Biophysical Modeling

Our research develops biophysical and mathematical models to understand how active processes shape the function and physical organization of the cell nucleus. Our work has shown how stresses generated by nuclear enzymatic activity can drive coherent chromatin motions and promote the spatial compartmentalization of euchromatin and heterochromatin. To do this, we develop continuum and polymer-based models that link microscopic nonequilibrium activity to large-scale nuclear dynamics, finding understanding through both simulation and mathematical analysis. In joint work with the Genomics group, we have developed ML-enabled mechanistic frameworks that clarify how sequence features and transition-state kinetics govern enzymatic reaction rates, with Cas9-mediated DNA cleavage serving as an important model system. Ongoing efforts address the dynamics and repair of nuclear rupture and seek to connect multiscale nuclear mechanics with genomic features and regulation.

The insides of cells are incredibly dynamic, in a state of nearly constant rearrangemnt. Much of this motion is driven by tiny molecular motors — dyneins, kinesins, and myosins — pulling, pushing, or walking along complex scaffolds of flexible filaments and membranes. In so doing, they directly move cargoes through the cell, and indirectly drive cytoplasmic flows that help to transport, mix, and localize nutrients and proteins. To understand such processes, our team develops and applies both discrete and continuum models, and develops software spanning relevant intracellular scales, from all-atom simulations of individual MTs (in collaboration with the SMBp group) to cell-spanning flows in massive oocytes. Our work has shown how geometry guides the positioning of centrosomes and the mitotic spindle across a huge range of cell sizes, and how microtubules spontaneously align to drive streaming flows and how those flows orient themselves within complex cell geometries. Ongoing work aims to understand how chromosomes are moved from outside the spindle to the division plane, how complex features of streaming flows arise and alter intracellular transport, and how microtubule polarity is organized within nerve cells.

Our research explores how mechanical forces and active processes shape collective behavior in multicellular systems in several distinct settings. In one line of work, we studied growing bacterial colonies using both particle-based simulations and an associated multi-scale continuum model, showing that stress-sensitive growth can give rise to large-scale spatial patterns. This study demonstrates how purely mechanical feedback can organize proliferating matter. In a separate effort, we modeled epithelial tissues as thick, viscoelastic slabs in three-dimensions. This continuum framework captures key aspects of morphogenesis, including the initiation of ventral furrow invagination and T1 transitions in developing Drosophila. More recently, we introduced a biophysical model of cell–cell adhesion that explicitly couples cadherin-based junctions to intercellular actomyosin dynamics, revealing how mechanical linkages across cell boundaries can generate collective polarization, oscillatory behavior, and supracellular stress chains. In ongoing work we are studying how collective motion and packing patterns arise in a wet ensemble of deformable droplets, each encapsulating an active filament suspension. Together, these studies use theory and computation to connect cellular-scale mechanics to emergent colony- and tissue-level structure and dynamics.

Rotational or chiral active matter appears broadly in soft and condensed matter physics, and in biological systems where torque-generating processes drive organization and flow. Our research develops theory and computational tools to understand how rotational activity produces emergent structures and material responses. We have shown how interacting rotors can crystallize, form hyperuniform and phase-enriched assemblies, and generate chiral fluids with odd stresses and unusual free-surface dynamics. Collaborations with the Irvine experimental group (UChicago) have revealed active crystals whose dynamic dislocations reorganize the material, as well as “vortlet” particles that self-propel, flock, and assemble into new chiral phases. The scalable computational platforms devoloped by our group enable high-fidelity simulation of dense rotor assemblies. (show a picture from Naomi's paper, or a simulation fiture insert)

A central focus of our group is the development of theoretical frameworks and state-of-the-art computational tools for studying complex biophysical systems. These efforts span multiple methodologies:

Agent-based models and software: We build discrete, agent-based models to capture the microscopic dynamics of cellular components, incorporating steric interactions, binding–unbinding kinetics, and active force generation. We then run large-scale simulations of these particle ensembles efficiently on high-performance computing architectures (see aLENS).

Explicit coarse-graining: We place strong emphasis on systematically coarse-graining microscopic models into continuum descriptions through kinetic and statistical-mechanical approaches, providing a rigorous link between microscopic mechanisms and system-scale behavior.

Continuum models and mixed formulations: We design advanced numerical solvers for our continuum models (PDEs) that can handle complex geometries, viscoelastic materials, moving interfaces, and strongly nonlinear constitutive laws, such as those arising in the cell cytoskeleton. We also develop mixed Eulerian–Lagrangian formulations to study systems where slender, flexible filaments (e.g., microtubules) deform, interact, and are transported within a surrounding fluid environment (see SkellySim).

Data-driven models and inference: We develop statistical and machine-learning methods to infer biophysical models from noisy data and to construct efficient, physics-aware surrogate operators that mitigate the computational cost of large-scale simulations. We also leverage such techniques to infer parameters and validate hypotheses in our existing models. By combining computational modeling with data-driven methods, we aim to bridge the gap between theory and experiment in biophysical systems.