Workflow in Simulation and ReaDDy Code Design.

<p><b>A:</b> 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 <i>BD Core</i> and a Monte Carlo based <i>MC Core</i>. The design is intended to encourage the incorporation of third party software to play the <i>Core</i>-role in the ReaDDy framework. <b>B:</b> Detailed view of the interplay between <i>Group/Reaction Module</i> (<i>Gr/Rk Module</i>), the <i>Core</i> 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 <i>Gr/Rk Module</i> module and is handled there before according changes of the Particle Configuration end that cycle (dashed arrows).</p

Particle Parameters and Resulting Properties of the Benchmark System.

<p>Parameters for particle types , and . : collision radius defining the onset of particle-particle repulsion. : apparent collision radius that arises from both the collision radius and the chosen inter-particle repulsion force constant . : interaction radius for particle-particle reactions. : microscopic diffusion constant.</p

Determination of the Brownian Dynamics Time Step Length .

<p><b>A:</b> 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>B:</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).</p

Particle Numbers and Particle Concentrations in Benchmark Systems.

<p>Particle numbers and their concentrations for the different benchmark system setups in the box of 100 nm edge length.</p>*<p>conditions similar to cytoplasm (compare <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0074261#pone-0074261-g003" target="_blank">Figure 3</a> for a visual illustration).</p

Possible Applications of ReaDDy at Different Levels of Modeling Detail.

<p>A model of vesicle fusion in the synaptic vesicle cycle is shown at two levels of detail. <b>A:</b> Snapshot of the simulation described in the ReaDDy tutorial. <b>i:</b> 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 <b>ii. </b><b>iii:</b> short range attraction potentials induce clustering of SNARE proteins. <b>B:</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.</p

CPU Runtimes to Simulate 1

<p>CPU runtimes in hours to simulate 1000 particles at densities of 10% and 30% occupied volume fraction in 3D box- or 2D disk geometry with for 10,000,000 steps.</p>*<p>2D systems will likely represent membrane models of higher viscosity, usually resulting in one order of magnitude smaller diffusion constants. This enables the system to be integrated with a one order of magnitude larger timestep.</p

3D-Benchmark System Setups used in this Study.

<p>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.</p

ReaDDy - A Software for Particle-Based Reaction-Diffusion Dynamics in Crowded Cellular Environments

<div><p>We introduce the software package ReaDDy for simulation of detailed spatiotemporal mechanisms of dynamical processes in the cell, based on reaction-diffusion dynamics with particle resolution. In contrast to other particle-based reaction kinetics programs, ReaDDy supports particle interaction potentials. This permits effects such as space exclusion, molecular crowding and aggregation to be modeled. The biomolecules simulated can be represented as a sphere, or as a more complex geometry such as a domain structure or polymer chain. ReaDDy bridges the gap between small-scale but highly detailed molecular dynamics or Brownian dynamics simulations and large-scale but little-detailed reaction kinetics simulations. ReaDDy has a modular design that enables the exchange of the computing core by efficient platform-specific implementations or dynamical models that are different from Brownian dynamics.</p></div

Mean Square Displacement (MSD) and Diffusion Constants for Particle Type in the Benchmark System.

<p>In finite-sized systems, the MSD over time (thick colored lines, lighter color for denser system density) showed a triphasic behavior. <b>A:</b> On long timescales, the MSD can only reach a bound set by the finite system size (dashed black line). <b>B:</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 . <b>C: </b> values for particle types and , obtained from linear fit of the second linear phase of the curves in B.</p

Apparent Particle Radii and Radial Distribution Functions (RDFs), Depending on Collision Radius and Potential Force Constant.

<p>Shown RDFs are based on particle-pairs of particle type in the 50% occupied volume fraction benchmark system. <b>A:</b> 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>B:</b> individual RDFs are depicted for different (i–vi). Same color code as in A.</p