The linear process of somatic evolution

Abstract

Cancer is the consequence of an unwanted evolutionary process. Cells receive mutations that alter their phenotype. Especially dangerous are those mutations that increase the net reproductive rate of cells, thereby leading to neoplasia and later to cancer. The standard models of evolutionary dynamics consider well mixed populations of individuals in symmetric positions. Here we introduce a spatially explicit, asymmetric stochastic process that captures the essential architecture of evolutionary dynamics operating within tissues of multicellular organisms. The "linear process" has the property of cancelling out selective differences among cells yet retaining the protective function of apoptosis. This design can slow down the rate of somatic evolution dramatically and therefore delay the onset of cancer.

Fig. 1.

Two stochastic processes of evolutionary dynamics. (a) In the Moran process, cells are in identical positions. For reproduction, a cell is chosen proportional to its reproductive rate. The offspring of this cell replaces a randomly chosen cell. The total number of cells is always constant. (b) In the linear process, cells are arranged in a row and labeled i = 1,..., N. For reproduction, cells are again chosen proportional to their reproductive rate. The reproducing cell is replaced by two daughter cells. All cells to the right are shifted by one position. The rightmost cell undergoes apoptosis (falls off the edge of the one-dimensional table). The linear process captures fundamental properties of the architecture of cell division in multicellular organisms. We propose that this architecture evolved to delay the onset of cancer. In the linear process, mutations in oncogenes or tumor suppressor genes that increase the reproductive rate of cells accumulate as slowly as neutral mutations.

Fig. 2.

The architecture of the linear process facilitates a number of mechanisms that slow down the unwanted somatic evolution leading to cancer. The cell in position i = 1 functions like a stem cell for this compartment. (a) Mutations that do not occur in stem cells are washed out. (b) If mutated stem cells undergo apoptosis, then mutated compartments can become entirely wild-type, given that cells in position i = 2 take over the stem cell function, or the whole compartment might die. Both processes prevent the accumulation of mutated cells. (c) If stem cells divide only once every 10 days, whereas all other cells divide once per day, then the rate of evolution in the linear process is reduced by a factor of 10.