MS09 - CDEV-08

Agent-based modelling of cell cytoskeletal phenomena

Friday, July 18 at 4:00pm

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Eric Cytrynbaum (University of British Columbia), Tim Tian (University of British Columbia)

Description:

Many cellular processes depend heavily on the dynamics and mechanics of the cytoskeleton. Actin and microtubules are non-equilibrium linear polymers whose localization, density, crosslinking and orientation are often controlled by the cell for various critical purposes (cell division, cell growth, motility etc.). Their influence involves both chemical properties (e.g. assembly dynamics, reactions with associated enzymes) and mechanical ones. In this session, we highlight some of the latest mathematical modelling efforts to understand the influence of the cytoskeleton on various cellular behaviours. We particularly highlight agent-based models which, while computationally intensive to simulate, allow for a detailed representation of geometry, mechanics and interactions.

Hannah Scanlon

Duke University

"Mechanisms of Microtubule Polarity Regulation in Neuronal Regeneration"

Across many organisms, neurons in the peripheral nervous system (PNS) can regenerate injured axons while neurons in the central nervous system cannot. Experimentalists have identified responses in polarized, cytoskeletal filaments called microtubules which are key to facilitating axon regeneration in injured PNS neurons. In a healthy neuron, microtubules maintain a strict polarity distribution over the lifetime of the cell. In response to axon injury in the PNS, microtubules rearrange dramatically to facilitate axonal regeneration. While several mechanisms have been hypothesized to regulate microtubule polarity organization, they are difficult to verify experimentally. Motivated by experiments in fruit flies, we use multi-scale mathematical modeling to investigate mechanisms related to microtubule polarity regulation. This work seeks to assess the efficacy of hypothesized mechanisms at producing the microtubule polarity observed in healthy neurons and in response to axon injury.

Taeyoon Kim

Purdue University

"Reconstituting the Mechanical and Dynamic Behaviors of the Actin Cytoskeleton"

Actin cytoskeleton is a dynamic structural scaffold used by eukaryotic cells to provide mechanical integrity and resistance to deformation, while simultaneously remodeling itself and adapting to diverse extracellular stimuli. The actin cytoskeleton utilizes these properties to play crucial roles in essential cellular processes such as cell migration and division. However, despite its known mechanical role in cell behaviors, a clear understanding of the mechanical properties of actin cytoskeleton and the molecular origin of these properties still lacks, partly due to experimental limitations. Computer simulations can access time and length scales inaccessible by experiments, and thus aid in creating a descriptive model of the molecular interactions that evolve into the mechanical properties observed on cellular scales. To this end, we have developed a cutting-edge computational model which is designed to reproduce the mechanical and dynamic behaviors of actin cytoskeleton within cells. Guided by explicit experimental data, we systematically explored, via simulation, how the mechanics and dynamics of actins and actin-binding proteins determine the deformation, flow, and stiffness of the passive actin cytoskeleton. We also investigated how interactions between the passive cytoskeletal constituents and active molecular motors lead to force generation, contraction, and morphological changes in the active actin cytoskeleton. In this talk, we will briefly introduce our foundational works and discuss our recent studies designed to illuminate the mechanisms of various cellular phenomena, including the pulsed contraction of cell cortex, actin retrograde flow in the lamellipodia, and cell blebbing.

Calina Copos

Northeastern University

"Modeling insights into actin cytoskeleton regulation with external size changes"

Actin is one of the most abundant proteins in eukaryotic cells and a fundamental component of the cytoskeleton, playing a critical role in maintaining cell structure and enabling motility. A compelling preliminary experimental observation underpins our work: in micropatterned epithelial cells of increasing sizes, the mechanical energy does not scale linearly with size. Instead, an optimal force is generated at a critical cell size, suggesting a force response that combines both passive and active mechanical components. To explore this phenomenon, we present a mechanical model of the actin cytoskeleton in an adherent cell that captures the observed biphasic response in force production, arising from an underlying scaling law in cytoskeletal mechanical properties. Complementing this, we develop an agent-based model that simulates the microscopic dynamics of actin filament formation, incorporating crosslinkers and myosin motors. Within this framework, we test various hypotheses — such as the impact of limited resources — that could give rise to the scaling law identified in the macroscopic model. Together, these efforts constitute a multiscale approach aimed at uncovering the mechanisms by which cell size regulates cytoskeletal force generation.

Tim Y.Y. Tian

University of British Columbia

"Organization of Plant Cortical Microtubules"

The self-organization of cortical microtubule arrays within plant cells is an emergent phenomenon with important consequences for the synthesis of the cell wall, cell shape, and subsequently the structure of plants. Mathematical modelling and experiments have elucidated the underlying processes involved. However, the mechanical influence of membrane curvature on these elastic filaments has largely been ignored. We previously proposed a model to describe how the anchoring process may control the deflection of individual microtubules seeking to minimize bending on a cylindrical cell. We implement this process into a model of interacting microtubules and find the cell curvature influence should be significant: the array favours orientations parallel to the direction of elongation rather than the expected transverse direction. Even without elasticity, the geometry of large cells hinders robust microtubule organization. These results suggest the necessity of additional processes to overcome these factors. Alongside this, there has been growing interest in modelling the influence of various other processes such as nucleation and membrane tension. We present ongoing efforts in piecing together our results with others from increasingly complex models, with the goal of better understanding the bigger picture of microtubule organization.

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Annual Meeting for the Society for Mathematical Biology, 2025.