Phase conjugation model for information transfer in the nervous system

In the nervous system, dispersion in propagation time sometimes brings delay distortion or phase distortion on the information transmission. Also in the memory retrieval processes in the brain, some parts of images may be retrieved more slowly than others. For smooth control of fast movements as well as for keeping exact thinking, these distortions have to be taken out. To understand the distortion cancelling mechanism, new neural network models for compensating the phase distortion are proposed. The models stand on the concept of "phase conjugate mirror" which is used in optical image processing. Simulation studies based on the model resulted in successful cancellation of the delay dispersion involved in the information transmission in the nervous system.     

Self-organization in prebiological systems: Simulations of a model for the origin of genetic information

Summary Computer simulations of a spin glass model for the origin of biological information are discussed. Selection is found to occur among a wide diversity of possible species, and in addition competition, adaptation, and hysteresis are all exhibited.     

A bistable model of cell polarity

Ultrasensitivity, as described by Goldbeter and Koshland, has been considered for a long time as a way to realize bistable switches in biological systems. It is not as well recognized that when ultrasensitivity and reinforcing feedback loops are present in a spatially distributed system such as the cell plasmamembrane, they may induce bistability and spatial separation of the system into distinct signaling phases. Here we suggest that bistability of ultrasensitive signaling pathways in a diffusive environment provides a basic mechanism to realize cell membrane polarity. Cell membrane polarization is a fundamental process implicated in several basic biological phenomena, such as differentiation, proliferation, migration and morphogenesis of unicellular and multicellular organisms. We describe a simple, solvable model of cell membrane polarization based on the coupling of membrane diffusion with bistable enzymatic dynamics. The model can reproduce a broad range of symmetry-breaking events, such as those observed in eukaryotic directional sensing, the apico-basal polarization of epithelium cells, the polarization of budding and mating yeast, and the formation of Ras nanoclusters in several cell types.     

Traveling waves in the discrete fast buffered bistable system

We study the existence and uniqueness of traveling wave solutions of the discrete buffered bistable equation. Buffered excitable systems are used to model, among other things, the propagation of waves of increased calcium concentration, and discrete models are often used to describe the propagation of such waves across multiple cells. We derive necessary conditions for the existence of waves, and, under some restrictive technical assumptions, we derive sufficient conditions. When the wave exists it is unique and stable.      

Soliton behaviour in a bistable reaction diffusion model

We analyze a generic reaction-diffusion model that contains the important features of Turing systems and that has been extensively used in the past to model biological interesting patterns. This model presents various fixed points. Analysis of this model has been made in the past only in the case when there is only a single fixed point, and a phase diagram of all the possible instabilities shows that there is a place where a Turing-Hopf bifurcation occurs producing oscillating Turing patterns. In here we focus on the interesting situation of having several fixed points, particularly when one unstable point is in between two equally stable points. We show that the solutions of this bistable system are traveling front waves, or solitons. The predictions and results are tested by performing extensive numerical calculations in one and two dimensions. The dynamics of these solitons is governed by a well defined spatial scale, and collisions and interactions between solitons depend on this scale. In certain regions of parameter space the wave fronts can be stationary, forming a pattern resembling spatial chaos. The patterns in two dimensions are particularly interesting because they can present a coherent dynamics with pseudo spiral rotations that simulate the myocardial beat quite closely. We show that our simple model can produce complicated spatial patterns with many different properties, and could be used in applications in many different fields.      

A model for the origin of life

Summary A simple statistical model is constructed, describing the transition from disorder to order in a population of mutually catalytic molecules undergoing random mutations. The consequences of the model are calculated, and its possible relevance to the problem of the origin of life is discussed. The main conclusion of the analysis is that the model allows populations of several thousand molecular units to make the transition from disorder to order with reasonable probability.     

A model for optimal processing of multisensory information in the system for maintaining body orientation in the human

Considered is the optimal processing of multisensory information to maintain body orientation in the human. It is supposed that the orientation is performed by a system of angular stabilization with only small deviations from the equilibrium believed to be coincided with the local vertical. The linear transformation is determined which minimizes the square loss function for the stabilization error. This transformation comprises two successive steps. One of them is the averaging procedure on the the sensory inputs and the other is the optimal Kalman filtering in time domain. It is shown that the presence of two interacting channels for angular position and angular velocity in the structure of the optimal filter ensures sufficient accuracy of stabilization in both channels for the stabilization system as a whole in spite of the substantial unreliability in transmission in the channel of the angular position.     

Speculations on the origin and evolution of metabolism

An autotrophic origin of metabolism is described, which requires clays, transition state metals, disulfide and dithiols, U.V. and cyanide ion. A general scheme is proposed, involving the fixation of CO2 and N2, for the evolution of intermediary metabolism based on the evolution of a complex system from a simple one. The basic conclusion is that metabolism could have evolved from a simple environment rather than from a complex one.     

The asymptotic behavior of solutions of the buffered bistable system

In this paper, we study a model for calcium buffering with bistable nonlinearity. We present some results on the stability of equilibrium states and show that there exists a threshold phenomenon in our model. In comparing with the model without buffers, we see that stationary buffers cannot destroy the asymptotic stability of the associated equilibrium states and the threshold phenomenon. Moreover, we also investigate the propagation property of solutions with initial data being a disturbance of one of the stable states which is confined to a half-line. We show that the more stable state will eventually dominate the whole dynamics and that the speed of this propagation (or invading process) is positive.     

The EBG system of E. coli: origin and evolution of a novel beta-galactosidase for the metabolism of lactose

The EBG system of E. coli has served as a model for the evolution of novel functions. This paper reviews the experimental evolution of the catabolism of -galactoside sugars in strains of E. coli that carry deletions of the classical lacZ -galactosidase gene. Evolution of the ebgA encoded Ebg -galactosidase for an expanded substrate range, evolution of the ebgR encoded Ebg repressor for sensitivity to an expanded range of inducers, the amino acid replacements responsible for those changes, and the evolutionary potential of the system are discussed. The EBG system has also served as a model for studying the detailed catalytic consequences of experimental evolution at the physical–chemical level. The analysis of free-energy profiles for the wildtype and all of the various evolved Ebg enzymes has permitted rejection of the Albery–Knowles hypothesis that relates likely changes in free-energy profiles to evolutionary change.     

Wave-pinning and cell polarity from a bistable reaction-diffusion system

Motile eukaryotic cells polarize in response to external signals. Numerous mechanisms have been suggested to account for this symmetry breaking and for the ensuing robust polarization. Implicated in this process are various proteins that are recruited to the plasma membrane and segregate at an emergent front or back of the polarizing cell. Among these are PI3K, PTEN, and members of the Rho family GTPases such as Cdc42, Rac, and Rho. Many such proteins, including the Rho GTPases, cycle between active membrane-bound forms and inactive cytosolic forms. In previous work, we have shown that this property, together with appropriate crosstalk, endows a biochemical circuit (Cdc42, Rac, and Rho) with the property of inherent polarizability. Here we show that this property is present in an even simpler system comprised of a single active/inactive protein pair with positive feedback to its own activation. The simplicity of this minimal system also allows us to explain the mechanism using insights from mathematical analysis. The basic idea resides in a well-known property of reaction-diffusion systems with bistable kinetics, namely, propagation of fronts. However, it crucially depends on exchange between active and inactive forms of the chemicals with unequal rates of diffusion, and overall conservation to pin the waves into a stable polar distribution. We refer to these dynamics as wave-pinning and we show that this phenomenon is distinct from Turing-instability-generated pattern formation that occurs in reaction-diffusion systems that appear to be very similar. We explain the mathematical basis of the phenomenon, relate it to spatial segregation of Rho GTPases, and show how it can account for spatial amplification and maintenance of polarity, as well as sensitivity to new stimuli typical in polarization of eukaryotic cells.