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.

A Computational Model of Interactions Between Neuronal and Astrocytic Networks: The Role of Astrocytes in the Stability of the Neuronal Firing Rate.

Recent research in neuroscience indicates the importance of tripartite synapses and gliotransmission mediated by astrocytes in neuronal system modulation. Although the astrocyte and neuronal network functions are interrelated, they are fundamentally different in their signaling patterns and, possibly, the time scales at which they operate. However, the exact nature of gliotransmission and the effect of the tripartite synapse function at the network level are currently elusive. In this paper, we propose a computational model of interactions between an astrocyte network and a neuron network, starting from tripartite synapses and spanning to a joint network level. Our model focuses on a two-dimensional setup emulating a mixed in vitro neuron-astrocyte cell culture. The model depicts astrocyte-released gliotransmitters exerting opposing effects on the neurons: increasing the release probability of the presynaptic neuron while hyperpolarizing the post-synaptic one at a longer time scale. We simulated the joint networks with various levels of astrocyte contributions and neuronal activity levels. Our results indicate that astrocytes prolong the burst duration of neurons, while restricting hyperactivity. Thus, in our model, the effect of astrocytes is homeostatic; the firing rate of the network stabilizes to an intermediate level independently of neuronal base activity. Our computational model highlights the plausible roles of astrocytes in interconnected astrocytic and neuronal networks. Our simulations support recent findings in neurons and astrocytes in vivo and in vitro suggesting that astrocytic networks provide a modulatory role in the bursting of the neuronal network.

Glutamate mediated astrocytic filtering of neuronal activity.

Neuron-astrocyte communication is an important regulatory mechanism in various brain functions but its complexity and role are yet to be fully understood. In particular, the temporal pattern of astrocyte response to neuronal firing has not been fully characterized. Here, we used neuron-astrocyte cultures on multi-electrode arrays coupled to Ca2+ imaging and explored the range of neuronal stimulation frequencies while keeping constant the amount of stimulation. Our results reveal that astrocytes specifically respond to the frequency of neuronal stimulation by intracellular Ca2+ transients, with a clear onset of astrocytic activation at neuron firing rates around 3-5 Hz. The cell-to-cell heterogeneity of the astrocyte Ca2+ response was however large and increasing with stimulation frequency. Astrocytic activation by neurons was abolished with antagonists of type I metabotropic glutamate receptor, validating the glutamate-dependence of this neuron-to-astrocyte pathway. Using a realistic biophysical model of glutamate-based intracellular calcium signaling in astrocytes, we suggest that the stepwise response is due to the supralinear dynamics of intracellular IP3 and that the heterogeneity of the responses may be due to the heterogeneity of the astrocyte-to-astrocyte couplings via gap junction channels. Therefore our results present astrocyte intracellular Ca2+ activity as a nonlinear integrator of glutamate-dependent neuronal activity.

Sparse short-distance connections enhance calcium wave propagation in a 3D model of astrocyte networks.

Traditionally, astrocytes have been considered to couple via gap-junctions into a syncytium with only rudimentary spatial organization. However, this view is challenged by growing experimental evidence that astrocytes organize as a proper gap-junction mediated network with more complex region-dependent properties. On the other hand, the propagation range of intercellular calcium waves (ICW) within astrocyte populations is as well highly variable, depending on the brain region considered. This suggests that the variability of the topology of gap-junction couplings could play a role in the variability of the ICW propagation range. Since this hypothesis is very difficult to investigate with current experimental approaches, we explore it here using a biophysically realistic model of three-dimensional astrocyte networks in which we varied the topology of the astrocyte network, while keeping intracellular properties and spatial cell distribution and density constant. Computer simulations of the model suggest that changing the topology of the network is indeed sufficient to reproduce the distinct ranges of ICW propagation reported experimentally. Unexpectedly, our simulations also predict that sparse connectivity and restriction of gap-junction couplings to short distances should favor propagation while long-distance or dense connectivity should impair it. Altogether, our results provide support to recent experimental findings that point toward a significant functional role of the organization of gap-junction couplings into proper astroglial networks. Dynamic control of this topology by neurons and signaling molecules could thus constitute a new type of regulation of neuron-glia and glia-glia interactions.