STEPS: efficient simulation of stochastic reaction-diffusion models in realistic morphologies.

BACKGROUND: Models of cellular molecular systems are built from components such as biochemical reactions (including interactions between ligands and membrane-bound proteins), conformational changes and active and passive transport. A discrete, stochastic description of the kinetics is often essential to capture the behavior of the system accurately. Where spatial effects play a prominent role the complex morphology of cells may have to be represented, along with aspects such as chemical localization and diffusion. This high level of detail makes efficiency a particularly important consideration for software that is designed to simulate such systems. RESULTS: We describe STEPS, a stochastic reaction-diffusion simulator developed with an emphasis on simulating biochemical signaling pathways accurately and efficiently. STEPS supports all the above-mentioned features, and well-validated support for SBML allows many existing biochemical models to be imported reliably. Complex boundaries can be represented accurately in externally generated 3D tetrahedral meshes imported by STEPS. The powerful Python interface facilitates model construction and simulation control. STEPS implements the composition and rejection method, a variation of the Gillespie SSA, supporting diffusion between tetrahedral elements within an efficient search and update engine. Additional support for well-mixed conditions and for deterministic model solution is implemented. Solver accuracy is confirmed with an original and extensive validation set consisting of isolated reaction, diffusion and reaction-diffusion systems. Accuracy imposes upper and lower limits on tetrahedron sizes, which are described in detail. By comparing to Smoldyn, we show how the voxel-based approach in STEPS is often faster than particle-based methods, with increasing advantage in larger systems, and by comparing to MesoRD we show the efficiency of the STEPS implementation. CONCLUSION: STEPS simulates models of cellular reaction-diffusion systems with complex boundaries with high accuracy and high performance in C/C++, controlled by a powerful and user-friendly Python interface. STEPS is free for use and is available at http://steps.sourceforge.net/

The diffusional properties of dendrites depend on the density of dendritic spines.

We combined computational modeling and experimental measurements to determine the influence of dendritic structure on the diffusion of intracellular chemical signals in mouse cerebellar Purkinje cells and hippocamal CA1 pyramidal cells. Modeling predicts that molecular trapping by dendritic spines causes diffusion along spiny dendrites to be anomalous and that the value of the anomalous exponent (d(w) ) is proportional to spine density in both cell types. To test these predictions we combined the local photorelease of an inert dye, rhodamine dextran, with two-photon fluorescence imaging to track diffusion along dendrites. Our results show that anomalous diffusion is present in spiny dendrites of both cell types. Further, the anomalous exponent is linearly related to the density of spines in pyramidal cells and d(w) in Purkinje cells is consistent with such a relationship. We conclude that anomalous diffusion occurs in the dendrites of multiple types of neurons. Because spine density is dynamic and depends on neuronal activity, the degree of anomalous diffusion induced by spines can dynamically regulate the movement of molecules along dendrites.

STEPS: Modeling and Simulating Complex Reaction-Diffusion Systems with Python.

We describe how the use of the Python language improved the user interface of the program STEPS. STEPS is a simulation platform for modeling and stochastic simulation of coupled reaction-diffusion systems with complex 3-dimensional boundary conditions. Setting up such models is a complicated process that consists of many phases. Initial versions of STEPS relied on a static input format that did not cleanly separate these phases, limiting modelers in how they could control the simulation and becoming increasingly complex as new features and new simulation algorithms were added. We solved all of these problems by tightly integrating STEPS with Python, using SWIG to expose our existing simulation code.

Interoperability of neuroscience modeling software: current status and future directions.

Neuroscience increasingly uses computational models to assist in the exploration and interpretation of complex phenomena. As a result, considerable effort is invested in the development of software tools and technologies for numerical simulations and for the creation and publication of models. The diversity of related tools leads to the duplication of effort and hinders model reuse. Development practices and technologies that support interoperability between software systems therefore play an important role in making the modeling process more efficient and in ensuring that published models can be reliably and easily reused. Various forms of interoperability are possible including the development of portable model description standards, the adoption of common simulation languages or the use of standardized middleware. Each of these approaches finds applications within the broad range of current modeling activity. However more effort is required in many areas to enable new scientific questions to be addressed. Here we present the conclusions of the "Neuro-IT Interoperability of Simulators" workshop, held at the 11th computational neuroscience meeting in Edinburgh ( July 19-20 2006; http://www.cnsorg.org ). We assess the current state of interoperability of neural simulation software and explore the future directions that will enable the field to advance.

Anomalous diffusion in Purkinje cell dendrites caused by spines.

We combined local photolysis of caged compounds with fluorescence imaging to visualize molecular diffusion within dendrites of cerebellar Purkinje cells. Diffusion of a volume marker, fluorescein dextran, within spiny dendrites was remarkably slow in comparison to its diffusion in smooth dendrites. Computer simulations indicate that this retardation is due to a transient trapping of molecules within dendritic spines, yielding anomalous diffusion. We considered the influence of spine trapping on the diffusion of calcium ions (Ca(2+)) and inositol-1,4,5-triphospate (IP(3)), two synaptic second messengers. Diffusion of IP(3) was strongly influenced by the presence of dendritic spines, while Ca(2+) was removed so rapidly that it could not diffuse far enough to be trapped. We conclude that an important function of dendritic spines may be to trap chemical signals and thereby create slowed anomalous diffusion within dendrites.