arXiv:1010.0370v1 [q-bio.PE] 2 Oct 2010 raetefeunyo e rarayeitn genetic existing in- already or may new selection of its Then, frequency to the survival. crease benefit facilitates a it provides carrier, If novel population. a resulting of the individuals some phe- in plastic response a notypic trigger can perturbation a to non-genetic Thus, potential on influences. the depending has different same phe- produce the plastic is, highly That have notypes. often organisms that servation 2010). al., et Raj 1997; al., Arkin, et and (Elowitz McAdams expression 2002; gene noisy organ- by caused an activity changes Non-genetic gene as in such “microenvironment”, fluctuations internal ism’s interactions. comprise biotic also or perturbations tem- diets, different to peratures, exposure as 2003; such non- al., perturbations, of et genetic role Price the emphasizes 2006; 2006; 2003) 1989, al., al., West-Eberhard, et et Pigliucci Newman 2007; 2004; Moczek, Palmer, 2001; perspec- natu- (Hall, “phenotype-first” through heterodox tive increase The may selection. population ral a whose muta- in phenotypes perspective, novel frequency pro- this with the individuals In produce in tions phenotypes. mutations new of of role duction the per- emphasizes evolu- “genotype-first” of spective orthodox origin The the innovations. about tionary exist perspectives main Two Introduction ∗ mi:C Espinosa-Soto C. Email: orsodn author Corresponding 1 4 3 2 hntpcrbsns a nraepeoyi variabilit phenotypic increase can Phenotypic nvriyo uih et fBohmsr,Bd.Y7Wint Y27 Bldg. Biochemistry, of Dept. Zurich, of University h at eIsiue 39Hd akRa,SnaF,N 8750 NM Fe, Santa Road, Park Hyde 1399 Institute, Fe Santa The NA M 30/UR82 G´en´etique 8120 V´eg´etale, UMR Gi / F-91190 0320 UMR INRA, h ws nttt fBonomtc.Qate og,Bat Sorge, Quartier Bioinformatics. of Institute Swiss The h hntp-rtprpciei ae nteob- the on based is perspective phenotype-first The oksget htnngntcprubtosmyinitiate traits. may expression perturbations non-geneti non-genetic that to suggests response evolutwork in many variability in important phenotypic are promotes circuits e Such this To circuits. variation. lation phenotypic phe novel a generate between to relationship the potential study non-geneti here We After phenotypes. variation. new unde such Populations accumulate process. this can in mutations role important an play innovation. may evolutionary selecti initiate advantage, thus fitness can a perturbations confers phenotype induced an If o-eei etrain,sc sevrnetlcag o change environmental as such perturbations, Non-genetic alsEspinosa-Soto Carlos o-eei etrain ngn euaoycircuits regulatory gene in perturbations non-genetic ∗ [email protected];OC atn–olivier.martin@u- – Martin O.C. [email protected]; – ∗ 1 , 2 lve .Martin C. Olivier Abstract eei aito hti o sal hntpclyvisib phenotypically usually not is that variation Genetic mn eooe 05Luan,Switzerland Lausanne, 1015 Genopode, iment 1 d eueawl-tde oe ftasrpinlregu- transcriptional of model well-studied a use we nd, oayinvtos efidta hntpcrobustness phenotypic that find We innovations. ionary 03 r,19) is,tertclwr shows work theoretical First, assimilation Crozier, and 1999). Jong that de Orr, see opinions, 2003; dissenting fac- (for non-genetic by tors induced traits of innovation for tance 1953). (Waddington, this process for stabilization assimilation genetic factors. term non-genetic phe- the of coined this Waddington independent it “stabilize” making or by refine notype exaggerate, that variants 97.Scn,lbrtr vlto experiments 1998; laboratory Rice, assimilation Second, that 2004; show al., et Masel, al., Espinosa-Soto et Wagner 1997). 1996; Wagner, 2009; 2002; 2007b; Bergman, and Siegal Lande, al., et 2010; (Ciliberti tions noainmr rqetyi uainlyrbs gene robust mutationally in frequently more innovation oms,adtesd ftelre rtca ndecapods in claw first larger (Pleuronecti- the the fishes as of flat side such in the occurs traits, and eye formes), (Palmer, many the response for which plastic on occurs side a This geneti- is not 2004). it is 1996, where asymmetry but the fixed, of cally direction taxa the or from which derived dextral in frequently determined are genetically morphologies sinistral with For taxa 2003). example, West-Eberhard, 2003; 2004; Murren, (Palmer, and rare Pigliucci not is factors trait non-genetic of by assimilation induced genetic natu- that in suggest Nijhout, studies populations and Third, ral Suzuki 1956). 1953, Waddington, 1998; 2006; Lindquist, and Rutherford rhrrtas 9 H85 uih Switzerland Zurich, CH-8057 190 erthurerstrasse etrain,btnti epnet uain Our mutation. to response in not but perturbations, c etrain,ti aito a eoeasuc of source a become can variation this perturbations, c nmypooeisgntcsaiiain Non-genetic stabilization. genetic its promote may on tblzn eeto napeoyeta srbs to robust is that phenotype a on selection stabilizing r eeomna os,cnidc oe phenotypes. novel induce can noise, developmental r -u-Yet,France Yvette, f-sur- oyesrbsns omttosadapopulation’s a and mutations to robustness notype’s ,USA 1, nraigaonso vdnespotteimpor- the support evidence of amounts Increasing 3 sdf .Wge [email protected] – Wagner A. ; psud.fr nra Wagner Andreas can does cu ne ra condi- broad under occur cu Edre l,2009; al., et (Eldar occur 1 , 2 after y , 4 le s (Thalassinidea) (Palmer, 1996). Transitions like these ness of a genotype and that of a phenotype. A geno- indicate of a direction of asymme- type G1 is mutationally more robust than another geno- try originally induced by non-inheritable factors. More type G2, if G1 is more likely to maintain the same phe- generally, traits where fixed differences among closely notype than G2 in response to mutation. By extension, related species are mirrored by plastic variation within a phenotype P1 is mutationally more robust than P2 if populations are good candidates for genetic assimilation. the that produce P1 preserve P1, on average, For example, amphibian traits, such as gut morphology more often than the genotypes adopting P2 preserve P2 (Ledon-Rettig et al., 2008) and limb length and snout in response to mutations. Perhaps surprisingly, muta- length (Gomez-Mestre and Buchholz, 2006), follow this tional phenotypic robustness can facilitate the produc- pattern. tion of novel phenotypes for RNA structure phenotypes A system is robust to genetic or non-genetic (Wagner, 2008b). The reason is that genotypes with a perturbations if its phenotype does not change when more robust phenotype form larger genotype networks perturbed. Mutational robustness and robustness and have, on average, more neighbors with the same to non-genetic perturbations are correlated with one phenotype. A population of such genotypes encoun- another in many cases (AncelandFontana, 2000; ters relatively few deleterious mutations that would slow Ciliberti et al., 2007b; de Visser et al., 2003; Lehner, its diversification and spreading through genotype space 2010; Meiklejohn and Hartl, 2002; Proulx et al., 2007; (while preserving its phenotype). It thus attains a higher Rutherford and Lindquist, 1998), although exceptions genotypic diversity which translates into greater pheno- exist (Cooperet al., 2006; Fraser and Schadt, 2010; typic variability in response to mutations, even though Masel and Siegal, 2009). every single genotype may have access to fewer other The ability to produce evolutionary innovation, phenotypes (Wagner, 2008a). is linked to the robustness of a biological sys- This mechanism, although corroborated for RNA tem (Ancel and Fontana, 2000; Ciliberti et al., 2007a; and protein structural phenotypes (Ferrada and Wagner, Draghi and Wagner, 2009; Wagner, 2005, 2008a). At 2008; Wagner, 2008b) may not lead to increased phe- first sight, robustness seems to hamper innovation. First, notypic variability in all systems. The reason is that it a mutationally robust system produces less phenotypic depends on how many different and unique phenotypes variation in response to mutations. It may thus not facil- the neighborhoodof different genotypes contains, and on itate the genotype-first scenario (Ciliberti et al., 2007a; how rapidly populations can spread through a genotype Draghi and Wagner, 2009). Second, a system robust network. In other words, it depends on the organization to non-genetic factors shows little . of genotype networks in genotype space, which may dif- Thus, it may not support innovationunder the phenotype- fer among different system classes. For example, a re- first scenario. However, the role of robustness in innova- cent theoretical analysis suggests that the relationship be- tion is subtler than it may seem. This becomes evident tween phenotypic mutational robustness and the potential when one considers how genotypes and their phenotypes to generate phenotypic variation through mutation need are organized in a space of genotypes. not even be monotonic (Draghi et al., 2010). Genotypes exist in a vast space of possible geno- The above considerations pertain to phenotypic types. Two genotypes are neighbors in this space if variability in response to mutations. One might think one can be transformed into the other by a single mu- that phenotypic variability in response to non-genetic tation. The distribution of phenotypes in genotype space perturbations may behave similarly since robustness to shows some qualitative similarities for different kinds of mutations and to non-genetic factors are often positively systems, from RNA and protein molecules to metabolic correlated (Ancel and Fontana, 2000; Ciliberti et al., networks and transcriptional regulation circuits. First, 2007b; deVisseretal., 2003; Lehner, 2010; in these systems large sets of genotypes produce the Meiklejohn and Hartl, 2002; Rutherford and Lindquist, same phenotype. Each of these sets can be traversed 1998). However, we show that this is not necessarily through single mutation steps that leave the phenotype so for transcriptional regulation circuits, which exist on unchanged. Such a set is also referred to as a neu- a higher level of organization than individual evolving tral network or genotype network (Schuster et al., 1994). molecules. Such circuits direct the production of specific Second, different neighborhoods of the same genotype gene activity patterns at particular times and places in network contain genotypes with very different geno- the developing organism. Changes in the expression of types (Ciliberti et al., 2007a; Ferrada and Wagner, 2008; their genes are involved in many evolutionary innova- Lipman and Wilbur, 1991; Rodrigues and Wagner, 2009; tions (Davidson and Erwin, 2006; Shubin et al., 2009). Schultes and Bartel, 2000; Schuster et al., 1994; Wagner, We study a generic computational model of transcrip- 2008b). tional regulation in which the genotypes correspond to To understand how mutational robustness relates to the cis-regulatory interactions in a transcriptional circuit. a system’s ability to produce evolutionary innovations, The phenotypes correspond to the gene activity pattern a it is useful to distinguish between the mutational robust- circuit produces.

2 For this system, we show that high phenotypic ro- gene activity pattern s∞ that a circuit attains when start- bustness to mutations increases the number of novel ing from s0. We here focus on circuits producing such expression phenotypes a circuit can produce in re- stable patterns and disregard circuits with more complex sponse to non-genetic perturbations. Thus, pheno- dynamics. We define a circuit’s fitness by a function that typic robustness to mutation facilitates innovation un- increases steeply with the similarity of its phenotype s∞ opt der the phenotype-first scenario. It does so by al- to a reference activity state s∞ , that is considered the lowing the accumulation of genetic variation that is optimal phenotype in a given environment. We consider not observed phenotypically under typical conditions, circuits that attain the same s∞ as equal with respect to but that may be exposed after non-genetic perturba- their gene expression phenotype. Under this assumption, tions (de Visser et al., 2003; Gibson and Dworkin, 2004; a mutation that transforms two such circuits into one an- Masel, 2006; Masel and Siegal, 2009). other would be neutral with respect to this phenotype (Fig. 1b). Methods Determination of 1-mutant neighborhoods Model In several of our analyses, we explored properties of the The model represents a regulatory circuit of N genes, circuits that differ from a reference circuit genotype G where each gene’s activity is regulated by other genes by one single mutation. For each entry aij in the matrix in the circuit. The circuit’s genotype is defined by a A of G we considered the following cases: i) if aij =0 real-valued matrix A = (aij ), in which non-zero el- we check the phenotype of two mutants, one in which ements represent regulatory interactions between genes aij < 0, and one in which aij > 0; ii) if aij =6 0 we (Fig. 1a). An interaction (aij =6 0) means that the ac- also check the phenotype of two mutants, one in which tivity of gene j can either have a positive (aij > 0)ora an interaction is lost (aij = 0), and one in which we negative (aij < 0) effect on the activity of gene i. We use changethe value of aij while keeping its sign unchanged. m to refer to the number of interactionsin a given circuit, Among all the variants in the one-mutation neighbor- and c to its interaction density, i.e. to the number of inter- hood, we allowed exclusively those that maintained the actions m divided by the maximum possible number of number of interactions within an interval [m−,m+], thus 2 (1) (N) interactions N . A vector st = (st , ..., st ) describes keeping interaction density at a value close to c. In all the activity state of the circuit at time t. cases m+ − m− = 5. We discarded circuits that did The activity of the genes in the circuit changes ac- not attain a steady-state gene activity pattern in this ap- cording to the difference equation proach. Whenever a new non-zero value was required for a given aij , we chose an N(0,1) pseudorandom number, N and forced its sign if needed. We defined the robustness (i)  (j) s = σ a s (1) to mutations of a genotype G as the fraction of G’s 1- t+τ X ij t j=1  mutant neighbors that produce the same phenotype as G when their dynamics start from the initial state s0. To where σ(x) equals -1 when x < 0, it equals 1 when assess the phenotypes that G can access through muta- x> 0, and it equals 0 when x =0. tions we registered and counted all the different pheno- Despite its level of abstraction, variants of this types produced by the set of single mutant circuits that model have proven useful for studying the evolution neighbor the reference circuit G. The approach is read- of robustness in gene regulatory circuits (Ciliberti et al., ily extended to entire populations, where we determined 2007b; Martin and Wagner, 2008; Siegal and Bergman, all the different phenotypes that occur in the neighbor- 2002; Wagner, 1996), the effect of recombination on hood circuits in the population. We counted phenotypes the production of negative (Azevedo et al., that occurred in the neighborhoodof two or more circuits 2006; Martin and Wagner, 2009), the evolution of mod- only once. ularity in gene circuits (Espinosa-Soto and Wagner, 2010) and the evolution of new gene activity pat- Evolving populations terns (Ciliberti et al., 2007a; Draghi and Wagner, 2009). For the model we use, a given pair of initial and final ex- opt Similar models have also been successfully used to pression states (s0, s∞ ) is representativeof all pairs with predict the dynamics of developmental processes in the same fraction d of individual genes’ expression val- opt plants and animals (Mendoza and Alvarez-Buylla, 1998; ues that differ between s0 and s∞ . For a pre-specified Mjolsness et al., 1991). d, we thus chose an arbitrary such pair, and followed pre- We consider circuits that start their dynamics from viously established procedures (Ciliberti et al., 2007b) to a particular initial gene expression state s0. One can identify a circuit genotype G that is able to drive the sys- opt view this initial state as being specified by factors exter- tem from s0 to s∞ . The regulatory interactions in the nal to the circuit, be they environmental factors, signals initial genotype G are real numbers sampled from a nor- from adjacent cells, maternal regulators, or any genes mal distribution with mean 0 and standard deviation 1, “upstream” of the circuit. The phenotype is the stable i.e., an N(0,1) distribution. After having identified one

3 such genotype G, we created a population of 200 copies trajectories. of it, and subjected this population to repeated cycles (“generations”) of mutations (with a probability of mu- tation of µ = 0.5 per circuit), and strong stabilizing se- opt lection on s∞ . Whenever a circuit underwent mutation, we picked one of the circuit’s 1-mutation neighbors at random (see above). We allowed exclusively those mu- tations that maintained the number of interactions within a predetermined interval [m−,m+], thus keeping inter- action density around a predetermined fraction c of non- zero interactions among all possible (N 2) interactions. In this study, m+ − m− =5 in all cases. Throughout, we interpret a circuit’s “fitness” as a survival probability. We followed the regulatory dynam- ics of each gene circuit with s0 as initial condition. As in previous work (Ciliberti et al., 2007a,b), we disregarded genotypes that did not produce fixed-point equilibrium states, or that produced phenotypes in which the activity of a gene was equal to zero (neither active nor inactive). We assigned genotypes that attained the reference pattern opt opt s∞ a maximally possible fitness of 1. Thus, s∞ repre- sents a pre-determinedoptimal gene expression state. We assigned genotypes that attained an equilibrium state s∞ opt that differed from s∞ in the activity state of k genes a Fig. 1. Gene regulatory circuit model. (a) A gene regulatory circuit. 5 fitness equal to (1 − k/N) , which ensures a steep de- Black bars indicate genes that encode proteins which regulate the crease in survival probability even for small deviations activity of other genes in a hypothetical circuit. The regulatory opt interactions are described by a matrix A = (a ). An interaction from s∞ . Each generation, we constructed a new pop- ij means that the activity of gene j can either have a positive (a > , ulation by sampling individuals with replacement from ij 0 red rectangles) or a negative (aij < 0, blue rectangles) effect on the the previous generation, and subjecting copies of them activity of gene i. (b) Gene circuits that differ in a single interaction to mutation with a probability µ. We kept each of these are neighbors in genotype space. . Each large circle surrounds a new individuals with a probability equal to its fitness, and distinct gene regulatory circuit. Red arrows represent activating interactions, and blue lines represent repressing interactions between continued sampling until the newly generated population different genes (black rectangles). Dashed lines represent the had 200 members. For all the populations we study, we interactions that are necessary to convert the indicated circuits into the let the initial population of identical genotypes evolve for middle circuit. a) and b) are modified with permission from 4 opt (Ciliberti et al., 2007b). (c) Example of novel phenotypes caused by 10 generations under selection for s∞ , before collect- three kinds of perturbations. A reference gene circuit produces ing any simulation data. This allows the population to phenotype s∞, in which four genes are active (genes 5-8; yellow) and erase any traces of the initial genotype and to reach a four genes are inactive (genes 1-4; red). In a one-mutation plateau where phenotypic variability in response to ei- neighborhood (all circuits that differ from the reference one by a new ther mutations or non-genetic perturbations varies little single interaction) we find four phenotypes s∞ different from the original s∞ (left). If we perturb the system state of the reference across generations. circuit without altering its genotype, other novel phenotypes are We define the genotypic distance between two cir- encountered (center and right panels). The perturbations we used are cuits as the minimum number of mutations needed to either all single-gene perturbations in the initial condition s0 (center), or perturbations of the dynamical trajectory of the circuit (‘noisy transform one circuit into the other, normalized by the dynamics’; right). maximally possible number of such mutations for cir- cuits with the same number of interactions. Random sampling of genotypes in genotype networks Noisy dynamics For each circuit in a population, we generated 5N dy- In order to sample properties of a given genotype net- namic trajectories, each of which started from s0. For work uniformly, we performed a randommutational walk each of these trajectories, and for each step of the regu- restricted to this genotype network, that is, to circuits that opt latory dynamics, we perturbed the activity of a randomly attain a given s∞ from the initial state s0. We then ex- picked gene with a probability of 0.5. We then followed amined properties of genotypes every n steps of this ran- each trajectory until an activity pattern s had consecu- dom walk, where n equaled 5 times the upper limit m+ tively repeated itself, and labeled this pattern as s∞. We of the number of interactions in the circuit. This sporadic then counted the number of different fixed-point equi- sampling serves to erase correlations in genotypes along librium states that each circuit could attain in these 5N this random walk.

4 Results dynamics, and lead to a new steady-state activity pattern new s∞ . Genotype networks of gene expression phenotypes have different sizes We emulated the perturbations produced by noise in two complementary ways. First, we changed the activity For our model, most or all genotypes that produce the state of single genes in the initial state s0, for each gene same phenotype form large connected genotype net- in a circuit, and determined the different new phenotypes new works (Ciliberti et al., 2007a,b). The size of any one s∞ that resulted from such change. Secondly, we ran- phenotype’s genotype network depends only on the frac- domly perturbed the dynamic trajectory from s0 to s∞ tion d of genes whose expression state differs between (‘noisy dynamics’), as described in Methods. the initial state s0, and the steady state activity pheno- opt We asked how the mutational robustness of a gene type s∞ (Ciliberti et al., 2007b). Specifically, pheno- expression phenotype affects the number of new pheno- types where these two states (regardless of their actual types that these two kinds of noise can produce in pop- expression values) are more similar have larger genotype ulations of evolving circuits. We evolved populations of networks (Fig. S1 in Supplementary Material). One can 200 circuits under stabilizing selection on a given gene view regulatory circuits as devices that compute an ex- opt opt expression state s∞ , as described in Methods. We then pression state s∞ from the initial state s . From this 0 counted the number of unique new phenotypes that the perspective, a larger number of gene expression differ- two different kinds of noise produced among the individ- ences between these states means that the computation uals in a population. Specifically, we counted phenotypes becomes increasingly difficult, in the sense that fewer that appeared multiple times only once, thus focusing on genotypes can perform it. unique phenotypes. We first examined, in our model, the relationship between the size of a phenotype P ’s genotype network Noise can produce a greater number of new phe- and the robustness of circuits with this phenotype P to notypes in populations evolving on large genotype net- mutations. To this end, we uniformly sampled 106 geno- works. Fig. 2 demonstrates these observations for cir- types from genotype networks of different sizes (differ- cuits with N = 20 genes and an interaction density ent d), and determined their mean robustness to muta- c ≈ 0.2. These observations also hold if we vary the tions, that is, the mean fraction of their neighbors with numbers of genes and regulatory interactions in a circuit the same phenotype. For all examined cases, the aver- (Figs. S3,4), with a single exception for perturbations age mutational robustness (i.e. phenotypic robustness) is in s0 when the number of regulatory interactions is very higher for genotypes on larger genotype networks (Fig. low (Fig. S3d). S2). Thus, phenotypic robustness to mutations increases with genotype network size, just as for RNA (Wagner, Populations with more robust phenotypes harbor 2008b). Therefore, we can simply use 1 − d as a proxy more diverse genotypes for genotype network size and phenotypic robustness to mutations. Increased genotypic diversity in populations evolving in large genotype networks might aid in producing in- Phenotypic robustness to mutations facilitates pheno- creased phenotypic variability, as discussed in the Intro- typic variability in response to noise duction. We next asked whether this mechanism may In this paper, we are concerned with the production apply to our system. To this end, we quantified the geno- new typic distance among two circuits (see Methods). of new steady-state gene expression patterns s∞ that opt are different from s∞ . We refer to such activity pat- As a measure of a population’s genotypic diversity, terns as new phenotypes. They could result from mu- we estimated the mean pairwise circuit distance, as well tations that change regulatory interactions in a circuit. as its maximum, in each of 500 populations evolved un- opt They could also result from non-genetic perturbations der stabilizing selection on a phenotype s∞ . We did so (Fig. 1c). We here consider two kinds of non-geneticper- for two classes of populations that differ in the robustness turbations, noise in a cell’s internal milieu, and change in of their phenotypes, and found that the mean genotypic the organism’s (external) environment. Both kinds can distance is significantly higher for populations with a ro- induce dramatic gene expression changes in organisms bust phenotype. The same holds also for the maximum ranging from bacteria to metazoans (Elowitz et al., 2002; genotypic distance. These observations are not sensitive Raj et al., 2010; Snell-Rood et al., 2010). We first focus to the number of genes and interactions in a circuit (Ta- on noise, which includes stochastic changes in protein or ble S1). Thus, populations with a robust phenotype are mRNA copy numbers in a cell, and can cause phenotypic genetically more diverse than populations with a less ro- heterogeneity in clonal populations (Elowitz et al., 2002; bust phenotype. These observations hint that the higher McAdams and Arkin, 1997; Raj et al., 2010). Such noise genetic diversity of populations with robust phenotypes may affect the activity or expression of circuit genes at a may be exposed as phenotypic variability in response to given time, which may alter a circuit’s gene expression noise.

5 Fig. 3. High phenotypic robustness does not facilitate phenotypic variability in response to mutations without preceding environmental change. ‘High’, ‘medium’ and ‘low’ correspond to expression phenotypes with high (d = 0.1), intermediate (d = 0.25), and low (d = 0.5) robustness. The figure shows results for N = 20 genes and a fraction c ≈ 0.2 of non-zero regulatory interactions. The panel shows the mean number of novel phenotypes averaged over 500 independent populations, at each level of robustness. The length of bars denotes one standard error. We found that populations with a highly robust phe- notype show lower phenotypic variability in response to Fig. 2. High phenotypic robustness facilitates phenotypic variability in mutations. This holds despite their somewhat higher response to noise in gene expression. The distance d between the genotypic diversity (Table S1, discussed above). Fig. 3 opt initial state s0 and the optimal phenotype s∞ is strongly associated shows pertinent data for circuits with 20 genes and inter- with genotype network size and with phenotypic mutational robustness (“phenotypic robustness”) hereafter. ‘High’, ‘medium’ and action density c ≈ 0.2. The same behavior holds for ‘low’ correspond to expression phenotypes with high (d = 0.1), populations of circuits with different number of genes intermediate (d = 0.25), and low (d = 0.5) robustness. The figure and different interaction densities (Fig. S5). In sum, ro- ≈ shows results for N = 20 genes and a fraction c 0.2 of non-zero bustness of a phenotype to mutations impairs phenotypic regulatory interactions. Both panels show mean numbers of novel phenotypes averaged over 500 independent populations, for each level variability to mutation, as opposed to what we saw for of robustness. The length of bars denotes one standard error. The variability in response to noise. number of different new phenotypes that a population can access after Our results suggest that a phenotype’s mutational perturbations of a) single genes in the initial state s0, or b) a circuit’s gene expression trajectory, increases with phenotypic robustness. robustness promotes phenotypic variability in response to noise, but hinders such variability in response to mu- tations. This may seem surprising, because robustness to mutations increases with robustness to noise for indi- vidual circuits (Ciliberti et al., 2007b). One might thus Phenotypic robustness does not facilitate phenotypic think that phenotypic variability also behaves similarly variability caused by mutations in response to these perturbations. However, robustness to mutations explains less than 25 percent of the vari- ance in robustness to noise, as shown by a new statistical analyses of our previously published data (Ciliberti et al., We next asked whether phenotypic robustness also facil- 2007b). Thus phenotypic variability in response to noise itates phenotypic variability in response to mutations for and to mutation are only weakly coupled. the regulatory circuits we study. We again studied popu- With these observations in mind, we analyzed the lations of circuits evolved under stabilizing selection on phenotypic variability in response to noise and mutations opt a phenotype s∞ . In such populations, we determined of individual circuits in populations evolving on differ- the 1-mutation neighborhood of each circuit, that is, all ent genotype networks (Table S2). After obtaining this circuits that differ from it in a single regulatory interac- data, we compared the mean number of new phenotypes tion. We then determinedthe numberof unique new gene that mutations or noise could produce from circuits in expression phenotypes in the population’s neighborhood. populations with different levels of phenotypic robust- That is, we counted only once a phenotype if it occurred ness (Table S3). We found that phenotypic variability in the neighborhood of two different circuits. This num- in response to gene expression noise decreases less with ber of unique phenotypesis a measure of the population’s phenotypic robustness to mutations than phenotypic vari- phenotypic variability in response to mutations. ability to mutations (Table S3). It may even increase with

6 phenotypic robustness. These observations suggest that der stabilizing selection on an optimal expression pheno- opt a the increased genotypic diversity attained on larger geno- type s∞ and a given gene activity pattern s0 as initial type networks is insufficient to compensate for the small condition. We counted the number of phenotypes in the (or null) reduction in variability in response to mutations. population, and compared it with the number of different a It is, however, sufficient to compensate for the smaller re- phenotypes that the same population displays when s0 is b duction in phenotypic variability in response to noise in replaced by a random gene activity pattern s0 as an initial gene expression. condition. We found that phenotypic variability increases a b after substitution of s0 with s0 (Figs. 4 and S6). In addi- Phenotypic robustness increases phenotypic variabil- tion, the magnitude of this increment increases with phe- ity after environmental change notypic robustness (Fig. 4). This last observation is gen- Thus far, we focused mostly on phenotypic variability erally not sensitive to the number of genes and regulatory in response to small, random non-genetic perturbations, interactions in a circuit (Fig. S6). The increase in phe- such as single gene expression perturbationsalong a gene notypic variability is significantly higher for populations expression trajectory. We now turn to the question of with a robust phenotype (Mann-Whitney U-test; Table what happens when a whole population is subject to the S4). The single exception to these observations were cir- same non-genetic perturbation. In nature, this may occur cuits of very low interaction density (N = 20; c ≈ 0.1 because of environmental change outside the organism, Fig. S6d), that also show other non-typical behaviors or colonization of a new habitat. (Ciliberti et al., 2007b). Our results suggest that, after The environment can have two different roles in this environmental change, observable phenotypic diversity context. The first is an inducing role, where the environ- increases to a larger extent in populations with a robust ment acts as an “agent of development” (West-Eberhard, phenotype. We note that because the identity of s∞ does 1989). In this role, it affects the phenotype produced not affect the production of phenotypes, but only their from a genotype. In many cases, environmentally in- viability, it is not appropriate to carry out an analogous opt duced phenotypic change is linked to major changes in analysis for changes in s∞ . gene expression (Snell-Rood et al., 2010). The second In earlier sections, we have shown that phenotypic role is an evaluating role, where the environment acts as robustness impedes phenotypic variability after muta- an “agent of selection” (West-Eberhard, 1989). In an- tions in populations evolving in a constant environment thropomorphic terms, the environment in this role distin- (Fig. 3). We next asked whether this also holds after guishes well-adapted from poorly adapted phenotypes. a change in the inducing role of the environment. We Conveniently, our model allows us to study these started out, as in our last analysis, with populations of roles independently. We model a change in the environ- circuits evolved under stabilizing selection on an optimal opt ment’s evaluation role as a change in the identity of the expression phenotype s∞ and with a given gene activ- opt a optimal phenotype s∞ , for all circuits in the population. ity pattern s0 as initial condition. Then, we changed the a We model a change in the environment’s inducing role initial condition s0 for all the circuits to a new random b as a change in the initial state s0 in the whole popula- initial condition s0, and allowed evolution to proceed. tion. Such a change could occur, for example, through a Before and after this change, we recorded the number signaling pathway that detects an environmental change, of different phenotypes accessible from the population and that affects genes upstream of the circuit. Put dif- through mutations. Under the new condition the popula- ferently, changes in s0 reflect the environment’s effect tion effectively searches genotype space for optimal phe- opt on phenotype production, while changes in s∞ affect notypes. During this search, many variant circuits may the survival probability of individuals, without inducing not pass to subsequent generations. Our primary focus, novel phenotypes. We note that other factors, such as however, is not this search, but the immediate increase in mutations in upstream genes, might also lead to changes a population’s phenotypic variability in response to envi- in s0. Any one such change, however, would initially ronmental change. affect only one individual in a population, and not the Before environmental change, populations with a whole population at the same time. robust phenotype have access to fewer phenotypic vari- We first asked how an environmentally induced , just as in our previous observations (Fig. 3). Imme- change in the initial gene activity pattern s0 affects the diately after environmental change (at t = 1), the num- number of different actual phenotypes that a population ber of new phenotypes accessible through mutations in- displays. We note that our populations may contain a creases, in a burst, in all populations. Importantly, this few individuals with phenotypes different from the op- increase is higher in populations with a robust phenotype opt timal phenotype s∞ . The reason is that, in contrast to (Figs. 5a and S7). This means that phenotypic robust- previous formulations (Ciliberti et al., 2007b), we here ness facilitates the phenotypic variability caused by mu- represent fitness as a continuous variable that depends tations, but only after environmental change. As in our opt on the similarity of a circuit’s phenotype s∞ to s∞ (see analysis above, the only exception occurs when interac- Methods). We started out with a population evolved un- tion density is very low (Fig. S7d).

7 occurs when interaction density is very low (Fig. S9d). These observations imply that the inductive role domi- nates in its immediate effect on phenotypic variability when both roles of the environmentchange. In sum, pop- ulations with a robust phenotype have mutational access to more phenotypic variants after environmental change. This increased access is caused by the inductive role of the environment,that is by the new phenotypesthat a new environment can bring forth. Discussion If non-genetic change is to be causally involved in evo- lutionary innovation, it needs to generate novel phe- notypes. Genetic assimilation can then stabilize these Fig. 4. High phenotypic robustness increases phenotypic diversity in populations of gene circuits after environmental change. The number phenotypes if the non-genetic perturbations that induced of different phenotypes that populations display increases after them appear recurrently. Here, we focused on whether changing the initial expression state s0. Such an increase is greater for the robustness of an existing phenotype and non-genetic populations with mutationally more robust phenotypes. The figure change can facilitate the origin of new phenotypes. To shows results for N = 20 genes and a fraction c ≈ 0.2 of non-zero regulatory interactions. The panel shows the mean number of observed address this question, we examined a generic model of phenotypes averaged over 500 independent populations, for each level transcriptional regulation circuitry, in which the rela- of robustness. The length of bars denotes one standard error. tionship between genotypes (patterns of regulatory in- We next asked whether the evaluation role of the en- teractions) and phenotypes (gene activity or expres- vironment has similar effects on the mutational access to sion patterns) is well-studied (Ciliberti et al., 2007a,b; new phenotypes. To this end, we repeated the above anal- Martin and Wagner, 2008, 2009; Wagner, 1996). In this opt,a ysis, but replaced, at t =1, the optimal phenotype s∞ model, we can use the size of a phenotype’s genotype opt,b by a randomly chosen optimal s∞ (without changing network as a proxy for a phenotype’s robustness to mu- s0). We also observed a transient, but more gradual, in- tations. crease in the number of phenotypes that are mutationally We broadly distinguished two kinds of non-genetic accessible. However, in this case, phenotypic variabil- perturbations. The first corresponds to fluctuations in ity is lower for populations with a robust phenotype after a gene circuit’s microenvironment that produce random environmental change (Figs. 5b and S8). Thus, the in- changes in gene expression. Such changes, are ubiqui- ductive role of environment, but not its evaluative role, tous and have important effects on cell biological pro- causes higher phenotypic variability in populations with cesses (Elowitz et al., 2002; McAdams and Arkin, 1997; robust phenotypes. Raj et al., 2010). The second kind comprises changes An open question is how mutation-accessible phe- in the (macro)environment external to an organism. For notypic variability changes when both the inductive and brevity, we refer to these kinds of change as noise and the evaluation roles of the environment change. This environmental change. question is important because a change in the inductive We first explored how noise and mutations affect role favors phenotypic variability to a larger extent in phenotypic variability in populations that differ in the populations with a robust phenotype, whereas a change robustness of their gene activity phenotypes. We found in the evaluative role particularly favors variability in that phenotypic mutational robustness increases pheno- populations with less robust phenotypes. Thus, a combi- typic variability of populations in response to noise but nation of both effects could result in a negligible effect of not in response to mutations. This last finding differs phenotypic robustness on variability after environmental from observations for RNA secondary structure, where change. To answer this question, we repeated our analy- phenotypic robustness facilitates the mutational access sis from the previous paragraph, but replaced the original to phenotypic variants (Wagner, 2008b). The reason a opt,a b opt,b pair of states (s0, s∞ )withanewpair(s0, s∞ ), such stems from differences in the organization of genotype opt that the distance d between s0 and s∞ was the same for space for these two system classes, i.e. in the dis- both pairs. tribution of different genotype networks in genotype In this new analysis, populations evolving on a large space (Ancel and Fontana, 2000; Ciliberti et al., 2007a; genotype network show greater phenotypic variability in Espinosa-Soto et al., 2010; Wagner, 2008b). A recent response to mutations immediately after this change (Fig. mathematical model (Draghi et al., 2010) shows that mu- 5c). These differences are statistically highly significant tational access to new phenotypes can depend on this or- (Table S5). The same observations hold for circuits of ganization, and on details of a population’s evolutionary different sizes and different connectivities (Fig. S9 and dynamics. Table S5). As in our analysis above, the only exception Next, we asked how phenotypic robustness af-

8 Fig. 5. High phenotypic robustness allows mutational access to more phenotypes after an environmental change produces novel phenotypes.The figure shows the number of different phenotypes in the 1-mutant neighborhood of a population, for three different scenarios of environmental change at generation t = 1. The insets show the number of phenotypes accessible through mutation immediately before (t = 0) and immediately after (t = 1) environmental change. The figure shows results for N = 20 genes and a fraction c ≈ 0.2 of non-zero regulatory interactions. ‘High’, ‘medium’ and ‘low’ correspond to expression phenotypes with high (d = 0.1), intermediate (d = 0.25), and low (d = 0.5) phenotypic robustness. Data are mean values averaged across 500 independent simulations for each level of robustness. The length of bars opt a denotes one standard error. (a) The initial state s0 changes. (b) The identity of the optimal phenotype s∞ changes. (c) The original pair (s0 , opt,a b opt,b s∞ ) changes to a new pair (s0, s∞ ). fects phenotypic variability in response to environmen- cuits with robust phenotypes. In fact, we observe a gen- tal change, which we modeled to affect all individuals eral increase in phenotypic variability after environmen- in a population. We showed that environmental change, tal change (Figs. 4 and 5). It is just that this increase is besides increasing observable phenotypic variation, tran- especially strong for robust phenotypes. siently increases phenotypic variability caused by mu- The general increase in phenotypic variability tations. Because mutational access to most novel vari- we observe is consistent with many empirical ob- ants is only possible in the new environment, these vari- servations on phenotypic variation that is conditional ants can be considered environmentally-induced pheno- on the environment. For example, severe environ- types, supporting the phenotype-first scenario. From this ments enhance phenotypic differences among fruit fly perspective, environmental change increases phenotypic strains (Kondrashov and Houle, 1994), and a temper- variability and the chances to refine, exaggerate and sta- ature rise due to an unshaded milieu increases the bilize phenotypic variation via genetic change. Impor- frequency of abnormal morphologies in fruit flies tantly, this increase in phenotypic variability is higher in (Roberts and Feder, 1999). Moreover, population genet- populations that had a more robust phenotype before en- ics studies show that the release of hidden genetic varia- vironmental change. tion after environmental change should be very common In sum, we found a positive effect of phenotypic (Hermisson and Wagner, 2004). robustness on phenotypic variability after non-genetic Unfortunately, because the mutational robustness perturbations. This positive effect is not sensitive to of most traits is unknown and difficult to measure the magnitude of non-genetic perturbations. Phenotypic (de Visser et al., 2003), these observations do not speak robustness favors phenotypic variability after single- directly to the question whether phenotypic robust- gene perturbations in the initial condition, which is the ness promotes phenotypic variability after environmen- smallest possible non-genetic perturbation in our model tal change. However, there is an intriguing phenomenon (Fig. 2a). It also favors phenotypic variability after re- with potential parallels to our observations. In the placing the initial condition by a completely new ran- fruit fly D. melanogaster and in the plant Arabidopsis dom activity pattern (Figs. 4 and 5a). In contrast, pop- thaliana, previously unobserved phenotypic variants ap- ulations with robust gene expression phenotypes pro- pear when the activity of the chaperone protein Hsp90 duce less phenotypic variation when only mutations are is impaired (by environmental stress or by other means) used to explore the phenotypic possibilities. Thus, a (Queitsch et al., 2002; Rutherford and Lindquist, 1998). mechanism that relies exclusively on mutation to pro- This observation suggests that an active Hsp90 protein duce novel phenotypes becomes less important for inno- usually conceals genetic variation that would otherwise vation as a phenotype’s robustness increases. Our results be visible phenotypically, although the appearance of suggest that plasticity-mediated innovation may be espe- new genetic variants may underlie some of the new phe- cially important for gene expression traits with high mu- notypic variation (Specchia et al., 2010). Hence, Hsp90 tational robustness. Our work is an initial step towards might increase phenotypic variability by allowing the ac- the definition of two different domains where either the cumulation of cryptic genetic variation that can become genotype-first or phenotype-first scenarios prevail over phenotypically visible in the right environment. Our the other. In this regard, we note that environmental in- analysis revealed an analogous phenomenon for robust duction of novel traits is not only expected for gene cir- gene expression phenotypes. Robustness of phenotypic

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