Antigenic diversity thresholds and hazard functions.

In this paper, we answer some points made in a recent paper by N.I. Stilianakis and coworkers on the antigenic diversity threshold model for acquired immune deficiency syndrome pathogenesis. An extended version of the model is then used to compute hazard functions for the human immunodeficiency virus incubation period that are in agreement with empirically observed hazard functions.

The simulation of density-dependent effects in the recirculation of T lymphocytes.

T-lymphocyte recirculation appears to be slower in nude or irradiated rats as compared with normal rats. A mathematical model of T-lymphocyte recirculation that incorporates interactions between T cells and dendritic cells in the lymphoid tissue is presented. It is shown that these interactions are able to explain the differences in recirculation times between normal and nude or irradiated rats, and also the time-scales seen in long-term thoracic duct cannulations.

The role of inter-cellular adhesion in the recirculation of T lymphocytes.

We refine an existing model of T lymphocyte recirculation, in order to incorporate a description of the adhesion between T cells and other cell types in the lymphoid tissue, such as dendritic cells. The new model is able to fit the animal experiments on lymphocyte recirculation. It also allows for the variation of these adhesive properties, as would occur in the presence of antigen, and it is shown that it is possible for the T cell counts in blood to reach very low levels, as a result of increased adhesion between T cells and dendritic or other cells present in the lymphoid tissue. We discuss the implications of this phenomenon for HIV infection.

A computer graphic simulation of squamous epithelium.

An epithelium maintains its integrity through the organized growth and orderly differentiation of a transient cell population derived from stem cells. This organization is dependent upon both physical mechanisms such as cell adhesion and attraction and the relationship between differentiation and cell division. The interactions between these processes are complex and difficult to conceptualize from a purely mathematical approach. We have therefore set out to develop a graphic model of an epithelium controlled by rules that can be modified. We have chosen to model epidermis, the most superficial part of skin, with cells differentiating from a stem cell population and being lost from the surface of the model. The model is novel not only in the rules that govern cell behaviour, but also because it does not require a predefined lattice to assign the position of cells. Each cell assumes a position depending upon the balance of adhesive and repulsive forces that it experiences. Chemical factors which affect the differentiation of individual cell types are assumed to be produced both by cells within the model and externally from the underlying connective tissue. These "chemical factors" diffuse through the model with a concentration that declines as an inverse square with distance from the source. The rules allow the model to grow from a single stem cell to reach a steady state. At steady state the pattern and clonal structure is strikingly similar to that seen in a range of normal epithelia. Furthermore, if part of the model is removed it is capable of regenerating itself without additional rules. The model allows the visualization of the effects of introducing new rules and modifying the interaction between chosen rules. This study demonstrates that a set of simple rules can be used to make a dynamic flexible model resembling skin.

The use of a computer model to simulate epithelial pathologies.

The complexity of the interactions of the many rules governing cell behaviour and the changes that lead to the pathological features seen in disease is such that linking cause and effect can be very difficult. However, the use of computers to model normal biological and pathological processes provides a powerful technique for studying the effects of the interactions of a variety of biological rules. Such an approach is strengthened by using a graphical display that simulates the organization of cells in a tissue. Skin, and specifically the epidermis, is characterized by a regular morphology and the ability to regenerate itself throughout adult life and there are considerable biological data available on the normal and pathological process that affect this organ. A model of normal skin has been developed which shows a structure similar to normal epidermis and is capable of healing itself if damaged. This paper describes the effects on the overall structure of introducing mutations to individual rules in the model. Changes that alter cell proliferation or differentiation are introduced and the effects that these produce are compared with epidermal pathologies. Even a simple model is capable of producing insights into the types of events that may occur in a variety of dermatopathological conditions.

The comparison of gene expression from multiple cDNA libraries.

We describe a method for comparing the abundance of gene transcripts in cDNA libraries. This method allows for the comparison of gene expression in any number of libraries, in a single statistical analysis, to identify differentially expressed genes. Such genes may be of potential biological or pharmaceutical relevance. The formula that we derive is essentially the entropy of a partitioning of genes among cDNA libraries. This work goes beyond previously published analyses, which can either compare only two libraries, or identify a single outlier in a group of libraries. This work also addresses the problem of false positives associated with repeating the test on many thousands of genes. A randomization procedure is described that provides a quantitative measure of the degree of belief in the results; the results are further verified by considering a theoretically derived large deviations rate for the test statistic. As an example, the analysis is applied to four prostate cancer libraries from the Cancer Genome Anatomy Project. The analysis identifies biologically relevant genes that are differentially expressed in the different tumor cell types.