Bulletin of Mathematical Biology

She, J.;Bertram, C. D.

doi: 10.1007/BF02458382pmid: 8953255

Abstract Collapsible-tube flow with self-excited oscillations has been extensively investigated. Though physiologically relevant, forced oscillation coupled with self-excited oscillation has received little attention in this context. Based on an ODE model of collapsible-tube flow, the present study applies modern dynamics methods to investigate numerically the responses of forced oscillation to a limit-cycle oscillation which has topological characteristics discovered in previous unforced experiments. A devil's staircase and period-doubling cascades are presented with forcing frequency and amplitude as control parameters. In both cases, details are provided in a bifurcation diagram. Poincaré sections, a frequency spectrum and the largest Lyapunov exponents verify the existence of chaos in some circumstances. The thin fractal structure found in the strange attractors is believed to be a result of high damping and low stiffness in such systems.

Walker, Wynn L.;Cook, Julian

doi: 10.1007/BF02458383pmid: 8953256

Abstract We develop a macroscopic model for delivering drug to brain tumors. The model accounts for bulk convective and diffusive transport across the blood-brain barrier and through the interstitial space. Through mathematical analysis and simulations, we assess the effects of changing parameters (within physiological bounds) on drug delivery. We find that there is an optimal treatment for convective drug delivery to the center of the tumor. We interpret this phenomenon in terms of traffic flow. The implications of our analyses on existing chemotherapeutic protocols are discussed.

Aharon, S.;Bercovier, M.;Parnas, H.

doi: 10.1007/BF02458384pmid: 8953257

Abstract Parallel computation employing a domain decomposition method was used to calculate precisely without approximations the spatio-temporal distribution of Ca2+ in nerve terminals. The results showed, contrary to expectations, that for equal admitted Ca2+ currents at low (one channel open) and high (four channels open) depolarization, the average Ca2+ concentration at the release area is higher at the low depolarization. These calculations provide additional support for the Ca2+-voltage hypothesis for neurotransmitter release.

Fishman, Michael A.;Segel, Lee A.

doi: 10.1007/BF02458385pmid: 8953258

Abstract Type I hypersensitivity, which functions to protect the organism from parasites, is caused by binding of antigen to IgE antibodies pre-attached to the cell surface of tissue mast cells and their circulating counterparts, the basophils. In “allergy,” type I hypersensitivity is inappropriately induced by protein-based foreign substances (such as pollen) or protein components of insect stings, which in the normal course of events would be cleared from the organism without causing any damage. Paradoxically, a successful clinical treatment of allergy involves repeated immunization of allergic persons with low doses of the allergen—immunotherapy. Investigation of the available experimental evidence leads to the conclusion that the phenomena of immunotherapy are best addressed in terms of the interplay among the mechanism(s) of immune memory—Th1/Th2 cross-regulation—and the physical compart-mentalization of the immune system. These conclusions are illustrated with a numerical simulation.

B-Rao, Chandrika;Stewart, John

doi: 10.1007/BF02458386pmid: 8953259

Abstract The concept of shape space proposed by Perelson and Oster (1979,J. Theor. Biol. 81, 645–670) has been a useful tool for theoretical immunologists, who have invoked it to model idiotypic binding, which plays a significant role in mathematical models of immune networks. The actual construction of such a space from its definition requires specialized experimental information, which is not completely available. In this article, we discuss, with illustrative examples, how graphical representations similar to the idea of shape space can be derived by analyzing real affinity matrices, and the relative merits of such representations to approximations that might be obtained by the approach of Perelson and Oster. We also give directions for future research with a view toward applications.

Sech, C. Le;Capderou, A.

doi: 10.1007/BF02458387pmid: 8953260

Abstract In this work, we show that a one-dimensional model of the blood flow across the lungs can reproduce the evolution of a bolus versus the time. Solving the differential equation governing the bolus concentration in the framework of this model, we determine the solution which fulfills Gaussian initial boundary conditions. An effective parameter related to the ratio of a diffusion coefficient to the square of the mean speed of the flow is defined. The determination of its numerical values following a semi-empirical approach enables us to know accurately the mean transit time and the cardiac output. The results have been compared to other methods, and were found in good agreement. Such an approach could be of interest in all studies where the knowledge of flow—including micro-circulation—is needed.

Wu, Richard;Wu, Tai Te

doi: 10.1007/BF02458388pmid: 8953261

Abstract A novel intact circular dsDNA supercoil is proposed as an alternative to the conventional DNA supercoil, so that the two complementary strands of ssDNA circles are separable without any covalent bond breakage. This new structure can be visualized by using two tubings: one black and one clear. Twist the black tubing a number of times and connect its two ends. Do the same for the clear tubing. Then wrap the two tubings together. This forms the separable or novel supercoil. On the other hand, the conventional supercoil can be modeled by twisting the black and clear tubings together and then connect their respective ends, so that the two tubings are not separable unless one of them is cut. Experimentally, in the absence of any enzyme, many intact plasmid dsDNA circles give two bands on agarose gel electrophoresis under a certain given condition, while the same plasmid molecules after cutting once by a restriction enzyme give only one band under the same, condition. In the case of intact pUC19 plasmids, these two bands can then be, recovered and sequenced separately, using two primers in opposite directions. Each band gives mostly one sequence which is complementary to that of the other band. The combination of the above theoretical model and experimental results strongly suggests that there is an alternative structure of DNA which does not have the usual difficulty of unwinding, rewinding and requiring numerous covalent bond breakages and ligations during semiconservative replication.

Barradas, Ignacio;Caswell, Hal;Cohen, Joel E.

doi: 10.1007/BF02458389pmid: N/A

Abstract How two species interact during and after colonization influences which of them will be present in each stage of succession. In the tolerance model of ecological succession in a patchy environment, empty patches can be colonized by any species, but the ability to tolerate reduced resource levels determines which species will exclude the other. Here, we analyze a meta-population model of the possible roles of competition in colonization and succession, using non-linear Markov chains as a mathematical framework. Different kinds of competition affect the final equilibrial, abundances of the species involved in qualitatively different ways. An explicit criterion is given to determine which interactions have stronger effects on the final equilibrial levels of the weaker, species. Precise conditions are stated for the co-existence of both species. Both species are more likely to co-exist in the presence of an intermediate disturbance frequency.