Vesicle and reaction-diffusion hybrid modeling with STEPS.

Vesicles carry out many essential functions within cells through the processes of endocytosis, exocytosis, and passive and active transport. This includes transporting and delivering molecules between different parts of the cell, and storing and releasing neurotransmitters in neurons. To date, computational simulation of these key biological players has been rather limited and has not advanced at the same pace as other aspects of cell modeling, restricting the realism of computational models. We describe a general vesicle modeling tool that has been designed for wide application to a variety of cell models, implemented within our software STochastic Engine for Pathway Simulation (STEPS), a stochastic reaction-diffusion simulator that supports realistic reconstructions of cell tissue in tetrahedral meshes. The implementation is validated in an extensive test suite, parallel performance is demonstrated in a realistic synaptic bouton model, and example models are visualized in a Blender extension module.

STEPS 4.0: Fast and memory-efficient molecular simulations of neurons at the nanoscale.

Recent advances in computational neuroscience have demonstrated the usefulness and importance of stochastic, spatial reaction-diffusion simulations. However, ever increasing model complexity renders traditional serial solvers, as well as naive parallel implementations, inadequate. This paper introduces a new generation of the STochastic Engine for Pathway Simulation (STEPS) project (http://steps.sourceforge.net/), denominated STEPS 4.0, and its core components which have been designed for improved scalability, performance, and memory efficiency. STEPS 4.0 aims to enable novel scientific studies of macroscopic systems such as whole cells while capturing their nanoscale details. This class of models is out of reach for serial solvers due to the vast quantity of computation in such detailed models, and also out of reach for naive parallel solvers due to the large memory footprint. Based on a distributed mesh solution, we introduce a new parallel stochastic reaction-diffusion solver and a deterministic membrane potential solver in STEPS 4.0. The distributed mesh, together with improved data layout and algorithm designs, significantly reduces the memory footprint of parallel simulations in STEPS 4.0. This enables massively parallel simulations on modern HPC clusters and overcomes the limitations of the previous parallel STEPS implementation. Current and future improvements to the solver are not sustainable without following proper software engineering principles. For this reason, we also give an overview of how the STEPS codebase and the development environment have been updated to follow modern software development practices. We benchmark performance improvement and memory footprint on three published models with different complexities, from a simple spatial stochastic reaction-diffusion model, to a more complex one that is coupled to a deterministic membrane potential solver to simulate the calcium burst activity of a Purkinje neuron. Simulation results of these models suggest that the new solution dramatically reduces the per-core memory consumption by more than a factor of 30, while maintaining similar or better performance and scalability.

Modeling Neurons in 3D at the Nanoscale.

For decades, neurons have been modeled by methods developed by early pioneers in the field such as Rall, Hodgkin and Huxley, as cable-like morphological structures with voltage changes that are governed by a series of ordinary differential equations describing the conductances of ion channels embedded in the membrane. In recent years, advances in experimental techniques have improved our knowledge of the morphological and molecular makeup of neurons, and this has come alongside ever-increasing computational power and the wider availability of computer hardware to researchers. This has opened up the possibility of more detailed 3D modeling of neuronal morphologies and their molecular makeup, a new, emerging component of the field of computational neuroscience that is expected to play an important role in building our understanding of neurons and their behavior into the future.Many readers may be familiar with 1D models yet unfamiliar with the more detailed 3D description of neurons. As such, this chapter introduces some of the techniques used in detailed 3D, molecular modeling, and shows the steps required for building such models from a foundation of the more familiar 1D description. This broadly falls into two categories; morphology and how to build a 3D computational mesh based on a cable-like description of the neuronal geometry or directly from imaging studies, and biochemically how to define a discrete, stochastic description of the molecular neuronal makeup. We demonstrate this with a full Purkinje cell model, implemented in 3D simulation in software STEPS.

A Model of Induction of Cerebellar Long-Term Depression Including RKIP Inactivation of Raf and MEK.

We report an updated stochastic model of cerebellar Long Term Depression (LTD) with improved realism. Firstly, we verify experimentally that dissociation of Raf kinase inhibitor protein (RKIP) from Mitogen-activated protein kinase kinase (MEK) is required for cerebellar LTD and add this interaction to an earlier published model, along with the known requirement of dissociation of RKIP from Raf kinase. We update Ca2+ dynamics as a constant-rate influx, which captures experimental input profiles accurately. We improve α-amino-3-hydroxy-5-methyl-4 isoxazolepropionic acid (AMPA) receptor interactions by adding phosphorylation and dephosphorylation of AMPA receptors when bound to glutamate receptor interacting protein (GRIP). The updated model is tuned to reproduce experimental Ca2+ peak vs. LTD amplitude curves at four different Ca2+ pulse durations as closely as possible. We find that the updated model is generally more robust with these changes, yet we still observe some sensitivity of LTD induction to copy number of the key signaling molecule Protein kinase C (PKC). We predict natural variability in this number by stochastic diffusion may influence the probabilistic LTD response to Ca2+ input in Purkinje cell spines and propose this as an extra source of stochasticity that may be important also in other signaling systems.

The role of dendritic spine morphology in the compartmentalization and delivery of surface receptors.

Since AMPA receptors are major molecular players in both short- and long-term plasticity, it is important to identify the time-scales of and factors affecting the lateral diffusion of AMPARs on the dendrite surface. Using a mathematical model, we study how the dendritic spine morphology affects two processes: (1) compartmentalization of the surface receptors in a single spine to retain local chemistry and (2) the delivery of receptors to the post-synaptic density (PSD) of spines via lateral diffusion following insertion onto the dendrite shaft. Computing the mean first passage time (MFPT) of surface receptors on a sample of real spine morphologies revealed that a constricted neck and bulbous head serve to compartmentalize receptors, consistent with previous works. The residence time of a Brownian diffusing receptor on the membrane of a single spine was computed to be ∼ 5 s. We found that the location of the PSD corresponds to the location at which the maximum MFPT occurs, the position that maximizes the residence time of a diffusing receptor. Meanwhile, the same geometric features of the spine that compartmentalize receptors inhibit the recruitment of AMPARs via lateral diffusion from dendrite insertion sites. Spines with narrow necks will trap a smaller fraction of diffusing receptors in the their PSD when considering competition for receptors between the spines, suggesting that ideal geometrical features involve a tradeoff depending on the intent of compartmentalizing the current receptor pool or recruiting new AMPARs in the PSD. The ultimate distribution of receptors among the spine PSDs by lateral diffusion from the dendrite shaft is an interplay between the insertion location and the shape and locations of both the spines and their PSDs. The time-scale for delivery of receptors to the PSD of spines via lateral diffusion was computed to be ∼ 60 s.

Efficient calculation of the quasi-static electrical potential on a tetrahedral mesh and its implementation in STEPS.

We describe a novel method for calculating the quasi-static electrical potential on tetrahedral meshes, which we call E-Field. The E-Field method is implemented in STEPS, which performs stochastic spatial reaction-diffusion computations in tetrahedral-based cellular geometry reconstructions. This provides a level of integration between electrical excitability and spatial molecular dynamics in realistic cellular morphology not previously achievable. Deterministic solutions are also possible. By performing the Rallpack tests we demonstrate the accuracy of the E-Field method. Efficient node ordering is an important practical consideration, and we find that a breadth-first search provides the best solutions, although principal axis ordering suffices for some geometries. We discuss potential applications and possible future directions, and predict that the E-Field implementation in STEPS will play an important role in the future of multiscale neural simulations.

Stochastic calcium mechanisms cause dendritic calcium spike variability.

Bursts of dendritic calcium spikes play an important role in excitability and synaptic plasticity in many types of neurons. In single Purkinje cells, spontaneous and synaptically evoked dendritic calcium bursts come in a variety of shapes with a variable number of spikes. The mechanisms causing this variability have never been investigated thoroughly. In this study, a detailed computational model using novel simulation routines is applied to identify the roles that stochastic ion channels, spatial arrangements of ion channels, and stochastic intracellular calcium have toward producing calcium burst variability. Consistent with experimental recordings from rats, strong variability in the burst shape is observed in simulations. This variability persists in large model sizes in contrast to models containing only voltage-gated channels, where variability reduces quickly with increase of system size. Phase plane analysis of Hodgkin-Huxley spikes and of calcium bursts identifies fluctuation in phase space around probabilistic phase boundaries as the mechanism determining the dependence of variability on model size. Stochastic calcium dynamics are the main cause of calcium burst fluctuations, specifically the calcium activation of mslo/BK-type and SK2 channels. Local variability of calcium concentration has a significant effect at larger model sizes. Simulations of both spontaneous and synaptically evoked calcium bursts in a reconstructed dendrite show, in addition, strong spatial and temporal variability of voltage and calcium, depending on morphological properties of the dendrite. Our findings suggest that stochastic intracellular calcium mechanisms play a crucial role in dendritic calcium spike generation and are therefore an essential consideration in studies of neuronal excitability and plasticity.

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/