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The binding energy of a very long molecular chain, composed of different classes of molecules, depends in general on the order of the molecules. It is shown that under very general conditions there exists for a givenbrutto chemical composition of a chain, a class of chains which is characterized by a total binding energy which is equal to the total binding energy of any other prescribed chain of different composition within the limits of unsharpness of the energy level. This establishes a criterion formapping of a class of configurations of long chain molecules on another class. To the extent that a mapping constitutes a generalized code those results contribute to the theory of molecular codes. Applying to our results the results of a previous paper (1959,Bull. Math. Biophysics,21, 309–326), we arrive at the conclusion that the self-replication of a living molecule may be the property not of a particular structure but of classes of structures.

Further consideration is given to assessing the degree of precision achieved in the localization of enzymes in cells by chemical staining techniques. Procedures discussed are those in which the enzyme acts on a substrate by a zero-order reaction, producing an intermediate which is then converted by an irreversible first-order reaction (velocity constantk) into a non-diffusible colored product. A relationship is obtained which permits the degree of localization for this type of process to be easily calculated. This localization factor is independent of the activity per unit volume of the site; it increases with the size of the site and, for experimental time ranges, is virtually independent of the time of staining. It is shown that, under usual circumstances, satisfactory localization is achieved in sites of radius 1 μ ifk/D is of the order 109 cm−2 and that when this ratio has the value 1011 cm−2 localization is very good.

Results by Volterra (1931) and Rescigno and Richardson (1965) are combined with an analysis by Leigh, (1968) to prove restrictions on the applicability of the conservative Volterra equations in ecological theory.

The nature of scientific research in mathematical and computational biology allows editors and reviewers to evaluate the findings of a scientific paper. Replication of a research study should be the minimum standard for judging its scientific claims and considering it for publication. This requires changes in the current peer review practice and a strict adoption of a replication policy similar to those adopted in experimental fields such as organic synthesis. In the future, the culture of replication can be easily adopted by publishing papers through dynamic computational notebooks combining formatted text, equations, computer algebra and computer code.

Aging in Caenorhabditis elegans is controlled, in part, by the insulin-like signaling and heat shock response pathways. Following thermal stress, expression levels of small heat shock protein-16.2 show a spatial patterning across the 20 intestinal cells that reside along the length of the worm. Here, we present a hypothesized mechanism that could lead to this patterned response and develop a mathematical model of this system to test our hypothesis. We propose that the patterned expression of heat shock protein is caused by a diffusion-driven instability within the pseudocoelom, or fluid-filled cavity, that borders the intestinal cells in C. elegans. This instability is due to the interactions between two classes of insulin-like peptides that serve antagonistic roles. We examine output from the developed model and compare it to experimental data on heat shock protein expression. Given biologically bounded parameters, the model presented is capable of producing patterns similar to what is observed experimentally and provides a first step in mathematically modeling aging-related mechanisms in C. elegans.

Multiplex DNA profiles are used extensively for biomedical and forensic purposes. However, while DNA profile data generation is automated, human analysis of those data is not, and the need for speed combined with accuracy demands a computer-automated approach to sample interpretation and quality assessment. In this paper, we describe an integrated mathematical approach to modeling the data and extracting the relevant information, while rejecting noise and sample artifacts. We conclude with examples showing the effectiveness of our algorithms.

A neurobiophysical mechanism which reacts todifferences in different modalities of a stimulus pattern is suggested. Another mechanism is suggested which reacts tosimilarity. The latter is measured by the number of neurons in common to the two stimulus patterns.