Mutational robustness and geometrical form in protein structures

Symmetry and simplicity spontaneously emerge from the algorithmic nature of evolution

SignificanceWhy does evolution favor symmetric structures when they only represent a minute subset of all possible forms? Just as monkeys randomly typing into a computer language will preferentially produce outputs that can be generated by shorter algorithms, so the coding theorem from algorithmic information theory predicts that random mutations, when decoded by the process of development, preferentially produce phenotypes with shorter algorithmic descriptions. Since symmetric structures need less information to encode, they are much more likely to appear as potential variation. Combined with an arrival-of-the-frequent mechanism, this algorithmic bias predicts a much higher prevalence of low-complexity (high-symmetry) phenotypes than follows from natural selection alone and also explains patterns observed in protein complexes, RNA secondary structures, and a gene regulatory network.

Quantifying the Mutational Robustness of Protein-Coding Genes

We use large-scale mutagenesis data and computer simulations to quantify the mutational robustness of protein-coding genes by taking into account constraints arising from protein function and the genetic code. Analyses of the distribution of amino acid substitutions from 18 mutagenesis studies revealed an average of 45% of neutral variants; while mutagenesis data of 12 proteins artificially designed under no other constraints but stability, reach an average of 60%. Simulations using a lattice protein model allow us to contrast these estimates to the expected mutational robustness of protein families by generating unbiased samples of foldable sequences, which we find to have 30% of neutral variants. In agreement with mutagenesis data of designed proteins, the model shows that maximally robust protein families might access up to twice the amount of neutral variants observed in the unbiased samples (i.e. 60%). A biophysical model of protein-ligand binding suggests that constraints associated to molecular function have only a moderate impact on robustness of approximately 5 to 10% of neutral variants; and that the direction of this effect depends on the relation between functional performance and thermodynamic stability. Although the genetic code constraints the access of a gene's nucleotide sequence to only 30% of the full distribution of amino acid mutations, it provides an extra 15 to 20% of neutral variants to the estimations above, such that the expected, observed, and maximal robustness of protein-coding genes are approximately 50, 65, and 75%, respectively. We discuss our results in the light of three main hypothesis put forward to explain the existence of mutationally robust genes.

The amino acid alphabet and the architecture of the protein sequence-structure map. I. Binary alphabets

The correspondence between protein sequences and structures, or sequence-structure map, relates to fundamental aspects of structural, evolutionary and synthetic biology. The specifics of the mapping, such as the fraction of accessible sequences and structures, or the sequences' ability to fold fast, are dictated by the type of interactions between the monomers that compose the sequences. The set of possible interactions between monomers is encapsulated by the potential energy function. In this study, I explore the impact of the relative forces of the potential on the architecture of the sequence-structure map. My observations rely on simple exact models of proteins and random samples of the space of potential energy functions of binary alphabets. I adopt a graph perspective and study the distribution of viable sequences and the structures they produce, as networks of sequences connected by point mutations. I observe that the relative proportion of attractive, neutral and repulsive forces defines types of potentials, that induce sequence-structure maps of vastly different architectures. I characterize the properties underlying these differences and relate them to the structure of the potential. Among these properties are the expected number and relative distribution of sequences associated to specific structures and the diversity of structures as a function of sequence divergence. I study the types of binary potentials observed in natural amino acids and show that there is a strong bias towards only some types of potentials, a bias that seems to characterize the folding code of natural proteins. I discuss implications of these observations for the architecture of the sequence-structure map of natural proteins, the construction of random libraries of peptides, and the early evolution of the natural amino acid alphabet.

Protein structural modularity and robustness are associated with evolvability

Theory suggests that biological modularity and robustness allow for maintenance of fitness under mutational change, and when this change is adaptive, for evolvability. Empirical demonstrations that these traits promote evolvability in nature remain scant however. This is in part because modularity, robustness, and evolvability are difficult to define and measure in real biological systems. Here, we address whether structural modularity and/or robustness confer evolvability at the level of proteins by looking for associations between indices of protein structural modularity, structural robustness, and evolvability. We propose a novel index for protein structural modularity: the number of regular secondary structure elements (helices and strands) divided by the number of residues in the structure. We index protein evolvability as the proportion of sites with evidence of being under positive selection multiplied by the average rate of adaptive evolution at these sites, and we measure this as an average over a phylogeny of 25 mammalian species. We use contact density as an index of protein designability, and thus, structural robustness. We find that protein evolvability is positively associated with structural modularity as well as structural robustness and that the effect of structural modularity on evolvability is independent of the structural robustness index. We interpret these associations to be the result of reduced constraints on amino acid substitutions in highly modular and robust protein structures, which results in faster adaptation through natural selection.

The evolutionary consequences of erroneous protein synthesis

Errors in protein synthesis disrupt cellular fitness, cause disease phenotypes and shape gene and genome evolution. Experimental and theoretical results on this topic have accumulated rapidly in disparate fields, such as neurobiology, protein biosynthesis and degradation and molecular evolution, but with limited communication among disciplines. Here, we review studies of error frequencies, the cellular and organismal consequences of errors and the attendant long-range evolutionary responses to errors. We emphasize major areas in which little is known, such as the failure rates of protein folding, in addition to areas in which technological innovations may enable imminent gains, such as the elucidation of translational missense error frequencies. Evolutionary responses to errors fall into two broad categories: adaptations that minimize errors and their attendant costs and adaptations that exploit errors for the organism's benefit.

Self containment, a property of modular RNA structures, distinguishes microRNAs

RNA molecules will tend to adopt a folded conformation through the pairing of bases on a single strand; the resulting so-called secondary structure is critical to the function of many types of RNA. The secondary structure of a particular substring of functional RNA may depend on its surrounding sequence. Yet, some RNAs such as microRNAs retain their specific structures during biogenesis, which involves extraction of the substructure from a larger structural context, while other functional RNAs may be composed of a fusion of independent substructures. Such observations raise the question of whether particular functional RNA substructures may be selected for invariance of secondary structure to their surrounding nucleotide context. We define the property of self containment to be the tendency for an RNA sequence to robustly adopt the same optimal secondary structure regardless of whether it exists in isolation or is a substring of a longer sequence of arbitrary nucleotide content. We measured degree of self containment using a scoring method we call the self-containment index and found that miRNA stem loops exhibit high self containment, consistent with the requirement for structural invariance imposed by the miRNA biogenesis pathway, while most other structured RNAs do not. Further analysis revealed a trend toward higher self containment among clustered and conserved miRNAs, suggesting that high self containment may be a characteristic of novel miRNAs acquiring new genomic contexts. We found that miRNAs display significantly enhanced self containment compared to other functional RNAs, but we also found a trend toward natural selection for self containment in most functional RNA classes. We suggest that self containment arises out of selection for robustness against perturbations, invariance during biogenesis, and modular composition of structural function. Analysis of self containment will be important for both annotation and design of functional RNAs. A Python implementation and Web interface to calculate the self-containment index are available at http://kim.bio.upenn.edu/software/.

An RNA molecule is made up of a linear sequence of nucleotides, which form pairwise interactions that define its folded three-dimensional structure; the particular structure largely depends on the specific sequence. These base-pairing interactions are stabilizing, and the RNA will tend to fold in a particular way to maximize stability. Consider some nucleotide sequence that optimally folds into some structure in isolation; if this sequence is now embedded inside a larger sequence, then either the original structure will be a robust subcomponent of the larger folded structure, or it will be disrupted due to new interactions between the original sequence and the surrounding sequence. We explore this property of context robustness of structure and in particular define the property of “self containment” to describe intrinsic context robustness—i.e., the tendency for certain sequences to be structurally robust in many different sequence contexts. Self containment turns out to be a strong characteristic of a class of RNAs called microRNAs, whose biogenesis process depends on the maintenance of structural robustness. This finding will be useful in future efforts to characterize novel miRNAs, as well as in understanding the regulation and evolution of noncoding functional RNAs as modular units.