Fig 1.
A cytoskeletal network in the MEDYAN model.
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 S1 Text for a more detailed description of all chemical reactions that can be included in a simulation.
Fig 2.
A polymer in the MEDYAN model.
A cylinder based scheme is used in the MEDYAN force fields to model semi-flexible polymers. Here, σ0 is the diameter of the cylinder and l0 is the equilibrium length, where l0 > > σ0. We assume that axial deformations of the cylinders are small and radial deformations are forbidden.
Fig 3.
Interactions in the the MEDYAN model.
A) A Schematic representation of two arbitrary points on the cylinders i and j, used to calculate excluded volume interactions. B) Representation of branching points. Position of the branching point on the “mother” filament is determined by a stochastic chemical reaction. C) Representation of the motor as a potential between two points
and
on bound cylinders. Positions of the binding points α and β are determined by stochastic chemical reactions.
Fig 4.
A flow diagram of a MEDYAN simulation.
(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 f(Fcurrent) where Fcurrent is the force on that reacting molecule after equilibration.
Fig 5.
A single trajectory snapshot of a 1 × 1 × 1 μm3 actomyosin system simulation at Rα:a = 0.1 and Rm:a = 0.01 after 2000 s of network evolution.
Actin filaments are represented as red connected cylinders, α-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.
Fig 6.
A heat map of actomyosin network Rg as a function of Rm:a and Rα:a after 2000 s of network evolution.
As NMIIA and α-actinin concentrations are increased, a very apparent correlation in overall network contraction results.
Fig 7.
Single trajectory snapshots of the actomyosin systems with various concentrations of Rα:a and Rm:a after 2000 s of network evolution.
These snapshots are shown without diffusing species for simplicity. For increasing α-actinin and NMIIA concentration, actin filament bundle formation is increasingly more apparent.
Fig 8.
Actomyosin network Rg,f/Rg,i over time for various Rα:a with fixed Rm:a = 0.01.
We see that above a threshold α-actinin concentration, contraction is observed, and the time of bundle formation for these contractile structure formations decreases with increasing α-actinin concentration. Standard deviations of the Rg,f/Rg,i values over all trajectories are shaded.
Fig 9.
A heat map of actomyosin network S as a function of Rm:a and Rα:a after 2000 s of network evolution.
As NMIIA and α-actinin concentrations are increased, a correlation in alignment results in a similar fashion to Rg in Fig 6.
Fig 10.
Actomyosin network Rg,f / Rg,i and S for various χ.
(A) Rg,f/Rg,i over the 2000 s network evolution for varying values of χ. Contractile behavior increases with decreasing χ. Standard deviations of the Rg,f/Rg,i values over all trajectories are shaded. (B) S after 2000 s of network evolution for varying values of χ. Global alignment peaks around χ = 0.5 to 2, and decreases for values outside of this range. Error bars represent standard deviation of S values over all trajectories.
Fig 11.
Single trajectory snapshots of the actomyosin systems, with various values of χ after 2000 s of network evolution.
These trajectories are colored with black and white beads for the plus and minus ends of actin filaments, respectively. (A) Low χ, corresponding to a slow turnover rate, produces large global contractions in the absence of polarity alignment. (B) The original turnover rate (χ = 1) produces global contraction as well as polarity alignment. (C) High χ produces no global contraction, but distinct local polarity organization.
Fig 12.
MSD analysis of actin filaments in simulation.
(A) MSD over time for various values of χ. Error bars represent the standard error of the MSD, for each set of trajectories, are smaller than the data points. (B) Diffusion exponent ν acquired from a log-log linear fit of (A). Error bars represent the standard linear regression error in ν.
Fig 13.
A single trajectory snapshot of a 3 × 3 × 3 μm3 actomyosin system simulation at Rα:a = 0.1 and Rm:a = 0.02 after 500 s of network evolution.
Actin filament cylinders are colored by their angle with respect to the x-y plane.