Figure 1.
Workflow in Simulation and ReaDDy Code Design.
A: Typical workflow and interplay between file input, file output and modules of ReaDDy. The left side of part A describes input and output functionalities of ReaDDy (sketched files) and how they interplay with code modules (squares). Among these modules, white drawn squares have access to both the particle level but also to information how particles are formed to groups. Grey squares are only based on particles to guarantee high computational efficiency. Modules communicate via interfaces, making them exchangeable. Currently two ReaDDy Core implementations exist, a Brownian dynamics based BD Core and a Monte Carlo based MC Core. The design is intended to encourage the incorporation of third party software to play the Core-role in the ReaDDy framework. B: Detailed view of the interplay between Group/Reaction Module (Gr/Rk Module), the Core module and their submodules during the main iteration loop. Most of the simulation time is spend on incrementing particle positions. As a result, the algorithm will circle between Particle Configuration, Neighbor List and Diffusion Engine (thick black arrows) to propagate diffusing particles. If a possible reaction event between two particle arises, this information is passed to the Gr/Rk Module module and is handled there before according changes of the Particle Configuration end that cycle (dashed arrows).
Figure 2.
Possible Applications of ReaDDy at Different Levels of Modeling Detail.
A model of vesicle fusion in the synaptic vesicle cycle is shown at two levels of detail. A: Snapshot of the simulation described in the ReaDDy tutorial. i: SNARE proteins syntaxin (blue), SNAP-25 (grey) and a calcium channel (green, large sphere) are modeled on a disk membrane, synaptic vesicles (yellow) float in the cytosol. Reactions allow the modeling of syntaxin’s conformational change (switch between light- and dark blue), the formation of SNARE complexes (red), vesicle tethering (yellow, orange and red vesicles, depending on the number of SNARE complexes involved) and calcium ion release (small green particles in panel ii. iii: short range attraction potentials induce clustering of SNARE proteins. B: Grouping of particles allows proteins to be modeled with complex shapes: syntaxins here consist of a membrane anchor (blue), a flexible peptide domain (red) and the Habc domain (dark grey). Synaptobrevin (orange and yellow) and synaptotagmin (dark green, grey, green) are also modeled as groups of particles, representing protein domains. Interaction potentials of plasma- (dark grey) and vesicle membrane (light blue) with anchor particles ensure, that membrane proteins can not leave the membrane.
Table 1.
Particle Parameters and Resulting Properties of the Benchmark System.
Figure 3.
3D-Benchmark System Setups used in this Study.
The occupied volume fraction ranges from 1% to 50% within a cube of 100 nm edge length. The 30% occupied volume fraction best resembles cytoplasm conditions.
Figure 4.
A: CPU time required (using single standard CPU cores) to run 100,000 simulation steps of benchmark particle systems at 10% occupied volume fraction with increasing system size and number of particles. Linear runtime can be observed. The blue curve represents a 3D container setup, the red line represents a 2D disk setup. B: Runtime performance for a fixed-volume simulation at different particle densities. Simulation volumes are a box of in 3D (blue, see Fig. 3 for illustration) and a disk of radius 297.4 nm in 2D (red). On average the density increase leads to a higher number of neighbors per particle and thus to a super-linear increase in runtime.
Table 2.
CPU Runtimes to Simulate 1
Table 3.
Particle Numbers and Particle Concentrations in Benchmark Systems.
Figure 5.
Apparent Particle Radii and Radial Distribution Functions (RDFs), Depending on Collision Radius and Potential Force Constant.
Shown RDFs are based on particle-pairs of particle type in the 50% occupied volume fraction benchmark system. A: smaller force constants
lead to larger overlap regions (grey area) and to larger differences between
(red) and
(black). The inset depicts the potential shape for different
. B: individual RDFs are depicted for different
(i–vi). Same color code as in A.
Figure 6.
Determination of the Brownian Dynamics Time Step Length .
A: Dependency of the computed radial distribution function for different time step lengths
. The black line shows the exact
of
-particles computed by Monte Carlo. The interaction potential was chosen to be a softcore repulsion potential (
) when their distance is closer than the sum of their collision radii
. The colored lines show
’s computed from time discretized Brownian dynamics simulations with different timesteps. B: Root mean square error of the difference between Monte Carlo derived g(r) and the discretized diffusion simulation (displayed in same color code as A).
Figure 7.
Mean Square Displacement (MSD) and Diffusion Constants for Particle Type in the Benchmark System.
In finite-sized systems, the MSD over time (thick colored lines, lighter color for denser system density) showed a triphasic behavior. A: On long timescales, the MSD can only reach a bound set by the finite system size (dashed black line). B: On short timescales it is visible that all curves share the same microscopic diffusion constant (dashed red line). In a setup where repulsion potentials between particles were switched off (thick black line), particles were only subjected to boundary repulsions and therefore remained diffusing closely to
. On intermediate timescales, particles in denser simulations including repulsion potentials, diffused according to a smaller apparent diffusion constant
(dashed black fits). The higher the occupied volume fraction and the stronger the crowding, the smaller
. C:
values for particle types
and
, obtained from linear fit of the second linear phase of the curves in B.
Figure 8.
Comparison of ODE Reaction Kinetics with ReaDDy Simulations at Different Reaction Rates.
Time-dependent concentrations of ,
,
species are reported for reaction
in the 30% benchmark system. ODE solutions (dotted lines) are compared to ReaDDy simulations (colored lines), simulated once with (light blue, orange) and without (dark blue, brown) particle repulsion. The reaction is simulated at different rates: A:
, B:
and C:
(see figure for values of the microscopic rates). A’, B’ and C’ depict magnifications of the gray areas in A, B and C. At condition A, reactions are slow enough to allow particles to mix well between reactions. If particle-particle repulsion potentials are switched off, the ODE solution agrees with the ReaDDy solution. If particles do have repulsion potentials, the corresponding minimal distance between reacting particles reduces the volume of space in which a reaction can take place. This effectively lowers the reaction probability and thus slows down the reaction. At conditions B and C the reaction rate is so fast that the well-mixed assumption of the system breaks down. Hence the ODE solution can no longer accurately predict the evolution of the reaction.