Recent experimental results show that even brief stimulation with antigen can cause antigenspecific CD8 T-cells to undergo sustained proliferation followed by differentiation into memory cells. These results show that the dynamics of these immune responses are not governed by constant monitoring of antigen levels, but rather that following stimulation immune cells commit to a ''program''. At present relatively little is known about the program which governs CD8 cell proliferation and differentiation. For example, we do not know whether the program is completely specified by the initial encounter of a T cell with antigen, or whether it subsequently can be modified by the amount of antigen present. Nor do we know whether the entire program for T cell proliferation and differentiation resides within the T cell itself, or whether some component(s) of the program are determined by cells or molecules external to the CD8 cell. In this paper we construct simple mathematical models which incorporate antigen-independent proliferation and differentiation of CD8 cells during acute infections. We use these models to determine what characteristics the program must have in order to be consistent with the existing data on the dynamics of CD8 responses, and in particular to answer the questions posed above. Our results suggest that the program is not completely defined by the initial encounter of T cell with antigen but may be augmented by exposure to antigen in a brief window shortly after infection; furthermore, parts of the program may reside external to the T-cells. Finally we examine some of the consequences of the ''program'' for pathogen-host coevolution. r

The CFSE dye dilution assay is widely used to determine the number of divisions a given CFSE labelled cell has undergone in vitro and in vivo. In this paper, we consider how the data obtained with the use of CFSE (CFSE data) can be used to estimate the parameters determining cell division and death. For a homogeneous cell population (i.e., a population with the parameters for cell division and death being independent of time and the number of divisions cells have undergone), we consider a specific biologically based bSmith-MartinQ model of cell turnover and analyze three different techniques for estimation of its parameters: direct fitting, indirect fitting and rescaling method. We find that using only CFSE data, the duration of the division phase (i.e., approximately the S + G 2 + M phase of the cell cycle) can be estimated with the use of either technique. In some cases, the average division or cell cycle time can be estimated using the direct fitting of the model solution to the data or by using the Gett-Hodgkin method [Gett A. and Hodgkin, P. 2000. A cellular calculus for signal integration by T cells. Nat. Immunol. 1:239-244]. Estimation of the death rates during commitment to division (i.e., approximately the G 1 phase of the cell cycle) and during the division phase may not be feasible with the use of only CFSE data. We propose that measuring an additional parameter, the fraction of cells in division, may allow estimation of all model parameters including the death rates during different stages of the cell cycle. D

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There has been much debate on the contribution of processes such as the persistence of antigens, cross-reactive stimulation, homeostasis, competition between different lineages of lymphocytes, and the rate of cell turnover on the duration of immune memory and the maintenance of the immune repertoire. We use simple mathematical models to investigate the contributions of these various processes to the longevity of immune memory (defined as the rate of decline of the population of antigen-specific memory cells). The models we develop incorporate a large repertoire of immune cells, each lineage having distinct antigenic specificities, and describe the dynamics of the individual lineages and total population of cells. Our results suggest that, if homeostatic control regulates the total population of memory cells, then, for a wide range of parameters, immune memory will be long-lived in the absence of persistent antigen (T 1͞2 > 1 year). We also show that the longevity of memory in this situation will be insensitive to the relative rates of cross-reactive stimulation, the rate of turnover of immune cells, and the functional form of the term for the maintenance of homeostasis.Although the ability to maintain memory after an encounter with an antigen is one of the central features of the immune system, the mechanism(s) by which immune memory is maintained are not yet fully understood. The initial view (1) suggesting that ''memory'' lymphocytes might be very longlived cells could be rejected because lymphocytes have turnover rates much shorter than the lifespan of the host (2, 3). The relatively high rates observed for the turnover particularly of antigen-specific cells after stimulation led to the hypothesis that maintenance of an elevated population of antigen-specific immune cells might require restimulation, either by persistent antigen or by repeated exposure to antigen. Several observations were marshaled in support of this hypothesis. First, antigen-antibody complexes were found to remain on follicular dendritic cells long after initial exposure to the antigen (4). Second, the transfer of lymphocytes (either B cells or CD4ϩ T-helper or CD8ϩ cytotoxic T lymphocyte) from an antigen-stimulated to a naive host (in the absence of transferred antigen) was followed by a rapid decline in the population of these cells (5-7). Although persistent antigen or repeated stimulation is likely to result in long-lasting immune memory, the question of the duration of immune memory in the absence of such restimulation remained. Several lines of evidence in support of the hypothesis that immune memory may be long-lived in the absence of persisting antigen include the long-standing ''natural history'' studies, which showed long-lived immunity to viruses such as the measles virus and yellow fever virus persisted for decades after infection under conditions in which repeated exposure was highly unlikely (8-10), and recent experimental studies that have followed populations of antigen-specific immune cells in the absence of their ...