General mathematical theory for fluctuations in cells
Our early approach was to consider analytically tractable toy models. Many of the predictions made were later ‘verified’ experimentally, but we derive little confidence from those successes because we have also shown that many other mechanisms make similar predictions. This motivates us to attempt to work towards a more coherent mathematical theory for fluctuations in cells that will allow us to rigorously instantiate general principles for particular examples rather than infer principles by extrapolating from particular examples. The theory will address what we believe are the greatest challenges facing current frameworks: 1) Combinations of fluctuations, nonlinearities, delays, non-exponential waiting times, cell division etc typically make stochastic models analytically intractable. 2) The tradition of accounting for all putative details, and formulating results in terms of specific parameters conceals the broader principles. 3) Most systems are incompletely characterized: one or two steps may be known in detail, others are known only qualitatively, and yet others have not even been identified. Conventional methods must then ignore or guess the unknown interactions. 4) The typical combination of models and theory formulates a specific mathematical model and then ‘tests’ if observations are consistent with predictions. But the tests are often much less useful than they may appear as many different models may fit the same data.
Drawing on a wide range of approaches from probability theory, statistical physics and information theory, we are working on systematic analytical approaches to these problems. This work also informs and guides our experimental projects. Some preliminary examples can be found in our published papers, but the bulk of this work is in preparation or under review.