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Splenic T cells exposed to concanavalin A (Con A), and subsequently to factors produced by rat spleen cells in response to Con A (Con A sup), acquire the ability to function as helper T (TH) cells in response to xenogeneic erythrocytes (RBC). Help is measured as the reconstitution of the plaque-forming cell response of a spleen cell population depleted of T cells by treatment with anti-Thy-1 serum and complement. We propose that precursor TH cells differentiate during the in vitro treatment into mature TH cells. As differentiation occurs under limiting dilution conditions, an estimation of the precursor frequency should in principle be possible. However, a single-hit Poisson distribution does not fit our data. Instead, we observe, dependent on the T cell concentration, three separate "peaks" of response. In many experiments, using sheep, horse, and chicken RBC as antigens, we reproducibly find these "peaks" at 40-190, 600-3,000, and 20,000- 100,000 T cells, placed into limiting dilution cultures, respectively. By various experiments we can show that the helper activity is not due to passively transferred rat factors, but to the titrated cells themselves. The active cell is a T cell that appears to function in an antigen-specific way and to require direct cell contact to do so. It thus resembles the classical helper T cell. As we find precursor TH cells already at very low concentrations of T cells, we titrated the range between 0 and 100 T cells/well carefully. The bent shape of the titration curves does not always allow a statistically satisfying regression analysis, and we therefore cannot estimate precise precursor frequencies from every experiment. However, a common sense argument can be made that these frequencies must be on the order of 1/10-1/100 T cells. We propose that the limiting dilution curves obtained in this system most likely reflect fundamentally important cellular interactions that regulate immunological effector functions. We favor a concept of independently interacting sets of helper and suppressor T cells of various frequencies, but other models are possible.

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Limiting dilution (LD) ~ analysis is one widely used way to analyze properties of lymphocytes at the clonai level (1). Many previous experiments have primarily studied LD systems that provided single hit results and, therefore, could be interpreted using the O-term of the Poisson distribution (reviewed in references 1, 2). The purpose of such experiments was exclusively the determination of precursor frequencies for various effector lymphocytes.Recently, we described a number of LD systems that suggested more than one limiting population of cells interacting with each other, rather than a single hit mechanism (3). These systems are aimed at studying T cells and are based on in vitro differentiation and/or clonal expansion by polyclonal activation rather than by specific antigen (4-7). In a few cases, results from antigen activation protocols have suggested multiple limiting cells as well (8-11, and I. Melchers, unpublished observation). We have previously proposed that in these LD systems not only the effector T cells under study but also regulatory T cells that can modify the generation of effector cells are detected (3-7).Because we strongly feel that these experimental protocols not only provide information on precursor frequencies but also represent a novel quantitative approach to the study of immune regulation, we have decided to establish the mathematical basis for the correct estimation of the precursor frequencies of effector and regulatory T cells from multi-component limiting dilution results. In this paper we present our mathematical approach and demonstrate that we can reproduce our experimental results by assuming the existence of multiple paired populations of effector and suppressor cells for any given T cell effector function studied. T suppressor cells distribute independently of effector T cells. Within the framework of these assumptions, only in one biological model and with a very restricted choice of parameters can we obtain curves that fit the data satisfactorily. Thus, we think that we can interpret LD results not only with J Abbreviations used in this paper: ~, frequency; a, number of Ts needed for suppression of 1 Tr; A, number of Ts needed for suppression of all TE in a culture well; Con A, concanavalin A, CTL, cytotoxic T lymphocytes; F0, probability to find a negative culture; HTL, helper T lymphocytes; LD, limiting dilution; N, cell number; P, probability to find a given number of cells/culture; R, ratio ~s/ ~; SRBC, sheep erythrocytes; TCGF, T cell growth factor; TE, effector T cell or its precursor; Ts, suppressor T cell or its precursor; u = (j), mean multiplicity (=~E.N) of Tr, distributed around the exact numberj of TE; v = (i), mean multiplicity (~s.N) of Ts, distributed around the exact number i of Ts. 40J. Exp. MED.

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