A cytoskeletal network in the MEDYAN model.

<p>A complex cytoskeletal network can be simulated with MEDYAN’s stochastic reaction-diffusion scheme. Chemical interactions will cause complex network evolution, such as the process of actin filament bundling. See Section A in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004877#pcbi.1004877.s001" target="_blank">S1 Text</a> for a more detailed description of all chemical reactions that can be included in a simulation.</p

MSD analysis of actin filaments in simulation.

<p>(A) MSD over time for various values of <i>χ</i>. Error bars represent the standard error of the MSD, for each set of trajectories, are smaller than the data points. (B) Diffusion exponent <i>ν</i> acquired from a log-log linear fit of (A). Error bars represent the standard linear regression error in <i>ν</i>.</p

A single trajectory snapshot of a 3 × 3 × 3 <i>μ</i>m³ actomyosin system simulation at R_α:a = 0.1 and R_m:a = 0.02 after 500 s of network evolution.

<p>Actin filament cylinders are colored by their angle with respect to the x-y plane.</p

Actomyosin network R_g,f / R_g,i and S for various <i>χ</i>.

<p>(A) <i>R</i>_g,f/<i>R</i>_g,i over the 2000 <i>s</i> network evolution for varying values of <i>χ</i>. Contractile behavior increases with decreasing <i>χ</i>. Standard deviations of the <i>R</i>_g,f/<i>R</i>_g,i values over all trajectories are shaded. (B) <i>S</i> after 2000 <i>s</i> of network evolution for varying values of <i>χ</i>. Global alignment peaks around <i>χ</i> = 0.5 to 2, and decreases for values outside of this range. Error bars represent standard deviation of <i>S</i> values over all trajectories.</p

A heat map of actomyosin network R_g as a function of R_m:a and R_α:a after 2000 s of network evolution.

<p>As NMIIA and <i>α</i>-actinin concentrations are increased, a very apparent correlation in overall network contraction results.</p

A heat map of actomyosin network S as a function of R_m:a and R_α:a after 2000 s of network evolution.

<p>As NMIIA and <i>α</i>-actinin concentrations are increased, a correlation in alignment results in a similar fashion to <i>R</i>_g in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004877#pcbi.1004877.g006" target="_blank">Fig 6</a>.</p

A single trajectory snapshot of a 1 × 1 × 1 <i>μ</i>m³ actomyosin system simulation at R_α:a = 0.1 and R_m:a = 0.01 after 2000 s of network evolution.

<p>Actin filaments are represented as red connected cylinders, <i>α</i>-actinin are represented as green cylinders, and NMIIA mini-filaments are represented as blue cylinders. The corresponding diffusing species are also shown in the same colors. The system is bounded by a cubic, hard-wall potential.</p

Single trajectory snapshots of the actomyosin systems with various concentrations of R_α:a and R_m:a after 2000 s of network evolution.

<p>These snapshots are shown without diffusing species for simplicity. For increasing <i>α</i>-actinin and NMIIA concentration, actin filament bundle formation is increasingly more apparent.</p

A flow diagram of a MEDYAN simulation.

<p>(1) After the chemical stochastic simulation evolves the network in time and (2) local deformations are formed, (3) a mechanical equilibration is performed and (4) reaction rates are updated according to chosen functional forms <i>f</i>(<i>F</i>_{<i>current</i>}) where <i>F</i>_{<i>current</i>} is the force on that reacting molecule after equilibration.</p

A polymer in the MEDYAN model.

<p>A cylinder based scheme is used in the MEDYAN force fields to model semi-flexible polymers. Here, <i>σ</i>₀ is the diameter of the cylinder and <i>l</i>₀ is the equilibrium length, where <i>l</i>₀ > > <i>σ</i>₀. We assume that axial deformations of the cylinders are small and radial deformations are forbidden.</p