Computational Modelling of the Brain: Modelling Approaches to Cells, Circuits and Networks (Advances in Experimental Medicine and Biology Book 1359)

This volume offers an up-to-date overview of essential concepts and modern approaches to computational modelling, including the use of experimental techniques related to or directly inspired by them. The book introduces, at increasing levels of complexity and with the non-specialist in mind, state-of-the-art topics ranging from single-cell and molecular descriptions to circuits and networks. Four major themes are covered, including subcellular modelling of ion channels and signalling pathways at the molecular level, single-cell modelling at different levels of spatial complexity, network modelling from local microcircuits to large-scale simulations of entire brain areas and practical examples. Each chapter presents a systematic overview of a specific topic and provides the reader with the fundamental tools needed to understand the computational modelling of neural dynamics. This book is aimed at experimenters and graduate students with little or no prior knowledge of modelling who are interested in learning about computational models from the single molecule to the inter-areal communication of brain structures. The book will appeal to computational neuroscientists, engineers, physicists and mathematicians interested in contributing to the field of neuroscience. Chapters 6, 10 and 11 are available open access under a Creative Commons Attribution 4.0 International License via link.springer.com. Preface Contents About the Editors Part I Cellular Scale 1 Modeling Neurons in 3D at the Nanoscale 1.1 Introduction 1.2 Stochastic Modeling 1.2.1 The Stochastic Simulation Algorithm for Molecular Simulation 1.2.1.1 Background 1.2.1.2 Implementation 1.3 Converting 1D Deterministic Models into 3D Stochastic Models 1.3.1 Morphology as a 3D Mesh 1.3.1.1 From LM Imaging to Tetrahedral Mesh 1.3.1.2 From EM Imaging to Tetrahedral Mesh 1.3.1.3 Advanced Topics in Mesh Generation 1.3.2 3D Membrane Potential 1.3.2.1 Passive Parameters 1.3.2.2 Voltage on Tetrahedral Meshes 1.3.3 Markov Models of Ion Channel Gating 1.3.3.1 Calculating the Number of Ion Channels in a Stochastic Simulation 1.3.3.2 Stochastic Channel Activation 1.3.3.3 Ligand-Gating 1.3.4 3D Calcium Dynamics 1.3.4.1 1D Modeling 1.3.4.2 3D Modeling in STEPS 1.4 Examples of 3D Models 1.4.1 Stochastic Calcium Spikes 1.4.2 Full Purkinje Neuron References 2 Modeling Dendrites and Spatially-Distributed Neuronal Membrane Properties 2.1 Introduction 2.2 Modeling of the Passive Properties of Dendrites 2.2.1 Ionic Movement Across the Membrane 2.2.2 Equivalent Circuitry 2.2.3 Cable Equation and Passive Properties of Dendrites 2.2.3.1 Linear Cable Equation 2.2.3.2 The Infinite Cable 2.2.3.3 The Finite Cable 2.2.4 *-24pt 2.2.4.1 Branching and Equivalent Cylinders 2.2.4.2 Isolated Branching Points (Junctions) 2.2.5 Multicompartmental Modeling 2.3 Computational Modeling of Active Dendrites 2.3.1 Biophysical Models of Dendritic Function 2.3.1.1 Modeling Active Conductances 2.3.1.2 Hodgkin–Huxley Mathematical Formalism 2.3.1.3 Thermodynamic Approach 2.3.1.4 Ionic Concentrations 2.3.1.5 Sodium Channels 2.3.1.6 Calcium Channels 2.3.1.7 Potassium Channels 2.4 Conclusions-Remarks A.1 Appendix: Mathematical Derivations A.1.1 A.1 General Solution to the Linear Cable Equation in Time and Space Given a Current Injection, I(x,t), at Some Point*-6pt A.1.2 A.2 Solution to a Constant, Localized Current References 3 A User's Guide to Generalized Integrate-and-Fire Models 3.1 Introduction to Leaky-Integrate-and-Fire Models 3.2 Generalizing the Leaky-Integrate-and-Fire Model 3.2.1 Spike-Triggered Adaptation 3.2.2 Stochasticity 3.2.3 Simplifications, Generalizations, and Limitations 3.3 Fitting the Generalized Integrate-and-Fire Model 3.3.1 Finding Parameter Values: Experiments vs. Optimization 3.3.2 Choosing an Input 3.3.3 Optimization 3.3.3.1 Quantifying Model Accuracy 3.3.3.2 Solving for Parameter Values 3.3.4 Extending the Subthreshold Model 3.4 Summary 3.5 Further Reading References 4 Neuron–Glia Interactions and Brain Circuits 4.1 Introduction 4.2 Neuron–Astrocyte Interactions and Altered Neuronal and Circuit Excitability 4.3 Neuron–Astrocyte Interactions, Synaptic Transmission, and Synaptic Plasticity 4.4 Computational Modeling and Simulation 4.4.1 The Scope and Complexity of Glial Computational Models 4.4.2 Simulation Tools 4.5 Computational Models 4.5.1 Models of Single Astrocytes and Astrocyte Networks 4.5.2 Models for Neuron–Astrocyte Interactions in Synapses 4.5.3 Models for Neuron–Astrocyte Interactions in Brain Circuits and Networks 4.6 Conclusions References 5 Short-Term Synaptic Plasticity: Microscopic Modelling and (Some) Computational Implications 5.1 Introduction 5.2 Basic Physiology of Chemical Synaptic Transmission 5.2.1 Quantal Release 5.2.2 Short-Term Plasticity 5.3 Modelling of Repetitive Synaptic Transmission: The Release-Site Formalism 5.3.1 The Tsodyks–Markram Model 5.3.2 Parameter Estimation from Experimental Recordings 5.4 Network Dynamics in the Presence of Short-Term Synaptic Plasticity 5.4.1 Depressing Transmission 5.4.2 Facilitating Transmission 5.5 Synaptic Theory of Working Memory 5.5.1 Implementation in a Spiking Network 5.5.2 Comparison with Experiments 5.6 Conclusions and Perspectives References Part II Microcircuit Scale 6 The Mean Field Approach for Populations of SpikingNeurons 6.1 Introduction 6.2 Networks of Binary Neurons 6.3 Characterization of Neural Activity 6.3.1 Firing Rate 6.4 The Mean Field Equations 6.4.1 Solving the Mean Field Equations 6.4.2 Random Weights 6.4.2.1 Heterogeneous Population 6.4.2.2 Homogeneous Population 6.4.3 Clustered Networks 6.5 Extensions 6.5.1 The Impact of the Input Variance on the Mean Firing Rates 6.5.1.1 The Moments of the Input Current 6.5.1.2 Extended Mean Field Theory 6.5.2 Random Connectivity 6.6 Networks of Integrate-and-Fire Neurons 6.6.1 Leaky Integrate-and-Fire Neuron 6.6.1.1 The Moments of the Free Membrane Potential 6.6.1.2 The Response Function of the LIF Neuron 6.7 Validity of the Mean Field Approximation 6.7.1 Implications of the Thermodynamic Limit and Synaptic Scaling 6.7.1.1 Balanced Networks 6.7.1.2 Mean Field Theory of Balanced Networks 6.7.2 The Role of Correlations 6.7.3 Finite Size Effects 6.8 Discussion and Conclusions A.1 Appendix A.1.1 Ensemble Average A.1.2 Mean and Variance for the LIF Neuron References 7 Multidimensional Dynamical Systems with Noise 7.1 Introduction 7.2 The Formalism 7.3 A Geometric View 7.3.1 Average Firing Rate vs. Average Membrane Potential 7.3.2 The Mesh as Visualisation 7.3.3 Fitzhugh–Nagumo Model 7.3.4 Izhikevich Model 7.3.5 Difficulties with Mesh Building 7.3.6 Current Compensation 7.3.7 The Grid Method 7.3.8 Higher Dimensions 7.3.9 Population Networks 7.4 Discussion 7.5 Software References 8 Computing Extracellular Electric Potentials from Neuronal Simulations 8.1 Introduction 8.2 From Electrodiffusion to Volume Conductor Theory 8.2.1 Ion Concentration Dynamics 8.2.2 Electrodynamics 8.2.3 Volume Conductor Theory 8.2.3.1 Current-Dipole Approximation 8.2.3.2 Assumptions in Volume Conductor Theory 8.2.4 Modeling Electrodes 8.3 Single-Cell Contributions to Extracellular Potentials 8.4 Intra-Cortical Extracellular Potentials from Neural Populations 8.4.1 Local Field Potentials 8.4.2 MUA 8.5 ECoG and EEG 8.5.1 Head Models 8.6 Conclusion References 9 Bringing Anatomical Information into Neuronal NetworkModels 9.1 Introduction 9.2 Brain Morphology and Cytoarchitecture 9.2.1 Brain Atlases 9.2.2 Cortical and Laminar Thicknesses 9.2.3 Numbers of Neurons 9.2.4 Local Variations in Cytoarchitecture 9.2.5 Use of Morphology and Cytoarchitecture in Models 9.3 Structural Connectivity 9.3.1 Microscopy 9.3.2 Paired Recordings 9.3.3 Glutamate Uncaging 9.3.4 Axonal Tracing 9.3.5 Diffusion Tensor Imaging (DTI) 9.4 Predictive Connectomics 9.4.1 Peters' Rule 9.4.2 Architectural Principles 9.4.3 Distance Dependence 9.4.4 Connectome Topology 9.4.5 Neurodevelopmental Underpinnings of Connectivity Heuristics 9.4.6 Reconstructing Connectivity from Activity 9.5 Validation of Predicted Connectivity 9.6 Concluding Remarks References Part III Network Scale 10 Computational Concepts for Reconstructing and Simulating Brain Tissue 10.1 Introduction 10.2 Data Organization 10.2.1 Knowledge Graph-Based Data Repository 10.2.2 Dataset Releases 10.2.3 Generalized Voxel-Based Data Structure 10.3 Model Building 10.3.1 Biophysical Neuron Models 10.3.1.1 Effective Distance Functions 10.3.1.2 Multi-dimensional Error Term 10.3.1.3 Search Strategy 10.3.1.4 Leveraging Other Constraints 10.3.2 Brain Tissue Models 10.3.2.1 Space as a Modality 10.3.2.2 Apposition-Based Constraints 10.3.2.3 Density-Based Constraints 10.3.2.4 Functional Parameterization Through Regularization and Sampling 10.4 Simulation Experiment 10.4.1 Global Unique Identifier 10.4.2 Explicit Model Definition 10.4.3 Cell Targets 10.4.4 Strategies for Efficient Simulation 10.5 Validation 10.5.1 High-Throughput Model Component Validation 10.5.2 Sample-Based In Situ Model Component Validation 10.5.3 Intrinsic Validation: Validation Against Input Parameters 10.5.4 Extrinsic Validations: Validation of Emergent Properties 10.6 Model and Experiment Refinement 10.7 Conclusions References 11 Reconstruction of the Hippocampus 11.1 Introduction 11.1.1 The Hippocampus Formation 11.1.2 Principles for Building a Computer Model of the Hippocampus 11.2 Morphologies 11.3 Ion Channels 11.4 Single Cell Models 11.4.1 Electrophysiological Features 11.4.2 Model Optimization 11.4.3 Library of Cell Models 11.5 Volume 11.5.1 Define the Volume 11.5.2 Cell Placement 11.6 Connections 11.6.1 Apposition-Based Constraints 11.6.2 Density-Based Constraints 11.7 Synapses 11.7.1 Postsynaptic Conductance 11.7.2 Short-Term Plasticity 11.7.3 Multivesicular Release 11.7.4 Data Heterogeneity 11.7.5 Data Sparseness 11.8 Simulation Experiment 11.9 Validation 11.9.1 Different Types of Validation 11.9.2 Sensitivity Analysis 11.10 Conclusions References 12 Challenges for Place and Grid Cell Models 12.1 Introduction 12.1.1 Main Anatomical Traits 12.1.2 Single Cell Selectivity 12.2 Place Cells: A Blissful Reconciliation Between David Marr and John O'Keefe? 12.2.1 Integrating Place Cells Within Memory Representations 12.2.1.1 A Theoretical Perspective on How the Hippocampus Does Memory 12.2.1.2 First Computational Theory Taking Place into Memory 12.2.1.3 Attractor Neural Networks Help Handle Spatial Information 12.2.1.4 Remapping: A Continuous Attractor for Each Familiar Environment 12.2.2 How Can Place Fields Be Set Up? 12.2.2.1 Non-associative Inputs in Associative Memory 12.2.2.2 Associative Model for DG Place Fields 12.2.2.3 CA3 Fields from DG Fields 12.2.2.4 Representations of Multiple Spatial Maps Within CA3 12.2.3 What Happens Within One Chart? 12.2.3.1 Phase Precession and Its Possible Role in the Memory Process 12.2.3.2 Replay, Preplay, and Goal-Directed Behavior 12.2.3.3 Further Computational Questions Arising from Recent Experiments 12.3 Grid Cells: From the Hope of Perfect Symmetry to the Beauty of Irregularity? 12.3.1 How Do Grid Maps Emerge? 12.3.1.1 Oscillatory Interference (OI) Models 12.3.1.2 Single Cell Plasticity Models 12.3.1.3 Continuous Attractors Neural Networks (cANN) Models 12.3.2 One Attractor or More? 12.3.3 Are Indeed Grids Always so Regular? References 13 Whole-Brain Modelling: Past, Present, and Future 13.1 Preliminaries 13.1.1 What Is Whole-Brain Modelling? 13.1.2 Overview of This Chapter 13.2 The Past 13.2.1 The Long and the Short 13.2.2 Origins of the Neural Population Model 13.2.3 Macroscopic Neural Field Models 13.2.4 Macro-Connectomics and the Emergence of the WBM Paradigm 13.3 The Present 13.3.1 The Canonical WBM Equations 13.3.2 Neural Population Models 13.3.2.1 Phenomenological Models 13.3.2.2 Physiological Models 13.3.3 Parameter Estimation 13.3.4 Connectivity 13.3.4.1 Scaling of Connection Weights 13.3.4.2 Atlases and Exemplar Datasets 13.3.5 Clinical Applications 13.3.5.1 The General Approach 13.3.5.2 Epilepsy 13.3.5.3 Stroke and Neurodegeneration 13.3.5.4 Neuropsychiatry and Neuromodulation 13.4 The Future 13.4.1 Multiscale 13.4.2 Standardized, Hybrid, Model Construction 13.4.3 Cross-Species 13.4.4 Translation 13.5 Conclusions References Glossary