Nonlinear diffusion in metabolic systems

Some general properties of the solution of the diffusion equation are deduced for the steady-state, spherically symmetric system. On the basis of these developments some results of N. Rashevsky (Bull. Math. Biophysics,11, 15, 1949) are discussed and the results of a previous investigation (Hearon,Bull. Math. Biophysics,12, 135, 1950b) are extended to more general conditions. In particular these extensions apply to the flow of a soluteagainst its concentration gradient, the nonzero gradient of an inert metabolite, and theaccumulation or exclusion of an inert metabolite in a metabolic system. A portion of this work was performed while the author was a research participant, Oak Ridge Institute of Nuclear Studies, assigned to the Mathematics Panel, Oak Ridge National Laboratory.     

On the analysis of oxygen diffusion and reaction in biological systems

An analysis of oxygen diffusion and reaction in multiregion biological systems is presented. This analysis considers a time-dependent flux boundary condition and oxygen consumption governed by Michaelis-Menten kinetics. The mathematical problem is developed in a uniform fashion, so as to include both the single cell and anisotropic systems with distinct regions which are characteristic of either a multicell spheroid or a tumor mass. Both transient and steady-state solutions are obtained, based on orthogonal collocation. Literature results on single-cell analysis are corroborated, and detailed transient solutions are presented for the oxygenation of a multicell spheroid, and for systemic oxygenation of both small and large tumors.     

Modelling logistic growth by a new diffusion process: Application to biological systems

The present paper introduces a new diffusion process for the purpose of modelling logistic-type behaviour patterns. Unlike other processes in the same context, this one verifies that its mean function is a logistic curve. In addition, its transition density can be found explicitly, which allows to analyse inference from the discrete sampling of trajectories. The main features of the process will be analysed and the maximum likelihood estimation of parameters will be carried out through discrete sampling. Regarding the numerical problems found to solve the likelihood equations, several strategies are developed for obtaining initial solutions for the usual numerical procedures. Such strategies are compared by means of a simulation example. Also, another simulation study is carried out in order to compare the estimation in this process to that developed by means of continuous sampling in the logistic diffusion model considered by Giovanis and Skiadas (1999). Finally an example is given for the growth of a microorganism culture. This example illustrates the predictive possibilities of the new process, as well as its ability to study time variables formulated as first-passage-times.     

The influence of energy-level fluctuation and acceptor local diffusion on electron transport in biological systems

The present work is a modification of nonadiabatic electron transfer theory for fixed electron exchanging groups. We attempt to account for the role of the relative motion of exchanging groups on electron transfer processes. We also show how the fluctuation of the potential surfaces of the initial and final states of solute molecules (here, the donor-acceptor pari) affect electron transfer.     

Nonlinear systems in medicine

Many achievements in medicine have come from applying linear theory to problems. Most current methods of data analysis use linear models, which are based on proportionality between two variables and/or relationships described by linear differential equations. However, nonlinear behavior commonly occurs within human systems due to their complex dynamic nature; this cannot be described adequately by linear models. Nonlinear thinking has grown among physiologists and physicians over the past century, and non-linear system theories are beginning to be applied to assist in interpreting, explaining, and predicting biological phenomena. Chaos theory describes elements manifesting behavior that is extremely sensitive to initial conditions, does not repeat itself and yet is deterministic. Complexity theory goes one step beyond chaos and is attempting to explain complex behavior that emerges within dynamic nonlinear systems. Nonlinear modeling still has not been able to explain all of the complexity present in human systems, and further models still need to be refined and developed. However, nonlinear modeling is helping to explain some system behaviors that linear systems cannot and thus will augment our understanding of the nature of complex dynamic systems within the human body in health and in disease states.     

Self-organization in biological systems

Biological systems are considered that are capable of dynamic self-organization, i.e., spontaneous emergence of spatio-temporal order with the formation of various spatio-temporal patterns. A cell is involved in the organization of ontogenesis of all stages. Embryonic cells exhibit coordinated social behavior and generate ordered morphological patterns displaying variability and equifinality of development. Physical and topological patterns are essential for biological systems as an imperative that restricts and directs biological morphogenesis. Biological self-organization is directed and fixed by natural selection during which selection of the most sustainable, flexible, modular systems capable of adaptive self-organization occurs.     

Maxwell's demon in biological systems

Summary Boltzmann's gas model representing the second law of thermodynamics is based on the improbability of certain molecular distributions in space. Maxwell argued that a hypothetical being with the faculty of seeing individual molecules (Maxwell's Demon) could bring about such improbable distributions, thus violating the law of entropy. However, it appears that to render the molecules visible for any observer would increase the entropy more than the demon could decrease it, hence Maxwell's Demon cannot operate (Brillouin, 1951). In the study presented here Maxwell's Demon is interpreted in a general way as a biological observer system within (possibly closed) systems which can upset thermodynamic probabilities provided that the relative magnitudes between observer system and observed system are appropriate.Maxwell's Demon within Boltzmann's Gas Model thus appears only as a special case of inappropriate, relative magnitude between the two systems.     

Histidine phosphorylation in biological systems

Histidine phosphorylation is important in prokaryotes and occurs to the extent of 6% of total phosphorylation in eukaryotes. Nevertheless phosphohistidine residues are not normally observed in proteins due to rapid hydrolysis of the phosphoryl group under acidic conditions. Many rapid processes employ phosphohistidines, including the bacterial phosphoenolpyruvate:sugar phosphotransferase system (PTS), the bacterial two-component systems and reactions catalyzed by enzymes such as nucleoside diphosphate kinase and succinyl-CoA synthetase. In the PTS, the NMR structure of the phosphohistidine moiety of the phosphohistidine-containing protein was determined but no X-ray structures of phosphohistidine forms of PTS proteins have been elucidated. There have been crystal structures of a few phosphohistidine-containing proteins determined: nucleoside diphosphate kinase, succinyl-CoA synthetase, a cofactor-dependent phosphoglycerate mutase and the protein PAE2307 from the hyperthermophilic archaeon Pyrobaculum aerophilum. A common theme for these stable phosphohistidines is the occurrence of ion-pair hydrogen bonds (salt bridges) involving the non-phosphorylated nitrogen atom of the histidine imidazole ring with an acidic amino acid side chain.     

Redox processes in biological systems

General principles of organization and distinctive features of the redox processes of biological systems are discussed. We paid special attention to the most examined parts of redox biology. As one of the approaches to the generalization of accumulated knowledge about redox processes, the so-called redox hypothesis of oxidative stress was examined. Extrapolation of this hypothesis on the processes taking place in plant cells, formulated on the basis of thiol-disulfide metabolism of animal cells, may help to systematize the available knowledge about redox processes in plants.     

Dioxygen-derived radicals in biological systems

Three instances of the involvement of dioxygen-derived radicals in biological systems are considered. The first concerns the formation of radicals in the haemolytic reactions induced by treatment of erythrocytes by phenylhydrazine, as an example of the so-called 'oxidant drugs'. The evidence for the formation of phenyl radicals is considered and their origin in the oxidation of phenylhydrazine by a ferryl derivative of haemoglobin postulated. The relevance to the formation of phenylated iron and porphyrin species is described. It is suspected that many instances of oxidative damage to cellular systems result from the coincidence of unsequestered redox-active metal ions (particularly those of iron and copper), reductants, and dioxygen. As an example, the damage to hepatocytes, grown in a culture medium containing cysteine, is described. The formation of radical species derived from dioxygen during the respiratory burst associated with phagocytosis is discussed. A new electrochemical method of detecting the superoxide ion produced during the respiratory burst is described. Particular emphasis is placed on the relation between the production of radical species such as the hydroxyl radical and the superoxide ion, and the extent of phagocytosis.