Incomplete penetrance: The role of stochasticity in developmental cell colonization.

Cell colonization during embryonic development involves cells migrating and proliferating over growing tissues. Unsuccessful colonization, resulting from genetic causes, can result in various birth defects. However not all individuals with the same mutation show the disease. This is termed incomplete penetrance, and it even extends to discordancy in monozygotic (identical) twins. A one-dimensional agent-based model of cell migration and proliferation within a growing tissue is presented, where the position of every cell is recorded at any time. We develop a new model that approximates this agent-based process - rather than requiring the precise configuration of cells within the tissue, the new model records the total number of cells, the position of the most advanced cell, and then invokes an approximation for how the cells are distributed. The probability mass function (PMF) for the most advanced cell is obtained for both the agent-based model and its approximation. The two PMFs compare extremely well, but using the approximation is computationally faster. Success or failure of colonization is probabilistic. For example for sufficiently high proliferation rate the colonization is assured. However, if the proliferation rate is sufficiently low, there will be a lower, say 50%, chance of success. These results provide insights into the puzzle of incomplete penetrance of a disease phenotype, especially in monozygotic twins. Indeed, stochastic cell behavior (amplified by disease-causing mutations) within the colonization process may play a key role in incomplete penetrance, rather than differences in genes, their expression or environmental conditions.