Nonlinear Fitness Landscape of a Molecular Pathway

Abstract

Genes are regulated because their expression involves a fitness cost to the organism. The production of proteins by transcription and translation is a well-known cost factor, but the enzymatic activity of the proteins produced can also reduce fitness, depending on the internal state and the environment of the cell. Here, we map the fitness costs of a key metabolic network, the lactose utilization pathway in Escherichia coli. We measure the growth of several regulatory lac operon mutants in different environments inducing expression of the lac genes. We find a strikingly nonlinear fitness landscape, which depends on the production rate and on the activity rate of the lac proteins. A simple fitness model of the lac pathway, based on elementary biophysical processes, predicts the growth rate of all observed strains. The nonlinearity of fitness is explained by a feedback loop: production and activity of the lac proteins reduce growth, but growth also affects the density of these molecules. This nonlinearity has important consequences for molecular function and evolution. It generates a cliff in the fitness landscape, beyond which populations cannot maintain growth. In viable populations, there is an expression barrier of the lac genes, which cannot be exceeded in any stationary growth process. Furthermore, the nonlinearity determines how the fitness of operon mutants depends on the inducer environment. We argue that fitness nonlinearities, expression barriers, and gene–environment interactions are generic features of fitness landscapes for metabolic pathways, and we discuss their implications for the evolution of regulation.

Synthetic approaches to understanding biological constraints

“…Although such experimental studies are necessarily limited by the exponential number of possible intermediates, various kinds of landscapes have been studied. Notably, the mapping involved in the definition of a landscape is not necessarily one-to-one: different genotypes can converge to the same phenotype [39] and, in case of multi-stable gene expression [40], the same genotype can produce different phenotypes. Moreover, even if genotype-to-phenotype landscapes may be approximately linear, the non-linearity of the further mapping between phenotype and growth rate leads to a non-linearity of the final genotype-to-fitness landscapes [32], which often display epistatic effects leading to diminishing returns [33, 34, 35].…”

Fitness Effects of Mutations in Bacteria

“…However, the approach can be taken at a smaller scale for wellcharacterized genetic systems. For example, Perfeito et al [2011] constructed a number of mutants with different levels of expression of the lac operon in E. coli . In this case, the genotype is known and the phenotypes are well defined and can be measured, namely the level of protein production and of protein activity of the lac genes.…”

Mapping the Environmental Fitness Landscape of a Synthetic Gene Circuit

“…From an evolutionary standpoint, fitness (cell population growth rate) may be the most important phenotype encoded, since it defines the competitive ability of a genotype in specific environments. The critical role of gene expression as a determinant of fitness in various environments was confirmed by a variety of gene expression measurement techniques, including beta-galactosidase assays [2]–[4] and microarrays [5]–[7]. Such techniques typically rely on pooling millions of cells, and therefore can only measure the average gene expression of a given sample.…”