Margaret E. Johnson

Membrane remodeling into vesicles is essential for processes such as receptor transport and viral budding. In many cases, this remodeling is driven by the assembly of multivalent protein lattices that stochastically grow while coupled to bending the membrane. Here, we ask how membrane mechanics can bias the structural pathways sampled during lattice growth. Using a continuum membrane model coupled to growing human immunodeficiency virus Gag lattice intermediates, we show that radially symmetric lattice growth is energetically favored over eccentric growth because it induces membrane bending at lower cost per protein. For rigid lattices, the penalty for asymmetric growth is controlled primarily by the shape of the lattice perimeter rather than by the density of protein-membrane links, with all membrane deformations retaining strong radial symmetry. Reevaluating the energy relative to the circumscribing radius of the lattice thus collapses all growth pathways to a similar curve. When the lattice is flexible, asymmetric growth introduces another cost, as these intermediates also generate weaker curvature. Analytical spherical-cap estimates support the trends in our numerical energy minimization calculations, and our results remain robust across a range of tested modeling assumptions including membrane spontaneous curvature. Although kinetic barriers along growth pathways are not assessed, our results show that membrane bending can strongly select for symmetric assembly pathways, providing a mechanical bias against irregular lattice growth during membrane remodeling.

Binding reactions in effectively one-dimensional systems, such as proteins diffusing along DNA or other filaments, pose a fundamental coarse-graining challenge because stochastic trajectories are recurrent in one dimension and, therefore, do not admit a unique, separation-independent macroscopic association rate. As a result, continuum rate equations are not exact in 1D even for initially homogeneous systems. Here, we develop a practical framework for mapping stochastic 1D reaction–diffusion dynamics onto effective kinetic models. We consider reversible protein dimerization (A+A or A+B) and reversible target binding (A+B), with and without excluded volume. Using mean-first-passage arguments and particle-based simulations, we define a density-dependent association rate and a corresponding single-rate approximation and quantify when each provides an accurate description of the underlying stochastic dynamics. We implement 1D reaction–diffusion in the NERDSS software using a free-propagator reweighting algorithm and validate it against known pairwise and many-body limits. Our results show that ordinary rate equations with a single effective rate can accurately reproduce 1D reaction kinetics when the dimensionless parameter governing the ratio of intrinsic to diffusion-limited reactivity is small, with excellent agreement in the strongly rate-limited regime and increasing deviations as diffusion control strengthens. We further show that excluded volume in 1D can appreciably alter both kinetics and equilibrium populations, even at modest particle densities, by reducing accessible length and introducing blockade effects. Together, these results provide quantitative guidance for selecting between spatial simulations, density-dependent rate models, and single-rate continuum descriptions of reversible 1D binding reactions.

Binding reactions in effectively one-dimensional systems, such as proteins diffusing along DNA or other filaments, pose a fundamental coarse-graining challenge because stochastic trajectories are recurrent in one dimension and therefore do not admit a unique, separation-independent macroscopic association rate. As a result, continuum rate equations are not exact in 1D even for initially homogeneous systems. Here we develop a practical framework for mapping stochastic 1D reaction-diffusion dynamics onto effective kinetic models. Using mean-first-passage arguments and particle-based simulations, we define a density-dependent association rate and a corresponding single-rate approximation, and quantify when each provides an accurate description of the underlying stochastic dynamics. We implement 1D reaction-diffusion with excluded volume in the NERDSS software using a free-propagator reweighting algorithm and validate it against known pairwise and many-body limits. Our results show that ordinary rate equations with a single effective rate can accurately reproduce 1D reaction kinetics when the dimensionless parameter governing the ratio of intrinsic to diffusion-limited reactivity is small, with excellent agreement in the strongly rate-limited regime and increasing deviations as diffusion control strengthens. We further show that excluded volume in 1D can appreciably alter both kinetics and equilibrium populations, even at modest particle densities, by reducing accessible length and introducing blockade effects. Together, these results provide quantitative guidance for selecting between spatial simulations, density-dependent rate models, and single-rate continuum descriptions of reversible 1D binding reactions.

Cellular decision-making based on information received from the external environment is frequently initiated by transmembrane receptors. These receptors are known to propagate such information by triggering a series of irreversible, energy-consuming reactions. While this active mechanism ensures switchlike responses, here we show how spontaneous self-assembly of native three-dimensional subunits on a two-dimensional substrate can similarly act as a tunable and robust switch for detecting receptors at physiological concentrations. This mechanism is much more sensitive than other passive mechanisms for receptor detection. We derive analytical expressions for the critical receptor density driving stable subunit assembly, in close agreement with stochastic reaction-diffusion simulations. The theory provides testable predictions for how lipids, subunits, and receptors each can control decision boundaries and magnitude of response.

The extent to which clathrin directly drives membrane curvature during endocytosis has remained a central, longstanding question in the field of endocytosis. Using a synthetic reconstitution system that recruits clathrin to lipid membranes independent of adaptor proteins, we demonstrate that clathrin alone can induce membrane fission and that its capacity to do so is governed by the mechanical properties of the lattice. Counterintuitively, conditions that strengthen lattice assembly suppress fission, whereas weakened assembly enhances fission despite reduced membrane association. Meso-scale Brownian dynamics reveal that assembly dependent changes in triskelion geometry and lattice stiffness dictate curvature generation, corroborating these findings. These principles are further extended when clathrin is recruited by adaptor proteins amphiphyin1 or epsin1, with clathrin either enhancing or restricting fission based on adaptor specific tuning of lattice mechanics. Lastly, perturbations to clathrin assembly in live cells shift endocytic pit dynamics, with Ca ²⁺ and EGTA producing opposing effects on pit lifetime and productive events consistent with modulation of the membrane fission barrier. Together, these results identify protein and lattice mechanics, not simply bound protein density, as the key determinant of clathrin’s ability to remodel membranes, elucidating its biophysical impact on vesicle formation during endocytosis.

Successful DNA transcription demands coordination between proteins that bind DNA while simultaneously binding to one another to form dimers or higher-order complexes. For proteins with numerous DNA targets throughout the genome, measurements that report on their dwell time or occupancy thus represent a convolution over a population interacting with specific DNA, nonspecific DNA, or protein partners on DNA. Dimerization is known to add contacts that can help a protein monomer to stably bind DNA. However, we show here that dimerization can also impair measured dwell times and occupancy on target sequences because the population redistributes across DNA. We combine spatial stochastic simulations of pairwise reversible reactions between proteins and DNA with mass-action kinetic models and theory to isolate the role of reversible dimerization on observed DNA dwell times, occupancy, and spatial distribution of proteins on DNA. Three key themes emerge: (i) Protein–protein interactions, in addition to protein–DNA interactions, can localize a protein to DNA, and rates of (un)binding can thus widely tune dwell times. (ii) Dimensional reduction achieved through nonspecific binding and subsequent 1D diffusion controls the order of magnitude of enhancements despite nucleosome barriers. (iii) Dimerization enhances selectivity for locally clustered targets and often impairs binding to widely spaced targets by sequestration. Compared with ChIP-seq data, our model explains how the distribution of the essential GAGA factor monomer throughout the genome is highly selective for clustered targets due to protein interactions. This model framework predicts when even weak dimerization can redistribute and stabilize proteins on DNA as a necessary part of transcription.

Macromolecular self-assembly is a fundamental process in living and engineered systems, producing molecular machines like the ribosome or highly symmetric viral capsids. Thanks to sources like the Protein Data Bank (PDB) and AlphaFold3, the final target complexes are often known, but these static structures do not provide information on the self-assembly process directly. Computational models provide critical tools to study these essential pathways of self-assembly, but substantial coarse-graining of assembly subunits is necessary to achieve computational tractability of these relatively slow processes while retaining multi-valency. While rule-based or local interactions overcome the often-prohibitive enumeration of all possible assembly intermediates, they must ensure global structural constraints are met. We here demonstrate ioNERDSS, a user-friendly Python package that transforms 3D atomic structures into coarse-grained models for immediate simulation with the stochastic reaction-diffusion NERDSS software, converting static structures into time-resolved assembly trajectories. NERDSS uses rule-based interactions to simulate multi-component self-assembly at the minutes timescales and without limits to complex size or growth pathways. With ioNERDSS, each protein chain is defined by a rigid subunit with discrete interfaces and explicit orientational constraints that enforce a structured assembly. Repeated subunits (such as in viral capsids) are regularized to preserve the target topology across distinct stochastic assembly pathways, supporting assembly of structures with thousands of subunits. We initialize pairwise binding affinities using open-source machine-learned prediction tools, and our default coarse-grained (CG) models are all constrained by thermodynamic reversibility to reach an equilibrium steady-state. The binding rates and subunit abundances necessary to perform simulations are initialized at default values but represent the key variables (along with affinities) that cells and thus users would tune to control productive assembly. Benchmarking on over 40,000 PDB structures shows that the majority of CG models stochastically assemble into target structures. The ioNERDSS Python library links directly to open-source tools for visualization and analysis to facilitate fast and user-friendly structure validation and analysis of output for thermodynamic, kinetic, and nonequilibrium drivers of macromolecular self-assembly.

Oscillations are ubiquitous features of biological organisms, playing crucial roles in processes from circadian rhythms to developmental patterning. Protein-based biochemical oscillators have particular applications in synthetic biology because they can access fast and slow timescales that are independent from the transcription-translation machinery required of genetic oscillators. Here, we introduce and model such a mass-conserving biochemical oscillator using mass-action reaction kinetics that exploits dynamic changes to membrane phospholipid concentrations to drive proteins on and off the membrane in robust, tunable rhythms. Importantly, the oscillations rely on amplification of reactions on the membrane via dimensional reduction, and they are therefore tunable by variations in the volume-to-surface area ratio (V/A) of the system. With components inspired by the endocytic machinery, we show that a wide range of physiologically relevant biochemical rates can produce oscillations in part due to this independent geometric control. A broad computational screen of the high-dimensional parameter space reveals that oscillations require relatively strict enzyme kinetic design rules for low V/A but much more permissive kinetics for larger V/A. We validate that oscillations persist with more realistic reaction-diffusion simulations that captures explicit diffusion and stochastic, integer valued copy numbers, in overall good agreement with the period and amplitude of the deterministic oscillators. Because the oscillations rely on time-dependent changes to the surface properties and not post-translational modifications to the protein subunits, we demonstrate that it can be coupled to a self-assembling trimer, driving not only changes in localization but trimer yield. Our analysis establishes this membrane-localization oscillator as a new, geometry tunable and programmable timing module and suggests a potential for geometry sensing in engineered or cell-free systems.