Network Inference and Biological Dynamics

Abstract

Network inference approaches are now widely used in biological applications to probe regulatory relationships between molecular components such as genes or proteins. Many methods have been proposed for this setting, but the connections and differences between their statistical formulations have received less attention. In this paper, we show how a broad class of statistical network inference methods, including a number of existing approaches, can be described in terms of variable selection for the linear model. This reveals some subtle but important differences between the methods, including the treatment of time intervals in discretely observed data. In developing a general formulation, we also explore the relationship between single-cell stochastic dynamics and network inference on averages over cells. This clarifies the link between biochemical networks as they operate at the cellular level and network inference as carried out on data that are averages over populations of cells. We present empirical results, comparing thirty-two network inference methods that are instances of the general formulation we describe, using two published dynamical models. Our investigation sheds light on the applicability and limitations of network inference and provides guidance for practitioners and suggestions for experimental design.

Figure 1

Two published dynamical systems models of cellular processes were used to generate datasets. Single cell trajectories were generated from an SDDE model (Eqn. 1) and averaged under measurement noise and nonlongitudinality due to destructive sampling. (a) Data generated from (a model due to) Cantone et al. [10], describing a synthetic network built in yeast. (b) Data generated from Swat et al. [54], a theory-driven model of the G₁/S transition in mammalian cells.

Figure 2

An empirical comparison of network inference schemes. Simulated experiments based on published dynamical systems allow benchmarking of performance in terms of area under ROC curves (AUR; higher scores correspond to better network inference performance).¹⁶ (a) Even sampling intervals. (b) Uneven sampling intervals.

Figure 3

Investigation of empirical consistency of network estimators, using the Cantone [10] model with even sampling intervals. Area under ROC curves are shown in the large dataset, zero cellular heterogeneity and zero measurement noise limits.

Figure 4

Variance functions used in literature provide partial approximation to the “true” functional form for Cantone et al. [10]. For small time steps a power law Δ^–α provides a good approximation, but for larger time steps a constant variance function may be more appropriate. In practice the precise form of h_true will be unknown.