An activity coefficient model for proteins

Modeling of the properties of biochemical components is gaining increasing interest due to its potential for further application within the area of biochemical process development. Generally protein solution properties such as protein solubility are expressed through component activity coefficients which are studied here. The original UNIQUAC model is chosen for the representation of protein activity coefficients and, to the best of our knowledge, this is the first time it has been directly applied to protein solutions. Ten different protein-salt-water systems with four different proteins, serum albumin, alphacymotrypsin, beta-lactoglobulin and ovalbumin, are investigated. A root-mean-squared deviation of 0.54% is obtained for the model by comparing calculated protein activity coefficients and protein activity coefficients deduced from osmotic measurements through virial expansion. Model predictions are used to analyze the effect of salt concentrations, pH, salt types, and temperature on protein activity coefficients and also on protein solubility and demonstrate consistency with results from other references. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 65-71, 1997.     

Mathematical model of activity of spinal generators producing rhythmic movement

Different organizational arrangements of scratching and locomotor rhythm generators were simulated by a computer-aided mathematical model. A functional group of neurons (a hemicenter constructed on the basis of a stochastically arranged neuronal network) served as the basis for the generator. Several organizational arrangements of scratching and locomotor rhythm generators are considered: two hemicenters with reciprocal inhibitory connections and tonic excitatory influences on both; two hemicenters with inhibitory-excitatory connections and tonic excitatory influences on only one of these; circular structures consisting of more than two functional groups of neurons with excitatory and inhibitory connections between them. All these arrangements would allow for generation of rhythmic activity with a similar time course to that of scratching and locomotor rhythm. It was found that the transition from locomotor to scratching rhythm could be based on fairly simply organized effects on generator neurons. Principles possibly guiding the construction of spinal generators of scratching and locomotor movements are discussed.A. A. Bogomolets Institute of Physiology, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Neirofiziologiya, Vol. 20, No. 5, pp. 586–597, September–October, 1988.     

In-phase and antiphase self-oscillations in a model of two electrically coupled pacemakers

The dynamic behavior of a model of two electrically coupled oscillatory neurons was studied while the external polarizing current was varied. It was found that the system with weak coupling can demonstrate one of five stable oscillatory modes: (1) in-phase oscillations with zero phase shift; (2) antiphase oscillations with halfperiod phase shift; (3) oscillations with any fixed phase shift depending on the value of the external polarizing current; (4) both in-phase and antiphase oscillations for the same current value, where the oscillation type depends on the initial conditions; (5) both in-phase and quasiperiodic oscillations for the same current value. All of these modes were robust, and they persisted despite small variations of the oscillator parameters. We assume that similar regimes, for example antiphase oscillations, can be detected in neurophysiological experiments. Possible applications to central pattern generator models are discussed.     

Mathematical model of children mortality

A mathematical model of infantile mortality is proposed. The model is based on the probability principle of organism-environment interactions assuming that the organism is able to remember the diseases encountered previously and resist them. The adequacy of the model was assessed using the demographic database for two countries. The dynamics of the model parameters during the last century is presented.     

Mathematical model of honeycomb construction

We developed a mathematical model and an algorithm for numerical treatment of a model of honeycomb construction in a beehive. The model contains essential features of the bee-bee and bee-wax interactions, and in a qualitative way captures the dynamics of parallel comb construction. The construction is represented by a set of dynamical coupled partial differential equations for the density of bees situated on the hive ceiling, and the quantity of wax distributed by the bees. A spectral algorithm is invented for treatment of these equations, based on a modified thin-sheet gain scheme and a fast Fourier transform technique.Work at City College supported in part by the Army Research Office and the Department of Energy     

Mathematical model of autoimmunity]

A mathematical model of autoimmunity is developed. This model is a system of two nonlinear differential equations, which describe the concentration dynamics of tissue cells and agressive lymphocytes. An analysis of the solutions shows that this model reproduces general behaviour of autoimmune diseases.     

Mathematical model of immune processes

In the model the time lags of the antibody production and immune memory formation are taken into account explicitly. The antibody-antigen reaction is supposed to be very fast. The cases of a reproducing antigen as well as that of a non-reproducting antigen are considered. The conditions of the infinite increase of the antigen quantity and of the antigen elimination are obtained. For the rapidly reproducing antigen the latter condition includes the requirement for the time lag of the immune response to be not too short or not too long. In the case of the poorly catabolized non-reproducing antigen the cyclic appearance of the antibody producing cells due to the immune memory is described in the frame-work of the model.The mathematical structure of the model is similar to that of the Volterra-Lotka jequations. The only difference is the presence of the time lags in the non-linear terms. The time lags lead to the instability of the stationary state. In the prolonged reaction the antigen quantity may perform several oscillations before the elimination of the antigen.     

Mathematical model of visual perception

A mathematical model of visual perception is presented with the intention of throwing some light on the problem of perceptual invariance. Two types of differential manifolds (receptive and effector) are associated with the repertoire which is the fundamental concept in the model. The elements of the repertoire carry weights which control the input-output relation in the repertoire and which can be modified by a learning process. It is shown that, under reasonable conditions, these repertoires possess good stability properties and can adjust to the various environments to which they may be subjected. In particular cases, it is shown that the stochastic learning process can be considered as deterministic to a first approximation.     

Mathematical model of self-cycling fermentation

This article presents a mathematical model for biomass, limiting substrate, and dissolved oxygen concentrations during stable operation of self-cycling fermentation (SCF). Laboratory experiments using the bacterium Acinetobacter calcoaceticus RAG-1 and ethanol as the limiting substrate were performed to validate the model. A computer simulation developed from the model successfully matched experimental SCF intracycle trends and end-of-cycle results and, most importantly, settled into an unimposed periodicity characteristic of stable SCF operation. (c) 1995 John Wiley & Sons, Inc.     

Mathematical model of retinal mosaic formation

The retina is one of the best examples of modular organisation in neural circuitry. This modular structure enables it to perform parallel processing. A mathematical model of the retina has been set up, focusing on mechanical features of retinal neurons and on the interaction and dendritic overlapping among retinal cells. The model focuses on the actions of local mechanical forces on the neuron's cytoskeleton. The cytoskeleton is regarded as a structure in which elastic and rigid elements are combined according to the tensegrity concept. We have assumed that dendritic overlap takes place in such a way as to favour uniform retinal neurons' distribution and that dendritic overlap is the only cause of neuron's motion on the retinal surface. This overlap depends on the growth of the dendrites due to the cytoskeletic deformation. The results obtained are in agreement with experimental results that support the notion that local mechanical interaction and dendritic overlapping are capable to transform random cell distributions into regular mosaics.     

Mathematical model of polar auxin transport

Polar auxin transport can be simulated by a model which achieves polarity through the preferential secretion of more auxin from the lower end than from the upper end of each cell. Solution of the model using a computer provides a possible explanation of the differences between the polarity expressed by different tissues and the differences between pieces of different lengths, on the basis of small differences in the polarity of auxin secretion from individual cells. A method of estimating the polarity of individual cells is described.     

Mathematical model of histamine bronchospasm]

A mathematical model of changes in histamine concentration in the wall of human bronchiole was constructed. The parameters of the model adequately characterize the state of patients with bronchial asthma.     

Mathematical model of heart rate variability

The study presents a mathematical model of non-linear dynamics of the heart rate variability (HRV). The model is based on quantitative characteristics of pulse conduction in the heart conducting system: the delays of sinoatrial (SA) and atrioventricular (AV) pulse conduction and refractors periods of the SA and AV nodes. The model predicts heart rate disturbances in fast electric activity of the atria, increase in the delay of the AV conduction, the critical value of atrial period where transition to non-linear dynamics of the heart rate variability starts. The correlation between indexes of HRV and period of stimulation of atria for 1-contour cardiac control model has been demonstrated.