Feed-forward regulation adaptively evolves via dynamics rather than topology when there is intrinsic noise

Abstract

In transcriptional regulatory networks (TRNs), a canonical 3-node feed-forward loop (FFL) is hypothesized to evolve to filter out short spurious signals. We test this adaptive hypothesis against a novel null evolutionary model. Our mutational model captures the intrinsically high prevalence of weak affinity transcription factor binding sites. We also capture stochasticity and delays in gene expression that distort external signals and intrinsically generate noise. Functional FFLs evolve readily under selection for the hypothesized function but not in negative controls. Interestingly, a 4-node "diamond" motif also emerges as a short spurious signal filter. The diamond uses expression dynamics rather than path length to provide fast and slow pathways. When there is no idealized external spurious signal to filter out, but only internally generated noise, only the diamond and not the FFL evolves. While our results support the adaptive hypothesis, we also show that non-adaptive factors, including the intrinsic expression dynamics, matter.

Fig. 1

Overview of the model. a Simulation of gene expression phenotypes. We show a simple TRN with one TF (yellow) and one effector gene (blue), with arrows for major biological processes simulated in the model. b Phenotype–fitness relationship. Fitness is primarily determined by the concentration of an effector protein (here shown as beneficial as in Eq. 4, but potentially deleterious in a different environment as in Eq. 5), with a secondary component coming from the cost of gene expression (proportional to the rate of protein production), combined to give an instantaneous fitness at each moment in gene expression time. c Evolutionary simulation. A single resident genotype is replaced when a mutant’s estimated fitness is high enough. Stochastic gene expression adds uncertainty to the estimated fitness, allowing less fit mutants to occasionally replace the resident, capturing the flavor of genetic drift

Fig. 2

The distribution of TFBSs determines the regulatory logic of effector expression. We use the pattern of TFBSs (red and yellow bars along black cis-regulatory sequences) to classify the regulatory logic of the effector gene. C1-FFLs are classified first by whether or not they are capable of simultaneously binding the signal and the TF (left 4 vs. right 3; see Supplementary Fig. 2 and Supplementary Methods for details about overlapping TFBSs). Further classification is based on whether either the signal or the TF has multiple nonoverlapping TFBSs, allowing it to activate the effector without help from the other (solid arrow). The three subtypes to the right (where the signal and TF cannot bind simultaneously) are rarely seen; they are unless otherwise indicated included in “Any logic” and “non-AND-gated” tallies, but are not analyzed separately. Two of them involve emergent repression, creating incoherent feed-forward loops (see Supplementary Fig. 1 for full FFL naming scheme). Emergent repression occurs when the binding of one activator to its only TFBS prevents the other activator from binding to either of its two TFBSs, hence preventing simultaneous binding of two activators

Fig. 3

Selection for filtering out short spurious signals. Each selection condition averages fitness across simulations in two environments. The effectors have different fitness effects in the two environments, and the signal also behaves differently in the two environments. Simulations begin with zero mRNA and protein, and all genes at the Repressed state (see Methods). Each simulation is burned in for a randomly sampled length of time in the absence of signal (shown here as 10 min in environment 1, and 15 min in environment 2), and continues for another 90 min after the burn-in. The signal is shown in black. Red illustrates a good solution in which the effector responds appropriately in each of the environments, while blue shows an inferior solution. N_{e_sat} marks the amount of effector protein at which the benefit from expressing the effector in environment 1 becomes saturated, as does the damage in environment 2 (see Methods). See Supplementary Fig. 3 for examples of high-fitness and low-fitness evolved phenotypes, where, as shown in this schematic, high-fitness solutions have longer delays followed by more rapid responses thereafter

Fig. 4

AND-gated C1-FFLs are associated with a successful response to selection. a Distribution of fitness outcomes across replicate simulations, calculated as the average fitness over the last 10,000 steps of the evolutionary simulation. We divide genotypes into a low-fitness group (blue) and a high-fitness group (red) using as a threshold an observed gap in the distribution. b High-fitness replicates are characterized by the presence of an AND-gated C1-FFL. “Any logic” counts the presence of any of the seven subtypes shown in Fig. 2b. Because one TRN can contain multiple C1-FFLs of different subtypes, each of which are scored, the sum of the occurrences of all seven subtypes will generally be more than “Any logic”. See Supplementary Methods for details on the calculation of the y axis. c The overrepresentation of AND-gated C1-FFLs becomes even more pronounced relative to alternative logic-gating when weak (two-mismatch) TFBSs are excluded while scoring motifs. Data are shown as mean ± s.e.m. of the occurrence over replicate evolution simulations

Fig. 5

Destroying the AND-logic of a C1-FFL removes its ability to filter out short spurious signals. a For each of the n = 25 replicates in the high-fitness group in Fig. 4, we perturbed the AND-logic in two ways, by adding one binding site of either the signal or the slow TF to the cis-regulatory sequence of the effector gene. b For each replicate, the fitness of the original motif (blue) or of the perturbed motif (red or orange) was averaged across the subset of evolutionary steps with an AND-gated C1-FFL and lacking other potentially confounding motifs (see Supplementary Fig. 4 and Supplementary Methods for details). Destroying the AND-logic slightly increases the ability to respond to the signal, but leads to a larger loss of fitness when short spurious signals are responded to. Fitness is shown as mean ± s.e.m. over replicate evolutionary simulations

Fig. 6

Selection for filtering out short spurious signals is the primary cause of C1-FFLs. TRNs are evolved under different selection conditions, and we score the probability that at least one C1-FFL is present (see Supplementary Methods). Schematics of selection, in which fitness is averaged with weights 2:1 over environment 1:2, are shown in (a). The effector is deleterious in environment 1 except in the “harmless” and “no selection” conditions. Weak (two-mismatch) TFBSs are included in (b) and are excluded in (c) during motif scoring. Data are shown as mean ± s.e.m. over evolutionary replicates. C1-FFL occurrence is similar for high-fitness and low-fitness outcomes in control selective conditions (Supplementary Fig. 5), and so all evolutionary outcomes were combined. “Spurious signal filter required (high fitness)” uses the same data as in Fig. 4

Fig. 7

AND-gated C1-FFLs and diamonds are associated with high fitness in complex networks. Out of 238 simulations (Supplementary Fig. 6), we took the 30 with the highest fitness (H), the 30 with the lowest fitness (L), and 30 of around median fitness (M). AND-gated motifs are scored while including weak TFBSs in the effectors’ cis-regulatory regions, near-AND-gated motifs are those scored only when these weak TFBSs are excluded. a Diagrams of enriched motifs when weak TFBSs are included. It is possible for the same genotype to contain one of each, resulting in overlap between the red AND-gated columns and the dotted near-AND-gated columns. Weak TFBSs upstream in the TRN, i.e. not in the effector, are shown both included (b) and excluded (c). See Supplementary Methods for y-axis calculation details. Error bars show mean ± s.e.m. of the proportion of evolutionary steps containing the motif in question, across replicate evolutionary simulations

Fig. 8

The two TFs in an AND-gated diamond propagate the signal at different speeds. Expression of the two TFs in one representative genotype from the one high-fitness evolutionary replicate in Fig. 7b that evolved an AND-gated isolated diamond is shown. Both the slow TF and the fast TF are encoded by three gene copies, shown separately in color, with the total for each TF in thick black. The expression of one TF plateaus faster than that of the other; this is characteristic of the AND-gated diamond motif, and leads to the same functionality as the AND-gated C1-FFL

Fig. 9

Isolated C1-FFLs and diamonds rely on AND gates to filter out short spurious signals. We add a TFBS of either the fast TF or the slow TF to break the AND gate. This slightly increases the ability to respond to the signal, but leads to a larger loss of fitness when effector expression is undesirable. We perform the perturbation on a 8 of the 18 high-fitness replicates from Fig. 7b that evolved an AND-gated C1-FFL, b 4 of the 26 high-fitness replicates that evolved an AND-gated diamond in Fig. 7b, and c 15 of the 37 replicates that evolved an AND-gated diamond in response to selection for signal recognition in the absence of an external spurious signal (Fig. 10b). Replicate exclusion was based on the co-occurrence of other motifs with the potential to confound results (see Supplementary Methods for details). Fitness is shown as mean ± s.e.m. of over replicate evolutionary simulations, calculated as described for Fig. 5

Fig. 10

AND-gated diamonds, but not AND-gated C1-FFLs, also evolve in negative controls. a Selection for filtering out a short spurious signal is the primary way to evolve AND-gated isolated C1-FFLs, but b AND-gated isolated diamonds also evolve in the absence of spurious signals. The selection conditions are the same as in Fig. 6, but we do not allow the signal to directly regulate the effector. In the “no spurious signal” and “harmless spurious signal” control conditions, motif frequencies are similar between low- and high-fitness genotypes (Supplementary Figs. 8 and 9), and so our analysis includes all evolutionary replicates. When scoring motifs, we exclude all two-mismatch TFBSs; results with inclusions, and for FFL-in-diamonds, are shown in Supplementary Fig. 10. Many non-AND-gated diamonds have the “no regulation” logic in Fig. 2, perhaps as an artifact created by the duplication and divergence of intermediate TFs; we excluded them from the “Any logic” and “Non-AND-gated” tallies in (b). See Supplementary Methods for the calculation of the y-axis. Data are shown as mean ± s.e.m. over evolutionary replicates. We reused data from Fig. 7 for “Spurious signal filter required (high fitness)”