Abstract
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.
Highlights
Complex behaviors in cells often emerge from surprisingly simple sets of underlying molecular interactions
Understanding how such emergent behaviors arise from well-described biochemistry, geometry, and mechanics is a current focus in the field of computational and mathematical biology
The method I propose for capturing the realistic biophysical behaviors of cytoskeletal filaments in agent-based computer simulations can match three critical properties of biological filaments: their deflection, relaxation time-constant, and thermal writhing (Fig. 4)
Summary
Complex behaviors in cells often emerge from surprisingly simple sets of underlying molecular interactions Understanding how such emergent behaviors arise from well-described biochemistry, geometry, and mechanics is a current focus in the field of computational and mathematical biology. The calculated interactions of components can alter biochemical states, create complexes of components with new properties, deplete or enrich scalar concentration fields of soluble components, and generate forces that repel, attract, or deform. This tracking of spatial and biochemical detail can reveal dynamic behavior important in cell function. Complex models of this type have been applied to actin-based motility [1,2], spindle-pole positioning and oscillations [3], the role of motors in mitotic spindle formation [4,5,6,7], load sharing in Brownian ratchet mechanisms [8], and to understanding cytokinetic furrow specification [9], to select a few
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