Parallelization of particle-based reaction-diffusion simulations using MPI.

Particle-based reaction-diffusion models offer a high-resolution alternative to the continuum reaction-diffusion approach, capturing the discrete and volume-excluding nature of molecules undergoing stochastic dynamics. These methods are thus uniquely capable of simulating explicit self-assembly of particles into higher-order structures like filaments, spherical cages, or heterogeneous macromolecular complexes, which are ubiquitous across living systems and in materials design. The disadvantage of these high-resolution methods is their increased computational cost.

Dynamin1 long- and short-tail isoforms exploit distinct recruitment and spatial patterns to form endocytic nanoclusters.

Endocytosis requires a coordinated framework of molecular interactions that ultimately lead to the fission of nascent endocytic structures. How cytosolic proteins such as dynamin concentrate at discrete sites that are sparsely distributed across the plasma membrane remains poorly understood. Two dynamin-1 major splice variants differ by the length of their C-terminal proline-rich region (short-tail and long-tail).

Discovering optimal kinetic pathways for self-assembly using automatic differentiation.

Macromolecular complexes are often composed of diverse subunits. The self-assembly of these subunits is inherently nonequilibrium and must avoid kinetic traps to achieve high yield over feasible timescales. We show how the kinetics of self-assembly benefits from diversity in subunits because it generates an expansive parameter space that naturally improves the "expressivity" of self-assembly, much like a deeper neural network.

Discovering optimal kinetic pathways for self-assembly using automatic differentiation.

During self-assembly of macromolecules ranging from ribosomes to viral capsids, the formation of long-lived intermediates or kinetic traps can dramatically reduce yield of the functional products. Understanding biological mechanisms for avoiding traps and efficiently assembling is essential for designing synthetic assembly systems, but learning optimal solutions requires numerical searches in high-dimensional parameter spaces. Here, we exploit powerful automatic differentiation algorithms commonly employed by deep learning frameworks to optimize physical models of reversible self-assembly, discovering diverse solutions in the space of rate constants for 3-7 subunit complexes.

GAGA zinc finger transcription factor searches chromatin by 1D-3D facilitated diffusion.

To elucidate how eukaryotic sequence-specific transcription factors (TFs) search for gene targets on chromatin, we used multi-color smFRET and single-particle imaging to track the diffusion of purified GAGA-Associated Factor (GAF) on DNA and nucleosomes. Monomeric GAF DNA-binding domain (DBD) bearing one zinc finger finds its cognate site by 1D or 3D diffusion on bare DNA and rapidly slides back-and-forth between naturally clustered motifs for seconds before escape. Multimeric, full-length GAF also finds clustered motifs on DNA by 1D-3D diffusion, but remains locked on target for longer periods.

Secretion-Catalyzed Assembly of Protein Biomaterials on a Bacterial Membrane Surface.

Protein-based biomaterials have played a key role in tissue engineering, and additional exciting applications as self-healing materials and sustainable polymers are emerging. Over the past few decades, recombinant expression and production of various fibrous proteins from microbes have been demonstrated; however, the resulting proteins typically must then be purified and processed by humans to form usable fibers and materials. Here, we show that the Gram-positive bacterium Bacillus subtilis can be programmed to secrete silk through its translocon via an orthogonal signal peptide/peptidase pair.

Structure of the HIV immature lattice allows for essential lattice remodeling within budded virions.

For HIV virions to become infectious, the immature lattice of Gag polyproteins attached to the virion membrane must be cleaved. Cleavage cannot initiate without the protease formed by the homo-dimerization of domains linked to Gag. However, only 5% of the Gag polyproteins, termed Gag-Pol, carry this protease domain, and they are embedded within the structured lattice.

Temporal control by cofactors prevents kinetic trapping in retroviral Gag lattice assembly.

For retroviruses like HIV to proliferate, they must form virions shaped by the self-assembly of Gag polyproteins into a rigid lattice. This immature Gag lattice has been structurally characterized and reconstituted in vitro, revealing the sensitivity of lattice assembly to multiple cofactors. Due to this sensitivity, the energetic criterion for forming stable lattices is unknown, as are their corresponding rates.

Modeling membrane reshaping driven by dynamic protein assemblies.

Remodeling of membranes in living systems is almost universally coupled to self-assembly of soluble proteins. Proteins assemble into semi-rigid shells that reshape attached membranes, and into filaments that protrude membranes. These assemblies are temporary, building from reversible protein and membrane interactions that must nucleate in the proper location.

Integrating protein copy numbers with interaction networks to quantify stoichiometry in clathrin-mediated endocytosis.

Proteins that drive processes like clathrin-mediated endocytosis (CME) are expressed at copy numbers within a cell and across cell types varying from hundreds (e.g. auxilin) to millions (e.

Large self-assembled clathrin lattices spontaneously disassemble without sufficient adaptor proteins.

Clathrin-coated structures must assemble on cell membranes to internalize receptors, with the clathrin protein only linked to the membrane via adaptor proteins. These structures can grow surprisingly large, containing over 20 clathrin, yet they often fail to form productive vesicles, instead aborting and disassembling. We show that clathrin structures of this size can both form and disassemble spontaneously when adaptor protein availability is low, despite high abundance of clathrin.

Correction: A continuum membrane model can predict curvature sensing by helix insertion.

Correction for 'A continuum membrane model can predict curvature sensing by helix insertion' by Yiben Fu , , 2021, , 10649-10663, DOI: 10.1039/D1SM01333E.

A continuum membrane model can predict curvature sensing by helix insertion.

Protein domains, such as ENTH (epsin N-terminal homology) and BAR (bin/amphiphysin/rvs), contain amphipathic helices that drive preferential binding to curved membranes. However, predicting how the physical parameters of these domains control this 'curvature sensing' behavior is challenging due to the local membrane deformations generated by the nanoscopic helix on the surface of a large sphere. We here use a deformable continuum model that accounts for the physical properties of the membrane and the helix insertion to predict curvature sensing behavior, with direct validation against multiple experimental datasets.

Speed limits of protein assembly with reversible membrane localization.

Protein assembly is often studied in a three-dimensional solution, but a significant fraction of binding events involve proteins that can reversibly bind and diffuse along a two-dimensional surface. In a recent study, we quantified how proteins can exploit the reduced dimensionality of the membrane to trigger complex formation. Here, we derive a single expression for the characteristic timescale of this multi-step assembly process, where the change in dimensionality renders rates and concentrations effectively time-dependent.

Thermodynamics and Free Energy Landscape of BAR-Domain Dimerization from Molecular Simulations.

Proteins with BAR domains function to bind to and remodel biological membranes, where the dimerization of BAR domains is a key step in this function. These domains can dimerize in solution or after localizing to the membrane surface. Here, we characterize the binding thermodynamics of homodimerization between the LSP1 BAR domain proteins in solution, using molecular dynamics (MD) simulations.

NERDSS: A Nonequilibrium Simulator for Multibody Self-Assembly at the Cellular Scale.

Currently, a significant barrier to building predictive models of cellular self-assembly processes is that molecular models cannot capture minutes-long dynamics that couple distinct components with active processes, whereas reaction-diffusion models cannot capture structures of molecular assembly. Here, we introduce the nonequilibrium reaction-diffusion self-assembly simulator (NERDSS), which addresses this spatiotemporal resolution gap. NERDSS integrates efficient reaction-diffusion algorithms into generalized software that operates on user-defined molecules through diffusion, binding and orientation, unbinding, chemical transformations, and spatial localization.

An implicit lipid model for efficient reaction-diffusion simulations of protein binding to surfaces of arbitrary topology.

Localization of proteins to a membrane is an essential step in a broad range of biological processes such as signaling, virion formation, and clathrin-mediated endocytosis. The strength and specificity of proteins binding to a membrane depend on the lipid composition. Single-particle reaction-diffusion methods offer a powerful tool for capturing lipid-specific binding to membrane surfaces by treating lipids explicitly as individual diffusible binding sites.

Modeling the Self-Assembly of Protein Complexes through a Rigid-Body Rotational Reaction-Diffusion Algorithm.

The reaction-diffusion equations provide a powerful framework for modeling nonequilibrium, cell-scale dynamics over the long time scales that are inaccessible by traditional molecular modeling approaches. Single-particle reaction-diffusion offers the highest resolution technique for tracking such dynamics, but it has not been applied to the study of protein self-assembly due to its treatment of reactive species as single-point particles. Here, we develop a relatively simple but accurate approach for building rigid structure and rotation into single-particle reaction-diffusion methods, providing a rate-based method for studying protein self-assembly.

Stoichiometric balance of protein copy numbers is measurable and functionally significant in a protein-protein interaction network for yeast endocytosis.

Stoichiometric balance, or dosage balance, implies that proteins that are subunits of obligate complexes (e.g. the ribosome) should have copy numbers expressed to match their stoichiometry in that complex.

Cytosolic proteins can exploit membrane localization to trigger functional assembly.

Cell division, endocytosis, and viral budding would not function without the localization and assembly of protein complexes on membranes. What is poorly appreciated, however, is that by localizing to membranes, proteins search in a reduced space that effectively drives up concentration. Here we derive an accurate and practical analytical theory to quantify the significance of this dimensionality reduction in regulating protein assembly on membranes.

Protein-protein binding selectivity and network topology constrain global and local properties of interface binding networks.

Protein-protein interactions networks (PPINs) are known to share a highly conserved structure across all organisms. What is poorly understood, however, is the structure of the child interface interaction networks (IINs), which map the binding sites proteins use for each interaction. In this study we analyze four independently constructed IINs from yeast and humans and find a conserved structure of these networks with a unique topology distinct from the parent PPIN.

Theory of bi-molecular association dynamics in 2D for accurate model and experimental parameterization of binding rates.

The dynamics of association between diffusing and reacting molecular species are routinely quantified using simple rate-equation kinetics that assume both well-mixed concentrations of species and a single rate constant for parameterizing the binding rate. In two-dimensions (2D), however, even when systems are well-mixed, the assumption of a single characteristic rate constant for describing association is not generally accurate, due to the properties of diffusional searching in dimensions d ≤ 2. Establishing rigorous bounds for discriminating between 2D reactive systems that will be accurately described by rate equations with a single rate constant, and those that will not, is critical for both modeling and experimentally parameterizing binding reactions restricted to surfaces such as cellular membranes.

Free-Propagator Reweighting Integrator for Single-Particle Dynamics in Reaction-Diffusion Models of Heterogeneous Protein-Protein Interaction Systems.

We present a new algorithm for simulating reaction-diffusion equations at single-particle resolution. Our algorithm is designed to be both accurate and simple to implement, and to be applicable to large and heterogeneous systems, including those arising in systems biology applications. We combine the use of the exact Green's function for a pair of reacting particles with the approximate free-diffusion propagator for position updates to particles.