Publications

We consider infinite-horizon discounted Markov decision processes and study the convergence rates of the natural policy gradient (NPG) and the Q-NPG methods with the log-linear policy class. Using the compatible function approximation framework, both methods with log-linear policies can be written as inexact versions of the policy mirror descent (PMD) method. We show that both methods attain linear convergence rates and $\tilde{\mathcal{O}}(1/\epsilon^2)$ sample complexities using a simple, non-adaptive geometrically increasing step size, without resorting to entropy or other strongly convex regularization. Lastly, as a byproduct, we obtain sublinear convergence rates for both methods with arbitrary constant step size.

The aggregation of epitopes that are also able to bind major histocompatibility complex (MHC) alleles raises questions around the potential connection between the formation of epitope aggregates and their affinities to MHC receptors. We first performed a general bioinformatic assessment over a public dataset of MHC class II epitopes, finding that higher experimental binding correlates with higher aggregation-propensity predictors. We then focused on the case of P10, an epitope used as a vaccine candidate against Paracoccidioides brasiliensis that aggregates into amyloid fibrils. We used a computational protocol to design variants of the P10 epitope to study the connection between the binding stabilities towards human MHC class II alleles and their aggregation propensities. The binding of the designed variants was tested experimentally, as well as their aggregation capacity. High-affinity MHC class II binders in vitro were more disposed to aggregate forming amyloid fibrils capable of binding Thioflavin T and congo red, while low affinity MHC class II binders remained soluble or formed rare amorphous aggregates. This study shows a possible connection between the aggregation propensity of an epitope and its affinity for the MHC class II cleft.

The aggregation of epitopes that are also able to bind major histocompatibility complex (MHC) alleles raises questions around the potential connection between the formation of epitope aggregates and their affinities to MHC receptors. We first performed a general bioinformatic assessment over a public dataset of MHC class II epitopes, finding that higher experimental binding correlates with higher aggregation-propensity predictors. We then focused on the case of P10, an epitope used as a vaccine candidate against Paracoccidioides brasiliensis that aggregates into amyloid fibrils. We used a computational protocol to design variants of the P10 epitope to study the connection between the binding stabilities towards human MHC class II alleles and their aggregation propensities. The binding of the designed variants was tested experimentally, as well as their aggregation capacity. High-affinity MHC class II binders in vitro were more disposed to aggregate forming amyloid fibrils capable of binding Thioflavin T and congo red, while low affinity MHC class II binders remained soluble or formed rare amorphous aggregates. This study shows a possible connection between the aggregation propensity of an epitope and its affinity for the MHC class II cleft.

Omicron BA.1 is a highly infectious variant of SARS-CoV-2 that carries more than thirty mutations on the spike protein in comparison to the Wuhan wild type (WT). Some of the Omicron mutations, located on the receptor-binding domain (RBD), are exposed to the surrounding solvent and are known to help evade immunity. However, the impact of buried mutations on the RBD conformations and on the mechanics of the spike opening is less evident. Here, we use all-atom molecular dynamics (MD) simulations with metadynamics to characterize the thermodynamic RBD-opening ensemble, identifying significant differences between WT and Omicron. Specifically, the Omicron mutations S371L, S373P, and S375F make more RBD interdomain contacts during the spike's opening. Moreover, Omicron takes longer to reach the transition state than WT. It stabilizes up-state conformations with fewer RBD epitopes exposed to the solvent, potentially favoring immune or antibody evasion.

Omicron BA.1 is a highly infectious variant of SARS-CoV-2 that carries more than thirty mutations on the spike protein in comparison to the Wuhan wild type (WT). Some of the Omicron mutations, located on the receptor-binding domain (RBD), are exposed to the surrounding solvent and are known to help evade immunity. However, the impact of buried mutations on the RBD conformations and on the mechanics of the spike opening is less evident. Here, we use all-atom molecular dynamics (MD) simulations with metadynamics to characterize the thermodynamic RBD-opening ensemble, identifying significant differences between WT and Omicron. Specifically, the Omicron mutations S371L, S373P, and S375F make more RBD interdomain contacts during the spike's opening. Moreover, Omicron takes longer to reach the transition state than WT. It stabilizes up-state conformations with fewer RBD epitopes exposed to the solvent, potentially favoring immune or antibody evasion.

When factorized approximations are used for variational inference (VI), they tend to underestimate the uncertainty -- as measured in various ways -- of the distributions they are meant to approximate. We consider two popular ways to measure the uncertainty deficit of VI: (i) the degree to which it underestimates the componentwise variance, and (ii) the degree to which it underestimates the entropy. To better understand these effects, and the relationship between them, we examine an informative setting where they can be explicitly (and elegantly) analyzed: the approximation of a Gaussian,~p, with a dense covariance matrix, by a Gaussian,~q, with a diagonal covariance matrix. We prove that q always underestimates both the componentwise variance and the entropy of p, \textit{though not necessarily to the same degree}. Moreover we demonstrate that the entropy of q is determined by the trade-off of two competing forces: it is decreased by the shrinkage of its componentwise variances (our first measure of uncertainty) but it is increased by the factorized approximation which delinks the nodes in the graphical model of p. We study various manifestations of this trade-off, notably one where, as the dimension of the problem grows, the per-component entropy gap between p and q becomes vanishingly small even though q underestimates every componentwise variance by a constant multiplicative factor. We also use the shrinkage-delinkage trade-off to bound the entropy gap in terms of the problem dimension and the condition number of the correlation matrix of p. Finally we present empirical results on both Gaussian and non-Gaussian targets, the former to validate our analysis and the latter to explore its limitations.

Multicellular organisms contain diverse tissues built from multiple cell types. It remains unclear how large numbers of interacting cells can precisely coordinate their gene expression during tissue self-organization. We develop a generalized model of multicellular gene expression that includes intracellular and intercellular gene interactions in tissue-like collectives. Motivated by modern transcriptomics, we represent multistable cellular phenotypes by mapping the binarized transcriptional patterns of individual cells onto Hopfield networks. We incorporate spatial cell-cell signaling by coupling transcriptional states of adjacent cells on a square lattice. We show that tuning the intercellular signaling strength results in a cascade of transitions toward different collective states with emergent single-cell phenotypes. Despite an enormous number of possible tissue states, we find that intercellular signaling tends to stabilize a small number of compositionally and spatially simple tissue types. These results establish a theoretical framework to investigate how cell collectives self-organize into distinct stable patterns.

We constrain the distribution of merging compact binaries across the celestial sphere using the GWTC-3 catalog from the LIGO-Virgo-KAGRA Collaborations' (LVK) third observing run. With 63 confident detections from O3, we constrain the relative variability (standard deviation) of the rate density across the sky to be ≲16% at 90\% confidence assuming the logarithm of the rate density is described by a Gaussian random field with correlation length ≥10∘. This tightens to ≲3.5% when the correlation length is ≥20∘. While the new O3 data provides the tightest constraints on anisotropies available to-date, we do not find overwhelming evidence in favor of isotropy, either. A simple counting experiment favors an isotropic distribution by a factor of isoani=3.7, which is nonetheless an improvement of more than a factor of two compared to analogous analyses based on only the first and second observing runs of the LVK.

The F-BAR protein Cdc15 is essential for cytokinesis in Schizosaccharomyces pombe and plays a key role in attaching the cytokinetic ring (CR) to the plasma membrane (PM). Cdc15’s abilities to bind to the membrane and oligomerize via its F-BAR domain are inhibited by phosphorylation of its intrinsically disordered region (IDR). Multiple cell polarity kinases regulate Cdc15 IDR phosphostate, and of these the DYRK kinase Pom1 phosphorylation sites on Cdc15 have been shown in vivo to prevent CR formation at cell tips. Here, we compared the ability of Pom1 to control Cdc15 phosphostate and cortical localization to that of other Cdc15 kinases: Kin1, Pck1, and Shk1. We identified distinct but overlapping cohorts of Cdc15 phosphorylation sites targeted by each kinase, and the number of sites correlated with each kinases’ abilities to influence Cdc15 PM localization. Coarse-grained simulations predicted that cumulative IDR phosphorylation moves the IDRs of a dimer apart and toward the F-BAR tips. Further, simulations indicated that the overall negative charge of phosphorylation masks positively charged amino acids necessary for F-BAR oligomerization and membrane interaction. Finally, simulations suggested that dephosphorylated Cdc15 undergoes phase separation driven by IDR interactions. Indeed, dephosphorylated but not phosphorylated Cdc15 undergoes liquid–liquid phase separation to form droplets in vitro that recruit Cdc15 binding partners. In cells, Cdc15 phosphomutants also formed PM-bound condensates that recruit other CR components. Together, we propose that a threshold of Cdc15 phosphorylation by assorted kinases prevents Cdc15 condensation on the PM and antagonizes CR assembly.

This manual describes the use of the Portable, Extensible Toolkit for Scientific Computation (PETSc) and the Toolkit for Advanced Optimization (TAO) for the numerical solution of partial differential equations and related problems on high-performance computers. PETSc/TAO is a suite of data structures and routines that provide the building blocks for the implementation of large-scale application codes on parallel (and serial) computers. PETSc uses the MPI standard for all distributed memory communication.