Computational models provide the ultimate level of control and information. Every detail of a computational model is by definition both available for observation and modification. Their main drawback is that many of the details of a biological system are not yet understood, so the representation of those details and dynamics in a computational model is in essence a hypothesis for what may be true of the biological system. In addition, representation of a biological system in a computation simulation requires the abstraction or exclusion of much of the complexity of the biology, and so the generality of the results of the models are always in question. Nevertheless, computational models have proved useful for the exploration of current theories, hypothesis generation, and the discovery of important holes in our understanding that are likely to be critical to the dynamics of the biological system. When one has to write down the details of the essential aspects of a biological system, one quickly realizes how little is known about that system.
Computational models can simulate the evolution of somatic cells over decades. We discovered that there is an important (and counterintuitive) interaction between the number of cancer genes (tumor suppressor genes or oncogenes) that must be mutated in a single allele (dominant mutations), for the development of malignancy, and mutator lesions that increase the rate of (epi)genetic lesions (11
). The requirement of more mutations for the development of malignancy actually increased the chance of progression to malignancy, because they provided more opportunities for a mutator lesion to hitchhike on an expansion of the clone with a dominant cancer gene mutation. The generation of a large, genetically unstable clone greatly increases the probability of progression in the model. This has been supported in a cohort of BE patients in which the size of a clone with p53 loss of heterozygosity (LOH), aneuploidy or tetraploidy was significantly associated with progression to EA (12
Recently, we used a computational model to examine the dynamics of clonal expansion and found that clones on two-dimensional surfaces, like BE, are likely to expand quadratically rather than exponentially (13
). This model fit p53 mutant clone size data from a skin cancer mouse model better than an exponential model of clonal expansion. We also found that the shape of a clone differed depending on whether it had a proliferative fitness advantage or a survival fitness advantage. If the lesion driving the clonal expansion gave the clone a proliferative advantage over its neighboring clones, then it tended to have a rougher, or concave border (looked more “invasive”) than clones with a survival advantage, which produced a relatively smooth, convex shape.
A variety of models have been developed to study the dynamics of cells within a crypt (14
), which likely also apply to BE. Most of these have been used to test the implications of alternative hypotheses for stem cell dynamics and differentiation, as well as lesions that may initiate carcinogenesis with uncontrolled growth (16
). Earlier models of stem cell dynamics were fit to data on the conversion of polyclonal murine intestinal crypts to monoclonal crypts as well as crypt density and used to infer crypt lifecycle dynamics (22