On the mathematical integration of the nervous tissue based on the S-propagator formalism

Genomic instantiation of consciousness in neurons through a biophoton field theory

A theoretical framework is developed based on the premise that brains evolved into sufficiently complex adaptive systems capable of instantiating genomic consciousness through self-awareness and complex interactions that recognize qualitatively the controlling factors of biological processes. Furthermore, our hypothesis assumes that the collective interactions in neurons yield macroergic effects, which can produce sufficiently strong electric energy fields for electronic excitations to take place on the surface of endogenous structures via alpha-helical integral proteins as electro-solitons. Specifically the process of radiative relaxation of the electro-solitons allows for the transfer of energy via interactions with deoxyribonucleic acid (DNA) molecules to induce conformational changes in DNA molecules producing an ultra weak non-thermal spontaneous emission of coherent biophotons through a quantum effect. The instantiation of coherent biophotons confined in spaces of DNA molecules guides the biophoton field to be instantaneously conducted along the axonal and neuronal arbors and in-between neurons and throughout the cerebral cortex (cortico-thalamic system) and subcortical areas (e.g., midbrain and hindbrain). Thus providing an informational character of the electric coherence of the brain - referred to as quantum coherence. The biophoton field is realized as a conscious field upon the re-absorption of biophotons by exciplex states of DNA molecules. Such quantum phenomenon brings about self-awareness and enables objectivity to have access to subjectivity in the unconscious. As such, subjective experiences can be recalled to consciousness as subjective conscious experiences or qualia through co-operative interactions between exciplex states of DNA molecules and biophotons leading to metabolic activity and energy transfer across proteins as a result of protein-ligand binding during protein-protein communication. The biophoton field as a conscious field is attributable to the resultant effect of specifying qualia from the metabolic energy field that is transported in macromolecular proteins throughout specific networks of neurons that are constantly transforming into more stable associable representations as molecular solitons. The metastability of subjective experiences based on resonant dynamics occurs when bottom-up patterns of neocortical excitatory activity are matched with top-down expectations as adaptive dynamic pressures. These dynamics of on-going activity patterns influenced by the environment and selected as the preferred subjective experience in terms of a functional field through functional interactions and biological laws are realized as subjectivity and actualized through functional integration as qualia. It is concluded that interactionism and not information processing is the key in understanding how consciousness bridges the explanatory gap between subjective experiences and their neural correlates in the transcendental brain.

The Neurobiological Basis of Cognition: Identification by Multi-Input, Multioutput Nonlinear Dynamic Modeling: A method is proposed for measuring and modeling human long-term memory formation by mathematical analysis and computer simulation of nerve-cell dynamics

The successful development of neural prostheses requires an understanding of the neurobiological bases of cognitive processes, i.e., how the collective activity of populations of neurons results in a higher level process not predictable based on knowledge of the individual neurons and/or synapses alone. We have been studying and applying novel methods for representing nonlinear transformations of multiple spike train inputs (multiple time series of pulse train inputs) produced by synaptic and field interactions among multiple subclasses of neurons arrayed in multiple layers of incompletely connected units. We have been applying our methods to study of the hippocampus, a cortical brain structure that has been demonstrated, in humans and in animals, to perform the cognitive function of encoding new long-term (declarative) memories. Without their hippocampi, animals and humans retain a short-term memory (memory lasting approximately 1 min), and long-term memory for information learned prior to loss of hippocampal function. Results of more than 20 years of studies have demonstrated that both individual hippocampal neurons, and populations of hippocampal cells, e.g., the neurons comprising one of the three principal subsystems of the hippocampus, induce strong, higher order, nonlinear transformations of hippocampal inputs into hippocampal outputs. For one synaptic input or for a population of synchronously active synaptic inputs, such a transformation is represented by a sequence of action potential inputs being changed into a different sequence of action potential outputs. In other words, an incoming temporal pattern is transformed into a different, outgoing temporal pattern. For multiple, asynchronous synaptic inputs, such a transformation is represented by a spatiotemporal pattern of action potential inputs being changed into a different spatiotemporal pattern of action potential outputs. Our primary thesis is that the encoding of short-term memories into new, long-term memories represents the collective set of nonlinearities induced by the three or four principal subsystems of the hippocampus, i.e., entorhinal cortex-to-dentate gyrus, dentate gyrus-to-CA3 pyramidal cell region, CA3-to-CA1 pyramidal cell region, and CA1-to-subicular cortex. This hypothesis will be supported by studies using in vivo hippocampal multineuron recordings from animals performing memory tasks that require hippocampal function. The implications for this hypothesis will be discussed in the context of "cognitive prostheses"-neural prostheses for cortical brain regions believed to support cognitive functions, and that often are subject to damage due to stroke, epilepsy, dementia, and closed head trauma.

A hierarchical modeling approach of hippocampus local circuit

The modeling and simulation of a realistic nervous tissue are difficult because of the number of implied cell types (neuronal and glial), the topology of the networks, and the various heterogeneous molecular mechanisms. The MTIP (Mathematical Theory of Integrative Physiology) is used as a new modeling approach based on a representation in terms of functional interactions and a formalism (S-Propagator) related to n-level field theory. This work presents the passage from a theoretical description of the biological system to a computing implementation in the general case. The specific case of the hippocampus is presented, as well as how a drug allows learning and memory improvement in the local circuit of the CA1 area of the hippocampus. This in silico result is used to experimentally predict the drug effect in vitro to confirm the accuracy of MTIP.

A new paradigm for theory in integrative biology: the principle of auto-associative stabilization: biochemical networks and the selection of neuronal groups

This paper discusses rationale for a theory in biology: what exactly is a theory in biology? Is it of a mathematical nature? How to conceive an integrative theory and why? Replies to these questions are offered for subsequent discussions as concerns the mathematical theory of integrative physiology (MTIP) proposed by the author. It is shown that such a theory is a theoretical framework built on a representation in terms of hierarchical functional interactions and a specific formalism, the S-Propagator, to traverse the levels of organization. As for all natural theories, the MTIP is based on a general principle specific to biology, the principle of auto-associative stabilization (PAAS). In this framework, two models are revisited for a novel interpretation: the first addresses the dynamics of biochemical networks, the second addresses the selection of groups of neurons (TSGN) as suggested by Edelman.

On the existence of physiological age based on functional hierarchy: a formal definition related to time irreversibility

The present approach of aging and time irreversibility is a consequence of the theory of functional organization that I have developed and presented over recent years (see e.g., Ref. 11). It is based on the effect of physically small and numerous perturbations known as fluctuations, of structural units on the dynamics of the biological system during its adult life. Being a highly regulated biological system, a simple realistic hypothesis, the time-optimum regulation between the levels of organization, leads to the existence of an internal age for the biological system, and time-irreversibility associated with aging. Thus, although specific genes are controlling aging, time-irreversibility of the system may be shown to be due to the degradation of physiological functions. In other words, I suggest that for a biological system, the nature of time is specific and is an expression of the highly regulated integration. An internal physiological age reflects the irreversible course of a living organism towards death because of the irreversible course of physiological functions towards dysfunction, due to the irreversible changes in the regulatory processes. Following the works of Prigogine and his colleagues in physics, and more generally in the field of non-integrable dynamical systems (theorem of Poincaré-Misra), I have stated this problem in terms of the relationship between the macroscopic irreversibility of the functional organization and the basic mechanisms of regulation at the lowest "microscopic" level, i.e., the molecular, lowest level of organization. The neuron-neuron elementary functional interaction is proposed as an illustration of the method to define aging in the nervous system.

ON THE INTEGRATION OF PHYSIOLOGICAL MECHANISMS IN THE NERVOUS TISSUE USING THE MTIP: SYNAPTIC PLASTICITY DEPENDING ON NEURONS-ASTROCYTES-CAPILLARIES INTERACTIONS

The objective in this work is twofold: (i) to illustrate the use of the Mathematical Theory of Integrative Physiology (MTIP) [13], that is a general theory and practical method for the systematic and progressive mathematical integration of physiological mechanisms; (ii) to study a complex neurobiological system taken as an example, i.e., the synaptic plasticity depending on brain activity, on astrocytic and neuronal metabolism, and on brain hemodynamics. The functional organization of the nervous tissue is presented in the framework of the MTIP, the ultimate objective being the study of learning and memory by coupling the three networks of neurons, astrocytes and capillaries. Specifically in this paper, we study the influence of the variation of capillaries arterial oxygen on the induction of LTP/LTD by coupling validated mathematical models of AMPA, NMDA, VDCC channels, calcium current in the dendritic spine, vesicular glutamate dynamics in the presynaptic bouton derived from glycolysis and neuronal glucose, mitochondrial respiration, Ca/Na pumps, glycolysis, and calcium dynamics in the astrocytes, hemodynamics of the capillaries. The integration of all these models is discussed by claiming the advantages of using a common framework and a specific dedicated computing system, PhysioMatica.

RATIONALE FOR A MODEL OF HUMAN SYSTEMS INTEGRATION: THE NEED OF A THEORETICAL FRAMEWORK

Human systems integration (HSI) involves augmented human design with the objectives of augmenting human capabilities and improving human performance using behavioral technologies. The fundamental matter of human systems integration and augmented human design is the organization and the nature of interactions that couple physiological systems, humans- and engineered systems, artifacts. By this definition, augmented human consists of interactive artefacts linked to physiological systems. This paper focuses on the rationale of a HSI model based on specific experiments (comparison of dynamical sensorimotor integration and motor performances in real and virtual environments) that confirm the hypothesis of functional interaction in the framework of Chauvet's mathematical theory of integrative physiology (MTIP). Epistemological constraints for HSI and the role of MTIP are briefly discussed in this context.

ON INDETERMINISM, CHAOS, AND SMALL NUMBER PARTICLE SYSTEMS IN THE BRAIN

This paper presents rational, theoretical, and empirical grounds for doubting the principle of determinism in nature and in the brain, and discusses implications of this for free will and the chaos model of the brain. Small number particle systems are practically indeterministic and may be intrinsically indeterministic. Determinism in nature has often been taken to preclude free will. Strict determinism is a concept frequently applied to systems theory, establishing, e.g., the uniqueness of state-space trajectories. In order to consider determinism as a law of nature, however, one must be able to subject it to empirical tests. Presently, one is not able to and whether this can be shown to enable free will or not is not clear. It does remove, at least for the present, determinism itself as a rationale for precluding free will. The work partially supports the chaos model, but weakens the computational computer metaphor of brain function.

SELF-WIRING IN NEURAL NETS OF POINT-LIKE CORTICAL NEURONS FAILS TO REPRODUCE CYTOARCHITECTURAL DIFFERENCES

We propose a model for description of activity-dependent evolution and self-wiring between binary neurons. Specifically, this model can be used for investigation of growth of neuronal connectivity in the developing neocortex. By using computational simulations with appropriate training pattern sequences, we show that long-term memory can be encoded in neuronal connectivity and that the external stimulations form part of the functioning neocortical circuit. It is proposed that such binary neuron representations of point-like cortical neurons fail to reproduce cytoarchitectural differences of the neocortical organization, which has implications for inadequacies of compartmental models.

fMRI MODELS OF DENDRITIC AND ASTROCYTIC NETWORKS

In order to elucidate the relationships between hierarchical structures within the neocortical neuropil and the information carried by an ensemble of neurons encompassing a single voxel, it is essential to predict through volume conductor modeling LFPs representing average extracellular potentials, which are expressed in terms of interstitial potentials of individual cells in networks of gap-junctionally connected astrocytes and synaptically connected neurons. These relationships have been provided and can then be used to investigate how the underlying neuronal population activity can be inferred from the measurement of the BOLD signal through electrovascular coupling mechanisms across the blood-brain barrier. The importance of both synaptic and extrasynaptic transmission as the basis of electrophysiological indices triggering vascular responses between dendritic and astrocytic networks, and sequential configurations of firing patterns in composite neural networks is emphasized. The purpose of this review is to show how fMRI data may be used to draw conclusions about the information transmitted by individual neurons in populations generating the BOLD signal.

THE USE OF REPRESENTATION AND FORMALISM IN A THEORETICAL APPROACH TO INTEGRATIVE NEUROSCIENCE

In the light of existing physical theories, it is shown that representation in terms of functional interactions and formalism (S-Propagators) should satisfy three physical and six biological constraints. Consequences are summarized for neurohormonal field, developmental phase, aging phase, functional hierarchy, Principle of Auto-Associative stability (PAAS), self-organization and neural selection, Darwinian evolution, and the intelligence of movement. Abstraction and complexity of the proposed theories are discussed relatively to their advantages for integrative neuroscience.

A DISCRETE APPROACH FOR A MODEL OF TEMPORAL LEARNING BY THE CEREBELLUM:IN SILICOCLASSICAL CONDITIONING OF THE EYEBLINK REFLEX

Cerebellar cortex is known to be involved in acquisition and expression of eyeblink conditioned reflex. These phenomena imply temporal intervals of learning. Several cellular and network mechanisms have been proposed to produce the eyeblink. In this paper we briefly review the main theories concerning temporal coding, and we propose an alternative way of producing and storing delays and signal sequences after supervised learning. A network of Leaky Integrate-and-Fire (LIF) neurons is built, taking into account several cerebellar features. This network is then trained to produce simple or multiple eyeblink delays using (i) the classical conditioning paradigm and (ii) known data on cerebellar spike timing dependent plasticity (STDP). The resulting model behaves like an adaptive temporal filter. It improves cell subpopulations effects according to their mean firing rate. This rate based selection allows robust supervised learning of temporal events (i.e., delayed signals) and gives the network ability to react with anticipation on the arousal of a noxious event.

On the mathematical integration of the nervous tissue based on the S-propagator formalism: II. Numerical simulations for molecular-dependent activity

In a previous article (G. A. Chauvet, 2002), presenting a theoretical approach for integrating physiological functions in nervous tissue, we showed that a specific hierarchical representation, incorporating the novel concepts of non-symmetry and non-locality, and an appropriate formalism (the S-propagator formalism) could provide a good description of a living system in general, and the nervous system in particular. We now show that, in the framework of this theory, in spite of the complexity inherent to nervous tissue and the great number of elementary mechanisms involved, the numerical resolution of the global non-local system allows us to envisage simulations that would otherwise be impossible to realize. Here, the study is limited to one physiological function, i.e., the spatiotemporal variation of membrane potential in neuronal tissue. We demonstrate that the role of the kinetic constants at the molecular level is in agreement with the observed activity of the neuronal network. The method also reveals the critical role of the maximum density of synapses along the dendritic tree in the behavior of the network. This illustrates the great advantage of the theoretical approach in studying separately any other complementary coupled function without having to modify the computational methods used here. The application of this method to the spatiotemporal variation of synaptic efficacy, which is the basis of the learning and memory function, will be treated in a forthcoming paper.

Recurrent biological neural networks: the weak and noisy limit

A perturbative method is developed for calculating the effects of recurrent synaptic interactions between neurons embedded in a network. A series expansion is constructed that converges for networks with noisy membrane potential and weak synaptic connectivity. The terms of the series can be interpreted as loops of interactions between neurons, so the technique is called a loop expansion. A diagrammatic method is introduced that allows for construction of analytic expressions for the parameter dependencies of the spike-probability function and correlation functions. An analytic expression is obtained to predict the effect of the surrounding network on a neuron during an intracellular current injection. The analytic results are compared with simulations to test the range of their validity and significant effects of the the recurrent connections in network are accurately predicted by the loop expansion.

Hierarchical model of the population dynamics of hippocampal dentate granule cells

A hierarchical modeling approach is used as the basis for a mathematical representation of the population activity of hippocampal dentate granule cells. Using neural field equations, the variation in time and space of dentate granule cell activity is derived from the summed synaptic potential and summed action potential responses of a population of granule cells evoked by monosynaptic excitatory input from entorhinal cortical afferents. In this formulation of the problem, we have considered a two-level hierarchy: the synapses of entorhinal cortical axons define the first level of organization, and dentate granule cells, which include these synapses, define the second, higher level of organization. The model is specified by two state field variables, for membrane potential and for synaptic efficacy, respectively, with both evolving according to different time scales. The two state field variables introduce new parameters, physiological and anatomical, which characterize the dentate from the point of view of neuronal and synaptic populations: (1) a set of geometrical constraints corresponding to the morphological properties of granule cells and anatomical characteristics of entorhinal-dentate connections; and (2) a set of neuronal parameters corresponding to physiological mechanisms. Assuming no interaction between granule cells, i.e., neither ephaptic nor synaptic coupling, the model is shown to be mathematically tractable and allows solution of the field equations leading to the determination of activity. This treatment leads to the definition of two state variables, volume of stimulated synapses and firing time, which describe observed activity. Numerical simulations are used to investigate the populational characterization of the dentate by individual parameters: (1) the relationship between the conditions of stimulation of active perforant path fibers, e.g., stimulating intensity, and activity in the granule cell layer; and (2) the influence of geometry on the generation of activity, i.e., the influence of neuron density and synaptic density-connectivity. As an example application of the model, the granule cell population spike is reconstructed and compared with experimental data.

TOWARDS AN INTEGRATIVE THEORY OF COGNITION

A framework is outlined for connecting brain imaging activity with the underlying biophysical properties of neural networks, and their mechanisms of action and organizing principles. The main thrust of the framework is a dynamic theory of semantics based on functional integration of biophysical neural networks. It asserts that higher-brain function arises from both synaptic and extrasynaptic integration in the neuropil where information on environmental changes are represented dynamically through a discourse of semantics. Consequently, integrative neural modeling is shown to be an important methodology for analyzing the response activities of functional imaging studies in elucidating the relationship between brain and structure, function and behavior.