Cell-to-cell and/or tissue-to-tissue communication is crucial for tissue organization. Its disruption can play an important role in the initiation of cancer [1, 2]. These communications involve substances analogous to a morphogen in the developing embryo that diffuse through the tissue creating a concentration gradient. Local concentrations of these substances influence the phenotype of neighboring cells. These substances have been called morphostats [3, 4]. Various models have been proposed to explain how the concentration gradient of morphogens generates differentiated tissues during embryogenesis ; these models could be applied to examine the role of morphostats in carcinogenesis but, for our purpose here, we assume a simple model in which the source of the morphostat gradient lies in the stroma.
One suggestive piece of evidence for the existence of morphostats is the development of tumors when foreign bodies, which serve as barriers to potential diffusion, have been inserted subcutaneously in mice. Early experiments found a carcinogenic response for various chemically inert substances inserted subcutaneously, but only when they were implanted intact and not in powdered form . If there were chemically induced genetic changes, the rate of tumor formation from a foreign-body implant in powdered form would be the same or greater than the rate of tumor formation from a solid implant of the same mass (and less surface area). Because this was not the case, it is highly doubtful that there was a chemically-induced genetic initiation (like a mutation). Without genetic initiation, it is unlikely that an intact implant would have the role of a promoter. Later experiments involving the subcutaneous insertion of a Millipore filter showed that tumors formed only when the pores in the filter were sufficiently small , suggesting a threshold size of pore that permits morphostat diffusion. An alternative explanation for the initiation of tumors in foreign-body experiments is that inflammatory responses lead to mutations that cause cancer. However, this explanation does not fit the fact that inflammation (specifically, filter invasion by cytoplasmic process and phagocytic and lysosomal activity) was associated with large pore implants when almost no tumors were observed, but was not associated with small pore implants when many tumors were observed . Thus, because an explanation for this peculiar phenomenon based on an initiating event involving genetic mutations appears unlikely, we have recently identified "foreign-body" carcinogenesis as a key paradox in the initial steps of carcinogenesis if one were to adopt the explanation suggested by the somatic mutation theory .
Other evidence consistent with the role of morphostats in carcinogenesis stems from transplantation experiments in which tumors arise when normal epithelial cells were transplanted next to stromal cells in rats treated with either a physical carcinogen  or a chemical carcinogen with a very short half-life to reduce the chance of indirect exposure of the epithelial cells to the carcinogen .
Even though some putative morphostats have been identified , the full spectrum is, as yet, unknown, as are the mechanisms by which they influence carcinogenesis. Based on the prevalent somatic mutation theory, one hypothesis would be that at least two mutations in genes regulating cell proliferation are required: one in an epithelial cell and one in a surrounding stromal cell . Recent data showing lack of evidence for mutations in the stroma of tumors argues against this option . An alternative hypothesis is that the perturbation in a morphostat gradient could initiate carcinogenesis without any requirement for a mutation. To investigate this latter hypothesis, we developed a simple mathematical model (computer simulation) of the process of cell renewal, the diffusion of a morphostat, and the effect of morphostat concentrations on cell phenotype. We then mathematically perturbed the model to simulate disruption of the morphostat gradient arising from a block in the stroma.
Our goal was to determine whether or not disruption of a morphostat gradient is sufficient to create aberrant cells in the context of cell renewal without the need to postulate a mutation in the epithelial cells to initiate the development of cancer. We define an aberrant cell as an epithelial cell created by a low morphostat level, the phenotype of which is no longer under the control of that morphostat gradient. Because these aberrant cells are unable to respond to a morphostat, we view them as precursors of cancer that have the potential to obtain a selective advantage as a result of higher proliferation rates or a propensity toward genetic or epigenetic aberration, or some combination of these.
If our mathematical model provides evidence that aberrant cells in a dynamic setting of cell renewal can indeed be generated without mutations, it would provide impetus for new research directions in carcinogenesis and, specifically, attempts at empiric experimental testing under a paradigm that is quite different from the dominant somatic mutation theory.
Most mathematical models of carcinogenesis [12–14] begin with a nascent tumor cell. In contrast our model begins with normal tissue. Our model is related to mathematical models for morphogenesis in that it depends on diffusion. The classic mathematical model for morphogenesis was a set of differential equations proposed by AM Turing  in a 1952 paper in which he coined the word "morphogen." Turing, who was a computer pioneer and a cryptologist, noted, then, the future possibility of modeling morphogen diffusion using a digital computer. A cell polarity model of carcinogenesis  also involves morphogens, but the morphogens in that model play a very different role from those in our model, in that they induce a loss of cell polarity leading to division in an abnormal direction rather than influencing tissue phenotype.