  Time-course gene expression datasets provide insight into the dynamics of
complex biological processes, such as immune response and organ development. It
is of interest to identify genes with similar temporal expression patterns
because such genes are often biologically related. However, this task is
challenging due to the high dimensionality of these datasets and the
nonlinearity of gene expression time dynamics. We propose an empirical Bayes
approach to estimating ordinary differential equation (ODE) models of gene
expression, from which we derive a similarity metric between genes called the
Bayesian lead-lag $R^2$ (LLR2). Importantly, the calculation of the LLR2
leverages biological databases that document known interactions amongst genes;
this information is automatically used to define informative prior
distributions on the ODE model's parameters. As a result, the LLR2 is a
biologically-informed metric that can be used to identify clusters or networks
of functionally-related genes with co-moving or time-delayed expression
patterns. We then derive data-driven shrinkage parameters from Stein's unbiased
risk estimate that optimally balance the ODE model's fit to both data and
external biological information. Using real gene expression data, we
demonstrate that our methodology allows us to recover interpretable gene
clusters and sparse networks. These results reveal new insights about the
dynamics of biological systems.
