Stuart P. Wilson

Modeling the Emergence of Whisker Direction Maps in Rat Barrel Cortex

Based on measuring responses to rat whiskers as they are mechanically stimulated, one recent study suggests that barrel-related areas in layer 2/3 rat primary somatosensory cortex (S1) contain a pinwheel map of whisker motion directions. Because this map is reminiscent of topographic organization for visual direction in primary visual cortex (V1) of higher mammals, we asked whether the S1 pinwheels could be explained by an input-driven developmental process as is often suggested for V1. We developed a computational model to capture how whisker stimuli are conveyed to supragranular S1, and simulate lateral cortical interactions using an established self-organizing algorithm. Inputs to the model each represent the deflection of a subset of 25 whiskers as they are contacted by a moving stimulus object. The subset of deflected whiskers corresponds with the shape of the stimulus, and the deflection direction corresponds with the movement direction of the stimulus. If these two features of the inputs are correlated during the training of the model, a somatotopically aligned map of direction emerges for each whisker in S1. Predictions of the model that are immediately testable include (1) that somatotopic pinwheel maps of whisker direction exist in adult layer 2/3 barrel cortex for every large whisker on the rats face, even peripheral whiskers; and (2) in the adult, neurons with similar directional tuning are interconnected by a network of horizontal connections, spanning distances of many whisker representations. We also propose specific experiments for testing the predictions of the model by manipulating patterns of whisker inputs experienced during early development. The results suggest that similar intracortical mechanisms guide the development of primate V1 and rat S1.

Blocking of Goal-Location Learning Based on Shape.

Using desktop, computer-simulated virtual environments (VEs), the authors conducted 5 experiments to investigate blocking of learning about a goal location based on Shape B as a consequence of preliminary training to locate that goal using Shape A. The shapes were large 2-dimensional horizontal figures on the ground. Blocking of spatial learning was found when the initially trained Shape A was presented in the context of auxiliary shapes that were anticipated to be irrelevant to goal localization. When Shape A was initially presented in the absence of these auxiliary shapes, no evidence of blocking between shapes was apparent. The results are discussed in terms of the similarity between spatial and other forms of contingency learning, the operation of a specialized geometric module, and changes in attention as a consequence of discrimination learning.

Self-organisation can generate the discontinuities in the somatosensory map

The primary somatosensory cortex contains a topographic map of the body surface, with two notable discontinuities-the representation of the face is next to that of the hands, and that of the feet is next to the genitals. Farah [Why does the somatosensory homunculus have hands next to face and feet next to genitals? a hypothesis. Neural Computation 10(8) (1998) 1983-1985] has suggested that these discontinuities are due to the mechanisms of self-organisation which underlie cortical map development. The typical position of the foetus in the womb means that these two pairs of body parts will often touch and hence their representations will be simultaneously co-active, even though they are distal in terms of the body surface. We use the Kohonen self-organising map algorithm to provide an existence proof of the plausibility of Farahs hypotheses. We then use the model to test the viability of other possible causes of the known map structure and to explore the limitations of self-organisation for explaining the features of the somatosensory map. The model shows that (a) the Kohonen algorithm requires high frequencies of co-activation to introduce a selective discontinuity into the map, and (b) that higher frequency of separate activation of the critical patterns alone is not sufficient to generate the selective discontinuity and (c) the consistency of near-optimal map formation, and in particular the medial-lateral ordering, cannot be reliably generated by a simple Kohonen algorithm.

A Self-Organising Model of Thermoregulatory Huddling

Endotherms such as rats and mice huddle together to keep warm. The huddle is considered to be an example of a self-organising system, because complex properties of the collective group behaviour are thought to emerge spontaneously through simple interactions between individuals. Groups of rodent pups display two such emergent properties. First, huddling undergoes a ‘phase transition’, such that pups start to aggregate rapidly as the temperature of the environment falls below a critical temperature. Second, the huddle maintains a constant ‘pup flow’, where cooler pups at the periphery continually displace warmer pups at the centre. We set out to test whether these complex group behaviours can emerge spontaneously from local interactions between individuals. We designed a model using a minimal set of assumptions about how individual pups interact, by simply turning towards heat sources, and show in computer simulations that the model reproduces the first emergent property—the phase transition. However, this minimal model tends to produce an unnatural behaviour where several smaller aggregates emerge rather than one large huddle. We found that an extension of the minimal model to include heat exchange between pups allows the group to maintain one large huddle but eradicates the phase transition, whereas inclusion of an additional homeostatic term recovers the phase transition for large huddles. As an unanticipated consequence, the extended model also naturally gave rise to the second observed emergent property—a continuous pup flow. The model therefore serves as a minimal description of huddling as a self-organising system, and as an existence proof that group-level huddling dynamics emerge spontaneously through simple interactions between individuals. We derive a specific testable prediction: Increasing the capacity of the individual to generate or conserve heat will increase the range of ambient temperatures over which adaptive thermoregulatory huddling will emerge.

What, if anything, are topological maps for?

What, if anything, is the functional significance of spatial patterning in cortical feature maps? We ask this question of four major theories of cortical map formation: self‐organizing maps, wiring optimization, place coding, and reaction‐diffusion. We argue that (i) self‐organizing maps yield spatial patterning only as a by‐product of efficient mechanisms for developing environmentally appropriate distributions of feature preferences, (ii) wiring optimization assumes rather than explains a map‐like organization, (iii) place‐coding mechanisms can at best explain only a subset of maps in functional terms, and (iv) reaction‐diffusion models suggest two factors in the evolution of maps, the first based on efficient development of feature distributions, and the second based on generating feature‐specific long‐range recurrent cortical circuitry. None of these explanations for the existence of topological maps requires spatial patterning in maps to be useful. Thus despite these useful frameworks for understanding how maps form and how they are wired, the possibility that patterns are merely epiphenomena in the evolution of mammalian neocortex cannot be rejected. The article is intended as a nontechnical introduction to the assumptions and predictions of these four important classes of models, along with other possible functional explanations for maps.

How self-organization can guide evolution

Self-organization and natural selection are fundamental forces that shape the natural world. Substantial progress in understanding how these forces interact has been made through the study of abstract models. Further progress may be made by identifying a model system in which the interaction between self-organization and selection can be investigated empirically. To this end, we investigate how the self-organizing thermoregulatory huddling behaviours displayed by many species of mammals might influence natural selection of the genetic components of metabolism. By applying a simple evolutionary algorithm to a well-established model of the interactions between environmental, morphological, physiological and behavioural components of thermoregulation, we arrive at a clear, but counterintuitive, prediction: rodents that are able to huddle together in cold environments should evolve a lower thermal conductance at a faster rate than animals reared in isolation. The model therefore explains how evolution can be accelerated as a consequence of relaxed selection, and it predicts how the effect may be exaggerated by an increase in the litter size, i.e. by an increase in the capacity to use huddling behaviours for thermoregulation. Confirmation of these predictions in future experiments with rodents would constitute strong evidence of a mechanism by which self-organization can guide natural selection.

Self-organised criticality in the evolution of a thermodynamic model of rodent thermoregulatory huddling

A thermodynamic model of thermoregulatory huddling interactions between endotherms is developed. The model is presented as a Monte Carlo algorithm in which animals are iteratively exchanged between groups, with a probability of exchanging groups defined in terms of the temperature of the environment and the body temperatures of the animals. The temperature-dependent exchange of animals between groups is shown to reproduce a second-order critical phase transition, i.e., a smooth switch to huddling when the environment gets colder, as measured in recent experiments. A peak in the rate at which group sizes change, referred to as pup flow, is predicted at the critical temperature of the phase transition, consistent with a thermodynamic description of huddling, and with a description of the huddle as a self-organising system. The model was subjected to a simple evolutionary procedure, by iteratively substituting the physiologies of individuals that fail to balance the costs of thermoregulation (by huddling in groups) with the costs of thermogenesis (by contributing heat). The resulting tension between cooperative and competitive interactions was found to generate a phenomenon called self-organised criticality, as evidenced by the emergence of avalanches in fitness that propagate across many generations. The emergence of avalanches reveals how huddling can introduce correlations in fitness between individuals and thereby constrain evolutionary dynamics. Finally, a full agent-based model of huddling interactions is also shown to generate criticality when subjected to the same evolutionary pressures. The agent-based model is related to the Monte Carlo model in the way that a Vicsek model is related to an Ising model in statistical physics. Huddling therefore presents an opportunity to use thermodynamic theory to study an emergent adaptive animal behaviour. In more general terms, huddling is proposed as an ideal system for investigating the interaction between self-organisation and natural selection empirically.

The Robot Vibrissal System: Understanding Mammalian Sensorimotor Co-ordination Through Biomimetics

We consider the problem of sensorimotor co-ordination in mammals through the lens of vibrissal touch, and via the methodology of embodied computational neuroscience—using biomimetic robots to synthesize and investigate models of mammalian brain architecture. The chapter focuses on five major brain sub-systems and their likely role in vibrissal system function—superior colliculus, basal ganglia, somatosensory cortex, cerebellum, and hippocampus. With respect to each of these we demonstrate how embodied modelling has helped elucidate their likely function in the brain of awake behaving animals. We also demonstrate how the appropriate co-ordination of these sub-systems, with a model of brain architecture, can give rise to integrated behaviour in a life-like whiskered robot.

Neural Computation via Neural Geometry: A Place Code for Inter-whisker Timing in the Barrel Cortex?

The place theory proposed by Jeffress (1948) is still the dominant model of how the brain represents the movement of sensory stimuli between sensory receptors. According to the place theory, delays in signalling between neurons, dependent on the distances between them, compensate for time differences in the stimulation of sensory receptors. Hence the location of neurons, activated by the coincident arrival of multiple signals, reports the stimulus movement velocity. Despite its generality, most evidence for the place theory has been provided by studies of the auditory system of auditory specialists like the barn owl, but in the study of mammalian auditory systems the evidence is inconclusive. We ask to what extent the somatosensory systems of tactile specialists like rats and mice use distance dependent delays between neurons to compute the motion of tactile stimuli between the facial whiskers (or ‘vibrissae’). We present a model in which synaptic inputs evoked by whisker deflections arrive at neurons in layer 2/3 (L2/3) somatosensory ‘barrel’ cortex at different times. The timing of synaptic inputs to each neuron depends on its location relative to sources of input in layer 4 (L4) that represent stimulation of each whisker. Constrained by the geometry and timing of projections from L4 to L2/3, the model can account for a range of experimentally measured responses to two-whisker stimuli. Consistent with that data, responses of model neurons located between the barrels to paired stimulation of two whiskers are greater than the sum of the responses to either whisker input alone. The model predicts that for neurons located closer to either barrel these supralinear responses are tuned for longer inter-whisker stimulation intervals, yielding a topographic map for the inter-whisker deflection interval across the surface of L2/3. This map constitutes a neural place code for the relative timing of sensory stimuli.

The synthetic littermate

I suggest how a new type of biohybrid society --- a huddle of neonatal rat pups comprising biological and synthetic litttermates --- could be used to model the interaction between self-organisation at the neural level and self-organisation at the level of group behaviours.