Sharing of Phosphatases Promotes Response Plasticity in Phosphorylation Cascades  Bhaswar Ghosh, Uddipan Sarma, Victor Sourjik, Stefan Legewie  Biophysical Journal  Volume 114, Issue 1, Pages 223-236 (January 2018) DOI: 10.1016/j.bpj.2017.10.037 Copyright © 2017 Biophysical Society Terms and Conditions

Figure 1 The degree of phosphatase sharing enhances robustness of bistability. (A–C) Schematic representation of the studied topologies of phosphorylation cascades. In the unshared case, four phosphatases (P1, P2, P3, P4) dephosphorylate the single- (MAPKK-P, MAPK-P) and double-phosphorylated (MAPKK-PP, MAPK-P) forms of the kinases (A). In the partially shared case (B), two specific phosphatases, P1dual and P2dual, respectively dephosphorylate MAPKK and MAPK layers completely. In the fully shared phosphatase case (C), the phosphatase (shown as P1shared) dephosphorylates the MAPKK and the MAPK. Light and dark ellipses represent monostable and bistable cascades with unshared phosphatases (blue), partially shared phosphatases (red), and fully shared phosphatase (cyan). (D) The percentages of bistable responses are shown for fully shared (25%), partially shared (10%), and unshared (5%) cascades obtained from 10,000 independently sampled parameters for each phosphatase-sharing design. (E) The mutational robustness (MR) for monostable (left panel) and bistable (right panel) responses as a function of the number of mutations are shown. To see this figure in color, go online. Biophysical Journal 2018 114, 223-236DOI: (10.1016/j.bpj.2017.10.037) Copyright © 2017 Biophysical Society Terms and Conditions

Figure 2 Robustness of bistability arises due to emergence of intrinsic positive feedback by phosphatase sharing. (A) The response coefficient from MAPK-PP to MAPKK-PP as a function of the shared phosphatase concentration at different input doses for the fully shared cascade (input doses are indicated as signal). (B) The dependence of the fraction of bistability on the shared phosphatase concentration for 100 different bistable parameter sets for the fully shared cascade. (C) The dependence of the fraction of bistability on the two shared phosphatase concentrations (indicated as P1dual and P2dual) for 100 different bistable parameter sets for the partially shared cascade. (D) The dependence of the fraction of bistability on the four phosphatase concentrations (indicated as P1, P2, P3, and P4) for 100 different bistable parameter sets for the unshared cascade. To see this figure in color, go online. Biophysical Journal 2018 114, 223-236DOI: (10.1016/j.bpj.2017.10.037) Copyright © 2017 Biophysical Society Terms and Conditions

Figure 3 Schematic representation of the evolutionary simulation pipeline with starting condition monostable signal response and desired evolutionary goal as bistability. (A) Pure population of monostable cascades and (B) equal mixture of fully shared, partially shared, and unshared designs and their transitions to bistability. First, a population of monostable or bistable cascades is created through sampling. The oval with gradient fill represents monostable cascade and oval with complete fill represents bistable cascade. Light blue, red, and dark blue color represent phenotypes corresponding to fully shared, partially shared, and unshared cascades. Evolutionary transition of a fully shared cascade population from monostable to bistable phenotype is shown schematically in (A). After assigning an evolutionary goal the cascades are mutated, the evolutionary processes are represented by the box. After several generations the desired phenotype is obtained (or not). In (B) a mixture of cascade, populations compete across generations for a common goal, to achieve bistability from monostability. To see this figure in color, go online. Biophysical Journal 2018 114, 223-236DOI: (10.1016/j.bpj.2017.10.037) Copyright © 2017 Biophysical Society Terms and Conditions

Figure 4 Phosphatase sharing facilitates transition from the monostable to bistable response (phenotype). (A) The time course of the median fitness of bistable or monostable phenotype over 1000 simulation trajectories with different starting genotypes (parameter values). The top panel shows the median evolutionary trajectories for transition from monostable to bistable and the bottom panel shows the same for the bistable to monostable transition. (B) shows corresponding distributions of the fitness for monostable to bistable transitions with the generation time for the three cases. The results reveal that the transition/adaptation speed toward bistability is a function of degree of phosphatase sharing, with fully shared > partially shared > unshared. The transition speeds are comparable for bistability to monostability transition (bottom panel in A). (C) The median evolutionary trajectories with a starting mixture of the three cascades, each with a population size of 100, evolving toward bistability (left panel) or monostability (right panel) for 100 different genotypes, indicate that the fully shared cascade quickly outcompetes the other two topologies as it transitions to bistability. To see this figure in color, go online. Biophysical Journal 2018 114, 223-236DOI: (10.1016/j.bpj.2017.10.037) Copyright © 2017 Biophysical Society Terms and Conditions

Figure 5 Adaptation in changing environment reveals the improvement in plasticity by phosphatase sharing. The evolution is performed for 400 generations starting with an initial equal mixture of population with the three cascade designs. The starting population is composed of 100 of each cascade type. The condition for selection is changed every 80 generations from bistability (shown in the top bars as B) to monostability (M) and vice versa. (A) The evolution of the number of fully shared population for 400 generations averaged over 50 independent genotypes. This shows that the fully shared cascade wins over the other two cascades in a changing environment, indicating its enhanced performance in evolutionary plasticity. (B) The number of fully shared cascades in an evolving population containing a mixture of fully shared and partially shared cascades with 150 of each cascade type. (C) The number of partially shared cascades is shown when a population of an equal mixture of partially shared and unshared cascades evolves. The partially shared cascade has better evolutionary plasticity compared with the unshared cascade. Biophysical Journal 2018 114, 223-236DOI: (10.1016/j.bpj.2017.10.037) Copyright © 2017 Biophysical Society Terms and Conditions

Figure 6 The two-step phenomenological model for the population evolving from bistability to monostability and vice versa. (A) Schematic diagram represents the models where the intrinsic transitions occur with probabilities of α and β, where B stands for bistable and M for monostable. Bistable and monostable responses have fitness f1 and f2, respectively. (B) The diagram indicates the procedure by which the intrinsic transition rates (α,β) are calculated. A sequence of transitions is generated through one mutation at each step. The transition rates are calculated from the sequence as described in Results and Methods. (C) Transition rates α and β for the fully shared, partially shared, and unshared topologies, calculated from the simulation as in (B) for 100 different initial states. To see this figure in color, go online. Biophysical Journal 2018 114, 223-236DOI: (10.1016/j.bpj.2017.10.037) Copyright © 2017 Biophysical Society Terms and Conditions

Figure 7 The mutational landscape of the evolving population and sensitivity analysis highlights critical parameters for monostable to bistable transitions. (A) The information contents of all the parameters for the three cascades when selected for monostability and bistability. The meaning of the values ki, i = 1…8 and kmi, i = 1…8 are explained in Supporting Material, Model equations. (B) Scatter plot shows mutational information of a parameter (x axis) and its respective sensitivity(y axis). The Spearman correlation coefficient (ρ) and p-value shows high correlation between mutational information of a parameter and its sensitivity to transition rate. (C) The median evolutionary time courses over 200 independent trajectories keeping either MAPK only or MAPK and P1shared constant are plotted, and show dramatic change in the transition rates compared with the control. (D) The median evolutionary time courses of 200 independent trajectories for monostable to bistable transition are shown for the fully shared cascade, where only P1shared and MAPK were allowed to mutate and the rest of the parameters were kept constant. To see this figure in color, go online. Biophysical Journal 2018 114, 223-236DOI: (10.1016/j.bpj.2017.10.037) Copyright © 2017 Biophysical Society Terms and Conditions