Stochastic Differential Equation Model for Cerebellar Granule Cell Excitability

Neurons in the brain express intrinsic dynamic behavior which is known to be stochastic in nature. A crucial question in building models of neuronal excitability is how to be able to mimic the dynamic behavior of the biological counterpart accurately and how to perform simulations in the fastest possible way. The well-established Hodgkin-Huxley formalism has formed to a large extent the basis for building biophysically and anatomically detailed models of neurons. However, the deterministic Hodgkin-Huxley formalism does not take into account the stochastic behavior of voltage-dependent ion channels. Ion channel stochasticity is shown to be important in adjusting the transmembrane voltage dynamics at or close to the threshold of action potential firing, at the very least in small neurons. In order to achieve a better understanding of the dynamic behavior of a neuron, a new modeling and simulation approach based on stochastic differential equations and Brownian motion is developed. The basis of the work is a deterministic one-compartmental multi-conductance model of the cerebellar granule cell. This model includes six different types of voltage-dependent conductances described by Hodgkin-Huxley formalism and simple calcium dynamics. A new model for the granule cell is developed by incorporating stochasticity inherently present in the ion channel function into the gating variables of conductances. With the new stochastic model, the irregular electrophysiological activity of an in vitro granule cell is reproduced accurately, with the same parameter values for which the membrane potential of the original deterministic model exhibits regular behavior. The irregular electrophysiological activity includes experimentally observed random subthreshold oscillations, occasional spontaneous spikes, and clusters of action potentials. As a conclusion, the new stochastic differential equation model of the cerebellar granule cell excitability is found to expand the range of dynamics in comparison to the original deterministic model. Inclusion of stochastic elements in the operation of voltage-dependent conductances should thus be emphasized more in modeling the dynamic behavior of small neurons. Furthermore, the presented approach is valuable in providing faster computation times compared to the Markov chain type of modeling approaches and more sophisticated theoretical analysis tools compared to previously presented stochastic modeling approaches

Modeling Signal Transduction Leading to Synaptic Plasticity: Evaluation and Comparison of Five Models

An essential phenomenon of the functional brain is synaptic plasticity which is associated with changes in the strength of synapses between neurons. These changes are affected by both extracellular and intracellular mechanisms. For example, intracellular phosphorylation-dephosphorylation cycles have been shown to possess a special role in synaptic plasticity. We, here, provide the first computational comparison of models for synaptic plasticity by evaluating five models describing postsynaptic signal transduction networks. Our simulation results show that some of the models change their behavior completely due to varying total concentrations of protein kinase and phosphatase. Furthermore, the responses of the models vary when models are compared to each other. Based on our study, we conclude that there is a need for a general setup to objectively compare the models and an urgent demand for the minimum criteria that a computational model for synaptic plasticity needs to meet.Peer reviewe

Sensitivity analysis of biophysically-detailed tripartite synapse model

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Accelerating Neural ODEs Using Model Order Reduction

Embedding nonlinear dynamical systems into artificial neural networks is a powerful new formalism for machine learning. By parameterizing ordinary differential equations (ODEs) as neural network layers, these Neural ODEs are memory-efficient to train, process time series naturally, and incorporate knowledge of physical systems into deep learning (DL) models. However, the practical applications of Neural ODEs are limited due to long inference times because the outputs of the embedded ODE layers are computed numerically with differential equation solvers that can be computationally demanding. Here, we show that mathematical model order reduction (MOR) methods can be used for compressing and accelerating Neural ODEs by accurately simulating the continuous nonlinear dynamics in low-dimensional subspaces. We implement our novel compression method by developing Neural ODEs that integrate the necessary subspace-projection and interpolation operations as layers of the neural network. We validate our approach by comparing it to neuron pruning and singular value decomposition (SVD)-based weight truncation methods from the literature in image and time-series classification tasks. The methods are evaluated by acceleration versus accuracy when adjusting the level of compression. On this spectrum, we achieve a favorable balance over existing methods by using MOR when compressing a convolutional Neural ODE. In compressing a recurrent Neural ODE, SVD-based weight truncation yields good performance. Based on our results, our integration of MOR with Neural ODEs can facilitate efficient, dynamical system-driven DL in resource-constrained applications.publishedVersionPeer reviewe

Analysis of network models with neuron-astrocyte interactions

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Morphological Differentiation Towards Neuronal Phenotype of SH-SY5Y Neuroblastoma Cells by Estradiol, Retinoic Acid and Cholesterol

Human SH-SY5Y neuroblastoma cells maintain their potential for differentiation and regression in culture conditions. The induction of differentiation could serve as a strategy to inhibit cell proliferation and tumor growth. Previous studies have shown that differentiation of SH-SY5Y cells can be induced by all-trans-retinoic-acid (RA) and cholesterol (CHOL). However, signaling pathways that lead to terminal differentiation of SH-SY5Y cells are still largely unknown. The goal of this study was to examine in the RA and CHOL treated SH-SY5Y cells the additive impacts of estradiol (E2) and brain-derived neurotrophic factor (BDNF) on cell morphology, cell population growth, synaptic vesicle recycling and presence of neurofilaments. The above features indicate a higher level of neuronal differentiation. Our data show that treatment for 10 days in vitro (DIV) with RA alone or when combined with E2 (RE) or CHOL (RC), but not when combined with BDNF (RB), significantly (p < 0.01) inhibited the cell population growth. Synaptic vesicle recycling, induced by high-K+ depolarization, was significantly increased in all treatments where RA was included (RE, RC, RB, RCB), and when all agents were added together (RCBE). Specifically, our results show for the first time that E2 treatment can alone increase synaptic vesicle recycling in SH-SY5Y cells. This work contributes to the understanding of the ways to improve suppression of neuroblastoma cells’ population growth by inducing maturation and differentiation

Postsynaptic Signal Transduction Models for Long-Term Potentiation and Depression

More than a hundred biochemical species, activated by neurotransmitters binding to transmembrane receptors, are important in long-term potentiation (LTP) and long-term depression (LTD). To investigate which species and interactions are critical for synaptic plasticity, many computational postsynaptic signal transduction models have been developed. The models range from simple models with a single reversible reaction to detailed models with several hundred kinetic reactions. In this study, more than a hundred models are reviewed, and their features are compared and contrasted so that similarities and differences are more readily apparent. The models are classified according to the type of synaptic plasticity that is modeled (LTP or LTD) and whether they include diffusion or electrophysiological phenomena. Other characteristics that discriminate the models include the phase of synaptic plasticity modeled (induction, expression, or maintenance) and the simulation method used (deterministic or stochastic). We find that models are becoming increasingly sophisticated, by including stochastic properties, integrating with electrophysiological properties of entire neurons, or incorporating diffusion of signaling molecules. Simpler models continue to be developed because they are computationally efficient and allow theoretical analysis. The more complex models permit investigation of mechanisms underlying specific properties and experimental verification of model predictions. Nonetheless, it is difficult to fully comprehend the evolution of these models because (1) several models are not described in detail in the publications, (2) only a few models are provided in existing model databases, and (3) comparison to previous models is lacking. We conclude that the value of these models for understanding molecular mechanisms of synaptic plasticity is increasing and will be enhanced further with more complete descriptions and sharing of the published models

Computational Methods for Estimation of Cell Cycle Phase Distributions of Yeast Cells

Two computational methods for estimating the cell cycle phase distribution of a budding yeast (Saccharomyces cerevisiae) cell population are presented. The first one is a nonparametric method that is based on the analysis of DNA content in the individual cells of the population. The DNA content is measured with a fluorescence-activated cell sorter (FACS). The second method is based on budding index analysis. An automated image analysis method is presented for the task of detecting the cells and buds. The proposed methods can be used to obtain quantitative information on the cell cycle phase distribution of a budding yeast S. cerevisiae population. They therefore provide a solid basis for obtaining the complementary information needed in deconvolution of gene expression data. As a case study, both methods are tested with data that were obtained in a time series experiment with S. cerevisiae. The details of the time series experiment as well as the image and FACS data obtained in the experiment can be found in the online additional material at http://www.cs.tut.fi/sgn/csb/yeastdistrib/