Webpages about Smoldyn and spatial simulation

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Smoldyn is a particle-based spatial stochastic simulator. Molecules are represented by point-like particles in 1-, 2-, or 3-dimensional continuous space. Molecules diffuse by Brownian motion, react when they collide into each other, and interact with surfaces (e.g. membranes) in a variety of realistic ways. Smoldyn is typically used for biophysics research or cell modeling research. Examples include:


Cell modeling:

To run a Smoldyn simulation, you need to describe your model in a plain-text configuration file. This file describes the system surfaces, molecular species, diffusion coefficients, and chemical reactions. It also lists parameters for the graphical display and any quantitative output. Smoldyn reads this file, sets up simulation parameters, and runs the simulation. During the simulation, Smoldyn displays the system to a graphics window and saves quantitative data to text files. Many simulation parameters, such as time step sizes, can be changed mid-simulation.


A simple simulation example derives from the classic Lotka-Volterra predator-prey model. In their model, the number of prey increase through reproduction and decrease through predation, while the number of predators increase through predation and decrease with a fixed death rate. This scheme can be written with chemical reaction notation, now using A for a prey "molecule" and B for a predator "molecule":

A --> 2 A
A + B --> 2 B
B --> nothing

Lotka and Volterra showed that this model, without spatial detail, leads to sustained regular population oscillations. Smoldyn simulations, which include spatial detail, produce different results. As shown below, even if the system starts well-mixed, it rapidly develops spatial organization; also, the population oscillations are irregular and have highly variable amplitudes. The Smoldyn configuration file is here.

time course phase diagram
Smoldyn graphical output for the Lotka-Volterra simulation. Red dots represent prey and green are predators. The system starts well-mixed but develops spatial structure. Populations of predators (green) and prey (red) over time. These oscillations vary much more, both in amplitude and in timing, than they do in non-spatial simulations. Phase diagram for predator (y-axis) and prey (x-axis) populations. The system starts at the metastable equilibrium point near the center of the cycles, and then develops spontaneous counter-clockwise cycles.

Smoldyn features

Molecular diffusion

Chemical reactions


User interface and support


Quantitative accuracy is one of Smoldyn's particular strengths. Although Smoldyn does not simulate all aspects of simulated systems exactly, it comes very close. Moreover, Smoldyn simulates all interaction rates (reaction rates, adsorption rates, etc.) within about 2% of the user-requested rates over all possible rate ranges. Among other things, this means that Smoldyn simulations show correct equilibrium concentrations.

Few biochemical parameters are experimentally known to high accuracy, so one might wonder why accuracy is so important for a biochemical simulator. The answers include:

Our Publications webpage lists the research papers that describe Smoldyn's algorithms and that describe how we made Smoldyn highly accurate. In brief, we accounted for a few aspects of diffusion-influenced reactions that prior authors tended to ignore. We considered (1) the molecular concentration changes that result from either the reaction or the surface interaction of interest, (2) the effects of reversible processes, such as reversible chemical reactions and reversible transmission through surfaces, and (3) the approximations that are made when the actual highly detailed microscopic trajectories of Brownian particles are simulated using straight line displacements.

reaction rate This figure compares Smoldyn's simulated bimolecular reaction rates (colored lines) with the mass-action theoretical rates (black and grey lines). It shows the number of 'A' molecules as a function of time for the reaction A + B -> C, using three different rate constants: slow (red), medium (green), and fast (blue). For the slow and medium reaction rates, Smoldyn's results agree essentially perfectly with mass-action theory, where the only difference arises from the stochastic noise that Smoldyn accounts for. For the fast reaction rate, the Smoldyn simulation is much faster than the grey line. This is not an error in Smoldyn, but arises from the fact that mass-action theory is only an approximation, and in fact is incorrect for fast diffusion-limited reactions that are not at steady-state. The nearby black line also represents mass action theory, but starts at a later time, when the system is closer to steady-state, and so agrees well with simulation.
The figure on the right shows the concentration of molecules that are adsorbed to a surface as a function of time. The simulation result is shown in blue and the theoretical result is in red. Again, agreement is essentially perfect, with the only differences arising from stochastic noise. The horizontal black line at the top of the figure shows the equilibrium surface concentration, which is the asymptote for the other curves. reversible adsorption

Utility programs

Two utility programs are distributed with Smoldyn: wrl2smol and SmolCrowd. These are not as user-friendly as the Smoldyn program, but still may be useful for users.

Smoldyn simulation of diffusion within a cell. The wrl2smol utility program converted the surface data from VRML format to Smodyn format. Smoldyn simulation of diffusion in a 2-dimensional crowded system. The black circles are fixed crowders, which obstruct diffusion, and the red dots are individual molecules. This crowded system was generated with the SmolCrowd utility program.