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Stochastic models of tumorigenesis have been developed to investigate the implications of experimental data on tumour induction in wild-type and p53-deficient mice for tumorigenesis mechanisms. Conventional multistage models in which inactivation of each p53 allele represents a distinct stage predict excessively large numbers of tumours in p53-deficient genotypes, allowing this category of model to be rejected. Multistage multipath models, in which a p53-mediated pathway co-exists with one or more p53-independent pathways, are consistent with the data, although these models require unknown pathways and do not enable age-specific curves of tumour appearance to be computed. An alternative model that fits the data is the 'multigate' model in which tumorigenesis results from a small number of gate-pass (enabling) events independently of p53 status. The role of p53 inactivation is as a rate modifier that accelerates the gate-pass events. This model implies that wild-type p53 acts as a 'caretaker' to maintain genetic uniformity in cell populations, and that p53 inactivation increases the probability of occurrence of a viable cellular mutant by a factor of about ten. The multigate model predicts a relationship between the time pattern of tumour occurrence and tumour genotype that should be experimentally testable. Stochastic modelling may help to distinguish 'gatekeeper' and 'caretaker' genes in other tumorigenic pathays.

Childhood leukaemia presenting at a young age has been suspected of resulting from a leukaemogenic mutation in parental germ cells, either spontaneously or due to the exposure of a parent to leukaemogenic environmental hazards, particularly ionizing radiation. Mathematical modelling of leukaemogenesis suggests that any such patient would be especially prone to multiple independent leukaemogenic events leading to multiclonality in terms of cell of origin (analogous to bilaterality in familial retinoblastoma). To test this hypothesis we have carried out a search for multiclonal leukaemogenesis in infant and childhood acute lymphoblastic leukaemia (ALL). We used a polymerase chain reaction-based analysis of the X-linked monoamine oxidase A (MAOA) gene locus to study the clonality of marrow samples obtained from female paediatric ALL patients at the time of disease presentation. We obtained presentation samples from 102 patients of whom 72 were found to be informative at the MAOA locus. These included 20 infant leukaemias (< 1 year at diagnosis). Sixty-six samples were found to be unequivocally monoclonal while the remaining six could not, with certainty, be assigned a clonal origin. We also obtained bone marrow aspirates at first relapse as well as at presentation from eight patients. In each case the same pattern of X-linked allelic inactivation was observed at both time points of the course of the disease. No evidence was found for leukaemic multiclonality in any age group at presentation or for leukaemic 'clone-switching' in relapse. These findings suggest that both infant and childhood ALL is of single-cell origin and implies that leukaemic predisposition resulting from germ cell mutation is unlikely to have a major role in their pathogenesis.

When the clonogenic survival of mouse haemopoietic stem cells (CFU-S) and leukaemia L1210 cells growth as ascites tumours are compared after being heated in vitro and assayed in vivo by spleen-colony assay, there is no significant difference in the terminal slopes of the survival curves. The shoulders of the survival curves differ, but this may be explained by differences in cell kinetics. By contrast, L1210 leukaemic marrow cells are considerably more susceptible to the lethal effects of hyperthermia (43 degrees C) than either normal marrow stem cells or L1210 leukaemic cells grown as ascites tumours. Moreover, the killing of L1210 ascites cells by hyperthermia can be enhanced by heating L1210 ascites cells with an equal number of normal marrow cells, or as upernatant removed from heated marrow cells. Most cells in lukaemic marrow are normal, and it is postulated that the increased thermal sensitivity of L1210 cells in leukaemic marrow is caused by diffusible factors (e.g. lysosomal enzymes) released by heating normal marrow cells.

To compare the relative heat sensitivities of human normal and neoplastic cells of the same tissue type, a study was carried out of the relative sensitivities to heat of granulocyte/macrophage progenitor cells (CFU-GM) derived from the peripheral blood and bone marrow of normal subjects and patients with chronic granulocytic leukaemia (CGL). Nucleated haemopoietic cells were incubated at temperatures in the range 41.5 degrees C to 44.0 degrees C for various periods before culture in agar. The results of these experiments showed that CFU-GM from normal blood were consistently less sensitive to damage by heat than normal marrow CFU-GM. There was no comparable difference in the relative heat sensitivities of CFU-GM from blood and marrow of patients with CGL and no significant difference between the heat sensitivities of CFU-GM derived from marrow from normal individuals and patients with CGL. The observed difference in heat sensitivity of CFU-GM from normal blood and marrow accords with other data suggesting that the two progenitor cell compartments are distinct: the blood CFU-GM may represent a more primitive population of committed progenitor cells. In CGL, CFU-GM in the blood may much more closely resemble those in the marrow. The data provide no support for the hypothesis that malignant cells differ intrinsically from their normal counterparts in respect of sensitivity to damage by hyperthermia.

In tumour regrowth-delay experiments, the analysis of results in the higher dose ranges may be complicated by a dose-dependent proportion of non-recurrent (cured) tumours, whose inclusion in the analysis is not straightforward. A study of the relation of growth delay to cure has been carried out using a model of tumour response which assumes Poisson (single-cell) cure statistics and exponential regrowth kinetics of recurrent tumours, and which makes use of Monte Carlo simulation techniques to represent the effects of inter-tumour heterogeneity. This approach yields correction factors compensating for tumour cures in growth-delay experiments. For homogeneous tumour systems (all tumours and treatments identical) these corrections are small and not significantly different from corrections obtained using the "long delay" procedure suggested previously (Denekamp, 1980; Fowler et al., 1980). For heterogeneous systems, however, correction factors increase with the heterogeneity of the system, and may become quite large. It is concluded that the quantitative assessment of heterogeneity is required, and a possible approach to this is suggested. Should evaluation of heterogeneity prove feasible, it will allow more efficient use of tumour-response data, and may permit realistic estimates of clonogenic cell survival in situ.

The kinetics of development and subsequent growth of a C3H mouse mammary tumour after implantation of 10(6) cells was quantified by observation and statistical analysis of latent period and growth rate for different categories of tumour. These comprised control tumours, tumours recurring after large single doses of X-rays alone and in combination with misonidazole, tumours developing from cells implanted both outside and within the sites of tumours previously cured by irradiation, tumours developing from cells implanted in heavily irradiated skin, and tumours developing from cells taken from tumours recurring after irradiation and re-implanted in untreated skin. The kinetics of development and growth of tumours in host animals previously treated by i.p. injection of killed tumour cells was also quantified. The results confirm that tumour development and growth is significantly perturbed by irradiation of host tissues both before and after tumour transplantation, and that this perturbation involves an extended latent period, a slower average rate of growth and a less uniform pattern of growth. These effects result from localized radiation damage to host tissues, are not attributable to residual damage to irradiated tumour cells, and are not markedly dose-dependent within the dose range 25--80 Gy. These results are consistent with the complete sterilization of host endothelial cells by doses of 25 or more. In marked contrast to the growth-slowing effect of irradiation, the treatment of host animals by previous injection of radiation-killed tumour cells led to a reduced latent period and a faster average rate of growth.

Using growth delay and clonogenic cell survival as end points, we have shown that the 3-dimensional structure of human lung tumour spheroids confers a degree of resistance to the anthracyclines adriamycin and 4'-deoxydoxorubicin, relative to cells grown as monolayer. 4'-deoxydoxorubicin induces a longer growth delay and greater clonogenic cell kill than adriamycin in spheroids, although it is no more cytotoxic in monolayer (exponential and plateau phase). There is a log linear relationship between clonogenic cell survival and duration of adriamycin exposure in monolayers, and biphasic curve with a lesser degree of cell kill for disaggregated spheroid cells. Using fluorescent microscopy we have demonstrated, qualitatively, that the more lipophilic analogue partitions into the spheroid more rapidly and to a greater degree than adriamycin. It is possible that adriamycin penetration is a relatively important aspect of spheroid drug resistance, which may be related to intraspheroidal pH gradients, and that we have partially overcome this by using a lipophilic analogue.

The regrowth rate of the rat sarcoma SSB1a was assessed, following treatment with either X-rays or hyperthermia. The growth rate of untreated tumours implanted in pre-irradiated or pre-heated normal tissue was also measured. For treatments giving similar levels of tumour regrowth delay, the regrowth of irradiated tumours was markedly slower than that of untreated tumours, whilst the regrowth rate of tumours subjected to hyperthermia did not differ from that of untreated tumours. The growth rate of untreated tumours implanted in pre-irradiated skin was also slower than that of control tumours, though the growth-rate reduction was less dramatic than for regrowth following tumour irradiation in situ. Tumours implanted in pre-heated skin grew at the same rate as control tumours. Slower regrowth in situ after X-rays than after hyperthermia would produce a larger growth delay for X-rays than for hyperthermia, for equal levels of tumour-cell kill or probability of tumour sterilization. This effect could lead to a systematic underestimation of the efficacy of hyperthermia relative to X-rays, when efficacy is assessed by growth delay.