  Biological structure and function depend on complex regulatory interactions
between many genes. A wealth of gene expression data is available from
high-throughput genome-wide measurement technologies, but effective gene
regulatory network inference methods are still needed. Model-based methods
founded on quantitative descriptions of gene regulation are among the most
promising, but many such methods rely on simple, local models or on ad hoc
inference approaches lacking experimental interpretability. We propose an
experimental design and develop an associated statistical method for inferring
a gene network by learning a standard quantitative, interpretable, predictive,
biophysics-based ordinary differential equation model of gene regulation. We
fit the model parameters using gene expression measurements from perturbed
steady-states of the system, like those following overexpression or knockdown
experiments. Although the original model is nonlinear, our design allows us to
transform it into a convex optimization problem by restricting attention to
steady-states and using the lasso for parameter selection. Here, we describe
the model and inference algorithm and apply them to a synthetic six-gene
system, demonstrating that the model is detailed and flexible enough to account
for activation and repression as well as synergistic and self-regulation, and
the algorithm can efficiently and accurately recover the parameters used to
generate the data.
