Significance of time scale differences in psychophysics.

We present modeling of both rational processes (thoughts) and emotional processes (feelings) on a two-dimensional lattice and on extremely simplified two-dimensional phase space of the brain. Our purpose is to analyze influence of differences in time-scales of various types of processes. In particular, we show that no 'central executive structure' between consciousness and unconsciousness, the existence of which was suggested by psychologists, is not needed.

Postural stability and fractal dynamics.

Methods of non-linear dynamics and deterministic chaos may provide us with effective quantitative descriptors of the dynamics of postural control. The goal of this study was to introduce a new measure, which would allow to determine the fractal structure of posturographic signals and to measure the effect of the loss of visual feedback information in postural control. The results of the study show that fractal dimension (Df) is a very useful, reliable and sensitive measure of the complexity of posturographic signals. Therefore Df can be used for the evaluation of postural stability and its changes due to pathology or an age-related decline.

Non-equilibrium proteins.

There exist no methodical studies concerning non-equilibrium systems in cellular biology. This paper is an attempt to partially fill this shortcoming. We have undertaken an extensive data-mining operation in the existing scientific literature to find scattered information about non-equilibrium subcellular systems, in particular concerning fast proteins, i.e. those with short turnover half-time. We have advanced the hypothesis that functionality in fast proteins emerges as a consequence of their intrinsic physical instability that arises due to conformational strains resulting from co-translational folding (the interdependence between chain elongation and chain folding during biosynthesis on ribosomes). Such intrinsic physical instability, a kind of conformon (Klonowski-Klonowska conformon, according to Ji, (Molecular Theories of Cell Life and Death, Rutgers University Press, New Brunswick, 1991)) is probably the most important feature determining functionality and timing in these proteins. If our hypothesis is true, the turnover half-time of fast proteins should be positively correlated with their molecular weight, and some experimental results (Ames et al., J. Neurochem. 35 (1980) 131) indeed demonstrated such a correlation. Once the native structure (and function) of a fast protein macromolecule is lost, it may not be recovered--denaturation of such proteins will always be irreversible; therefore, we searched for information on irreversible denaturation. Only simulation and modeling of protein co-translational folding may answer the questions concerning fast proteins (Ruggiero and Sacile, Med. Biol. Eng. Comp. 37 (Suppl. 1) (1999) 363). Non-equilibrium structures may also be built up of protein subunits, even if each one taken by itself is in thermodynamic equilibrium (oligomeric proteins; sub-cellular sol-gel dissipative network structures).

Quantitative measure of complexity of EEG signal dynamics.

Since electroencephalographic (EEG) signal may be considered chaotic, Nonlinear Dynamics and Deterministic Chaos Theory may supply effective quantitative descriptors of EEG dynamics and of underlying chaos in the brain. We have used Karhunen-Loeve decomposition of the covariance matrix of the EEG signal to analyse EEG signals of 4 healthy subjects, under drug-free condition and under the influence of Diazepam. We found that what we call KL-complexity of the signal differs profoundly for the signals registered in different EEG channels, from about 5-8 for signals in frontal channels up to 40 and more in occipital ones. But no consistency in the influence of Diazepam administration on KL-complexity is observed. We also estimated the embedding dimension of the EEG signals of the same subjects, which turned to be between 7 and 11, so endorsing the presumption about existence of low-dimensional chaotic attractor. We are sure that nonlinear time series analysis can be used to investigate the dynamics underlying the generation of EEG signal. This approach does not seem practical yet, but deserves further study.

Kinetics of actin-myosin binding. ATP-ase activity and sol-gel dissipative structures.

The simple kinetic model of actin-myosin binding-dissociation process including ATP-ase activity is considered. We demonstrated how one may easily include cooperativity in such a model by using effectivity factors introduced in our previous papers. A possibility of further simplifying the model through quasi-stationary approximation for some variables is considered. Sol-gel dissipative structures and possible biological implications of such structures are discussed.

Intrinsic physical instability of the proteins with short half-time: possible role in aging and in carcinogenesis.

Different proteins have vastly different lifetime in cells, some survive as long as or even longer than the cell does, whereas others survive for just minutes. Proteins showing short half-times play an extremely important role as cellular regulators, in particular in controlling cell mitosis and in carcinogenesis. These proteins probably possess an intrinsic physical instability, i.e. they are biologically active only while being in a meta-stable non-equilibrium state resulting from the very mechanisms of protein biosynthesis on ribosomes. Aging of these proteins consists of internal equilibration through protein chain folding rather than in accumulation of errors due to intermolecular interactions. We want to attract more attention to such fast (short-lived) proteins. The question of what determines these protein lifetimes is of practical as well as theoretical interest.

Kinetics of actin-myosin binding. Myosin cooperativity and mixed single-headed and two-headed binding.

A model is proposed for the kinetics of actin-myosin interaction that allows for the presence of both one- and two-headed myosin fragments, cooperativity between myosin sites, and the molecular weight distribution of actin filaments. The approach employed makes use of the notion of effectivity factors. In the most general case, the system is described by six coupled first-order differential equations. When only single-headed myosin (S1) is present, the model reduces to simpler versions introduced previously.

Representing and defining patterns by graphs: applications to sol-gel patterns and to cytoskeleton.

The problems of interdisciplinary interests--applying methods of graph theory to sol-gel patterns and to cytoskeleton--are discussed. The importance of sol-gel transition phenomena in living cells and the possibility of periodic sol-gel transition phenomena are briefly reviewed. Representing patterns by graphs and using graph probabilistic representation for calculating structure-property relationships are discussed and applied to sol-gel transition patterns.

Kinetics of actin-myosin binding. I. An exactly soluble one-variable model.

To treat the kinetics of actin-myosin binding as simply as possible, a one-variable model is developed and the notion of effectivity factors is introduced. An effectivity factor is a ratio of the reaction rate in the presence of cooperativity to that in the noncooperative case and is calculated by averaging cooperativity factors over all sites belonging to one seven-site actin unit. The technique is applicable to a variety of models involving cooperative association and dissociation processes. This averaging assumes the equivalence of all regulated actin units. The model may be solved exactly for arbitrary degrees of "preloading" of subfragment 1 (S1) on the regulated actin.

Kinetics of actin-myosin binding. II. Two-variable model and actin gelation.

We consider a model of actin-myosin interaction in which the sites belonging to each seven-site regulated actin unit are subdivided into two classes, "internal" and "external." The time evolution of each class of sites is considered separately, leading to a pair of coupled differential equations that may be integrated numerically. We also consider the critical sol-gel transition point for actin filaments crosslinked by two-headed heavy meromyosin (HMM). The possibility of new types of chemical oscillation and pattern formation arising from periodic sol-gel transitions is discussed.

Simplifying principles for chemical and enzyme reaction kinetics.

Tihonov's Theorems for systems of first-order ordinary differential equations containing small parameters in the derivatives, which form the mathematical foundation of the steady-state approximation, are restated. A general procedure for simplifying chemical and enzyme reaction kinetics, based on the difference of characteristic time scales, Is presented. Korzuhin's Theorem, which makes it possible to approximate any kinetic system by a closed chemical system, is also reported. The notions and theorems are illustrated with examples of Michaelis-Menten enzyme kinetics and of a simple autocatalytic system. Another example illustrates how the differences in the rate constants of different elementary reactions may be exploited to simplify reaction kinetics by using Tihonov's Theorem. All necessary mathematical notions are explained in the appendices. The most simple formulation of Tihonov's 1st Theorem 'for beginners' is also given.