Abstract
Genes are connected in complex networks of interactions where often the product of one gene is a transcription factor that alters the expression of another. Many of these networks are based on a few fundamental motifs leading to switches and oscillators of various kinds. And yet, there is more to the story than which transcription factors control these various circuits. These transcription factors are often themselves under the control of effector molecules that bind them and alter their level of activity. Traditionally, much beautiful work has shown how to think about the stability of the different states achieved by these fundamental regulatory architectures by examining how parameters such as transcription rates, degradation rates and dissociation constants tune the circuit, giving rise to behavior such as bistability. However, such studies explore dynamics without asking how these quantities are altered in real time in living cells as opposed to at the fingertips of the synthetic biologist's pipette or on the computational biologist's computer screen. In this paper, we make a departure from the conventional dynamical systems view of these regulatory motifs by using statistical mechanical models to focus on endogenous signaling knobs such as effector concentrations rather than on the convenient but more experimentally remote knobs such as dissociation constants, transcription rates and degradation rates that are often considered. We also contrast the traditional use of Hill functions to describe transcription factor binding with more detailed thermodynamic models. This approach provides insights into how biological parameters are tuned to control the stability of regulatory motifs in living cells, sometimes revealing quite a different picture than is found by using Hill functions and tuning circuit parameters by hand.