  The gene networks that comprise the circadian clock modulate biological
function across a range of scales, from gene expression to performance and
adaptive behaviour. The clock functions by generating endogenous rhythms that
can be entrained to the external 24-h day?night cycle, enabling organisms to
optimally time biochemical processes relative to dawn and dusk. In recent
years, computational models based on differential equations have become useful
tools for dissecting and quantifying the complex regulatory relationships
underlying the clock's oscillatory dynamics. However, optimizing the large
parameter sets characteristic of these models places intense demands on both
computational and experimental resources, limiting the scope of in silico
studies. Here, we develop an approach based on Boolean logic that dramatically
reduces the parametrization, making the state and parameter spaces finite and
tractable. We introduce efficient methods for fitting Boolean models to
molecular data, successfully demonstrating their application to synthetic time
courses generated by a number of established clock models, as well as
experimental expression levels measured using luciferase imaging. Our results
indicate that despite their relative simplicity, logic models can (i) simulate
circadian oscillations with the correct, experimentally observed phase
relationships among genes and (ii) flexibly entrain to light stimuli,
reproducing the complex responses to variations in daylength generated by more
detailed differential equation formulations. Our work also demonstrates that
logic models have sufficient predictive power to identify optimal regulatory
structures from experimental data. By presenting the first Boolean models of
circadian circuits together with general techniques for their optimization, we
hope to establish a new framework for the systematic modelling of complex
clocks.
