ALBERT

Notes: Abstract More than 20 years after its proposal, Keller and Segel's model (1971,J. theor. Biol.,30, 235–248) remains by far the most popular model for chemical control of cell movement. However, before the Keller-Segel equations can be applied to a particular system, appropriate functional forms must be specified for the dependence on chemical concentration of the cell transport coefficients and the chemical degradation rate. In the vast majority of applications, these functional forms have been chosen using simple intuitive criteria. We focus on the particular case of eukaryotic cell movement, and derive an approximation to the detailed model of Sherrattet al. (1993,J. theor. Biol.,162, 23–40). The approximation consists of the Keller-Segel equations, with specific forms predicted for the cell transport coefficients and chemical degradation rate. Moreover, the parameter values in these functional forms can be directly measured experimentally. In the case of the much studied neutrophil-peptide system, we test our approximation using both the Boyden chamber and under-agarose assays. Finally, we show that for other cell-chemical interactions, a simple comparison of time scales provides a rapid check on the validity of our Keller-Segel approximation.

Notes: Abstract The formal structure of evolutionary theory is based upon the dynamics of alleles, individuals and populations. As such, the theory must assume the prior existence of these entities. This existence problem was recognized nearly a century ago, when DeVries (1904,Species and Varieties: Their Origin by Mutation) stated. “Natural selection may explain the survival of the fittest, but it cannot explain the arrival of the fittest.” At the heart of the existence problem is determining how biological organizations arise in ontogeny and in phylogeny. We develop a minimal theory of biological organization based on two abstractions from chemistry. The theory is formulated using λ-calculus, which provides a natural framework capturing (i) the constructive feature of chemistry, that the collision of molecules generates specific new molecules, and (ii) chemistry's diversity of equivalence classes, that many different reactants can yield the same stable product. We employ a well-stirred and constrained stochastic flow reactor to explore the generic behavior of large numbers of applicatively interacting λ-expressions. This constructive dynamical system generates fixed systems of transformation characterized by syntactical and functional invariances. Organizations are recognized and defined by these syntactical and functional regularities. Objects retained within an organization realize and algebraic structure and possess a grammar which is invariant under the interaction between objects. An organization is self-maintaining, and is characterized by (i) boundaries established by the invariances, (ii) strong self-repair capabilities responsible for a robustness to perturbation, and (iii) a center, defined as the smallest kinetically persistent and self-maintaining generator set of the algebra. Imposition of different boundary conditions on the stochastic flow reactor generates different levels of organization, and a diversity of organizations within each level. Level 0 is defined by selfcopying objects or simple ensembles of copying objects. Level 1 denotes a new object class, whose objects are self-maintaining organizations made of Level 0 objects, and Level 2 is defined by self-maintaining metaorganizations composed of Level 1 organizations. These results invite analogy to the history of life, that is, to the progression from self-replication to self-maintaining procaryotic organizations to ultimately yield self-maintaining eucaryotic organizations. In our system self-maintaining organizations arise as a generic consequence of two features of chemistry, without appeal to natural selection. We hold these findings as calling for increased attention to the structural basis of biological order.

Notes: Abstract A model is developed to describe neuronal elongation as a result of the polymerization of microtubules and elastic stretching of the neurites by force produced by the growth cone. The model for a single segment with a single growth cone revealed a constant elongation rate, while the concentration of tubulin in the soma rises, and the concentration of tubulin becomes constant in the growth cone. Extending the model to a neurite with a single branch point and two growth cones revealed the same results. When the assembly or the disassembly rate of microtubules is unequal in both growth cones, transient retraction of one of the terminal segments occurs, which results in complete retraction of the segment when the difference in (dis)assembly rate between the two growth cones is large enough. When the model is applied to large trees, a maximal sustainable number of terminal segments as a function of the production rate of tubulin appears. Mechanisms to stop outgrowth are discussed in relation to the establishment of synaptical contacts between cells.

Notes: Abstract We have developed a new model describing the relationship between plasma and red cell tracers flowing through the lung. The model is the result of an analysis of the transport of radiolabeled plasma albumin between two flowing phases and shows that differences between red cell and plasma tracer curves are related to microvascular hematocrit. The model was tested in an isolated, blood-perfused dog lung preparation in which we injected51Cr-labeled red cells and125I-labeled plasma albumin into the pulmonary artery. From the tracer concentration-time curves at the venous outflow, we calculatedh r, the ratio of microvascular hematocrit to large-vessel hematocrit. In 18 baseline experiments,h r=0.92±0.01 (mn±sem) at a blood flow rate of 10.7±0.3 ml s−1. We determined the effects of (a) glass bead embolization, (b) alloxan, and (c) lobe ligation onh r. Embolization attenuated the separation between plasma and red cells (increasedh r), probably as a consequence of passive vasodilation. Alloxan enhanced separation of plasma and red cells (decreasedh r), possibly as a result of arteriolar vasoconstriction. Ligation of a fraction of the perfused tissue at constant flow did not cause significant change inh r in the remaining perfused tissue. The model assumes that large-vessel transit times are uniform and that all dispersion occurs in the microvasculature. A theoretical analysis apportioning dispersion between large and small vessels disclosed that the error associated with these assumptions is likely to be less than 15% of the measuredh r. We conclude from this study that the microvascular hematocrit model describes experimental plasma and red cell curves. The results imply thath r can be readily deduced from tagged red cells and plasma and can be accounted for in calculating permeability-surface area in diffusing tracer experiments.

Notes: Abstract We present a mathematical model of the cytotoxic T lymphocyte response to the growth of an immunogenic tumor. The model exhibits a number of phenomena that are seenin vivo, including immunostimulation of tumor growth, “sneaking through” of the tumor, and formation of a tumor “dormant state”. The model is used to describe the kinetics of growth and regression of the B-lymphoma BCL1 in the spleen of mice. By comparing the model with experimental data, numerical estimates of parameters describing processes that cannot be measuredin vivo are derived. Local and global bifurcations are calculated for realistic values of the parameters. For a large set of parameters we predict that the course of tumor growth and its clinical manifestation have a recurrent profile with a 3- to 4-month cycle, similar to patterns seen in certain leukemias.

Notes: Abstract We present a new, practical algorithm to resolve the experimental data in restriction site analysis, which is a common technique for mapping DNA. Specifically, we assert that multiple digestions with a single restriction enzyme can provide sufficient information to identify the positions of the restriction sites with high probability. The motivation for the new approach comes from combinatorial results on the number of mutually homeometric sets in one dimension, where two sets ofn points are homeometric if the multiset ofn(n−1)/2 distances they determine are the same. Since experimental data contain errors, we propose algorithms for reconstructing sets from noisy interpoint distances, including the possibility of missing fragments. We analyse the performance of these algorithms under a reasonable probability distribution, establishing a relative error limit ofr=Θ(1/n 2) beyond which our technique becomes infeasible. Through simulations, we establish that our technique is robust enough to reconstruct data with relative errors of up to 7.0% in the measured fragment lengths for typical problems, which appears sufficient for certain biological applications.

Notes: Abstract A simple chemical model of the idiotypic network of immune systems, namely the AB model, has been developed by De Boeret al. The complexity of the system, such as the steady states, periodic oscillations and chaotic motions, has been examined by the authors mentioned above. In the present paper, the periodic motions and chaotic behaviours exhibited by the system are intuitively described. To clarify in which parameter domains concerned the system exhibits periodic oscillations and in which parameter domains the system demonstrates chaotic behaviours the Lyapounov exponent is explored. To characterize the strangeness of the attractors, the fractal dimension problem is worked out.

Notes: Abstract We consider a stochastic mechanism of the loss of resistance of cancer cells to cytotoxic agents, in terms of unstable gene amplification. Two models being different versions of a time-continuous branching random walk are presented. Both models assume strong dependence in replication and segregation of the extrachromosomal elements. The mathematical part of the paper includes the expression for the expected number of cells with a given number of gene copies in terms of modified Bessel functions. This adds to the collection of rare explicit solutions to branching process models. Original asymptotic expansions are also demonstrated. Fitting the model to experimental data yields estimates of the probabilities of gene amplification and deamplification. The thesis of the paper is that purely stochastic mechanisms may explain the dynamics of reversible drug resistance of cancer cells. Various stochastic approaches and their limitations are discussed.