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The cell membrane defines the shape of the cell and plays an indispensable role in bridging intra- and extra-cellular environments. The membrane, consisting of a lipid bilayer and various attaching proteins, mechanochemically interacts with the active cytoskeletal network that dynamically self-organizes, playing a vital role in cellular biomechanics and mechanosensing. Comprehensive simulations of membrane-cytoskeleton dynamics can bring insight in understanding how the cell mechanochemically responds to external signals, but a computational model that captures the complex cytoskeleton-membrane with both refined details and computational efficiency is lacking. To address this, we introduce in this thesis a triangulated membrane model and incorporate it with the active biological matter simulation platform MEDYAN ("Mechanochemical Dynamics of Active Networks"). This model accurately captures the membrane physical properties, showing how the membrane rigidity, the structure of actin networks and local chemical environments regulate the membrane deformations. Then, we present a new method for simulating membrane proteins, using stochastic reaction-diffusion sampling on unstructured membrane meshes. By incorporating a surface potential energy field into the reaction-diffusion sampling, we demonstrate rich membrane protein collective behaviors such as confined diffusion, liquid-liquid phase separation and membrane curvature sensing. Finally, in order to capture stretching, bending, shearing and twisting of actin filaments which are not all available with traditional actomyosin simulations, we introduce new finite-radius filament models based off Cosserat theory of elastic rods, with efficient implementation using finite-dimensional configurational spaces. Using the new filament models, we show that the filaments' torsional compliance can induce chiral symmetry breaking in a cross-linked actin bundle. All the new models are implemented in the MEDYAN platform, shedding lig

In most eukaryotic cells, actin filaments assemble into a shell-like actin cortex under the plasma membrane, controlling cellular morphology, mechanics, and signaling. The actin cortex is highly polymorphic, adopting diverse forms such as the ring-like structures found in podosomes, axonal rings, and immune synapses. The biophysical principles that underlie the formation of actin rings and cortices remain unknown. Using a molecular simulation platform, called MEDYAN, we discovered that varying the filament treadmilling rate and myosin concentration induces a finite size phase transition in actomyosin network structures. We found that actomyosin networks condense into clusters at low treadmilling rates or high myosin concentration but form ring-like or cortex-like structures at high treadmilling rates and low myosin concentration. This mechanism is supported by our corroborating experiments on live T cells, which exhibit ring-like actin networks upon activation by stimulatory antibody. Upon disruption of filament treadmilling or enhancement of myosin activity, the pre-existing actin rings are disrupted into actin clusters or collapse towards the network center respectively. Our analyses suggest that the ring-like actin structure is a preferred state of low mechanical energy, which is, importantly, only reachable at sufficiently high treadmilling rates.

The plasma membrane defines the shape of the cell and plays an indispensable role in bridging intra- and extra-cellular environments. Mechanochemical interactions between plasma membrane and cytoskeleton are vital for cell biomechanics and mechanosensing. A computational model that comprehensively captures the complex, cell-scale cytoskeleton-membrane dynamics is still lacking. In this work, we introduce a triangulated membrane model that accounts for membrane's elastic properties, as well as for membrane-filament steric interactions. The corresponding force-field was incorporated into the active biological matter simulation platform, MEDYAN ("Mechanochemical Dynamics of Active Networks"). Simulations using the new model shed light on how actin filament bundling affects generation of tubular membrane protrusions. In particular, we used membrane-MEDYAN simulations to investigate protrusion initiation and dynamics while varying geometries of filament bundles, membrane rigidities and local G-Actin concentrations. We found that bundles' protrusion propensities sensitively depend on the synergy between bundle thickness and inclination angle at which the bundle approaches the membrane. The new model paves the way for simulations of biological systems involving intricate membrane-cytoskeleton interactions, such as occurring at the leading edge and the cortex, eventually helping to uncover the fundamental principles underlying the active matter organization in the vicinity of the membrane.

Bundled actin structures play a key role in maintaining cellular shape, in aiding force transmission to and from extracellular substrates, and in affecting cellular motility. Recent studies have also brought to light new details on stress generation, force transmission and contractility of actin bundles. In this work, we are primarily interested in the question of what determines the stability of actin bundles and what network geometries do unstable bundles eventually transition to. To address this problem, we used the MEDYAN mechano-chemical force field, modeling several micron-long actin bundles in 3D, while accounting for a comprehensive set of chemical, mechanical and transport processes. We developed a hierarchical clustering algorithm for classification of the different long time scale morphologies in our study. Our main finding is that initially unipolar bundles are significantly more stable compared with an apolar initial configuration. Filaments within the latter bundles slide easily with respect to each other due to myosin activity, producing a loose network that can be subsequently severely distorted. At high myosin concentrations, a morphological transition to aster-like geometries was observed. We also investigated how actin treadmilling rates influence bundle dynamics, and found that enhanced treadmilling leads to network fragmentation and disintegration, while this process is opposed by myosin and crosslinking activities. Interestingly, treadmilling bundles with an initial apolar geometry eventually evolve to a whole gamut of network morphologies based on relative positions of filament ends, such as sarcomere-like organization. We found that apolar bundles show a remarkable sensitivity to environmental conditions, which may be important in enabling rapid cytoskeletal structural reorganization and adaptation in response to intracellular and extracellular cues.