Genotype to Phenotype Mapping and the Fitness Landscape of the E. coli lac Promoter

Otwinowski, Jakub; Nemenman, Ilya

doi:10.1371/journal.pone.0061570

Cited by 58 publications

(68 citation statements)

References 53 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This is arguably the simplest non-trivial model of the fitness landscape with many local maxima and minima and thus it presents an ideal test ground to investigate the role of connectivity on the accessibility of FLs. Although real landscapes are known to be moderately correlated [10, 37–39], we shall show later that our conclusions are robust in the presence of such correlations.…”

Section: Introductionmentioning

confidence: 58%

Beyond the Hypercube: Evolutionary Accessibility of Fitness Landscapes with Realistic Mutational Networks

2016

View full text Add to dashboard Cite

Evolutionary pathways describe trajectories of biological evolution in the space of different variants of organisms (genotypes). The probability of existence and the number of evolutionary pathways that lead from a given genotype to a better-adapted genotype are important measures of accessibility of local fitness optima and the reproducibility of evolution. Both quantities have been studied in simple mathematical models where genotypes are represented as binary sequences of two types of basic units, and the network of permitted mutations between the genotypes is a hypercube graph. However, it is unclear how these results translate to the biologically relevant case in which genotypes are represented by sequences of more than two units, for example four nucleotides (DNA) or 20 amino acids (proteins), and the mutational graph is not the hypercube. Here we investigate accessibility of the best-adapted genotype in the general case of K > 2 units. Using computer generated and experimental fitness landscapes we show that accessibility of the global fitness maximum increases with K and can be much higher than for binary sequences. The increase in accessibility comes from the increase in the number of indirect trajectories exploited by evolution for higher K. As one of the consequences, the fraction of genotypes that are accessible increases by three orders of magnitude when the number of units K increases from 2 to 16 for landscapes of size N ∼ 106 genotypes. This suggests that evolution can follow many different trajectories on such landscapes and the reconstruction of evolutionary pathways from experimental data might be an extremely difficult task.

show abstract

Section: Introductionmentioning

confidence: 58%

Beyond the Hypercube: Evolutionary Accessibility of Fitness Landscapes with Realistic Mutational Networks

2016

View full text Add to dashboard Cite

show abstract

“…We also performed regression similar to that used in machine learning approaches (36,37,43), which results in the formula g 123 = g 12 g 13 g 23 =g 1 g 2 g 3 (Methods). This regression formula shows poor performance (Fig.…”

Section: Significancementioning

confidence: 99%

Prediction of multidimensional drug dose responses based on measurements of drug pairs

Zimmer

Katzir

Dekel

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

145

174

View full text Add to dashboard Cite

Finding potent multidrug combinations against cancer and infections is a pressing therapeutic challenge; however, screening all combinations is difficult because the number of experiments grows exponentially with the number of drugs and doses. To address this, we present a mathematical model that predicts the effects of three or more antibiotics or anticancer drugs at all doses based only on measurements of drug pairs at a few doses, without need for mechanistic information. The model provides accurate predictions on available data for antibiotic combinations, and on experiments presented here on the response matrix of three cancer drugs at eight doses per drug. This approach offers a way to search for effective multidrug combinations using a small number of experiments.drug combinations | drug cocktails | cancer treatment | mechanism-free formula | predictive formula T o kill cancer cells or bacteria, combination therapy can be more effective than individual drugs (1-6). Combination therapy is thought to allow increased efficacy at low doses, thus reducing side effects and toxicity; it is also believed to minimize the chances of resistance (7-9), a pressing problem in treating cancer and infectious diseases.Much work has been devoted to classifying how pairs of drugs interact (10)(11)(12)(13)(14). Across systems, a good first approximation is the Bliss independence model (15,16), in which the pair effect is the product of the individual drug effects: If the effect of the drugs are g 1 and g 2 , the effect of the combination is g 12 = g 1 · g 2 . The Bliss model ignores interactions in which drugs enhance each other effectssynergism-or inhibit each other's effects-antagonism. Some drugs even inhibit each other so much that the combined effect is lower than either drug alone, an effect called hyperantagonism (17)(18)(19)(20)(21).Going beyond drug pairs has been difficult. Experimentally testing high-order combinations beyond pairs in a systematic way is challenging because it requires an exponentially large number of experiments (22-25): For N drugs at D doses, one needs D N experiments. For N = 10 drugs and D = 8 doses, this means ∼10 9 measurements. The combinatorial explosion makes exhaustive testing of drug dose combinations unfeasible. This problem is especially acute in cases where material is scarce, such as testing of patient-derived samples (26)(27)(28)(29). Hence, models for predicting high-order effects are essential.Apart from detailed simulations of particular systems (22,30,31), there has been little study of general mechanism-independent models for multiple drugs. An exception is the elegant study by Wood et al. (32) that showed that combinations of antibiotics can be predicted by an Iserliss-like formula that uses pair effects to predict the effects of higher-order mixtures. For example, the effect of a drug triplet is modeled as g 123 = g 12 g 3 + g 13 g 2 + g 23 g 1 − 2g 1 g 2 g 3 . This formula has not been tested on cancer drug mixtures, to the best of our knowledge.Another line of research u...

show abstract

“…One obvious way to incorporate epistasis into this additive model is by including explicit terms for interactions between each pair of sites, and possibly higher-order interactions as well [7,8]. By contrast, we develop a model and inference procedure for a different form of epistasis, motivated by examining the deviations between empirical data sets and their best-fit non-epistatic models.…”

Section: A Model Of Global Epistasismentioning

confidence: 99%

“…Statistical models are therefore required to derive biological insight from these sparsely sampled genotype-phenotype maps. One approach has been to fit models that include terms for each pairwise interaction between genetic sites [7,8].…”

Section: Introductionmentioning

confidence: 99%

Inferring the shape of global epistasis

Otwinowski

McCandlish

Plotkin

2018

Preprint

Self Cite

View full text Add to dashboard Cite

Genotype-phenotype relationships are notoriously complicated. Idiosyncratic interactions between specific combinations of mutations occur, and are difficult to predict. Yet it is increasingly clear that many interactions can be understood in terms of global epistasis. That is, mutations may act additively on some underlying, unobserved trait, and this trait is then transformed via a nonlinear function to the observed phenotype as a result of subsequent biophysical and cellular processes. Here we infer the shape of such global epistasis in three proteins, based on published high-throughput mutagenesis data. To do so, we develop a maximum-likelihood inference procedure using a flexible family of monotonic nonlinear functions spanned by an I-spline basis. Our analysis uncovers dramatic nonlinearities in all three proteins; in some proteins a model with global epistasis accounts for virtually all the measured variation, whereas in others we find substantial local epistasis as well. This method allows us to test hypotheses about the form of global epistasis and to distinguish variance components attributable to global epistasis, local epistasis, and measurement error.

show abstract

Genotype to Phenotype Mapping and the Fitness Landscape of the E. coli lac Promoter

Cited by 58 publications

References 53 publications

Beyond the Hypercube: Evolutionary Accessibility of Fitness Landscapes with Realistic Mutational Networks

Beyond the Hypercube: Evolutionary Accessibility of Fitness Landscapes with Realistic Mutational Networks

Prediction of multidimensional drug dose responses based on measurements of drug pairs

Inferring the shape of global epistasis

Contact Info

Product

Resources

About