| | Models | Description |
| 1. |
A neuronal circuit simulator for non Monte Carlo analysis of neuronal noise (Kilinc & Demir 2018)
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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. |
| 2. |
Ca2+ requirements for Long-Term Depression in Purkinje Cells (Criseida Zamora et al 2018)
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An updated stochastic model of cerebellar Long-Term Depression (LTD) to study the requirements of calcium to induce LTD. Calcium signal is generated as a train of calcium pulses and this can be modulated by its amplitude, frequency, width and number of pulses.
CaMKII activation and its regulatory pathway are added to an earlier published model to study the sensitivity to calcium frequency. The model is useful to investigate systematically the dependence of LTD induction on calcium stimuli parameters. |
| 3. |
Dynamics of ERK signaling pathways during L-LTP induction(Miningou et al 2021)
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Biochemical model of five signaling pathways (3 activated by cAMP and 2 activated by calcium) leading to ERK activation during L-LTP induction. Simulations show that calcium and cAMP work synergistically to activate ERK and that stimuli given with large inter-trial intervals activate more ERK than shorter intervals. Epac and RasGRF pathways contribute to early dynamics and PKA and CaMKII contribute to late dynamics of ERK activation. |
| 4. |
Effect of cortical D1 receptor sensitivity on working memory maintenance (Reneaux & Gupta 2018)
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Alterations in cortical D1 receptor density and reactivity of dopamine-binding sites, collectively termed as D1 receptor-sensitivity in the present study, have been experimentally shown to affect the working memory maintenance during delay-period. However, computational models addressing the effect of D1 receptor-sensitivity are lacking. A quantitative neural mass model of the prefronto-mesoprefrontal system has been proposed to take into account the effect of variation in cortical D1 receptor-sensitivity on working memory maintenance during delay. The model computes the delay-associated equilibrium states/operational points of the system for different values of D1 receptor-sensitivity through the nullcline and bifurcation analysis. Further, to access the robustness of the working memory maintenance during delay in the presence of alteration in D1 receptor-sensitivity, numerical simulations of the stochastic formulation of the model are performed to obtain the global potential landscape of the dynamics.
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| 5. |
Kesten and Langevin synaptic size fluctuation simulator (Hazan & Ziv 2020)
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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. In this paper 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. This simulator shows how synaptic size fluctuations governed by a stochastic process known as a Kesten process (as well as a specific form of a non-linear Langevin process) can give rise to this size diversity. |
| 6. |
Mesoscopic model of spontaneous synaptic size fluctuations (Hazan & Ziv 2020)
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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. |
| 7. |
On the long time behaviour of single stochastic Hodgkin-Huxley neurons (Höpfner 2023)
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This is the R program associated to the paper
R. Hoepfner
On the long time behaviour of
single stochastic Hodgkin-Huxley neurons with constant signal,
and a construction of circuits of interacting neurons
showing self-organized rhythmic interactions
Mathematical Neuroscience and Applications, to appear
arXiv:2203:16160 |
| 8. |
Simple and accurate Diffusion Approximation algor. for stochastic ion channels (Orio & Soudry 2012)
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" ... We derived the (Stochastic Differential Equations) SDE explicitly for any given ion channel kinetic scheme. The resulting generic equations were surprisingly simple and interpretable – allowing an easy, transparent and efficient (Diffusion Approximation) DA implementation, avoiding unnecessary approximations. The algorithm was tested in a voltage clamp simulation and in two different current clamp simulations, yielding the same results as (Markov Chains) MC modeling. Also, the simulation efficiency of this DA method demonstrated considerable superiority over MC methods, except when short time steps or low channel numbers were used." |
| 9. |
Stochastic Hodgkin-Huxley Model: 14x28D Langevin Simulation (Pu and Thomas, 2020).
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This model provides a natural 14-dimensional Langevin dynamics for the Hodgkin Huxley system in which each directed edge in the ion channel state transition graph acts as an independent noise source, leading to a 14 dimensional state space (1 dimension for voltage, 5 for potassium and 8 for sodium) and 14 × 28 noise coefficient matrix S. In [Pu and Thomas (2020) Neural Computation] we show that this 14 x 28 dimensional model is pathwise equivalent to the 14 x 11 dimensional Langevin model proposed in [Fox and Lu (1994) Phys Rev E], as well as an 14 x 14 model described in [Orio and Soudry (2012) PLoS One]. Unlike Fox and Lu's model, our construction does not require a matrix root extraction step, and runs significantly faster. Unlike Orio and Soudry's model, each directed edge acts as an independent noise source, which facilitates the application of stochastic shielding methods for even greater simulation speed. For comparison, we provide implementations of the following models: 1. Discrete-state Markov chain model (slow, but provides the "gold standard" model), adapted from [Goldwyn and Shea-Brown (2011) PLoS Comp. Biol.] 2. 14 x 11 Langevin model from [Fox and Lu (1994) Phys. Rev. E]. (We implement versions with three different boundary conditions: open boundaries, reflecting boundaries, and resampling/rejection at the boundaries.) 3. 4 x 3 Langevin model from [Fox (1997) Biophys. J.] 4. 14 x 13 Langevin model from [Goldwyn and Shea (2011) PLoS Comp. Biol.] 5. 14 x 14 Langevin model from [Dangerfield et al (2012) Phys. Rev. E] 6. 14 x 14 Langevin model from [Orio and Soudry (2012) PLoS One] 7. 14 x 28 Langevin model from [Pu and Thomas (2020) Neural Computation] implemented both with and without stochastic shielding 8. 14 x 0 deterministic HH model (also from [Pu and Thomas (2020) Neural Computation], with the full 14 dimensional state space but no noise) The Read_me.md file provides more detailed simulations.
To cite the code: Pu, Shusen, and Peter J. Thomas. "Fast and Accurate Langevin Simulations of Stochastic Hodgkin-Huxley Dynamics." Neural Computation 32, 1775–1835 (2020)
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