Extreme Robustness Requires Extreme Phenotypes

bioRxiv preprint doi: https://doi.org/10.1101/478784; this version posted November 27, 2018. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC-ND 4.0 International license.

5 Extreme robustness requires extreme phenotypes

9 10 11 Felipe Bastos Rocha1* and Louis Bernard Klaczko2 12 1 Departamento de Genética e Biologia Evolutiva, Universidade de São Paulo – USP, SP, Brazil. 13 2 Departamento de Genética, Evolução e Bioagentes, Universidade Estadual de Campinas – 14 Unicamp, Campinas, Brazil. 15 16 * Corresponding author: 17 e-mail: [email protected]

18 An outstanding feature of living organisms is their ability to develop in shifting and often

19 perturbing conditions and still yield a defined set of traits with stable phenotypes. Here we show

20 that this ability – phenotypic robustness – may be achieved via a possibly universal mechanism

21 that emerges from basic rules relating gene activity and development. First, we demonstrate that

22 phenotypic stability is strongly associated with extreme phenotypes using a comprehensive dataset

23 of reaction norms of plants, animals, and bacteria from the literature1. This association suggests

24 that genetic variation affects robustness mainly through saturation or depletion – and not

25 stabilization – of developmental systems. Second, we build a simple developmental model to

26 assess how genetic variation for gene activity may affect the pattern of phenotypic response of a

27 given trait to perturbations of transcription. The results show that organisms may achieve

28 phenotypic robustness in the absence transcriptional stability by yielding extreme phenotypes.

29 Third, we show that this model may offer a simple and coherent explanation for experimental

30 results (from Crocker et al.2) associating cis-regulatory sequence variation to phenotypic

31 robustness. These results suggest that, even though specific systems of developmental buffering

32 may play a role in phenotypic robustness, natural selection often resorts to the genetic variation

33 controlling the level of trait induction to yield phenotypic stability.

34 Gene activity is the primary trigger of the developmental processes that lead to the formation of a

35 trait. Such processes are influenced by the internal cellular environment, the individual’s genetic

36 makeup, and the surrounding environment. Hence, the final phenotype of an individual depends on

37 the resultant of these factors – hereafter the level of trait induction. In contrast to laboratory

38 mutants, wild-type organisms can typically fully develop and yield fairly constant phenotypes even

39 when submitted to variable genetic backgrounds and environmental conditions. At least since

40 Waddington3, this observation is seen as evidence that wild-type organisms can compensate or

41 avoid changes in the level of trait induction when submitted to perturbations (Fig. 1a, b).

42 Typically, this is assumed to be due to specific systems that evolved by natural selection to

43 perform such buffering4–6. However, with few exceptions (e.g., the chaperone Hsp907,8), genes

44 whose function is to confer phenotypic stability against perturbations are seldom found.

45 Is it possible to achieve phenotypic robustness in the absence of buffering genes? A possible

46 answer lies in the effect that two developmental properties have on the relationship between trait

47 induction and phenotype formation (see Fig. 1c – analogous rationales are found in Refs9,10 and

48 date back to Wright11 and Plunkett12). The first is the fact that no trait can increase indefinitely.

49 The second is the fact that most traits require the level of induction to reach a non-zero value to

50 yield phenotypic increments from the minimum possible phenotype. These properties create two

51 regions in the induction-phenotype curve where changes in the level of trait induction, regardless

52 of their cause, will not lead to phenotypic changes because the developmental system is either

53 depleted or saturated (see Fig. 1c).

54 What is the relevance of this dynamics of saturation/depletion in the observed variation of

55 robustness? To address this question, one could assess how the amount of response to a given

56 perturbation varies across the phenotypic space: while saturation/depletion will necessarily yield

57 phenotypic robustness only near extreme phenotypes, buffering may potentially confer robustness

58 at any phenotypic value within the limits of the phenotypic space.

59 Following this rationale, we analyzed phenotypic reaction norms – the arrays of phenotypes

60 produced by different genotypes in response to a given array of environmental conditions – from a

61 dataset compiled by Murren et al.1. After filtering (see Methods) we analyzed 856 reaction norms

62 from 29 plants, 43 animal species and three bacteria. To make these diverse responses comparable,

63 we first normalized all phenotypic values by species and trait and all environmental values by

64 experiment, so that all reaction norms fitted a 1x1 plot. Then, to circumvent the complexity of

65 forms that reaction norms may assume (see 13,14), we used Global Plasticity (GP), a shape-

66 independent parameter15 to quantify the total amount of phenotypic response in each reaction

67 norm. Thus, we characterized phenotypic robustness, regardless of trait, species, and experiment,

68 as near-zero GP values, and high phenotypic plasticity as near-one GP values. For each trait in

69 each species, we estimated the phenotypic space by the interval of values between the maximum

70 and minimum observed phenotypes. Then, to characterize the position of each reaction norm in the

71 phenotypic space, we took the distance between the across-environment mean phenotype and the

72 closest extreme phenotype (see Methods for details). Thus, the relevance of saturation/depletion

73 could be assessed by whether GP varied independently from the distance from the limits of the

74 phenotypic space.

75 Despite the extensive heterogeneity of organisms, traits, and perturbations included in this

76 analysis, more than 50% of GP variation could be explained by a linear function that increased

77 from near-zero (high robustness) to near-one (high plasticity) as the distance from the trait limits

78 varied from minimal to maximal (R² = 0.520; F = 930.122; p < 0.00001 - Fig. 2a). Likewise,

79 extreme robustness, as characterized by reaction norms with GP below 0.2 (i.e., whose response

80 was lower than 1/5 of the phenotypic space), were strongly concentrated towards the phenotypic

81 extremes (Fig. 2b – D = 0.309, p < 0.001). These findings are substantial evidence that the

82 saturation/depletion dynamics is the leading cause of phenotypic robustness in this dataset. This

83 scenario is somewhat conflicting with the paradigmatic view of organisms as masters of their

84 development. Instead, it might be the case, as Smith-Gill16 once stated, that organisms may often

85 be doing the best they can to minimize environmentally induced changes, and failure to do so

86 could often be what we call phenotypic plasticity.

87 How can such a clear pattern emerge from such a diverse dataset? Recent studies have repeatedly

88 found that cis-regulatory sequences affect phenotypic robustness following a consistent pattern in

89 various systems. Genotypes enriched for cis-regulatory sequences that drive similar patterns of

90 expression (shadow enhancers and homotypic clusters of transcription factor binding sites) yield

91 stability of high phenotypic values2,17–23. Conversely, stability of low phenotypic values seems to

92 be achieved by the loss of such sequences and gain of sequences with negative effect on gene

93 activity24. These results are remarkably consistent with the pattern of reaction norm variation we

94 found and imply a fundamental biological principle – the direct control of trait induction by gene

95 activity – in the control of phenotypic robustness by saturation/depletion.

96 Oddly, however, the relationship between the multiplicity of functionally similar cis-regulatory

97 sequences and robustness may work in the opposite direction for transcription at the whole-

98 genome scale25. To assess how genetic variation for gene activity may shape the patterns of

99 robustness variation at the transcriptional and phenotypic levels, we built a simple model of trait

100 development that generates phenotypic reaction norms from the effect of a perturbation that

101 directly affects transcription. Briefly, our model describes a trait formed by a limited group of cells

102 that differentiate when an inducer gene is expressed at or above a threshold. Perturbation was

103 introduced by linearly reducing the probability of transcription initiation at a constant rate for all

104 genotypes. Given the stochastic nature of gene activity26,27 and evidence that multiple similar cis-

105 regulatory sequences cumulatively increase their target gene activity28–30, genetic variation was

106 introduced by varying the probability of transcription initiation at optimal conditions. We

107 simulated both transcriptional and phenotypic reaction norms (Fig. 3a and b) and then analyzed

108 their patterns of GP variation as a function of the level of trait induction, as given by mean

109 probability of gene activation.

110 Both transcriptional and phenotypic GP values increased towards genotypes with intermediary

111 levels of trait induction and decreased towards extreme levels of trait induction (Fig. 3c). This

112 feature was independent from the developmental setup and the intensity of perturbation (Extended

113 Data Fig. 1). Nonetheless, despite the similarity of forms, the curves of GP variation for

114 transcription and phenotype were not related one-to-one, as many transcriptionally plastic

115 genotypes were phenotypically robust (see Fig. 3c). This pattern arises because phenotypic

116 stability was not the result of stability of transcription, but rather the outcome of the saturation or

117 depletion of the developmental system leading to the trait formation (Fig. 3d). Thus, a genotype

118 with stable phenotype is one whose transcription, even if perturbed, is either below the depletion

119 threshold or above the saturation threshold, not necessarily one that is transcriptionally robust to

120 perturbations (see Figs. 1b and 3d). Of course, the same principle pertains to any kind perturbation

121 that might affect a gene’s activity, and a genotype that is phenotypically robust due to saturation or

122 depletion will be robust to multiple forms of perturbations: within-locus genetic perturbation

123 (where robustness equals dominance), between-loci genetic perturbation, and multi-variate

124 environmental perturbation.

125 We then set out to evaluate whether this model could fit to the pattern of robustness variation that

126 is caused by multiplicity of similar cis-regulatory sequences. We used RNs described by Crocker

127 et al.2, which portray the response of the number of larval trichomes of eight genotypes of

128 Drosophila melanogaster to temperature. Each reaction norm corresponds to a genotype with a

129 specific arrangement of homotypic binding sites for the Ubx-Exd transcription factors in an

130 enhancer driving expression of the gene shavenbaby (svb). To simulate the GP values using our

131 model, we assumed that all genotypes suffered the same impact of temperature on svb activity and

132 the only cause of response variation was saturation/depletion. The model offered an excellent

133 prediction of the observed GP values (R² = 0.829 – Fig. 4a), suggesting that the observed amount

134 of response of the number of larval trichomes varied mainly due to saturation or depletion. This

135 result suggests that the number of Ubx binding sites in the enhancer had a cumulative (rather than

136 redundant) effect on the level of induction of larval trichomes. Accordingly, the across-temperature

137 mean phenotype was significantly correlated with the number of unmutated Ubx-Exd binding sites

138 (Fig. 4b). These findings seem to diverge from the authors’ interpretation that the observed

139 variation in phenotypic robustness was due to a positive association between redundancy

140 (multiplicity) of Ubx binding sites and robustness of gene activity.

141 We may thus outline a coherent scenario of how natural selection may shape regulatory variation

142 when robustness is favored. Frequently (and as observed), selection for phenotypic robustness may

143 lead to changes in the level of trait induction via modulation of gene activity. Cis-regulatory

144 sequences of genes promoting traits will be enriched for shadow enhancers and homotypic binding

145 sites when high phenotypic values are favored. This pattern will be inverted when low phenotypes

146 are selected. In some (perhaps rare) cases, however, two different outcomes of selection for

147 robustness may be observed. First, genes whose activity inhibits the trait formation will display

148 opposite cis-regulatory patterns: enrichment of enhancers and TF binding sites when the favored

149 phenotype is low and reduction when the favored phenotype is high. Second, if selection favors

150 robustness of intermediary phenotypes, alleles creating narrower phenotypic limits will be favored,

151 which could be achieved via trans-regulatory changes. Lastly, if selection for phenotypic constancy

152 is ubiquitous and there is, as it seems, a universal mechanism to achieve this property, selection for

153 robustness may be a major force shaping non-coding regulatory DNA.

154 Methods

155 Analysis of reaction norms extracted from the dataset compiled by Murren et al. (2014a):

156 We retrieved the data compiled by Murren et al.1 from Dryad31 and filtered for reaction norms that

157 had continuous (non-qualitative) environmental variables and more than one reaction norm by trait

158 in each species. This preliminary assessment resulted in a dataset of 858 reaction norms. We then

159 normalized all environmental values by experiment and all phenotypic values by trait and species

160 so that all reaction norms were fitted within a 1x1 plot. Global Plasticity values were estimated by

161 the reaction norm range (the difference between the maximum and minimum phenotypes observed

162 in each reaction norm). For each species-specific trait, the upper and lower extreme values were

163 estimated by the maximum and minimum observed phenotypes regardless of genotype or

164 environment. To characterize how distant each genotype was from either limit of the phenotypic

165 space, we calculated the difference between the across-environment mean phenotype of each

166 reaction norm and the closest extreme value as (0.5 − |푃̅ − 0.5|), where 푃̅ is the across-

167 environment mean phenotype of each reaction norm. We tested the dependency of Global

168 Plasticity on the distance from the closest extreme phenotype by performing a least-squares linear

169 regression and the distribution of highly robust genotypes (i.e., the reaction norms with GP lower

170 or equal to 0.2) against a uniform distribution using a Kolmogorov-Smirnov test.

171 Model

172 The model describes a trait that is formed by a set of cells that may or may not follow a

173 differentiation path; the individual phenotype is given by the number of cells that differentiate.

174 Cell differentiation is triggered by the expression of an inducer gene (IG) at or above a threshold

175 value (t). Each individual has a constant number of 100 cells that may or not express the IG,

176 representing a constant trans-regulatory landscape of cells that constitutively express the

177 transcription factor (TF) necessary for the IG activity. There is a developmental time-window in

178 which the IG expression may trigger differentiation. The maximum number of times each cell may

179 or may not activate the transcription of the IG (rounds of activation) during this developmental

180 time window is given by n. Whether transcription is activated at each round of activation depends

181 on the probability of activation (p). This probability is given by a negative linear function of an

182 environmental variable (E) that varies from 0 to 1 with eleven values used to estimate each

183 genotype’s response. The equation of environmental perturbation is p = A + s E, where A is the

184 probability of transcription activation at E = 0 and s is the slope that determines how the

185 environmental variable affects the A; p was limited to vary between zero and one. The realized

186 transcription (RT) in each cell is given by the product of the number of times that IG is activated

187 (k) within the developmental time-window, i.e., we set the rate of transcription to be a constant.

188 Therefore, the phenotypic value of an individual is given by the number of cells activating the IG

189 at or above the minimum number of activations necessary to reach t. The probability of each cell to 푛 190 activate IG k times was given by the binomial distribution: 푃푟(푘; 푛, 푝) = ( ) 푝푘(1 − 푝)푛−푘. 푘

191 Since p is constant for each genotype in each environmental value, we may assume that the

192 proportion of cells activating IG k times in an infinite number of individuals raised in each

193 environmental value is given by the binomial probability Pr(k;n,p).

194 Therefore, transcriptional reaction norms were simulated by calculating the mean Realized

195 Transcription (푅푇̅̅̅̅) as the mean number of activations (푝 ∙ 푛). The mean phenotype in a given

196 environment may be calculated from the proportion of cells activating IG at or above kmin. We

197 calculated this from the cumulative probability function of the binomial equation:

⌊ ⌋ 푛 198 푃̅ = 푃푟(푋 ≥ 푡) = 1 − (∑ 푘푚푖푛 ( ) 푝푖(1 − 푝)푛−푖). 푖=0 푖

199 We explored different developmental setups (given by t and n) using, in each setup, a variation of

200 A that was sufficient to yield both phenotype saturation and depletion for s values ranging from 0

201 to -1 (Extended Data Fig. 1a gives an example for t = 50 and n = 101).

202 Adjustment to the dataset extracted from Crocker et al.2’s reaction norms:

203 In order to fit our model to the set of reaction norms from Crocker et al.2, we captured each

204 reaction norm point available in Figure 6 from their study using tps.dig33 and converted the values

205 to normalized phenotypic and environmental values. As the reaction norms in their data are non-

206 monotonic and our model does not consider changes in the reaction norm direction, we analyzed

207 only the lower segment (17-25° C). We then used the localized slope of this segment of each

208 reaction norm (Local Plasticity – LP, from Ref32) to estimate GP.

209 In our model, each specific slope of perturbation (s) generated a specific curve of GP variation as a

210 function of the genotype’s level of trait induction, which may be characterized by the mean

211 phenotype across different conditions. These curves converge at extreme phenotypes (due to

212 saturation and depletion) and diverge at intermediary mean phenotypes, where the peak of GP

213 values occur (Extended Data Fig.1b). Therefore, we took the reaction norm with most intermediary

214 mean phenotype and determined which value of s was necessary to yield a curve of equivalent GP,

215 following a linear variation of GP by s when the mean phenotype is 0.5 in the model (s =

216 0.0015216 - 0.134379 GP). We then used this s (-0.062813) to calibrate our model (keeping t at 50

217 and n at 101) and estimate GP for the remaining genotypes (i.e., those not involved in the model

218 calibration) based on their mean phenotype only. We calculated the R² between observed and

219 predicted values to evaluate the goodness of fit of our model to their experimental results.

220 Data availability

221 The set of data extracted from the reaction norms compiled by Murren et al. 2014 used in the

222 analysis is available in Supplementary Table 1. Additional data supporting the findings of this

223 study are available from the corresponding author upon reasonable request.

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293 Acknowledgements 294 We thank the financial support of the following: Coordenação de Aperfeiçoamento de Pessoal de 295 Nível Superior (CAPES), Conselho Nacional de Desenvolvimento Científico e Tecnológico 296 (CNPq), Fundação de Amparo ao Ensino, à Pesquisa e à Extensão (FAEPEX), and Fundação de 297 Amparo à Pesquisa do Estado de São Paulo (FAPESP). FBR was supported by a postdoctoral 298 fellowship from FAPESP (processo nº 2013/04980-0) and a fellowship from the Programa 299 Nacional de Pós-Doutorado from CAPES. FBR thanks F. Uno, I.M. Ventura and Prof. M. D. 300 Vibranovski for comments on the manuscript. 301

302 Author Contributions 303 FBR conceived and carried out the analyses of phenotypic reaction norms, designed the model, 304 performed the numerical simulations and adjustments and wrote the manuscript. 305 LBK supervised the analysis of reaction norms and contributed to the final version of the 306 manuscript. 307

308 Author Information

309 Reprints and permissions information is available at www.nature.com/reprints 310 The authors declare no conflict of interest. 311 Correspondence and requests for materials should be addressed to FBR ([email protected]). 312

313 Figures

314 315 a b 316 Underlying processes Observable outcome Underlying processes Observable outcome Perturbation of Perturbation of 317 induction induction

318 Buffering Buffering Phenotype Phenotype

Phenotype 319 Phenotype 320 321

322 Trait induction Perturbing conditions Trait induction Perturbing conditions 323 324 c 325 Underlying processes Observable outcome

326 Perturbation of Perturbation of Perturbation of 327 induction induction induction

328 max

329 Phenotypic space

330 331 Phenotype Phenotype

332

333

334 min

Saturation 335 Depletion Perturbing conditions Lower threshold Upper threshold 336 Trait induction 337 338 339 Figure 1. Phenotypic robustness may be the outcome of two contrasting underlying 340 mechanisms. a, perturbations of the level of trait induction (left) due to alleles or environments 341 that either inhibit or promote the trait’s formation are prone to yield observable phenotypic 342 responses (right). b, developmental buffering (left), which avoids (or cancels out) the changes in 343 the level of trait induction potentially caused by such perturbations are often thought to underlie 344 observable phenotypic robustness (right). c, when there is no such buffering system, basic 345 developmental principles entail a nonlinear relationship between trait induction and the phenotype 346 (left). This creates two regions of phenotypic robustness where even individuals submitted to 347 perturbing conditions will be phenotypically stable. The same perturbation, when applied to 348 genotypes conferring intermediary levels of trait induction will yield an unavoidable phenotypic 349 response, thus yielding a pattern of association between the amount of phenotypic response and the 350 position of a genotype in the phenotypic space (right). 351

352 a 353 1.2

354 1

355 0.8 R² = 0.5216 356 0.6 357

358 GlobalPlasticity 0.4

359 0.2 Highly robust genotypes 360 0 361 0 0.1 0.2 0.3 0.4 0.5 0.6 Distance from extreme phenotypes 362

b 30% 363 364 25% 365 20%

15% 366

367 10% 368 369 5%

370 of% genotypes robust highly 371 0% 372 373 374 Distance from extreme phenotypes 375 376 377 Figure 2. Phenotypic robustness variation in a large sample of 856 reaction norms of diverse 378 animal, plant and bacteria species is mostly explained by the position of the genotype in the 379 phenotypic space. a, observed Global Plascitiy increases with the distance between the genotype’s 380 mean phenotype and the trait limits in the dataset extracted from Murren et al. (2014). b, highly 381 robust genotypes are significantly concentrated near the phenotypic extremes in this sample of 382 reaction norms. 383 384

385 a b 386

387

388

389 Phenotype 390 Transcription

391 392 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 393 Environment Environment 394 c d

1.0 1.1 395 0.9 1.0

396 0.8 0.9 0.8 397 0.7 0.7 0.6 398 0.6 0.5 0.5 399 0.4 0.4 GlobalPlasticity environment phenotype environment 400 0.3 - 0.3 0.2 0.2 401 0.1 0.1 402 0.0 0.0

0 0.2 0.4 0.6 0.8 1 Mean across 0 0.2 0.4 0.6 0.8 1 403 Probability of gene activation Probability of gene activation 404 405 406 407 Figure 3. A simple model of trait development shows that phenotypic robustness may be 408 achieved without transcriptional robustness. a, simulated transcriptional reaction norms. b, 409 simulated phenotypic reaction norms. c, Global Plasticity variation for transcriptional (triangles) 410 and phenotypic (circles) reaction norms for genotypes with varying probability of transcription 411 initiation. Yellow shaded areas highlight “genotypes” with total phenotypic robustness (zero GP) 412 despite having maximum transcriptional plasticity. d, mean phenotype as a function of probability 413 of gene activation gives a depletion/saturation curve due to the minimal threshold of gene activity 414 and the limitedness of the phenotype. c and d, red – “genotypes” with phenotypically responsive 415 reaction norms; blue – “genotypes” with phenotypically robust reaction norms. Values shown 416 correspond to t = 50, n = 101 and s = -0.25. 417

418 419 420 a b 421 422 0.6 1 423 R² = 0.829 R² = 0.7426 0.5 0.8 -

424 0.4 0.6 across

425 0.3 0.4

426 0.2 0.2 Global Plasticity Phenotypic environment mean 427 0.1 0 -0.2 428 0 0 0.25 0.5 0.75 1 0 1 2 3 4 429 Mean phenotype Number of unmutated Ubx-Exd binding sites 430 observed estimated 431 432 Figure 4. A model of robustness by saturation and depletion explains the pattern of 433 association between cis-regulatory multiplicity and robustness described by Crocker et al. 434 (2015). a, a model adjustment assuming that all genotypes suffer the same impact of temperature 435 on transcription allows to describe 84% of Global Plasticity variation as a function of the across- 436 environment mean phenotype. b, the across-environment mean phenotype is positively associated 437 with the number of unmutated Ubx-Exd binding sites (R² = 0.70; p = 0.005942). [Data extracted 438 from Crocker et al. (2015) Fig. 6.] 439