Computational Neuroscience: A Comprehensive Approach (Chapman & Hall/Crc Mathematical Biology & Medicine Series)

How does the brain work? After a century of research, we still lack a coherent view of how neurons process signals and control our activities. But as the field of computational neuroscience continues to evolve, we find that it provides a theoretical foundation and a set of technological approaches that can significantly enhance our understanding.Computational Neuroscience: A Comprehensive Approach provides a unified treatment of the mathematical theory of the nervous system and presents concrete examples demonstrating how computational techniques can illuminate difficult neuroscience problems. In chapters contributed by top researchers, the book introduces the basic mathematical concepts, then examines modeling at all levels, from single-channel and single neuron modeling to neuronal networks and system-level modeling. The emphasis is on models with close ties to experimental observations and data, and the authors review application of the models to systems such as olfactory bulbs, fly vision, and sensorymotor systems.Understanding the nature and limits of the strategies neural systems employ to process and transmit sensory information stands among the most exciting and difficult challenges faced by modern science. This book clearly shows how computational neuroscience has and will continue to help meet that challenge. Contents......Page 5 Preface......Page 15 1.1 Introduction......Page 23 1.2.1 Basic notation and techniques......Page 24 1.2.2 Single neuron modelling......Page 26 1.2.3 Phase model......Page 28 1.3.1 Jump processes......Page 29 1.3.2 Diffusion processes......Page 32 1.3.4 Perturbation of deterministic dynamical systems......Page 35 1.4.1 Shannon information......Page 38 1.4.3 Fisher information......Page 39 1.4.4 Relationship between the various measurements of information......Page 40 1.5.1 Optimal control of movement......Page 41 1.5.2 Optimal control of single neuron......Page 43 References......Page 46 2.1.1 Scope of this chapter......Page 53 2.1.2 Ion channels......Page 54 2.2 Simulation methods......Page 59 2.2.1 Molecular dynamics......Page 61 2.2.2 Continuum electrostatics......Page 65 2.2.3 Brownian dynamics......Page 67 2.3.1 Simplified systems......Page 69 2.3.2 Gramicidin A......Page 71 2.3.3 Alamethicin......Page 72 2.3.4 OmpF......Page 75 2.3.5 The potassium channel KcsA......Page 79 2.4 Outlook......Page 85 References......Page 87 3.1 Introduction......Page 96 3.2 Basic principles......Page 98 3.2.1 Intracellular calcium stores......Page 100 3.2.3 Calcium pumps and exchangers......Page 102 3.2.4 Mitochondrial calcium......Page 103 3.3 Special calcium signaling for neurons......Page 105 3.3.1 Local domain calcium......Page 106 3.3.2 Cross-talk between channels......Page 108 3.3.3 Control of gene expression......Page 110 References......Page 112 4.1 Introduction......Page 117 4.2.1 Equations governing NO diffusion in the brain......Page 120 4.2.2.1 Modelling NO diffusion from a point-source......Page 122 4.2.2.2 Modelling NO diffusion from a symmetrical 3D structure......Page 123 4.2.2.3 Numerical integration of analytical solutions......Page 126 4.2.3.1 Finite difference methods for diffusive problems......Page 128 4.2.3.2 Finite difference schemes used......Page 131 4.2.4.1 Diffusion coefficient and decay rate......Page 132 4.2.4.2 NO production rate......Page 133 4.3 Results......Page 134 4.3.1 Diffusion from a typical neuron......Page 135 4.3.2 Effect of neuron size......Page 138 4.3.3 Small sources......Page 139 4.4 Exploring functional roles with more abstract models......Page 144 4.4.2 Gas diffusion in the networks......Page 145 4.4.3 Modulation......Page 146 References......Page 147 5.1 Introduction......Page 151 5.3 Single channel models......Page 154 5.3.1 A three-state mechanism......Page 155 5.3.2 A simple channel-block mechanism......Page 156 5.3.3 A five-state model......Page 157 5.4 Transition probabilities, macroscopic currents and noise......Page 159 5.4.1 Transition probabilities......Page 160 5.4.2 Macroscopic currents and noise......Page 161 5.5.1 The duration of stay in an individual state......Page 162 5.5.2 The distribution of open times and shut times......Page 164 5.5.3 Joint distributions......Page 166 5.5.4 Correlations between intervals......Page 167 5.5.5 Bursting behaviour......Page 168 5.6 Time interval omission......Page 169 5.7.2 Hidden Markov Methods of analysis......Page 171 References......Page 172 6.1 Introduction......Page 179 6.2 Typical input is correlated and irregular......Page 180 6.3 Synaptic unreliability......Page 181 6.4 Postsynaptic ion channel noise......Page 183 6.5 Integration of a transient input by cortical neurons......Page 185 6.6 Noisy spike generation dynamics......Page 188 6.7 Dynamics of NMDA receptors......Page 191 6.8 Class 1 and class 2 neurons show different noise sensitivities......Page 193 6.9 Cortical cell dynamical classes......Page 194 6.10 Implications for synchronous firing......Page 196 References......Page 198 Generating Quantitatively Accurate, but Computationally Concise, Models of Single Neurons......Page 205 7.1.1 The scale of the problem......Page 206 7.1.2 Strategies for developing computationally concise models......Page 209 7.2 The hypothalamo-hypophysial system......Page 210 7.2.1 Firing patterns of vasopressin neurons......Page 211 7.2.2 Implications of membrane bistability for responsiveness to afferent input......Page 213 7.2.4 Intrinsic properties......Page 214 7.2.5 Intracellular Ca2+ concentration......Page 216 7.3.1 Selecting recordings for analysis......Page 217 7.3.3 Modelling......Page 218 7.3.4 Simulating oxytocin cell activity......Page 219 7.3.5 Experimental testing of the model......Page 221 7.3.6 Firing rate analysis......Page 223 7.3.7 Index of dispersion......Page 225 7.3.8 Autocorrelation analysis......Page 226 7.4 Summary and conclusions......Page 227 References......Page 232 Bursting Activity in Weakly Electric Fish......Page 234 8.1.1 What is a burst?......Page 235 8.2 Overview of the electrosensory system......Page 236 8.2.2 Neuroanatomy of the electrosensory system......Page 239 8.2.3 Electrophysiology and encoding of amplitude modulations......Page 241 8.3.1 Bursts reliably indicate relevant stimulus features......Page 242 8.3.2 Feature extraction analysis......Page 244 8.4 Factors shaping burst firing......Page 248 8.5.1 Experimental evidence for conditional backpropagation......Page 250 8.5.2 Multicompartmental model of pyramidal cell bursts......Page 252 8.5.3 Reduced models of burst firing......Page 254 8.6 Comparison with other bursting neurons......Page 257 8.6.1 Ping-pong between soma and dendrite......Page 258 8.6.2 Dynamical properties of burst oscillations......Page 259 8.7 Conclusions......Page 260 References......Page 262 9.1 Introduction......Page 272 9.2.1 The conditional intensity function and interspike interval probability......Page 274 9.2.2 The likelihood function of a point process model......Page 277 9.2.3 Summarizing the likelihood function: maximum likelihood estimation and Fisher information......Page 279 9.2.4 Properties of maximum likelihood estimates......Page 280 9.2.5 Model selection and model goodness-of-fit......Page 281 9.3.1 An analysis of the spiking activity of a retinal neuron......Page 282 9.3.2 An analysis of hippocampal place-specific firing activity......Page 289 9.3.3 An analysis of the spatial receptive field dynamics of a hippocampal neuron......Page 295 9.4 Conclusion......Page 301 9.5 Appendix......Page 302 References......Page 303 10.1 Introduction......Page 306 10.2 Cells......Page 308 10.2.2 Modelling cerebellum neurons......Page 309 10.3 Synapses......Page 310 10.4.1 Network topology......Page 311 10.4.2 Number of connections......Page 312 10.4.3 Distribution of connections......Page 313 10.5.1.1 Spatial pattern of OB inputs......Page 316 10.5.2 Inputs to individual cells......Page 317 10.5.2.3 Current pulses......Page 318 10.7 Validation......Page 319 References......Page 320 11.1 Hebbian models of plasticity......Page 324 11.2 Spike-timing dependent plasticity......Page 326 11.3 Role of constraints in Hebbian learning......Page 328 11.3.2 Constraints based on postsynaptic rate......Page 329 11.3.3 Constraints on total synaptic weights......Page 330 11.4.1 STDP is stable and competitive by itself......Page 332 11.4.2 Temporal correlation between inputs and output neuron......Page 333 11.4.3 Mean rate of change in synaptic strength......Page 334 11.4.4 Equilibrium synaptic strengths......Page 336 11.4.5.1 Constant Poisson inputs......Page 338 11.4.5.2 Correlations with different time constants......Page 342 11.4.5.3 Gradient of correlations......Page 343 11.5 Temporal aspects of STDP......Page 345 11.6.1 Hebbian models of map development and plasticity......Page 346 11.6.2 Distributed synchrony in a recurrent network......Page 350 11.7 Conclusion......Page 351 References......Page 352 12.1 Introduction: the timing game......Page 359 12.2.1 Stimulus representation......Page 361 12.2.2 Information flow......Page 363 12.3 Correlations arising from common input......Page 365 12.4 Correlations arising from local network interactions......Page 368 12.5 When are neurons sensitive to correlated input?......Page 371 12.5.2 Fluctuations and integrator models......Page 372 12.6.1 Parameterizing the input......Page 375 12.6.2 A random walk in voltage......Page 377 12.6.3 Quantitative relationships between input and output......Page 380 12.7 Correlations and neuronal variability......Page 382 12.8 Conclusion......Page 383 References......Page 385 13.1 Introduction......Page 393 13.2.1 Quantifying neuronal responses and stimuli......Page 394 13.2.2 Mutual information and sampling bias......Page 395 13.2.3 Series expansion approach to information estimation......Page 396 13.2.3.2 PSTH Similarity......Page 397 13.2.3.4 Stimulus-independent spike patterns......Page 398 13.2.4 Generalised series expansion......Page 399 13.3.1 Whisking behaviour......Page 400 13.3.2 Anatomy of the whisker system......Page 401 13.4.1 Introduction......Page 402 13.4.2 Role of spike timing......Page 403 13.4.2.2 Role of spike patterns......Page 404 13.4.2.4 Pooling......Page 406 13.5.1 Decoding first spike times......Page 407 13.5.2 Role of cross-correlations in population codes......Page 408 13.6 Conclusions......Page 410 References......Page 411 14.1 The fly motion vision system: an overview......Page 414 14.2 Mechanisms of local motion detection: the correlation detector......Page 417 14.2.1.1 Velocity tuning......Page 418 14.2.1.2 Pattern dependence......Page 419 14.2.1.3 Orientation tuning......Page 422 14.2.2 Dynamic response properties......Page 423 14.2.3 Additional filters and adaptive properties......Page 425 14.3.1 Compartmental models of tangential cells......Page 428 Figure 14.10......Page 429 14.3.2 Dendritic integration and gain control......Page 431 Figure 14.12......Page 433 14.3.3 Binocular interactions......Page 434 14.3.4 Dendro-dendritic interactions......Page 435 Figure 14.13......Page 436 Figure 14.14......Page 437 14.4 Conclusions......Page 438 References......Page 440 Mean - Field Theory of Irregularly Spiking Neuronal Populations and Working Memory in Recurrent Cortical Networks......Page 447 15.1 Introduction......Page 448 15.2.1 The leaky integrate-and-fire neuron......Page 450 15.2.2 Temporal structure of the afferent synaptic current......Page 451 15.2.3 The diffusion approximation......Page 452 15.2.4 Computation of the mean firing rate and CV......Page 455 15.2.5 Effect of synaptic time constants......Page 459 15.2.6 Approximate treatment of realistic synaptic dynamics......Page 461 15.3.1 Self-consistent steady-state solutions in large unstructured networks......Page 468 15.3.2 Stability and dynamics......Page 475 15.3.3 Bistability in a single population network......Page 479 15.3.4 Persistent neural activity in an object working memory model......Page 484 15.3.5 Stability of the persistent activity state......Page 485 15.3.6 Multistability in balanced networks......Page 490 15.4 Summary and future directions......Page 494 Appendix 1: The diffusion approximation......Page 495 Appendix 2: Stability of the steady-state solutions......Page 497 References......Page 498 The Operation of Memory Systems in the Brain......Page 507 16.2 Functions of the hippocampus in long-term memory......Page 508 16.2.1 Effects of damage to the hippocampus and connected structures on object-place and episodic memory......Page 509 16.2.2 Neurophysiology of the hippocampus and connected areas......Page 511 16.2.3 Hippocampal models......Page 514 16.2.4 Continuous spatial representations, path integration, and the use of idiothetic inputs......Page 516 16.2.5 A unified theory of hippocampal memory: mixed continuous and discrete attractor networks......Page 526 16.2.6 The speed of operation of memory networks: the integrate-and- fire approach......Page 527 16.3.1 Prefrontal cortex short-term memory networks, and their relation to temporal and parietal perceptual networks......Page 528 16.3.2 Computational details of the model of short-term memory......Page 530 16.3.3 Computational necessity for a separate, prefrontal cortex, shortterm memory system......Page 534 16.3.5 Synaptic modification is needed to set up but not to reuse shortterm memory systems......Page 535 16.4 Invariant visual object recognition......Page 536 16.5 Visual stimulusÒreward association, emotion, and motivation......Page 537 16.6 Effects of mood on memory and visual processing......Page 538 References......Page 541 Modelling Motor Control Paradigms......Page 551 17.1 Introduction: the ecological nature of motor control......Page 552 17.2.1 Logical decomposition of motor control into cascaded computational......Page 555 17.2.2 The Achilles’ heel of feedback control......Page 557 17.3.1 Motor equivalence and spatio-temporal invariances......Page 560 17.3.2 The viscous-elastic properties of the human muscles......Page 564 17.3.3 Dynamic compensation: anticipatory feedforward and feedback......Page 565 17.4 The role of cerebellum in the coordination of multiple joints......Page 566 17.4.1 Abnormal feedforward control in ataxic patients......Page 569 17.5.1 Stabilisation of the standing posture: evidence of anticipatory compensation......Page 572 17.5.2 Arm trajectory in a divergent force field: evidence of stiffness modulation......Page 575 17.5.3 Choosing between stiffness modulation and anticipatory compensation......Page 576 17.5.4 Implementing anticipatory compensation......Page 578 17.6.2 Adaptive behaviour and motor learning......Page 581 17.6.3 A distributed computational architecture......Page 582 References......Page 585 18.1 Introduction......Page 590 18.2 A conceptual framework for real-time neural computation......Page 591 18.4 Towards a non-Turing theory for real-time neural computation......Page 597 18.5.1 Speech recognition......Page 599 18.5.2 Predicting movements and solving the aperture problem......Page 604 18.6.1 Temporal integration in neural microcircuit models......Page 609 18.6.2 Kernel function of neural microcircuit models......Page 614 18.7 Software for evaluating the computational capabilities of neural microcircuit models......Page 615 18.8 Discussion......Page 616 References......Page 618 19.1 Introduction......Page 621 19.2 Brain areas......Page 622 19.3.1 Visual search and pop-out......Page 624 19.3.2 Computational models and the saliency map......Page 625 19.4.1 Are we blind outside of the focus of attention?......Page 628 19.4.2 Attentional modulation of early vision......Page 629 19.5.2 Influence of task......Page 630 19.6 Attention and scene understanding......Page 631 19.6.2 Cooperation between where and what......Page 632 19.7 Discussion......Page 633 References......Page 636 CONTRIBUTORS......Page 20 How does the brain work? After a century of research, we still lack a coherent view of how neurons process signals and control our activities. But as the field of computational neuroscience continues to evolve, we find that it provides a theoretical foundation and a set of technological approaches that can significantly enhance our understanding. Computational A Comprehensive Approach provides a unified treatment of the mathematical theory of the nervous system and presents concrete examples demonstrating how computational techniques can illuminate difficult neuroscience problems. In chapters contributed by top researchers, the book introduces the basic mathematical concepts, then examines modeling at all levels, from single-channel and single neuron modeling to neuronal networks and system-level modeling. The emphasis is on models with close ties to experimental observations and data, and the authors review application of the models to systems such as olfactory bulbs, fly vision, and sensorymotor systems. Understanding the nature and limits of the strategies neural systems employ to process and transmit sensory information stands among the most exciting and difficult challenges faced by modern science. This book clearly shows how computational neuroscience has and will continue to help meet that challenge. This book covers three levels of modeling neuroscience: subcellular, cellular, and neuron network. It includes a twin chapter, written by a biologist, for each modeling approach that is heavily theoretical. This book provides concrete examples that demonstrate how computational techniques can shed new light on complex neuroscience problems and the limitations and advantages of using such methods. It covers three levels of modeling -subcellular, cellular, and neuronal network-and the models that connect these levels. Expert contributors present a complete survey of up-to-date research in computational neuroscience. A unique feature of the book is that for each heavily theoretical modeling approach, it provides a twin chapter written by a biologist