Publications

An obstacle is immersed in an externally driven 2D Stokes or Navier-Stokes fluid. We study the self-equilibration conditions for that obstacle under steady state assumptions on the flow. We then seek to optimize the translational and/or angular velocity of the obstacle by varying its shape. To allow general variations, we must consider a very large class of obstacles for which the notion of trace is meaningless. This forces us to revisit the notion of self-equilibration for both Stokes and Navier-Stokes in a measure theoretic environment.

An obstacle is immersed in an externally driven 2D Stokes or Navier-Stokes fluid. We study the self-equilibration conditions for that obstacle under steady state assumptions on the flow. We then seek to optimize the translational and/or angular velocity of the obstacle by varying its shape. To allow general variations, we must consider a very large class of obstacles for which the notion of trace is meaningless. This forces us to revisit the notion of self-equilibration for both Stokes and Navier-Stokes in a measure theoretic environment.

DNA methylation, a covalent modification, fundamentally shapes mammalian gene regulation and cellular identity. This review examines methylation's biochemical underpinnings, genomic distribution patterns, and analytical approaches. We highlight three distinctive aspects that separate methylation from other epigenetic marks: its remarkable stability as a silencing mechanism, its capacity to maintain distinct states independently of DNA sequence, and its effectiveness as a quantitative trait linking genotype to disease risk. We also explore the phenomenon of methylation clocks and their biological significance. The review addresses technical considerations across major assay types—both array-based technologies and sequencing approaches—with emphasis on data normalization, quality control, cell proportion inference, and the specialized statistical models required for next-generation sequencing analysis.

A great deal is known about biochemical aspects of transcription, but we still lack an understanding of how transcription is causally regulated in space and time. A major unanswered question is the extent to which transcription at different locations in the nucleus are independent from each other or, instead, are spatially coordinated. We propose two classes of models of coordination: 1) the shared environment model, in which neighboring loci exhibit coordinated transcriptional dynamics due to sharing the same local biochemical environment; 2) the mechanical crosstalk model, in which forces propagate from one actively transcribing locus to affect transcription of another. Determining the prevalence of the spatial coordination of transcription, and the underlying mechanisms when it occurs, is an exciting challenge in nuclear biophysics.

How thousands of microtubules and molecular motors self-organize into spindles remains poorly understood. By combining static, nanometer-resolution, large-scale electron tomography reconstructions and dynamic, optical-resolution, polarized light microscopy, we test an active liquid crystal continuum model of mitotic spindles in human tissue culture cells. The predictions of this coarse-grained theory quantitatively agree with the experimentally measured spindle morphology and fluctuation spectra. These findings argue that local interactions and polymerization produce collective alignment, diffusive-like motion, and polar transport which govern the behaviors of the spindle's microtubule network, and provide a means to measure the spindle's material properties. This work demonstrates that a coarse-grained theory featuring measurable, physically-interpretable parameters can quantitatively describe the mechanical behavior and self-organization of human mitotic spindles.

The male fruit fly produces ~1.8 mm long sperm, thousands of which can be stored until mating in a ~200 micron sac, the seminal vesicle. While the evolutionary pressures driving such extreme sperm (flagellar) lengths have long been investigated, the physical consequences of their gigantism are unstudied. Through high-resolution three-dimensional reconstructions of in vivo sperm morphologies and rapid live imaging, we discovered that stored sperm are organized into a dense and highly aligned state. The packed flagella exhibit system-wide collective 'material' flows, with persistent and slow-moving topological defects; individual sperm, despite their extraordinary lengths, propagate rapidly through the flagellar material, moving in either direction along material director lines. To understand how these collective behaviors arise from the constituents' nonequilibrium dynamics, we conceptualize the motion of individual sperm as topologically confined to a reptation-like tube formed by its neighbors. Therein, sperm propagate through observed amplitude-constrained and internally driven flagellar bending waves, pushing off counter-propagating neighbors. From this conception, we derive a continuum theory that produces an extensile material stress that can sustain an aligned flagellar material. Experimental perturbations and simulations of active elastic filaments verify our theoretical predictions. Our findings suggest that active stresses in the flagellar material maintain the sperm in an unentangled, hence functional state, in both sexes, and establish giant sperm in their native habitat as a novel and physiologically relevant active matter system

Recent breakthroughs in protein structure prediction have led to a surge in high-quality 3D models, highlighting the need for efficient computational solutions. In our work, we examine the structural clusters from the AlphaFold Protein Structure Database (AFDB), a high-quality subset of ESMAtlas, and the Microbiome Immunity Project (MIP). We create a single cohesive low-dimensional representation of the resulting protein space. We show that, while each database occupies distinct regions, they collectively exhibit significant overlap in their functional profiles. High-level biological functions tend to cluster in particular regions, revealing a shared functional landscape despite the diverse sources of data. By creating a representation of protein structure space, localizing functional annotations within this space, and providing an open-access web-server for exploration, this work offers insights for future research concerning protein sequence-structure-function relationships, enabling biological questions to be asked about taxonomic assignments, environmental factors, or functional specificity. This approach is generalizable, thus enabling further discovery beyond findings presented here.

Synchronization among a group of active agents is ubiquitous in nature. Although synchronization based on direct interactions between agents described by the Kuramoto model is well understood, the other general mechanism based on indirect interactions among agents sharing limited resources are less known. Here, we propose a minimal thermodynamically consistent model for the altruistic resource-sharing (ARS) mechanism wherein resources are needed for an individual agent to advance but a more advanced agent has a lower competence to obtain resources. We show that while differential competence in ARS mechanism provides a negative feedback leading to synchronization it also breaks detailed balance and thus requires additional energy dissipation besides the cost of driving individual agents. By solving the model analytically, our study reveals a general trade-off relation between the total energy dissipation rate and the two key performance measures of the system: average speed and synchronization accuracy. For a fixed dissipation rate, there is a distinct speed-accuracy Pareto front traversed by the scarcity of resources: scarcer resources lead to slower speed but more accurate synchronization. Increasing energy dissipation eases this trade-off by pushing the speed-accuracy Pareto front outward. The connections of our work to realistic biological systems such as the KaiABC system in cyanobacterial circadian clock and other theoretical results based on thermodynamic uncertainty relation are also discussed.

The brain encodes external stimuli through patterns of neural activity, forming internal representations of the world. Increasing experimental evidence showed that neural representations for a specific stimulus can change over time in a phenomenon called “representational drift” (RD). However, the underlying mechanisms for this widespread phenomenon remain poorly understood. Here, we study RD in the piriform cortex of the olfactory system with a realistic neural network model that incorporates two general mechanisms for synaptic weight dynamics operating at two well-separated timescales: spontaneous multiplicative fluctuations on a scale of days and spike-timing-dependent plasticity (STDP) effects on a scale of seconds. We show that the slow multiplicative fluctuations in synaptic sizes, which lead to a steady-state distribution of synaptic weights consistent with experiments, can induce RD effects that are in quantitative agreement with recent empirical evidence. Furthermore, our model reveals that the fast STDP learning dynamics during presentation of a given odor drives the system toward a low-dimensional representational manifold, which effectively reduces the dimensionality of synaptic weight fluctuations and thus suppresses RD. Specifically, our model explains why representations of already “learned” odors drift slower than unfamiliar ones, as well as the dependence of the drift rate with the frequency of stimulus presentation—both of which align with recent experimental data. The proposed model not only offers a simple explanation for the emergence of RD and its relation to learning in the piriform cortex, but also provides a general theoretical framework for studying representation dynamics in other neural systems.

Convergence analysis can characterize genetic elements underlying morphological adaptations. However, its performance on regulatory elements is limited due to their modular composition of transcription factor motifs, which have rapid turnover and experience different evolutionary pressures.

We introduce phyloConverge, a phylogenetic method that performs scalable, fine-grained local convergence analysis of genomic elements at flexible length scales. Using a benchmarking case of convergent subterranean mammal adaptation, phyloConverge identifies rate-accelerated conserved noncoding elements (CNEs) with high specificity and statistical robustness relative to competing methods. From CNE-level scoring, we detect the convergent regression of entire CNE units and highlight the contrast that subterranean-associated coding region regression is highly specific to ocular functions, whereas regulatory element regression is enriched for accompanying neuronal phenotypes and other developmental processes. From transcription factor motif-level scoring, we dissect elements into subregions with uneven convergence signals and demonstrate the modular adaptation of CNEs with high functional specificity. Finally, we demonstrate phyloConverge’s scalability to perform high-resolution convergence analysis genome-wide.