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

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 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.

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.

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.