Publications

An important but missing component in the application of the kernel independent fast multipole method (KIFMM) is the capability for flexibly and efficiently imposing singly, doubly, and triply periodic boundary conditions. In most popular packages such periodicities are imposed with the hierarchical repetition of periodic boxes, which may give an incorrect answer due to the conditional convergence of some kernel sums. Here we present an efficient method to properly impose periodic boundary conditions using a near-far splitting scheme. The near-field contribution is directly calculated with the KIFMM method, while the far-field contribution is calculated with a multipole-to-local (M2L) operator which is independent of the source and target point distribution. The M2L operator is constructed with the far-field portion of the kernel function to generate the far-field contribution with the downward equivalent source points in KIFMM. This method guarantees the sum of the near-field & far-field converge pointwise to results satisfying periodicity and compatibility conditions. The computational cost of the far-field calculation observes the same O(N) complexity as FMM and is designed to be small by reusing the data computed by KIFMM for the near-field. The far-field calculations require no additional control parameters, and observes the same theoretical error bound as KIFMM. We present accuracy and timing test results for the Laplace kernel in singly periodic domains and the Stokes velocity kernel in doubly and triply periodic domains.

The number of microbial and metagenomic studies has increased drastically due to advancements in next-generation sequencing-based measurement techniques. Statistical analysis and the validity of conclusions drawn from (time series) 16S rRNA and other metagenomic sequencing data is hampered by the presence of significant amount of noise and missing data (sampling zeros). Accounting uncertainty in microbiome data is often challenging due to the difficulty of obtaining biological replicates. Additionally, the compositional nature of current amplicon and metagenomic data differs from many other biological data types adding another challenge to the data analysis. To address these challenges in human microbiome research, we introduce a novel probabilistic approach to explicitly model overdispersion and sampling zeros by considering the temporal correlation between nearby time points using Gaussian Processes. The proposed Temporal Gaussian Process Model for Compositional Data Analysis (TGP-CODA) shows superior modeling performance compared to commonly used Dirichlet-multinomial, multinomial, and non-parametric regression models on real and synthetic data. We demonstrate that the nonreplicative nature of human gut microbiota studies can be partially overcome by our method with proper experimental design of dense temporal sampling. We also show that different modeling approaches have a strong impact on ecological interpretation of the data, such as stationarity, persistence, and environmental noise models. A Stan implementation of the proposed method is available under MIT license at

We introduce methods for large-scale Brownian Dynamics (BD) simulation of many rigid particles
of arbitrary shape suspended in a fluctuating fluid. Our method adds Brownian motion to the rigid
multiblob method [F. Balboa Usabiaga et al., Commun. Appl. Math. Comput. Sci. 11(2), 217-296
(2016)] at a cost comparable to the cost of deterministic simulations. We demonstrate that we can
efficiently generate deterministic and random displacements for many particles using preconditioned
Krylov iterative methods, if kernel methods to efficiently compute the action of the Rotne-Prager-
Yamakawa (RPY) mobility matrix and its “square” root are available for the given boundary conditions.
These kernel operations can be computed with near linear scaling for periodic domains using the
positively split Ewald method. Here we study particles partially confined by gravity above a no-
slip bottom wall using a graphical processing unit implementation of the mobility matrix-vector
product, combined with a preconditioned Lanczos iteration for generating Brownian displacements.
We address a major challenge in large-scale BD simulations, capturing the stochastic drift term that
arises because of the configuration-dependent mobility. Unlike the widely used Fixman midpoint
scheme, our methods utilize random finite differences and do not require the solution of resistance
problems or the computation of the action of the inverse square root of the RPY mobility matrix. We
construct two temporal schemes which are viable for large-scale simulations, an Euler-Maruyama
traction scheme and a trapezoidal slip scheme, which minimize the number of mobility problems to
be solved per time step while capturing the required stochastic drift terms. We validate and compare
these schemes numerically by modeling suspensions of boomerang-shaped particles sedimented near
a bottom wall. Using the trapezoidal scheme, we investigate the steady-state active motion in dense
suspensions of confined microrollers, whose height above the wall is set by a combination of thermal
noise and active flows. We find the existence of two populations of active particles, slower ones closer
to the bottom and faster ones above them, and demonstrate that our method provides quantitative
accuracy even with relatively coarse resolutions of the particle geometry.

The cellular cytoskeleton is an active material, driven out of equilibrium by molecular motor proteins. It is not understood how the collective behaviors of cytoskeletal networks emerge from the properties of the network's constituent motor proteins and filaments. Here we present experimental results on networks of stabilized microtubules in Xenopus oocyte extracts, which undergo spontaneous bulk contraction driven by the motor protein dynein, and investigate the effects of varying the initial microtubule density and length distribution. We find that networks contract to a similar final density, irrespective of the length of microtubules or their initial density, but that the contraction timescale varies with the average microtubule length. To gain insight into why this microscopic property influences the macroscopic network contraction time, we developed simulations where microtubules and motors are explicitly represented. The simulations qualitatively recapitulate the variation of contraction timescale with microtubule length, and allowed stress contributions from different sources to be estimated and decoupled.

A body submerged in active matter feels the swim pressure through a kinetic accumulation boundary layer on its surface. The boundary layer results from a balance between translational diffusion and advective swimming and occurs on the microscopic length scale $$\lambda^{-1} = \delta/\sqrt{2[1 + \frac{1}{6}(\ell/\delta)^2]}$$ . Here $$\delta = \sqrt{D_T\tau_R}$$ , $$D_T$$ is the Brownian translational diffusivity, $$\tau_R$$ is the reorientation time and $$\ell = U_0\tau_R$$ is the swimmer's run length, with $$U_0$$ the swim speed. In this work we analyze the swim pressure on arbitrary shaped bodies by including the effect of local shape curvature in the kinetic boundary layer. When $$\delta\ll L$$ and $$\ell \ll L$$ , where $$L$$ is the body size, the leading order effects of curvature on the swim pressure are found analytically to scale as $$J_S\lambda\delta^2/L$$ , where $$J_S$$ is twice the (non-dimensional) mean curvature. Particle-tracking simulations and direct solutions to the Smoluchowski equation governing the probability distribution of the active particles show that $\lambda\delta^2/L$ is a universal scaling parameter not limited to the regime $$\delta, \ell\ll L$$ . The net force exerted on the body by the swimmers is found to scale as $$\bF^{net} /\left(n^\infty k_sT_s L^2\right) = f(\lambda\delta^2/L)$$ , where $$f(x)$$ is a dimensionless function that is quadratic when $$x\ll1$$ and linear when $$x\sim 1$$ . Here, $$k_sT_s = \zeta U_0^2\tau_R/6$$ defines the `activity' of the swimmers, with $$\zeta$$ the drag coefficient, and $$n^\infty$$ is the uniform number density of swimmers far from the body. We discuss the connection of this boundary layer to continuum mechanical descriptions of active matter and briefly present how to include hydrodynamics into this purely kinetic study.

Chemically active Brownian particles with surface catalytic reactions may repel each other due to diffusiophoretic interactions in the reaction and product concentration fields. The system behavior can be described by a “chemical” coupling parameter $$\Gamma_c$$ that compares the strength of diffusiophoretic repulsion to Brownian motion, and by a mapping to the classical electrostatic one component plasma (OCP) system. When confined to a constant-volume domain, body-centered cubic (bcc) crystals spontaneously form from random initial configurations when the repulsion is strong enough to overcome Brownian motion. Face-centered cubic (fcc) crystals may also be stable. The “melting point” of the “liquid-to-crystal transition” occurs at $$\Gamma_c \approx 140$$ for both bcc and fcc lattices.

Autism spectrum disorder (ASD) is a complex neurodevelopmental disorder with a strong genetic basis. Yet, only a small fraction of potentially causal genes-about 65 genes out of an estimated several hundred-are known with strong genetic evidence from sequencing studies. We developed a complementary machine-learning approach based on a human brain-specific gene network to present a genome-wide prediction of autism risk genes, including hundreds of candidates for which there is minimal or no prior genetic evidence. Our approach was validated in a large independent case-control sequencing study. Leveraging these genome-wide predictions and the brain-specific network, we demonstrated that the large set of ASD genes converges on a smaller number of key pathways and developmental stages of the brain. Finally, we identified likely pathogenic genes within frequent autism-associated copy-number variants and proposed genes and pathways that are likely mediators of ASD across multiple copy-number variants. All predictions and functional insights are available at http://asd.princeton.edu.

Broad-spectrum antibiotics are frequently prescribed to children. Early childhood represents a dynamic period for the intestinal microbial ecosystem, which is readily shaped by environmental cues; antibiotic-induced disruption of this sensitive community may have long-lasting host consequences. Here we demonstrate that a single pulsed macrolide antibiotic treatment (PAT) course early in life is sufficient to lead to durable alterations to the murine intestinal microbiota, ileal gene expression, specific intestinal T-cell populations, and secretory IgA expression. A PAT-perturbed microbial community is necessary for host effects and sufficient to transfer delayed secretory IgA expression. Additionally, early-life antibiotic exposure has lasting and transferable effects on microbial community network topology. Our results indicate that a single early-life macrolide course can alter the microbiota and modulate host immune phenotypes that persist long after exposure has ceased.High or multiple doses of macrolide antibiotics, when given early in life, can perturb the metabolic and immunological development of lab mice. Here, Ruiz et al. show that even a single macrolide course, given early in life, leads to long-lasting changes in the gut microbiota and immune system of mice.

Background: Inflammatory bowel diseases (IBD) are believed to be driven by dysregulated interactions between the host and the gut microbiota. Our goal is to characterize and infer relationships between mucosal T cells, the host tissue environment, and microbial communities in patients with IBD who will serve as basis for mechanistic studies on human IBD.

Methods: We characterized mucosal CD4+ T cells using flow cytometry, along with matching mucosal global gene expression and microbial communities data from 35 pinch biopsy samples from patients with IBD. We analyzed these data sets using an integrated framework to identify predictors of inflammatory states and then reproduced some of the putative relationships formed among these predictors by analyzing data from the pediatric RISK cohort.

Results: We identified 26 predictors from our combined data set that were effective in distinguishing between regions of the intestine undergoing active inflammation and regions that were normal. Network analysis on these 26 predictors revealed SAA1 as the most connected node linking the abundance of the genus Bacteroides with the production of IL17 and IL22 by CD4+ T cells. These SAA1-linked microbial and transcriptome interactions were further reproduced with data from the pediatric IBD RISK cohort.

Conclusions: This study identifies expression of SAA1 as an important link between mucosal T cells, microbial communities, and their tissue environment in patients with IBD. A combination of T cell effector function data, gene expression and microbial profiling can distinguish between intestinal inflammatory states in IBD regardless of disease types.

Venom peptide toxins such as conotoxins play a critical role in the characterization of nicotinic acetylcholine receptor (nAChR) structure and function and have potential as nervous system therapeutics as well. However, the lack of solved structures of conotoxins bound to nAChRs and the large size of these peptides are barriers to their computational docking and design. We addressed these challenges in the context of the α4β2 nAChR, a widespread ligand-gated ion channel in the brain and a target for nicotine addiction therapy, and the 19-residue conotoxin α-GID that antagonizes it. We developed a docking algorithm, ToxDock, which used ensemble-docking and extensive conformational sampling to dock α-GID and its analogs to an α4β2 nAChR homology model. Experimental testing demonstrated that a virtual screen with ToxDock correctly identified three bioactive α-GID mutants (α-GID[A10V], α-GID[V13I], and α-GID[V13Y]) and one inactive variant (α-GID[A10Q]). Two mutants, α-GID[A10V] and α-GID[V13Y], had substantially reduced potency at the human α7 nAChR relative to α-GID, a desirable feature for α-GID analogs. The general usefulness of the docking algorithm was highlighted by redocking of peptide toxins to two ion channels and a binding protein in which the peptide toxins successfully reverted back to near-native crystallographic poses after being perturbed. Our results demonstrate that ToxDock can overcome two fundamental challenges of docking large toxin peptides to ion channel homology models, as exemplified by the α-GID:α4β2 nAChR complex, and is extendable to other toxin peptides and ion channels.