Models that contain the Model Concept : Reaction-diffusion

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    Models   Description
1.  A multiscale approach to analyze circadian rhythms (Vasalou & Henson, 2010) (CellML)
" ... We developed a firing rate code model to incorporate known electrophysiological properties of SCN (suprachiasmatic nucleus) pacemaker cells, including circadian dependent changes in membrane voltage and ion conductances. Calcium dynamics were included in the model as the putative link between electrical firing and gene expression. Individual ion currents exhibited oscillatory patterns matching experimental data both in current levels and phase relationships. VIP and GABA neurotransmitters, which encode synaptic signals across the SCN, were found to play critical roles in daily oscillations of membrane excitability and gene expression. Blocking various mechanisms of intracellular calcium accumulation by simulated pharmacological agents (nimodipine, IP3- and ryanodine-blockers) reproduced experimentally observed trends in firing rate dynamics and core-clock gene transcription. The intracellular calcium concentration was shown to regulate diverse circadian processes such as firing frequency, gene expression and system periodicity. The model predicted a direct relationship between firing frequency and gene expression amplitudes, demonstrated the importance of intracellular pathways for single cell behavior and provided a novel multiscale framework which captured characteristics of the SCN at both the electrophysiological and gene regulatory levels."
2.  A multiscale approach to analyze circadian rhythms (Vasalou & Henson, 2010) (SBML)
" ... We developed a firing rate code model to incorporate known electrophysiological properties of SCN (suprachiasmatic nucleus) pacemaker cells, including circadian dependent changes in membrane voltage and ion conductances. Calcium dynamics were included in the model as the putative link between electrical firing and gene expression. Individual ion currents exhibited oscillatory patterns matching experimental data both in current levels and phase relationships. VIP and GABA neurotransmitters, which encode synaptic signals across the SCN, were found to play critical roles in daily oscillations of membrane excitability and gene expression. Blocking various mechanisms of intracellular calcium accumulation by simulated pharmacological agents (nimodipine, IP3- and ryanodine-blockers) reproduced experimentally observed trends in firing rate dynamics and core-clock gene transcription. The intracellular calcium concentration was shown to regulate diverse circadian processes such as firing frequency, gene expression and system periodicity. The model predicted a direct relationship between firing frequency and gene expression amplitudes, demonstrated the importance of intracellular pathways for single cell behavior and provided a novel multiscale framework which captured characteristics of the SCN at both the electrophysiological and gene regulatory levels."
3.  A neuronal circuit simulator for non Monte Carlo analysis of neuronal noise (Kilinc & Demir 2018)
cirsiumNeuron is a neuronal circuit simulator that can directly and efficiently compute characterizations of stochastic behavior, i.e., noise, for multi-neuron circuits. In cirsiumNeuron, we utilize a general modeling framework for biological neuronal circuits which systematically captures the nonstationary stochastic behavior of the ion channels and the synaptic processes. In this framework, we employ fine-grained, discrete-state, continuous-time Markov Chain (MC) models of both ion channels and synaptic processes in a unified manner. Our modeling framework can automatically generate the corresponding coarse-grained, continuous-state, continuous-time Stochastic Differential Equation (SDE) models. In addition, for the stochastic characterization of neuronal variability and noise, we have implemented semi-analytical, non Monte Carlo analysis techniques that work both in time and frequency domains, which were previously developed for analog electronic circuits. In these semi-analytical noise evaluation schemes, (differential) equations that directly govern probabilistic characterizations in the form of correlation functions (time domain) or spectral densities (frequency domain) are first derived analytically, and then solved numerically. These semi-analytical noise analysis techniques correctly and accurately capture the second order statistics (mean, variance, autocorrelation, and power spectral density) of the underlying neuronal processes as compared with Monte Carlo simulations.
4.  Action potential-evoked Na+ influx similar in axon and soma (Fleidervish et al. 2010) (Python)
"In cortical pyramidal neurons, the axon initial segment (AIS) is pivotal in synaptic integration. It has been asserted that this is because there is a high density of Na+ channels in the AIS. However, we found that action potential-associated Na+ flux, as measured by high-speed fluorescence Na+ imaging, was about threefold larger in the rat AIS than in the soma. Spike-evoked Na+ flux in the AIS and the first node of Ranvier was similar and was eightfold lower in basal dendrites. ... In computer simulations, these data were consistent with the known features of action potential generation in these neurons."
5.  Active dendrites shape signaling microdomains in hippocampal neurons (Basak & Narayanan 2018)
The spatiotemporal spread of biochemical signals in neurons and other cells regulate signaling specificity, tuning of signal propagation, along with specificity and clustering of adaptive plasticity. Theoretical and experimental studies have demonstrated a critical role for cellular morphology and the topology of signaling networks in regulating this spread. In this study, we add a significantly complex dimension to this narrative by demonstrating that voltage-gated ion channels (A-type Potassium channels and T-type Calcium channels) on the plasma membrane could actively amplify or suppress the strength and spread of downstream signaling components. We employed a multiscale, multicompartmental, morphologically realistic, conductance-based model that accounted for the biophysics of electrical signaling and the biochemistry of calcium handling and downstream enzymatic signaling in a hippocampal pyramidal neuron. We chose the calcium – calmodulin – calcium/calmodulin-dependent protein kinase II (CaMKII) – protein phosphatase 1 (PP1) signaling pathway owing to its critical importance to several forms of neuronal plasticity, and employed physiologically relevant theta-burst stimulation (TBS) or theta-burst pairing (TBP) protocol to initiate a calcium microdomain through NMDAR activation at a synapse.
6.  Ca+/HCN channel-dependent persistent activity in multiscale model of neocortex (Neymotin et al 2016)
"Neuronal persistent activity has been primarily assessed in terms of electrical mechanisms, without attention to the complex array of molecular events that also control cell excitability. We developed a multiscale neocortical model proceeding from the molecular to the network level to assess the contributions of calcium regulation of hyperpolarization-activated cyclic nucleotide-gated (HCN) channels in providing additional and complementary support of continuing activation in the network. ..."
7.  CA1 pyramidal cell receptor dependent cAMP dynamics (Chay et al. 2016)
We use a combination of live cell imaging and stochastic modeling of signaling pathways to investigate how noradrenergic receptor stimulation interacts with calcium to control cAMP, required for synaptic plasticity and memory in the hippocampus. Our simulation results explain the mechanism whereby prior noradrenergic receptor stimulation does not enhance the subsequent NMDA stimulated cAMP elevation. Specifically, our results demonstrate the the negative feedback loop from cAMP, through PKA, to PDE4 cannot explain the results, and that switching of the noradrenergic receptor from Gs to Gi is required.
8.  Changes of ionic concentrations during seizure transitions (Gentiletti et al. 2016)
"... In order to investigate the respective roles of synaptic interactions and nonsynaptic mechanisms in seizure transitions, we developed a computational model of hippocampal cells, involving the extracellular space, realistic dynamics of Na+, K+, Ca2+ and Cl - ions, glial uptake and extracellular diffusion mechanisms. We show that the network behavior with fixed ionic concentrations may be quite different from the neurons’ behavior when more detailed modeling of ionic dynamics is included. In particular, we show that in the extended model strong discharge of inhibitory interneurons may result in long lasting accumulation of extracellular K+, which sustains the depolarization of the principal cells and causes their pathological discharges. ..."
9.  Compartmental differences in cAMP signaling pathways in hippocam. CA1 pyr. cells (Luczak et al 2017)
Model of cAMP signaling pathways in hippocampal CA1 pyramidal neurons investigate mechanisms underlying the experimentally observed difference in cAMP and PKA FRET between proximal and distal dendrites. Simulations show that compartmental difference in PKA activity required enrichment of protein phosphatase in small compartments; neither reduced PKA subunits nor increased PKA substrates were sufficient.
10.  Cortical Layer 5b pyr. cell with [Na+]i mechanisms, from Hay et al 2011 (Zylbertal et al 2017)
" ... Based on a large body of experimental recordings from both the soma and dendrites of L5b pyramidal cells in adult rats, we characterized key features of the somatic and dendritic firing and quantified their statistics. We used these features to constrain the density of a set of ion channels over the soma and dendritic surface via multi-objective optimization with an evolutionary algorithm, thus generating a set of detailed conductance-based models that faithfully replicate the back-propagating action potential activated Ca(2+) spike firing and the perisomatic firing response to current steps, as well as the experimental variability of the properties. Furthermore, we show a useful way to analyze model parameters with our sets of models, which enabled us to identify some of the mechanisms responsible for the dynamic properties of L5b pyramidal cells as well as mechanisms that are sensitive to morphological changes. ..."
11.  Dendritic spine geometry, spine apparatus organization: spatiotemporal Ca dynamics (Bell et al 2019)
" ... we systematically investigated the relationship between the shape and size of both the spine head and spine apparatus, a specialized endoplasmic reticulum compartment within the spine head, in modulating rapid calcium dynamics using mathematical modeling. ..."
12.  Discrimination on behavioral time-scales mediated by reaction-diffusion in dendrites (Bhalla 2017)
Sequences of events are ubiquitous in sensory, motor, and cognitive function. Key computational operations, including pattern recognition, event prediction, and plasticity, involve neural discrimination of spatio-temporal sequences. Here we show that synaptically-driven reaction diffusion pathways on dendrites can perform sequence discrimination on behaviorally relevant time-scales. We used abstract signaling models to show that selectivity arises when inputs at successive locations are aligned with, and amplified by, propagating chemical waves triggered by previous inputs. We incorporated biological detail using sequential synaptic input onto spines in morphologically, electrically, and chemically detailed pyramidal neuronal models based on rat data.
13.  Genetic, biochemical and bioelectrical dynamics in pattern regulation (Pietak & Levin 2017)
"Gene regulatory networks (GRNs) describe interactions between gene products and transcription factors that control gene expression. In combination with reaction–diffusion models, GRNs have enhanced comprehension of biological pattern formation. However, although it is well known that biological systems exploit an interplay of genetic and physical mechanisms, instructive factors such as transmembrane potential (Vmem) have not been integrated into full GRN models. Here we extend regulatory networks to include bioelectric signalling, developing a novel synthesis: the bioelectricity-integrated gene and reaction (BIGR) network. ..."
14.  Mesoscopic model of spontaneous synaptic size fluctuations (Hazan & Ziv 2020)
Sizes of glutamatergic synapses vary tremendously, even when formed on the same neuron. This diversity is commonly thought to reflect the outcome of activity-dependent forms of synaptic plasticity, yet activity-independent processes might also play some part. Here we show that in neurons with no history of activity whatsoever, synaptic sizes are no less diverse. We show that this diversity is the product of activity-independent size fluctuations, which are sufficient to generate a full repertoire of synaptic sizes at correct proportions. By combining modeling and experimentation we expose reciprocal relationships between size fluctuations, synaptic sizes and synaptic counts, and show how these phenomena might be connected through the dynamics of synaptic molecules as they move in, out and between synapses.
15.  Multitarget pharmacology for Dystonia in M1 (Neymotin et al 2016)
" ... We developed a multiscale model of primary motor cortex, ranging from molecular, up to cellular, and network levels, containing 1715 compartmental model neurons with multiple ion channels and intracellular molecular dynamics. We wired the model based on electrophysiological data obtained from mouse motor cortex circuit mapping experiments. We used the model to reproduce patterns of heightened activity seen in dystonia by applying independent random variations in parameters to identify pathological parameter sets. ..."
16.  Neuronal dendrite calcium wave model (Neymotin et al, 2015)
"... We developed a reaction-diffusion model of an apical dendrite with diffusible inositol triphosphate (IP3 ), diffusible Ca2+, IP3 receptors (IP3 Rs), endoplasmic reticulum (ER) Ca2+ leak, and ER pump (SERCA) on ER. ... At least two modes of Ca2+ wave spread have been suggested: a continuous mode based on presumed relative homogeneity of ER within the cell; and a pseudo-saltatory model where Ca2+ regeneration occurs at discrete points with diffusion between them. We compared the effects of three patterns of hypothesized IP3 R distribution: 1. continuous homogeneous ER, 2. hotspots with increased IP3R density (IP3 R hotspots), 3. areas of increased ER density (ER stacks). All three modes produced Ca2+ waves with velocities similar to those measured in vitro (~50 - 90µm /sec). ... The measures were sensitive to changes in density and spacing of IP3 R hotspots and stacks. ... An extended electrochemical model, including voltage gated calcium channels and AMPA synapses, demonstrated that membrane priming via AMPA stimulation enhances subsequent Ca2+ wave amplitude and duration. Our modeling suggests that pharmacological targeting of IP3 Rs and SERCA could allow modulation of Ca2+ wave propagation in diseases where Ca2+ dysregulation has been implicated. "
17.  Parallel STEPS: Large scale stochastic spatial reaction-diffusion simulat. (Chen & De Schutter 2017)
" ... In this paper, we describe an MPI-based, parallel operator-splitting implementation for stochastic spatial reaction-diffusion simulations with irregular tetrahedral meshes. The performance of our implementation is first examined and analyzed with simulations of a simple model. We then demonstrate its application to real-world research by simulating the reaction-diffusion components of a published calcium burst model in both Purkinje neuron sub-branch and full dendrite morphologies..."
18.  Reaction-diffusion in the NEURON simulator (McDougal et al 2013)
"In order to support research on the role of cell biological principles (genomics, proteomics, signaling cascades and reaction dynamics) on the dynamics of neuronal response in health and disease, NEURON's Reaction-Diffusion (rxd) module in Python provides specification and simulation for these dynamics, coupled with the electrophysiological dynamics of the cell membrane. Arithmetic operations on species and parameters are overloaded, allowing arbitrary reaction formulas to be specified using Python syntax. These expressions are then transparently compiled into bytecode that uses NumPy for fast vectorized calculations. At each time step, rxd combines NEURON's integrators with SciPy's sparse linear algebra library."
19.  Spatially-varying glutamate diffusion coefficient at CA1 synaptic cleft space (Gupta et al. 2016)
Due to the heterogeneous macromolecular crowding and geometrical irregularity at central excitatory synapses, the diffusion coefficient of glutamate may exhibit spatial variation across the cleft space. To take into account the effect of emergent cleft heterogeneity on the generation of excitatory postsynaptic currents (EPSCs), a gamma statistical distribution of the glutamate diffusion coefficient is considered and, using the principle of superstatistics, the glutamate transients are computed as well as the activation of AMPA receptors is performed. This model demonstrates the numerical simulation of the Brownian diffusion of glutamate under distributed diffusion coefficient, the subsequent stochastic activation of AMPA receptors using Milstein-Nicoll scheme and modified Gillespie algorithm with minimum time-step correction, and the eventual stochastic profile of EPSC generation. The study is based on the CA1 synapses located at the dendrites of CA1 pyramidal neurons in the mammalian hippocampal region.
20.  Using NEURON for reaction-diffusion modeling of extracellular dynamics (Newton et al 2018)
Development of credible clinically-relevant brain simulations has been slowed due to a focus on electrophysiology in computational neuroscience, neglecting the multiscale whole-tissue modeling approach used for simulation in most other organ systems. We have now begun to extend the NEURON simulation platform in this direction by adding extracellular modeling. NEURON's extracellular reaction-diffusion is supported by an intuitive Python-based where/who/what command sequence, derived from that used for intracellular reaction diffusion, to support coarse-grained macroscopic extracellular models. This simulation specification separates the expression of the conceptual model and parameters from the underlying numerical methods. In the volume-averaging approach used, the macroscopic model of tissue is characterized by free volume fraction—the proportion of space in which species are able to diffuse, and tortuosity—the average increase in path length due to obstacles. These tissue characteristics can be defined within particular spatial regions, enabling the modeler to account for regional differences, due either to intrinsic organization, particularly gray vs. white matter, or to pathology such as edema. We illustrate simulation development using spreading depression, a pathological phenomenon thought to play roles in migraine, epilepsy and stroke.

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