Peto’s paradox revisited: black box vs mechanistic approaches to understanding the roles of mutations and promoting factors in cancer

Abstract

It is not often the case that scientific papers describing mathematical models of cancer, especially those including complex equations, can be described as "entertaining", but this is certainly the case for several seminal papers written by Richard Peto. The purpose of this short review is to revisit one such paper, written in 1984, entitled "The need for ignorance in cancer research" [1].In this particular article, which thankfully did not include the equations, Peto first discussed implications arising from statistical analyses of the incidence of cancer in humans and mice, identifying questions that came to be known as "Peto's paradox". Armitage and Doll had in 1954 published a detailed study of human cancer incidence, concluding that the rate increased in proportion to the 6th power of age [2]. In 1975 Peto carried out a mouse study that involved repeated treatment of mice with a mutagen (benzpyrene) for many months, also showing that the cancer incidence rate increased as a power of the duration of exposure to the carcinogen [3]. These data were widely interpreted as supporting a model of cancer, both in mice and humans, as being caused by a sequential series of around 4-6 mutations due to repeated long term exposure to agents that damage DNA. The paradox arose from the observation that cancer incidence and mortality in mice and humans appear to be independent of body size and longevity, in spite of huge differences in the number of cells in each species, and the length of time during which target cells may be susceptible to transformation [4]. Humans have about 2-3000 times * Allan Balmain

Mammographic density mediates the protective effect of early-life body size on breast cancer risk

“…Uncovering the mechanistic links in both relationships (as partly done in this work with respect to childhood body size) will identify different pathways that could be modifiable and, together, could contribute a very substantial component of modifiable breast cancer risk. Another important consideration relating to mechanistic links is the distinction between mutagenesis and promoters in breast cancer causation 56 , which may also contribute to the differential effects of childhood adiposity and age at menarche on breast cancer risk.…”

Oncogenic RAS drives rapid onset cellular plasticity and elicits a tumour-promoting neutrophil response at the inception of preneoplastic development

“…Tumours are initiated by clonal expansion of mutated somatic cells that have oncogenic potential, but the immediate subsequent steps that enable mutant cells to progress toward cancer in vivo remain unclear 2,3,4 . Mutations in oncogenes or tumour-suppressors genes reported to confer a cell with uncontrolled proliferative capacity and enhanced invasive properties in vitro , do not necessarily confer mutant cells with advantages that out-compete normal cells to form a tumour in vivo ; indeed, it is now clear that a permissive cellular and tissue environment is also necessary for tumour initiation 5, 6, 7 . Recent deep sequencing studies have revealed that a significant proportion of cells in healthy human epithelial tissues carry cancer-driving mutations that appear to have undergone clonal expansion but do not proceeded to form tumours 8, 9, 10, 11, 12, 13, 14, 15 .…”