The Neural Marketplace: I. General Formalism and Linear Theory


We propose a mathematical theory for how networks of neurons in the brain self-organize into functional networks, similarly to the self-organization of supply networks in a free-market economy. The theory is inspired by recent experimental results showing how information about changes to output synapses can travel backward along axons to affect a neuron’s inputs. In neuronal development, competition for such “retroaxonal” signals determines which neurons live and which die. We suggest that in adults, an analogous form of competition occurs between neurons, to supply their targets with appropriate information in exchange for a “payment” returned to them backward along the axon. We review experimental evidence suggesting that neurotrophins may constitute such a signaling pathway in the adult brain. We construct a mathematical model, in which a small number of “consumer” neurons receive explicit fast error signals while a larger number of “producer” neurons compete to supply them with information, guided by retroaxonal signals from the consumers and from each other. We define a loss function to measure network performance and define the “worth” of a producer to be the increase in loss that would result if that neuron were to fall silent. We show how slow retroaxonal signals can allow producers to estimate their worth, and how these estimates allow the network to perform a form of parallel search over multiple producer cells. We validate our approximations and demonstrate the proposed learning rule using simulations.

Stimulus set meaningfulness and neurophysiological differentiation: a functional magnetic resonance imaging study

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A meaningful set of stimuli, such as a sequence of frames from a movie, triggers a set of different experiences. By contrast, a meaningless set of stimuli, such as a sequence of ‘TV noise’ frames, triggers always the same experience – of seeing ‘TV noise’ – even though the stimuli themselves are as different from each other as the movie frames. We reasoned that the differentiation of cortical responses underlying the subject’s experiences, as measured by Lempel-Ziv complexity (incompressibility) of functional MRI images, should reflect the overall meaningfulness of a set of stimuli for the subject, rather than differences among the stimuli. We tested this hypothesis by quantifying the differentiation of brain activity patterns in response to a movie sequence, to the same movie scrambled in time, and to ‘TV noise’, where the pixels from each movie frame were scrambled in space. While overall cortical activation was strong and widespread in all conditions, the differentiation (Lempel-Ziv complexity) of brain activation patterns was correlated with the meaningfulness of the stimulus set, being highest in the movie condition, intermediate in the scrambled movie condition, and minimal for ‘TV noise’. Stimulus set meaningfulness was also associated with higher information integration among cortical regions. These results suggest that the differentiation of neural responses can be used to assess the meaningfulness of a given set of stimuli for a given subject, without the need to identify the features and categories that are relevant to the subject, nor the precise location of selective neural responses.

Faciotopy—a face-feature map with face-like topology in the human occipital face area

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The occipital face area (OFA) and fusiform face area (FFA) are brain regions thought to be specialized for face perception. However, their intrinsic functional organization and status as cortical areas with well-defined boundaries remains unclear. Here we test these regions for “faciotopy”, a particular hypothesis about their intrinsic functional organisation. A faciotopic area would contain a face-feature map on the cortical surface, where cortical patches represent face features and neighbouring patches represent features that are physically neighbouring in a face. The faciotopy hypothesis is motivated by the idea that face regions might develop from a retinotopic protomap and acquire their selectivity for face features through natural visual experience. Faces have a prototypical configuration of features, are usually perceived in a canonical upright orientation, and are frequently fixated in particular locations. To test the faciotopy hypothesis, we presented images of isolated face-features at fixation to subjects during functional magnetic resonance imaging. The responses in V1 were best explained by low-level image properties of the stimuli. OFA, and to a lesser degree FFA, showed evidence for a faciotopic organization. When a single patch of cortex was estimated for each face feature, the cortical distances between the feature patches reflected the physical distance between the features in a face. Faciotopy would be the first example, to our knowledge, of a cortical map reflecting the topology, not of a part of the organism itself (its retina in retinotopy, its body in somatotopy), but of an external object of particular perceptual significance.

Rapid, transient, and frequency-specific topological reorganization of cognitive networks


Cognition emerges from interactions within spatially distributed but synchronized brain networks. Such networks are transient and dynamic, established on the timescale of milliseconds in order to perform specific cognitive operations. But it is not known whether topological features of transient cognitive networks contribute to cognitive processing. Cognition might merely change weights of intrinsic functional networks or, conversely, cognitive processing might require qualitatively new topological arrangements. To address this question, we recorded high-density EEG when subjects performed a visual discrimination task and characterized source-space weighted functional networks with graph measures. We revealed rapid, transient, and frequency-specific reorganization of the network’s topology during cognition. Specifically, cognitive networks were characterized by strong clustering, low modularity, and strong interactions between hub-nodes. Our findings suggest that dense and clustered connectivity between the hub nodes belonging to different modules is the “network fingerprint” of cognition. Such reorganization patterns might facilitate global integration of information and provide a substrate for a “global workspace”; necessary for cognition and consciousness to occur. Thus, characterizing topology of the event-related networks opens new vistas to interpret cognitive dynamics in the broader conceptual framework of graph theory.

Pre-synaptic modulation of afferent feedback in the macaque spinal cord does not modulate with cycles of peripheral oscillations around 10 Hz


Spinal interneurons are partially phase-locked to physiological tremor around 10Hz. The phase of spinal activity is approximately opposite to descending drive to motoneurons, leading to partial phase cancellation and tremor reduction. Pre-synaptic inhibition of afferent feedback has been demonstrated to increase during voluntary movements, but it is not known whether it tracks more rapid fluctuations in output such as during tremor. In this study, we recorded dorsal root potentials (DRPs) from the C8 and T1 roots in two macaque monkeys following intra-spinal micro-stimulation (1-3Hz, 30-100µA), whilst the animals performed an index finger flexion task which elicited substantial peripheral oscillations around 10Hz. Forty one responses were identified with latency <5ms; these were narrow (mean width 0.59 ms), and likely resulted from antidromic activation of afferents following stimulation near terminals. Significant modulation during task performance occurred in 16/41 responses, reflecting terminal excitability changes generated by pre-synaptic inhibition (Wall’s excitability test). Stimuli falling during large-amplitude 8-12Hz oscillations in finger acceleration were extracted, and sub-averages of DRPs constructed for stimuli delivered at different oscillation phases. Although some apparent phase-dependent modulation was seen, this was not above the level expected by chance fluctuation. We conclude that although pre-synaptic inhibition modulates over the timescale of a voluntary movement (around one second), it does not follow more rapid changes in motor output. This suggests that pre-synaptic inhibition is not part of the spinal systems for tremor reduction described previously, and that it plays a role in overall – but not moment-by-moment – regulation of feedback gain.

Bridging psychology and genetics using large-scale spatial analysis of neuroimaging and neurogenetic data

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Understanding how microscopic molecules give rise to complex cognitive processes is a major goal of the biological sciences. The countless hypothetical molecule-cognition relationships necessitate discovery-based techniques to guide scientists toward the most productive lines of investigation. To this end, we present a novel discovery tool that uses spatial patterns of neural gene expression from the Allen Brain Institute (ABI) and large-scale functional neuroimaging meta-analyses from the Neurosynth framework to bridge neurogenetic and neuroimaging data. We quantified the spatial similarity between over 20,000 genes from the ABI and 48 psychological topics derived from lexical analysis of neuroimaging articles, producing a comprehensive set of gene/cognition mappings that we term the Neurosynth-gene atlas. We demonstrate the ability to independently replicate known gene/cognition associations (e.g., between dopamine and reward), and subsequently use it to identify a range of novel associations between individual molecules or genes and complex psychological phenomena such as reward, memory and emotion. Our results complement existing discovery-based methods such as GWAS, and provide a novel means of generating hypotheses about the neurogenetic substrates of complex cognitive functions.

Structured dynamics of neural activity across developing neocortex

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The cerebral cortex exhibits spontaneous and sensory evoked patterns of activity during early development that is vital for the formation and refinement of neural circuits. Identifying the source and flow of this activity locally and globally is critical for understanding principles guiding self-organization in the developing brain. Here we use whole brain transcranial optical imaging at high spatial and temporal resolution to demonstrate that dynamical patterns of neuronal activity in developing mouse neocortex consist of spatially discrete domains that are coordinated in an age, areal, and behavior- dependent fashion. Ongoing cortical activity displays mirror-symmetric activation patterns across the cerebral hemispheres and stereotyped network architectures that are shaped during development, with parietal-sensorimotor subnetworks functionally connected to occipital regions through frontal-medial cortical areas. This study provides the first broad description of population activity in the developing neocortex at a scope and scale that bridges the microscopic and macroscopic spatiotemporal resolutions provided by traditional neurophysiological and functional neuroimaging techniques. Mesoscale maps of cortical population dynamics within animal models will be crucial for future efforts to understand and treat neurodevelopmental disorders.