Figure 1.
Schematics of Analytic Approaches and Network Determination Algorithm
(A) Networks of module regulation were analyzed along four conceptual axes: (1) regulatory implications—if module 1 (purple) represses module 2 (blue), then an increase in the expression of module 1 will trigger a later reduction in the expression level of module 2; (2) behavior across scales—modules 1 and 2 are composed of genes that comprise parts of modules at finer scales with their own regulatory interactions; (3) the effect of module 1 on module 2 may vary depending on the length of the intervening time interval; and (4) module 1 and 2 may correspond to processes described by the GO database, such as protein synthesis or mitochondria.
(B) Schematic of the algorithm used to generate multiscale networks of regulation from the same global collection of genes. Genes are divided into groups by similarity of behavior, and the mutual regulatory influences are determined. The process is repeated with a larger number of groups.
Figure 2.
Effective Regulatory Influences at Many Scales (Top to Bottom) over a 1.5-h Interval
(A,E,I,M) Regulatory influence networks, with red arrows indicating inhibition and black activation. An influence is included if the magnitude of its mean across all regulatory contexts is more than twice its standard deviation. Predominantly activating modules (green boxes), predominant inhibitors (red boxes), and modules without outputs (white boxes) are adjacent. Numbers in boxes are SOM module numbers.
(B–C,F–G,J–K,N–O) Average magnitudes of outputs (B,F,J,N) and inputs (C,G,K,O) of modules arranged in SOM array order. Stronger inhibition, activation, or neither are indicated by brighter red, green, or gray, respectively.
(D,H,L,P) Complete unthresholded n × n regulatory transition matrices. Rows are sorted by similarity in functional inputs, and columns are sorted by similarity in functional outputs.
Figure 3.
Scaling Properties of Regulatory Networks
(A) Sparseness (number of regulatory interactions divided by the total number of possible interactions) plotted versus number of modules (scale).
(B) Distribution of number of regulatory inputs at each scale.
(C) Distribution of number of regulatory outputs at each scale.
(D) Power-law fit of the module output number distribution in the n = 72 case.
(E) The quality (r2) of power-law fits to module output (black) and input (gray) distributions versus scale, showing increasingly good fit for output distributions.
(F) The fraction of modules that are activating (green), inhibiting (red), mixed activating and inhibiting (yellow), or nonregulatory targets (blue) versus scale.
(G) Regulatory influence magnitude distributions at all scales (log-linear plot). The data are approximately exponential (line). Influences were included here if the standard deviation of their estimation replicates was less than 1, regardless of the mean.
(H) The correlation (r) across modules of the average regulatory input and output versus scale. Note the negative y-axis scale.
Figure 4.
Targets of Module Regulation, Showing Increasing Specificity at Finer Scales
(A) Examples of regulatory targets. Activated (green) or inhibited (red) modules of the regulatory module marked in gray. Influences passing the edge inclusion threshold are shown. Targeted modules tend to be spatially localized in the SOM array, i.e., modules expressed similarly across perturbations tend to receive inputs from the same activators and inhibitors).
(B–E) Target influence SOM arrays (unthresholded) clustered by similarity at n = 12, 20, 42, and 72 (B–E, respectively). For example, the first array in (A) corresponds to module 8 in (E) (second row, second position from the right).
(F) The degree of target specificity (fraction of branch points not on the longest arm of the clustering tree) versus network scale. The sigmoidal shape of this curve is suggestive of a transition around n = 30 from global regulation to higher target specificity.
Figure 5.
Contribution of Smaller-Scale Modules to Larger-Scale Modules and Aggregation of Ontological Function
(A–C) Mappings of modules at finer scales (right array) to larger scales (left array). Size of a wedge of a particular color indicates the fraction of genes in that module that were placed in the larger-scale module of matching color. All arrays are in the SOM order.
(D) Colored outer circles indicate representative GO category labels that are statistically overrepresented in modules at n = 12 and 20. Inner circles are the same as (A).
(E) Individual GO labels within the GO category transcription regulation clustered by similarity of their enrichment fraction across the n = 12 and 20 SOM modules. Gray and blue indicate under- and overrepresentation, respectively. See scale.
(F) Similar to (E) for the GO category lipid processing.
(G) GO labels appearing 10 or more times clustered by distribution across the n = 12 and 20 modules. Doubly outlined boxes indicate clades with closely related function. Singly outlined boxes are within four branches of functionally related ontologies, indicated by the arcs.