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Emergent systems energy laws for predicting myosin ensemble processivity.

Egan P, Moore J, Schunn C, Cagan J, LeDuc P - PLoS Comput. Biol. (2015)

Bottom Line: On the basis of prior experimental evidence that longer processive lifetimes are enabled by larger myosin ensembles, it is hypothesized that emergent scaling laws could coincide with myosin-actin contact probability or system energy consumption.Because processivity is difficult to predict analytically and measure experimentally, agent-based computational techniques are developed to simulate processive myosin ensembles and produce novel processive lifetime measurements.It is demonstrated that only systems energy relationships hold regardless of isoform configurations or ensemble size, and a unified expression for predicting processive lifetime is revealed.

View Article: PubMed Central - PubMed

Affiliation: Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania, United States of America.

ABSTRACT
In complex systems with stochastic components, systems laws often emerge that describe higher level behavior regardless of lower level component configurations. In this paper, emergent laws for describing mechanochemical systems are investigated for processive myosin-actin motility systems. On the basis of prior experimental evidence that longer processive lifetimes are enabled by larger myosin ensembles, it is hypothesized that emergent scaling laws could coincide with myosin-actin contact probability or system energy consumption. Because processivity is difficult to predict analytically and measure experimentally, agent-based computational techniques are developed to simulate processive myosin ensembles and produce novel processive lifetime measurements. It is demonstrated that only systems energy relationships hold regardless of isoform configurations or ensemble size, and a unified expression for predicting processive lifetime is revealed. The finding of such laws provides insight for how patterns emerge in stochastic mechanochemical systems, while also informing understanding and engineering of complex biological systems.

No MeSH data available.


Related in: MedlinePlus

Agent-based simulation of myosin systems.(a) Logic rules that each individual myosin agent autonomously follows each step of the simulation. (b) Three rendered frames of myosin ensembles interacting with a single long actin filament. Myosins only generate force when attached to actin and based on their state generate positive force promoting filament motility (left pointing arrows) or negative force retarding motility (right pointing arrows).
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pcbi.1004177.g002: Agent-based simulation of myosin systems.(a) Logic rules that each individual myosin agent autonomously follows each step of the simulation. (b) Three rendered frames of myosin ensembles interacting with a single long actin filament. Myosins only generate force when attached to actin and based on their state generate positive force promoting filament motility (left pointing arrows) or negative force retarding motility (right pointing arrows).

Mentions: The agent-based simulation consists of a discrete number of independently configured and autonomous myosin agents interacting with a filament in a virtual environment. The simulation operates in discrete spatial and temporal steps, with a filament translating dX = 1nm each step over a duration dT determined by v = dX/dT, which is a small enough step size to capture individual myosin behaviors while keeping required computational effort to a minimum. Each myosin agent has three possible states of either (0) detached, (1) being attached to the filament during a power-stroke, or (2) being attached to the filament during a drag-stroke. During each timestep of the simulation, each myosin agent follows programmed logic as presented Fig 2A that is representative of a myosin’s mechanochemical states and behaviors. Depending on a myosin’s current state, it will begin following rules in one of three ‘Start’ blocks and continue through if/then statements until an ‘End’ command is reached. For instance, a myosin that is not bound to actin (state 0) will first check if a binding site is near, where xnb is the distance from a myosin’s zero strain location to the nearest binding site, xz represents how close a myosin head must be to a binding site to have a chance of binding, and step size δ+ represents the distance of a myosin head from the point of zero strain. If the check fails, the myosin ceases its actions until the next time step. If the check succeeds, a random number is generated and compared to a myosin’s chance of attachment for that time step to determine whether it binds and enters the power-stroke state for the next simulation step or ceases its actions. The chance to attach is based on the actin's attachment rate parameter kon and the window of time a binding site is available such that P(kon) = kon ∙ dT. If a myosin agent attaches, it remains in its power-stroke (state 1) until it has a head displacement d of zero, as its head translates with the travelling filament and has initial displacement d = δ+ that reduces by dX each step. In the drag-stroke (state 2), a myosin has a random chance of detaching according to its detachment rate koff and P(koff) = koff ∙ dT. Fig 2B demonstrates a rendering of myosins operating as an ensemble according to the rules in Fig 2A.


Emergent systems energy laws for predicting myosin ensemble processivity.

Egan P, Moore J, Schunn C, Cagan J, LeDuc P - PLoS Comput. Biol. (2015)

Agent-based simulation of myosin systems.(a) Logic rules that each individual myosin agent autonomously follows each step of the simulation. (b) Three rendered frames of myosin ensembles interacting with a single long actin filament. Myosins only generate force when attached to actin and based on their state generate positive force promoting filament motility (left pointing arrows) or negative force retarding motility (right pointing arrows).
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4401713&req=5

pcbi.1004177.g002: Agent-based simulation of myosin systems.(a) Logic rules that each individual myosin agent autonomously follows each step of the simulation. (b) Three rendered frames of myosin ensembles interacting with a single long actin filament. Myosins only generate force when attached to actin and based on their state generate positive force promoting filament motility (left pointing arrows) or negative force retarding motility (right pointing arrows).
Mentions: The agent-based simulation consists of a discrete number of independently configured and autonomous myosin agents interacting with a filament in a virtual environment. The simulation operates in discrete spatial and temporal steps, with a filament translating dX = 1nm each step over a duration dT determined by v = dX/dT, which is a small enough step size to capture individual myosin behaviors while keeping required computational effort to a minimum. Each myosin agent has three possible states of either (0) detached, (1) being attached to the filament during a power-stroke, or (2) being attached to the filament during a drag-stroke. During each timestep of the simulation, each myosin agent follows programmed logic as presented Fig 2A that is representative of a myosin’s mechanochemical states and behaviors. Depending on a myosin’s current state, it will begin following rules in one of three ‘Start’ blocks and continue through if/then statements until an ‘End’ command is reached. For instance, a myosin that is not bound to actin (state 0) will first check if a binding site is near, where xnb is the distance from a myosin’s zero strain location to the nearest binding site, xz represents how close a myosin head must be to a binding site to have a chance of binding, and step size δ+ represents the distance of a myosin head from the point of zero strain. If the check fails, the myosin ceases its actions until the next time step. If the check succeeds, a random number is generated and compared to a myosin’s chance of attachment for that time step to determine whether it binds and enters the power-stroke state for the next simulation step or ceases its actions. The chance to attach is based on the actin's attachment rate parameter kon and the window of time a binding site is available such that P(kon) = kon ∙ dT. If a myosin agent attaches, it remains in its power-stroke (state 1) until it has a head displacement d of zero, as its head translates with the travelling filament and has initial displacement d = δ+ that reduces by dX each step. In the drag-stroke (state 2), a myosin has a random chance of detaching according to its detachment rate koff and P(koff) = koff ∙ dT. Fig 2B demonstrates a rendering of myosins operating as an ensemble according to the rules in Fig 2A.

Bottom Line: On the basis of prior experimental evidence that longer processive lifetimes are enabled by larger myosin ensembles, it is hypothesized that emergent scaling laws could coincide with myosin-actin contact probability or system energy consumption.Because processivity is difficult to predict analytically and measure experimentally, agent-based computational techniques are developed to simulate processive myosin ensembles and produce novel processive lifetime measurements.It is demonstrated that only systems energy relationships hold regardless of isoform configurations or ensemble size, and a unified expression for predicting processive lifetime is revealed.

View Article: PubMed Central - PubMed

Affiliation: Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania, United States of America.

ABSTRACT
In complex systems with stochastic components, systems laws often emerge that describe higher level behavior regardless of lower level component configurations. In this paper, emergent laws for describing mechanochemical systems are investigated for processive myosin-actin motility systems. On the basis of prior experimental evidence that longer processive lifetimes are enabled by larger myosin ensembles, it is hypothesized that emergent scaling laws could coincide with myosin-actin contact probability or system energy consumption. Because processivity is difficult to predict analytically and measure experimentally, agent-based computational techniques are developed to simulate processive myosin ensembles and produce novel processive lifetime measurements. It is demonstrated that only systems energy relationships hold regardless of isoform configurations or ensemble size, and a unified expression for predicting processive lifetime is revealed. The finding of such laws provides insight for how patterns emerge in stochastic mechanochemical systems, while also informing understanding and engineering of complex biological systems.

No MeSH data available.


Related in: MedlinePlus