A versatile framework for simulating the structure and dynamics of cytoskeletal networks
Project Leader: Ellie Hajizadeh
Primary Contact: Ellie Hajizadeh (firstname.lastname@example.org)
Keywords: biopolymers; cell mechanics; computational materials science; fluid dynamics; rheology
Disciplines: Biomedical Engineering,Chemical & Biomolecular Engineering,Mechanical Engineering
Mechanical properties of cells are tightly coupled with their biological functions. Therefore, cell mechanics significantly affects cellular behaviour and determines mechanical properties of supra-cellular structures such as tissues. We develop mechanical models of cells, which allow us to quantify experimental measurements and help us understand how different cellular structures contribute to the mechanical response and behaviour of biological cells.
Mechanical properties of biological cells are often measured by direct cell deformation, eg, by using microplate compression. However, quantitative interpretation of cell deformation is significantly complicated by the complex structure of biological cells, since they consist of a lipid membrane with an elastic cortex, bulk cytoskeleton, and organelles. Ideally, we have to be able to dissect the different contributions of cell properties to the observed deformation, including membrane elasticity and bending rigidity, cytoskeleton elasticity, and internal viscosity.
The actin cytoskeleton is a network of proteins that enables cells to control their shapes, exert forces internally and externally, and direct their movements. Globular actin proteins polymerise into polar filaments (F-actin) that are microns long and nano-meters thick. Many different proteins bind to actin filaments; such proteins often have multiple binding sites that enable them to cross-link actin filaments into networks that can transmit force. Myosin proteins are composed of head, neck, and tail domains and aggregate via their tails to form minifilaments that can attach multiple heads to actin filaments. Each myosin head can bind to actin and harness the energy from ATP hydrolysis such that a mini-filament can walk along an actin filament in a directed fashion—ie, it is a motor. These dynamics have been extensively studied. It is well understood, for example, how they give rise to muscle contraction. In muscle cells, myosin II minifilaments bind to regularly arrayed antiparallel actin filaments and walk toward the barbed ends. In other types of cells lacking this level of network organisation, however, the ways in which the elementary molecular dynamics (MD) act in concert to give rise to complex cytoskeletal behaviours remain poorly understood.
Addressing this issue requires a combination of experiment, physical theory, and accurate simulation. The last of these is our focus here—we will develop a nonequilibrium MD simulation framework that can be used to efficiently explore the structural and dynamical state space of assemblies of semiflexible filaments, molecular motors, and cross-linkers. By allowing independent manipulation of parameters normally coupled in experiment, this computational model can guide our understanding of the relationship between the microscopic biochemical protein-protein interactions and the macroscopic mechanical functions of assemblies. Additionally, because the model simulates filaments, motors, and cross-linkers explicitly, we can elucidate microscopic mechanisms by studying its stochastic trajectories at levels of detail that are experimentally inaccessible. The fact that complex behaviours can emerge from simple interactions also allows simulations to be used to evaluate predictions from theory.
We will introduce a coarse-grained model that enables simulation of networks of actin filaments, myosin motors, and cross-linking proteins at biologically relevant time and length scales. We will demonstrate that the model qualitatively and quantitatively captures a suite of trends observed experimentally, including the statistics of filament fluctuations, and mechanical responses to shear, motor motilities, and network rearrangements. We will use the simulation to predict the viscoelastic scaling behaviour of cross-linked actin networks, characterise the trajectories of actin in a myosin motility assay, and develop order parameters to measure contractility of a simulated actin network. The model can thus serve as a platform for interpretation and design of cytoskeletal materials experiments, as well as for further development of simulations incorporating active elements [1–7].
Related articles on methodologies
 Elnaz Hajizadeh, Shi Yu, Shihu Wang, and Ronald G. Larson, “A novel hybrid population balance—Brownian dynamics method for simulating the dynamics of polymer-bridged colloidal latex particle suspensions”, J. Rheol. 62, 235–247 (2018).
 Elnaz Hajizadeh, Billy Todd, Peter Daivis, Journal of Rheology, 58, 281-305 (2014)
 Elnaz Hajizadeh, Billy Todd, Peter Daivis, J. Chem. Phys, 142, 174911 (2015)
 Elnaz Hajizadeh, Billy Todd, Peter Daivis, J. Chem. Phys, 141, 194905 (2014)
 Guorui Zhu, Hossein Rezvantalab, Elnaz Hajizadeh, Xiaoyi Wang, Ronald G Larson, Journal of Rheology, 60, 327–343 (2016)
 Elnaz Hajizadeh, Ronald G Larson, Soft Matter, 13, 5942–5949 (2017)
 Elnaz Hajizadeh, Hamid Garmabi, International Journal of Chemical and Biomolecular Engineering, 1, 40-44, (2008)