Initiation and propagation of a neuronal intracellular calcium wave

Differential behaviors of calcium-induced calcium release in one dimensional dendrite by Nernst-Planck equation, cable model and pure diffusion model

The source and dynamics of calcium is the key factor that regulates dendritic integration. Apart from the voltage-gated and ligand-gated calcium influx, an important source of calcium is from inner store of endoplasmic reticulum with a regenerative process of calcium-induced calcium release (CICR). To trigger this process, inositol 1,4,5-trisphosphate (IP3) and calcium are needed to satisfy certain requirements. The aim of our paper is to investigate how the CICR depends on the dynamics of membrane potential. We utilize one dimensional dendritic model to calculate membrane potential by Nernst-Planck Equation (NPE) and cable model and Pure Diffusion (PD) model, computational simulations are carried out to inject the calcium influx by synaptic stimulation and to predict subsequent CICR and calcium wave propagation. Our results demonstrate that CICR initiation and calcium wave propagation have much difference between electro-diffusion process of NPE and cable model. We find that cable model has lower threshold of IP3 stimulation to trigger CICR but is more difficult for calcium propagation than NPE, PD model requires even higher threshold of IP3 to initiate CICR process and calcium duration is shorter than NPE; the regenerative calcium wave propagates with faster speed in NPE than that in cable model and in PD model. Our work addresses the important role of electro-diffusion dynamics of charged ions in regulating CICR process in dendritic structure; and provides theoretical predictions for neurological process which requires sustaining calcium for downstream signaling processes.

Reproducibility in Computational Neuroscience Models and Simulations

OBJECTIVE

Like all scientific research, computational neuroscience research must be reproducible. Big data science, including simulation research, cannot depend exclusively on journal articles as the method to provide the sharing and transparency required for reproducibility.

METHODS

Ensuring model reproducibility requires the use of multiple standard software practices and tools, including version control, strong commenting and documentation, and code modularity.

RESULTS

Building on these standard practices, model-sharing sites and tools have been developed that fit into several categories: 1) standardized neural simulators; 2) shared computational resources; 3) declarative model descriptors, ontologies, and standardized annotations; and 4) model-sharing repositories and sharing standards.

CONCLUSION

A number of complementary innovations have been proposed to enhance sharing, transparency, and reproducibility. The individual user can be encouraged to make use of version control, commenting, documentation, and modularity in development of models. The community can help by requiring model sharing as a condition of publication and funding.

SIGNIFICANCE

Model management will become increasingly important as multiscale models become larger, more detailed, and correspondingly more difficult to manage by any single investigator or single laboratory. Additional big data management complexity will come as the models become more useful in interpreting experiments, thus increasing the need to ensure clear alignment between modeling data, both parameters and results, and experiment.

Calcium regulation of HCN channels supports persistent activity in a multiscale model of neocortex

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 (Ca(2+)) regulation of hyperpolarization-activated cyclic nucleotide-gated (HCN) channels in providing additional and complementary support of continuing activation in the network. The network contained 776 compartmental neurons arranged in the cortical layers, connected using synapses containing AMPA/NMDA/GABAA/GABAB receptors. Metabotropic glutamate receptors (mGluR) produced inositol triphosphate (IP3) which caused the release of Ca(2+) from endoplasmic reticulum (ER) stores, with reuptake by sarco/ER Ca(2+)-ATP-ase pumps (SERCA), and influence on HCN channels. Stimulus-induced depolarization led to Ca(2+) influx via NMDA and voltage-gated Ca(2+) channels (VGCCs). After a delay, mGluR activation led to ER Ca(2+) release via IP3 receptors. These factors increased HCN channel conductance and produced firing lasting for ∼1min. The model displayed inter-scale synergies among synaptic weights, excitation/inhibition balance, firing rates, membrane depolarization, Ca(2+) levels, regulation of HCN channels, and induction of persistent activity. The interaction between inhibition and Ca(2+) at the HCN channel nexus determined a limited range of inhibition strengths for which intracellular Ca(2+) could prepare population-specific persistent activity. Interactions between metabotropic and ionotropic inputs to the neuron demonstrated how multiple pathways could contribute in a complementary manner to persistent activity. Such redundancy and complementarity via multiple pathways is a critical feature of biological systems. Mediation of activation at different time scales, and through different pathways, would be expected to protect against disruption, in this case providing stability for persistent activity.

Neuronal calcium wave propagation varies with changes in endoplasmic reticulum parameters: a computer model

Calcium (Ca²⁺) waves provide a complement to neuronal electrical signaling, forming a key part of a neuron's second messenger system. We developed a reaction-diffusion model of an apical dendrite with diffusible inositol triphosphate (IP₃), diffusible Ca²⁺, IP₃ receptors (IP₃Rs), endoplasmic reticulum (ER) Ca²⁺ leak, and ER pump (SERCA) on ER. Ca²⁺ is released from ER stores via IP₃Rs upon binding of IP₃ and Ca²⁺. This results in Ca²⁺-induced-Ca²⁺-release (CICR) and increases Ca²⁺ spread. 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 IP₃R distribution: (1) continuous homogeneous ER, (2) hotspots with increased IP₃R density (IP₃R hotspots), and (3) areas of increased ER density (ER stacks). All three modes produced Ca²⁺ waves with velocities similar to those measured in vitro (approximately 50-90 μm /sec). Continuous ER showed high sensitivity to IP₃R density increases, with time to onset reduced and speed increased. Increases in SERCA density resulted in opposite effects. The measures were sensitive to changes in density and spacing of IP₃R hotspots and stacks. Increasing the apparent diffusion coefficient of Ca²⁺ substantially increased wave speed. 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 IP₃Rs and SERCA could allow modulation of Ca²⁺ wave propagation in diseases where Ca²⁺ dysregulation has been implicated.

Reaction-diffusion in the NEURON simulator

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.

Extending the IP3 receptor model to include competition with partial agonists

The inositol 1,4,5-trisphosphate (IP(3)) receptor is a Ca(2+) channel located in the endoplasmic reticulum and is regulated by IP(3) and Ca(2+). This channel is critical to calcium signaling in cell types as varied as neurons and pancreatic beta cells to mast cells. De Young and Keizer (1992) created an eight-state, nine-variable model of the IP(3) receptor. In their model, they accounted for three binding sites, a site for IP(3), activating Ca(2+), and deactivating Ca(2+). The receptor is only open if IP(3) and activating Ca(2+) is bound. Li and Rinzel followed up this paper in 1994 by introducing a reduction that made it into a two variable system. A recent publication by Rossi et al. (2009) studied the effect of introducing IP(3)-like molecules, referred to as partial agonists (PA), into the cell to determine the structure-function relationship between IP(3) and its receptor. Initial results suggest a competitive model, where IP(3) and PA fight for the same binding site. We extend the original eight-state model to a 12-state model in order to illustrate this competition, and perform a similar reduction to that of Li and Rinzel in the first modeling study we are aware of considering PA effect on an IP(3) receptor. Using this reduction we solve for the equilibrium open probability for calcium release in the model. We replicate graphs provided by the Rossi paper, and find that optimizing the subunit affinities for IP(3) and PA yields a good fit to the data. We plug our extended reduced model into a full cell model, in order to analyze the effects PA have on whole cell properties specifically the propagation of calcium waves in two dimensions. We conclude that PA creates qualitatively different calcium dynamics than would simply reducing IP(3), but that effectively PA can act as an IP(3) knockdown.

Inositol-1,4,5-trisphosphate receptor-mediated Ca2+ waves in pyramidal neuron dendrites propagate through hot spots and cold spots

We studied inositol-1,4,5-trisphosphate (IP(3)) receptor-dependent intracellular Ca(2+) waves in CA1 hippocampal and layer V medial prefrontal cortical pyramidal neurons using whole-cell patch-clamp recordings and Ca(2+) fluorescence imaging. We observed that Ca(2+) waves propagate in a saltatory manner through dendritic regions where increases in the intracellular concentration of Ca(2+) ([Ca(2+)](i)) were large and fast ('hot spots') separated by regions where increases in [Ca(2+)](i) were comparatively small and slow ('cold spots'). We also observed that Ca(2+) waves typically initiate in hot spots and terminate in cold spots, and that most hot spots, but few cold spots, are located at dendritic branch points. Using immunohistochemistry, we found that IP(3) receptors (IP(3)Rs) are distributed in clusters along pyramidal neuron dendrites and that the distribution of inter-cluster distances is nearly identical to the distribution of inter-hot spot distances. These findings support the hypothesis that the dendritic locations of Ca(2+) wave hot spots in general, and branch points in particular, are specially equipped for regenerative IP(3)R-dependent internal Ca(2+) release. Functionally, the observation that IP(3)R-dependent [Ca(2+)](i) rises are greater at branch points raises the possibility that this novel Ca(2+) signal may be important for the regulation of Ca(2+)-dependent processes in these locations. Futhermore, the observation that Ca(2+) waves tend to fail between hot spots raises the possibility that influences on Ca(2+) wave propagation may determine the degree of functional association between distinct Ca(2+)-sensitive dendritic domains.