A tractable genotype-phenotype map for the self-assembly of protein quaternary structure

The mapping between biological genotypes and phenotypes is central to the study of biological evolution. Here we introduce a rich, intuitive, and biologically realistic genotype-phenotype (GP) map, that serves as a model of self-assembling biological structures, such as protein complexes, and remains computationally and analytically tractable. Our GP map arises naturally from the self-assembly of polyomino structures on a 2D lattice and exhibits a number of properties: $\textit{redundancy}$ (genotypes vastly outnumber phenotypes), $\textit{phenotype bias}$ (genotypic redundancy varies greatly between phenotypes), $\textit{genotype component disconnectivity}$ (phenotypes consist of disconnected mutational networks) and $\textit{shape space covering}$ (most phenotypes can be reached in a small number of mutations). We also show that the mutational robustness of phenotypes scales very roughly logarithmically with phenotype redundancy and is positively correlated with phenotypic evolvability. Although our GP map describes the assembly of disconnected objects, it shares many properties with other popular GP maps for connected units, such as models for RNA secondary structure or the HP lattice model for protein tertiary structure. The remarkable fact that these important properties similarly emerge from such different models suggests the possibility that universal features underlie a much wider class of biologically realistic GP maps.Comment: 12 pages, 6 figure

Genetic Correlations Greatly Increase Mutational Robustness and Can Both Reduce and Enhance Evolvability.

Mutational neighbourhoods in genotype-phenotype (GP) maps are widely believed to be more likely to share characteristics than expected from random chance. Such genetic correlations should strongly influence evolutionary dynamics. We explore and quantify these intuitions by comparing three GP maps-a model for RNA secondary structure, the HP model for protein tertiary structure, and the Polyomino model for protein quaternary structure-to a simple random null model that maintains the number of genotypes mapping to each phenotype, but assigns genotypes randomly. The mutational neighbourhood of a genotype in these GP maps is much more likely to contain genotypes mapping to the same phenotype than in the random null model. Such neutral correlations can be quantified by the robustness to mutations, which can be many orders of magnitude larger than that of the null model, and crucially, above the critical threshold for the formation of large neutral networks of mutationally connected genotypes which enhance the capacity for the exploration of phenotypic novelty. Thus neutral correlations increase evolvability. We also study non-neutral correlations: Compared to the null model, i) If a particular (non-neutral) phenotype is found once in the 1-mutation neighbourhood of a genotype, then the chance of finding that phenotype multiple times in this neighbourhood is larger than expected; ii) If two genotypes are connected by a single neutral mutation, then their respective non-neutral 1-mutation neighbourhoods are more likely to be similar; iii) If a genotype maps to a folding or self-assembling phenotype, then its non-neutral neighbours are less likely to be a potentially deleterious non-folding or non-assembling phenotype. Non-neutral correlations of type i) and ii) reduce the rate at which new phenotypes can be found by neutral exploration, and so may diminish evolvability, while non-neutral correlations of type iii) may instead facilitate evolutionary exploration and so increase evolvability.This work was funded under EP/P504287/1 by the Engineering and Physical Sciences Research Council (https://www.epsrc.ac.uk). SEA is supported by The Royal Society (https://royalsociety.org/).This is the final version of the article. It first appeared from PLOS via http://dx.doi.org/10.1371/journal.pcbi.100477

Precision identification of high-risk phenotypes and progression pathways in severe malaria without requiring longitudinal data

More than 400,000 deaths from severe malaria (SM) are reported every year, mainly in African children. The diversity of clinical presentations associated with SM indicates important differences in disease pathogenesis that require specific treatment, and this clinical heterogeneity of SM remains poorly understood. Here, we apply tools from machine learning and model-based inference to harness large-scale data and dissect the heterogeneity in patterns of clinical features associated with SM in 2904 Gambian children admitted to hospital with malaria. This quantitative analysis reveals features predicting the severity of individual patient outcomes, and the dynamic pathways of SM progression, notably inferred without requiring longitudinal observations. Bayesian inference of these pathways allows us assign quantitative mortality risks to individual patients. By independently surveying expert practitioners, we show that this data-driven approach agrees with and expands the current state of knowledge on malaria progression, while simultaneously providing a data-supported framework for predicting clinical risk

The effect of scale-free topology on the robustness and evolvability of genetic regulatory networks

We investigate how scale-free (SF) and Erdos-Renyi (ER) topologies affect the interplay between evolvability and robustness of model gene regulatory networks with Boolean threshold dynamics. In agreement with Oikonomou and Cluzel (2006) we find that networks with SFin topologies, that is SF topology for incoming nodes and ER topology for outgoing nodes, are significantly more evolvable towards specific oscillatory targets than networks with ER topology for both incoming and outgoing nodes. Similar results are found for networks with SFboth and SFout topologies. The functionality of the SFout topology, which most closely resembles the structure of biological gene networks (Babu et al., 2004), is compared to the ER topology in further detail through an extension to multiple target outputs, with either an oscillatory or a non-oscillatory nature. For multiple oscillatory targets of the same length, the differences between SFout and ER networks are enhanced, but for non-oscillatory targets both types of networks show fairly similar evolvability. We find that SF networks generate oscillations much more easily than ER networks do, and this may explain why SF networks are more evolvable than ER networks are for oscillatory phenotypes. In spite of their greater evolvability, we find that networks with SFout topologies are also more robust to mutations than ER networks. Furthermore, the SFout topologies are more robust to changes in initial conditions (environmental robustness). For both topologies, we find that once a population of networks has reached the target state, further neutral evolution can lead to an increase in both the mutational robustness and the environmental robustness to changes in initial conditions.Comment: 16 pages, 15 figure

The structure of genotype-phenotype maps makes fitness landscapes navigable.

Fitness landscapes are often described in terms of 'peaks' and 'valleys', indicating an intuitive low-dimensional landscape of the kind encountered in everyday experience. The space of genotypes, however, is extremely high dimensional, which results in counter-intuitive structural properties of genotype-phenotype maps. Here we show that these properties, such as the presence of pervasive neutral networks, make fitness landscapes navigable. For three biologically realistic genotype-phenotype map models-RNA secondary structure, protein tertiary structure and protein complexes-we find that, even under random fitness assignment, fitness maxima can be reached from almost any other phenotype without passing through fitness valleys. This in turn indicates that true fitness valleys are very rare. By considering evolutionary simulations between pairs of real examples of functional RNA sequences, we show that accessible paths are also likely to be used under evolutionary dynamics. Our findings have broad implications for the prediction of natural evolutionary outcomes and for directed evolution

The structure of genotype-phenotype maps makes fitness landscapes navigable

Fitness landscapes are often described in terms of 'peaks' and 'valleys', indicating an intuitive low-dimensional landscape of the kind encountered in everyday experience. The space of genotypes, however, is extremely high dimensional, which results in counter-intuitive structural properties of genotype-phenotype maps. Here we show that these properties, such as the presence of pervasive neutral networks, make fitness landscapes navigable. For three biologically realistic genotype-phenotype map models-RNA secondary structure, protein tertiary structure and protein complexes-we find that, even under random fitness assignment, fitness maxima can be reached from almost any other phenotype without passing through fitness valleys. This in turn indicates that true fitness valleys are very rare. By considering evolutionary simulations between pairs of real examples of functional RNA sequences, we show that accessible paths are also likely to be used under evolutionary dynamics. Our findings have broad implications for the prediction of natural evolutionary outcomes and for directed evolution

A tractable genotype-phenotype map modelling the self-assembly of protein quaternary structure

The mapping between biological genotypes and phenotypes is central to the study of biological evolution. Here, we introduce a rich, intuitive and biologically realistic genotype–phenotype (GP) map that serves as a model of self-assembling biological structures, such as protein complexes, and remains computationally and analytically tractable. Our GP map arises naturally from the self-assembly of polyomino structures on a two-dimensional lattice and exhibits a number of properties: redundancy (genotypes vastly outnumber phenotypes), phenotype bias (genotypic redundancy varies greatly between phenotypes), genotype component disconnectivity (phenotypes consist of disconnected mutational networks) and shape space covering (most phenotypes can be reached in a small number of mutations). We also show that the mutational robustness of phenotypes scales very roughly logarithmically with phenotype redundancy and is positively correlated with phenotypic evolvability. Although our GP map describes the assembly of disconnected objects, it shares many properties with other popular GP maps for connected units, such as models for RNA secondary structure or the hydrophobic-polar (HP) lattice model for protein tertiary structure. The remarkable fact that these important properties similarly emerge from such different models suggests the possibility that universal features underlie a much wider class of biologically realistic GP maps

Illustration of further non-neutral correlations.

<p>A) On the right, the orange phenotype is over-represented relative to the null model: The red genotype in the centre has more orange neighbours than would be expected by the global frequency of orange. B) The phenotypes that appear in the mutational neighbourhood of two neutral neighbours are expected to be more similar (right) than two non-neighbouring genotypes of the same phenotype (left).</p

GP map nomenclature.

<p>GP map nomenclature.</p