Fig. 5

Outputs of simulated gene regulatory networks with transcriptional adaptation and robustness to mutation dependency on model parameters. A Schematic of a gene regulatory network with transcriptional adaptation to mutation. Two alleles of each gene, with bursty transcription of gene products at each allele. A mutated reference gene, A (dark gray), regulates downstream effector gene B (orange). When mutated, nonsense copies of A product upregulate a paralog of A, called A’ (light gray). A’ can also regulate B, albeit with different strengths. Hill functions are used in propensities for regulatory relationships between gene products and target alleles. See the “Methods” section for full model specification. Parameter descriptions in the table at right of the panel. B Example simulation output and inference of single-cell expression distributions from pseudo-single-cells taken every 300 time-steps. See the “Methods” section. C Example classification of gene expression distribution shapes. See the “Methods” section for classification algorithm. D Analysis schematic: under what network conditions does the network output (i.e., distribution of B expression levels) remain unchanged, either in shape or in average expression level, after mutation of gene A? E Decision tree trained on model parameters to classify parameter sets, restricted to those in which B is unimodal symmetric in the wildtype genotype, by whether B distribution remains unimodal symmetric or if it changes distribution shape class. Nodes marked “robust”: > 70% of considered parameter sets robust, “maybe”: 30–70% robust, “not robust”: < 30% robust. F Analysis schematic: How parameter subspaces for terminal decision tree nodes relate to rules. Each rule limits the parameter subspace for the terminal node. Colored planes correspond to the decision rule-defined thresholds. When a subspace only encodes one decision rule for a given parameter, the subspace range is limited to the corresponding full parameter space boundary (e.g., if a decision rule sets only a new minimum parameter value, then the maximum parameter value for the subspace is the maximum parameter value of the full parameter space). G Mean B expression changes after mutation in each decision tree leaf for unimodal symmetric robust parameter sets. H Parameter subspace bounded by decision tree rules for nodes 15 + 16 in E, resampled. I Enrichment of robustness of both shape and mean for unimodal symmetric distributions of B after mutation, subsampled from the full parameter space and from the subspace marked in D. Robustness of mean here defined as absolute log2 fold-change after mutation < 0.35