Design of a MAPK signalling cascade balances energetic cost versus accuracy of information transmission

Abstract

Cellular processes are inherently noisy, and the selection for accurate responses in presence of noise has likely shaped signalling networks. Here, we investigate the trade-off between accuracy of information transmission and its energetic cost for a mitogen-activated protein kinase (MAPK) signalling cascade. Our analysis of the pheromone response pathway of budding yeast suggests that dose-dependent induction of the negative transcriptional feedbacks in this network maximizes the information per unit energetic cost, rather than the information transmission capacity itself. We further demonstrate that futile cycling of MAPK phosphorylation and dephosphorylation has a measurable effect on growth fitness, with energy dissipation within the signalling cascade thus likely being subject to evolutionary selection. Considering optimization of accuracy versus the energetic cost of information processing, a concept well established in physics and engineering, may thus offer a general framework to understand the regulatory design of cellular signalling systems.

Fig. 1. Activation of the pheromone response pathway induces multiple feedback loops.

a Simplified depiction of the pathway and its feedback regulators. Activation of the pheromone receptor Ste2 leads, through a signalling cascade, to activation of MAP kinase Fus3. Fus3-dependent phosphorylation of transcriptional activator Ste12 stimulates the expression of Ste2 and Fus3 as well as of two negative pathway regulators: Sst2, a GTPase activating protein (GAP) for Gα protein Gpa1; and Msg5, a phosphatase for Fus3. These upregulated components are coloured according to relative EC₅₀ values (normalized to the lowest value, approximately 4 nM for STE2) of their mRNA dose responses; mRNA levels of pathway components in white boxes were not upregulated. Black arrows denote transcriptional feedback regulation, green (dashed) arrows denote (indirect) activation and red blunt-end arrows indicate inhibiting activity. b Dose dependence of pheromone activation for the indicated genes encoding pathway components. Shown are normalized RNA levels as measured in two independent RNA sequencing experiments (symbols with and without frames, respectively) at 60 min after addition of respective dose of pheromone in a strain deleted for α-pheromone protease gene BAR1 (Supplementary Table 1). Lines are fits with a sigmoidal function used to infer EC₅₀ values, used for the colour scale in a, b.

Fig. 2. Negative feedback regulators improve accuracy of input estimation and information transmission.

a Dose dependence of pathway activation, measured using activity of a P_FUS1-GFP pathway reporter, for wild type (black) and strains deleted for negative regulators (colours as indicated). Data were collected between 140 and 210 min after pheromone addition, using time-lapse microscopy (see “Methods”), in two independent experiments (shown with different symbols). Dashed lines connect means for both experiments and serve as a guide to the eye; shaded areas centred on those lines show cell-to-cell variabilities (s.d.) across the cell populations, again averaged over both experiments with at least 300 cells per point and experiment. b Pathway noise, calculated as the coefficient of variation of P_FUS1-GFP levels across the population, in the individual experiments (symbols as in a), plotted against the P_FUS1-GFP output. Dashed lines connect the means of noise and P_FUS1-GFP output for both independent experiments. c, d Fisher (c) and mutual (d) information, calculated as described in “Methods” independently for both experiments (symbols are as in a). Notably, although mutual information was calculated between the pheromone input and the pathway output, it was plotted against the pathway output at a particular pheromone input for better comparison between strains that have different sensitivities to pheromone. Dashed lines connect means for both independent experiments. Fisher and mutual information are not shown for sst2Δ strain. Insets in a–d show results of stochastic simulations using a simplified mathematical model of the pheromone pathway (see main text). e Aggregated, i.e. summed up over the whole output range, Fisher (left) and mutual (right) information, with individual contributions at different output levels shown in different shades of grey. Aggregated information was calculated from means for both independent experiments. Edges of bars are coloured according to the strains as indicated in a.

Fig. 3. Sensitized MSG5 induction leads to improved input estimation.

a Dependence of simulated Fisher information on sensitivity of MSG5 feedback induction, altered by adjusting the parameter defining binding affinity of active Ste12-P to the MSG5 promoter (K_D P_MSG5). For simulation of the wild type in Fig. 2, K_D was 700 nM. b–d Effect of sensitized MSG5 feedback induction on dose dependence of the pathway response (b), noise (c) and Fisher information (d). MSG5 induction was sensitized by replacing its native promoter with P_FUS1 promoter that responds with higher sensitivity to pheromone. Data were acquired between 110 and 170 min after pheromone addition in two independent experiments (shown with different symbols in b–d). Dashed lines serve as guides to the eye and connect means for both experiments; shaded areas in b centred on those lines show cell-to-cell variabilities (s.d.) across the cell populations, again averaged over both experiments. Similar results were observed when MSG5 induction was sensitized using other promoters (Supplementary Fig. 6). Inset in d shows aggregated Fisher information calculated with means for both experiments.

Fig. 4. Induction of negative feedback regulators may balance accuracy versus energy investment.

a Simulated dependence of pathway accuracy (information) on sensitivities of SST2 and MSG5 induction. The heat map shows total Fisher information of active Fus3 (Fus3-PP) over the same 5 × 10⁶ range of stimulus strength (see main text and Supplementary Fig. 8 for details) for varying binding affinities (K_D) of Ste12-P to SST2 and MSG5 promoters. b, c Simulated energy (ATP+GTP) consumption rates as a function of relative active Fus3 (Fus3-PP normalized to maximum per plot) for different induction sensitivities of SST2 (b) and MSG5 (c). Binding affinities of Ste12-P to SST2 and MSG5 promoters were changed individually while keeping affinity to the respective other promoter fixed at 8 nM. d Simulated dependence of information per energy on sensitivities of feedback induction. The heat map shows total Fisher information per energy (see text for details) simulated as in a. e Cartoon illustrating difference between energetic costs of negative feedback regulation at two stages of a simulated signalling cascade. Here, activities of two consecutive positive regulators (X and Y), indicated by filling heights of the respective circles, are determined by the influx (e.g. phosphorylation) and outflux (e.g. dephosphorylation) rates of energy. Influx rates at the upper (lower) level depend on the signal strength (e.g. pheromone stimulation) and activity of the upstream regulator, respectively. Outflux rate constants (r_X, r_Y) correlate with the activities of negative regulators (e.g. phosphatases). Red colour indicates increase in quantities compared to the initial situation (upper panel). In order to sustain constant cascade output Y_active while increasing r_x (middle panel), the increased outflux requires compensation by higher influx into X (i.e. stronger stimulation is required to achieve the same output). In this case, increased flux of energy solely at the affected level is sufficient for compensation. However, when increasing r_Y (lower panel), the compensatory higher influx into Y additionally requires an increase in X_active, which in turn requires higher influx into X. Thus compensation of increased r_Y entails increased energy fluxes on both cascade levels.

Fig. 5. Continuous dephosphorylation/phosphorylation of enzymatically inactive Fus3 lowers competitive growth fitness.

a Schematic depiction of employed Fus3 variants. A single amino acid replacement renders Fus3-K42R and -KTY enzymatically inactive and thus incapable of transmitting the signal. Fus3-KTY additionally carries amino acid replacements at both phosphorylation sites. b Fitness cost of phosphorylation cycle, monitored over time as the ratio between mNeongreen (Ng)- and mTurquoise (Tq)-expressing cells grown in a co-culture in the presence of pheromone (20 nM), normalized to the corresponding ratio in absence of pheromone. Different colours depict co-cultures of competing strains that carry different fus3 alleles and fluorescent markers: fus3Δ+Ng vs. fus3Δ+Tq (black), fus3-K42R+Ng vs. fus3-KTY+Tq (green) and fus3-KTY+Ng vs. fus3-K42R+Tq (blue). For each pair, four co-cultures per genotype with independent transformants were tested. Co-cultures were grown for several days with re-inoculation twice a day and flow cytometric measurements once a day to determine ratios of Ng- to Tq-expressing cells. Combinations of fus3-K42R- and -KTY-expressing cells were analysed in two independent experiments (depicted by different symbols), while control of fus3Δ vs. fus3Δ was analysed in one experiment. Lines are linear fits for individual co-cultures. Slopes derived from these fits quantify the rate of divergence of Ng/Tq ratios between co-cultures grown in the presence and absence of pheromone (Inset). Centres and boundaries of boxes in the Inset depict means +/− s.d.; colouring for different co-cultures is according to the main plot. In pairwise comparisons using two-sided t test, p value was 7.08e−5 with 95% confidence interval (CI) ranging from 0.0169 to 0.0338 for fus3Δ-fus3Δ (black, n = 4 biologically independent samples) against K42R-KTY co-cultures (green, n = 4 biologically independent samples examined over 2 independent experiments) and p value was 9.0e−4 with CI from −0.0287 to −0.0105 for fus3Δ-fus3Δ (black) against KTY-K42R co-cultures (blue, n = 4 biologically independent samples examined over 2 independent experiments). c Fitness of mutants with reduced dephosphorylation rate (msg5Δ, left) or abolished phosphorylation (ste7Δ, right) compared to wild type. Wild-type pairs (wt, symbols and colours as in b, dashed lines for linear fits) in co-cultures were same as in b. Each of those strains was subjected to gene deletion and the resulting deletion strains (one and two clones per parental strain for msg5Δ and ste7Δ, respectively) were grown in co-cultures (diamond symbols, solid lines for linear fits) in a competition experiment alongside parental/wild-type co-cultures. Insets show divergences of ratios between fus3-KTY- and -K42R-expressing cells between co-cultures grown in the presence or absence of pheromone, as derived from the slopes of linear fits shown in the main figures. Centres and boundaries of boxes in the inset depict means +/− s.d. In pairwise comparisons with two-sided t test, p value was 4.62e−5 with CI from 0.0198 to 0.0429 for wild type (n = 8 biologically independent samples) against msg5Δ (n = 8 biologically independent samples) co-cultures and p value was 4.32e−12 with CI from 0.0445 to 0.0577 for wild type against ste7Δ (n = 16 biologically independent samples) co-cultures. To increase throughput, co-cultures were grown here in 96-well plates without shaking, which might explain slightly higher absolute divergence rates in these experiments compared to b where co-cultures were grown in 24-well plates with shaking.