Information recovery in molecular biology: causal modelling of regulated promoter switching experiments

The recovery of information from indirect measurements takes different forms depending on the sophistication with which the process being researched can be modelled mathematically. The forms range from (1) the historical and classical inverse problems regularization situation where explicit models which guaranteed existence and uniqueness have been formulated, through (2) situations where model formulation is performed implicitly as a calibration-and-prediction ansatz, to (3) the exploratory (biology) situation where the underlying mechanism is unknown and constraining information about its dynamics is being sought through appropriate experimentation. Each represents a different aspect of the solution of inverse problems. It is the nature of the exploratory form that is discussed in this paper. The focus is the causal modelling of regulated promoter switching experiments performed to understand the dynamics of the genetic control of various biological developmental processes such as vernalization in plants; in particular, regulated promoter switching experiments used to examine the relationship between FLC transcription activity and the associated histone H3 lysine 27 trimethylation at a vernalization-responsive gene in plants. Using a causal representation with Kohlrausch function fading memory, it is shown how such modelling can be used to quantitatively assess the closeness of the linking of one biological process with another, and, in particular, to conclude that the dynamics of FLC transcription and associated H3K27me3 activity are closely linked biologically.