Cell proliferation and migration are two of the key processes regulating the growth rate and structure of engineered tissues. These important cellular processes are strongly influenced by the extracellular environment. Extracellular pH and the concentrations of dissolved oxygen, sugar sources, and growth factors are among the many factors that affect the dynamics of the cell cycle. They are all linked to the cell cycle by regulating the amount of energy and protein in the cell. ATP is an energy carrier that plays a crucial role in the cell cycle. It is necessary for phosphorylating the substrates of the key kinases that regulate the cell cycle. ATP is also necessary to synthesize proteins involved in the cell cycle.

In an earlier work, we utilized a bottom-up approach to develop a dynamic model that captured the ideal mitotic oscillator behavior while incorporating the current biological knowledge. Here, we will utilize a similar approach to link the mitotic oscillator to the extracellular environment by incorporating ATP into our model that now includes four coupled subsystems:

a)The subsystem responsible for activating the metaphase promoting factor (MPF) which triggers cellular division when it reaches some critical concentration.

b)The subsystem producing phosphorylated Cdc25A species that activate MPF and are stabilized by MPF, thereby forming a positive feedback loop.

c)The subsystem producing phosphorylated Wee1 species that inhibit MPF and are inhibited and destabilized by MPF, thereby forming a double negative or positive feedback loop.

d)The subsystem leading to the activation of the anaphase promoting complex (APC) which becomes activated by MPF and, in turn, contributes to the degradation of MPF and Cdc25A species, thus forming a negative feedback loop.

ATP is incorporated into the model in two different places. First, MPF and Wee1 must bind to ATP to phosphorylate their substrates. In addition, ATP is necessary for synthesizing MPF, Wee1, and Cdc25A.

A sensitivity analysis was performed to elucidate the effect of model parameters on the oscillatory characteristics of our system. Specifically, we investigated the effects of each parameter on the size of the oscillatory region, the amplitude and period of the oscillations, and whether or not the oscillations were frequency encoded. We also searched for the region of the parameter space that exhibited multiple steady states since hysteresis has been observed experimentally in the MPF subsystem.

While it is known that MPF inhibits Wee1 via two different pathways, there is still significant uncertainty about the structure of the underlying network. To elucidate the mechanism of Wee1 inhibition, we analyzed four different reaction networks that lead to Wee1 inhibition and studied the effect of these networks on the oscillatory characteristics of the mitotic oscillator.

Finally, we linked the intracellular ATP to extracellular glucose and incorporated substrate limitations into the protein synthesis rates. This model can now be tuned to multiple cell lines that grow under different extracellular glucose concentrations. Although glucose (or any single nutrient) is not the only environmental condition affecting cell proliferation, this work is an important first step in capturing the effects of the extracellular environment on the mitotic oscillator and advances our ability to accurately model tissue regeneration processes.