Adult stem cells,which exist throughout the body,multiply by cell division to replenish dying cells or to promote regeneration to repair damaged tissues.To perform these functions during the lifetime of organs or tissues,stem cells need to maintain their populations in a faithful distribution of their epigenetic states,which are susceptible to stochastic fluctuations during each cell division,unexpected injury,and potential genetic mutations that occur during many cell divisions.However,it remains unclear how the three processes of differentiation,proliferation and apoptosis in regulating stem cells collectively manage these challenging tasks.Here,without considering any molecular details,we propose a genetic optimal control model for adult stem-cell regeneration that includes the three fundamental processes,along with cell division and adaptation based on differential fitnesses of phenotypes.In the model,stem cells with a distribution of epigenetic states are required to maximize expected performance after each cell division.Through analytical estimates and direct numerical simulations,we show that heterogeneous proliferation that depends on the epigenetic states of stem cells can improve the maintenance of stem-cell distributions to create balanced populations.A control strategy during each cell division is derived from the model,leading to a feedback mechanism involving heterogeneous proliferation that can accelerate regeneration with less fluctuation in the stem cell population.When mutation is allowed,apoptosis evolves to maximize the performance during homeostasis after multiple cell divisions.The overall modeling results highlight the importance of crosstalk between genetic and epigenetic regulation and the performance objectives during homeostasis in shaping a desirable heterogeneous distribution of stem cells in terms of epigenetic states.This work is in collaboration with Simon A.Levin from Princeton University and Qing Nie from UC Irvine,and has been published at PNAS (doi:10.1073/pnas.1324267111).