Automatic inference of multicellular regulatory networks using informative priors

Abstract

To fully understand the mechanisms governing animal development, computational models and algorithms are needed to enable quantitative studies of the underlying regulatory networks. We developed a mathematical model based on dynamic Bayesian networks to model multicellular regulatory networks that govern cell differentiation processes. A machine-learning method was developed to automatically infer such a model from heterogeneous data. We show that the model inference procedure can be greatly improved by incorporating interaction data across species. The proposed approach was applied to C. elegans vulval induction to reconstruct a model capable of simulating C. elegans vulval induction under 73 different genetic conditions.

Figure 1

C. elegans vulval induction: (a) during the L3 stage of worm development, an inductive signal from the Anchor Cell (AC) and the lateral signals among the six multipotent VPCs (named P3.p, P4.p, P5.p, P6.p, P7.p, and P8.p) collaboratively specify each VPC to adopt one of the three fates termed 1°, 2°, or 3°. In wildtype C. elegans, VPCs form a precise formation of the 3°-3°-2°-1°-2°-3° pattern. The thickness of arrows indicates the strength of the signals and (b) the diagrammatic model of the cellular regulatory network controlling the fate of one VPC. Arrow represents activation. Bar represents repression. See text for details

Figure 2

A simple multicellular regulatory model is unrolled along the developmental time line to have T time slices. It consists of six identical cell modules (P3-8) in rounded rectangles. Each cell module contains five nodes representing five cellular network components (A, B, C, D, E). The subscription index of a node denotes the cell ID and the time slice. Nodes E represent the lateral signal among cells. Nodes C represent the receptor of the lateral signal E. To ensure that all cells are structurally and parametrically identical, dumb nodes (in gray) are introduced as additional lateral signals to P3 and P8. The values of dumb nodes are always set to 0 (i.e., no lateral signal). The control nodes (in diamond shape) are used to indicate the genetic states of their children nodes

Figure 3

(a) The interaction map derived from the interaction data of D. melanogaster, H. sapiens, and S. cerevisiae. There are 21 interactions in total and (b) the map derived from the interaction data of C. elegans. There are 85 interactions in the map. Node LS denotes the ligand set (apx-1, dsl-1, and lag-2) of the Notch receptor, and node lst-1_2_4 denotes the gene group consisted of lst-1, lst-2 and lst-4. A link is added between a group node X and another node Y if there is at least one interaction between Y and one of members in X (see online version for colours)

Figure 4

The structure of one of the best vulval induction multicellular regulatory models. Only one cell module is shown. Solid edges are intra-slice links, and dashed edges are inter-slice links. L_LS is the lateral signal from the left neighbouring VPC, i.e., the LS node in the left VPC module. R_LS is the lateral signal from the right neighbouring VPC, i.e., the LS node in the right VPC module. Sum_LS is the signal integration node. dpy-23_lst-3 denotes the gene group of dpy-23 and lst-3, lst-1_2_4 denotes the gene group of lst-1, lst-2 and lst-4. The marker gene of fate 1° is egl-17. Nodes 2° and 3° represent gene groups specific to fates 2° and 3°, respectively