Recombinatoric exploration of novel folded structures: A heteropolymer-based model of protein evolutionary landscapes

Abstract

The role of recombination in evolution is compared with that of point mutations (substitutions) in the context of a simple, polymer physics-based model mapping between sequence (genotype) and conformational (phenotype) spaces. Crossovers and point mutations of lattice chains with a hydrophobic polar code are investigated. Sequences encoding for a single ground-state conformation are considered viable and used as model proteins. Point mutations lead to diffusive walks on the evolutionary landscape, whereas crossovers can ''tunnel'' through barriers of diminished fitness. The degree to which crossovers allow for more efficient sequence and structural exploration depends on the relative rates of point mutations versus that of crossovers and the dispersion in fitness that characterizes the ruggedness of the evolutionary landscape. The probability that a crossover between a pair of viable sequences results in viable sequences is an order of magnitude higher than random, implying that a sequence's overall propensity to encode uniquely is embodied partially in local signals. Consistent with this observation, certain hydrophobicity patterns are significantly more favored than others among fragments (i.e., subsequences) of sequences that encode uniquely, and examples reminiscent of autonomous folding units in real proteins are found. The number of structures explored by both crossovers and point mutations is always substantially larger than that via point mutations alone, but the corresponding numbers of sequences explored can be comparable when the evolutionary landscape is rugged. Efficient structural exploration requires intermediate nonextreme ratios between point-mutation and crossover rates.crossovers ͉ neutral nets ͉ sequence space ͉ thermodynamic stability ͉ lattice protein models I t is widely recognized that key events in evolution may involve large-scale genomic rearrangements (1-6). Experiments on plants suggest that dramatic restructuring of the genome in response to traumas may underlie formations of many new species (1). The presence of introns in the genes of higher organisms implies that even a single base change can result in the deletion or insertion of whole sequences in the protein product (2). It has been argued that cellular ''natural genetic engineering'' machineries have evolved to modulate genomic reorganization in lower organisms (3). Moreover, certain peculiarities in present-day genomes and cellular organizations may be explained best by ''lateral'' or ''horizontal'' transfers in the past (4, 5). Indeed, it is large-scale genomic rearrangements rather than the accumulation of point mutations that bear the main responsibility for the alarmingly quick emergence of bacterial antibiotic resistance.Therefore, to capture evolutionary complexities better, theoretical perspectives that focus exclusively on point mutations should be augmented to include other types of sequence transformations. Such efforts would benefit the development of in vitro evolution for protein engineering (7-9) as well. In a ...

Biophysics of protein evolution and evolutionary protein biophysics

“…Because the surface-core ratio of folded structures on the 2D square lattice with chain lengths approximately 16 is similar to the surface-core ratio of 3D folded structures with chain length approximately 150 [317], the energetics of short-chain 2D HP models should bear resemblance to that of real proteins with approximately 100 amino acid residues. Second, as has been argued [324], although the simple potentials of the HP model and its two-letter variants, and for that matter even 20-letter lattice potentials, are not sufficient to capture more detailed thermodynamic [325] and/or kinetic [326] properties of protein folding, the HP potential may still provide a useful caricature of the mapping between sequence and folded structure of real globular proteins because of the 'consistency principle' [327] or 'principle of minimal frustration' [328]. These principles stipulate consistency or near-consistency among various energy terms that contribute to the stability of natural proteins.…”

“…The latter observation may bear on the question of whether the currently known set of globular protein folds is nearly complete in its coverage of all physically possible compact folds, as discussed in §3.1 [286][287][288][289][290], but one has to also keep in mind that the HP model interaction potential is less heterogeneous, and thus entails fewer encodable structures, than model potentials that contain repulsive interactions or otherwise more heterogeneous interactions [158,322,323]. Fourth, the 2D HP lattice model provides sequences that act like evolutionary bridges [161, 178,204,239,299] (see §3.5), encode for autonomous folding units [292,316,324], and exhibit homology-like behaviours [295], all similar to properties observed in real proteins. Two likely physical reasons underlie the similarity between the sequence -structure mapping of the 2D HP model and that of real globular proteins.…”

A polymetamorphic protein

“…14 Limited mutagenesis of small natural proteins populates alternate folds in certain cases, [15][16][17] and accumulation of simple mutations can lead to evolution of new folds. [17][18][19] Some modeling studies have found numerous close approaches or paths between different structures in sequence space [20][21][22][23] and even sequence ''supernetworks'' 24,25 that span many protein folds. In addition, sequences with two folds or functions may confer a fitness advantage under certain models of adaptive evolution.…”

Foldamer hypothesis for the growth and sequence differentiation of prebiotic polymers

“…H P polymers have been studied extensively as a model for the folding and evolution of proteins (51,(60)(61)(62)(63)(64)(65)(66)(67)(68)(69)(70)(71)(72)(73). Those studies show that unique folded structures can be encoded simply in the binary patterning of polar and hydrophobic residues, with finer tuning by specific interresidue contacts.…”