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.

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.

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

The integration of physiological functions in living organisms corresponds to the reconstruction of a biological system from its components. This calls for a sound theoretical framework based on the rigorous definition of the elementary physiological function within the context of multiple levels of biological organization. One of the main problems encountered in the neurosciences is that of extending the current theory of automata, as used in the study of artificial neural networks, to real neural networks. The difficulty arises because the theory of automata fails to take into account the various levels of biological organization involved in nervous activity. This article recalls the main elements of G. A. Chauvet's novel n-level field theory, i.e., the properties of non-symmetry and non-locality of functional interactions, and the S-propagator formalism that governs the propagation of a functional interaction across the different levels of the structural organization of a biological system. The neural field equations derived from this theory allow the inclusion of multiple organizational levels of a biological system into the analysis by incorporating specific local models into a global non-local model. The main advantage of the method presented here is the simplification obtained by breaking down the physiological function into its components according to the time scales and space scales of operation. Moreover, the method takes into account the non-locality of the functional interaction, assuming it to be propagated at finite velocity in a continuous and hierarchical space. Finally, this approach allows the systematic study of physiological functions within a single theoretical framework, the complexity of which could be progressively increased by integrating specific local models as new findings become available.

A discrete approach for a model of temporal learning by the cerebellum: in silico classical 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.