Bulletin of Mathematical Biology

Pavlidis, Theo

doi: 10.1007/BF02460599pmid: 743563

Abstract This paper summarizes in a nonmathematical way the major properties of coupled oscillators which relate to circadian rhythms. For certain values of the coupling strength it is far easier to maintain synchrony than to achieve it among the various interacting units. This property not only simulates the free run period lability but also the effects of critical pulses.

Yu, C. P.

doi: 10.1007/BF02460600pmid: 743564

Abstract The deposition of aerosol particles in the human lung airways is due to two distinct mechanisms. One is by direct deposition resulting from diffusion, sedimentation and impaction as the aerosol moves in and out of the lung. The other is an indirect mechanism by which particles are transported mechanically from the tidal air to the residential air and eventually captured by the airways due to intrinsic particle motion. This last mechanism is not well understood at present. Using a trumpet airway model constructed from Weibel's data, a two-component theory is developed. In this theory, the particle concentrations in the airways and the alveoli at a given airway depth are considered to be quantitatively different. This difference in concentrations will cause a net mixing between the tidal and residential aerosol as the aerosol is breathed in and out. A distribution parameter is then introduced to account for the distribution of ventilation. The effect of intrinsic particle motion on the aerosol mixing is also included. From this theory, total and regional deposition in the lung at the steady mouth breathing without pause is calculated for several different respiratory cycles. The results agree reasonably well with the experimental data.

Kemper, John T.

doi: 10.1007/BF02460601pmid: 743565

Abstract A deterministic model for a multi-agent disease epidemic with asymptomatic attacks is proposed and investigated. The limitations inherent in the assumptions of the model are discussed in connection with specific agents of disease. The mathematical treatment of the model is separated into analyses of the equilibrium situation and the transient behavior of the disease outbreak. Explicit formulas are derived for the number of susceptibles in the population as well as for the numbers of each type of infective—those with and without symptoms. These theoretical results are followed by a discussion of the practical considerations which must be taken into account to obtain useful information from the model.

Bhaumik, Debajyoti;Bhaumik, Kamales;Ray, Asim Kumar;Dutta-Roy, Binayak

doi: 10.1007/BF02460602pmid: 743566

Abstract The recently observed enhancement, by laser irradiation, of the specific activity of the enzyme chymotrypsin (which hydrolyses Benzoyl-L-tyrosine-ethyl ester) at low enzyme concentration is considered. The enhancement of the reaction rate is attributed to a coherently excited state of the enzyme molecule (activated through Raman scattering of the laser light) following a prediction due to Fröhlich. The model is described, the kinetics of the process is framed and the observed enzyme-concentration dependence of the specific activity is reproduced. Predictions of the model are delineated to urge verification of the main contentions through further experimentation.

Darvey, I. G.;Klotz, A. H.;Ritter, M.

doi: 10.1007/BF02460603pmid: 743567

Abstract The Abel type differential equation governing the kinetics of the enzyme reactions is derived. Approximate solutions of this equation corresponding to the transient phase of the reaction, before a steady state is reached, are considered. It is shown that in several cases it is possible to obtain explicit, approximate solutions to the transient phase.

Anderson, N.;Arthurs, A. M.

doi: 10.1007/BF02460604pmid: 743568

Abstract Maximum and minimum principles for the steady-state finite cable model of nerve membranes are derived from the canonical theory of complementary variational principles. An accurate variational solution is obtained in an illustrative calculation.

Schuster, P.;Sigmund, K.;Wolff, R.

doi: 10.1007/BF02460605pmid: 743569

Abstract The paper presents a qualitative analysis of the following systems ofn differential equations:\(\dot x_i = x_i x_j - x_i \sum\nolimits_r^n { = 1} x_r x_s {\mathbf{ }}(j = i - 1 + n\delta _{i1} {\mathbf{ }}and{\mathbf{ }}s = r - 1 + n\delta _{r1} )\), which show cyclic symmetry. These dynamical systems are of particular interest in the theory of selforganization and biological evolution as well as for application to other fields.

Erneux, T.;Hiernaux, J.;Nicolis, G.

doi: 10.1007/BF02460606pmid: 743570

Abstract Bifurcation theoretical and numerical analyses of one of Turing's models are performed. It is shown that at the first instability point of the homogeneous state the bifurcating branches aresubcritical, and thus emerge as unstable solutions. This, together with the presence of concentration-independent sink terms is responsible for the solutions becoming negative ast→∞. It is pointed out that this deficiency is an accident related to the choice of the model, and that the general idea of symmetry-breaking is perfectly compatible with the generation of regular morphogenetic patterns.

Mikulecky, D. C.

doi: 10.1007/BF02460607pmid: 743571

Abstract The global force-flow equations of nonequilibrium thermodynamics are obtained by solving the local equations of motion for a system ofn-components (n−1 solutes plus water) passing through a membrane. When viscous forces and position dependent membranepermeating species frictional interactions are considered, it becomes more difficult to obtain the result because even the stationary state problem becomes one of solving a second order linear ordinary differential equation for the barycentric velocity in a space divided inton+1 regions. Using the continuity of the boundary velocities and their gradients as well as the usual boundary conditions for the hydrodynamic problem, a set of 2n+1 linear equations in the intergration constants can be obtained and a closed form solution is possible. The resultant global description of the system does not obey Onsager reciprocity. What is more, the interpretation of global phenomenological coefficients in terms of local interactions in any simple way is next to impossible. This makes the hope of a molecular level interpretation of phenomenological membrane transport coefficients very slim. The relevance of this finding to the validity of reductionist approaches to biological transport is discussed.

Rescigno, Aldo

doi: 10.1007/BF02460608pmid: 217472

Abstract Several models have been proposed to underststand the patterns of nerve impulses produced by periodic stimuli. This paper shows that for a very large class of such models there exists a pattern of phases that repeats periodically after a finite number of pulses; the actual pulses produced by the model depend on its initial condition, but in all cases they either follow such a pattern or approach it asymptotically.