Comparing the development of cortex-wide gene expression patterns between two species in a common reference frame.

Advances in sequencing techniques have made comparative studies of gene expression a current focus for understanding evolutionary and developmental processes. However, insights into the spatial expression of genes have been limited by a lack of robust methodology. To overcome this obstacle, we developed methods and software tools for quantifying and comparing tissue-wide spatial patterns of gene expression within and between species. Here, we compare cortex-wide expression of RZRß and Id2 mRNA across early postnatal development in mice and voles. We show that patterns of RZRß expression in neocortical layer 4 are highly conserved between species but develop rapidly in voles and much more gradually in mice, who show a marked expansion in the relative size of the putative primary visual area across the first postnatal week. Patterns of Id2 expression, by contrast, emerge in a dynamic and layer-specific sequence that is consistent between the two species. We suggest that these differences in the development of neocortical patterning reflect the independent evolution of brains, bodies, and sensory systems in the 35 million years since their last common ancestor.

Biological action at a distance: Correlated pattern formation in adjacent tessellation domains without communication.

Tessellations emerge in many natural systems, and the constituent domains often contain regular patterns, raising the intriguing possibility that pattern formation within adjacent domains might be correlated by the geometry, without the direct exchange of information between parts comprising either domain. We confirm this paradoxical effect, by simulating pattern formation via reaction-diffusion in domains whose boundary shapes tessellate, and showing that correlations between adjacent patterns are strong compared to controls that self-organize in domains with equivalent sizes but unrelated shapes. The effect holds in systems with linear and non-linear diffusive terms, and for boundary shapes derived from regular and irregular tessellations. Based on the prediction that correlations between adjacent patterns should be bimodally distributed, we develop methods for testing whether a given set of domain boundaries constrained pattern formation within those domains. We then confirm such a prediction by analysing the development of 'subbarrel' patterns, which are thought to emerge via reaction-diffusion, and whose enclosing borders form a Voronoi tessellation on the surface of the rodent somatosensory cortex. In more general terms, this result demonstrates how causal links can be established between the dynamical processes through which biological patterns emerge and the constraints that shape them.

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.

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.

Understanding brain functional architecture through robotics.

Robotics is increasingly seen as a useful test bed for computational models of the brain functional architecture underlying animal behavior. We provide an overview of past and current work, focusing on probabilistic and dynamical models, including approaches premised on the free energy principle, situating this endeavor in relation to evidence that the brain constitutes a layered control system. We argue that future neurorobotic models should integrate multiple neurobiological constraints and be hybrid in nature.

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.

Scaffolding layered control architectures through constraint closure: insights into brain evolution and development.

The functional organization of the mammalian brain can be considered to form a layered control architecture, but how this complex system has emerged through evolution and is constructed during development remains a puzzle. Here we consider brain organization through the framework of constraint closure, viewed as a general characteristic of living systems, that they are composed of multiple sub-systems that constrain each other at different timescales. We do so by developing a new formalism for constraint closure, inspired by a previous model showing how within-lifetime dynamics can constrain between-lifetime dynamics, and we demonstrate how this interaction can be generalized to multi-layered systems. Through this model, we consider brain organization in the context of two major examples of constraint closure-physiological regulation and visual orienting. Our analysis draws attention to the capacity of layered brain architectures to scaffold themselves across multiple timescales, including the ability of cortical processes to constrain the evolution of sub-cortical processes, and of the latter to constrain the space in which cortical systems self-organize and refine themselves. This article is part of the theme issue 'Systems neuroscience through the lens of evolutionary theory'.

Modelling the emergence of whisker barrels.

Brain development relies on an interplay between genetic specification and self-organization. Striking examples of this relationship can be found in the somatosensory brainstem, thalamus, and cortex of rats and mice, where the arrangement of the facial whiskers is preserved in the arrangement of cell aggregates to form precise somatotopic maps. We show in simulation how realistic whisker maps can self-organize, by assuming that information is exchanged between adjacent cells only, under the guidance of gene expression gradients. The resulting model provides a simple account of how patterns of gene expression can constrain spontaneous pattern formation to faithfully reproduce functional maps in subsequent brain structures.

How does the brain wire itself up? One possibility is that a precise genetic blueprint tells every brain cell explicitly how it should be connected to other cells. Another option is that complex patterns emerge from relatively simple interactions between growing cells, which are more loosely controlled by genetic instruction. The barrel cortex in the brains of rats and mice features one of the most distinctive wiring patterns. There, cylindrical clusters of cells ­ or barrels ­ are arranged in a pattern that closely matches the arrangement of the whiskers on the face. Neurons in a barrel become active when the corresponding whisker is stimulated. This precise mapping between individual whiskers and their brain counterparts makes the whisker-barrel system ideal for studying brain wiring. Guidance fields are a way the brain can create cell networks with wiring patterns like the barrels. In this case, genetic instructions help to create gradients of proteins across the brain. These help the axons that connect neurons together to grow in the right direction, by navigating towards regions of higher or lower concentrations. A large number of guidance fields could map out a set of centre-point locations for axons to grow towards, ensuring the correct barrel arrangement. However, there are too few known guidance fields to explain how the barrel cortex could form by this kind of genetic instruction alone. Here, James et al. tried to find a mechanism that could create the structure of the barrel cortex, relying only on two simple guidance fields. Indeed, two guidance fields should be enough to form a coordinate system on the surface of the cortex. In particular, it was examined whether the cortical barrel map could reliably self-organize without a full genetic blueprint pre-specifying the barrel centre-points in the cortex. To do so, James et al. leveraged a mathematical model to create computer simulations; these showed that only two guidance fields are required to reproduce the map. However, this was only the case if axons related to different whiskers competed strongly for space while making connections, causing them to concentrate into whisker-specific clusters. The simulations also revealed that the target tissue does not need to specify centre-points if, instead, the origin tissue directs how strongly the axons should respond to the guidance fields. So this model describes a simple way that specific structures can be copied across the central nervous system. Understanding the way the barrel cortex is set up could help to grasp how healthy brains develop, how brain development differs in certain neurodevelopmental disorders, and how brain wiring reorganizes itself in different contexts, for example after a stroke. Computational models also have the potential to reduce the amount of animal experimentation required to understand how brains are wired, and to cast light on how brain wiring is shaped by evolution.

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.

Limit cycle dynamics can guide the evolution of gene regulatory networks towards point attractors.

Developmental dynamics in Boolean models of gene networks self-organize, either into point attractors (stable repeating patterns of gene expression) or limit cycles (stable repeating sequences of patterns), depending on the network interactions specified by a genome of evolvable bits. Genome specifications for dynamics that can map specific gene expression patterns in early development onto specific point attractor patterns in later development are essentially impossible to discover by chance mutation alone, even for small networks. We show that selection for approximate mappings, dynamically maintained in the states comprising limit cycles, can accelerate evolution by at least an order of magnitude. These results suggest that self-organizing dynamics that occur within lifetimes can, in principle, guide natural selection across lifetimes.

Failure to demonstrate short-cutting in a replication and extension of Tolman et al.'s spatial learning experiment with humans.

Successful demonstrations of novel short-cut taking by animals, including humans, are open to interpretation in terms of learning that is not necessarily spatial. A classic example is that of Tolman, Ritchie, and Kalish (1946) who allowed rats to repeat a sequence of turns through the corridors of a maze to locate a food reward. When the entrance to the corridors was subsequently blocked and alternative corridors were made available, rats successfully selected the corridor leading most directly to the food location. However, the presence of a distinctive light above the goal, in both the training and testing phases, means that approach to the light as a beacon could have been the source of successful short-cutting. We report a replication of the experimental design of Tolman et al. with human participants who explored geometrically equivalent virtual environments. An experimental group, who followed the original procedure in the absence of any distinctive cues proximal to the goal, did not select the corridor which led most directly to the goal. A control group, who experienced a light above the goal during training and testing, were more likely to select a corridor which led in the direction of the goal. A second control group experienced the light above the goal during training, but in the test the location of this cue was shifted by 90° with respect to the start point of exploration. This latter group responded unsystematically in the test, neither selecting a corridor leading to the original goal location, nor one leading directly to the relocated light cue. The results do not support the hypothesis that travelling a multi-path route automatically leads to an integrated cognitive representation of that route. The data offer support for the importance of local cues which can serve as beacons to indicate the location of a goal.

Modelling the emergence of rodent filial huddling from physiological huddling.

Huddling behaviour in neonatal rodents reduces the metabolic costs of physiological thermoregulation. However, animals continue to huddle into adulthood, at ambient temperatures where they are able to sustain a basal metabolism in isolation from the huddle. This 'filial huddling' in older animals is known to be guided by olfactory rather than thermal cues. The present study aimed to test whether thermally rewarding contacts between young mice, experienced when thermogenesis in brown adipose fat tissue (BAT) is highest, could give rise to olfactory preferences that persist as filial huddling interactions in adults. To this end, a simple model was constructed to fit existing data on the development of mouse thermal physiology and behaviour. The form of the model that emerged yields a remarkable explanation for filial huddling; associative learning maintains huddling into adulthood via processes that reduce thermodynamic entropy from BAT metabolism and increase information about social ordering among littermates.

Familiarization: A theory of repetition suppression predicts interference between overlapping cortical representations.

Repetition suppression refers to a reduction in the cortical response to a novel stimulus that results from repeated presentation of the stimulus. We demonstrate repetition suppression in a well established computational model of cortical plasticity, according to which the relative strengths of lateral inhibitory interactions are modified by Hebbian learning. We present the model as an extension to the traditional account of repetition suppression offered by sharpening theory, which emphasises the contribution of afferent plasticity, by instead attributing the effect primarily to plasticity of intra-cortical circuitry. In support, repetition suppression is shown to emerge in simulations with plasticity enabled only in intra-cortical connections. We show in simulation how an extended 'inhibitory sharpening theory' can explain the disruption of repetition suppression reported in studies that include an intermediate phase of exposure to additional novel stimuli composed of features similar to those of the original stimulus. The model suggests a re-interpretation of repetition suppression as a manifestation of the process by which an initially distributed representation of a novel object becomes a more localist representation. Thus, inhibitory sharpening may constitute a more general process by which representation emerges from cortical re-organisation.

Cortical Maps.

In this article, we review functional organization in sensory cortical regions-how the cortex represents the world. We consider four interrelated aspects of cortical organization: (1) the set of receptive fields of individual cortical sensory neurons, (2) how lateral interaction between cortical neurons reflects the similarity of their receptive fields, (3) the spatial distribution of receptive-field properties across the horizontal extent of the cortical tissue, and (4) how the spatial distributions of different receptive-field properties interact with one another. We show how these data are generally well explained by the theory of input-driven self-organization, with a family of computational models of cortical maps offering a parsimonious account for a wide range of map-related phenomena. We then discuss important challenges to this explanation, with respect to the maps present at birth, maps present under activity blockade, the limits of adult plasticity, and the lack of some maps in rodents. Because there is not at present another credible general theory for cortical map development, we conclude by proposing key experiments to help uncover other mechanisms that might also be operating during map development.

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.

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.

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 rat's 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.