unmerged.R2.fastq.gz} ihist = {histogram.txt} adapter1=AGATCGGAAGAGCACACGTCTGAACTCCAGTCACCCAACAATCTC adapter2=AGATCGGAAGAGCGTCGTGTAGGGAAAGAGTGTAGATCTCGGTGG –mininsert=1. Short inserts (below 20 nt, following removal of the unique molecular identifier (UMI) and internal index) were removed with bbduk.sh v. 38.72 bbduk.sh in = {infile} out = {out} minlen=34. The UMI was removed from reads and written to the header with UMI_tools v.1.0.0: umi_tools extract –bc-pattern=NNNXXXXXXNNNNN -I {IN.fastq.gz} -−3prime –stdout = {OUT.fastq.gz}, followed by separation of replicates with flexbar v.3.5.0: flexbar -r INPUT.fastq.gz -b barcodes.fa –barcode-trim-end RTAIL –barcode-error-rate 0.2 –zip-output GZ. Reads were aligned first to abundant RNAs such as transfer RNA, small nuclear RNA, small nucleolar RNA and ribonuclear RNA, then to the genome with bowtie2 v.2.3.5: bowtie2 –no-unal –un-gz -L 16 –very-sensitive-local -x bt2_index -U fastq_in.fastq.gz -o bam_out.bam. Unaligned reads were remapped to the genome with bbmap.sh v.38.72 to capture spliced reads: bbmap.sh -Xmx50G in = {fastq_in} out = {bam_out} outu = {unmapped_out} ref = {reference.fa} sam=1.3 mappedonly=t mdtag=t trimreaddescriptions=t nodisk. Finally, PCR duplicates were removed using UMI-tools: umi_tools dedup -I in_bam -S out_bam –spliced-is-unique –soft-clip-threshold 3 –output-stats = {stats}. Coverage files were generated with bamCoverage v.3.3.1: bamCoverage -b bam –filterRNAstrand [forward | reverse] –binSize 1 –normalizeUsing CPM –exactScaling -o out_file.

UMAP of FLASH data

For construction of the UMAP, peak calling was carried out on all profiles using HOMER: findPeaks {tag_directory} -style factor -strand separate -o {peaks.txt} -i {background_tag_directory}. Peaks from all profiles were then merged with: mergePeaks -strand -d given -matrix {peaks1.txt peaks2.txt …} > merged.peaks.txt. A count matrix, using all alignments from all profiles against merged peaks, was then created with featureCounts v.2.0.1: featureCounts -F SAF -Q 10 –primary -s 1 -T 12 -a {merged_peaks} -o {merged_peaks.counts.txt} {all_bam_files}. The count matrix was imported into a Jupyter notebook with pandas: peaks = pd.read_csv(“merged_peaks.counts.txt”, sep = ”\t”, index_col = ”Geneid”), scaled with sklearn.preprocessing.StardardScaler: peaks_scaled = StandardScaler().fit_transform(peaks), which was then used to create the UMAP: peaks_scaled_mapper = umap.UMAP(n_neighbors=15, random_state=42).fit(peaks_scaled), and plotted using umap.plot.points function. Clusters were called with HDBSCAN: clusterable_embedding = umap.UMAP(n_neighbors=30, min_dist=0.0, n_components=14, random_state=42).fit_transform(peaks_scaled), then hdbscan_labels = hdbscan.HDBSCAN(min_samples=100, min_cluster_size=600, core_dist_n_jobs=1).fit_predict(clusterable_embedding).

Sample and library preparation for RNA-seq

Flp-In T-REx HEK293 and HeLa ACC57 cells were transfected at a final concentration of 5 nM each (in the case of triple knockdown, total siRNA concentration became 15 nM and hence single-knockdown transfections were increased to 15 nM with the addition of 10 nM negative control siRNA) using Silencer Select siRNAs (Thermo Fisher Scientific, catalogue no. 4427037 for 1 nM scale) and RNAiMAX (Thermo Fisher Scientific, catalogue no. 13778030) on six-well plates (around 200,000 were used per replicate). Silencer Select siRNAs are 21 nt long, chemically modified (the exact modification is proprietary; Thermo Fisher) and reduce overall off-target effects by up to 90% without compromising potency. This modification also exaggerates strand bias, which correlates with better knockdown, and therefore they are 5- to 100-fold more potent than other siRNAs. The siRNA ID for human SAFB1 is s12452, for SAFB2 is s18599 and for SLTM is s36384. Cells were harvested on the second day of knockdown.

The Silencer Select siRNAs used were s29362 for MPP8 was s23449 for TASOR.

Flp-In 3T3 cells were first reverse transfected (roughly 100,000 per replicate) with 5 nM siRNA, boosted with the same amount 24 h following knockdown (forward transfected) and harvested on the third day following initial transfection. The siRNA ID for mouse Safb1 is s104978, for Safb2 is s104977 and, because the human SLTM siRNA also targets mouse mRNA, the same siRNA was used.

Drosophila S2R+ cells (DGRC no. 150) were transfected with control dsRNA against GFP or Saf-B using FuGENE HD (Promega) for 3 days, after which cells were harvested for RNA isolation.

Total RNA from human, mouse or Drosophila cells was extracted with the Quick-RNA MicroPrep kit (Zymo). Polyadenylated RNA was isolated from total RNA with the Dynabeads mRNA Purification Kit (Thermo). Purification was carried out twice to enrich poly(A)+ RNA. Sequencing libraries were generated using the KAPA Stranded RNA-Seq Library Preparation Kit (Roche).

Isolation of nuclear and cytoplasmic RNA for RNA-seq

Forty-eight hours following siRNA transfection (control or SAFB1 + SAFB2 + SLTM, 5 nM each), approximately 1 million Flp-ln T-REx HEK293 cells per replicate were trypsinized and either used directly for RNA isolation (total sample) or resuspended with a buffer containing 0.5% Igepal CA-630 to separate nuclear and cytoplasmic fractions, as described in ref. ⁵⁷. Nuclear and cytoplasmic RNAs were isolated with the Quick-RNA MicroPrep kit (Zymo). Ribo-depleted RNA-seq samples were prepared using the KAPA RNA HyperPrep Kit with RiboErase (HMR) (no. KK8560, Roche).

Transient transfections in rescue experiments and sample preparation for qPCR detection

SAFB triple knockdown was performed on Flp-In T-REx HEK293 cells as described above, and then FuGENE HD forward transfected with WT or truncation mutants as shown in Extended Data Fig. 7f while at the same time refreshing the medium 6 h following transfection of siRNAs. Transgenes were induced on day 1 of knockdown with 0.1 µg ml⁻¹ DOX for 24 h. On day 2 of knockdown, total RNA extracts were prepared with the Zymo Quick-RNA Kit and first-strand cDNA synthesis was carried out with PrimerScript RT Master Mix (TaKaRa, no. RR036A). Quantitative real-time PCR was performed using the oligos listed in Supplementary Table 1 with the Blue S’Green qPCR Kit (Biozym, no. 331416).

ONT direct RNA-seq

Isolation of polyA-enriched mRNA from Flp-ln T-REx HEK293 cells treated with either control siRNA or siRNAs against SAFB1, SAFB2 and SLTM (5 nM each) for 2 days was carried out using the Dynabeads mRNA DIRECT purification kit (Thermo Fisher Scientific) following the manufacturer’s instructions, with minor modifications. In brief, approximately 4 × 10⁶ cells were subjected to the standard protocol and hybridization of the beads/mRNA complex was carried out for 10 min on a Mini Rotator (Grant-bio). DNA containing supernatant was removed and the beads were resuspended with 2 × 2 ml of buffer A following a second wash step with 2 × 1 ml of buffer B. Purified RNA was eluted with 10 µl of preheated elution buffer (10 mM Tris-HCl pH 7.5) for 5 min at 80 °C. Quantification of isolated mRNA was performed using a Qubit Fluorometer together with the RNA HS Assay kit (Thermo Fisher Scientific). For direct RNA-seq, 700 ng of freshly isolated polyA-enriched mRNA was processed according to the manufacturer’s protocol (no. SQK-RNA002). Final sequencing libraries were then loaded on R9.4 flow cells and sequenced on MinION and PromethION sequencers.

Retrotransposition assay

The transfection and experimental timeline for the retrotransposition assay was followed as described in ref. ¹⁸. Initially around 200,000 HeLa cells were transfected, with the same siRNAs and under the conditions listed above, on a six-well plate with 5 nM final concentration each of negative control, SAFB1, SAFB2 and SLTM siRNAs. The following day, knockdown HeLa cells were transfected with 200 ng of plasmids pYX015 (based on JM111, which has a point mutation in ORF1p) for background control and pYX017 (pCAG-driven L1RP) for L1 activity in triplicates, using Lipofectamine 2000 on a 48-well plate in triplicate. Twenty-four hours following reporter construct transfection, 2.5 µg ml⁻¹ puromycin selection was started and maintained for 3 days (that is, day 5 of knockdown). Cells were washed with PBS before lysing with 40 µl of passive lysis buffer from the Dual-Luciferase Reporter Assay System (Promega, catalogue no. E1960). Half of the lysate was transferred to a 96-well, reading-compatible plate and measured using an Omega Lumistar machine.

RNA–FISH

FISH was carried out in HCT116 cells transfected with control versus siRNAs against SAFB1 and SLTM (no SAFB2 expression was detected in HCT116 cells) for 48 h using the Stellaris RNA–FISH kit (https://www.biosearchtech.com/assets/bti_stellaris_protocol_adherent_cell.pdf). Probes against L1Hs were synthesized by LGC Biosearch Technologies (see Supplementary Table 2 for sequences). Probes against GAPDH were sourced from LGC Biosearch Technologies (SMF-2026-1), provided by M. Bothe. Probes were used at a concentration of 125 nM and hybridized for 16 h at 37 °C. Samples were imaged using a Leica Stellaris 8 confocal microscope.

EMSA with recombinant Halo, Halo-SAFB1^RRM and Halo-TRA2B^RRM

The RNA-binding domain of TRA2B (residues 111:201) and SAFB1 (residues 386:485) were cloned into a plasmid encoding 10× His-TEV-Halo. Three constructs (Halo only, Halo-TRA2B^RRM and Halo-SAFB1^RRM) were then expressed using BL21-CodonPlus(DE3)-RIL bacteria, which were induced when an optical density of roughly 0.6 was reached, with 0.2 mM isopropyl-ß-d-thiogalactopyranoside for 4 h at 37 °C, then collected by centrifugation. Bacteria were resuspended with lysis buffer (50 mM HEPES pH 8.0, 300 mM NaCl, 5 mM imidazole and 0.05% Igepal CA-630) and disrupted with a Branson sonifier, clarified by centrifugation and filtered through a 0.45 µm membrane. Cleared lysates were incubated with cOmplete His-Tag Purification Resin (Roche), washed extensively with lysis buffer and incubated with 0.5 µM OregonGreen (Promega) on beads in lysis buffer at room temperature for 30 min for fluorescent labelling of proteins. Beads were first washed extensively with lysis buffer, then with high-salt wash buffer (50 mM Tris.Cl pH 8.0, 1 M NaCl, 5 mM imidazole) and lastly with lysis buffer. Proteins were eluted with elution buffer (50 mM Tris.Cl pH 8.0, 100 mM KCl, 200 mM imidazole). Eluates were pooled, dithiothreitol (DTT, 1 mM final concentration) and TEV protease (home-made, 6× His-tagged, approximately 1:100) were added and samples dialysed against 25 mM Tris.Cl pH 7.4, 50 mM KCl, 5% glycerol and 1 mM DTT overnight in a cold room (about 8 °C). Dialysed eluates were then incubated with cOmplete His-Tag Purification Resin (Roche) for removal of TEV protease and undigested proteins, and flowthrough was centrifuged at 23,000 rcf for 30 min and filtered through a 0.22 µm membrane to remove particulate matter. The UV spectra showed no significant absorption at 260 nm and were used to quantify purified proteins, which were then normalized and their quality checked with PAGE and Coomassie staining (Fig. 4a). Concentrations used in EMSAs were: Halo-TRA2B^RRM (lanes 2–6: 3.6, 7.2, 14.4, 57.6 and 102.4 µM, respectively); Halo-SAFB^RRM (lanes 7–11: 3.6, 7.2, 14.4, 57.6 and 102.4 µM, respectively); and Halo (lane 12: 102.4 µM). Lane 1 contained only those probes with no added protein.

The RNA probes were prepared by in vitro transcription. Briefly, a plasmid containing the relevant sequence TAATACGACTCACTATAGGGAAGAAGAAGAAGAAGAAGAAGAT^ATC, in which the T7 promoter sequence is underlined, was digested with EcoRV (site of digestion, indicating that the last nucleotide of the final RNA is marked—indicated by ^), purified and in vitro transcribed using a HighYield T7 RNA Synthesis Kit (Jena Biosciences, no. RNT-101) with either 1 mM (final) CTP/UTP/GTP/ATP or 1 mM CTP/UTP/GTP and 1 mM N6-Methyl-ATP (Jena Biosciences, no. RNT-112-S), completely replacing ATP. RNA was cleaned up using SPRI beads to remove the plasmid and other potential high-molecular-weight products, then with the OCC-5 kit (Zymo). RNA was then oxidized using freshly prepared sodium periodate (250 mM in water, final concentration 10 mM; Sigma, no. 311448) in 60 mM NaOAc pH 5.5 for 1 h on ice, with tubes kept in the dark. After a further clean-up with OCC-5, RNA was then labelled with CF 647 Hydrazide (Sigma, no. SCJ4600046; 10 mM in water, 0.8 mM final concentration in approximately 120 mM NaOAc, pH 5.5) at room temperature overnight. RNA was purified with OCC-5, eluted in water and normalized to 5 µM. EMSAs were carried out in 25 mM Tris.Cl pH 7.4, 50 mM KCl, 5% glycerol and 1 mM DTT with an RNA probe of around 100 nM and the indicated concentration of the protein of interest. Following incubation of RNA and proteins on ice for 30 min, mixtures were loaded directly on a Nature 8% polyacrylamide gel cast with 0.5× Tris-borate-EDTA (final) and run in 0.5× Tris-borate-EDTA in a cold room for 45 min at 100 V (gels were prerun at 100 V for 15 min). Proteins and RNA were sequentially visualized on the same gel using a Typhoon Scanner with appropriate excitation lasers and emission filters.

In vitro unmethylated and methylated RNA-binding assay

Nuclei were isolated from wt-HCT116 cells using a buffer containing 0.5% Igepal CA-630, following Lubelsky and Ulitsky⁵⁷, and snap-frozen in liquid nitrogen until use. Nuclei were resuspended with 500 µl of 25 mM Tris.Cl pH 7.4, 150 mM KCl, 2 mM MgCl₂, 0.5% Igepal CA-630, 5% glycerol, 5 mM β-mercaptoethanol, 1× protease inhibitors and 1× PhosSTOP and sonicated with a Branson sonifier. Next, 15 µl of TURBO-DNase was added followed by incubation at 25 °C for 20 min and then by the slow addition to the lysate of 1.5 m of base buffer (25 mM Tris.Cl pH 7.4, 50 mM KCl, 5% glycerol) to bring the KCl concentration to 75 mM and Igepal CA-630 concentration to 0.125% (final). Lysate was incubated with 50 µl of Pierce Control Agarose Resin (no. 26150) for 20 min, with rotation in a cold room, and spun down at full speed for 10 min at 4 °C to remove insoluble material. A 949 bp fragment of L1 ORF2 was amplified from pYX017 using primers AATAATACGACTCACTATAGCGTATCACCACCGATCCCACAG (T7 promoter underlined) and GGCTGAGACGATGGGGTTTT and in vitro transcribed using a HighYield T7 RNA Synthesis Kit (Jena Biosciences, no. RNT-101) with either 1 mM (final) CTP/UTP/GTP/ATP or 1 mM CTP/UTP/GTP and 1 mM N6-methyl-ATP (Jena Biosciences, no. RNT-112-S), completely replacing ATP. RQ1 DNase (Promega) was added to each reaction with incubation for for 20 min at 37 °C, after which RNA was cleaned up using RCC-25 (Zymo) and oxidized with freshly prepared sodium periodate (250 mM in water, final concentration 10 mM; Sigma, no. 311448) in 60 mM NaOAc pH 5.5 for 1 h on ice, with tubes kept in the dark. After a further clean-up with RCC-25, RNA was then labelled with biotin Hydrazide (Sigma, no. 87639; 50 mM in DMSO, 2 mM final concentration in approximately 120 mM NaOAc, pH 5.5) at room temperature overnight. RNA was purified with RCC-25, eluted in water and quantified with Nanodrop, then 5 µg of each RNA or buffer was incubated with 25 µl of MyONE C1 streptavidin beads in base buffer + 0.1% Igepal CA-630 for 1 h at room temperature and washed twice with base buffer + 0.1% Igepal CA-630. The nuclear lysate was incubated with these beads for 1 h at 16 °C, with shaking at 1,100 rpm. Beads were washed and transferred from fresh tubes with base buffer + 0.1% Igepal CA-630. Proteins bound to the beads were eluted with base buffer + 0.1% Igepal CA-630 + 2 µl of RNaseA + T1 (no. EN0551, Thermo Fisher Scientific) for 30 min at 30 °C and demonstrated by immunoblotting.

RNA blotting

HCT116 cells were transfected with 5 nM siRNA (as indicated in Fig. 2h) then, 48 h later, were either transfected with a plasmid encoding L1Hs and driven by a minimal EF1alpha (without an intron) promoter or mock transfected. Twenty-four hours later (72 h post siRNA transfection), cells were trypsinized and resuspended with a buffer containing 0.5% Igepal CA-630, essentially as described in ref. ⁵⁷. The cytoplasmic fraction was purified with RNA Clean & Concentrator columns (Zymo), 2 µg of which was loaded onto 1.2% agarose gel and electroblotted to a nylon membrane. DIG-labelled probes against ORF2 were prepared with in vitro transcription (see Supplementary Table 2 for primers) and probe hybridization, washes and imumunodetection were carried out as described in the manual of the DIG Northern Starter Kit (Roche, no. 12 039 672 910).

p-SR (1H4) and DHX9 FLASH in SAFB-depleted cells

Flp-In T-REx HEK293 cells were transfected with either control siRNA or siRNAs against SAFB1, SAFB2 and SLTM 48 h following transfection, then washed with PBS and UV-crosslinked with 0.2 mJ cm⁻² UV-C light on ice. Nuclei were isolated as described in ref. ⁵⁷, resuspended in 1× NLB + 5 mM MgCl₂ with protease and phosphatase inhibitors and sonicated using a Branson sonifier. Following centrifugation, to remove insoluble material the supernatant was incubated with an agarose resin (Pierce, no. 26150) for 20 min in a cold room followed by further incubation with Dynabeads Protein G beads prebound to p-SR antibody (10 µl per IP; 1H4, Santa Cruz, no. sc-13509) for 90 min in a cold room. The supernatant from 1H4 IP was used for DHX9 IP (2.5 µl per IP; abcam, no. ab26271). The FLASH protocol was identical to that described above, except that all HSB washes were replaced with NLB and s-oligos were pre-dephosphorylated to skip the recombinant shrimp alkaline phosphatase treatment that could dephosphorylate SR proteins on the beads, potentially leading to their elution.

RIP–qPCR

Flp-In T-REx HEK293 cells were crosslinked with 0.2% formaldeyhde for 10 min at room temperature, extensively washed with PBS, resuspended with 1× NLB and sonicated using a Branson sonifier. The lysate was centrifuged at 23,000 rcf for 10 min at 4 °C to remove insoluble material and the supernatant then incubated with an agarose resin (Pierce, no. 26150) for 30 min in a cold room. Following brief centrifugation, the supernatant was used for IP with Dynabeads Protein G beads coupled to either an antibody against SAFB1 (10 µl per IP; Santa Cruz, no. sc-393403) or control IgG (Santa Cruz, no. sc-2025) overnight in a cold room. Beads were washed with 1× NLB and bead-bound RNA was eluted with proteinase K, as described above, purified using RCC-5 (Zymo) and utilized for RT–qPCR.

Generation of the Dnmt3c-null allele

Dnmt3C knockout animals were generated as described in ref. ⁵⁸. For specific abolition of enzymatic activity we designed a sgRNA against the methyltransferase domain of Dnmt3C targeted to exon 15 with the following protospacer sequence: 5′-GGACATCTCACGATTCCTGG-3′. P0 animals were genotyped using Sanger sequencing following PCR with primers 5′-CTGGCCGGCTCTTCTTTGAG-3′ and 5′-GGAAATCATTCCCACCTGTCAGC-3′. The founding animal was chosen based on a 31 bp deletion, which resulted not only in a frameshift mutation beginning at codon 598 but simultaneous removal of a PfoI restriction enzyme digestion site for straightforward genotyping. The founder mutation was subsequently backcrossed into the C57BL/6 J background. Homozygous knockout males were validated as infertile, with significantly smaller and disordered testes by P42, as reported previously⁵¹. The generation of these experimental animals was regulated following ethical review by Yale University Institutional Animal Care and Use Committee (protocol no. 2020-20357) and was performed according to governmental and public health service requirements. No sample size selection, randomization or blinding was performed.

Direct antibody labelling

The Mix-n-Stain CF488 A Antibody Labelling Kit (Biotium, no. 92253) and Mix-n-Stain CF555 Antibody Labelling Kit (Biotium, no. 92254) were used to label rabbit antihuman SAFB1/SAFB antibody (LSBio, LS-C286411) and rabbit anti-LINE-1-ORF1p antibody (abcam, no. ab216324), respectively. The standard protocol listed on the product website was followed, including the ultrafiltration protocol, with minor modifications. In brief, 25–35 μg of antibody was placed in the ultrafiltration vial provided and centrifuged at 14,000g for 2 min to remove all liquid. Depending on the initial amount of antibody, antibodies were eluted in 1× PBS to a final concentration of 0.75 ng μl⁻¹ and the appropriate volume of 10X Mix-n-Stain Reaction Buffer added. The entire solution was transferred to the vial containing the dye and the labelling reaction allowed to proceed at room temperature (22–23 °C) in the dark for 30 min. Finally, 150 μl of storage buffer was added to each reaction with storage in aliquots of 50 μl at −20 °C until use.

Testis sectioning and Immunofluorescence microscopy

Testes from P25 Dnmt3C homozygous and heterozygous mutant males were dissected and embedded in O.C.T. compound (Tissue-Tek). Using cryosectioning, 8 μm sections were obtained with a Leica CM3050S and spotted onto Fisherbrand Superfrost Plus Microscope Slides (Fisher Scientific, no. 12-550-15) and stored at −80 °C until use. For immunofluorescence detection, slides were thawed at room temperature for over 10 min before fixing in 4% paraformaldehyde for 8 min. Permeabilization and blocking were performed at room temperature for 1 h with blocking buffer (5% bovine serum albumin (BSA), 0.2% Triton X-100 and PBS). Sections were incubated with directly labelled antibodies overnight at 4 °C, followed by three 5 min washes in 1× PBS and mounting with VECTASHIELD PLUS Antifade Mounting Medium and DAPI (Vector Laboratories, no. H-2000). Images were acquired using a Leica THUNDER Imaging System at ×40 magnification.

Mass spectrometry

Flp-In T-REx HEK293 cells stably expressing SAFB1, SAFB2 or SLTM (same cell lines used for FLASH) were induced with 0.1 µg ml⁻¹ DOX for 16 h in triplicate, lightly crosslinked with formaldehyde (0.016% final) at room temperature for 10 min, extensively washed with PBS, resuspended with HMGT-K200 buffer (25 mM HEPES-KOH pH 7.4, 10 mM MgCl₂, 10% glycerol, 0.2% Tween-20) and homogenized using a water bath sonicator. Following centrifugation, supernatants were then incubated with MyONE C1 streptavidin beads to pull down proteins of interest. Beads were washed with HMGT-K200, 20 mM Tris-Cl pH 7.4 and 1 M NaCl and finally with 20 mM Tris-Cl pH 7.4 and 50 mM NaCl, then submitted to the in-house MS-facility for further processing. Silver gel staining was performed using a SilverQuest Silver Staining Kit (Thermo Fisher Scientific, no. LC6070) for SAFB1 to ensure that conditions were sufficiently stringent in comparison with GFP pulldown (Extended Data Fig. 7b).

On-beads digest and mass spectrometry analysis

Twelve samples were boiled at 95 °C and 500 rpm for 10 min, followed by tryptic digest including reduction and alkylation of cysteines. The reduction was performed by the addition of tris(2-carboxyethyl)phosphine at a final concentration of 5.5 mM at 37 °C on a rocking platform (500 rpm) for 30 min. To perform alkylation, chloroacetamide was added at a final concentration of 24 mM at room temperature on a rocking platform (500 rpm) for 30 min. Proteins were then digested with 200 ng of trypsin (Roche) per sample, shaking at 800 rpm and 37 °C for 18 h. Samples were acidified by the addition of 1.3 µl of 100% formic acid (2% final concentration), centrifuged and placed on a magnetic rack. Supernatants containing the digested peptides were transferred to a new low-protein-binding tube. Peptide desalting was performed on self-packed C18 columns in a Tip. Eluates were lyophilized and reconstituted in 19 µl of 5% acetonitrile and 2% formic acid in water, briefly vortexed and sonicated in a water bath for 30 s before injection into nano-liquid chromatography–tandem mass spectrometry (nano-LC–MS/MS).

LC–MS/MS instrument settings for shotgun proteome profiling and data analysis

LC–MS/MS was carried out by nanoflow reverse-phase liquid chromatography (Dionex Ultimate 3000, Thermo Scientific) coupled online to a Q-Exactive HF Orbitrap mass spectrometer (Thermo Scientific), as reported previously⁵⁹. In brief, LC separation was performed using a PicoFrit analytical column (75 μm internal diameter × 50 cm length, 15 µm Tip ID; New Objectives) and packed in house with 3 µm of C18 resin (Reprosil-AQ Pur, Dr Maisch). Peptides were eluted using a gradient from 3.8 to 38% solvent B in solvent A over 120 min at a flow rate of 266 nl min⁻¹. Solvent A was 0.1% formic acid and solvent B comprised 79.9% acetonitrile, 20% H₂O and 0.1% formic acid. Nanoelectrospray was generated by the application of 3.5 kV. A cycle of one full Fourier transformation scan mass spectrum (300–1,750 m/z, resolution 60,000 at m/z 200, automatic gain control target 1 × 10⁶) was followed by 12 data-dependent MS/MS scans (resolution of 30,000, automatic gain control target 5 × 10⁵) with a normalized collision energy of 25 eV. To avoid repeated sequencing of the same peptides, a dynamic exclusion window of 30 s was used.

Raw MS data were processed with MaxQuant software (v.1.6.17.0) and searched against the human proteome database UniProtKB UP000005640 (containing 75,074 protein entries, released May 2020). The parameters of MaxQuant database searching were a false discovery rate of 0.01 for proteins and peptides, a minimum peptide length of seven amino acids, a first-search mass tolerance for peptides of 20 ppm and a main search tolerance of 4.5 ppm. A maximum of two missed cleavages was allowed for the tryptic digest. Cysteine carbamidomethylation was set as a fixed modification whereas N-terminal acetylation and methionine oxidation were set as variable modifications. The MaxQuant-processed output files can be found in Supplementary Table 3, showing peptide and protein identification, accession numbers, percentage sequence coverage of the protein and q-values.

IP

Native whole-cell extracts prepared using 0.5× NLB were incubated with ProtG Dynabeads (Life Technologies, no. 10004D) coupled to 1 μg of either SAFB antibody (‘Antibodies’) or IgG (mouse; Santa Cruz, no. sc-2025) in a cold room for 150 min. Beads were washed twice in 0.5× NLB for 5 min then once with NDB. RNase-treated samples were resuspended in 90 µl of NDB to which 10 µl of RNaseA + T1 mix (Thermo Scientific, no EN0551) was added. Samples were then incubated at 20 °C for 15 min and washed twice with 0.5× NLB. Elution from the beads was performed in 1× protein-loading dye by incubation for 5 min at 95 °C with shaking. Interaction partners were detected using the antibodies against proteins shown in Extended Data Fig. 7 (‘Antibodies’).

Immunofluorescence

Cells were crosslinked with 4% methanol-free formaldehyde in PBS at room temperature for 10 min, permeabilized with 0.5% Triton X for 10 min then blocked with 5% BSA in PBS for 30 min at room temperature. Primary antibodies (further details in ‘Antibodies’) were diluted in PBS with 0.1% Triton X and 1% BSA and incubated with fixed cells at 4 °C for about 16 h. Fluorescently labelled secondary antibodies with the appropriate serotype were used to demonstrate target proteins. Hoechst 33342 was used to stain DNA.

Antibodies

The following antibodies were used: AFB1 (Santa Cruz, no. sc-393403), SAFB2 (Santa Cruz, no. sc-514963), SAFB1/2 (HET) (human: Merck/Sigma-Aldrich, no. sc05-588; mouse: LSBio, no. LS-C2886411), SLTM (Invitrogen, no. PA5-59154), ORF1p (human: abcam, no. ab230966; mouse: abcam, no. ab216324), TASOR (Sigma-Aldrich, no. HPA006735), 1H4 (p-SR) (Merck/Sigma-Aldrich, no. MABE50), RBM12B (Bethyl, no. A305-871A-T), RBMX (Cell Signaling Technology, no. 14794 S), NCOA5 (Bethyl, no. A300-790A-T), ZNF638 (Sigma-Aldrich, no. ZRB1186), ZNF326 (Santa Cruz, no. sc-390606), TRA2B (Bethyl, no. A305-011A-M), U2AF2 (U2AF65; Santa Cruz, no. sc-53942), TUBULIN (Santa Cruz, no. sc-32293), SRRM1 (abcam, no. ab221061), SRRM2 (SC35) (Sigma-Aldrich, no. S4045), SON (Sigma-Aldrich, no. HPA023535), DHX9 (abcam, no. ab183731), U1-70K (SySy, no. 203011), PRP8 (Santa Cruz, no. sc-55533), RNAPII (Creative Biolabs, no. CBMAB-XB0938-YC), IgG normal mouse (Santa Cruz, no. sc-2025), SRSF1 (Santa Cruz, no. sc-33652), SRSF2 (abcam, no. ab204916), SRSF3 (Elabscience, no. E-AB-32966), SRSF7 (MBL, no. RN079PW), RB1 (Cell Signaling Technology, no. 9309 S), TRA2B (Santa Cruz, no. sc-166829) and YTHDC1 (Proteintech, no. 14392-1-AP).

TE expression analysis

RNA-seq data from human (HEK293, HeLa, HCT116), mouse (3T3) and Drosophila (S2) cells were mapped to their respective genome (hg38, mm10 and dm6, respectively) using the snakePipes non-coding-RNA-seq pipeline⁶⁰. Internally this pipeline uses TEtranscripts²³, which estimates both gene and TE transcript abundance in RNA-seq data and conducts differential expression analysis on the resultant count tables, which is carried out by DESeq2 (ref. ⁶¹). The outputs of this analysis can be found in Supplementary Tables 4–11.

SAFB peak annotation and TE enrichment

Overlapping SAFB1, SAFB2 and SLTM regions called by HOMER on FLASH data were merged using the function IRanges::reduce(), resulting in a single set of 29,806 SAFB-bound genomic intervals (SAFB peaks), 23,136 of which were located inside GENCODE-annotated genes (within-gene SAFB peaks). All GENCODE v.29 genes located on standard chromosomes were used as a control set (n = 58,721). repeatMasker annotation was downloaded from the UCSC genome browser, and the fraction of total length contributed by different transposable elements was calculated for 23,136 SAFB peaks and 58,721 GENCODE-annotated genes, separately for TEs inserted in sense and antisense orientation. Enrichment was calculated for a subset of sense and antisense TEs by dividing the TE fraction in peaks (that is, observed TE fraction) by that in whole genes (that is, fraction expected if SAFB peaks were distributed randomly on transcripts), followed by log₂-transformation of values.

Short-read RNA-seq data analysis

Raw RNA-seq reads were subject to adaptor and quality trimming using cutadapt 4.1. Default options were used, except for -q 16 –trim-n -m 25 -a AGATCGGAAGAGC -A AGATCGGAAGAGC.

Trimmed reads from human and mouse cell lines were mapped to human GRCh38 (HEK293, HeLa and HCT116 cell lines) and mouse GRCm38 (3T3 cell line) genomes using the STAR 2.7.9a aligner⁶². To improve the sensitivity of spliced read detection and quantification, mapping was done in two passes. In the first pass, all reads were mapped simultaneously to the STAR genome index built with GENCODE gene models (v.29 for human, v.19 for mouse) using default options, with the exception of –outFilterMismatchNoverReadLmax 0.05 –outSAMtype None. In the second pass, each sequenced library was mapped to a genome index with GENCODE gene models extended with new splice junctions detected in the first pass (–sjdbFileChrStartEnd pass1.SJ.out.tab). Other non-default STAR options used included –outFilterMismatchNoverReadLmax 0.05 –quantMode GeneCounts –alignIntronMax 1000000 –alignMatesGapMax 2000000 –sjdbOverhang 100 –limitSjdbInsertNsj 2000000.

Trimmed reads from the fruitfly S2 cell line were mapped to the dm6 genome assembly using STAR 2.7.4a, and reads were counted using featureCounts (subread package v.2.0.0).

Differential gene expression

Differential gene expression analysis was performed using the DESeq2 package⁶¹ on reverse-stranded gene counts from the STAR alignment step. Genes with fewer than ten mapped reads were discarded; lfcThreshold = 1 and alpha = 0.05 were used for calling of differentially expressed genes, and results were shrunk using lfcShrink(…, type = “ashr”).

Differential exon usage

To avoid assignment of exonic reads to SAFB peaks, within-gene SAFB peak fragments or entire peaks overlapping GENCODE v.29-annotated exons were masked and ignored in exon usage analysis. The 22,129 peaks remaining (intronic SAFB peaks) were assigned to their host genes and RNA-seq reads were counted on both annotated exons and intronic SAFB peaks using the function Rsubread::featureCounts() with default arguments, except for countMultiMappingReads = FALSE, strandSpecific = 2, juncCounts = TRUE, and isPairedEnd = TRUE. Differentially expressed SAFB peaks were identified using the DEXSeq R package⁶³ and, for each gene, the peak with the lowest DEXSeq P value was used as a reference for gene fragmentation. In total, 5,394 affected genes were fragmented into pre- and post-peak parts. Exonic read counts were aggregated separately for pre- and post-peak fragments and their differential expression measured using DESeq. Genes hosting SAFB peaks with DEXSeq P_adjusted < 0.05 and log-fold change above 2 were classified as (genes with) upregulated peaks (n = 878) whereas those hosting peaks with DEXSeq P_adjusted > 0.05 and log-fold change between −0.5 and 0.5 were used as the control set (n = 1,457).

Differential splice junction usage

The number of RNA-seq reads supporting each splice junction was counted in the second STAR alignment pass (SJ.out.tab file). Splice junctions that could not be unambiguously assigned a host gene, or that were supported by fewer than ten reads in total across all treatments and replicates in a given cell line, were ignored. Differentially used splice junctions were identified using DEXSeq, with default settings; splice junctions were treated as feature IDs and host genes as group IDs.

Splice site strength quantification

For each gene in the human genome, the probability of each nucleotide acting as a splice donor or acceptor was estimated using SpliceAI²⁶, with default options. SpliceAI scores were matched to splice junctions detected and quantified by STAR.

Splice site to TE distance measurement

Distances between splice sites and nearest upstream or downstream TEs were calculated for a set of ten repeat families (L1, L2, Alu, SVA, ERVL, ERV1, TcMar-Tigger, MIR, Simple_repeat, hAT_Charlie) as follows: (1) all GENCODE genes were flattened using the function IRanges::reduce() in R; (2) STAR-detected splice junctions and repetitive elements outside annotated genes were dropped; and (3) for each remaining splice donor and acceptor, the distance (in nucleotides) to the nearest sense or antisense TE within the same flattened gene was measured separately for each of the ten repeat families. Donors and acceptors within TEs were assigned the distance of 0 nt.

New splice acceptors within SAFB peaks in human tissues

The number of reads supporting splice junctions in the GTEx consortium tissue data was extracted using the recount3 R package⁶⁴. Tissues with fewer than 1 billion spliced reads were excluded from further analysis. Alternative splicing was quantified in an intron-centric manner—that is, splicing index was calculated separately for each splice donor and acceptor. We extracted all splice junctions located within an annotated human gene, with splice donor annotated in GENCODE v.29 and splice acceptor sited within a fully intronic SAFB peak (n_peaks = 16,929). A further 21,693 such splice junctions were filtered for junction where the donor participated in multiple events, had a splicing index above 1% in at least one tissue and was supported by at least 500 reads in all 27 tissues (that is, used ubiquitously), resulting in a highly stringent set of of 1,104 splice junctions.

p-SR and DHX9 FLASH analysis

FLASH reads uniquely mapping to the hg38 genome were counted using featureCounts on two custom gene annotation reference sets. The first of these contained exons and SAFB peaks, with exons prioritized over SAFB peaks in the case of overlaps. SAFB peaks were assigned to their host genes and treated as exons for read counting. The second reference contained genes fully fragmented into exons, repetitive elements and introns, with exons prioritized over repeats and introns, and repeats prioritized over introns where their genomic coordinates were overlapping. Whereas the first reference allows for increased sensitivity when quantifying FLASH signal on known SAFB-binding regions, the latter sacrifices sensitivity (because it contains many short genomic fragments) for the power of recognizing regions of increased binding outside of SAFB peaks, or in SAFB peaks not called by the peak-calling software. DEXSeq analysis was performed separately on exon/peak and exon/repeat/intron counts. Regions with adjusted P < 0.05 were considered differentially bound.

Alternative polyadenylation sites

Aligned ONT direct RNA-seq performed on control and triple KD samples was screened for their end coordinates, under the assumption that these are derived from the close proximity of a polyadenylation site. Genomic coordinates of this collection of almost 1.5 million single-nucleotide-resolution read end sites were extended by 50 nt upstream and downstream, and overlapping intervals were collapsed into a total of 274,330 putative polyadenylation regions. The number of control and triple KD reads ending in each of these regions was counted and, for each gene, the fraction of ONT reads ending in each of its polyadenylation regions was calculated separately for control and triple KD libraries. Genes supported by at least 20 reads in which the contribution of at least one polyA isoform was changed by at least 20 percentage points between triple KD and control were considered differentially polyadenylated. In total, 14,148 genes (4,433 of genomic length over 50 kb) were supported by 20 or more reads, and 247 (231 longer than 50 kb) showed differential polyA site usage.

Locus-specific L1 quantification

Raw reads from HEK293 fractionation RNA-seq libraries were aligned to the hg38 genome using bwa aln, and alignments further processed with L1EM⁶⁵, both with default options. L1EM counts from categories ‘only’, ‘3prunon’ and ‘passive_sense’ were summed. These total read counts were combined with read counts on individual genes (GENCODE v.29 annotation), and DESeq2 differential gene expression analysis was performed together on gene and L1 counts, treating L1 elements as independent genes.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

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Tag: multidisciplinary

Theory

TCMT: critical coupling for an isolated mode

Open-resonator TCMT

FW condition

Supercritical coupling

Coupled-resonance-induced transparency in far-field representation

Near-field representation

Maximum enhancement at the FW quasi-BIC

Further discussion

RCWA validation

Fabrication

Optical characterization

Photoluminescence, enhancement-factor and radiance-enhancement estimation

FDTD simulations

Directivity measurements

Sample preparation

XRD and Raman spectroscopy

TEM sample preparation

Microstructure characterization

First-principles calculations

Deformability factor calculation

Molecular dynamics simulation

Mechanical property characterization

In situ synchrotron radiation XRD measurements

In situ TEM nanopillar compression

The All of Us cohort

Data accessibility through a ‘data passport’

EHR data

Biospecimen collection and processing

Genome sequencing

Genome Center sample receipt, accession and QC

WGS library construction, sequencing and primary data QC

Array genotyping

Genomic data curation

Single-sample QC

Joint call set QC

Batch effect analysis

Sensitivity and precision evaluation

Genetic ancestry inference

Relatedness

LDL-C common variant GWAS

Genotype-by-phenotype replication

Reporting summary

Cell culture and generation of stable cell lines

FLASH

FLASH data processing

UMAP of FLASH data

Sample and library preparation for RNA-seq

Isolation of nuclear and cytoplasmic RNA for RNA-seq

Transient transfections in rescue experiments and sample preparation for qPCR detection

ONT direct RNA-seq

Retrotransposition assay

RNA–FISH

EMSA with recombinant Halo, Halo-SAFB1RRM and Halo-TRA2BRRM

In vitro unmethylated and methylated RNA-binding assay

RNA blotting

p-SR (1H4) and DHX9 FLASH in SAFB-depleted cells

RIP–qPCR

Generation of the Dnmt3c-null allele

Direct antibody labelling

Testis sectioning and Immunofluorescence microscopy

Mass spectrometry

On-beads digest and mass spectrometry analysis

LC–MS/MS instrument settings for shotgun proteome profiling and data analysis

IP

Immunofluorescence

Antibodies

TE expression analysis

SAFB peak annotation and TE enrichment

Short-read RNA-seq data analysis

Differential gene expression

Differential exon usage

Differential splice junction usage

Splice site strength quantification

Splice site to TE distance measurement

New splice acceptors within SAFB peaks in human tissues

p-SR and DHX9 FLASH analysis

Alternative polyadenylation sites

Locus-specific L1 quantification

EMSA with recombinant Halo, Halo-SAFB1^RRM and Halo-TRA2B^RRM