Bringing NKS to Bear on Fundamental Issues in Cancer and Biology

Ilan R. Kirsch
National Cancer Institute

Todd Rowland
Wolfram Research

Some fundamental insights are needed to begin the transition of biomedical opinion of NKS from disinterest to application and utilization. Subjectively, it would seem that the application of NKS to biological systems that are already recognized as models of other physical systems while interesting in their own right, represent more variations on a theme than convincing demonstrations of inroads of NKS into virgin territory. It is in this context that consideration of the contribution of NKS to more fundamental principles in biology becomes critical.

Cancer and cancer biology represent vital systems for exploring the potential of NKS to illuminate biology. In many respects, cancer, the disruption and dysregulation of normal growth, development, and differentiation is a microcosm of biology itself. Cancer is sometimes portrayed as a complex disease that no simple approach can encompass, prevent, or cure. On the other hand, NKS suggests that there could be some simple underlying behavior, or possibly instead that some simple model could capture the essential features of cancer.

If we already knew the deterministic rule for the development of cancer (if one exists) then we could employ it in the development of a pattern whose cancer predictive capability could be tested. In the absence of that knowledge, a possible approach is to model cancer by creating an image consistent (hopefully) with the evolution of a definitive or probabilistic cellular automata and then try to work from that picture back to the relevant condition and rule that generated it. More to the point, the idea would be to create a rough picture which captures some essential elements of the development of a primary tumor within a particular cell lineage. It would send out exploratory representatives across the field of the pattern.  Sooner or later one of those emissaries that has landed in another region triggers a clonal proliferation. It’s easy to visualize this occurring on a kind of CA background, for example an evolution of rule 110 that has distinct pattern elements with transitional zones between them.  One scenario for the cause of clonal proliferation is a local change of the rule dictated by the background patterns and the underlying rule.  In the case of a deterministic underlying rule, it would have to be a rare configuration, while in the case of a probabilistic rule it could also be unlikely.

Once candidate patterns have been identified, will some initial condition and rule provide distinctive insight into the process of malignant transformation? Only doing the experiment and trying to interpret the result will answer that question.

Created by Mathematica  (April 20, 2004)