Significance Controlled transitions of human cells between proliferating and nonproliferating states are essential for normal development and tissue homeostasis. To understand how the decision to proliferate is made in response to positive input from growth factors and negative input from the DNA damage response, we have built a mathematical model of the underlying molecular network, based on data from live cell-imaging experiments. Our model suggests that two major cell-cycle transitions are crucial for decision making: the restriction point, which integrates pro- and antiproliferative signals, and the G1/S transition, which temporarily insulates cells from some aspects of the DNA damage response. Together, our model gives mechanistic insight into how cells maintain both sensitivity and robustness to external signals.