Cell cycles and growth laws: the CCC model.
In the cell-cycle-with-control model (CCC model), cells have to satisfy a condition before they are allowed to pass a control point during G1. Different cycle durations within a cell population are explained by individual time spans needed to satisfy the passing condition. If the distribution of cycle durations is time invariant, the population will grow exponentially. However, if the average cycle duration becomes longer, while the population grows, non-exponential population growth results. Simple functions for the lengthening of the average cycle duration, like linear or exponential ones, yield the well-known growth laws found in the biological literature. The same functions can be represented by an "S-system" differential equation that was derived earlier as an approximation for biochemical systems with many fast reactions (metabolism) and one slow process (e.g. ageing).