Biophysically Realistic Filament Bending Dynamics in Agent-Based Biological Simulation

An appealing tool for study of the complex biological behaviors that can emerge from networks of simple molecular interactions is an agent-based, computational simulation that explicitly tracks small-scale local interactions – following thousands to millions of states through time. For many critical cell processes (e.g. cytokinetic furrow specification, nuclear centration, cytokinesis), the flexible nature of cytoskeletal filaments is likely to be critical. Any computer model that hopes to explain the complex emergent behaviors in these processes therefore needs to encode filament flexibility in a realistic manner. Here I present a numerically convenient and biophysically realistic method for modeling cytoskeletal filament flexibility in silico. Each cytoskeletal filament is represented by a series of rigid segments linked end-to-end in series with a variable attachment point for the translational elastic element. This connection scheme allows an empirically tuning, for a wide range of segment sizes, viscosities, and time-steps, that endows any filament species with the experimentally observed (or theoretically expected) static force deflection, relaxation time-constant, and thermal writhing motions. I additionally employ a unique pair of elastic elements – one representing the axial and the other the bending rigidity– that formulate the restoring force in terms of single time-step constraint resolution. This method is highly local –adjacent rigid segments of a filament only interact with one another through constraint forces—and is thus well-suited to simulations in which arbitrary additional forces (e.g. those representing interactions of a filament with other bodies or cross-links / entanglements between filaments) may be present. Implementation in code is straightforward; Java source code is available at www.celldynamics.org.