Peto's "Paradox" and Six Degrees of Cancer Prevalence

Abstract

Peto's paradox and the epidemiologic observation of the average six degrees of tumor prevalence are studied and hypothetically solved. A simple consideration, Petho's paradox challenges our intuitive understanding of cancer risk and prevalence. Our simple consideration is that the more a cell divides, the higher the chance of acquiring cancerous mutations, and so the larger or longer-lived organisms have more cells and undergo more cell divisions over their lifetime, expecting to have a higher risk of developing cancer. Paradoxically, it is not supported by the observations. The allometric scaling of species could answer the Peto paradox. Another paradoxical human epidemiology observation in six average mutations is necessary for cancer prevalence, despite the random expectations of the tumor causes. To solve this challenge, game theory could be applied. The inherited and random DNA mutations in the replication process nonlinearly drive cancer development. The statistical variance concept does not reasonably describe tumor development. Instead, the Darwinian natural selection principle is applied. The mutations in the healthy organism's cellular population can serve the species' evolutionary adaptation by the selective pressure of the circumstances. Still, some cells collect multiple uncorrected mutations, adapt to the extreme stress in the stromal environment, and develop subclinical phases of cancer in the individual. This process needs extensive subsequent DNA replications to heritage and collect additional mutations, which are only marginal alone. Still, together, they are preparing for the first stage of the precancerous condition. In the second stage, when one of the caretaker genes is accidentally mutated, the caused genetic instability prepares the cell to fight for its survival and avoid apoptosis. This can be described as a competitive game. In the third stage, the precancerous cell develops uncontrolled proliferation with the damaged gatekeeper gene and forces the new game strategy with binary cooperation with stromal cells for alimentation. In the fourth stage, the starving conditions cause a game change again, starting a cooperative game, where the malignant cells cooperate and force the cooperation of the stromal host, too. In the fifth stage, the resetting of homeostasis finishes the subclinical stage, and in the fifth stage, the clinical phase starts. The prevention of the development of mutated cells is more complex than averting exposure to mutagens from the environment throughout the organism's lifetime. Mutagenic exposure can increase the otherwise random imperfect DNA reproduction, increasing the likelihood of cancer development, but mutations exist. Toxic exposure is more challenging; it may select the tolerant cells on this particular toxic stress, so these mutations have more facility to avoid apoptosis in otherwise collected random mutational states.

Keywords: Darwin’s law; Peto’s paradox; allometry; evolutional game; mutations; six degrees of stages.

Figure 1

Some cancer-causing occurrences for humans. These are possibilities. All have a nonzero probability of cancer but are not sure to develop a malignancy. Having multiple factors rapidly increases the likelihood of cancerous diseases.

Figure 2

The homeostatic control loop under the permanent random mutations by the nonperfect DNA replication and the changing internal and external conditions. The development of the mutated genetic network needs an energetic decision to repair and spend energy, or it does not care about it because it is decided to be nonharmful. When the mutation could cause lethal damage, repair is necessary, and control is established. When judged as marginal, it was exposed to new mutations accumulated by cell cycles. It could cause apoptosis, which solves the problem, or it could go directly to the cancerous line.

Figure 3

The six stages of cancer growth. The first stage produces precancerous cells by marginalizing some mutations during the repeated cell cycles. In the second stage, the caretaker genes are damaged. Their mutation causes genetic instability. The gatekeeper genes are mutated in the third stage, leaving the growth uncontrolled. The next stage changes the game. The cancer cells cooperatively adapt to the challenges, and the healthy cells support it. The central physiological networks are remodeled in the fifth stage to support malignant growth and invasion. In the last stage, the tumor is clinically manifested. The case could be epidemiologically registered when the cancer leaves the subclinical stages and appears in the clinical statistics.

Figure 4

The malignancy evades immune surveillance. The standard immune control is diverted in all of its steps, causing tumor evasion.

Figure 5

The physiological changes reshape homeostatic control. The charge (injury current), liquid (blood and lymph) transport, and immune inhibition set a condition to reset homeostasis. The consequences are the dissemination of the malignant cells, a particular hormone production, increased diffusional possibilities, and lowered pH. Note that the retuning of the body’s equilibrium supports the tumor-organs hypothesis and does not fit the atavistic explanations.