Parallel Stochastic Discrete Event Simulation of Calcium Dynamics in Neuron

A computational model to uncover the biophysical underpinnings of neural firing heterogeneity in dissociated hippocampal cultures

Calcium (Ca2+ ) imaging reveals a variety of correlated firing in cultures of dissociated hippocampal neurons, pinpointing the non-synaptic paracrine release of glutamate as a possible mediator for such firing patterns, although the biophysical underpinnings remain unknown. An intriguing possibility is that extracellular glutamate could bind metabotropic receptors linked with inositol trisphosphate (IP3 ) mediated release of Ca2+ from the endoplasmic reticulum of individual neurons, thereby modulating neural activity in combination with sarco/endoplasmic reticulum Ca2+ transport ATPase (SERCA) and voltage-gated Ca2+ channels (VGCC). However, the possibility that such release may occur in different neuronal compartments and can be inherently stochastic poses challenges in the characterization of such interplay between various Ca2+ channels. Here we deploy biophysical modeling in association with Monte Carlo parameter sampling to characterize such interplay and successfully predict experimentally observed Ca2+ patterns. The results show that the neurotransmitter level at the plasma membrane is the extrinsic source of heterogeneity in somatic Ca2+ transients. Our analysis, in particular, identifies the origin of such heterogeneity to an intrinsic differentiation of hippocampal neurons in terms of multiple cellular properties pertaining to intracellular Ca2+ signaling, such as VGCC, IP3 receptor, and SERCA expression. In the future, the biophysical model and parameter estimation approach used in this study can be upgraded to predict the response of a system of interconnected neurons.

Elementary intracellular Ca signals approximated as a transition of release channel system from a metastable state

Cardiac muscle contraction is initiated by an elementary Ca signal (called Ca spark) which is achieved by collective action of Ca release channels in a cluster. The mechanism of this synchronization remains uncertain. We approached Ca spark activation as an emergent phenomenon of an interactive system of release channels. We constructed a weakly lumped Markov chain that applies an Ising model formalism to such release channel clusters and probable open channel configurations and demonstrated that spark activation is described as a system transition from a metastable to an absorbing state, analogous to the pressure required to overcome surface tension in bubble formation. This yielded quantitative estimates of the spark generation probability as a function of various system parameters. We performed numerical simulations to find spark probabilities as a function of sarcoplasmic reticulum Ca concentration, obtaining similar values for spark activation threshold as our analytic model, as well as those reported in experimental studies. Our parametric sensitivity analyses also showed that the spark activation threshold decreased as Ca sensitivity of RyR activation and RyR cluster size increased.

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.

Computational analysis of NIRS and BOLD signal from neurovascular coupling with three neuron-system feedforward inhibition network

Several neurological disorders occur due to hypoxic condition in brain arising from impairment of cerebral functionality, which can be controlled by neural stimulation driven vasoactive response mediated through biological response in astrocyte, a phenomenon known as neurovascular coupling. Brain can adjust with the problem of hypoxic condition by causing vasodilation with the help of this mechanism. To deduce the mechanism behind vasodilation of blood vessel caused by neuronal stimulus, current study articulates a mathematical model involving neuronal system feedforward inhibition network model (FFI) with two other functional components of neurovascular coupling, i.e. astrocyte and smooth muscle cell lining blood vessel. This study includes the neural inhibition network system where glutamatergic pyramidal neuron and GABAergic interneuron act antagonistically with each other. The proposed model successfully includes the implication of the inhibition system to design mathematical model for neurovascular coupling. Result of the proposed model shows that the increase in neuronal stimulus from 20 to 60 µA/cm² has the ability to increase the vasodilatory activity of blood tissue vasculature. Oxygenation level and hemodynamic response due to input synaptic stimulation has been calculated by regional cerebral oxygenation level (rS0₂) and blood oxygen level dependent (BOLD) imaging signal which supports vasodilation of blood vessel with increase in synaptic input stimulus.