Computational Neuroscience: A Comprehensive Approach

Contents......Page 6
Preface......Page 16
1.1 Introduction......Page 24
1.2.1 Basic notation and techniques......Page 25
1.2.2 Single neuron modelling......Page 27
1.2.3 Phase model......Page 29
1.3.1 Jump processes......Page 30
1.3.2 Diffusion processes......Page 33
1.3.4 Perturbation of deterministic dynamical systems......Page 36
1.4.1 Shannon information......Page 39
1.4.3 Fisher information......Page 40
1.4.4 Relationship between the various measurements of information......Page 41
1.5.1 Optimal control of movement......Page 42
1.5.2 Optimal control of single neuron......Page 44
References......Page 47
2.1.1 Scope of this chapter......Page 54
2.1.2 Ion channels......Page 55
2.2 Simulation methods......Page 60
2.2.1 Molecular dynamics......Page 62
2.2.2 Continuum electrostatics......Page 66
2.2.3 Brownian dynamics......Page 68
2.3.1 Simplified systems......Page 70
2.3.2 Gramicidin A......Page 72
2.3.3 Alamethicin......Page 73
2.3.4 OmpF......Page 76
2.3.5 The potassium channel KcsA......Page 80
2.4 Outlook......Page 86
References......Page 88
3.1 Introduction......Page 97
3.2 Basic principles......Page 99
3.2.1 Intracellular calcium stores......Page 101
3.2.3 Calcium pumps and exchangers......Page 103
3.2.4 Mitochondrial calcium......Page 104
3.3 Special calcium signaling for neurons......Page 106
3.3.1 Local domain calcium......Page 107
3.3.2 Cross-talk between channels......Page 109
3.3.3 Control of gene expression......Page 111
References......Page 113
4.1 Introduction......Page 118
4.2.1 Equations governing NO diffusion in the brain......Page 121
4.2.2.1 Modelling NO diffusion from a point-source......Page 123
4.2.2.2 Modelling NO diffusion from a symmetrical 3D structure......Page 124
4.2.2.3 Numerical integration of analytical solutions......Page 127
4.2.3.1 Finite difference methods for diffusive problems......Page 129
4.2.3.2 Finite difference schemes used......Page 132
4.2.4.1 Diffusion coefficient and decay rate......Page 133
4.2.4.2 NO production rate......Page 134
4.3 Results......Page 135
4.3.1 Diffusion from a typical neuron......Page 136
4.3.2 Effect of neuron size......Page 139
4.3.3 Small sources......Page 140
4.4 Exploring functional roles with more abstract models......Page 145
4.4.2 Gas diffusion in the networks......Page 146
4.4.3 Modulation......Page 147
References......Page 148
5.1 Introduction......Page 152
5.3 Single channel models......Page 155
5.3.1 A three-state mechanism......Page 156
5.3.2 A simple channel-block mechanism......Page 157
5.3.3 A five-state model......Page 158
5.4 Transition probabilities, macroscopic currents and noise......Page 160
5.4.1 Transition probabilities......Page 161
5.4.2 Macroscopic currents and noise......Page 162
5.5.1 The duration of stay in an individual state......Page 163
5.5.2 The distribution of open times and shut times......Page 165
5.5.3 Joint distributions......Page 167
5.5.4 Correlations between intervals......Page 168
5.5.5 Bursting behaviour......Page 169
5.6 Time interval omission......Page 170
5.7.2 Hidden Markov Methods of analysis......Page 172
References......Page 173
6.1 Introduction......Page 180
6.2 Typical input is correlated and irregular......Page 181
6.3 Synaptic unreliability......Page 182
6.4 Postsynaptic ion channel noise......Page 184
6.5 Integration of a transient input by cortical neurons......Page 186
6.6 Noisy spike generation dynamics......Page 189
6.7 Dynamics of NMDA receptors......Page 192
6.8 Class 1 and class 2 neurons show different noise sensitivities......Page 194
6.9 Cortical cell dynamical classes......Page 195
6.10 Implications for synchronous firing......Page 197
References......Page 199
Generating Quantitatively Accurate, but Computationally Concise, Models of Single Neurons......Page 206
7.1.1 The scale of the problem......Page 207
7.1.2 Strategies for developing computationally concise models......Page 210
7.2 The hypothalamo-hypophysial system......Page 211
7.2.1 Firing patterns of vasopressin neurons......Page 212
7.2.2 Implications of membrane bistability for responsiveness to afferent input......Page 214
7.2.4 Intrinsic properties......Page 215
7.2.5 Intracellular Ca2+ concentration......Page 217
7.3.1 Selecting recordings for analysis......Page 218
7.3.3 Modelling......Page 219
7.3.4 Simulating oxytocin cell activity......Page 220
7.3.5 Experimental testing of the model......Page 222
7.3.6 Firing rate analysis......Page 224
7.3.7 Index of dispersion......Page 226
7.3.8 Autocorrelation analysis......Page 227
7.4 Summary and conclusions......Page 228
References......Page 233
Bursting Activity in Weakly Electric Fish......Page 235
8.1.1 What is a burst?......Page 236
8.2 Overview of the electrosensory system......Page 237
8.2.2 Neuroanatomy of the electrosensory system......Page 240
8.2.3 Electrophysiology and encoding of amplitude modulations......Page 242
8.3.1 Bursts reliably indicate relevant stimulus features......Page 243
8.3.2 Feature extraction analysis......Page 245
8.4 Factors shaping burst firing......Page 249
8.5.1 Experimental evidence for conditional backpropagation......Page 251
8.5.2 Multicompartmental model of pyramidal cell bursts......Page 253
8.5.3 Reduced models of burst firing......Page 255
8.6 Comparison with other bursting neurons......Page 258
8.6.1 Ping-pong between soma and dendrite......Page 259
8.6.2 Dynamical properties of burst oscillations......Page 260
8.7 Conclusions......Page 261
References......Page 263
9.1 Introduction......Page 273
9.2.1 The conditional intensity function and interspike interval probability......Page 275
9.2.2 The likelihood function of a point process model......Page 278
9.2.3 Summarizing the likelihood function: maximum likelihood estimation and Fisher information......Page 280
9.2.4 Properties of maximum likelihood estimates......Page 281
9.2.5 Model selection and model goodness-of-fit......Page 282
9.3.1 An analysis of the spiking activity of a retinal neuron......Page 283
9.3.2 An analysis of hippocampal place-specific firing activity......Page 290
9.3.3 An analysis of the spatial receptive field dynamics of a hippocampal neuron......Page 296
9.4 Conclusion......Page 302
9.5 Appendix......Page 303
References......Page 304
10.1 Introduction......Page 307
10.2 Cells......Page 309
10.2.2 Modelling cerebellum neurons......Page 310
10.3 Synapses......Page 311
10.4.1 Network topology......Page 312
10.4.2 Number of connections......Page 313
10.4.3 Distribution of connections......Page 314
10.5.1.1 Spatial pattern of OB inputs......Page 317
10.5.2 Inputs to individual cells......Page 318
10.5.2.3 Current pulses......Page 319
10.7 Validation......Page 320
References......Page 321
11.1 Hebbian models of plasticity......Page 325
11.2 Spike-timing dependent plasticity......Page 327
11.3 Role of constraints in Hebbian learning......Page 329
11.3.2 Constraints based on postsynaptic rate......Page 330
11.3.3 Constraints on total synaptic weights......Page 331
11.4.1 STDP is stable and competitive by itself......Page 333
11.4.2 Temporal correlation between inputs and output neuron......Page 334
11.4.3 Mean rate of change in synaptic strength......Page 335
11.4.4 Equilibrium synaptic strengths......Page 337
11.4.5.1 Constant Poisson inputs......Page 339
11.4.5.2 Correlations with different time constants......Page 343
11.4.5.3 Gradient of correlations......Page 344
11.5 Temporal aspects of STDP......Page 346
11.6.1 Hebbian models of map development and plasticity......Page 347
11.6.2 Distributed synchrony in a recurrent network......Page 351
11.7 Conclusion......Page 352
References......Page 353
12.1 Introduction: the timing game......Page 360
12.2.1 Stimulus representation......Page 362
12.2.2 Information flow......Page 364
12.3 Correlations arising from common input......Page 366
12.4 Correlations arising from local network interactions......Page 369
12.5 When are neurons sensitive to correlated input?......Page 372
12.5.2 Fluctuations and integrator models......Page 373
12.6.1 Parameterizing the input......Page 376
12.6.2 A random walk in voltage......Page 378
12.6.3 Quantitative relationships between input and output......Page 381
12.7 Correlations and neuronal variability......Page 383
12.8 Conclusion......Page 384
References......Page 386
13.1 Introduction......Page 394
13.2.1 Quantifying neuronal responses and stimuli......Page 395
13.2.2 Mutual information and sampling bias......Page 396
13.2.3 Series expansion approach to information estimation......Page 397
13.2.3.2 PSTH Similarity......Page 398
13.2.3.4 Stimulus-independent spike patterns......Page 399
13.2.4 Generalised series expansion......Page 400
13.3.1 Whisking behaviour......Page 401
13.3.2 Anatomy of the whisker system......Page 402
13.4.1 Introduction......Page 403
13.4.2 Role of spike timing......Page 404
13.4.2.2 Role of spike patterns......Page 405
13.4.2.4 Pooling......Page 407
13.5.1 Decoding first spike times......Page 408
13.5.2 Role of cross-correlations in population codes......Page 409
13.6 Conclusions......Page 411
References......Page 412
14.1 The fly motion vision system: an overview......Page 415
14.2 Mechanisms of local motion detection: the correlation detector......Page 418
14.2.1.1 Velocity tuning......Page 419
14.2.1.2 Pattern dependence......Page 420
14.2.1.3 Orientation tuning......Page 423
14.2.2 Dynamic response properties......Page 424
14.2.3 Additional filters and adaptive properties......Page 426
14.3.1 Compartmental models of tangential cells......Page 429
Figure 14.10......Page 430
14.3.2 Dendritic integration and gain control......Page 432
Figure 14.12......Page 434
14.3.3 Binocular interactions......Page 435
14.3.4 Dendro-dendritic interactions......Page 436
Figure 14.13......Page 437
Figure 14.14......Page 438
14.4 Conclusions......Page 439
References......Page 441
Mean - Field Theory of Irregularly Spiking Neuronal Populations and Working Memory in Recurrent Cortical Networks......Page 448
15.1 Introduction......Page 449
15.2.1 The leaky integrate-and-fire neuron......Page 451
15.2.2 Temporal structure of the afferent synaptic current......Page 452
15.2.3 The diffusion approximation......Page 453
15.2.4 Computation of the mean firing rate and CV......Page 456
15.2.5 Effect of synaptic time constants......Page 460
15.2.6 Approximate treatment of realistic synaptic dynamics......Page 462
15.3.1 Self-consistent steady-state solutions in large unstructured networks......Page 469
15.3.2 Stability and dynamics......Page 476
15.3.3 Bistability in a single population network......Page 480
15.3.4 Persistent neural activity in an object working memory model......Page 485
15.3.5 Stability of the persistent activity state......Page 486
15.3.6 Multistability in balanced networks......Page 491
15.4 Summary and future directions......Page 495
Appendix 1: The diffusion approximation......Page 496
Appendix 2: Stability of the steady-state solutions......Page 498
References......Page 499
The Operation of Memory Systems in the Brain......Page 508
16.2 Functions of the hippocampus in long-term memory......Page 509
16.2.1 Effects of damage to the hippocampus and connected structures on object-place and episodic memory......Page 510
16.2.2 Neurophysiology of the hippocampus and connected areas......Page 512
16.2.3 Hippocampal models......Page 515
16.2.4 Continuous spatial representations, path integration, and the use of idiothetic inputs......Page 517
16.2.5 A unified theory of hippocampal memory: mixed continuous and discrete attractor networks......Page 527
16.2.6 The speed of operation of memory networks: the integrate-and- fire approach......Page 528
16.3.1 Prefrontal cortex short-term memory networks, and their relation to temporal and parietal perceptual networks......Page 529
16.3.2 Computational details of the model of short-term memory......Page 531
16.3.3 Computational necessity for a separate, prefrontal cortex, shortterm memory system......Page 535
16.3.5 Synaptic modification is needed to set up but not to reuse shortterm memory systems......Page 536
16.4 Invariant visual object recognition......Page 537
16.5 Visual stimulusÒreward association, emotion, and motivation......Page 538
16.6 Effects of mood on memory and visual processing......Page 539
References......Page 542
Modelling Motor Control Paradigms......Page 552
17.1 Introduction: the ecological nature of motor control......Page 553
17.2.1 Logical decomposition of motor control into cascaded computational......Page 556
17.2.2 The Achilles’ heel of feedback control......Page 558
17.3.1 Motor equivalence and spatio-temporal invariances......Page 561
17.3.2 The viscous-elastic properties of the human muscles......Page 565
17.3.3 Dynamic compensation: anticipatory feedforward and feedback......Page 566
17.4 The role of cerebellum in the coordination of multiple joints......Page 567
17.4.1 Abnormal feedforward control in ataxic patients......Page 570
17.5.1 Stabilisation of the standing posture: evidence of anticipatory compensation......Page 573
17.5.2 Arm trajectory in a divergent force field: evidence of stiffness modulation......Page 576
17.5.3 Choosing between stiffness modulation and anticipatory compensation......Page 577
17.5.4 Implementing anticipatory compensation......Page 579
17.6.2 Adaptive behaviour and motor learning......Page 582
17.6.3 A distributed computational architecture......Page 583
References......Page 586
18.1 Introduction......Page 591
18.2 A conceptual framework for real-time neural computation......Page 592
18.4 Towards a non-Turing theory for real-time neural computation......Page 598
18.5.1 Speech recognition......Page 600
18.5.2 Predicting movements and solving the aperture problem......Page 605
18.6.1 Temporal integration in neural microcircuit models......Page 610
18.6.2 Kernel function of neural microcircuit models......Page 615
18.7 Software for evaluating the computational capabilities of neural microcircuit models......Page 616
18.8 Discussion......Page 617
References......Page 619
19.1 Introduction......Page 622
19.2 Brain areas......Page 623
19.3.1 Visual search and pop-out......Page 625
19.3.2 Computational models and the saliency map......Page 626
19.4.1 Are we blind outside of the focus of attention?......Page 629
19.4.2 Attentional modulation of early vision......Page 630
19.5.2 Influence of task......Page 631
19.6 Attention and scene understanding......Page 632
19.6.2 Cooperation between where and what......Page 633
19.7 Discussion......Page 634
References......Page 637
CONTRIBUTORS......Page 21