Scale-Change Symmetry in the Rules Governing Neural Systems

Collapse of complexity of brain and body activity due to excessive inhibition and MeCP2 disruption

Complex body movements require complex dynamics and coordination among neurons in motor cortex. Conversely, a long-standing theoretical notion supposes that if many neurons in motor cortex become excessively synchronized, they may lack the necessary complexity for healthy motor coding. However, direct experimental support for this idea is rare and underlying mechanisms are unclear. Here we recorded three-dimensional body movements and spiking activity of many single neurons in motor cortex of rats with enhanced synaptic inhibition and a transgenic rat model of Rett syndrome (RTT). For both cases, we found a collapse of complexity in the motor system. Reduced complexity was apparent in lower-dimensional, stereotyped brain-body interactions, neural synchrony, and simpler behavior. Our results demonstrate how imbalanced inhibition can cause excessive synchrony among movement-related neurons and, consequently, a stereotyped motor code. Excessive inhibition and synchrony may underlie abnormal motor function in RTT.

Neuronal Avalanches Across the Rat Somatosensory Barrel Cortex and the Effect of Single Whisker Stimulation

Since its first experimental signatures, the so called "critical brain hypothesis" has been extensively studied. Yet, its actual foundations remain elusive. According to a widely accepted teleological reasoning, the brain would be poised to a critical state to optimize the mapping of the noisy and ever changing real-world inputs, thus suggesting that primary sensory cortical areas should be critical. We investigated whether a single barrel column of the somatosensory cortex of the anesthetized rat displays a critical behavior. Neuronal avalanches were recorded across all cortical layers in terms of both multi-unit activities and population local field potentials, and their behavior during spontaneous activity compared to the one evoked by a controlled single whisker deflection. By applying a maximum likelihood statistical method based on timeseries undersampling to fit the avalanches distributions, we show that neuronal avalanches are power law distributed for both multi-unit activities and local field potentials during spontaneous activity, with exponents that are spread along a scaling line. Instead, after the tactile stimulus, activity switches to a transient across-layers synchronization mode that appears to dominate the cortical representation of the single sensory input.

Neural Systems Under Change of Scale

We derive a theoretical construct that allows for the characterisation of both scalable and scale free systems within the dynamic causal modelling (DCM) framework. We define a dynamical system to be "scalable" if the same equation of motion continues to apply as the system changes in size. As an example of such a system, we simulate planetary orbits varying in size and show that our proposed methodology can be used to recover Kepler's third law from the timeseries. In contrast, a "scale free" system is one in which there is no characteristic length scale, meaning that images of such a system are statistically unchanged at different levels of magnification. As an example of such a system, we use calcium imaging collected in murine cortex and show that the dynamical critical exponent, as defined in renormalization group theory, can be estimated in an empirical biological setting. We find that a task-relevant region of the cortex is associated with higher dynamical critical exponents in task vs. spontaneous states and vice versa for a task-irrelevant region.

Unique scales preserve self-similar integrate-and-fire functionality of neuronal clusters

Brains demonstrate varying spatial scales of nested hierarchical clustering. Identifying the brain's neuronal cluster size to be presented as nodes in a network computation is critical to both neuroscience and artificial intelligence, as these define the cognitive blocks capable of building intelligent computation. Experiments support various forms and sizes of neural clustering, from handfuls of dendrites to thousands of neurons, and hint at their behavior. Here, we use computational simulations with a brain-derived fMRI network to show that not only do brain networks remain structurally self-similar across scales but also neuron-like signal integration functionality ("integrate and fire") is preserved at particular clustering scales. As such, we propose a coarse-graining of neuronal networks to ensemble-nodes, with multiple spikes making up its ensemble-spike and time re-scaling factor defining its ensemble-time step. This fractal-like spatiotemporal property, observed in both structure and function, permits strategic choice in bridging across experimental scales for computational modeling while also suggesting regulatory constraints on developmental and evolutionary "growth spurts" in brain size, as per punctuated equilibrium theories in evolutionary biology.

A Complex Systems Perspective on Neuroimaging Studies of Behavior and Its Disorders

The study of complex systems deals with emergent behavior that arises as a result of nonlinear spatiotemporal interactions between a large number of components both within the system, as well as between the system and its environment. There is a strong case to be made that neural systems as well as their emergent behavior and disorders can be studied within the framework of complexity science. In particular, the field of neuroimaging has begun to apply both theoretical and experimental procedures originating in complexity science—usually in parallel with traditional methodologies. Here, we illustrate the basic properties that characterize complex systems and evaluate how they relate to what we have learned about brain structure and function from neuroimaging experiments. We then argue in favor of adopting a complex systems-based methodology in the study of neuroimaging, alongside appropriate experimental paradigms, and with minimal influences from noncomplex system approaches. Our exposition includes a review of the fundamental mathematical concepts, combined with practical examples and a compilation of results from the literature.

Computing by modulating spontaneous cortical activity patterns as a mechanism of active visual processing

Cortical populations produce complex spatiotemporal activity spontaneously without sensory inputs. However, the fundamental computational roles of such spontaneous activity remain unclear. Here, we propose a new neural computation mechanism for understanding how spontaneous activity is actively involved in cortical processing: Computing by Modulating Spontaneous Activity (CMSA). Using biophysically plausible circuit models, we demonstrate that spontaneous activity patterns with dynamical properties, as found in empirical observations, are modulated or redistributed by external stimuli to give rise to neural responses. We find that this CMSA mechanism of generating neural responses provides profound computational advantages, such as actively speeding up cortical processing. We further reveal that the CMSA mechanism provides a unifying explanation for many experimental findings at both the single-neuron and circuit levels, and that CMSA in response to natural stimuli such as face images is the underlying neurophysiological mechanism of perceptual "bubbles" as found in psychophysical studies.