Dynamics of Cancer: Incidence, Inheritance, and Evolution

  • Steven A. Frank
Princeton University Press: 2007. 400 pp. $99.50, £59.95 0691133654 9780691133652 | ISBN: 0-691-13365-4

Multicellular animals have been around for about 600 million years, and cancer has been a problem for most of this time. There is a risk of cancer whenever the component cells grow and divide, so cancer incidence has increased progressively as the size and lifespan of organisms extended. In a lifetime, humans experience up to 1016 mitoses, the process by which a cell duplicates its DNA and divides to make two identical daughter cells. Each mitosis is an invitation to genetic disaster, due to miscopying of DNA, inadvertent breakage of chromosomes, and mishaps in chromosomal segregation. Given these vast opportunities for accumulating mutations, it is surprising that we don't generate numerous life-threatening cancerous cell clones during our first years of life.

The reason for our long and generally cancer-free lives is a series of anticancer defence mechanisms that have co-evolved with our increasing complexity. Most of these defences are wired into the intracellular signalling circuits that govern cell behaviour, although the organization of our tissues and immune systems contributes too. At least five or six of these mechanisms must be breached before a full-blown tumour appears.

Credit: A. MARTIN

These multiple lines of defence explain the complexity of tumour formation, which in most tissues involves a sequence of steps, each of which breaches one or more of the defences. We can describe some of these steps in biochemical detail, such as the activation of a ras oncogene or the inactivation of the p53 tumour-suppressor gene. But a description of the process as a whole is currently well beyond our reach.

Steven Frank, in his new book Dynamics of Cancer, is the latest in a line of biologists and mathematicians who have taken on the challenge. Can we describe tumour formation in terms of rate equations and probabilities? Are there aspects of each step that can be reduced to mathematical formulation? And can we develop a general model of multi-step tumorigenesis as it occurs in a variety of human tissues?

Can algebraic formulae tell us more than reasoning about the behaviour of complex biological systems?

Solutions to these problems have ramifications beyond our understanding of tumorigenesis. For example, if we could assign values to the parameters governing the rates of each step of tumorigenesis, including the ways environmental and genetic factors affect these parameters, we could predict why cancer strikes at certain ages and in certain individuals.

Frank's approach to this problem raises the question of whether we know enough biology and biochemistry to create truly useful, predictive models of multi-step tumour development. We have learned much over the past three decades about the biochemistry of cell transformation and the physiology of neoplastic cell growth, but we still have only a crude understanding of how these processes play out in living tissues. We don't understand in any quantitative way how endogenous mutagenic processes and environmental mutagens work. Nor do we understand the mechanisms or the kinetics governing the methylation of gene promoters and the resulting silencing of tumour-suppressor genes.

The fate of most of the pre-neoplastic cell clones remains an enigma. We don't understand how specific mutant alleles or mutant oncoproteins affect the darwinian processes of clonal selection and expansion. In fact, we don't really know how many distinct biological steps drive or accompany the formation of any type of human tumour. We know the approximate number of the slowest, rate-limiting steps, but almost nothing about the more rapid ones, yet these are just as important in driving multi-step tumour progression.

Frank is an evolutionary biologist with a strong mathematics bent. His book grapples with many of these issues, offering insights from his mathematical modelling of various steps of tumour progression. Those who aspire to digest all of his arguments, many of which are embedded in equations, will not find this easy reading. The text often appears in the formal voice of a mathematical proof.

A school of mathematical biology arose at the University of Chicago in the 1960s, only to decline in the following decade. It became apparent that a multitude of parameters needed to be assumed or arbitrarily fitted to existing data sets to ensure that the predictive powers of mathematical models conformed with actual observations. In the end, the proponents of mathematical biology drifted away, disenchanted.

Perhaps the biologists posed the most pointed question: can algebraic formulae tell us more than reasoning about the behaviour of complex biological systems? This question echoes almost half a century later, but Frank is undeterred. One day he may be seen as the pioneer who began the difficult task of building a sturdy foundation for a truly useful mathematical model of cancer development.