Training deep neural density estimators to identify mechanistic models of neural dynamics

Mechanistic modeling in neuroscience aims to explain observed phenomena in terms of underlying causes. However, determining which model parameters agree with complex and stochastic neural data presents a significant challenge. We address this challenge with a machine learning tool which uses deep neural density estimators-- trained using model simulations-- to carry out Bayesian inference and retrieve the full space of parameters compatible with raw data or selected data features. Our method is scalable in parameters and data features, and can rapidly analyze new data after initial training. We demonstrate the power and flexibility of our approach on receptive fields, ion channels, and Hodgkin-Huxley models. We also characterize the space of circuit configurations giving rise to rhythmic activity in the crustacean stomatogastric ganglion, and use these results to derive hypotheses for underlying compensation mechanisms. Our approach will help close the gap between data-driven and theory-driven models of neural dynamics

Non-trivial dynamics in a model of glial membrane voltage driven by open potassium pores

Despite the molecular evidence that close to linear steady state I-V relationship in mammalian astrocytes reflects a total current resulting from more than one differently regulated K+ conductances, detailed ODE models of membrane voltage Vm incorporating multiple conductances are lacking. Repeated results of deregulated expressions of major K+ channels in glia, Kir4.1, in models of disease, as well as their altered rectification when assembling heteromeric Kir4.1/Kir5.1 channels have motivated us to attempt a detailed model adding the weaker potassium K2P current, in addition to Kir4.1, and study the stability of the resting state Vr. We ask whether with a deregulated Kir conductivity the nominal resting state Vr remains stable, and the cell retains a potassium electrode behavior with Vm following E_K. The minimal 2-dimensional model near Vr showed that certain alterations of Kir4.1 current may result in multistability of Vm if the model incorporates the typically observed K+ currents: Kir, K2P, and non-specific potassium leak. More specifically, a decrease or loss of outward Kir4.1 conductance introduces instability of Vr, near E_K. That happens through a fold bifurcation giving birth to a much more depolarized second, stable resting state Vdr>-10 mV. Realistic timeseries were used to perturb the membrane model, from recordings at the glial membrane during electrographic seizures. Simulations of the perturbed system by constant current through GJCs and transient seizure-like discharges as local field potentials led to depolarization of the astrocyte and switching of Vm between the two stable states, in a down-state / up-state manner. If the prolonged depolarizations near Vdr prove experimentally plausible, such catastrophic instability would impact all aspects of the glial function, from metabolic support to membrane transport and practically all neuromodulatory roles assigned to glia

Training deep neural density estimators to identify mechanistic models of neural dynamics

Mechanistic modeling in neuroscience aims to explain observed phenomena in terms of underlying causes. However, determining which model parameters agree with complex and stochastic neural data presents a significant challenge. We address this challenge with a machine learning tool which uses deep neural density estimators—trained using model simulations—to carry out Bayesian inference and retrieve the full space of parameters compatible with raw data or selected data features. Our method is scalable in parameters and data features and can rapidly analyze new data after initial training. We demonstrate the power and flexibility of our approach on receptive fields, ion channels, and Hodgkin–Huxley models. We also characterize the space of circuit configurations giving rise to rhythmic activity in the crustacean stomatogastric ganglion, and use these results to derive hypotheses for underlying compensation mechanisms. Our approach will help close the gap between data-driven and theory-driven models of neural dynamics

Calibration of ionic and cellular cardiac electrophysiology models

© 2020 The Authors. WIREs Systems Biology and Medicine published by Wiley Periodicals, Inc. Cardiac electrophysiology models are among the most mature and well-studied mathematical models of biological systems. This maturity is bringing new challenges as models are being used increasingly to make quantitative rather than qualitative predictions. As such, calibrating the parameters within ion current and action potential (AP) models to experimental data sets is a crucial step in constructing a predictive model. This review highlights some of the fundamental concepts in cardiac model calibration and is intended to be readily understood by computational and mathematical modelers working in other fields of biology. We discuss the classic and latest approaches to calibration in the electrophysiology field, at both the ion channel and cellular AP scales. We end with a discussion of the many challenges that work to date has raised and the need for reproducible descriptions of the calibration process to enable models to be recalibrated to new data sets and built upon for new studies. This article is categorized under: Analytical and Computational Methods > Computational Methods Physiology > Mammalian Physiology in Health and Disease Models of Systems Properties and Processes > Cellular Models

Nonlinear Dynamic Modeling, Simulation And Characterization Of The Mesoscale Neuron-electrode Interface

Extracellular neuroelectronic interfacing has important applications in the fields of neural prosthetics, biological computation and whole-cell biosensing for drug screening and toxin detection. While the field of neuroelectronic interfacing holds great promise, the recording of high-fidelity signals from extracellular devices has long suffered from the problem of low signal-to-noise ratios and changes in signal shapes due to the presence of highly dispersive dielectric medium in the neuron-microelectrode cleft. This has made it difficult to correlate the extracellularly recorded signals with the intracellular signals recorded using conventional patch-clamp electrophysiology. For bringing about an improvement in the signalto-noise ratio of the signals recorded on the extracellular microelectrodes and to explore strategies for engineering the neuron-electrode interface there exists a need to model, simulate and characterize the cell-sensor interface to better understand the mechanism of signal transduction across the interface. Efforts to date for modeling the neuron-electrode interface have primarily focused on the use of point or area contact linear equivalent circuit models for a description of the interface with an assumption of passive linearity for the dynamics of the interfacial medium in the cell-electrode cleft. In this dissertation, results are presented from a nonlinear dynamic characterization of the neuroelectronic junction based on Volterra-Wiener modeling which showed that the process of signal transduction at the interface may have nonlinear contributions from the interfacial medium. An optimization based study of linear equivalent circuit models for representing signals recorded at the neuron-electrode interface subsequently iv proved conclusively that the process of signal transduction across the interface is indeed nonlinear. Following this a theoretical framework for the extraction of the complex nonlinear material parameters of the interfacial medium like the dielectric permittivity, conductivity and diffusivity tensors based on dynamic nonlinear Volterra-Wiener modeling was developed. Within this framework, the use of Gaussian bandlimited white noise for nonlinear impedance spectroscopy was shown to offer considerable advantages over the use of sinusoidal inputs for nonlinear harmonic analysis currently employed in impedance characterization of nonlinear electrochemical systems. Signal transduction at the neuron-microelectrode interface is mediated by the interfacial medium confined to a thin cleft with thickness on the scale of 20-110 nm giving rise to Knudsen numbers (ratio of mean free path to characteristic system length) in the range of 0.015 and 0.003 for ionic electrodiffusion. At these Knudsen numbers, the continuum assumptions made in the use of Poisson-Nernst-Planck system of equations for modeling ionic electrodiffusion are not valid. Therefore, a lattice Boltzmann method (LBM) based multiphysics solver suitable for modeling ionic electrodiffusion at the mesoscale neuron-microelectrode interface was developed. Additionally, a molecular speed dependent relaxation time was proposed for use in the lattice Boltzmann equation. Such a relaxation time holds promise for enhancing the numerical stability of lattice Boltzmann algorithms as it helped recover a physically correct description of microscopic phenomena related to particle collisions governed by their local density on the lattice. Next, using this multiphysics solver simulations were carried out for the charge relaxation dynamics of an electrolytic nanocapacitor with the intention of ultimately employing it for a simulation of the capacitive coupling between the neuron and the v planar microelectrode on a microelectrode array (MEA). Simulations of the charge relaxation dynamics for a step potential applied at t = 0 to the capacitor electrodes were carried out for varying conditions of electric double layer (EDL) overlap, solvent viscosity, electrode spacing and ratio of cation to anion diffusivity. For a large EDL overlap, an anomalous plasma-like collective behavior of oscillating ions at a frequency much lower than the plasma frequency of the electrolyte was observed and as such it appears to be purely an effect of nanoscale confinement. Results from these simulations are then discussed in the context of the dynamics of the interfacial medium in the neuron-microelectrode cleft. In conclusion, a synergistic approach to engineering the neuron-microelectrode interface is outlined through a use of the nonlinear dynamic modeling, simulation and characterization tools developed as part of this dissertation research

Action potentials as indicators of metabolic perturbations for temporal proteomic analysis

The single largest cause of compound attrition during drug development is due to inadequate tools capable of predicting and identifying protein interactions. Several tools have been developed to explore how a compound interferes with specific pathways. However, these tools lack the potential to chronically monitor the time dependent temporal changes in complex biochemical networks, thus limiting our ability to identify possible secondary signaling pathways that could lead to potential toxicity. To overcome this, we have developed an in silico neuronal-metabolic model by coupling the membrane electrical activity to intracellular biochemical pathways that would enable us to perform non-invasive temporal proteomics. This model is capable of predicting and correlating the changes in cellular signaling, metabolic networks and action potential responses to metabolic perturbation. The neuronal-metabolic model was experimentally validated by performing biochemical and electrophysiological measurements on NG108-15 cells followed by testing its prediction capabilities for pathway analysis. The model accurately predicted the changes in neuronal action potentials and the changes in intracellular biochemical pathways when exposed to metabolic perturbations. NG108-15 cells showed a large effect upon exposure to 2DG compared to cyanide and malonate as these cells have elevated glycolysis. A combinational treatment of 2DG, cyanide and malonate had a much higher and faster effect on the cells. A time-dependent change in neuronal action potentials occurred based on the inhibited pathway. We conclude that the experimentally validated in silico model accurately predicts the changes in neuronal action potential shapes and proteins activities to perturbations, and would be a powerful tool for performing proteomics facilitating drug discovery by using action potential peak shape analysis to determine pathway perturbation from an administered compound

Modèles numériques de la stimulation optique de neurones assistée par nanoparticules plasmoniques

La stimulation de neurones par laser émerge depuis plusieurs années comme une alternative aux techniques plus traditionnelles de stimulation artificielle. Contrairement à celles-ci, la stimulation lumineuse ne nécessite pas d’interagir directement avec le tissu organique, comme c’est le cas pour une stimulation par électrodes, et ne nécessite pas de manipulation génétique comme c’est le cas pour les méthodes optogénétiques. Plus récemment, la stimulation lumineuse de neurones assistée par nanoparticules a émergé comme un complément à la stimulation simplement lumineuse. L’utilisation de nanoparticules complémentaires permet d’augmenter la précision spatiale du procédé et de diminuer la fluence nécessaire pour observer le phénomène. Ceci vient des propriétés d’interaction entre les nanoparticules et le faisceau laser, comme par exemple les propriétés d’absorption des nanoparticules. Deux phénomènes princpaux sont observés. Dans certains cas, il s’agit d’une dépolarisation de la membrane, ou d’un potentiel d’action. Dans d’autres expériences, un influx de calcium vers l’intérieur du neurone est détecté par une augmentation de la fluorescence d’une protéine sensible à la concentration calcique. Certaines stimulations sont globales, c’est à dire qu’une perturbation se propage à l’ensemble du neurone : c’est le cas d’un potentiel d’action. D’autres sont, au contraire, locales et ne se propagent pas à l’ensemble de la cellule. Si une stimulation lumineuse globale est rendue possible par des techniques relativement bien maîtrisées à l’heure actuelle, comme l’optogénétique, une stimulation uniquement locale est plus difficile à réaliser. Or, il semblerait que les méthodes de stimulation lumineuse assistées par nanoparticules puissent, dans certaines conditions, offrir cette possibilité. Cela serait d’une grande aide pour conduire de nouvelles études sur le fonctionnement des neurones, en offrant de nouvelles possibilités expérimentales en complément des possibilités actuelles. Cependant, le mécanisme physique à l’origine de la stimulation lumineuse de neurones, ainsi que celui à l’orgine de la stimulation lumineuse assistée par nanoparticules, n’est à ce jour pas totalement compris. Des hypothèses ont été formulées concernant ce mécanisme : il pourrait être photothermique, photomécanique, ou encore photochimique. Il se pourrait également que plusieurs mécanismes soient à l’oeuvre conjointement, étant donné la variété des observations. La littérature ne converge pas à ce sujet et l’existence d’un mécanisme commun aux différentes situations n’a pas été démontrée.----------Abstract For several years, laser light has been used as an alternative means of artificially stimulating neurons. Unlike more traditional methods, this technique does not require a direct interaction with the organic tissue, such as those based on electrical stimulation. In addition, no genetic manipulation is needed, as it is required in optogenetic frameworks. More recently, nanoparticles have been added to the experimental process of light stimulation of neurons. These particles allow for a better spatial control of the method and potentially necessitate smaller fluences to trigger a neuron reaction, thanks to the specific properties of the interaction between a laser light and nanoparticles, such as absorption. This stimulation consists in two main phenomena. In some cases, depolarisation of the neuron membrane occurs, or an action potentiel can even be triggered. In other cases, an inward calcium influx is detected by the fluorescence of a calcium sensitive protein. On the one hand, some of these stimulations are global, which means that a perturbation of the neuron propagates to the whole cell. Action potentials belong to this category of stimulation. On the other hand, some stimulations remain local and do not propagate any further. Whereas a global stimulation with light is relatively well achieved with contemporary methods such as optogenetics, a local stimulation is more difficult to evoke. Nanoparticle assisted light stimulation techniques seem to provide this possibility, which would open new opportunities of experimental studies on the biophysics of neurons. However, the physical mechanism responsible for the light stimulation and the nanoparticle assisted light stimulation of neurons is not yet completely understood. Several hypothesis have been proposed to explain the experimental results : photothermal, photomechanical, or photochemical mechanisms have been mentioned. Furthermore, a simultaneous combination of several of these mechanisms could be responsible for the effect. The existence of a common mechanism for all experiments has not been determined yet in the literature. The most popular assumption is the one of a photothermal mechanism, which seems to be the most likely experimentally. We analyse this possibility and we propose theoretical models to compare numerical calculations to experimental observations. Firstly, we study models based on thermosensitive ion channels. Ion channels are proteins populating the cell membrane and are essential to many biological processes. Several methods exist to evaluate the effect of temperature on ion channels, such as Hodgkin-Huxley models, thermodynamic models and Markov models

Pacemaking Neurons in the study of Parkinson’s Disease

Parkinson’s disease is the second most common neurodegenerative disorder with a signiVcant social cost. The disease that develops over years results in signiVcant movement related problems for the aUected. The pathogenesis however is partially understood. Computational approaches are signiVcant in the analysis of events that are multi-factorial. Parkinson’s Disease results from a system failure that leads to severe degeneration in the substantia nigra , a locus in the mid-brain. Traditional approaches tend to focus on isolated sub-components of the pathogenic pathways. However, such an approach may be inadequate to describe the pathogenesis. Substantia nigra neurons function on an expensive energy budget, due to a high level of arborisation and pacemaking activity. Spontaneous oscillations of these neurons are an important feature of motor control. Pacemaking involves the L-type calcium channel, and could impose long-term accumulation of calcium within its organelles. Modelling of this activity is an important part of developing an understanding of the pathogenic process. We develop a mathematical paradigm to describe this activity with a single compartment approach. To develop the mathematical framework we initially identify the components that contribute to the process and investigate an appropriate mathematical representation for the respective components. In the next part, we bring together such representation to develop a model that can reproduce measured data. Global optimisation strategies are adopted to tune important parameters. The model explicitly describes the dynamics of the transmembrane potential with changes in the levels of important cations. The model is veriVed for two major observations in literature regarding its response in the presence of channel blockers. The model is analysed for parameter bifurcation and stability of oscillations. Finally a framework is proposed to extend the model to include aspects of calcium homeostasis

COMPUTATIONAL BIOENGINEERING OF THE GASTROINTESTINAL TRACT

Ph.DDOCTOR OF PHILOSOPH