Publications

Score-based diffusion models are a powerful class of generative AI systems capable of sampling from complex, high-dimensional probability distributions. Their dynamics consist of a forward diffusion process that transforms data into noise and a learned reverse process that reconstructs data by reversing the probability flow. Here, we develop a stochastic thermodynamic framework for diffusion models and their score-matching objective. We introduce a trajectory-dependent quantity, time-asymmetry entropy production (TAEP), defined from the forward and reverse diffusion dynamics, and show that it obeys exact fluctuation theorems. Remarkably, Hyvärinen's implicit score-matching kernel emerges naturally as a fluctuating component of TAEP, while the average TAEP is exactly proportional to the score-matching objective. We further show that fluctuations of TAEP quantify sampling unevenness and provide a thermodynamic measure of data-manifold coverage. These results yield a quantitative explanation for the superior sampling diversity of diffusion models and reveal a thermodynamic mechanism by which stochastic gradient descent favors flatter, more generalizable solutions. By uncovering the entropic nature of score matching, our work establishes fundamental statistical-mechanical principles underlying diffusion-based generative AI.

We present a new computational tool for the simulation of aligned assemblies of thin, bendable, but inextensible fibers immersed in a linear Stokes fluid. Such systems are of great importance in cellular mechanics because they arise in many intracellular (e.g., cytoskeleton-cytoplasm interactions) and extracellular (e.g., ciliary locomotion) microscale biological processes. The fiber bed is represented as an anisotropic poroelastic medium that obeys the Euler-Bernoulli beam theory and is hydrodynamically coupled to the viscous fluid through local-slender body theory. We develop two methodologies to solve the resulting fluid-structure interaction problem: (1) a classical approach where the solid is solved in the Lagrangian frame, and the fluid is solved using an Arbitrary-Lagrangian-Eulerian (ALE) method, and (2) a novel approach where the solid equations are expressed in the Eulerian frame and the fiber-fluid system is solved together using an ALE method. In both cases, the resulting set of equations is approximated using a Petrov-Galerkin stabilized finite element method specifically designed for the fiber-fluid interaction problem. Equal-order continuous finite elements are used for the spatial discretization of the deforming physical domain, and finite differences are used for temporal discretization. Both approaches are shown to be numerically stable and convergent at the expected order; and additionally, the pure ALE method can resolve extreme fiber deformations without the need for mesh reconstruction. Finally, our methods are validated by direct comparisons to discrete fiber simulations in two benchmark tests: (a) the shearing of an anchored fiber bed and (b) the emergence and evolution of cell-spanning vortices in cellular geometries.

Solid-phase peptide synthesis enables the study of countless peptides, but aggregation during synthesis hinders production of many sequences of interest. Now, machine learning models enable prior identification of aggregation-prone sequences, and highlight amino acid composition, rather than specific sequence, as the major determinant of aggregation.

Stochastic Gradient Descent (SGD) introduces anisotropic noise that is correlated with the local curvature of the loss landscape, thereby biasing optimization toward flat minima. Prior work often assumes an equivalence between the Fisher Information Matrix and the Hessian for negative log-likelihood losses, leading to the claim that the SGD noise covariance C is proportional to the Hessian H. We show that this assumption holds only under restrictive conditions that are typically violated in deep neural networks. Using the recently discovered Activity--Weight Duality, we find a more general relationship agnostic to the specific loss formulation, showing that C∝𝔼p[h2p], where hp denotes the per-sample Hessian with H=𝔼p[hp]. As a consequence, C and H commute approximately rather than coincide exactly, and their diagonal elements follow an approximate power-law relation Cii∝Hγii with a theoretically bounded exponent 1≤γ≤2, determined by per-sample Hessian spectra. Experiments across datasets, architectures, and loss functions validate these bounds, providing a unified characterization of the noise-curvature relationship in deep learning.

During development, highly ordered structures emerge as cells collectively coordinate with each other. While recent advances have clarified how individual cells process and respond to external signals, understanding collective cellular decision making remains a major challenge. Here, we introduce a minimal, analytically tractable model of cell patterning via local cell-cell communication. Using this framework, we identify a trade-off between the speed and accuracy of collective pattern formation and, by adapting techniques from stochastic chemical kinetics, quantify how information flows between cells during patterning. Our analysis reveals counterintuitive features of collective patterning: globally optimized solutions do not necessarily maximize intercellular information transfer and individual cells may appear suboptimal in isolation. Moreover, the model predicts that instantaneous information shared between cells can be nonmonotonic in time as patterning occurs. An analysis of recent experimental data from lateral inhibition in Drosophila pupal abdomen finds a qualitatively similar effect.

Protein denaturation-based assays, such as thermal proximity coaggregation (TPCA) and ion-based proteome-integrated solubility alteration (I-PISA), are powerful tools for characterizing global protein–protein interaction (PPI) networks. These workflows utilize different denaturation methods to probe PPIs, i.e., thermal- or ion-based. How denaturation differences influence PPI network mapping remained to be better understood. Here, we provide an experimental and computational characterization of the effect of the denaturation-based PPI assay on the observed PPI networks. We establish the value of both soluble and insoluble fractions in PPI prediction, determine the ability to minimize sample amount requirement, and assess different relative quantification methods during virus infection. Generating paired TPCA and I-PISA datasets, we define both overlapping sets of proteins and distinct PPI networks specifically captured by these methods. Assessing protein physical properties and subcellar localizations, we show that size, structural complexity, hydrophobicity, and localization influence PPI detection in a workflow-specific manner. We show that the insoluble fractions expand the detectable PPI landscape, underscoring their value in these workflows. Focusing on selected PPI networks (cytoskeletal and DNA repair), we observe the detection of distinct functional populations. Using influenza A infection as a model for cellular perturbation, we demonstrate that the integration of PPI predictions from soluble and insoluble workflows enhances the ability to build biologically informative and interconnected networks. Examining the effects of reducing starting material for TPCA assays, we find that PPI prediction quality remains robust when using a single well of a 96-well plate, a ∼500× reduction in sample input from usual workflows. Introducing simple workflow modifications, we show that label-free data-independent acquisition (DIA) TPCA yields performance comparable to the traditional tandem mass tag (TMT) data-dependent acquisition (DDA) TPCA workflow. This work provides insights into denaturation-based assays, highlights the value of insoluble fractions, and offers practical improvements for enhancing global PPI network mapping.

I review recent advances in nonequilibrium thermodynamics of biochemical networks, organized around two central questions. First, why is free energy dissipation essential for enabling or enhancing biological function? Second, how do energetic costs constrain functional performance? Using several representative systems—beginning with the classical kinetic proofreading mechanism and extending to more recent examples such as accurate sensory adaptation, ultrasensitive responses, and synchronization of biochemical oscillators—I show that this framework not only provides new insights into the molecular mechanisms underlying these diverse processes but also reveals the general thermodynamic principles that govern their biological functions. I highlight the characteristic signatures of nonequilibrium behavior and the emergence of fundamental energy–performance trade-offs. This review strives to present the framework pedagogically and with sufficient technical detail to enable theory-inclined biophysicists to apply it to their own systems of interest. I conclude by proposing a nonequilibrium thermodynamic law for living systems and outlining promising directions for extending this theoretical approach to an even broader range of biological phenomena.

How developmental timings are regulated is a fundamental open question. Two widely considered mechanisms are the clock, in which an internal timer determines when each stage occurs, and the domino, in which the completion of each stage triggers the next. It is often unclear how to establish either mechanism. Here, we construct a quantitative framework that uses the correlation structure of developmental timings to test the clock and domino mechanisms. We apply this framework to human pre-implantation development by using ~1 million images of 2946 embryos acquired during IVF treatment, establishing mathematical models of developmental rate. We find that a domino mechanism governs the cleavage timings, while a pronuclei fade-triggered clock mechanism governs the morula and blastocyst timings. These results are consistent with the cell cycle oscillator governing the cleavage timings and the accumulation of embryonic gene products or the degradation of maternally deposited factors governing the morula and blastocyst timings. We next investigate the physiological regulators of developmental timing by analyzing how the timings are statistically associated with the clinical pregnancy outcome. While embryos that result in a clinical pregnancy tend to exhibit shorter cleavage timings, this association is primarily driven by patient-specific properties. In contrast, embryo-specific properties independently influence the pregnancy outcome and the cleavage timings, so that factors directly determining implantation potential, such as aneuploidy, can only weakly impact the cleavage timings. Taken together, this work provides a robust framework for decoding developmental timing mechanisms, with significant implications for fundamental biology and clinical practice.

Stochastic gradient descent (SGD) is central to deep learning, yet the dynamical origin of its preference for flatter, more generalizable solutions remains unclear. Here, by analyzing SGD learning dynamics, we identify a nonequilibrium mechanism governing solution selection. Numerical experiments reveal a transient exploratory phase in which SGD trajectories repeatedly escape sharp valleys and transition toward flatter regions of the loss landscape. By using a tractable physical model, we show that the SGD noise reshapes the landscape into an effective potential that favors flat solutions. Crucially, we uncover a transient freezing mechanism: as training proceeds, growing energy barriers suppress inter-valley transitions and ultimately trap the dynamics within a single basin. Increasing the SGD noise strength delays this freezing, which enhances convergence to flatter minima. Together, these results provide a unified physical framework linking learning dynamics, loss-landscape geometry, and generalization, and suggest principles for the design of more effective optimization algorithms.

Flagellar motors enable bacteria to navigate their environments by switching rotation direction in response to external cues with high sensitivity. Previous work indicated that the ultrasensitivity of the flagellar motor originates from conformational spread, in which subunits of the switching complex are strongly coupled to their neighbours as in an equilibrium Ising model. However, dynamic single-motor measurements indicated that rotation switching is driven out of equilibrium, and the mechanism for this dissipative driving remains unknown. Here we propose that local mechanical torques on motor subunits can affect their conformation dynamics, based on recent structures observed with cryo-electron microscopy. This gives rise to a tug of war between stator-associated subunits that produces cooperative, non-equilibrium switching responses without requiring nearest-neighbour interactions. Our model predicts that the motor response cooperativity grows with the number of stators driving rotation, which is consistent with published experimental results. Finally, we show that operating out of equilibrium enables motors to achieve high cooperativity with faster responses compared with equilibrium motors. Our results indicate a general role for mechanics in sensitive chemical regulation.