Computational models in immunological methods: an historical review.

The utilization of computational models in immunology dates from the birth of the science. From the description of antibody-antigen binding to the structural models of receptors, models are utilized to bring fundamental understandings of the processes together with laboratory measurements to uncover implications of these data. In this review, an historical view of the role of computational models in the immunology laboratory is presented, and short mathematical descriptions are given of fundamental assays. In addition, the range of current uses of models is explored -- especially as seen through papers which have appeared in the Journal of Immunological Methods from volume 1 (1971/1972) to volume 208 (1997). Each paper which introduced a new mathematical, statistical, or computer simulation model, or introduced an enhancement to an instrument through a model in those volumes is cited and the type of computational model noted.

The necessity of cofactors in the pathogenesis of AIDS: a mathematical model.

Current arguments for the role of cofactors in the initiation of a chronic HIV infection and progression of AIDS are given. The natural history of an HIV infection as affected by cofactors which provide additional stimulatory signals is explored through a mathematical model. The model demonstrates that "antigen load" plays a role in determining susceptibility to an HIV infection. It also suggests that certain individuals may not be able to be infected by small doses of HIV and that the identification and treatment of existing cofactors may be useful in treating early stages of HIV infection. Prevention of cofactor exposures may also protect against HIV infection.

Conditions for uniqueness of limit cycles in general predator-prey systems.

Using a transformation to a generalized Lienard system, theorems are presented that give conditions under which unique limit cycles for generalized ecological systems, including those of predator-prey form, exist. The generalized systems contain those studied by Rosenzweig and MacArthur (1963); Hsu, Hubbell, and Waltman (1978); Kazarinnoff and van den Driessche (1978); Cheng (1981); Liou and Cheng (1987); and Kuang and Freedman (1988). Although very similar in approach to the result presented by Kuang and Freedman, the conditions presented here are of simpler form and in terms of the original (untransformed) functions. The results also apply to more general growth terms for the prey as shown in the examples provided. In particular, an immigration term is allowable.

Stochastic models of tumor growth and the probability of elimination by cytotoxic cells.

The probability of tumor extinction due to the action of cytotoxic cell populations is investigated by several one dimensional stochastic models of the population growth and elimination processes of a tumor. The several models are made necessary by the nonlinearity of the processes and the different parameter ranges explored. The deterministic form of the model is T' = gamma 0T - k'6T/(K1 + T) where gamma 0, k'6 and K1 are positive constants. The parameter of most import is lambda 0 = gamma 0 - k'6/K1 which determines the stability of the T = 0 equilibrium. With an initial tumor size of one, a (linear) branching process is used to estimate the extinction probability. However, in the case lambda = 0 when the linearization of the deterministic model gives no information (T = 0 is actually unstable) the branching model is unsatisfactory. This makes necessary the utilization of a density-dependent branching process to approximate the population. Through scaling a diffusion limit is reached which enables one to again compute the probability of extinction. For populations away from one a sequence of density-dependent jump Markov processes are approximated by a sequence of diffusion processes. In limiting cases, the estimates of extinction correspond to that computed from the original branching process. Table 1 summarizes the results.

A model of the role of natural killer cells in immune surveillance--II.

The functioning of natural killer (NK) cells as immune surveillance effector cells against tumors is explored. In part I (J. Math. Biol. 12, 363-373 (1981], it was predicted that susceptible tumors would be eliminated if they have parameter lambda 0 value negative. They would not be eliminated if lambda 0 greater than 0. As the lambda 0 less than 0 result was local, one expected either that tumors of all sizes with lambda 0 less than 0 will be eliminated (global stability) or that tumor population will go to zero if in a domain of attraction of the critical point which is not all of the positive orthant. In this paper, the second is shown to be true. The general results are illustrated by a specific model.

A model of the role of natural killer cells in immune surveillance--I.

The theory of immune surveillance of Thomas and Burnet stated in part that antigenic differences between neoplastic and normal cells provide the stimulus for their destruction by cells of the immune system. Burnet pointed to the T lymphocyte as the cell which mediated this surveillance. The existence of some form of surveillance in cases of no T lymphocyte functioning presents the possibility that surveillance, if present at all, is mediated by non T cells. Cells identified as naturally cytotoxic killer (NK) cells appear to have properties required of a surveillance effector population. This paper utilizes properties of NK cells and the effects of interferon on this population to construct a mathematical model of the characteristics that an NK cell surveillance would have. A two level theory of immune surveillance is proposed.