Sparse Regression Based Structure Learning of Stochastic Reaction Networks from Single Cell Snapshot Time Series

Stochastic chemical reaction networks constitute a model class to quantitatively describe dynamics and cell-to-cell variability in biological systems. The topology of these networks typically is only partially characterized due to experimental limitations. Current approaches for refining network topology are based on the explicit enumeration of alternative topologies and are therefore restricted to small problem instances with almost complete knowledge. We propose the reactionet lasso, a computational procedure that derives a stepwise sparse regression approach on the basis of the Chemical Master Equation, enabling large-scale structure learning for reaction networks by implicitly accounting for billions of topology variants. We have assessed the structure learning capabilities of the reactionet lasso on synthetic data for the complete TRAIL induced apoptosis signaling cascade comprising 70 reactions. We find that the reactionet lasso is able to efficiently recover the structure of these reaction systems, ab initio, with high sensitivity and specificity. With only 6000 possible reactions and over 102000 network topologies. In conjunction with information rich single cell technologies such as single cell RNA sequencing or mass cytometry, the reactionet lasso will enable large-scale structure learning, particularly in areas with partial network structure knowledge, such as cancer biology, and thereby enable the detection of pathological alterations of reaction networks. We provide software to allow for wide applicability of the reactionet lasso.Author Summary: Virtually all biological processes are driven by biochemical reactions. However, their quantitative description in terms of stochastic chemical reaction networks is often precluded by the computational difficulty of structure learning, i.e. the identification of biologically active reaction networks among the combinatorially many possible topologies. This work describes the reactionet lasso, a structure learning approach that takes advantage of novel, information-rich single cell data and a tractable problem formulation to achieve structure learning for problem instances hundreds of orders of magnitude larger than previously reported. This approach opens the prospect of obtaining quantitative and predictive reaction models in many areas of biology and medicine, and in particular areas such as cancer biology, which are characterized by significant system alterations and many unknown reactions.