Liquid behavior of cross-linked actin bundles. Proc Natl Acad Sci U S A. 2017;114:2131-2136. [PMID: 28202730 DOI: 10.1073/pnas.1616133114]

Mechanics of Single Cytoskeletal Filaments

The cytoskeleton comprises networks of different biopolymers, which serve various cellular functions. To accomplish these tasks, their mechanical properties are of particular importance. Understanding them requires detailed knowledge of the mechanical properties of the individual filaments that make up these networks, in particular, microtubules, actin filaments, and intermediate filaments. Far from being homogeneous beams, cytoskeletal filaments have complex mechanical properties, which are directly related to the specific structural arrangement of their subunits. They are also versatile, as the filaments' mechanics and biochemistry are tightly coupled, and their properties can vary with the cellular context. In this review, we summarize decades of research on cytoskeletal filament mechanics, highlighting their most salient features and discussing recent insights from this active field of research.

Active and passive crosslinking of cytoskeleton scaffolds tune the effects of cell inclusions on composite structure

Incorporating cells within active biomaterial scaffolds is a promising strategy to develop forefront materials that can autonomously sense, respond, and alter the scaffold in response to environmental cues or internal cell circuitry. Using dynamic biocompatible scaffolds that can self-alter their properties via crosslinking and motor-driven force-generation opens even greater avenues for actuation and control. However, the design principles associated with engineering active scaffolds embedded with cells are not well established. To address this challenge, we design a dynamic scaffold material of bacteria cells embedded within a composite cytoskeletal network of actin and microtubules that can be passively or actively crosslinked by either biotin-streptavidin or multimeric kinesin motors. Using quantitative microscopy, we demonstrate the ability to embed cells of volume fractions 0.4-2% throughout the network without compromising the structural integrity of the network or inhibiting crosslinking or motor-driven dynamics. Our findings suggest that both passive and active crosslinking promote entrainment of cells within the network, while depletion interactions play a more important role in uncrosslinked networks. Moreover, we show that large-scale structures emerge with the addition of cell fractions as low as 0.4%, but these structures do not influence the microscale structural length scale of the materials. Our work highlights the potential of our composite biomaterial in designing autonomous materials controlled by cells, and provides a roadmap for effectively coupling cells to complex composite materials with an eye towards using cells as in situ factories to program material modifications.

ATR-hippo drives force signaling to nuclear F-actin and links mechanotransduction to neurological disorders

The mechanical environment is sensed through cell-matrix contacts with the cytoskeleton, but how signals transit the nuclear envelope to affect cell fate decisions remains unknown. Nuclear actin coordinates chromatin motility during differentiation and genome maintenance, yet it remains unclear how nuclear actin responds to mechanical force. The DNA-damage kinase ataxia telangiectasia and Rad3-related protein (ATR) translocates to the nuclear envelope to protect the nucleus during cell motility or compression. Here, we show that ATR drives nuclear actin assembly via recruitment of Filamin-A to the inner nuclear membrane through binding of the hippo pathway scaffold and ATR substrate, RASSF1A. Moreover, we demonstrate how germline RASSF1 mutation disables nuclear mechanotransduction resulting in cerebral cortex thinning and associates with common psychological traits. Thus, defective mechanical-regulated pathways may contribute to complex neurological disorders.

Plasma membrane and nuclear phosphatidylinositol 4,5-bisphosphate signalling in cancer

The development of metastasis is a leading cause of cancer-related death that involves specific changes in the plasma membrane (PM) and nucleus of cancer cells. Elevated levels of membrane lipids, including sphingomyelin, cholesterol, and phosphatidylinositol 4,5-bisphosphate (PI(4,5)P2), in the PM, contribute to changes in membrane rigidity, lipid raft formation, and actin polymerisation dynamics, processes that drive cell invasion. This review discusses the relationship between well-studied cytoplasmic phosphoinositides and their lesser-known nuclear counterparts, highlighting their functional role in metastatic progression. Nuclear phosphoinositides, particularly PI(4,5)P2, are essential for regulating transcription factors and chromatin organisation, thereby shaping gene expression patterns. We also explore the role of PI(4,5)P2 and its metabolism in cancer cell invasiveness and metastasis, proposing a model in which the dysregulation of cytosolic and/or nuclear PI(4,5)P2 pool triggers malignant transformation. Understanding the PI(4,5)P2-related mechanisms underlying metastasis may provide insights into potential therapeutic targets, paving the way for more effective therapies and improved patient outcomes.

Direct detection of deformation modes on varying length scales in active biopolymer networks

Correlated flows and forces that emerge from active matter orchestrate complex processes such as shape regulation and deformations in biological cells and tissues. The active materials central to cellular mechanics are cytoskeletal networks, where molecular motor activity drives deformations and remodeling. Here, we investigate deformation modes in contractile actin networks driven by the molecular motor myosin II through quantitative fluorescence microscopy. We examine the deformation anisotropy at different length scales in networks of sparsely cross-linked and bundled actin. In sparsely cross-linked networks, we find myosin-dependent biaxial buckling modes across length scales. Interestingly, both long and short-wavelength buckling may contribute to network contractility. In cross-linked bundled networks, uniaxial contraction predominates on long length scales, while the uniaxial or biaxial nature of the deformation depends on bundle microstructure at shorter length scales. The anisotropy of deformations may provide insight to the mechanical origins of contractility in actin networks and regulation of collective behavior in a variety of active materials.

Cellular Function of a Biomolecular Condensate Is Determined by Its Ultrastructure

Biomolecular condensates play key roles in the spatiotemporal regulation of cellular processes. Yet, the relationship between atomic features and condensate function remains poorly understood. We studied this relationship using the polar organizing protein Z (PopZ) as a model system, revealing how its material properties and cellular function depend on its ultrastructure. We revealed PopZ's hierarchical assembly into a filamentous condensate by integrating cryo-electron tomography, biochemistry, single-molecule techniques, and molecular dynamics simulations. The helical domain drives filamentation and condensation, while the disordered domain inhibits them. Phase-dependent conformational changes prevent interfilament contacts in the dilute phase and expose client binding sites in the dense phase. These findings establish a multiscale framework that links molecular interactions and condensate ultrastructure to macroscopic material properties that drive cellular function.

DNA-amphiphilic nanostructures: synthesis, characterization and applications

DNA's extraordinary potential reaches far beyond its role as a carrier of genetic information. It serves as a remarkably adaptable structural foundation for constructing intricate nanostructures with a diverse range of functionalities. This inherent programmability sets DNA apart from other biomolecules like peptides, proteins, and small molecules. By covalently attaching DNA to synthetic hydrophobic moieties, researchers create DNA amphiphiles capable of interacting with artificial lipid bilayers and cell membranes. These hybrid structures have rapidly gained prominence due to their promising potential in the medical field. This review provides a comprehensive overview of the latest advancements in the synthesis of DNA amphiphiles and their assembly into well-defined nanostructures. It explores the diverse applications of these nanostructures across various medical domains, including targeted drug delivery, innovative immunotherapies, and gene-silencing techniques. Moreover, the review delves into the current challenges and prospects of this rapidly evolving field, highlighting the potential of DNA hybrid materials to revolutionize medical treatments and diagnostics. By addressing the limitations and exploring new avenues of research, scientists aim to unlock the full potential of DNA nanotechnology for the benefit of human health.

TPM4 condensates glycolytic enzymes and facilitates actin reorganization under hyperosmotic stress

Actin homeostasis is fundamental for cell structure and consumes a large portion of cellular ATP. It has been documented in the literature that certain glycolytic enzymes can interact with actin, indicating an intricate interplay between the cytoskeleton and cellular metabolism. Here we report that hyperosmotic stress triggers actin severing and subsequent phase separation of the actin-binding protein tropomyosin 4 (TPM4). TPM4 condensates recruit glycolytic enzymes such as HK2, PFKM, and PKM2, while wetting actin filaments. Notably, the condensates of TPM4 and glycolytic enzymes are enriched of NADH and ATP, suggestive of their functional importance in cell metabolism. At cellular level, actin filament assembly is enhanced upon hyperosmotic stress and TPM4 condensation, while depletion of TPM4 impairs osmolarity-induced actin reorganization. At tissue level, colocalized condensates of TPM4 and glycolytic enzymes are observed in renal tissues subjected to hyperosmotic stress. Together, our findings suggest that stress-induced actin perturbation may act on TPM4 to organize glycolytic hubs that tether energy production to cytoskeletal reorganization.

Cell-Free Nonequilibrium Assembly for Hierarchical Protein/Peptide Nanopillars

Cells contain intricate protein nanostructures, but replicating them outside of cells presents challenges. One such example is the vertical fibronectin pillars observed in embryos. Here, we demonstrate the creation of cell-free vertical fibronectin pillar mimics using nonequilibrium self-assembly. Our approach utilizes enzyme-responsive phosphopeptides that assemble into nanotubes. Enzyme action triggers shape changes in peptide assemblies, driving the vertical growth of protein nanopillars into bundles. These bundles, with peptide nanotubes serving as a template to remodel fibronectin, can then recruit collagen, which forms aggregates or bundles depending on their types. Nanopillar formation relies on enzyme-catalyzed nonequilibrium self-assembly and is governed by the concentrations of enzyme, protein, peptide, the structure of the peptide, and peptide assembly morphologies. Cryo-EM reveals unexpected nanotube thinning and packing after dephosphorylation, indicating a complex sculpting process during assembly. Our study demonstrates a cell-free method for constructing intricate, multiprotein nanostructures with directionality and composition.

Bridging the Gap-Thermofluidic Designs for Precision Bioelectronics

Bioelectronics, the merging of biology and electronics, can monitor and modulate biological behaviors across length and time scales with unprecedented capability. Current bioelectronics research largely focuses on devices' mechanical properties and electronic designs. However, the thermofluidic control is often overlooked, which is noteworthy given the discipline's importance in almost all bioelectronics processes. It is believed that integrating thermofluidic designs into bioelectronics is essential to align device precision with the complexity of biofluids and biological structures. This perspective serves as a mini roadmap for researchers in both fields to introduce key principles, applications, and challenges in both bioelectronics and thermofluids domains. Important interdisciplinary opportunities for the development of future healthcare devices and precise bioelectronics will also be discussed.

Ionic strength alters crosslinker-driven self-organization of microtubules

The microtubule cytoskeleton is a major structural element inside cells that directs self-organization using microtubule-associated proteins and motors. It has been shown that finite-sized, spindle-like microtubule organizations, called "tactoids," can form in vitro spontaneously from mixtures of tubulin and the antiparallel crosslinker, MAP65, from the MAP65/PRC1/Ase family. Here, we probe the ability of MAP65 to form tactoids as a function of the ionic strength of the buffer to attempt to break the electrostatic interactions binding MAP65 to microtubules and inter-MAP65 binding. We observe that, with increasing monovalent salts, the organizations change from finite tactoids to unbounded length bundles, yet the MAP65 binding and crosslinking appear to stay intact. We further explore the effects of ionic strength on the dissociation constant of MAP65 using both microtubule pelleting and single-molecule binding assays. We find that salt can reduce the binding, yet salt never negates it. Instead, we believe that the salt is affecting the ability of the MAP65 to form phase-separated droplets, which cause the nucleation and growth of tactoids, as recently demonstrated.

Designer peptide-DNA cytoskeletons regulate the function of synthetic cells

The bottom-up engineering of artificial cells requires a reconfigurable cytoskeleton that can organize at distinct locations and dynamically modulate its structural and mechanical properties. Here, inspired by the vast array of actin-binding proteins and their ability to reversibly crosslink or bundle filaments, we have designed a library of peptide-DNA crosslinkers varying in length, valency and geometry. Peptide filaments conjoint through DNA hybridization give rise to tactoid-shaped bundles with tunable aspect ratios and mechanics. When confined in cell-sized water-in-oil droplets, the DNA crosslinker design guides the localization of cytoskeletal structures at the cortex or within the lumen of the synthetic cells. The tunable spatial arrangement regulates the passive diffusion of payloads within the droplets and complementary DNA handles allow for the reversible recruitment and release of payloads on and off the cytoskeleton. Heat-induced reconfiguration of peptide-DNA architectures triggers shape deformations of droplets, regulated by DNA melting temperatures. Altogether, the modular design of peptide-DNA architectures is a powerful strategy towards the bottom-up assembly of synthetic cells.

Cholesteric Tactoids with Tunable Helical Pitch Assembled by Lysozyme Amyloid Fibrils

Amyloid fibrils are biological rod-like particles showing liquid-liquid crystalline phase separation into cholesteric phases through a complex behavior of nucleation, growth, and order-order transitions. Yet, controlling the self-assembly of amyloids into liquid crystals, and particularly the resulting helical periodicity, remains challenging. Here, a novel cholesteric system is introduced and characterized based on hen egg white lysozyme (HEWL) amyloid fibrils and the results rationalized via a combination of experiments and theoretical scaling arguments. Specifically, the transition behaviors are elucidated from homogenous nematic, bipolar nematic to cholesteric tactoids following the classic Onsager model and the free energy functional model from Frank-Oseen elasticity theory. Additionally, the critical effects of pH and ionic strength on these order-order-transitions, as well as on the shape and helical pitch of the cholesteric tactoids are demonstrated. It is found that a small increase in pH from 2.0 to 2.8 results in a 34% decrease in pitch, while, on the contrary, increasing ionic strength from 0 to 10 mm leads to a 39% increase in pitch. The present study provides an approach to obtain controllable chiral nematic structures from HEWL amyloid fibrils, and may contribute further to the application of protein-based liquid crystals in pitch-sensitive biosensors or biomimetic architectures.

Capillarity in Interfacial Liquids and Marbles: Mechanisms, Properties, and Applications

The mechanics of capillary force in biological systems have critical roles in the formation of the intra- and inter-cellular structures, which may mediate the organization, morphogenesis, and homeostasis of biomolecular condensates. Current techniques may not allow direct and precise measurements of the capillary forces at the intra- and inter-cellular scales. By preserving liquid droplets at the liquid-liquid interface, we have discovered and studied ideal models, i.e., interfacial liquids and marbles, for understanding general capillary mechanics that existed in liquid-in-liquid systems, e.g., biomolecular condensates. The unexpectedly long coalescence time of the interfacial liquids revealed that the Stokes equation does not hold as the radius of the liquid bridge approaches zero, evidencing the existence of a third inertially limited viscous regime. Moreover, liquid transport from a liquid droplet to a liquid reservoir can be prohibited by coating the droplet surface with hydrophobic or amphiphilic particles, forming interfacial liquid marbles. Unique characteristics, including high stability, transparency, gas permeability, and self-assembly, are observed for the interfacial liquid marbles. Phase transition and separation induced by the formation of nanostructured materials can be directly observed within the interfacial liquid marbles without the need for surfactants and agitation, making them useful tools to research the interfacial mechanics.

Spa2 remodels ADP-actin via molecular condensation under glucose starvation

Actin nucleotide-dependent actin remodeling is essential to orchestrate signal transduction and cell adaptation. Rapid energy starvation requires accurate and timely reorganization of the actin network. Despite distinct treadmilling mechanisms of ADP- and ATP-actin filaments, their filament structures are nearly identical. How other actin-binding proteins regulate ADP-actin filament assembly is unclear. Here, we show that Spa2 which is the polarisome scaffold protein specifically remodels ADP-actin upon energy starvation in budding yeast. Spa2 triggers ADP-actin monomer nucleation rapidly through a dimeric core of Spa2 (aa 281-535). Concurrently, the intrinsically disordered region (IDR, aa 1-281) guides Spa2 undergoing phase separation and wetting on the surface of ADP-G-actin-derived F-actin and bundles the filaments. Both ADP-actin-specific nucleation and bundling activities of Spa2 are actin D-loop dependent. The IDR and nucleation core of Spa2 are evolutionarily conserved by coexistence in the fungus kingdom, suggesting a universal adaptation mechanism in the fungal kingdom in response to glucose starvation, regulating ADP-G-actin and ADP-F-actin with high nucleotide homogeneity.

Dynamics of elongation of nematic tactoids in an electric field

Nematic tactoids are spindle-shaped droplets of a nematic phase nucleated in the co-existing isotropic phase. According to equilibrium theory, their internal structure and shape are controlled by a balance between the elastic deformation of the director field, induced by the preferred anchoring of that director field to the interface, and the interfacial free energy. Recent experiments on tactoids of chitin nanocrystals dispersed in water show that electrical fields can very strongly elongate tactoids, at least if the tactoids are sufficiently large in volume. However, this observation contradicts the predictions of equilibrium theory as well as findings from Monte Carlo simulations that do not show this kind of extreme elongation to take place at all. To explain this, we put forward a relaxational model based on the Oseen-Frank free energy of elastic deformation of a director field coupled to an anisotropic surface free energy. In our model, we use two reaction coordinates to describe the director field and the extent of elongation of the droplets and evaluate the evolution of both as a function of time following the switching on of an electric field. Depending on the relative magnitude of the fundamental relaxation rates associated with the two reaction coordinates, we find that the aspect ratio of the drops may develop a large and very long-lived overshoot before eventually relaxing to the much smaller equilibrium value. In that case, the response of the curvature of the director field lags behind, explaining the experimental observations. Our theory describes the experimental data reasonably well.

Motor crosslinking augments elasticity in active nematics

In active materials, uncoordinated internal stresses lead to emergent long-range flows. An understanding of how the behavior of active materials depends on mesoscopic (hydrodynamic) parameters is developing, but there remains a gap in knowledge concerning how hydrodynamic parameters depend on the properties of microscopic elements. In this work, we combine experiments and multiscale modeling to relate the structure and dynamics of active nematics composed of biopolymer filaments and molecular motors to their microscopic properties, in particular motor processivity, speed, and valency. We show that crosslinking of filaments by both motors and passive crosslinkers not only augments the contributions to nematic elasticity from excluded volume effects but dominates them. By altering motor kinetics we show that a competition between motor speed and crosslinking results in a nonmonotonic dependence of nematic flow on motor speed. By modulating passive filament crosslinking we show that energy transfer into nematic flow is in large part dictated by crosslinking. Thus motor proteins both generate activity and contribute to nematic elasticity. Our results provide new insights for rationally engineering active materials.

Supramolecular polymers form tactoids through liquid-liquid phase separation

Liquid-liquid phase separation (LLPS) of biopolymers has recently been shown to play a central role in the formation of membraneless organelles with a multitude of biological functions1-3. The interplay between LLPS and macromolecular condensation is part of continuing studies4,5. Synthetic supramolecular polymers are the non-covalent equivalent of macromolecules but they are not reported to undergo LLPS yet. Here we show that continuously growing fibrils, obtained from supramolecular polymerizations of synthetic components, are responsible for phase separation into highly anisotropic aqueous liquid droplets (tactoids) by means of an entropy-driven pathway. The crowding environment, regulated by dextran concentration, affects not only the kinetics of supramolecular polymerizations but also the properties of LLPS, including phase-separation kinetics, morphology, internal order, fluidity and mechanical properties of the final tactoids. In addition, substrate-liquid and liquid-liquid interfaces proved capable of accelerating LLPS of supramolecular polymers, allowing the generation of a myriad of three-dimensional-ordered structures, including highly ordered arrays of micrometre-long tactoids at surfaces. The generality and many possibilities of supramolecular polymerizations to control emerging morphologies are demonstrated with several supramolecular polymers, opening up a new field of matter ranging from highly structured aqueous solutions by means of stabilized LLPS to nanoscopic soft matter.

Subtle Molecular Changes Largely Modulate Chiral Helical Assemblies of Achiral Conjugated Polymers by Tuning Solution-State Aggregation

Understanding the solution-state aggregate structure and the consequent hierarchical assembly of conjugated polymers is crucial for controlling multiscale morphologies during solid thin-film deposition and the resultant electronic properties. However, it remains challenging to comprehend detailed solution aggregate structures of conjugated polymers, let alone their chiral assembly due to the complex aggregation behavior. Herein, we present solution-state aggregate structures and their impact on hierarchical chiral helical assembly using an achiral diketopyrrolopyrrole-quaterthiophene (DPP-T4) copolymer and its two close structural analogues wherein the bithiophene is functionalized with methyl groups (DPP-T2M2) or fluorine atoms (DPP-T2F2). Combining in-depth small-angle X-ray scattering analysis with various microscopic solution imaging techniques, we find distinct aggregate in each DPP solution: (i) semicrystalline 1D fiber aggregates of DPP-T2F2 with a strongly bound internal structure, (ii) semicrystalline 1D fiber aggregates of DPP-T2M2 with a weakly bound internal structure, and (iii) highly crystalline 2D sheet aggregates of DPP-T4. These nanoscopic aggregates develop into lyotropic chiral helical liquid crystal (LC) mesophases at high solution concentrations. Intriguingly, the dimensionality of solution aggregates largely modulates hierarchical chiral helical pitches across nanoscopic to micrometer scales, with the more rigid 2D sheet aggregate of DPP-T4 creating much larger pitch length than the more flexible 1D fiber aggregates. Combining relatively small helical pitch with long-range order, the striped twist-bent mesophase of DPP-T2F2 composed of highly ordered, more rigid 1D fiber aggregate exhibits an anisotropic dissymmetry factor (g-factor) as high as 0.09. This study can be a prominent addition to our knowledge on a solution-state hierarchical assembly of conjugated polymers and, in particular, chiral helical assembly of achiral organic semiconductors that can catalyze an emerging field of chiral (opto)electronics.

How it feels in a cell

Life emerges from thousands of biochemical processes occurring within a shared intracellular environment. We have gained deep insights from in vitro reconstitution of isolated biochemical reactions. However, the reaction medium in test tubes is typically simple and diluted. The cell interior is far more complex: macromolecules occupy more than a third of the space, and energy-consuming processes agitate the cell interior. Here, we review how this crowded, active environment impacts the motion and assembly of macromolecules, with an emphasis on mesoscale particles (10-1000 nm diameter). We describe methods to probe and analyze the biophysical properties of cells and highlight how changes in these properties can impact physiology and signaling, and potentially contribute to aging, and diseases, including cancer and neurodegeneration.

Motor-free contractility of active biopolymer networks

Contractility in animal cells is often generated by molecular motors such as myosin, which require polar substrates for their function. Motivated by recent experimental evidence of motor-independent contractility, we propose a robust motor-free mechanism that can generate contraction in biopolymer networks without the need for substrate polarity. We show that contractility is a natural consequence of active binding-unbinding of crosslinkers that breaks the principle of detailed balance, together with the asymmetric force-extension response of semiflexible biopolymers. We have extended our earlier work to discuss the motor-free contraction of viscoelastic biopolymer networks. We calculate the resulting contractile velocity using a microscopic model and show that it can be reduced to a simple coarse-grained model under certain limits. Our model may provide an explanation of recent reports of motor-independent contractility in cells. Our results also suggest a mechanism for generating contractile forces in synthetic active materials.

Anillin forms linear structures and facilitates furrow ingression after septin and formin depletion

During cytokinesis, a contractile ring consisting of unbranched filamentous actin (F-actin) and myosin II constricts at the cell equator. Unbranched F-actin is generated by formin, and without formin no cleavage furrow forms. In Caenorhabditis elegans, depletion of septin restores furrow ingression in formin mutants. How the cleavage furrow ingresses without a detectable unbranched F-actin ring is unknown. We report that, in this setting, anillin (ANI-1) forms a meshwork of circumferentially aligned linear structures decorated by non-muscle myosin II (NMY-2). Analysis of ANI-1 deletion mutants reveals that its disordered N-terminal half is required for linear structure formation and sufficient for furrow ingression. NMY-2 promotes the circumferential alignment of the linear ANI-1 structures and interacts with various lipids, suggesting that NMY-2 links the ANI-1 network with the plasma membrane. Collectively, our data reveal a compensatory mechanism, mediated by ANI-1 linear structures and membrane-bound NMY-2, that promotes furrowing when unbranched F-actin polymerization is compromised.

Contractility-induced self-organization of smooth muscle cells: from multilayer cell sheets to dynamic three-dimensional clusters

Smooth muscle cells (SMCs) are mural cells that play a vital contractile function in many tissues. Abnormalities in SMC organization are associated with many diseases including atherosclerosis, asthma, and uterine fibroids. Various studies have reported that SMCs cultured on flat surfaces can spontaneously form three-dimensional clusters whose organization resembles that encountered in some of these pathological settings. Remarkably, how these structures form remains unknown. Here we combine in vitro experiments and physical modeling to show that three-dimensional clusters initiate when cellular contractile forces induce a hole in a flat SMC sheet, a process that can be modeled as the brittle fracture of a viscoelastic material. The subsequent evolution of the nascent cluster can be modeled as an active dewetting process with cluster shape evolution driven by a balance between cluster surface tension, arising from both cell contractility and adhesion, and cluster viscous dissipation. The description of the physical mechanisms governing the spontaneous emergence of these intriguing three-dimensional clusters may offer insight into SMC-related disorders.

Biomolecular condensation involving the cytoskeleton

Biomolecular condensation of proteins contributes to the organization of the cytoplasm and nucleoplasm. A number of condensation processes appear to be directly involved in regulating the structure, function and dynamics of the cytoskeleton. Liquid-liquid phase separation of cytoskeleton proteins, together with polymerization modulators, promotes cytoskeletal fiber nucleation and branching. Furthermore, the attachment of protein condensates to the cytoskeleton can contribute to cytoskeleton stability and organization, regulate transport, create patterns of functional reaction containers, and connect the cytoskeleton with membranes. Surface-bound condensates can exert and buffer mechanical forces that give stability and flexibility to the cytoskeleton, thus, may play a large role in cell biology. In this review, we introduce the concept and role of cellular biomolecular condensation, explain its special function on cytoskeletal fiber surfaces, and point out potential definition and experimental caveats. We review the current literature on protein condensation processes related to the actin, tubulin, and intermediate filament cytoskeleton, and discuss some of them in the context of neurobiology. In summary, we provide an overview about biomolecular condensation in relation to cytoskeleton structure and function, which offers a base for the exploration and interpretation of cytoskeletal condensates in neurobiology.

Multiscale Modeling of Protein-RNA Condensation in and Out of Equilibrium

A vast number of intracellular membraneless bodies also known as biomolecular condensates form through a liquid-liquid phase separation (LLPS) of biomolecules. To date, phase separation has been identified as the main driving force for a membraneless organelles such as nucleoli, Cajal bodies, stress granules, and chromatin compartments. Recently, the protein-RNA condensation is receiving increased attention, because it is closely related to the biological function of cells such as transcription, translation, and RNA metabolism. Despite the multidisciplinary efforts put forth to study the biophysical properties of protein-RNA condensates, there are many fundamental unanswered questions regarding the mechanism of formation and regulation of protein-RNA condensates in eukaryotic cells. Major challenges in studying protein-RNA condensation stem from (i) the molecular heterogeneity and conformational flexibility of RNA and protein chains and (ii) the nonequilibrium nature of transcription and cellular environment. Computer simulations, bioinformatics, and mathematical models are uniquely positioned for shedding light on the microscopic nature of protein-RNA phase separation. To this end, there is an urgent need for innovative models with the right spatiotemporal resolution for confronting the experimental observables in a comprehensive and physics-based manner. In this chapter, we will summarize the currently emerging research efforts, which employ atomistic and coarse-grained molecular models and field theoretical models to understand equilibrium and nonequilibrium aspects of protein-RNA condensation.

Direct Measurement of Solid-Liquid Interfacial Energy Using a Meniscus

Solid-liquid interactions are central to diverse processes. The interaction strength can be described by the solid-liquid interfacial free energy (γ_{SL}), a quantity that is difficult to measure. Here, we present the direct experimental measurement of γ_{SL} for a variety of solid materials, from nonpolar polymers to highly wetting metals. By attaching a thin solid film on top of a liquid meniscus, we create a solid-liquid interface. The interface determines the curvature of the meniscus, analysis of which yields γ_{SL} with an uncertainty of less than 10%. Measurement of classically challenging metal-water interfaces reveals γ_{SL}∼30-60  mJ/m^{2}, demonstrating quantitatively that water-metal adhesion is 80% stronger than the cohesion energy of bulk water, and experimentally verifying previous quantum chemical calculations.

Kinetochore- and chromosome-driven transition of microtubules into bundles promotes spindle assembly

Mitotic spindle assembly is crucial for chromosome segregation and relies on bundles of microtubules that extend from the poles and overlap in the middle. However, how these structures form remains poorly understood. Here we show that overlap bundles arise through a network-to-bundles transition driven by kinetochores and chromosomes. STED super-resolution microscopy reveals that PRC1-crosslinked microtubules initially form loose arrays, which become rearranged into bundles. Kinetochores promote microtubule bundling by lateral binding via CENP-E/kinesin-7 in an Aurora B-regulated manner. Steric interactions between the bundle-associated chromosomes at the spindle midplane drive bundle separation and spindle widening. In agreement with experiments, theoretical modeling suggests that bundles arise through competing attractive and repulsive mechanisms. Finally, perturbation of overlap bundles leads to inefficient correction of erroneous kinetochore-microtubule attachments. Thus, kinetochores and chromosomes drive coarsening of a uniform microtubule array into overlap bundles, which promote not only spindle formation but also chromosome segregation fidelity.

The coilin N-terminus mediates multivalent interactions between coilin and Nopp140 to form and maintain Cajal bodies

Cajal bodies (CBs) are ubiquitous nuclear membraneless organelles (MLOs) that concentrate and promote efficient biogenesis of snRNA-protein complexes involved in splicing (snRNPs). Depletion of the CB scaffolding protein coilin disperses snRNPs, making CBs a model system for studying the structure and function of MLOs. Although it is assumed that CBs form through condensation, the biomolecular interactions responsible remain elusive. Here, we discover the unexpected capacity of coilin’s N-terminal domain (NTD) to form extensive fibrils in the cytoplasm and discrete nuclear puncta in vivo. Single amino acid mutational analysis reveals distinct molecular interactions between coilin NTD proteins to form fibrils and additional NTD interactions with the nuclear Nopp140 protein to form puncta. We provide evidence that Nopp140 has condensation capacity and is required for CB assembly. From these observations, we propose a model in which coilin NTD–NTD mediated assemblies make multivalent contacts with Nopp140 to achieve biomolecular condensation in the nucleus.

Cajal bodies are membraneless organelles scaffolded by coilin protein. Here, coilin–coilin and coilin–Nopp140 interaction sites are identified and perturbed, revealing coilin’s capacity to form long fibrils and be remodeled into spherical structures.

Nucleation causes an actin network to fragment into multiple high-density domains

Actin networks rely on nucleation mechanisms to generate new filaments because spontaneous nucleation is kinetically disfavored. Branching nucleation of actin filaments by actin-related protein (Arp2/3), in particular, is critical for actin self-organization. In this study, we use the simulation platform for active matter MEDYAN to generate 2000 s long stochastic trajectories of actin networks, under varying Arp2/3 concentrations, in reaction volumes of biologically meaningful size (>20 μm3). We find that the dynamics of Arp2/3 increase the abundance of short filaments and increases network treadmilling rate. By analyzing the density fields of F-actin, we find that at low Arp2/3 concentrations, F-actin is organized into a single connected and contractile domain, while at elevated Arp2/3 levels (10 nM and above), such high-density actin domains fragment into smaller domains spanning a wide range of volumes. These fragmented domains are extremely dynamic, continuously merging and splitting, owing to the high treadmilling rate of the underlying actin network. Treating the domain dynamics as a drift-diffusion process, we find that the fragmented state is stochastically favored, and the network state slowly drifts toward the fragmented state with considerable diffusion (variability) in the number of domains. We suggest that tuning the Arp2/3 concentration enables cells to transition from a globally coherent cytoskeleton, whose response involves the entire cytoplasmic network, to a fragmented cytoskeleton, where domains can respond independently to locally varying signals.

Leveraging ultra-low interfacial tension and liquid-liquid phase separation in embedded 3D bioprinting

Many recently developed 3D bioprinting strategies operate by extruding aqueous biopolymer solutions directly into a variety of different support materials constituted from swollen, solvated, aqueous, polymer assemblies. In developing these 3D printing methods and materials, great care is often taken to tune the rheological behaviors of both inks and 3D support media. By contrast, much less attention has been given to the physics of the interfaces created when structuring one polymer phase into another in embedded 3D printing applications. For example, it is currently unclear whether a dynamic interfacial tension between miscible phases stabilizes embedded 3D bioprinted structures as they are shaped while in a liquid state. Interest in the physics of interfaces between complex fluids has grown dramatically since the discovery of liquid-liquid phase separation (LLPS) in living cells. We believe that many new insights coming from this burst of investigation into LLPS within biological contexts can be leveraged to develop new materials and methods for improved 3D bioprinting that leverage LLPS in mixtures of biopolymers, biocompatible synthetic polymers, and proteins. Thus, in this review article, we highlight work at the interface between recent LLPS research and embedded 3D bioprinting methods and materials, and we introduce a 3D bioprinting method that leverages LLPS to stabilize printed biopolymer inks embedded in a bioprinting support material.

Capillary forces generated by biomolecular condensates

Liquid-liquid phase separation and related phase transitions have emerged as generic mechanisms in living cells for the formation of membraneless compartments or biomolecular condensates. The surface between two immiscible phases has an interfacial tension, generating capillary forces that can perform work on the surrounding environment. Here we present the physical principles of capillarity, including examples of how capillary forces structure multiphase condensates and remodel biological substrates. As with other mechanisms of intracellular force generation, for example, molecular motors, capillary forces can influence biological processes. Identifying the biomolecular determinants of condensate capillarity represents an exciting frontier, bridging soft matter physics and cell biology.

Formation of actin-cofilin rods by depletion forces

Various stress conditions induce the formation of actin-cofilin rods in either the nucleus or the cytoplasm, although the mechanism of rod formation is unclear. In this study, we constituted actin-cofilin rods using purified actin, cofilin and actin interacting protein 1 (AIP1) in the presence of a physiological buffer containing a crowding agent, 0.8% methylcellulose (MC), which led to bundled actin filaments formed by depletion forces. Most of the F-actin bundles formed with methylcellulose were linear, whereas cofilin-bound F-actin bundles often had bent, looped, and often ring-like shapes. Increasing the amount of AIP1 shortened actin-cofilin bundles into rod-like bundles with tapering at both ends. As much shorter actin-cofilin filaments were formed in the presence of AIP1 before MC was added to the mixture, the rod-like bundle might be a mass of those short filaments. Furthermore, the small rods fused with each other to become larger rods, indicating that these rods were anisotropic liquid droplets. Several minutes after the addition of MC to the F-actin-cofilin-AIP1 mixture, we observed some long bundles in which the thick and thin parts appear alternately, reminiscent of a Plateau-Rayleigh instability observed in fluid columns. Simultaneously, we found images in which thin parts were interrupted, but the thick parts were arranged in a row in the longitudinal direction. These structures were also observed in cytoplasmic actin-cofilin rods in cells overexpressing cofilin-GFP, suggesting that cytoplasmic actin-cofilin rods have the same structure formation process as the rods reconstituted in vitro.

Catapulting of topological defects through elasticity bands in active nematics

Active materials are those in which individual, uncoordinated local stresses drive the material out of equilibrium on a global scale. Examples of such assemblies can be seen across scales from schools of fish to the cellular cytoskeleton and underpin many important biological processes. Synthetic experiments that recapitulate the essential features of such active systems have been the object of study for decades as their simple rules allow us to elucidate the physical underpinnings of collective motion. One system of particular interest has been active nematic liquid crystals (LCs). Because of their well understood passive physics, LCs provide a rich platform to interrogate the effects of active stress. The flows and steady state structures that emerge in an active LCs have been understood to result from a competition between nematic elasticity and the local activity. However most investigations of such phenomena consider only the magnitude of the elastic resistance and not its peculiarities. Here we investigate a nematic liquid crystal and selectively change the ratio of the material's splay and bend elasticities. We show that increases in the nematic's bend elasticity specifically drives the material into an exotic steady state where elongated regions of acute bend distortion or "elasticity bands" dominate the structure and dynamics. We show that these bands strongly influence defect dynamics, including the rapid motion or "catapulting" along the disintegration of one of these bands thus converting bend distortion into defect transport. Thus, we report a novel dynamical state resultant from the competition between nematic elasticity and active stress.

Active condensation of filaments under spatial confinement

Living systems exhibit self-organization, a phenomenon that enables organisms to perform functions essential for life. The interior of living cells is a crowded environment in which the self-assembly of cytoskeletal networks is spatially constrained by membranes and organelles. Cytoskeletal filaments undergo active condensation in the presence of crosslinking motor proteins. In past studies, confinement has been shown to alter the morphology of active condensates. Here, we perform simulations to explore systems of filaments and crosslinking motors in a variety of confining geometries. We simulate spatial confinement imposed by hard spherical, cylindrical, and planar boundaries. These systems exhibit non-equilibrium condensation behavior where crosslinking motors condense a fraction of the overall filament population, leading to coexistence of vapor and condensed states. We find that the confinement lengthscale modifies the dynamics and condensate morphology. With end-pausing crosslinking motors, filaments self-organize into half asters and fully-symmetric asters under spherical confinement, polarity-sorted bilayers and bottle-brush-like states under cylindrical confinement, and flattened asters under planar confinement. The number of crosslinking motors controls the size and shape of condensates, with flattened asters becoming hollow and ring-like for larger motor number. End pausing plays a key role affecting condensate morphology: systems with end-pausing motors evolve into aster-like condensates while those with non-end-pausing crosslinking motor proteins evolve into disordered clusters and polarity-sorted bundles.

Screening membraneless organelle participants with machine-learning models that integrate multimodal features

Protein self-assembly is one of the formation mechanisms of biomolecular condensates. However, most phase-separating systems (PS) demand multiple partners in biological conditions. In this study, we divided PS proteins into two groups according to the mechanism by which they undergo PS: PS-Self proteins can self-assemble spontaneously to form droplets, while PS-Part proteins interact with partners to undergo PS. Analysis of the amino acid composition revealed differences in the sequence pattern between the two protein groups. Existing PS predictors, when evaluated on two test protein sets, preferentially predicted self-assembling proteins. Thus, a comprehensive predictor is required. Herein, we propose that properties other than sequence composition can provide crucial information in screening PS proteins. By incorporating phosphorylation frequencies and immunofluorescence image-based droplet-forming propensity with other PS-related features, we built two independent machine-learning models to separately predict the two protein categories. Results of independent testing suggested the superiority of integrating multimodal features. We performed experimental verification on the top-scored proteins DHX9, K_i-67, and NIFK. Their PS behavior in vitro revealed the effectiveness of our models in PS prediction. Further validation on the proteome of membraneless organelles confirmed the ability of our models to identify PS-Part proteins. We implemented a web server named PhaSePred (http://predict.phasep.pro/) that incorporates our two models together with representative PS predictors. PhaSePred displays proteome-level quantiles of different features, thus profiling PS propensity and providing crucial information for identification of candidate proteins.

Progress on Crowding Effect in Cell-like Structures

Several biological macromolecules, such as proteins, nucleic acids, and polysaccharides, occupy about 30% of the space in cells, resulting in a crowded macromolecule environment. The crowding effect within cells exerts an impact on the functions of biological components, the assembly behavior of biomacromolecules, and the thermodynamics and kinetics of metabolic reactions. Cell-like structures provide confined and independent compartments for studying the working mechanisms of cells, which can be used to study the physiological functions arising from the crowding effect of macromolecules in cells. This article mainly summarizes the progress of research on the macromolecular crowding effects in cell-like structures. It includes the effects of this crowding on actin assembly behavior, tubulin aggregation behavior, and gene expression. The challenges and future trends in this field are presented at the end of the paper.

Shape and structural relaxation of colloidal tactoids

Facile geometric-structural response of liquid crystalline colloids to external fields enables many technological advances. However, the relaxation mechanisms for liquid crystalline colloids under mobile boundaries remain still unexplored. Here, by combining experiments, numerical simulations and theory, we describe the shape and structural relaxation of colloidal liquid crystalline micro-droplets, called tactoids, where amyloid fibrils and cellulose nanocrystals are used as model systems. We show that tactoids shape relaxation bears a universal single exponential decay signature and derive an analytic expression to predict this out of equilibrium process, which is governed by liquid crystalline anisotropic and isotropic contributions. The tactoids structural relaxation shows fundamentally different paths, with first- and second-order exponential decays, depending on the existence of splay/bend/twist orientation structures in the ground state. Our findings offer a comprehensive understanding on dynamic confinement effects in liquid crystalline colloidal systems and may set unexplored directions in the development of novel responsive materials.

Tactoids, consisting of micro-confined liquid crystalline colloids with self-selected shape, bear both fundamental and technological significance. The authors show that the shape relaxation of tactoids follows an exponential decay and develop a model to predict this out-of-the-equilibrium process.

Purine biosynthetic enzymes assemble into liquid-like condensates dependent on the activity of chaperone protein HSP90

Enzymes within the de novo purine biosynthetic pathway spatially organize into dynamic intracellular assemblies called purinosomes. The formation of purinosomes has been correlated with growth conditions resulting in high purine demand, and therefore, the cellular advantage of complexation has been hypothesized to enhance metabolite flux through the pathway. However, the properties of this cellular structure are unclear. Here, we define the purinosome in a transient expression system as a biomolecular condensate using fluorescence microscopy. We show that purinosomes, as denoted by formylglycinamidine ribonucleotide synthase granules in purine-depleted HeLa cells, are spherical and appear to coalesce when two come into contact, all liquid-like characteristics that are consistent with previously reported condensates. We further explored the biophysical and biochemical means that drive the liquid-liquid phase separation of these structures. We found that the process of enzyme condensation into purinosomes is likely driven by the oligomeric state of the pathway enzymes and not a result of intrinsic disorder, the presence of low-complexity domains, the assistance of RNA scaffolds, or changes in intracellular pH. Finally, we demonstrate that the heat shock protein 90 KDa helps to regulate the physical properties of the condensate and maintain their liquid-like state inside HeLa cells. We show that disruption of heat shock protein 90 KDa activity induced the transformation of formylglycinamidine ribonucleotide synthase clusters into more irregularly shaped condensates, suggesting that its chaperone activity is essential for purinosomes to retain their liquid-like properties. This refined view of the purinosome offers new insight into how metabolic enzymes spatially organize into dynamic condensates within human cells.

Structure of nematic tactoids of hard rods

We study by means of Monte Carlo simulations the internal structure of nematic droplets or tactoids formed by hard, rod-like particles in a gas of spherical ghost particles that act as depletion agents for the rods. We find that the shape and internal structure of tactoids are strongly affected by the size of the droplets. The monotonically increasing degree of nematic order with increasing particle density that characterizes the bulk nematic phase is locally violated and more so the smaller the tactoid. We also investigate the impact of an external quadrupolar alignment field on tactoids and find that this tends to make the director field more uniform, but not to very significantly increase the tactoid’s aspect ratio. This agrees with recent theoretical predictions yet is at variance with experimental observations and dynamical simulations. We explain this discrepancy in terms of competing relaxation times.

Essence determines phenomenon: Assaying the material properties of biological condensates

Intracellular spaces are partitioned into separate compartments to ensure that numerous biochemical reactions and cellular functions take place in a spatiotemporally controlled manner. Biomacromolecules including proteins and RNAs undergo liquid–liquid phase separation and subsequent phase transition to form biological condensates with diverse material states. The material/physical properties of biological condensates are crucial for fulfilling their distinct physiological functions, and abnormal material properties can cause deleterious effects under pathological conditions. Here, we review recent studies showing the role of the material properties of biological condensates in their physiological functions. We also summarize several classic methods as well as newly emerging techniques for characterization and/or measurement of the material properties of biological condensates.

Interplay between Brownian motion and cross-linking kinetics controls bundling dynamics in actin networks

Morphology changes in cross-linked actin networks are important in cell motility, division, and cargo transport. Here, we study the transition from a weakly cross-linked network of actin filaments to a heavily cross-linked network of actin bundles through microscopic Brownian dynamics simulations. We show that this transition occurs in two stages: first, a composite bundle network of small and highly aligned bundles evolves from cross-linking of individual filaments and, second, small bundles coalesce into the clustered bundle state. We demonstrate that Brownian motion speeds up the first stage of this process at a faster rate than the second. We quantify the time to reach the composite bundle state and show that it strongly increases as the mesh size increases only when the concentration of cross-links is small and that it remains roughly constant if we decrease the relative ratio of cross-linkers as we increase the actin concentration. Finally, we examine the dependence of the bundling timescale on filament length, finding that shorter filaments bundle faster because they diffuse faster.

Toward the cellular-scale simulation of motor-driven cytoskeletal assemblies

The cytoskeleton - a collection of polymeric filaments, molecular motors, and crosslinkers - is a foundational example of active matter, and in the cell assembles into organelles that guide basic biological functions. Simulation of cytoskeletal assemblies is an important tool for modeling cellular processes and understanding their surprising material properties. Here, we present aLENS (a Living Ensemble Simulator), a novel computational framework designed to surmount the limits of conventional simulation methods. We model molecular motors with crosslinking kinetics that adhere to a thermodynamic energy landscape, and integrate the system dynamics while efficiently and stably enforcing hard-body repulsion between filaments. Molecular potentials are entirely avoided in imposing steric constraints. Utilizing parallel computing, we simulate tens to hundreds of thousands of cytoskeletal filaments and crosslinking motors, recapitulating emergent phenomena such as bundle formation and buckling. This simulation framework can help elucidate how motor type, thermal fluctuations, internal stresses, and confinement determine the evolution of cytoskeletal active matter.

Simulations of dynamically cross-linked actin networks: Morphology, rheology, and hydrodynamic interactions

Cross-linked actin networks are the primary component of the cell cytoskeleton and have been the subject of numerous experimental and modeling studies. While these studies have demonstrated that the networks are viscoelastic materials, evolving from elastic solids on short timescales to viscous fluids on long ones, questions remain about the duration of each asymptotic regime, the role of the surrounding fluid, and the behavior of the networks on intermediate timescales. Here we perform detailed simulations of passively cross-linked non-Brownian actin networks to quantify the principal timescales involved in the elastoviscous behavior, study the role of nonlocal hydrodynamic interactions, and parameterize continuum models from discrete stochastic simulations. To do this, we extend our recent computational framework for semiflexible filament suspensions, which is based on nonlocal slender body theory, to actin networks with dynamic cross linkers and finite filament lifetime. We introduce a model where the cross linkers are elastic springs with sticky ends stochastically binding to and unbinding from the elastic filaments, which randomly turn over at a characteristic rate. We show that, depending on the parameters, the network evolves to a steady state morphology that is either an isotropic actin mesh or a mesh with embedded actin bundles. For different degrees of bundling, we numerically apply small-amplitude oscillatory shear deformation to extract three timescales from networks of hundreds of filaments and cross linkers. We analyze the dependence of these timescales, which range from the order of hundredths of a second to the actin turnover time of several seconds, on the dynamic nature of the links, solvent viscosity, and filament bending stiffness. We show that the network is mostly elastic on the short time scale, with the elasticity coming mainly from the cross links, and viscous on the long time scale, with the effective viscosity originating primarily from stretching and breaking of the cross links. We show that the influence of nonlocal hydrodynamic interactions depends on the network morphology: for homogeneous meshworks, nonlocal hydrodynamics gives only a small correction to the viscous behavior, but for bundled networks it both hinders the formation of bundles and significantly lowers the resistance to shear once bundles are formed. We use our results to construct three-timescale generalized Maxwell models of the networks.

Shape bistability in 2D chromonic droplets

An extensive experimental study of the shapes of two-dimensional bipolar droplets of the chromonic nematic phase of disodium cromoglycate (DSCG) sandwiched between glass plates, by Kimet alwas published in (2013J. Phys.: Condens. Matter25404202). The paper includes a mathematical model of this system. We have extended this study by further theoretical modelling. Our results are in good, quantitative agreement with the experimental data. The model has produced what promises to be a more accurate estimate for the isotropic surface tension at the nematic/isotropic solution interface-and predicts a regime of shape bistability (which has not yet been observed) for larger droplets, where tactoids (pointed, zeppelin-shaped droplets) and smooth-edged discoids can coexist in equilibrium. The general method presented in this paper is also applied to the tactoids formed by F-actin filaments in solution, for which an estimate is given for the value of the isotropic surface tension at the nematic/isotropic interface.

Phase Separation and Mechanical Forces in Regulating Asymmetric Cell Division of Neural Stem Cells

Asymmetric cell division (ACD) of neural stem cells and progenitors not only renews the stem cell population but also ensures the normal development of the nervous system, producing various types of neurons with different shapes and functions in the brain. One major mechanism to achieve ACD is the asymmetric localization and uneven segregation of intracellular proteins and organelles into sibling cells. Recent studies have demonstrated that liquid-liquid phase separation (LLPS) provides a potential mechanism for the formation of membrane-less biomolecular condensates that are asymmetrically distributed on limited membrane regions. Moreover, mechanical forces have emerged as pivotal regulators of asymmetric neural stem cell division by generating sibling cell size asymmetry. In this review, we will summarize recent discoveries of ACD mechanisms driven by LLPS and mechanical forces.

Mechanics of neural tube morphogenesis

The neural tube is an important model system of morphogenesis representing the developmental module of out-of-plane epithelial deformation. As the embryonic precursor of the central nervous system, the neural tube also holds keys to many defects and diseases. Recent advances begin to reveal how genetic, cellular and environmental mechanisms work in concert to ensure correct neural tube shape. A physical model is emerging where these factors converge at the regulation of the mechanical forces and properties within and around the tissue that drive tube formation towards completion. Here we review the dynamics and mechanics of neural tube morphogenesis and discuss the underlying cellular behaviours from the viewpoint of tissue mechanics. We will also highlight some of the conceptual and technical next steps.

Modeling spatiotemporally varying protein-protein interactions in CyLaKS, the Cytoskeleton Lattice-based Kinetic Simulator

Interaction of cytoskeletal filaments, motor proteins, and crosslinking proteins drives important cellular processes such as cell division and cell movement. Cytoskeletal networks also exhibit nonequilibrium self-assembly in reconstituted systems. An emerging problem in cytoskeletal modeling and simulation is spatiotemporal alteration of the dynamics of filaments, motors, and associated proteins. This can occur due to motor crowding, obstacles along the filament, motor interactions and direction switching, and changes, defects, or heterogeneity in the filament binding lattice. How such spatiotemporally varying cytoskeletal filaments and motor interactions affect their collective properties is not fully understood. We developed the Cytoskeleton Lattice-based Kinetic Simulator (CyLaKS) to investigate such problems. The simulation model builds on previous work by incorporating motor mechanochemistry into a simulation with many interacting motors and/or associated proteins on a discretized lattice. CyLaKS also includes detailed balance in binding kinetics, movement, and lattice heterogeneity. The simulation framework is flexible and extensible for future modeling work and is available on GitHub for others to freely use or build upon. Here we illustrate the use of CyLaKS to study long-range motor interactions, microtubule lattice heterogeneity, motion of a heterodimeric motor, and how changing crosslinker number affects filament separation.