Learning a nonlinear dynamical system model of gene regulation: A perturbed steady-state approach

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.