Publications

The segregation of the epiblast (EPI) and primitive endoderm (PE) cell types in the preimplantation mouse embryo is not only a crucial decision that sets aside the precursors of the embryo proper from extraembryonic cells, respectively, but also has served as a central model to study a key concept in mammalian development: how much of developmental patterning is predetermined vs. stochastically emergent. Here, we address this question by quantitative live imaging of multiple endogenously tagged transcription factors key to this fate decision and trace their dynamics at a single-cell resolution through the formation of EPI and PE cell fates. Strikingly, we reveal an initial symmetry breaking event, the formation of a primary EPI cell lineage, and show that this is linked to the dynamics of the prior inner cell mass/trophectoderm fate decision through the expression of SOX2. This primary EPI lineage, through fibroblast growth factor (FGF) signaling, induces an increase in the transcription factor GATA6 in other inner cell mass cells, setting them on the course toward PE differentiation. Interestingly, this trajectory can switch during a defined developmental window, leading to the emergence of secondary EPI cells. Finally, we show that early expression levels of NANOG, which are seemingly stochastic, can bias whether a cell’s trajectory switches to secondary EPI or continues as PE. Our data give unique insight into how fate patterning is initiated and propagated during unperturbed embryonic development through the interplay of lineage-history-biased and stochastic cell-intrinsic molecular features, unifying previous models of EPI/PE segregation.

We present a randomized algorithm for producing a quasi-optimal hierarchically semi-
separable (HSS) approximation to an N ×N matrix A using only matrix-vector products with A and
AT. We prove that, using O(k log(N/k)) matrix-vector products and O(N k2 log(N/k)) additional
runtime, the algorithm returns an HSS matrix B with rank-k blocks whose expected Frobenius norm
error E[∥A − B∥2
F] is at most O(log(N/k)) times worse than the best possible approximation error by
an HSS rank-k matrix. In fact, the algorithm we analyze in a simple modification of an empirically
effective method proposed by [Levitt & Martinsson, SISC 2024]. As a stepping stone towards our
main result, we prove two results that are of independent interest: a similar guarantee for a variant of
the algorithm which accesses A’s entries directly, and explicit error bounds for near-optimal subspace
approximation using projection-cost-preserving sketches. To the best of our knowledge, our analysis
constitutes the first polynomial-time quasi-optimality result for HSS matrix approximation, both in
the explicit access model and the matrix-vector product query model.

The first cell fate bifurcation in mammalian development directs cells toward either the trophectoderm (TE) or inner cell mass (ICM) compartments in pre-implantation embryos. This decision is regulated by the subcellular localization of a transcriptional co-activator YAP and takes place over several progressively asynchronous cleavage divisions. As a result of this asynchrony and variable arrangement of blastomeres, reconstructing the dynamics of the TE/ICM cell specification from fixed embryos is extremely challenging. To address this, we developed a live-imaging approach and applied it to measure pairwise dynamics of nuclear YAP and its direct target genes, CDX2 and SOX2, which are key transcription factors of the TE and ICM, respectively. Using these datasets, we constructed a generative model of the first cell fate bifurcation, which reveals the time-dependent statistics of the TE and ICM cell allocation. In addition to making testable predictions for the joint dynamics of the full YAP/CDX2/SOX2 motif, the model revealed the stochastic nature of the induction timing of the key cell fate determinants and identified the features of YAP dynamics that are necessary or sufficient for this induction. Notably, temporal heterogeneity was particularly prominent for SOX2 expression among ICM cells. As heterogeneities within the ICM have been linked to the initiation of the second cell fate decision in the embryo, understanding the origins of this variability is of key significance. The presented approach reveals the dynamics of the first cell fate choice and lays the groundwork for dissecting the next cell fate decisions in mouse development.

The quasi-2D electrostatic systems, characterized by periodicity in two dimensions with a free third dimension, have garnered significant interest in many fields. We apply the sum-of-Gaussians (SOG) approximation to the Laplace kernel, dividing the interactions into near-field, mid-range, and long-range components. The near-field component, singular but compactly supported in a local domain, is directly calculated. The mid-range component is managed using a procedure similar to nonuniform fast Fourier transforms in three dimensions. The long-range component, which includes Gaussians of large variance, is treated with polynomial interpolation/anterpolation in the free dimension and Fourier spectral solver in the other two dimensions on proxy points. Unlike the fast Ewald summation, which requires extensive zero padding in the case of high aspect ratios, the separability of Gaussians allows us to handle such case without any zero padding in the free direction. Furthermore, while NUFFTs typically rely on certain upsampling in each dimension, and the truncated kernel method introduces an additional factor of upsampling due to kernel oscillation, our scheme eliminates the need for upsampling in any direction due to the smoothness of Gaussians, significantly reducing computational cost for large-scale problems. Finally, whereas all periodic fast multipole methods require dividing the periodic tiling into a smooth far part and a near part containing its nearest neighboring cells, our scheme operates directly on the fundamental cell, resulting in better performance with simpler implementation. We provide a rigorous error analysis showing that upsampling is not required in NUFFT-like steps, achieving O(N N) complexity with a small prefactor. The performance of the scheme is demonstrated via extensive numerical experiments.

Structuring the photon density of states and light-matter coupling in optical cavities has emerged as a promising approach to modifying the equilibrium properties of materials through strong light-matter interactions. In this article, we employ state-of-the-art quantum electrodynamical density functional theory (QEDFT) to study the modifications of the electronic and structural properties of two-dimensional (2D) van der Waals (vdW) layered materials by the cavity vacuum field fluctuations. We find that cavity photons modify the electronic density through localization along the photon polarization directions, a universal effect observed for all the 2D materials studied here. This modification of the electronic structure tunes the material properties, such as the shifting of energy valleys in monolayer h-BN and 2H-MoS2, enabling tunable band gaps. Also, it tunes the interlayer spacing in bilayer 2H-MoS2 and Td-MoTe2, allowing for adjustable ferroelectric, nonlinear Hall effect, and optical properties, as a function of light-matter coupling strength. Our findings open an avenue for engineering a broad range of 2D layered quantum materials by tuning vdW interactions through fluctuating cavity photon fields.

A fundamental problem in computer system performance, as well as in the natural sciences, concerns inferring from observations an understanding of the behavior of stochastic processes of interacting system components whose dynamics are driven by an unknown underlying stochastic differential equation (SDE). The objective in solving this problem is to infer the underlying equations of the dynamics of the system from sets of system measurements, indexed over time. Given the stochastic nature of such systems, together with a lack of information on stochastic trajectories in many cases [1, 3], this represents a very challenging problem in general.

During the first cell fate decision in mammalian embryos, the inner cell mass cells, which will give rise to the embryo proper and other extraembryonic tissues, segregate from the trophectoderm cells, the precursors of the placenta. Cell fate segregation proceeds in a gradual manner encompassing two rounds of cell division, as well as cell positional and morphological changes. While it is known that the activity of the Hippo signaling pathway and the subcellular localization of its downstream effector YAP dictate lineage specific gene expression, the response of YAP to these dynamic cellular changes remains incompletely understood. Here we address these questions by quantitative live imaging of endogenously tagged YAP while simultaneously monitoring geometric cellular features and cell cycle progression throughout cell fate segregation. We apply a probabilistic model to our dynamic data, providing a quantitative characterization of the mutual effects of YAP and cellular relative exposed area, which has previously been shown to correlate with subcellular YAP localization in fixed samples. Additionally, we study how nuclear YAP levels are influenced by other factors, such as the decreasing pool of maternally provided YAP that is partitioned to daughter cells through cleavage divisions, cell cycle-associated nuclear volume changes, and a delay after divisions in adjusting YAP levels to new cell positions. Interestingly, we find that establishing low nuclear YAP levels required for the inner cell mass fate is largely achieved by passive cell cycle-associated mechanisms. Moreover, contrary to expectations, we find that mechanical perturbations that result in cell and nuclear shape changes do not influence YAP localization in the embryo. Together our work identifies how various inputs are integrated over a dynamic developmental time course to shape the levels of a key molecular determinant of the first cell fate choice.

The translation and shape deformations of a passive viscous Newtonian droplet immersed in an active nematic liquid crystal under circular confinement are analyzed using a linear stability analysis. We focus on the case of a sharply aligned active nematic in the limit of strong elastic relaxation in two dimensions. Using an active liquid crystal model, we employ the Lorentz reciprocal theorem for Stokes flow to study the growth of interfacial perturbations as a result of both active and elastic stresses. Instabilities are uncovered in both extensile and contractile systems, for which growth rates are calculated and presented in terms of the dimensionless ratios of active, elastic, and capillary stresses, as well as the viscosity ratio between the two fluids. We also extend our theory to analyze the inverse scenario, namely, the stability of an active nematic droplet surrounded by a passive viscous layer. Our results highlight the subtle interplay of capillary, active, elastic, and viscous stresses in governing droplet stability. The instabilities uncovered here may be relevant to a plethora of biological active systems, from the dynamics of passive droplets in bacterial suspensions to the organization of subcellular compartments inside the cell and the cell nucleus.

Cystic fibrosis (CF) is due to loss-of-function variants of the CF transmembrane conductance regulator (CFTR) channel. The most effective treatment for people with CF carrying the F508del mutation is the triple combination of elexacaftor–tezacaftor–ivacaftor (ETI). ETI can correct the underlying defect(s) in other CFTR mutants. The use of disease-relevant predictive models such as patient-derived human nasal epithelial cells allow to investigate the response to CFTR modulators of specific genotypes, possibly supporting patients' access to treatment.

Accurate prediction of drug-target binding and unbinding kinetics and thermodynamics is essential for guiding drug discovery and lead optimization. However, traditional atomistic simulations are often too computationally expensive to capture rare events that govern ligand (un)binding. Several enhanced sampling methods exist to overcome these limitations, but they require extensive manual intervention and introduce variability and artifacts in free energy and kinetic estimates that limit high-throughput scalability. The present work introduces seekrflow, an automated multiscale milestoning simulation pipeline that streamlines the entire workflow from a single receptor-ligand input structure to kinetic and thermodynamic predictions in a single step. This integrated approach minimizes manual intervention, reduces computational overhead, and enhances the reproducibility and accuracy of kinetic and thermodynamic predictions. The accuracy and efficiency of the pipeline is demonstrated on multiple receptor-ligand complexes, including inhibitors of heat shock protein 90, threonine-tyrosine kinase, and the trypsin protein, with predicted kinetic parameters closely matching experimental estimates. seekrflow establishes a new benchmark for automated and high-throughput physics-based predictions of kinetics and thermodynamics.