Quantitating effector and regulatory T lymphocytes in immune responses by limiting dilution analysis modeling

Although there is currently no doubt that regulatory lymphocytes represent a master player in the immune system, a major unresolved problem is the accurate quantitation of these cells among unfractionated cell populations. This difficulty mainly arises because there are no specific immunophenotypic markers that can reliably discriminate between effector and regulatory lymphocytes. To face this problem, we have developed computational models of limiting dilution analyses addressing the question of the accurate estimation of the frequencies of effector and regulatory cells functionally engaged in an immune response. A set of generic equations were provided to form a framework for modeling limiting dilution data, enabling discrimination between qualitatively different models of suppression. These models include either one or two subpopulations of regulatory cells, featured by either low or potent regulatory activity. The potential of this modeling approach was illustrated by the accurate determination of the frequencies of effector and regulatory T lymphocytes in one real limiting dilution experiment of CD4+ CD25+ T lymphocytes performed in the context of an allogeneic response in the human system. The crucial advantage of the limiting dilution method over the "static, phenotype-based" method is the dynamic evaluation of effector and regulatory T cell biology through their actual functional activity.     

Evaluating the mean frequency of responding cells in limiting dilution assays

Summary The validity of limiting dilution assays can be compromised or negated by the use of statistical methodology which does not consider all issues surrounding the biological process. This study critically evaluates statistical methods for estimating the mean frequency of responding cells in multiple sample limiting dilution assays. We show that methods that pool limiting dilution assay data, or samples, are unable to estimate the variance appropriately. In addition, we use Monte Carlo simulations to evaluate an unweighted mean of the maximum likelihood estimator, an unweighted mean based on the jackknife estimator, and a log transform of the maximum likelihood estimator. For small culture replicate size, the log transform outperforms both unweighted mean procedures. For moderate culture replicate size, the unweighted mean based on the jackknife produces the most acceptable results. This study also addresses the important issue of experimental design in multiple sample limiting dilution assays. In particular, we demonstrate that optimization of multiple sample limiting dilution assays is achieved by increasing the number of biological samples at the expense of repeat cultures.     

A simplified and rapid limiting dilution assay of T lymphocytes

We report here the development of an alternative limiting dilution assay (LDA) of T lymphocytes (T cells). Blood mononuclear cells were first stimulated for 60 hr with PHA and then cultured in microwells in the presence of recombinant interleukin-2 without feeder cells. After 4 days of culture, wells were scored for proliferation. Clonal expansion of T cells followed the single-hit model of the Poisson distribution. The progenitor frequency (f) in the mononuclear cells and E-rosette-positive cells from normal donors were 0.082 +/- 0.025 (n = 12) and 0.236 +/- 0.029 (n = 5), respectively, but this was markedly decreased in patients who underwent marrow-ablative chemotherapy and autografts with blood hematopoietic stem cells. This LDA system should be of value in routine use for the evaluation of T cell proliferative activities.     

Graphical representation of a generalized linear model-based statistical test estimating the fit of the single-hit Poisson model to limiting dilution assays.

Standardized statistical and graphical methods for analysis of limiting dilution assays are highly desirable to enable investigators to compare and interpret results and conclusions with greater accuracy and precision. According to these requirements, we present in this work a powerful statistical slope test that estimates the fit of the single-hit Poisson model to limiting dilution experiments. This method is readily amenable to a graphical representation. This slope test is obtained by modeling limiting dilution data according to a linear log-log regression model, which is a generalized linear model specially designed for modeling binary data. The result of the statistical slope test can then be graphed to visualize whether the data are compatible or not with the single-hit Poisson model. We demonstrate this statistical test and its graphical representation by using two examples: a real limiting dilution experiment evaluating the growth frequency of IL-2-responsive tumor-infiltrating T cells in a malignant lymph node involved by a B cell non-Hodgkin's lymphoma, and a simulation of a limiting dilution assay corresponding to a theoretical non-single-hit Poisson model, suppressor two-target Poisson model.     

Interleukin 2 enhancement of lymphokine secretion by T lymphocytes: analysis of established clones and primary limiting dilution microcultures

The effect of exogenous interleukin 2 (IL 2) on lymphokine production by T lymphocytes was examined in two systems: the secretion of macrophage-activating factor (MAF) and interferon (IFN) by cloned long-term T cell lines, and a limiting dilution system for estimating the frequency of precursors of MAF-secreting cells in normal spleen. An IL 2-containing, MAF- and IFN-free supernatant from the EL-4 thymoma (EL-4 SN) significantly enhanced release of MAF and IFN by mitogen- or antigen-stimulated, cytolytic or noncytolytic T lymphocyte clones directed against alloantigens or Moloney leukemia virus-associated antigens. Highly purified IL 2 produced equivalent enhancement as EL-4 SN in cultures of alloreactive clones stimulated with concanavalin A. Kinetics experiments showed that EL-4 SN increased both the rate and duration of MAF release by T cell clones. EL-4 SN also increased MAF production when added during restimulation of limiting dilution cultures of positively selected Lyt-2+ and Lyt-2- C57BL/6 splenic T lymphocytes activated against DBA/2 alloantigens. This enhancement resulted in a threefold increase in the apparent precursor frequency of MAF-secreting cells among Lyt-2+ lymphocytes, but did not affect the frequency among Lyt-2- cells. Additional analysis indicated that average MAF production in cultures of Lyt-2-+ cells was sixfold lower than in cultures of Lyt-2- cells, and hence that EL-4 SN allowed detection of a significant proportion of Lyt-2+ cell cultures secreting low levels of MAF. Under these improved conditions, the MAF assay detected the majority of responding Lyt-2+ and Lyt-2- lymphocytes.     

In vivo priming of helper and suppressor T cells by alloantigens. Frequency analysis with the use of an in vitro limiting dilution assay

Earlier studies have demonstrated that T cells activated in mixed lymphocyte reactions can exert positive as well as negative allogeneic effects on B cells expressing the appropriate alloantigens on their surface. We investigated the effect of in vivo priming of T cells with alloantigens on their capacity to help or suppress allogeneic B cell cultures against sheep erythrocytes. We used immunization protocols that have been shown to be optimal for induction of alloantigen-specific delayed-type hypersensitivity (DTH) and alloantigen-specific suppressor T (Ts) cells for DTH. The results show that in vivo stimulation with alloantigens, depending on the immunization route and the lymphoid organ studied, can be as effective as in vitro stimulation in increasing the frequency of alloantigen-specific helper T (Th) cells and Ts cells. Subcutaneous immunization induced a 10-fold frequency raise of Th cells as well as of Ts cells in the lymph nodes. In the spleen the Th cell population was hardly affected by s.c. immunization, whereas the Ts cell population increased by at least a factor 20. Intravenous immunization, on the other hand, selectively expanded the Th cell population in the spleen, whereas the splenic Ts cell population and the Th and Ts cells in the lymph nodes were not affected. Comparison of these results with our previous data concerning characteristics and the requirements of in vivo activation of alloantigen-specific DTH reactive T cells and of alloantigen-specific Ts cells suggest that different Ts cell populations are involved in suppression of alloantigen-specific DTH in vivo and of allogeneic suppression of in vitro induced sheep erythrocytes specific antibody formation.     

Comparison of logistic regression and linear regression in modeling percentage data

Percentage is widely used to describe different results in food microbiology, e.g., probability of microbial growth, percent inactivated, and percent of positive samples. Four sets of percentage data, percent-growth-positive, germination extent, probability for one cell to grow, and maximum fraction of positive tubes, were obtained from our own experiments and the literature. These data were modeled using linear and logistic regression. Five methods were used to compare the goodness of fit of the two models: percentage of predictions closer to observations, range of the differences (predicted value minus observed value), deviation of the model, linear regression between the observed and predicted values, and bias and accuracy factors. Logistic regression was a better predictor of at least 78% of the observations in all four data sets. In all cases, the deviation of logistic models was much smaller. The linear correlation between observations and logistic predictions was always stronger. Validation (accomplished using part of one data set) also demonstrated that the logistic model was more accurate in predicting new data points. Bias and accuracy factors were found to be less informative when evaluating models developed for percentage data, since neither of these indices can compare predictions at zero. Model simplification for the logistic model was demonstrated with one data set. The simplified model was as powerful in making predictions as the full linear model, and it also gave clearer insight in determining the key experimental factors.     

Inhibition of suppressor T lymphocytes (Ts) by cimetidine

Cyclophosphamide (CY) is the most extensively studied inhibitor of suppressor T lymphocyte (Ts) function. However, repeated administration of CY can abrogate sensitization. Therefore, we were interested in identifying noncytotoxic inhibitors of Ts function as adjuncts in the immunotherapy of Ts-inducing murine tumors. The effect of cimetidine (a histamine type 2 receptor antagonist) and diphenhydramine (a histamine type 1 receptor antagonist) on the Ts mediating tolerance to 2,4-dinitrofluorobenzene was studied. We report our data regarding the specific inhibition of Ts by cimetidine.     

The induction of nonspecific T suppressor lymphocytes by prostaglandin E1

Suppressor cell activity is induced by the addition of prostaglandin E₁ to normal mouse spleen cells (NSC). When this population is added to fresh NSC, it suppresses the primary in vitro antibody response to DNP-LPS. This suppressor cell induction requires a brain-associated thy-1 antigen-bearing cell. No role for a nylon-wool-adherent cell could be demonstrated. Suppression occurs in the absence of T cells in the responding population. The addition of indomethacin to prevent endogenous synthesis of prostaglandins suggests that prostaglandininduced suppressor activity does not require further prostaglandin synthesis in the suppressor population but does require such synthesis in the responding population.     

Limiting dilution analysis of alloantigen-reactive T lymphocytes. IV. High frequency of cytolytic T lymphocyte precursor cells in MLC blasts separated by velocity sedimentation

A sensitive limiting dilution microculture system was used to obtain minimal estimates of the frequency of cytolytic T lymphocyte precursor cells (CTL-P) directed against DBA/2 alloantigens, after priming of spleen cells in unidirectional mixed leukocyte cultures (MLC, C57BL/6 anti-DBA/2). The mean CTL-P frequency in day 4 to 5 MLC populations was found to be approximately 50- to 100-fold greater than the frequency in normal spleen, and up to 25% of the cells present in such MLC could be identified operationally as CTL-P. Even higher frequencies (up to 50%) of CTL-P were obtained in a population of large-sized cells separated from day 4 MLC by velocity sedimentation. Furthermore, since a strikingly quantitative correlation was observed between CTL activity and CTL-P frequency in such separated MLC populations, it is likely that mature CTL in MLC are not end cells, but can further proliferate and thus behave operationally as CTL-P.     

Quantifying the frequency of tumor-propagating cells using limiting dilution cell transplantation in syngeneic zebrafish

Self-renewing cancer cells are the only cell types within a tumor that have an unlimited ability to promote tumor growth, and are thus known as tumor-propagating cells, or tumor-initiating cells. It is thought that targeting these self-renewing cells for destruction will block tumor progression and stop relapse, greatly improving patient prognosis. The most common way to determine the frequency of self-renewing cells within a tumor is a limiting dilution cell transplantation assay, in which tumor cells are transplanted into recipient animals at increasing doses; the proportion of animals that develop tumors is used the calculate the number of self-renewing cells within the original tumor sample. Ideally, a large number of animals would be used in each limiting dilution experiment to accurately determine the frequency of tumor-propagating cells. However, large scale experiments involving mice are costly, and most limiting dilution assays use only 10-15 mice per experiment. Zebrafish have gained prominence as a cancer model, in large part due to their ease of genetic manipulation and the economy by which large scale experiments can be performed. Additionally, the cancer types modeled in zebrafish have been found to closely mimic their counterpart human disease. While it is possible to transplant tumor cells from one fish to another by sub-lethal irradiation of recipient animals, the regeneration of the immune system after 21 days often causes tumor regression. The recent creation of syngeneic zebrafish has greatly facilitated tumor transplantation studies. Because these animals are genetically identical, transplanted tumor cells engraft robustly into recipient fish, and tumor growth can be monitored over long periods of time. Syngeneic zebrafish are ideal for limiting dilution transplantation assays in that tumor cells do not have to adapt to growth in a foreign microenvironment, which may underestimate self-renewing cell frequency. Additionally, one-cell transplants have been successfully completed using syngeneic zebrafish and several hundred animals can be easily and economically transplanted at one time, both of which serve to provide a more accurate estimate of self-renewing cell frequency. Here, a method is presented for creating primary, fluorescently-labeled T-cell acute lymphoblastic leukemia (T-ALL) in syngeneic zebrafish, and transplanting these tumors at limiting dilution into adult fish to determine self-renewing cell frequency. While leukemia is provided as an example, this protocol is suitable to determine the frequency of tumor-propagating cells using any cancer model in the zebrafish.     

Inferring the location of tumor suppressor genes by modeling frequency of allelic loss

Allelic loss is often part of a multistep process leading to tumorigenesis. Analysis of genomic markers highlights regions of elevated allelic loss, which in turn suggests a nearby tumor suppressor. Furthermore, pooling published analyses to combine evidence can increase the power to detect a tumor suppressor gene. If the pattern of loss for each tumor, or allelotype, is known, a stochastic model proposed by Newton et al. (1998, Statistics in Medicine 17, 1425-1445) can be used to analyze the correlated binary data. Many studies report only incomplete allelotypes, augmented with frequencies of allelic loss (FAL) at each marker, in which the number of informative tumors showing allelic loss is provided along with the number of informative tumors. We describe an extension of the allelotype model to handle FAL data, using a hidden Markov model or a normal approximation to compute the likelihood. The FAL model is illustrated using data from a study of colorectal cancer.     

The effect of age on the antigen-presenting mechanism in limiting dilution precursor cell frequency analysis

We have utilized limiting dilution analysis (LDA)2 to compare the intrinsic precursor cytotoxic T lymphocyte (pCTL) frequency for influenza-plus-self in young and old C57BL/6 mice. Under conditions of excess interleukin 2 (IL-2) and antigen presenting cells (APC) derived from spleens of mice matched in age to those being tested, we found more than a twofold difference in pCTL frequency between young and old animals. However, there was no difference in pCTL frequency between the two age groups if antigen was presented to the old responder cells on spleen cells derived from young mice. The apparent decrease in pCTL frequency in old mice by standard LDA may in fact be due to a defect in the antigen processing and/or presentation mechanism of old spleen cells. We conclude that the age-associated defective CTL activity previously reported by us and by others may be due at least in part to a defect in the antigen presentation mechanism of aging mice.     

Deficiencies in suppressor T cell activity seen in patients with active systemic lupus erythematosus are due to the dilution of normally functioning suppressor T cells by nonsuppressor T cells

Concanavalin A (Con A)-activated T lymphocytes from patients with active, but not inactive, systemic lupus erythematosus (SLE) failed to express normal suppressor activity, regardless of the phenotype of CD4+ or CD8+. Con A-activated CD4+ or CD8+ T lymphocytes from the SLE patients and from normal controls were further separated into two populations, using the autologous erythrocyte rosette technique. One population very rich in cells capable of forming rosettes with autologous erythrocytes from the active patients showed the same degree of suppressor activity, as did that from normal controls; the CD4+ or CD8+ population poor in autorosetting cells derived from Con A-activated T lymphocytes from both the controls and patients did not express suppressor activity. Moreover, when autorosetting T cells from the active patients and nonrosetting cells from the same patients were mixed at a normal ratio (4:6), normal suppressor activity could be restored. It was notable that the frequency of autorosette-forming cells was markedly reduced in the Con A-activated T lymphocytes from the active, but not inactive, SLE patients, regardless of the phenotype of CD4+ or CD8+. These findings indicate the presence of a normally functioning suppressor T cell population in patients with active SLE. It seems that the lack of suppressor T cell function in patients with active SLE is due to the dilution of a few normal suppressor T cells by large numbers of nonsuppressor T lymphocytes.     

Long-lasting deficit of functional T cell precursors in human bone marrow transplant recipients revealed by limiting dilution methods

We have applied limiting dilution methods suitable for the estimation of mitogen-reactive helper (pHTL) and cytotoxic (pCTL) T cell frequencies to the analysis of immune function in patients 1 mo to 6 yr after allogeneic bone marrow transplantation (BMT). Although the majority of these patients have regained normal levels of Leu-3+ (helper) and Leu-2+ (killer/suppressor) cells by 6 to 12 mo after BMT as assessed by cytofluorimetry, the fraction of these cells that can function in limiting dilution cultures is substantially below normal levels in nearly all patients. Although some BMT patients eventually recover normal frequencies of pCTL and pHTL, values typically remain greatly depressed even in patients transplanted as many as 4 to 6 yr previously. In contrast, recovery of precursors able to proliferate (without expressing either helper or cytotoxic function) in response to phytohemagglutinin (PHA) and interleukin 2 occurs in many patients by 1 yr after transplant. In spite of the decreased frequency of functional precursor cells found after BMT, each precursor is capable of giving rise to the same amount of function at limiting dilutions as that produced by cells from normal controls. In many BMT patients, proliferation in conventional PHA-stimulated cultures returns to near-normal levels even though precursor frequencies remain low. The limiting dilution method is sensitive to residual immune dysfunction in BMT recipients not easily quantitated by other, more conventional techniques.