Membrane shape-mediated wave propagation of cortical protein dynamics

Dynamic Plasma Membrane Topography Linked With Arp2/3 Actin Network Induction During Cell Shape Change

Recent studies show the importance of mesoscale changes to plasma membrane (PM) topography during cell shape change. Local folding and flattening of the cell surface is mechanosensitive, changing in response to both microenvironment structural elements and intracellular cytoskeletal activities. These topography changes elicit local mechanical signaling events that act in conjunction with molecular signal transduction pathways to remodel the cell cortex. Experimental manipulations of local PM curvature show its sufficiency for recruiting Arp2/3 actin network induction pathways. Additionally, studies of diverse cell shape changes-ranging from neutrophil migration to early Drosophila embryo cleavage to neural stem cell asymmetric division-show that local generation of PM folding is linked with local Arp2/3 actin network induction, which then remodels the PM topography during dynamic control of cell structure. These examples are reviewed in detail, together with known and potential causes of PM topography changes, downstream effects, and higher-order feedback.

Curvature-sensing and generation by membrane proteins: a review

Membrane proteins are crucial in regulating biomembrane shapes and controlling the dynamic changes in membrane morphology during essential cellular processes. These proteins can localize to regions with their preferred curvatures (curvature sensing) and induce localized membrane curvature. Thus, this review describes the recent theoretical development in membrane remodeling performed by membrane proteins. The mean-field theories of protein binding and the resulting membrane deformations are reviewed. The effects of hydrophobic insertions on the area-difference elasticity energy and that of intrinsically disordered protein domains on the membrane bending energy are discussed. For the crescent-shaped proteins, such as Bin/Amphiphysin/Rvs superfamily proteins, anisotropic protein bending energy and orientation-dependent excluded volume significantly contribute to curvature sensing and generation. Moreover, simulation studies of membrane deformations caused by protein binding are reviewed, including domain formation, budding, and tubulation.

Turing patterns on polymerized membranes: coarse-grained lattice modelling with an internal degree of freedom for polymer direction

We numerically study Turing patterns (TPs) on two-dimensional surfaces with a square boundary in R3 using a surface model for polymerized membranes. The variables used to describe the membranes correspond to two distinct degrees of freedom: an internal degree of freedom for the polymer directions in addition to the positional degree of freedom. This generalised surface model enables us to identify non-trivial interference between the TP system and the membranes. To this end, we employ a hybrid numerical technique, utilising Monte Carlo updates for membrane configurations and discrete time iterations for the FitzHugh-Nagumo type Turing equation. The simulation results clearly show that anisotropies in the mechanical deformation properties, particularly the easy axes associated with the stretching and bending of the membranes, determine the direction of the TPs to be perpendicular or parallel to the easy axes. Additionally, by calculating the dependence of the maximum entropy on the internal degree of freedom, we can obtain information on the relaxation with respect to the polymer structure. This crucial information serves to remind us that non-equilibrium configurations can be captured within the canonical Monte Carlo simulations.

Spatiotemporal pattern formation of membranes induced by surface molecular binding/unbinding

Nonequilibrium membrane pattern formation is studied using meshless membrane simulation. We consider that molecules bind to either surface of a bilayer membrane and move to the opposite leaflet by flip-flop. When binding does not modify the membrane properties and the transfer rates among the three states are cyclically symmetric, the membrane exhibits spiral-wave and homogeneous-cycling modes at high and low binding rates, respectively, as in an off-lattice cyclic Potts model. When binding changes the membrane spontaneous curvature, these spatiotemporal dynamics are coupled with microphase separation. When two symmetric membrane surfaces are in thermal equilibrium, the membrane domains form 4.8.8 tiling patterns in addition to stripe and spot patterns. In nonequilibrium conditions, moving biphasic domains and time-irreversible fluctuating patterns appear. The domains move ballistically or diffusively depending on the conditions.

Spatial heterogeneity accelerates phase-to-trigger wave transitions in frog egg extracts

Cyclin-dependent kinase 1 (Cdk1) activity rises and falls throughout the cell cycle: a cell-autonomous process called mitotic oscillations. Mitotic oscillators can synchronize when spatially coupled, facilitating rapid, synchronous divisions in large early embryos of Drosophila (~0.5 mm) and Xenopus (~1.2 mm). Diffusion alone cannot achieve such long-range coordination. Instead, studies proposed mitotic waves-phase and trigger waves-as mechanisms of the coordination. How waves establish over time remains unclear. Using Xenopus laevis egg extracts and a Cdk1 Förster resonance energy transfer sensor, we observe a transition from phase to trigger wave dynamics in initially homogeneous cytosol. Spatial heterogeneity promotes this transition. Adding nuclei accelerates entrainment. The system transitions almost immediately when driven by metaphase-arrested extracts. Numerical simulations suggest phase waves appear transiently as trigger waves take time to entrain the system. Therefore, we show that both waves belong to a single biological process capable of coordinating the cell cycle over long distances.

Wave-driven phase wave patterns in a ring of FitzHugh-Nagumo oscillators

We explore a biomimetic model that simulates a cell, with the internal cytoplasm represented by a two-dimensional circular domain and the external cortex by a surrounding ring, both modeled using FitzHugh-Nagumo systems. The external ring is dynamically influenced by a pacemaker-driven wave originating from the internal domain, leading to the emergence of three distinct dynamical states based on the varying strengths of coupling. The range of dynamics observed includes phase patterning, the propagation of phase waves, and interactions between traveling and phase waves. A simplified linear model effectively explains the mechanisms behind the variety of phase patterns observed, providing insights into the complex interplay between a cell's internal and external environments.

Roles of membrane mechanics-mediated feedback in membrane traffic

Synthesizing the recent progresses, we present our perspectives on how local modulations of membrane curvature, tension, and bending energy define the feedback controls over membrane traffic processes. We speculate the potential mechanisms of, and the control logic behind, the different membrane mechanics-mediated feedback in endocytosis and exo-endocytosis coupling. We elaborate the path forward with the open questions for theoretical considerations and the grand challenges for experimental validations.

Cycling and spiral-wave modes in an active cyclic Potts model

We studied the nonequilibrium dynamics of a cycling three-state Potts model using simulations and theory. This model can be tuned from thermal-equilibrium to far-from-equilibrium conditions. At low cycling energy, the homogeneous dominant state cycles via nucleation and growth, while spiral waves are formed at high energy. For large systems, a discontinuous transition occurs from these cyclic homogeneous phases to spiral waves, while the opposite transition is absent. Conversely, these two modes can coexist for small systems. The waves can be reproduced by a continuum theory, and the transition can be understood from the competition between nucleation and growth.

Research progress on the regulatory role of cell membrane surface tension in cell behavior

Cell membrane surface tension has emerged as a pivotal biophysical factor governing cell behavior and fate. This review systematically delineates recent advances in techniques for cell membrane surface tension quantification, mechanosensing mechanisms, and regulatory roles of cell membrane surface tension in modulating major cellular processes. Micropipette aspiration, tether pulling, and newly developed fluorescent probes enable the measurement of cell membrane surface tension with spatiotemporal precision. Cells perceive cell membrane surface tension via conduits including mechanosensitive ion channels, curvature-sensing proteins (e.g. BAR domain proteins), and cortex-membrane attachment proteins (e.g. ERM proteins). Through membrane receptors like integrins, cells convert mechanical cues into biochemical signals. This conversion triggers cytoskeletal remodeling and extracellular matrix interactions in response to environmental changes. Elevated cell membrane surface tension suppresses cell spreading, migration, and endocytosis while facilitating exocytosis. Moreover, reduced cell membrane surface tension promotes embryonic stem cell differentiation and cancer cell invasion, underscoring cell membrane surface tension as a regulator of cell plasticity. Outstanding questions remain regarding cell membrane surface tension regulatory mechanisms and roles in tissue development/disease in vivo. Emerging tools to manipulate cell membrane surface tension with high spatiotemporal control in combination with omics approaches will facilitate the elucidation of cell membrane surface tension-mediated effects on signaling networks across various cell types/states. This will accelerate the development of cell membrane surface tension-based biomarkers and therapeutics for regenerative medicine and cancer. Overall, this review provides critical insights into cell membrane surface tension as a potent orchestrator of cell function, with broader impacts across mechanobiology.

Protein-membrane interactions: sensing and generating curvature

Biological membranes are integral cellular structures that can be curved into various geometries. These curved structures are abundant in cells as they are essential for various physiological processes. However, curved membranes are inherently unstable, especially on nanometer length scales. To stabilize curved membranes, cells can utilize proteins that sense and generate membrane curvature. In this review, we summarize recent research that has advanced our understanding of interactions between proteins and curved membrane surfaces, as well as work that has expanded our ability to study curvature sensing and generation. Additionally, we look at specific examples of cellular processes that require membrane curvature, such as neurotransmission, clathrin-mediated endocytosis (CME), and organelle biogenesis.

Membrane curvature catalyzes actin nucleation through nano-scale condensation of N-WASP-FBP17

Actin remodeling is spatiotemporally regulated by surface topographical cues on the membrane for signaling across diverse biological processes. Yet, the mechanism dynamic membrane curvature prompts quick actin cytoskeletal changes in signaling remain elusive. Leveraging the precision of nanolithography to control membrane curvature, we reconstructed catalytic reactions from the detection of nano-scale curvature by sensing molecules to the initiation of actin polymerization, which is challenging to study quantitatively in living cells. We show that this process occurs via topographical signal-triggered condensation and activation of the actin nucleation-promoting factor (NPF), Neuronal Wiskott-Aldrich Syndrome protein (N-WASP), which is orchestrated by curvature-sensing BAR-domain protein FBP17. Such N-WASP activation is fine-tuned by optimizing FBP17 to N-WASP stoichiometry over different curvature radii, allowing a curvature-guided macromolecular assembly pattern for polymerizing actin network locally. Our findings shed light on the intricate relationship between changes in curvature and actin remodeling via spatiotemporal regulation of NPF/BAR complex condensation.

Collective dynamics of actin and microtubule and its crosstalk mediated by FHDC1

The coordination between actin and microtubule network is crucial, yet this remains a challenging problem to dissect and our understanding of the underlying mechanisms remains limited. In this study, we used travelling waves in the cell cortex to characterize the collective dynamics of cytoskeletal networks. Our findings show that Cdc42 and F-BAR-dependent actin waves in mast cells are mainly driven by formin-mediated actin polymerization, with the microtubule-binding formin FH2 domain-containing protein 1 (FHDC1) as an early regulator. Knocking down FHDC1 inhibits actin wave formation, and this inhibition require FHDC1's interaction with both microtubule and actin. The phase of microtubule depolymerization coincides with the nucleation of actin waves and microtubule stabilization inhibit actin waves, leading us to propose that microtubule shrinking and the concurrent release of FHDC1 locally regulate actin nucleation. Lastly, we show that FHDC1 is crucial for multiple cellular processes such as cell division and migration. Our data provided molecular insights into the nucleation mechanisms of actin waves and uncover an antagonistic interplay between microtubule and actin polymerization in their collective dynamics.

Mitotic waves in frog egg extracts: Transition from phase waves to trigger waves

Cyclin-dependent kinase 1 (Cdk1) activity rises and falls throughout the cell cycle, a cell-autonomous process known as mitotic oscillations. These oscillators can synchronize when spatially coupled, providing a crucial foundation for rapid synchronous divisions in large early embryos like Drosophila (~ 0.5 mm) and Xenopus (~ 1.2 mm). While diffusion alone cannot achieve such long-range coordination, recent studies have proposed two types of mitotic waves, phase and trigger waves, to explain the phenomena. How the waves establish over time for efficient spatial coordination remains unclear. Using Xenopus laevis egg extracts and a Cdk1 FRET sensor, we observe a transition from phase waves to a trigger wave regime in an initially homogeneous cytosol. Adding nuclei accelerates such transition. Moreover, the system transitions almost immediately to this regime when externally driven by metaphase-arrested extracts from the boundary. Employing computational modeling, we pinpoint how wave nature, including speed-period relation, depends on transient dynamics and oscillator properties, suggesting that phase waves appear transiently due to the time required for trigger waves to entrain the system and that spatial heterogeneity promotes entrainment. Therefore, we show that both waves belong to a single biological process capable of coordinating the cell cycle over long distances.

Self-organizing glycolytic waves fuel cell migration and cancer progression

Glycolysis has traditionally been thought to take place in the cytosol but we observed the enrichment of glycolytic enzymes in propagating waves of the cell cortex in human epithelial cells. These waves reflect excitable Ras/PI3K signal transduction and F-actin/actomyosin networks that drive cellular protrusions, suggesting that localized glycolysis at the cortex provides ATP for cell morphological events such as migration, phagocytosis, and cytokinesis. Perturbations that altered cortical waves caused corresponding changes in enzyme localization and ATP production whereas synthetic recruitment of glycolytic enzymes to the cell cortex enhanced cell spreading and motility. Interestingly, the cortical waves and ATP levels were positively correlated with the metastatic potential of cancer cells. The coordinated signal transduction, cytoskeletal, and glycolytic waves in cancer cells may explain their increased motility and their greater reliance on glycolysis, often referred to as the Warburg effect.

Forceful patterning: theoretical principles of mechanochemical pattern formation

Biological pattern formation is essential for generating and maintaining spatial structures from the scale of a single cell to tissues and even collections of organisms. Besides biochemical interactions, there is an important role for mechanical and geometrical features in the generation of patterns. We review the theoretical principles underlying different types of mechanochemical pattern formation across spatial scales and levels of biological organization.

A dynamic partitioning mechanism polarizes membrane protein distribution

The plasma membrane is widely regarded as the hub of the numerous signal transduction activities. Yet, the fundamental biophysical mechanisms that spatiotemporally compartmentalize different classes of membrane proteins remain unclear. Using multimodal live-cell imaging, here we first show that several lipid-anchored membrane proteins are consistently depleted from the membrane regions where the Ras/PI3K/Akt/F-actin network is activated. The dynamic polarization of these proteins does not depend upon the F-actin-based cytoskeletal structures, recurring shuttling between membrane and cytosol, or directed vesicular trafficking. Photoconversion microscopy and single-molecule measurements demonstrate that these lipid-anchored molecules have substantially dissimilar diffusion profiles in different regions of the membrane which enable their selective segregation. When these diffusion coefficients are incorporated into an excitable network-based stochastic reaction-diffusion model, simulations reveal that the altered affinity mediated selective partitioning is sufficient to drive familiar propagating wave patterns. Furthermore, normally uniform integral and lipid-anchored membrane proteins partition successfully when membrane domain-specific peptides are optogenetically recruited to them. We propose "dynamic partitioning" as a new mechanism that can account for large-scale compartmentalization of a wide array of lipid-anchored and integral membrane proteins during various physiological processes where membrane polarizes.

From actin waves to mechanism and back: How theory aids biological understanding

Actin dynamics in cell motility, division, and phagocytosis is regulated by complex factors with multiple feedback loops, often leading to emergent dynamic patterns in the form of propagating waves of actin polymerization activity that are poorly understood. Many in the actin wave community have attempted to discern the underlying mechanisms using experiments and/or mathematical models and theory. Here, we survey methods and hypotheses for actin waves based on signaling networks, mechano-chemical effects, and transport characteristics, with examples drawn from Dictyostelium discoideum, human neutrophils, Caenorhabditis elegans, and Xenopus laevis oocytes. While experimentalists focus on the details of molecular components, theorists pose a central question of universality: Are there generic, model-independent, underlying principles, or just boundless cell-specific details? We argue that mathematical methods are equally important for understanding the emergence, evolution, and persistence of actin waves and conclude with a few challenges for future studies.

Disappearance, division, and route change of excitable reaction-diffusion waves in deformable membranes

Shapes of biomembrane in living cells are regulated by curvature-inducing proteins. However, the effects of membrane deformation on signal transductions such as chemical waves have not been researched adequately. Here, we report that membrane deformation can alter the propagation of excitable reaction-diffusion waves using state-of-the-art simulations. Reaction waves can induce large shape transformations, such as membrane budding and necking, that erase or divide the wave, depending on the curvature generated by the waves, feedback to the wave propagation, and the ratio of the reaction and deformation times. In genus-2 vesicles, wave division occurs at branching points and collided waves disappear together. We demonstrate that the occasional disappearance of the waves can alter the pathway of wave propagation. Our findings suggest that membrane deformation and reaction waves can together regulate signal transductions on biomembranes.

Exploring membrane mechanics: The role of membrane-cortex attachment in cell dynamics

The role of plasma membrane (PM) tension in cell dynamics has gained increasing interest in recent years to understand the mechanism by which individual cells regulate their dynamic behavior. Membrane-to-cortex attachment (MCA) is a component of apparent PM tension, and its assembly and disassembly determine the direction of cell motility, controlling the driving forces of migration. There is also evidence that membrane tension plays a role in malignant cancer cell metastasis and stem cell differentiation. Here, we review recent important discoveries that explore the role of membrane tension in the regulation of diverse cellular processes, and discuss the mechanisms of cell dynamics regulated by this physical parameter.

Plasma membrane topography governs the 3D dynamic localization of IgM B cell antigen receptor clusters

B lymphocytes recognize bacterial or viral antigens via different classes of the B cell antigen receptor (BCR). Protrusive structures termed microvilli cover lymphocyte surfaces, and are thought to perform sensory functions in screening antigen-bearing surfaces. Here, we have used lattice light-sheet microscopy in combination with tailored custom-built 4D image analysis to study the cell-surface topography of B cells of the Ramos Burkitt's Lymphoma line and the spatiotemporal organization of the IgM-BCR. Ramos B-cell surfaces were found to form dynamic networks of elevated ridges bridging individual microvilli. A fraction of membrane-localized IgM-BCR was found in clusters, which were mainly associated with the ridges and the microvilli. The dynamic ridge-network organization and the IgM-BCR cluster mobility were linked, and both were controlled by Arp2/3 complex activity. Our results suggest that dynamic topographical features of the cell surface govern the localization and transport of IgM-BCR clusters to facilitate antigen screening by B cells.

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. The interactions are strongly influenced by the nonequilibrium environment of the cell, such as gradients of components or active modifications by kinases. From a modeling perspective, understanding mechanisms and control thus requires 1. time-dependent approaches that ideally incorporate 2. macromolecular structure, 3. out-of-equilibrium processes, and 4. deformable membranes over microns and seconds. Realistically, tradeoffs must be made with these last three features. However, we see recent developments from the highly coarsened molecule-based scale, the continuum reaction-diffusion scale, and hybrid approaches as stimulating efforts in diverse applications. We discuss here methodological advances and progress towards simulating these processes as they occur physiologically.

Membrane domain formation induced by binding/unbinding of curvature-inducing molecules on both membrane surfaces

The domain formation of curvature-inducing molecules, such as peripheral or transmembrane proteins and conical surfactants, is studied in thermal equilibrium and nonequilibrium steady states using meshless membrane simulations. These molecules can bind to both surfaces of a bilayer membrane and also move to the opposite leaflet by a flip-flop. Under symmetric conditions for the two leaflets, the membrane domains form checkerboard patterns in addition to striped and spot patterns. The unbound membrane stabilizes the vertices of the checkerboard. Under asymmetric conditions, the domains form kagome-lattice and thread-like patterns. In the nonequilibrium steady states, a flow of the binding molecules between the upper and lower solutions can occur via flip-flop.

Modulation of self-organizing circuits at deforming membranes by intracellular and extracellular factors

Mechanical forces exerted to the plasma membrane induce cell shape changes. These transient shape changes trigger, among others, enrichment of curvature-sensitive molecules at deforming membrane sites. Strikingly, some curvature-sensing molecules not only detect membrane deformation but can also alter the amplitude of forces that caused to shape changes in the first place. This dual ability of sensing and inducing membrane deformation leads to the formation of curvature-dependent self-organizing signaling circuits. How these cell-autonomous circuits are affected by auxiliary parameters from inside and outside of the cell has remained largely elusive. Here, we explore how such factors modulate self-organization at the micro-scale and its emerging properties at the macroscale.

A dynamic partitioning mechanism polarizes membrane protein distribution

The plasma membrane is widely regarded as the hub of the signal transduction network activities that drives numerous physiological responses, including cell polarity and migration. Yet, the symmetry breaking process in the membrane, that leads to dynamic compartmentalization of different proteins, remains poorly understood. Using multimodal live-cell imaging, here we first show that multiple endogenous and synthetic lipid-anchored proteins, despite maintaining stable tight association with the inner leaflet of the plasma membrane, were unexpectedly depleted from the membrane domains where the signaling network was spontaneously activated such as in the new protrusions as well as within the propagating ventral waves. Although their asymmetric patterns resembled those of standard peripheral "back" proteins such as PTEN, unlike the latter, these lipidated proteins did not dissociate from the membrane upon global receptor activation. Our experiments not only discounted the possibility of recurrent reversible translocation from membrane to cytosol as it occurs for weakly bound peripheral membrane proteins, but also ruled out the necessity of directed vesicular trafficking and cytoskeletal supramolecular structure-based restrictions in driving these dynamic symmetry breaking events. Selective photoconversion-based protein tracking assays suggested that these asymmetric patterns instead originate from the inherent ability of these membrane proteins to "dynamically partition" into distinct domains within the plane of the membrane. Consistently, single-molecule measurements showed that these lipid-anchored molecules have substantially dissimilar diffusion profiles in different regions of the membrane. When these profiles were incorporated into an excitable network-based stochastic reaction-diffusion model of the system, simulations revealed that our proposed "dynamic partitioning" mechanism is sufficient to give rise to familiar asymmetric propagating wave patterns. Moreover, we demonstrated that normally uniform integral and lipid-anchored membrane proteins in Dictyostelium and mammalian neutrophil cells can be induced to partition spatiotemporally to form polarized patterns, by optogenetically recruiting membrane domain-specific peptides to these proteins. Together, our results indicate "dynamic partitioning" as a new mechanism of plasma membrane organization, that can account for large-scale compartmentalization of a wide array of lipid-anchored and integral membrane proteins in different physiological processes.

Moving through a changing world: Single cell migration in 2D vs. 3D

Migration of single adherent cells is frequently observed in the developing and adult organism and has been the subject of many studies. Yet, while elegant work has elucidated molecular and mechanical cues affecting motion dynamics on a flat surface, it remains less clear how cells migrate in a 3D setting. In this review, we explore the changing parameters encountered by cells navigating through a 3D microenvironment compared to cells crawling on top of a 2D surface, and how these differences alter subcellular structures required for propulsion. We further discuss how such changes at the micro-scale impact motion pattern at the macro-scale.

Membrane curvature as a signal to ensure robustness of diverse cellular processes

An increasing corpus of research has demonstrated that membrane shape, generated either by the external environment of the cell or by intrinsic mechanisms such as cytokinesis and vesicle or organelle formation, is an important parameter in the control of diverse cellular processes. In this review we discuss recent findings that demonstrate how membrane curvature (from nanometer to micron length-scales) alters protein function. We describe an expanding toolkit for experimentally modulating membrane curvature to reveal effects on protein function, and discuss how membrane curvature - far from being a passive consequence of the physical environment and the internal protein activity of a cell - is an important signal that controls protein affinity and enzymatic activity to ensure robust forward progression of key processes within the cell.

Spatiotemporal dynamics of membrane surface charge regulates cell polarity and migration

During cell migration and polarization, numerous signal transduction and cytoskeletal components self-organize to generate localized protrusions. Although biochemical and genetic analyses have delineated many specific interactions, how the activation and localization of so many different molecules are spatiotemporally orchestrated at the subcellular level has remained unclear. Here we show that the regulation of negative surface charge on the inner leaflet of the plasma membrane plays an integrative role in the molecular interactions. Surface charge, or zeta potential, is transiently lowered at new protrusions and within cortical waves of Ras/PI3K/TORC2/F-actin network activation. Rapid alterations of inner leaflet anionic phospholipids-such as PI(4,5)P2, PI(3,4)P2, phosphatidylserine and phosphatidic acid-collectively contribute to the surface charge changes. Abruptly reducing the surface charge by recruiting positively charged optogenetic actuators was sufficient to trigger the entire biochemical network, initiate de novo protrusions and abrogate pre-existing polarity. These effects were blocked by genetic or pharmacological inhibition of key signalling components such as AKT and PI3K/TORC2. Conversely, increasing the negative surface charge deactivated the network and locally suppressed chemoattractant-induced protrusions or subverted EGF-induced ERK activation. Computational simulations involving excitable biochemical networks demonstrated that slight changes in feedback loops, induced by recruitment of the charged actuators, could lead to outsized effects on system activation. We propose that key signalling network components act on, and are in turn acted upon, by surface charge, closing feedback loops, which bring about the global-scale molecular self-organization required for spontaneous protrusion formation, cell migration and polarity establishment.

Membrane tension propagation couples axon growth and collateral branching

Neuronal axons must navigate a mechanically heterogeneous environment to reach their targets, but the biophysical mechanisms coupling mechanosensation, growth, and branching are not fully understood. Here, we show that local changes in membrane tension propagate along axons at approximately 20 μm/s, more than 1000-fold faster than in most other nonmotile cells where this property has been measured. Local perturbations to tension decay along the axon with a length constant of approximately 41 μm. This rapid and long-range mechanical signaling mediates bidirectional competition between axonal branch initiation and growth cone extension. Our data suggest a mechanism by which mechanical cues at one part of a growing axon can affect growth dynamics remotely.

Excitable reaction-diffusion waves of curvature-inducing proteins on deformable membrane tubes

Living cells employ excitable reaction-diffusion waves for internal cellular functions, in which curvature-inducing proteins are often involved. However, the role of their mechanochemical coupling is not well understood. Here, we report the membrane deformation induced by the excitable reaction-diffusion waves of curvature-inducing proteins and the alternation in the waves due to the deformation, using a coarse-grained simulation of tubular membranes with a modified FitzHugh-Nagumo model. Protein-propagating waves deform tubular membranes and large deformations induce budding and erase waves. The wave speed and shape are determined by a combination of membrane deformation and spatial distribution of the curvature-inducing protein. Waves are also undulated in the azimuthal direction depending on the condition. Rotationally symmetric waves locally deform the tubes into a symmetric shape but maintain a straight shape on average. Our simulation method can be applied to other chemical reaction models and used to investigate various biomembrane phenomena.

Binding of anisotropic curvature-inducing proteins onto membrane tubes

Bin/Amphiphysin/Rvs superfamily proteins and other curvature-inducing proteins have anisotropic shapes and anisotropically bend biomembranes. Here, we report how the anisotropic proteins bind the membrane tube and are orientationally ordered using mean-field theory including an orientation-dependent excluded volume. The proteins exhibit a second-order or first-order nematic transition with increasing protein density depending on the radius of the membrane tube. The tube curvatures for the maximum protein binding and orientational order are different and varied by the protein density and rigidity. As the external force along the tube axis increases, a first-order transition from a large tube radius with low protein density to a small radius with high density occurs once, and subsequently, the protein orientation tilts to the tube-axis direction. When an isotropic bending energy is used for the proteins with an elliptic shape, the force-dependence curves become symmetric and the first-order transition occurs twice. This theory quantitatively reproduces the results of meshless membrane simulation for short proteins, whereas deviations are seen for long proteins owing to the formation of protein clusters.

Intercellular water exchanges trigger soliton-like waves in multicellular systems

Oscillations and waves are ubiquitous in living cellular systems. Generations of these spatiotemporal patterns are generally attributed to some mechanochemical feedbacks. Here, we treat cells as open systems, i.e., water and ions can pass through the cell membrane passively or actively, and reveal a new origin of wave generation. We show that osmotic shocks above a shock threshold will trigger self-sustained cell oscillations and result in long-range waves propagating without decrement, a phenomenon that is analogous to the excitable medium. The traveling wave propagates along the intercellular osmotic pressure gradient, and its wave speed scales with the magnitude of intercellular water flows. Furthermore, we also find that the traveling wave exhibits several hallmarks of solitary waves. Together, our findings predict a new mechanism of wave generation in living multicellular systems. The ubiquity of intercellular water exchanges implies that this mechanism may be relevant to a broad class of systems.

Cortical softening elicits zygotic contractility during mouse preimplantation development

Actomyosin contractility is a major engine of preimplantation morphogenesis, which starts at the 8-cell stage during mouse embryonic development. Contractility becomes first visible with the appearance of periodic cortical waves of contraction (PeCoWaCo), which travel around blastomeres in an oscillatory fashion. How contractility of the mouse embryo becomes active remains unknown. We have taken advantage of PeCoWaCo to study the awakening of contractility during preimplantation development. We find that PeCoWaCo become detectable in most embryos only after the second cleavage and gradually increase their oscillation frequency with each successive cleavage. To test the influence of cell size reduction during cleavage divisions, we use cell fusion and fragmentation to manipulate cell size across a 20- to 60-μm range. We find that the stepwise reduction in cell size caused by cleavage divisions does not explain the presence of PeCoWaCo or their accelerating rhythm. Instead, we discover that blastomeres gradually decrease their surface tensions until the 8-cell stage and that artificially softening cells enhances PeCoWaCo prematurely. We further identify the programmed down-regulation of the formin Fmnl3 as a required event to soften the cortex and expose PeCoWaCo. Therefore, during cleavage stages, cortical softening, mediated by Fmnl3 down-regulation, awakens zygotic contractility before preimplantation morphogenesis.

During preimplantation morphogenesis, the mouse embryo relies on forces generated by the actomyosin cytoskeleton. This study uncovers how periodic actomyosin contractions increase in frequency during cleavage stages as blastomeres soften with each cleavage division.

Microtopographical guidance of macropinocytic signaling patches

Morphologies of amoebae and immune cells are highly deformable and dynamic, which facilitates migration in various terrains, as well as ingestion of extracellular solutes and particles. It remains largely unexplored whether and how the underlying membrane protrusions are triggered and guided by the geometry of the surface in contact. In this study, we show that in Dictyostelium, the precursor of a structure called macropinocytic cup, which has been thought to be a constitutive process for the uptake of extracellular fluid, is triggered by micrometer-scale surface features. Imaging analysis and computational simulations demonstrate how the topographical dependence of the self-organizing dynamics supports efficient guidance and capturing of the membrane protrusion and hence movement of an entire cell along such surface features.

In fast-moving cells such as amoeba and immune cells, dendritic actin filaments are spatiotemporally regulated to shape large-scale plasma membrane protrusions. Despite their importance in migration, as well as in particle and liquid ingestion, how their dynamics are affected by micrometer-scale features of the contact surface is still poorly understood. Here, through quantitative image analysis of Dictyostelium on microfabricated surfaces, we show that there is a distinct mode of topographical guidance directed by the macropinocytic membrane cup. Unlike other topographical guidance known to date that depends on nanometer-scale curvature sensing protein or stress fibers, the macropinocytic membrane cup is driven by the Ras/PI3K/F-actin signaling patch and its dependency on the micrometer-scale topographical features, namely PI3K/F-actin–independent accumulation of Ras-GTP at the convex curved surface, PI3K-dependent patch propagation along the convex edge, and its actomyosin-dependent constriction at the concave edge. Mathematical model simulations demonstrate that the topographically dependent initiation, in combination with the mutually defining patch patterning and the membrane deformation, gives rise to the topographical guidance. Our results suggest that the macropinocytic cup is a self-enclosing structure that can support liquid ingestion by default; however, in the presence of structured surfaces, it is directed to faithfully trace bent and bifurcating ridges for particle ingestion and cell guidance.

Rho and F-actin self-organize within an artificial cell cortex

The cell cortex, comprised of the plasma membrane and underlying cytoskeleton, undergoes dynamic reorganizations during a variety of essential biological processes including cell adhesion, cell migration, and cell division.^1,2 During cell division and cell locomotion, for example, waves of filamentous-actin (F-actin) assembly and disassembly develop in the cell cortex in a process termed "cortical excitability."^3-7 In developing frog and starfish embryos, cortical excitability is generated through coupled positive and negative feedback, with rapid activation of Rho-mediated F-actin assembly followed in space and time by F-actin-dependent inhibition of Rho.^7,8 These feedback loops are proposed to serve as a mechanism for amplification of active Rho signaling at the cell equator to support furrowing during cytokinesis while also maintaining flexibility for rapid error correction in response to movement of the mitotic spindle during chromosome segregation.⁹ In this paper, we develop an artificial cortex based on Xenopus egg extract and supported lipid bilayers (SLBs), to investigate cortical Rho and F-actin dynamics.¹⁰ This reconstituted system spontaneously develops two distinct types of self-organized cortical dynamics: singular excitable Rho and F-actin waves, and non-traveling oscillatory Rho and F-actin patches. Both types of dynamic patterns have properties and dependencies similar to the excitable dynamics previously characterized in vivo.⁷ These findings directly support the long-standing speculation that the cell cortex is a self-organizing structure and present a novel approach for investigating mechanisms of Rho-GTPase-mediated cortical dynamics.

Site of Cholesterol Oxidation Impacts Its Localization and Domain Formation in the Neuronal Plasma Membrane

Cholesterol is integral to the structure of mammalian cell membranes. Oxidation of cholesterol alters how it behaves in the membrane and influences the membrane biophysical properties. Elevated levels of oxidized cholesterol are associated with neurodegenerative diseases such as Alzheimer's disease, Parkinson's disease, multiple sclerosis, and Huntington's disease. Previous work has investigated the impact of oxidized cholesterol in the context of simple model membrane systems. However, there is a growing body of literature that shows that complex membranes possessing physiological phospholipid distributions have different properties from those of binary or trinary model membranes. In the current work, the impact of oxidized cholesterol on the biophysical properties of a complex neuronal plasma membrane is investigated using coarse-grained Martini molecular dynamics simulations. Comparison of the native neuronal membrane to neuronal membranes containing 10% tail-oxidized or 10% head-oxidized cholesterol shows that the site of oxidization changes the behavior of the oxidized cholesterol in the membrane. Furthermore, species-specific domain formation is observed between each oxidized cholesterol and minor lipid classes. Although both tail-oxidized and head-oxidized cholesterols modulate the biophysical properties of the membrane, smaller changes are observed in the complex neuronal membrane than seen in the previous work on simple binary or trinary model membranes. This work highlights the presence of compensatory effects of lipid diversity in the complex neuronal membrane. Overall, this study improves our molecular-level understanding of the effects of oxidized cholesterol on the properties of neuronal tissue and emphasizes the importance of studying membranes with realistic lipid compositions.

Reaction-diffusion waves coupled with membrane curvature

The reaction-diffusion waves of proteins are known to be involved in fundamental cellular functions, such as cell migration, cell division, and vesicular transportation. In some of these phenomena, pattern formation on the membranes is induced by the coupling between membrane deformation and the reaction-diffusion system through curvature-inducing proteins that bend the biological membranes. Although the membrane shape and the dynamics of the curvature-inducing proteins affect each other in these systems, the effect of such mechanochemical feedback loops on the waves has not been studied in detail. In this study, reaction-diffusion waves coupled with membrane deformation are investigated using simulations combining a dynamically triangulated membrane model with the Brusselator model extended to include the effect of membrane curvature. It is found that the propagating wave patterns change into nonpropageting patterns and spiral wave patterns due to the mechanochemical effects. Moreover, the wave speed is positively or negatively correlated with the local membrane curvature depending on the spontaneous curvature and bending rigidity. In addition, self-oscillation of the vesicle shape occurs, associated with the reaction-diffusion waves of curvature-inducing proteins. This agrees with the experimental observation of GUVs with a reconstituted Min system, which plays a key role in the cell division of Escherichia coli. The findings of this study demonstrate the importance of mechanochemical coupling in biological phenomena.

Three-dimensional stochastic simulation of chemoattractant-mediated excitability in cells

During the last decade, a consensus has emerged that the stochastic triggering of an excitable system drives pseudopod formation and subsequent migration of amoeboid cells. The presence of chemoattractant stimuli alters the threshold for triggering this activity and can bias the direction of migration. Though noise plays an important role in these behaviors, mathematical models have typically ignored its origin and merely introduced it as an external signal into a series of reaction-diffusion equations. Here we consider a more realistic description based on a reaction-diffusion master equation formalism to implement these networks. In this scheme, noise arises naturally from a stochastic description of the various reaction and diffusion terms. Working on a three-dimensional geometry in which separate compartments are divided into a tetrahedral mesh, we implement a modular description of the system, consisting of G-protein coupled receptor signaling (GPCR), a local excitation-global inhibition mechanism (LEGI), and signal transduction excitable network (STEN). Our models implement detailed biochemical descriptions whenever this information is available, such as in the GPCR and G-protein interactions. In contrast, where the biochemical entities are less certain, such as the LEGI mechanism, we consider various possible schemes and highlight the differences between them. Our simulations show that even when the LEGI mechanism displays perfect adaptation in terms of the mean level of proteins, the variance shows a dose-dependence. This differs between the various models considered, suggesting a possible means for determining experimentally among the various potential networks. Overall, our simulations recreate temporal and spatial patterns observed experimentally in both wild-type and perturbed cells, providing further evidence for the excitable system paradigm. Moreover, because of the overall importance and ubiquity of the modules we consider, including GPCR signaling and adaptation, our results will be of interest beyond the field of directed migration.

Though the term noise usually carries negative connotations, it can also contribute positively to the characteristic dynamics of a system. In biological systems, where noise arises from the stochastic interactions between molecules, its study is usually confined to genetic regulatory systems in which copy numbers are small and fluctuations large. However, noise can have important roles when the number of signaling molecules is large. The extension of pseudopods and the subsequent motion of amoeboid cells arises from the noise-induced trigger of an excitable system. Chemoattractant signals bias this triggering thereby directing cell motion. To date, this paradigm has not been tested by mathematical models that account accurately for the noise that arises in the corresponding reactions. In this study, we employ a reaction-diffusion master equation approach to investigate the effects of noise. Using a modular approach and a three-dimensional cell model with specific subdomains attributed to the cell membrane and cortex, we explore the spatiotemporal dynamics of the system. Our simulations recreate many experimentally-observed cell behaviors thereby supporting the biased-excitable network hypothesis.

Binding of thermalized and active membrane curvature-inducing proteins

The phase behavior of a membrane induced by the binding of curvature-inducing proteins is studied by a combination of analytical and numerical approaches. In thermal equilibrium under the detailed balance between binding and unbinding, the membrane exhibits three phases: an unbound uniform flat phase (U), a bound uniform flat phase (B), and a separated/corrugated phase (SC). In the SC phase, the bound proteins form hexagonally-ordered bowl-shaped domains. The transitions between the U and SC phases and between the B and SC phases are second order and first order, respectively. At a small spontaneous curvature of the protein or high surface tension, the transition between B and SC phases becomes continuous. Moreover, a first-order transition between the U and B phases is found at zero spontaneous curvature driven by the Casimir-like interactions between rigid proteins. Furthermore, nonequilibrium dynamics is investigated by the addition of active binding and unbinding at a constant rate. The active binding and unbinding processes alter the stability of the SC phase.

Rapid viscoelastic changes are a hallmark of early leukocyte activation

To accomplish their critical task of removing infected cells and fighting pathogens, leukocytes activate by forming specialized interfaces with other cells. The physics of this key immunological process are poorly understood, but it is important to understand them because leukocytes have been shown to react to their mechanical environment. Using an innovative micropipette rheometer, we show in three different types of leukocytes that, when stimulated by microbeads mimicking target cells, leukocytes become up to 10 times stiffer and more viscous. These mechanical changes start within seconds after contact and evolve rapidly over minutes. Remarkably, leukocyte elastic and viscous properties evolve in parallel, preserving a well-defined ratio that constitutes a mechanical signature specific to each cell type. Our results indicate that simultaneously tracking both elastic and viscous properties during an active cell process provides a new, to our knowledge, way to investigate cell mechanical processes. Our findings also suggest that dynamic immunomechanical measurements can help discriminate between leukocyte subtypes during activation.

Undulation of a moving fluid membrane pushed by filament growth

Biomembranes experience out-of-equilibrium conditions in living cells. Their undulation spectra are different from those in thermal equilibrium. Here, we report on the undulation of a fluid membrane pushed by the stepwise growth of filaments as in the leading edge of migrating cells, using three-dimensional Monte Carlo simulations. The undulations are largely modified from equilibrium behavior. When the tension is constrained, the low-wave-number modes are suppressed or enhanced at small or large growth step sizes, respectively, for high membrane surface tensions. In contrast, they are always suppressed for the tensionless membrane, wherein the wave-number range of the suppression depends on the step size. When the membrane area is constrained, in addition to these features, a specific mode is excited for zero and low surface tensions. The reduction of the undulation first induces membrane buckling at the lowest wave-number, and subsequently, other modes are excited, leading to a steady state.

Quantifying the roles of space and stochasticity in computer simulations for cell biology and cellular biochemistry

Most of the fascinating phenomena studied in cell biology emerge from interactions among highly organized multimolecular structures embedded into complex and frequently dynamic cellular morphologies. For the exploration of such systems, computer simulation has proved to be an invaluable tool, and many researchers in this field have developed sophisticated computational models for application to specific cell biological questions. However, it is often difficult to reconcile conflicting computational results that use different approaches to describe the same phenomenon. To address this issue systematically, we have defined a series of computational test cases ranging from very simple to moderately complex, varying key features of dimensionality, reaction type, reaction speed, crowding, and cell size. We then quantified how explicit spatial and/or stochastic implementations alter outcomes, even when all methods use the same reaction network, rates, and concentrations. For simple cases, we generally find minor differences in solutions of the same problem. However, we observe increasing discordance as the effects of localization, dimensionality reduction, and irreversible enzymatic reactions are combined. We discuss the strengths and limitations of commonly used computational approaches for exploring cell biological questions and provide a framework for decision making by researchers developing new models. As computational power and speed continue to increase at a remarkable rate, the dream of a fully comprehensive computational model of a living cell may be drawing closer to reality, but our analysis demonstrates that it will be crucial to evaluate the accuracy of such models critically and systematically.

Pattern formation in reaction-diffusion system on membrane with mechanochemical feedback

Shapes of biological membranes are dynamically regulated in living cells. Although membrane shape deformation by proteins at thermal equilibrium has been extensively studied, nonequilibrium dynamics have been much less explored. Recently, chemical reaction propagation has been experimentally observed in plasma membranes. Thus, it is important to understand how the reaction-diffusion dynamics are modified on deformable curved membranes. Here, we investigated nonequilibrium pattern formation on vesicles induced by mechanochemical feedback between membrane deformation and chemical reactions, using dynamically triangulated membrane simulations combined with the Brusselator model. We found that membrane deformation changes stable patterns relative to those that occur on a non-deformable curved surface, as determined by linear stability analysis. We further found that budding and multi-spindle shapes are induced by Turing patterns, and we also observed the transition from oscillation patterns to stable spot patterns. Our results demonstrate the importance of mechanochemical feedback in pattern formation on deforming membranes.

Comparative Study of Curvature Sensing Mediated by F-BAR and an Intrinsically Disordered Region of FBP17

Membrane curvature has emerged as an intriguing physical principle underlying biological signaling and membrane trafficking. The CIP4/FBP17/Toca-1 F-BAR subfamily is unique in the BAR family because its structurally folded F-BAR domain does not contain any hydrophobic motifs that insert into membrane. Although widely assumed so, whether the banana-shaped F-BAR domain alone can sense curvature has never been experimentally demonstrated. Using a nanobar-supported lipid bilayer system, we found that the F-BAR domain of FBP17 displayed minimal curvature sensing in vitro. In comparison, an alternatively spliced intrinsically disordered region (IDR) adjacent to the F-BAR domain has the membrane curvature-sensing ability greatly exceeding that of F-BAR domain alone. In living cells, the presence of the IDR delayed the recruitment of FBP17 in curvature-coupled cortical waves. Collectively, we propose that contrary to the common belief, FBP17's curvature-sensing capability largely originates from IDR, and not the F-BAR domain alone.

Mechanobiology in cortical waves and oscillations

Cortical actin waves have emerged as a widely prevalent phenomena and brought pattern formation to many fields of cell biology. Cortical excitabilities, reminiscent of the electric excitability in neurons, are likely fundamental property of the cell cortex. Although they have been mostly considered to be biochemical in nature, accumulating evidence support the role of mechanics in the pattern formation process. Both pattern formation and mechanobiology approach biological phenomena at the collective level, either by looking at the mesoscale dynamical behavior of molecular networks or by using collective physical properties to characterize biological systems. As such they are very different from the traditional reductionist, bottom-up view of biology, which brings new challenges and potential opportunities. In this essay, we aim to provide our perspectives on what the proposed mechanochemical feedbacks are and open questions regarding their role in cortical excitable and oscillatory dynamics.

Aster swarming by symmetry breaking of cortical dynein transport and coupling kinesins

Microtubule (MT) radial arrays or asters establish the internal topology of a cell by interacting with organelles and molecular motors. We proceed to understand the general pattern forming potential of aster-motor systems using a computational model of multiple MT asters interacting with motors in cellular confinement. In this model dynein motors are attached to the cell cortex and plus-ended motors resembling kinesin-5 diffuse in the cell interior. The introduction of 'noise' in the form of MT length fluctuations spontaneously results in the emergence of coordinated, achiral vortex-like rotation of asters. The coherence and persistence of rotation require a threshold density of both cortical dyneins and coupling kinesins, while the onset is diffusion-limited with relation to the cortical dynein mobility. The coordinated rotational motion emerges due to the resolution of a 'tug-of-war' of multiple cortical dynein motors bound to MTs of the same aster by 'noise' in the form of MT dynamic instability. This transient symmetry breaking is amplified by local coupling by kinesin-5 complexes. The lack of widespread aster rotation across cell types suggests that biophysical mechanisms that suppress such intrinsic dynamics may have evolved. This model is analogous to more general models of locally coupled self-propelled particles (SPP) that spontaneously undergo collective transport in the presence of 'noise' that have been invoked to explain swarming in birds and fish. However, the aster-motor system is distinct from SPP models with regard to the particle density and 'noise' dependence, providing a set of experimentally testable predictions for a novel sub-cellular pattern forming system.

Interplay between membrane curvature and the actin cytoskeleton

An intimate interplay of the plasma membrane with curvature-sensing and curvature-inducing proteins would allow for defining specific sites or nanodomains of action at the plasma membrane, for example, for protrusion, invagination, and polarization. In addition, such connections are predestined to ensure spatial and temporal order and sequences. The combined forces of membrane shapers and the cortical actin cytoskeleton might hereby in particular be required to overcome the strong resistance against membrane rearrangements in case of high plasma membrane tension or cellular turgor. Interestingly, also the opposite might be necessary, the inhibition of both membrane shapers and cytoskeletal reinforcement structures to relieve membrane tension to protect cells from membrane damage and rupturing during mechanical stress. In this review article, we discuss recent conceptual advances enlightening the interplay of plasma membrane curvature and the cortical actin cytoskeleton during endocytosis, modulations of membrane tensions, and the shaping of entire cells.

An Excitable Ras/PI3K/ERK Signaling Network Controls Migration and Oncogenic Transformation in Epithelial Cells

The Ras/PI3K/extracellular signal-regulated kinases (ERK) signaling network plays fundamental roles in cell growth, survival, and migration and is frequently activated in cancer. Here, we show that the activities of the signaling network propagate as coordinated waves, biased by growth factor, which drive actin-based protrusions in human epithelial cells. The network exhibits hallmarks of biochemical excitability: the annihilation of oppositely directed waves, all-or-none responsiveness, and refractoriness. Abrupt perturbations to Ras, PI(4,5)P2, PI(3,4)P2, ERK, and TORC2 alter the threshold, observations that define positive and negative feedback loops within the network. Oncogenic transformation dramatically increases the wave activity, the frequency of ERK pulses, and the sensitivity to EGF stimuli. Wave activity was progressively enhanced across a series of increasingly metastatic breast cancer cell lines. The view that oncogenic transformation is a shift to a lower threshold of excitable Ras/PI3K/ERK network, caused by various combinations of genetic insults, can facilitate the assessment of cancer severity and effectiveness of interventions.

Why a Large-Scale Mode Can Be Essential for Understanding Intracellular Actin Waves

During the last decade, intracellular actin waves have attracted much attention due to their essential role in various cellular functions, ranging from motility to cytokinesis. Experimental methods have advanced significantly and can capture the dynamics of actin waves over a large range of spatio-temporal scales. However, the corresponding coarse-grained theory mostly avoids the full complexity of this multi-scale phenomenon. In this perspective, we focus on a minimal continuum model of activator-inhibitor type and highlight the qualitative role of mass conservation, which is typically overlooked. Specifically, our interest is to connect between the mathematical mechanisms of pattern formation in the presence of a large-scale mode, due to mass conservation, and distinct behaviors of actin waves.

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. By connecting the fast processes of binding with the slow timescales of large-scale assembly, NERDSS integrates molecular resolution with reversible formation of ordered, multisubunit complexes. NERDSS encodes models using rule-based formatting languages to facilitate model portability, usability, and reproducibility. Applying NERDSS to steps in clathrin-mediated endocytosis, we design multicomponent systems that can form lattices in solution or on the membrane, and we predict how stochastic but localized dephosphorylation of membrane lipids can drive lattice disassembly. The NERDSS simulations reveal the spatial constraints on lattice growth and the role of membrane localization and cooperativity in nucleating assembly. By modeling viral lattice assembly and recapitulating oscillations in protein expression levels for a circadian clock model, we illustrate the adaptability of NERDSS. NERDSS simulates user-defined assembly models that were previously inaccessible to existing software tools, with broad applications to predicting self-assembly in vivo and designing high-yield assemblies in vitro.