Publications

We use a combination of unsupervised clustering and sparsity-promoting inference algorithms to learn locally dominant force balances that explain macroscopic pattern formation in self-organized active particle systems. The self-organized emergence of macroscopic patterns from microscopic interactions between self-propelled particles can be widely observed in nature. Although hydrodynamic theories help us better understand the physical basis of this phenomenon, identifying a sufficient set of local interactions that shape, regulate and sustain self-organized structures in active particle systems remains challenging. We investigate a classic hydrodynamic model of self-propelled particles that produces a wide variety of patterns, such as asters and moving density bands. Our data-driven analysis shows that propagating bands are formed by local alignment interactions driven by density gradients, while steady-state asters are shaped by a mechanism of splay-induced negative compressibility arising from strong particle interactions. Our method also reveals analogous physical principles of pattern formation in a system where the speed of the particle is influenced by the local density. This demonstrates the ability of our method to reveal physical commonalities across models. The physical mechanisms inferred from the data are in excellent agreement with analytical scaling arguments and experimental observations.

We study the dynamics of proliferating cell collectives whose microscopic constituents’ growth is inhibited by macroscopic growth-induced stress. Discrete particle simulations of a growing collective show the emergence of concentric-ring patterns in cell size whose spatiotemporal structure is closely tied to the individual cell’s stress response. Motivated by these observations, we derive a multiscale continuum theory whose parameters map directly to the discrete model. Analytical solutions of this theory show the concentric patterns arise from anisotropically accumulated resistance to growth over many cell cycles. This Letter shows how purely mechanical processes can affect the internal patterning and morphology of cell collectives, and provides a concise theoretical framework for connecting the micro- to macroscopic dynamics of proliferating matter.

Nucleocytoplasmic transport is essential for cellular function, presenting a canonical example of rapid molecular sorting inside cells. It consists of a coordinated interplay between import/export of molecules in/out the cell nucleus. Here, we investigate the role of spatiotemporal dynamics of the nucleocytoplasmic transport and its regulation. We develop a biophysical model that captures the main features of the nucleocytoplasmic transport, in particular, its regulation through the Ran cycle. Our model yields steady-state profiles for the molecular components of the Ran cycle, their relaxation times, as well as the nuclear-to-cytoplasmic molecule ratio. We show that these quantities are affected by their spatial dynamics and heterogeneity within the nucleus. Specifically, we find that the spatial nonuniformity of Ran guanine exchange factor (RanGEF)—particularly its proximity to the nuclear envelope—increases the Ran content in the nucleus. We further show that RanGEF's accumulation near the nuclear envelope results from its intrinsic dynamics as a nuclear cargo, transported by the Ran cycle itself. Overall, our work highlights the critical role of molecular spatial dynamics in cellular processes and proposes new avenues for theoretical and experimental inquiries into the nucleocytoplasmic transport.

Habituation—a phenomenon in which a dynamical system exhibits a diminishing response to repeated stimulations that eventually recovers when the stimulus is withheld—is universally observed in living systems from animals to unicellular organisms. Despite its prevalence, generic mechanisms for this fundamental form of learning remain poorly defined. Drawing inspiration from prior work on systems that respond adaptively to step inputs, we study habituation from a nonlinear dynamics perspective. This approach enables us to formalize classical hallmarks of habituation that have been experimentally identified in diverse organisms and stimulus scenarios. We use this framework to investigate distinct dynamical circuits capable of habituation. In particular, we show that driven linear dynamics of a memory variable with static nonlinearities acting at the input and output can implement numerous hallmarks in a mathematically interpretable manner. This work establishes a foundation for understanding the dynamical substrates of this primitive learning behavior and offers a blueprint for the identification of habituating circuits in biological systems.

Huntington’s disease (HD) is a fatal neurodegenerative disorder resulting from an abnormal expansion of polyglutamine (polyQ) repeats in the N-terminus of the huntingtin protein. When the polyQ tract surpasses 35 repeats, the mutated protein undergoes misfolding, culminating in the formation of intracellular aggregates. Research in mouse models suggests that HD pathogenesis involves the aggregation of N-terminal fragments of the huntingtin protein (htt). These early oligomeric assemblies of htt, exhibiting diverse characteristics during aggregation, are implicated as potential toxic entities in HD. However, a consensus on their specific structures remains elusive. Understanding the heterogeneous nature of htt oligomers provides crucial insights into disease mechanisms, emphasizing the need to identify various oligomeric conformations as potential therapeutic targets. Employing coarse-grained molecular dynamics, our study aims to elucidate the mechanisms governing the aggregation process and resultant aggregate architectures of htt. The polyQ tract within htt is flanked by two regions: an N-terminal domain (N17) and a short C-terminal proline-rich segment. We conducted self-assembly simulations involving five distinct N17 + polyQ systems with polyQ lengths ranging from 7 to 45, utilizing the ProMPT force field. Prolongation of the polyQ domain correlates with an increase in β-sheet-rich structures. Longer polyQ lengths favor intramolecular β-sheets over intermolecular interactions due to the folding of the elongated polyQ domain into hairpin-rich conformations. Importantly, variations in polyQ length significantly influence resulting oligomeric structures. Shorter polyQ domains lead to N17 domain aggregation, forming a hydrophobic core, while longer polyQ lengths introduce a competition between N17 hydrophobic interactions and polyQ polar interactions, resulting in densely packed polyQ cores with outwardly distributed N17 domains. Additionally, at extended polyQ lengths, we observe distinct oligomeric conformations with varying degrees of N17 bundling. These findings can help explain the toxic gain-of-function that htt with expanded polyQ acquires.

Mathematical models are indispensable for disentangling the interactions through which biological components work together to generate the forces and flows that position, mix, and distribute proteins, nutrients, and organelles within the cell. To illuminate the ever more specific questions studied at the edge of biological inquiry, such models inevitably become more complex. Solving, simulating, and learning from these more realistic models requires the development of new analytic techniques, numerical methods, and scalable software. In this review, we discuss some recent developments in tools for understanding how large numbers of cytoskeletal filaments, driven by molecular motors and interacting with the cytoplasm and other structures in their environment, generate fluid flows, instabilities, and material deformations which help drive crucial cellular processes.

Organisms must perform sensory-motor behaviors to survive. What bounds or constraints limit behavioral performance? Previously, we found that the gradient-climbing speed of a chemotaxing Escherichia coli is near a bound set by the limited information they acquire from their chemical environments (1). Here we ask what limits their sensory accuracy. Past theoretical analyses have shown that the stochasticity of single molecule arrivals sets a fundamental limit on the precision of chemical sensing (2). Although it has been argued that bacteria approach this limit, direct evidence is lacking. Here, using information theory and quantitative experiments, we find that E. coli’s chemosensing is not limited by the physics of particle counting. First, we derive the physical limit on the behaviorally-relevant information that any sensor can get about a changing chemical concentration, assuming that every molecule arriving at the sensor is recorded. Then, we derive and measure how much information E. coli’s signaling pathway encodes during chemotaxis. We find that E. coli encode two orders of magnitude less information than an ideal sensor limited only by shot noise in particle arrivals. These results strongly suggest that constraints other than particle arrival noise limit E. coli’s sensory fidelity.

The recognizable shapes of landforms arise from processes such as erosion by wind or water currents. However, explaining the physical origin of natural structures is challenging due to the coupled evolution of complex flow fields and three-dimensional (3D) topographies. We investigate these issues in a laboratory setting inspired by yardangs, which are raised, elongate formations whose characteristic shape suggests erosion of heterogeneous material by directional flows. We combine experiments and simulations to test an origin hypothesis involving a harder or less erodible inclusion embedded in an outcropping of softer material. Optical scans of clay objects fixed within flowing water reveal a transformation from a featureless mound to a yardang-like form resembling a lion in repose. Phase-field simulations reproduce similar shape dynamics and show their dependence on the erodibility contrast and flow strength. Through visualizations of the flow fields and analysis of the local erosion rate, we identify effects associated with flow funneling and the turbulent wake that are responsible for carving the unique geometrical features. This highly 3D scouring process produces complex shapes from simple and commonplace starting conditions and is thus a candidate explanation for natural yardangs. The methods introduced here should be generally useful for geomorphological problems and especially those for which material heterogeneity is a primary factor.

Diffuse midline glioma (DMG), including Diffuse intrinsic pontine glioma (DIPG), is an aggressive brain tumor in children with limited treatment options. Recent developments of phase 1 clinical trials have shown early promise for chimeric antigen receptor (CAR) T cells in patients with DMG/DIPG. However, several barriers such as the absence of tumor-specific antigens, restricted trafficking to the tumor site, and poor persistence hinder the full therapeutic potential of CAR T cell therapy in DMG/DIPG.

Error correction is central to many biological systems and is critical for protein function and cell health. During mitosis, error correction is required for the faithful inheritance of genetic material. When functioning properly, the mitotic spindle segregates an equal number of chromosomes to daughter cells with high fidelity. Over the course of spindle assembly, many initially erroneous attachments between kinetochores and microtubules are fixed through the process of error correction. Despite the importance of chromosome segregation errors in cancer and other diseases, there is a lack of methods to characterize the dynamics of error correction and how it can go wrong. Here, we present an experimental method and analysis framework to quantify chromosome segregation error correction in human tissue culture cells with live cell confocal imaging, timed premature anaphase, and automated counting of kinetochores after cell division. We find that errors decrease exponentially over time during spindle assembly. A coarse-grained model, in which errors are corrected in a chromosome-autonomous manner at a constant rate, can quantitatively explain both the measured error correction dynamics and the distribution of anaphase onset times. We further validated our model using perturbations that destabilized microtubules and changed the initial configuration of chromosomal attachments. Taken together, this work provides a quantitative framework for understanding the dynamics of mitotic error correction.