Electrically silent neurons in the substantia gelatinosa of the rat spinal cord

Primal-size neural circuits in meta-periodic interaction

Experimental observations of simultaneous activity in large cortical areas have seemed to justify a large network approach in early studies of neural information codes and memory capacity. This approach has overlooked, however, the segregated nature of cortical structure and functionality. Employing graph-theoretic results, we show that, given the estimated number of neurons in the human brain, there are only a few primal sizes that can be attributed to neural circuits under probabilistically sparse connectivity. The significance of this finding is that neural circuits of relatively small primal sizes in cyclic interaction, implied by inhibitory interneuron potentiation and excitatory inter-circuit potentiation, generate relatively long non-repetitious sequences of asynchronous primal-length periods. The meta-periodic nature of such circuit interaction translates into meta-periodic firing-rate dynamics, representing cortical information. It is finally shown that interacting neural circuits of primal sizes 7 or less exhaust most of the capacity of the human brain, with relatively little room to spare for circuits of larger primal sizes. This also appears to ratify experimental findings on the human working memory capacity.

Probabilistically segregated neural circuits and subcritical linguistics

Early studies of cortical information codes and memory capacity have assumed large neural networks, which, subject to evenly probable binary (on/off) activity, were found to be endowed with large storage and retrieval capacities under the Hebbian paradigm. Here, we show that such networks are plagued with exceedingly high cross-network connectivity, yielding long code words, which are linguistically non-realistic and difficult to memorize and comprehend. Noting that the neural circuit activity code is jointly governed by somatic and synaptic activity states, termed neural circuit polarities, we show that, subject to subcritical polarity probability, random-graph-theoretic considerations imply small neural circuit segregation. Such circuits are shown to represent linguistically plausible cortical code words which, in turn, facilitate storage and retrieval of both circuit connectivity and firing-rate dynamics.

Primal categories of neural polarity codes

Neuronal membrane and synapse polarities have been attracting considerable interest in recent years. Certain functional roles for such polarities have been suggested, yet, they have largely remained a subject for speculation and debate. Here, we note that neural circuit polarity codes, defined as sets of polarity permutations, divide into primal-size circuit polarity subcodes, which, sharing certain connectivity attributes, are called categories. Two long-debated, seemingly competing paradigms of neuronal self-feedback, namely, axonal discharge and synaptic mediation, are shown to jointly define the distinction between these categories. However, as the second paradigm contains the first, it is mathematically sufficient for complete specification of all categories. The analysis of primal-size circuit polarity categories is found to reveal, explain and extend experimentally observed cortical information capacity values termed "magical numbers", associated with "working memory". While these have been previously argued on grounds of psychological experiments, here they are further supported on analytic grounds by the so-called Hebbian memory paradigm. The information dimensionality associated with these capacities is found to be a consequence of prime factorization of composite circuit polarity code sizes. Different categories of circuit polarity, identical in size and neuronal parameters, are shown to generate different firing rate dynamics.

Circuit Polarity Effect of Cortical Connectivity, Activity, and Memory

Experimental constraints have traditionally implied separate studies of different cortical functions, such as memory and sensory-motor control. Yet certain cortical modalities, while repeatedly observed and reported, have not been clearly identified with one cortical function or another. Specifically, while neuronal membrane and synapse polarities with respect to a certain potential value have been attracting considerable interest in recent years, the purposes of such polarities have largely remained a subject for speculation and debate. Formally identifying these polarities as on-off neuronal polarity gates, we analytically show that cortical circuit structure, behavior, and memory are all governed by the combined potent effect of these gates, which we collectively term circuit polarity. Employing widely accepted and biologically validated firing rate and plasticity paradigms, we show that circuit polarity is mathematically embedded in the corresponding models. Moreover, we show that the firing rate dynamics implied by these models are driven by ongoing circuit polarity gating dynamics. Furthermore, circuit polarity is shown to segregate cortical circuits into internally synchronous, externally asynchronous subcircuits, defining their firing rate modes in accordance with different cortical tasks. In contrast to the Hebbian paradigm, which is shown to be susceptible to mutual neuronal interference in the face of asynchrony, circuit polarity is shown to block such interference. Noting convergence of synaptic weights, we show that circuit polarity holds the key to cortical memory, having a segregated capacity linear in the number of neurons. While memory concealment is implied by complete neuronal silencing, memory is restored by reactivating the original circuit polarity. Finally, we show that incomplete deterioration or restoration of circuit polarity results in memory modification, which may be associated with partial or false recall, or novel innovation.

The histology, physiology, neurochemistry and circuitry of the substantia gelatinosa Rolandi (lamina II) in mammalian spinal cord

The substantia gelatinosa Rolandi (SGR) was first described about two centuries ago. In the following decades an enormous amount of information has permitted us to understand - at least in part - its role in the initial processing of pain and itch. Here, I will first provide a comprehensive picture of the histology, physiology, and neurochemistry of the normal SGR. Then, I will analytically discuss the SGR circuits that have been directly demonstrated or deductively envisaged in the course of the intensive research on this area of the spinal cord, with particular emphasis on the pathways connecting the primary afferent fibers and the intrinsic neurons. The perspective existence of neurochemically-defined sets of primary afferent neurons giving rise to these circuits will be also discussed, with the proposition that a cross-talk between different subsets of peptidergic fibers may be the structural and functional substrate of additional gating mechanisms in SGR. Finally, I highlight the role played by slow acting high molecular weight modulators in these gating mechanisms.

Developmental metaplasticity in neural circuit codes of firing and structure

Firing-rate dynamics have been hypothesized to mediate inter-neural information transfer in the brain. While the Hebbian paradigm, relating learning and memory to firing activity, has put synaptic efficacy variation at the center of cortical plasticity, we suggest that the external expression of plasticity by changes in the firing-rate dynamics represents a more general notion of plasticity. Hypothesizing that time constants of plasticity and firing dynamics increase with age, and employing the filtering property of the neuron, we obtain the elementary code of global attractors associated with the firing-rate dynamics in each developmental stage. We define a neural circuit connectivity code as an indivisible set of circuit structures generated by membrane and synapse activation and silencing. Synchronous firing patterns under parameter uniformity, and asynchronous circuit firing are shown to be driven, respectively, by membrane and synapse silencing and reactivation, and maintained by the neuronal filtering property. Analytic, graphical and simulation representation of the discrete iteration maps and of the global attractor codes of neural firing rate are found to be consistent with previous empirical neurobiological findings, which have lacked, however, a specific correspondence between firing modes, time constants, circuit connectivity and cortical developmental stages.