Mathematical-Computational Simulation of Cytoskeletal Dynamics

Abstract

Actin and microtubules are components of the cytoskeleton, and are key mediators of neuron growth and maintenance. Knowing how they are regulated enhances our understanding of neural development, ageing, degeneration, and regeneration. However, biological investigation alone will not unravel the complex cytoskeletal machinery. We expect that inquiries about the cytoskeleton can be significantly enhanced if their physico-chemical behavior is concealed and summarized in mathematical and computational models that can be coupled to concepts of biological regulation. Our computational modeling concerns the mechanical aspects associated with the dynamics of relatively simple, finger-like membrane protrusions called filopodia. Here we propose an alternative approach for representing the displacement of molecules and cytoplasmic fluid in the extremely narrow and long filopodia and discuss strategies to couple the particle-in-cell method with algorithms for laminar flow to model the two phases of actin dynamics: polymerization into filaments which are pulled back into the cell and compensatory G-actin drift towards its tip to supply polymerization. We use nerve cells of the fruit fly Drosophila as an effective, genetically amenable biological system to generate experimental data as the basis for the abstract models and their validation.

From Systems to Organisations

“…de Moura [134], we started to include a further hypothesis, where a mixture of cytosol and G-actin circulates changing organisation at the tip and bottom of the filopodium (Figure 20), from an incoming diluted solution into an outgoing tube formed by cytosol trapped into the actin filament bundle. The tip polymerisation drives a steady back-flow of the F-actin filament bundle at the core of the filopodium, with cytoplasm caught between the filaments (Phase B).…”

“…They can oscillate around a state in P, which means that their instantiations V ⊂ P (the "phase-space" retract) oscillate around a stable "set-value" in ℘(P ) or γ cyclicly exchanges some of its lower-complexity parts with elements available in its Γ-neighbourhood, like when a protein docking-site is constantly being flip-flopped. One of the main features of the formalism underlying this perspective is the ability to enforce distinguishing organisational fluctuations in a complex P from dynamics [134]. Nevertheless, a would-be methodology of virtual behaviours (counterpart of virtual displacements) needs to encompass evolutionary perspectives to be effective in explaining how the actual organisation of 'problems of complexity' came to be.…”