Nonlinear Fitness Landscape of a Molecular Pathway

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

Predicting the Tolerated Sequences for Proteins and Protein Interfaces Using RosettaBackrub Flexible Backbone Design

Predicting the set of sequences that are tolerated by a protein or protein interface, while maintaining a desired function, is useful for characterizing protein interaction specificity and for computationally designing sequence libraries to engineer proteins with new functions. Here we provide a general method, a detailed set of protocols, and several benchmarks and analyses for estimating tolerated sequences using flexible backbone protein design implemented in the Rosetta molecular modeling software suite. The input to the method is at least one experimentally determined three-dimensional protein structure or high-quality model. The starting structure(s) are expanded or refined into a conformational ensemble using Monte Carlo simulations consisting of backrub backbone and side chain moves in Rosetta. The method then uses a combination of simulated annealing and genetic algorithm optimization methods to enrich for low-energy sequences for the individual members of the ensemble. To emphasize certain functional requirements (e.g. forming a binding interface), interactions between and within parts of the structure (e.g. domains) can be reweighted in the scoring function. Results from each backbone structure are merged together to create a single estimate for the tolerated sequence space. We provide an extensive description of the protocol and its parameters, all source code, example analysis scripts and three tests applying this method to finding sequences predicted to stabilize proteins or protein interfaces. The generality of this method makes many other applications possible, for example stabilizing interactions with small molecules, DNA, or RNA. Through the use of within-domain reweighting and/or multistate design, it may also be possible to use this method to find sequences that stabilize particular protein conformations or binding interactions over others

Human cooperation in groups: variation begets variation

Many experiments on human cooperation have revealed that individuals differ systematically in their tendency to cooperate with others. It has also been shown that individuals condition their behaviour on the overall cooperation level of their peers. Yet, little is known about how individuals respond to heterogeneity in cooperativeness in their neighbourhood. Here, we present an experimental study investigating whether and how people respond to heterogeneous behaviour in a public goods game. We find that a large majority of subjects does respond to heterogeneity in their group, but they respond in quite different ways. Most subjects contribute less to the public good when the contributions of their peers are more heterogeneous, but a substantial fraction of individuals consistently contributes more in this case. In addition, we find that individuals that respond positively to heterogeneity have a higher general cooperation tendency. The finding that social responsiveness occurs in different forms and is correlated with cooperativeness may have important implications for the outcome of cooperative interactions

Leukocyte Tyrosine Kinase Functions in Pigment Cell Development

A fundamental problem in developmental biology concerns how multipotent precursors choose specific fates. Neural crest cells (NCCs) are multipotent, yet the mechanisms driving specific fate choices remain incompletely understood. Sox10 is required for specification of neural cells and melanocytes from NCCs. Like sox10 mutants, zebrafish shady mutants lack iridophores; we have proposed that sox10 and shady are required for iridophore specification from NCCs. We show using diverse approaches that shady encodes zebrafish leukocyte tyrosine kinase (Ltk). Cell transplantation studies show that Ltk acts cell-autonomously within the iridophore lineage. Consistent with this, ltk is expressed in a subset of NCCs, before becoming restricted to the iridophore lineage. Marker analysis reveals a primary defect in iridophore specification in ltk mutants. We saw no evidence for a fate-shift of neural crest cells into other pigment cell fates and some NCCs were subsequently lost by apoptosis. These features are also characteristic of the neural crest cell phenotype in sox10 mutants, leading us to examine iridophores in sox10 mutants. As expected, sox10 mutants largely lacked iridophore markers at late stages. In addition, sox10 mutants unexpectedly showed more ltk-expressing cells than wild-type siblings. These cells remained in a premigratory position and expressed sox10 but not the earliest neural crest markers and may represent multipotent, but partially-restricted, progenitors. In summary, we have discovered a novel signalling pathway in NCC development and demonstrate fate specification of iridophores as the first identified role for Ltk

Adaptive Evolution of the Lactose Utilization Network in Experimentally Evolved Populations of Escherichia coli

Adaptation to novel environments is often associated with changes in gene regulation. Nevertheless, few studies have been able both to identify the genetic basis of changes in regulation and to demonstrate why these changes are beneficial. To this end, we have focused on understanding both how and why the lactose utilization network has evolved in replicate populations of Escherichia coli. We found that lac operon regulation became strikingly variable, including changes in the mode of environmental response (bimodal, graded, and constitutive), sensitivity to inducer concentration, and maximum expression level. In addition, some classes of regulatory change were enriched in specific selective environments. Sequencing of evolved clones, combined with reconstruction of individual mutations in the ancestral background, identified mutations within the lac operon that recapitulate many of the evolved regulatory changes. These mutations conferred fitness benefits in environments containing lactose, indicating that the regulatory changes are adaptive. The same mutations conferred different fitness effects when present in an evolved clone, indicating that interactions between the lac operon and other evolved mutations also contribute to fitness. Similarly, changes in lac regulation not explained by lac operon mutations also point to important interactions with other evolved mutations. Together these results underline how dynamic regulatory interactions can be, in this case evolving through mutations both within and external to the canonical lactose utilization network

Rosetta FlexPepDock ab-initio: Simultaneous Folding, Docking and Refinement of Peptides onto Their Receptors

Flexible peptides that fold upon binding to another protein molecule mediate a large number of regulatory interactions in the living cell and may provide highly specific recognition modules. We present Rosetta FlexPepDock ab-initio, a protocol for simultaneous docking and de-novo folding of peptides, starting from an approximate specification of the peptide binding site. Using the Rosetta fragments library and a coarse-grained structural representation of the peptide and the receptor, FlexPepDock ab-initio samples efficiently and simultaneously the space of possible peptide backbone conformations and rigid-body orientations over the receptor surface of a given binding site. The subsequent all-atom refinement of the coarse-grained models includes full side-chain modeling of both the receptor and the peptide, resulting in high-resolution models in which key side-chain interactions are recapitulated. The protocol was applied to a benchmark in which peptides were modeled over receptors in either their bound backbone conformations or in their free, unbound form. Near-native peptide conformations were identified in 18/26 of the bound cases and 7/14 of the unbound cases. The protocol performs well on peptides from various classes of secondary structures, including coiled peptides with unusual turns and kinks. The results presented here significantly extend the scope of state-of-the-art methods for high-resolution peptide modeling, which can now be applied to a wide variety of peptide-protein interactions where no prior information about the peptide backbone conformation is available, enabling detailed structure-based studies and manipulation of those interactions

Structure-Based Design of Non-Natural Amino Acid Inhibitors of Amyloid Fibrillation

Many globular and natively disordered proteins can convert into amyloid fibers. These fibers are associated with numerous pathologies1 as well as with normal cellular functions2,3, and frequently form during protein denaturation4,5. Inhibitors of pathological amyloid fibers could serve as leads for therapeutics, provided the inhibitors were specific enough to avoid interfering with normal processes. Here we show that computer-aided, structure-based design can yield highly specific peptide inhibitors of amyloid formation. Using known atomic structures of segments of amyloid fibers as templates, we have designed and characterized an all D-amino acid inhibitor of fibrillation of the tau protein found in Alzheimer’s disease, and a non-natural L-amino acid inhibitor of an amyloid fiber that enhances sexual transmission of HIV. Our results indicate that peptides from structure-based designs can disrupt the fibrillation of full-length proteins, including those like tau that lack fully ordered native structures.We thank M.I. Ivanova, J. Corn, T. Kortemme, D. Anderson, M.R. Sawaya, M. Phillips, S. Sambashivan, J. Park, M. Landau, Q. Zhang, R. Clubb, F. Guo, T. Yeates, J. Nowick, J. Zheng, and M.J. Thompson for discussions, HHMI, NIH, NSF, the GATES foundation, and the Joint Center for Translational Medicine for support, R. Peterson for help with NMR experiments, E. Mandelkow for providing tau constructs, R. Riek for providing amyloid beta, J. Stroud for amyloid beta preparation. Support for JK was from the Damon Runyon Cancer Research Foundation, for HWC by the Ruth L. Kirschstein National Research Service Award, for JM from the programme for junior-professors by the ministry of science, Baden-Württemberg, and for SAS by a UCLA-IGERT bioinformatics traineeship

Computational Design of a PDZ Domain Peptide Inhibitor that Rescues CFTR Activity

The cystic fibrosis transmembrane conductance regulator (CFTR) is an epithelial chloride channel mutated in patients with cystic fibrosis (CF). The most prevalent CFTR mutation, ΔF508, blocks folding in the endoplasmic reticulum. Recent work has shown that some ΔF508-CFTR channel activity can be recovered by pharmaceutical modulators (“potentiators” and “correctors”), but ΔF508-CFTR can still be rapidly degraded via a lysosomal pathway involving the CFTR-associated ligand (CAL), which binds CFTR via a PDZ interaction domain. We present a study that goes from theory, to new structure-based computational design algorithms, to computational predictions, to biochemical testing and ultimately to epithelial-cell validation of novel, effective CAL PDZ inhibitors (called “stabilizers”) that rescue ΔF508-CFTR activity. To design the “stabilizers”, we extended our structural ensemble-based computational protein redesign algorithm to encompass protein-protein and protein-peptide interactions. The computational predictions achieved high accuracy: all of the top-predicted peptide inhibitors bound well to CAL. Furthermore, when compared to state-of-the-art CAL inhibitors, our design methodology achieved higher affinity and increased binding efficiency. The designed inhibitor with the highest affinity for CAL (kCAL01) binds six-fold more tightly than the previous best hexamer (iCAL35), and 170-fold more tightly than the CFTR C-terminus. We show that kCAL01 has physiological activity and can rescue chloride efflux in CF patient-derived airway epithelial cells. Since stabilizers address a different cellular CF defect from potentiators and correctors, our inhibitors provide an additional therapeutic pathway that can be used in conjunction with current methods

A Linear Framework for Time-Scale Separation in Nonlinear Biochemical Systems

Cellular physiology is implemented by formidably complex biochemical systems with highly nonlinear dynamics, presenting a challenge for both experiment and theory. Time-scale separation has been one of the few theoretical methods for distilling general principles from such complexity. It has provided essential insights in areas such as enzyme kinetics, allosteric enzymes, G-protein coupled receptors, ion channels, gene regulation and post-translational modification. In each case, internal molecular complexity has been eliminated, leading to rational algebraic expressions among the remaining components. This has yielded familiar formulas such as those of Michaelis-Menten in enzyme kinetics, Monod-Wyman-Changeux in allostery and Ackers-Johnson-Shea in gene regulation. Here we show that these calculations are all instances of a single graph-theoretic framework. Despite the biochemical nonlinearity to which it is applied, this framework is entirely linear, yet requires no approximation. We show that elimination of internal complexity is feasible when the relevant graph is strongly connected. The framework provides a new methodology with the potential to subdue combinatorial explosion at the molecular level