Sir

There was a striking absence of discussion of quantitative methods in the recent interesting theoretical debate on the timing and nature of mutations controlling acquisition of the metastatic phenotype in invasive cancers (R. Bernards and R. A. Weinberg Nature 418, 823; 200210.1038/418823a and Correspondence Nature 419, 559–560; 200210.1038/419559b). Without the discipline imposed by mathematical rigour, the arguments have to rely on intuitive reasoning and small pieces of data singled out from the vast extant literature. The reader is unable to independently evaluate the hypotheses or understand them in the context of all available experimental information or of theoretical models that organize information in integrally related phenomena such as carcinogenesis and tumour invasion. Although this state of affairs is normal in some disciplines such as tumour research, it would be unthinkable in the physical sciences.

Medical investigators often eschew mathematical models as too “simplistic” for the dynamics governing processes such as those in tumour biology. Instead, the general underlying principles in complex biological processes are expected to become apparent, as if by magic, once sufficient data are accumulated. Not surprisingly, this passive approach has failed to yield a comprehensive theoretical framework of understanding carcinogenesis, tumour invasion and metastatic behaviour. Clinical therapy thus remains largely empirical, based more on trial and error than a comprehensive understanding of biological first principles.

In most other scientific disciplines, there is an active search for broad generalizations through hypotheses framed in mathematical models that can be examined for internal consistency and compatibility with extant data. Predictions from these models can be tested by experiment and revised when necessary. Surely the success of this integrative approach, combining quantitative theoretical methods and experiment in highly complex systems in physics (including biophysics), chemistry, engineering and biological disciplines, such as ecology or structural biology, should motivate its enthusiastic application to other nonlinear biological processes such as carcinogenesis and tumour invasion.

In the absence of consistent application of rigorous mathematical models, theoretical medicine will largely remain empirical, phenomenological and anecdotal, successful only in linear systems that can be defined by a single experiment or a few experiments. Until the quantitative methods of the physical sciences are applied, many difficult and clinically important problems in tumour biology, including the dynamics that give rise to the metastatic phenotype, will remain unresolved.