Publications

Markov state models (MSMs) are widely employed to analyze the kinetics of complex systems. But despite their effectiveness in many applications, MSMs are prone to systematic or statistical errors, often exacerbated by suboptimal hyperparameter choice. In this article, we attempt to understand how these choices affect the error of estimates of mean first-passage times and committors, key quantities in chemical rate theory. We first evaluate the performance of the recently introduced “stopped-process estimator” [Strahan, J. Long-time-scale predictions from short-trajectory data: A benchmark analysis of the trp-cage miniprotein. J. Chem. Theory Comput. 2021, 17, 2948–2963. 10.1021/acs.jctc.0c00933.] that attempts to reduce error caused by choosing a too-large lag time. We then study the effect of statistical errors on Markov state model construction using the condition number, which measures an MSM’s sensitivity to perturbation. This analysis helps give an insight into which factors cause an MSM to be more or less sensitive to statistical error. Our work highlights the importance of choosing a good sampling measure, the measure from which the initial points are drawn, and has implications for recent work applying a variational principle for evaluating the committor.

Pose estimation is a general problem in computer vision with wide applications. The relative orientation of a 3D reference object can be determined from a 3D rotated version of that object, or from a projection of the rotated object to a 2D planar image. This projection can be a perspective projection (the PnP problem) or an orthographic projection (the OnP problem). We restrict our attention here to the OnP problem and the full 3D pose estimation task (the EnP problem). Here we solve the least squares systems for both the error-free EnP and OnP problems in terms of the determinant ratio matrix (DRaM) approach. The noisy-data case can be addressed with a straightforward rotation correction scheme. While the SVD and optimal quaternion eigensystem methods solve the noisy EnP 3D-3D alignment exactly, the noisy 3D-2D orthographic (OnP) task has no known comparable closed form, and can be solved by DRaM-class methods. We note that while previous similar work has been presented in the literature exploiting both the QR decomposition and the Moore-Penrose pseudoinverse transformations, here we place these methods in a larger context that has not previously been fully recognized in the absence of the corresponding DRaM solution. We term this class of solutions as the DRaM family, and conduct comparisons of the behavior of the families of solutions for the EnP and OnP rotation estimation problems. Overall, this work presents both a new solution to the 3D and 2D orthographic pose estimation problems and provides valuable insight into these classes of problems. With hindsight, we are able to show that our DRaM solutions to the exact EnP and OnP problems possess derivations that could have been discovered in the time of Gauss, and in fact generalize to all analogous N-dimensional Euclidean pose estimation problems.

Building upon a foundational Human Kidney resource, we present a comprehensive multi-modal atlas that defines spatially resolved versus unresolved repair states and mechanisms in human kidney disease. Homeostatic interactions between injured kidney epithelium and its surrounding milieu determine successful repair outcomes, while pathogenic signaling promotes unresolved inflammation and fibrosis leading to chronic disease. We integrated multiple single-cell and spatial modalities across ∼700 samples from >350 patients (∼250 research biopsies), analyzing ∼1.7 million cells alongside complementary mouse multi-omic profiles spanning acute-to-chronic injury and aging (>300,000 cells) and spatial transcriptomic analysis of >150 human biopsies. This cross-species atlas delineates functional pathways and druggable targets across the nephron and defines gene regulatory networks and chromatin landscapes governing tubular, fibroblast, and immune cell transitions from injury to either recovery or failed repair states. We identified distinct cellular states associated with specific pathological features that show dynamic distributions between acute kidney injury (AKI) and chronic kidney disease (CKD), organized within unique spatial niches that reveal progression mechanisms from early injury to unresolved disease. Gene regulatory analyses prioritized key transcription factor activities (SOX4, SOX9, NFKB1, REL, KLFs) and their target networks establishing disease states and tissue microenvironments. These regulatory programs were directly linked to clinical outcomes, identifying molecular signatures of recovery and secreted biomarkers predictive of AKI-to-CKD progression, providing a key resource for therapeutic development and precision medicine approaches in kidney disease.

Phase separation of proteins plays a critical role in cellular organization. How phase-separated protein condensates underpin biological function and how condensates achieve specificity remain elusive. We investigated the phase separation of MUT-16, a scaffold protein in Mutator foci, and its role in recruiting the client protein MUT-8, a key component in RNA silencing in Caenorhabditis elegans. We employed a multi-scale approach that combined coarse-grained (residue-level CALVADOS2 and near-atomistic Martini3) and atomistic simulations. Simulations across different resolutions provide a consistent perspective on how MUT-16 condensates recruit MUT-8, enabling the fine-tuning of chemical details and balancing the computational cost. Both coarse-grained models (CALVADOS2 and Martini3) predicted the relative phase-separation propensities of MUT-16’s disordered regions, which we confirmed through in vitro experiments. Simulations also identified key sequence features and residues driving phase separation and revealed differences in residue interaction propensities between CALVADOS2 and Martini3. Furthermore, Martini3 and 350-μs atomistic simulations on Folding@Home of MUT-8’s N-terminal prion-like domain with MUT-16 M8BR cluster highlighted the importance of cation-interactions between Tyr residues of MUT-8 and Arg residues of MUT-16 M8BR. Lys residues were observed to be more prone to interact in Martini3. Atomistic simulations revealed that the guanidinium group of Arg also engages in interactions and hydrogen bonds with the backbone of Tyr, possibly contributing to the greater strength of Arg-Tyr interactions compared to Lys-Tyr, where these additional favorable contacts are absent. In agreement with our simulations, in vitro co-expression pull-down experiments demonstrated a progressive loss of MUT-8 recruitment after the mutation of Arg in MUT-16 M8BR to Lys or Ala, confirming the critical role of Arg in this interaction. These findings advance our understanding of MUT-16 phase separation and subsequent MUT-8 recruitment, key processes in assembling Mutator foci that drive RNA silencing in C. elegans.

Phase separation of proteins plays a critical role in cellular organization. How phase-separated protein condensates underpin biological function and how condensates achieve specificity remain elusive. We investigated the phase separation of MUT-16, a scaffold protein in Mutator foci, and its role in recruiting the client protein MUT-8, a key component in RNA silencing in Caenorhabditis elegans. We employed a multi-scale approach that combined coarse-grained (residue-level CALVADOS2 and near-atomistic Martini3) and atomistic simulations. Simulations across different resolutions provide a consistent perspective on how MUT-16 condensates recruit MUT-8, enabling the fine-tuning of chemical details and balancing the computational cost. Both coarse-grained models (CALVADOS2 and Martini3) predicted the relative phase-separation propensities of MUT-16’s disordered regions, which we confirmed through in vitro experiments. Simulations also identified key sequence features and residues driving phase separation and revealed differences in residue interaction propensities between CALVADOS2 and Martini3. Furthermore, Martini3 and 350-μs atomistic simulations on Folding@Home of MUT-8’s N-terminal prion-like domain with MUT-16 M8BR cluster highlighted the importance of cation-interactions between Tyr residues of MUT-8 and Arg residues of MUT-16 M8BR. Lys residues were observed to be more prone to interact in Martini3. Atomistic simulations revealed that the guanidinium group of Arg also engages in interactions and hydrogen bonds with the backbone of Tyr, possibly contributing to the greater strength of Arg-Tyr interactions compared to Lys-Tyr, where these additional favorable contacts are absent. In agreement with our simulations, in vitro co-expression pull-down experiments demonstrated a progressive loss of MUT-8 recruitment after the mutation of Arg in MUT-16 M8BR to Lys or Ala, confirming the critical role of Arg in this interaction. These findings advance our understanding of MUT-16 phase separation and subsequent MUT-8 recruitment, key processes in assembling Mutator foci that drive RNA silencing in C. elegans.

During epithelial morphogenesis, cell polarity aligns individual cell behaviors into collective motions that shape developing tissues. Here, we combine experiments with computational modeling to investigate how cell-scale forces oriented by Planar Cell Polarity (PCP) direct the collective, counter-rotational cell flows that occur during hair placode morphogenesis. We rule out that PCP directs apical neighbor exchanges, as junctional myosin and PCP protein localization are not co-correlated with junction shrinkage. Instead, we find that PCP directs anterior-directed crawling of placode cells along the basal surface of the tissue through a mechanism that requires cell crawling regulator Rac1. Modeling the placode as a continuum viscoelastic fluid, we find that active forces from cell crawling at the basal surface is sufficient to generate the experimentally observed counter-rotational cell motion at the apical surface. Our results show an unexpected role for PCP in epithelial morphogenesis, centering the basal surface as the site of force generation.

3D chromatin structure is critical for the regulation of gene expression during development. Here we used Micro-C assays at 100-bp resolution to map genome organization in Drosophila melanogaster throughout the first half of embryogenesis. These high-resolution contact maps reveal fine-scale features such as loops and boundaries delineating topologically associating domains. Notably, we observe that 3D chromatin structures form prior to zygotic genome activation and persist during successive mitotic cycles. Integrative analysis with 149 public chromatin immunoprecipitation sequencing (ChIP-seq) datasets identifies four classes of chromatin structuring elements, including a distinct group enriched for GAGA-associated factor (GAF) and Zelda binding, associated with developmental-gene regulation. These elements are mitotically retained and exhibit sequence and structure similarity between D. melanogaster and D. virilis. We propose that 3D chromatin organization in the pre-cellular embryo facilitates deployment of developmentally regulated genes during Drosophila embryogenesis.

Despite the rise of single particle cryo-electron microscopy (cryo-EM) as a premier method for resolving macromolecular structures at atomic resolution, methods to address molecular heterogeneity in vitrified samples have yet to reach maturity. With an increasing number of new methods to analyze the multitude of heterogeneous states captured in single particle images, a systematic approach to validation in this field is needed. With this motivation, we issued a challenge to the community to analyze two cryo-EM particle image sets of thyroglobulin that exhibit continuous conformational heterogeneity. The first dataset was experimental and the second was generated with a simulator, allowing control over the distribution of molecular structures and enabled direct comparison between participants’ submissions and the ground truth molecular structures and distributions. Participants were asked to submit 80 volumes representing the heterogeneous ensemble and estimate their respective populations in the image sets provided. Participation of the research community in the challenge was strong, with submissions from nearly all developers of heterogeneity methods, resulting in 41 submissions across both datasets. Submissions qualitatively exceeded expectations, with the molecular motions identified by methods resembling both each other and the ground truth motion. However, quantitatively assessing these similarities was a challenge in and of itself. In the process of assessing the submissions, we developed several validation metrics, most of which require reference to the underlying ground truth volumes. However, we have also explored the use of metrics that do not necessarily reference ground truth. This is particularly apt for experimental datasets where ground truth is inaccessible. These approaches allowed us to assess the similarity and accuracy in volume quality, molecular motions, and conformational distribution of di!erent submissions. These metrics and the e!orts of all participants help chart a path forward for the improvements of heterogeneity methods for cryo-EM and for future challenges to validate these new methods as they continue to be developed by the community.

Despite the rise of single particle cryo-electron microscopy (cryo-EM) as a premier method for resolving macromolecular structures at atomic resolution, methods to address molecular heterogeneity in vitrified samples have yet to reach maturity. With an increasing number of new methods to analyze the multitude of heterogeneous states captured in single particle images, a systematic approach to validation in this field is needed. With this motivation, we issued a challenge to the community to analyze two cryo-EM particle image sets of thyroglobulin that exhibit continuous conformational heterogeneity. The first dataset was experimental and the second was generated with a simulator, allowing control over the distribution of molecular structures and enabled direct comparison between participants’ submissions and the ground truth molecular structures and distributions. Participants were asked to submit 80 volumes representing the heterogeneous ensemble and estimate their respective populations in the image sets provided. Participation of the research community in the challenge was strong, with submissions from nearly all developers of heterogeneity methods, resulting in 41 submissions across both datasets. Submissions qualitatively exceeded expectations, with the molecular motions identified by methods resembling both each other and the ground truth motion. However, quantitatively assessing these similarities was a challenge in and of itself. In the process of assessing the submissions, we developed several validation metrics, most of which require reference to the underlying ground truth volumes. However, we have also explored the use of metrics that do not necessarily reference ground truth. This is particularly apt for experimental datasets where ground truth is inaccessible. These approaches allowed us to assess the similarity and accuracy in volume quality, molecular motions, and conformational distribution of di!erent submissions. These metrics and the e!orts of all participants help chart a path forward for the improvements of heterogeneity methods for cryo-EM and for future challenges to validate these new methods as they continue to be developed by the community.

Septins can assemble into scaffolds at the plasma membrane to regulate cell morphology. While septins preferentially bind convex membranes via amphipathic helices, their assembly on varied geometries in cells suggests additional localization cues. We tested the hypothesis that lipid composition directs septin assembly through the property of lipid packing. We used pharmacological perturbations that alter fatty acid chain saturation to manipulate lipid packing and found septin structures were selectively disrupted at flat regions of the plasma membrane. To determine whether lipid packing is sufficient to impact septin assembly, molecular dynamics simulations were used to design lipid mixtures with varied packing to monitor septin adsorption in vitro. Septins strongly favored loosely packed lipid bilayers, but additional geometrical cues act in conjunction with this membrane property. This work demonstrates that packing defects and geometry jointly regulate septin localization, highlighting how distinct membrane properties are integrated to organize the septin cytoskeleton.