Publications

We explore a quaternion adjugate matrix-based representation for rotational motion in the Perspective-n-Point (PnP) problem. Leveraging quadratic quaternion terms within a Determinant Ratio Matrix (DRaM) estimation framework, we extend its application to perspective scenarios, providing a robust and efficient initialization for iterative PnP pose estimation. Notably, by solving the orthographic projection least-squares problem, DRaM provides a reliable initialization that enhances the accuracy and stability of iterative PnP solvers. Experiments on synthetic and real data demonstrate its efficiency, accuracy, and robustness, particularly under high noise conditions. Furthermore, our non-minimal formulation ensures numerical stability, making it effective for real-world applications.

Simulation-based inference provides a powerful framework for cryoelectron microscopy, employing neural networks in methods like CryoSBI to infer biomolecular conformations via learned latent representations. This latent space represents a rich opportunity, encoding valuable information about the physical system and the inference process. Harnessing this potential hinges on understanding the underlying geometric structure of these representations. We investigate this structure by applying manifold learning techniques to CryoSBI representations of a simulated benchmark dataset and both simulated and experimental images of hemagglutinin. We reveal that these high-dimensional data inherently populate low-dimensional, smooth manifolds, with simulated data effectively covering the experimental counterpart. By characterizing the manifold's geometry using Diffusion Maps and identifying its principal axes of variation via coordinate interpretation methods, we establish a direct link between the latent structure and key physical parameters. Discovering this intrinsic low-dimensionality and interpretable geometric organization not only validates the CryoSBI approach but also enables us to learn more from the data structure and provides opportunities for improving future inference strategies by exploiting this revealed manifold geometry.

Wnt-signaling, via β-catenin or the planar cell polarity (PCP) branch, is crucial for development, tissue homeostasis, and linked to many diseases. LRP5/6, arrow (arr) in Drosophila, is the obligate co-receptor in Wnt/β-catenin signaling, with ligand binding to a Frizzled (Fz) family member and LRP5/6 mediating formation of the signalosome complex with Dishevelled (Dsh/Dvl in mammals) and Axin. Current models for Wnt/PCP signaling omit Arr/LRP5/6 and the notion is that it functions without these co-receptors. Here we show that arr/LRP5/6 is positively required in Wnt/PCP signaling. In Drosophila, loss of arr results in PCP mediated cellular orientation defects, aberrant wing hair formation, and loss of polarity, as described for core PCP factors fz, fmi/Celsr, and dsh. In the eye, arr mutant tissue displays cell fate changes in photoreceptors R3/R4 and chirality defects, classical PCP phenotypes. During Wnt/PCP establishment, defects are manifest as reduced levels of Fmi/Celsr and Dsh along with loss of their asymmetric localization. Functional interactions indicate that Fz can recruit Arr, and this potentiates Fz and Dsh function in PCP signaling in all tissues tested. Taken together, our data support an essential Arr/LRP5/6 function in promoting Wnt/Fz-Dsh PCP-complex activity.

Simulation-based inference provides a powerful framework for cryoelectron microscopy, employing neural networks in methods like CryoSBI to infer biomolecular conformations via learned latent representations. This latent space represents a rich opportunity, encoding valuable information about the physical system and the inference process. Harnessing this potential hinges on understanding the underlying geometric structure of these representations. We investigate this structure by applying manifold learning techniques to CryoSBI representations of a simulated benchmark dataset and both simulated and experimental images of hemagglutinin. We reveal that these high-dimensional data inherently populate low-dimensional, smooth manifolds, with simulated data effectively covering the experimental counterpart. By characterizing the manifold's geometry using Diffusion Maps and identifying its principal axes of variation via coordinate interpretation methods, we establish a direct link between the latent structure and key physical parameters. Discovering this intrinsic low-dimensionality and interpretable geometric organization not only validates the CryoSBI approach but also enables us to learn more from the data structure and provides opportunities for improving future inference strategies by exploiting this revealed manifold geometry.

The collective migration of epithelial groups of cells plays a central role in processes such as embryo development, wound healing, and cancer invasion. While finite cell clusters are known to collectively migrate in response to external gradients, the competing effect of possible endogenous cues is largely this http URL, we demonstrate that the polarization of peripheral cells that pull the cluster's edge outward is sufficient to induce and sustain the collective migration of confluent clusters. We use a general continuum model to show that the underlying shape-sensing mechanism is purely mechanical, relying on long-range hydrodynamic interactions and cell-cell alignment forces. As a proof-of-concept, we validate our findings with experiments on monolayer clusters from various cell lines, where we control initial shapes and sizes. The mechanism operates independently of external signals and will generally interfere with them. Specifically, we predict and observe experimentally that it can override collective durotaxis, reversing the direction of migration. Together, our results offer a physical framework for understanding how cell interactions govern the interplay between global shape and collective motion and afford engineering principles for optimal control and manipulation of cell cluster shape and motion.

nferring dynamic cellular processes from static single-cell measurements remains a central challenge in genomics. Here we introduce ArchVelo, a new method for modeling gene regulation and inferring cell trajectories using single-cell simultaneous chromatin accessibility (scATAC-seq) and transcriptomic (scRNA-seq) profiling. ArchVelo represents chromatin accessibility as a set of archetypes—shared regulatory programs—and models their dynamic influence on transcription. Compared to previous methods, ArchVelo improves inference accuracy and gene-level latent time alignment, and enables identification of the underlying transcription factor activity. We benchmark ArchVelo on developing mouse brain and human hematopoiesis datasets and apply it to CD8 T cells responding to viral infection, revealing distinct trajectories of differentiation and proliferation. Focusing on the progenitor CD8 T cell population with key roles in sustaining immune responses and translationally linked to immunotherapy outcomes, we identify a previously uncharacterized differentiation trajectory from Ccr6− to Ccr6+ progenitors, shared between acute and chronic infection. In sum, ArchVelo provides a principled framework for modeling dynamic gene regulation in multi-omic single-cell data across biological systems.

In multicellular systems, adhesion complexes, such as those composed of E-cadherin and associated catenins, mechanically couple neighboring cells by directly linking their actin-based cytoskeletal assemblies. However, the mechanics of how forces are transmitted across these adhesions remains largely unstudied. Here, we introduce a biophysical model that explicitly couples adhesion complex dynamics to intracellular mechanics across cell boundaries. A cadherin dimer plus associated catenins connecting two cells is represented as a spring whose ends experience drag with respect to the moving actin cytoskeleton. The cytoskeleton is modeled as a contractile gel driven by myosin activity in its bulk and forces from adhesion on its boundaries. Our model captures this bidirectional coupling via a coarse-grained continuum framework and reveals a range of observed cell- and tissue-scale behaviors. These include global cell polarization of the multicellular collective, other polarization patterns and oscillatory dynamics, spontaneously formed actin rings within cells, and supracellular stress chains. Many of these features arise from modeling the direct mechanical coupling between cytoskeleton and adhesion. This model can be extended to other adhesion-cytoskeleton feedback systems and used to advance our understanding of multicellular tissue dynamics, particularly during development.

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.

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.

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.