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Biophysically realistic filament bending dynamics in agent-based biological simulation.

Alberts JB - PLoS ONE (2009)

Bottom Line: 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.Implementation in code is straightforward; Java source code is available at www.celldynamics.org.

View Article: PubMed Central - PubMed

Affiliation: Department of Biology, Center for Cell Dynamics, University of Washington, Seattle Washington, United States of America. jalberts@u.washington.edu

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.

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Related in: MedlinePlus

Colliding spheres demonstrate PAIRS method stability and failures.In A, calculation of the force F required to separate two spheres in an actual pairwise interaction (i.e. no other forces besides F are present) yields a stable collision resolution that can be accomplished in a single time-step, if desired. In B, the sum of the forces on , from collisions with the three other spheres, can lead to an overshoot, and non-convergent oscillations for some geometries. To avoid this failure, the PAIRS forces should be applied fractionally, such that collisions are resolved over multiple time-steps. C shows sphere  with drag  attached to a fixed wall by spring . For an applied external force  the equilibrium position is  (assuming the spring is unstrained at x = 0) and the system should relax from that equilibrium, once the force is removed, with time-constant . Modeling this simplest dynamic system by the PAIRS method involved replacing the spring force with a force calculated to return the system to its relaxed position in a single time-step. That force is then modulated by a PAIRS coefficient to allow tuning of the system to match physical properties of the system, such as expected deflection and relaxation time-constant.
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pone-0004748-g001: Colliding spheres demonstrate PAIRS method stability and failures.In A, calculation of the force F required to separate two spheres in an actual pairwise interaction (i.e. no other forces besides F are present) yields a stable collision resolution that can be accomplished in a single time-step, if desired. In B, the sum of the forces on , from collisions with the three other spheres, can lead to an overshoot, and non-convergent oscillations for some geometries. To avoid this failure, the PAIRS forces should be applied fractionally, such that collisions are resolved over multiple time-steps. C shows sphere with drag attached to a fixed wall by spring . For an applied external force the equilibrium position is (assuming the spring is unstrained at x = 0) and the system should relax from that equilibrium, once the force is removed, with time-constant . Modeling this simplest dynamic system by the PAIRS method involved replacing the spring force with a force calculated to return the system to its relaxed position in a single time-step. That force is then modulated by a PAIRS coefficient to allow tuning of the system to match physical properties of the system, such as expected deflection and relaxation time-constant.

Mentions: Consider two colliding spheres and in Fig. 1A, with viscous drag coefficients and . The spheres overlap by at time – we will determine the force that will just separate the spheres at .


Biophysically realistic filament bending dynamics in agent-based biological simulation.

Alberts JB - PLoS ONE (2009)

Colliding spheres demonstrate PAIRS method stability and failures.In A, calculation of the force F required to separate two spheres in an actual pairwise interaction (i.e. no other forces besides F are present) yields a stable collision resolution that can be accomplished in a single time-step, if desired. In B, the sum of the forces on , from collisions with the three other spheres, can lead to an overshoot, and non-convergent oscillations for some geometries. To avoid this failure, the PAIRS forces should be applied fractionally, such that collisions are resolved over multiple time-steps. C shows sphere  with drag  attached to a fixed wall by spring . For an applied external force  the equilibrium position is  (assuming the spring is unstrained at x = 0) and the system should relax from that equilibrium, once the force is removed, with time-constant . Modeling this simplest dynamic system by the PAIRS method involved replacing the spring force with a force calculated to return the system to its relaxed position in a single time-step. That force is then modulated by a PAIRS coefficient to allow tuning of the system to match physical properties of the system, such as expected deflection and relaxation time-constant.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2654463&req=5

pone-0004748-g001: Colliding spheres demonstrate PAIRS method stability and failures.In A, calculation of the force F required to separate two spheres in an actual pairwise interaction (i.e. no other forces besides F are present) yields a stable collision resolution that can be accomplished in a single time-step, if desired. In B, the sum of the forces on , from collisions with the three other spheres, can lead to an overshoot, and non-convergent oscillations for some geometries. To avoid this failure, the PAIRS forces should be applied fractionally, such that collisions are resolved over multiple time-steps. C shows sphere with drag attached to a fixed wall by spring . For an applied external force the equilibrium position is (assuming the spring is unstrained at x = 0) and the system should relax from that equilibrium, once the force is removed, with time-constant . Modeling this simplest dynamic system by the PAIRS method involved replacing the spring force with a force calculated to return the system to its relaxed position in a single time-step. That force is then modulated by a PAIRS coefficient to allow tuning of the system to match physical properties of the system, such as expected deflection and relaxation time-constant.
Mentions: Consider two colliding spheres and in Fig. 1A, with viscous drag coefficients and . The spheres overlap by at time – we will determine the force that will just separate the spheres at .

Bottom Line: 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.Implementation in code is straightforward; Java source code is available at www.celldynamics.org.

View Article: PubMed Central - PubMed

Affiliation: Department of Biology, Center for Cell Dynamics, University of Washington, Seattle Washington, United States of America. jalberts@u.washington.edu

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.

Show MeSH
Related in: MedlinePlus