On the thermodynamic hypothesis of protein folding

Do Ionic Liquids Exhibit the Required Characteristics to Dissolve, Extract, Stabilize, and Purify Proteins? Past-Present-Future Assessment

Proteins are highly labile molecules, thus requiring the presence of appropriate solvents and excipients in their liquid milieu to keep their stability and biological activity. In this field, ionic liquids (ILs) have gained momentum in the past years, with a relevant number of works reporting their successful use to dissolve, stabilize, extract, and purify proteins. Different approaches in protein-IL systems have been reported, namely, proteins dissolved in (i) neat ILs, (ii) ILs as co-solvents, (iii) ILs as adjuvants, (iv) ILs as surfactants, (v) ILs as phase-forming components of aqueous biphasic systems, and (vi) IL-polymer-protein/peptide conjugates. Herein, we critically analyze the works published to date and provide a comprehensive understanding of the IL-protein interactions affecting the stability, conformational alteration, unfolding, misfolding, and refolding of proteins while providing directions for future studies in view of imminent applications. Overall, it has been found that the stability or purification of proteins by ILs is bispecific and depends on the structure of both the IL and the protein. The most promising IL-protein systems are identified, which is valuable when foreseeing market applications of ILs, e.g., in "protein packaging" and "detergent applications". Future directions and other possibilities of IL-protein systems in light-harvesting and biotechnology/biomedical applications are discussed.

Evolutionary Processes and Biophysical Mechanisms: Revisiting Why Evolved Proteins Are Marginally Stable

Evolved proteins observed in natural organisms are found to be only marginally stable. Several mechanistic hypotheses have been presented to date to explain this observation. One idea that has been put forward is that active selection prevents proteins from becoming too stable to enable proper function. A second idea is that marginal stability reflects the point of mutation-selection-drift balance, where it is mutational pressure that generates marginal stability. A third idea explored in this issue of Journal of Molecular Evolution is that a physical limit prevents the evolution of more stable proteins rather than an evolutionary process. While the first two notions are based upon specific evolutionary processes, discussion here is aimed at reconciling evolutionary processes with the physics of protein folding, drawing upon the ideas that have been presented.

In silico minimalist approach to study 2D HP protein folding into an inhomogeneous space mimicking osmolyte effect: First trial in the search of foldameric backbones

We have employed our bioinformatics workbench, named Evolution, a Multi-Agent System based architecture with lattice-bead-models, evolutionary-algorithms, and correlated-networks as inhomogeneous spaces, with different correlation lengths, mimicking osmolyte effect (molecular crowding), to in silico survey protein folding. Resolution is with hydrophobic-polar (H-P) sequences in inhomogeneous 2D square lattices, since general biophysicochemical trends consider i) that the backbone is one of the major components responsible for protein folding and ii) osmolyte effect plays an important role to better folding kinetics and reach deeper optima. We have designed foldamers, as square n × n (n = 3, 4, 5, 6) arrays of hydrophobic cores stabilized by H⋯H contacts, attached through short PP (P₂) or long PPPP (P₄) loops, giving rise to 8 sequences (S₁ to S₈) with known optimal scores. Designed sequences were folded into different inhomogeneous spaces and indeed crowded media induced deeper optima, being crowding necessary to best fold, but the space should be enough constrained to induce folding without banning chain movement. The constrained space plays an important role to reach the optimal structure, depending on designed foldamer sequence size, for an optimal correlation length, implying that media affects the folding pathways as happens in real systems. Designed structures were found, moreover, they undergo to degenerated states, both folding states could survey considering i) backbone information and ii) osmolyte effect. In nature, the proteins fold in different structures aiming to reach a global minimum, but a local minimum could be enough to the protein to be functional or dysfunctional.

Selection for Protein Stability Enriches for Epistatic Interactions

A now classical argument for the marginal thermodynamic stability of proteins explains the distribution of observed protein stabilities as a consequence of an entropic pull in protein sequence space. In particular, most sequences that are sufficiently stable to fold will have stabilities near the folding threshold. Here, we extend this argument to consider its predictions for epistatic interactions for the effects of mutations on the free energy of folding. Although there is abundant evidence to indicate that the effects of mutations on the free energy of folding are nearly additive and conserved over evolutionary time, we show that these observations are compatible with the hypothesis that a non-additive contribution to the folding free energy is essential for observed proteins to maintain their native structure. In particular, through both simulations and analytical results, we show that even very small departures from additivity are sufficient to drive this effect.

Automated design evolution of stereochemically randomized protein foldamers

Diversification of chain stereochemistry opens up the possibilities of an 'in principle' increase in the design space of proteins. This huge increase in the sequence and consequent structural variation is aimed at the generation of smart materials. To diversify protein structure stereochemically, we introduced L- and D-α-amino acids as the design alphabet. With a sequence design algorithm, we explored the usage of specific variables such as chirality and the sequence of this alphabet in independent steps. With molecular dynamics, we folded stereochemically diverse homopolypeptides and evaluated their 'fitness' for possible design as protein-like foldamers. We propose a fitness function to prune the most optimal fold among 1000 structures simulated with an automated repetitive simulated annealing molecular dynamics (AR-SAMD) approach. The highly scored poly-leucine fold with sequence lengths of 24 and 30 amino acids were later sequence-optimized using a Dead End Elimination cum Monte Carlo based optimization tool. This paper demonstrates a novel approach for the de novo design of protein-like foldamers.

Functionality and the Evolution of Marginal Stability in Proteins: Inferences from Lattice Simulations

It has been known for some time that many proteins are marginally stable. This has inspired several explanations. Having noted that the functionality of many enzymes is correlated with subunit motion, flexibility, or general disorder, some have suggested that marginally stable proteins should have an evolutionary advantage over proteins of differing stability. Others have suggested that stability and functionality are contradictory qualities, and that selection for both criteria results in marginally stable proteins, optimised to satisfy the competing design pressures. While these explanations are plausible, recent research simulating the evolution of model proteins has shown that selection for stability, ignoring any aspects of functionality, can result in marginally stable proteins because of the underlying makeup of protein sequence-space. We extend this research by simulating the evolution of proteins, using a computational protein model that equates functionality with binding and catalysis. In the model, marginal stability is not required for ligand-binding functionality and we observe no competing design pressures. The resulting proteins are marginally stable, again demonstrating that neutral evolution is sufficient for explaining marginal stability in observed proteins.

Accelerated simulation of evolutionary trajectories in origin-fixation models

We present an accelerated algorithm to forward-simulate origin-fixation models. Our algorithm requires, on average, only about two fitness evaluations per fixed mutation, whereas traditional algorithms require, per one fixed mutation, a number of fitness evaluations of the order of the effective population size, Ne Our accelerated algorithm yields the exact same steady state as the original algorithm but produces a different order of fixed mutations. By comparing several relevant evolutionary metrics, such as the distribution of fixed selection coefficients and the probability of reversion, we find that the two algorithms behave equivalently in many respects. However, the accelerated algorithm yields less variance in fixed selection coefficients. Notably, we are able to recover the expected amount of variance by rescaling population size, and we find a linear relationship between the rescaled population size and the population size used by the original algorithm. Considering the widespread usage of origin-fixation simulations across many areas of evolutionary biology, we introduce our accelerated algorithm as a useful tool for increasing the computational complexity of fitness functions without sacrificing much in terms of accuracy of the evolutionary simulation.

Predictability of evolutionary trajectories in fitness landscapes

Experimental studies on enzyme evolution show that only a small fraction of all possible mutation trajectories are accessible to evolution. However, these experiments deal with individual enzymes and explore a tiny part of the fitness landscape. We report an exhaustive analysis of fitness landscapes constructed with an off-lattice model of protein folding where fitness is equated with robustness to misfolding. This model mimics the essential features of the interactions between amino acids, is consistent with the key paradigms of protein folding and reproduces the universal distribution of evolutionary rates among orthologous proteins. We introduce mean path divergence as a quantitative measure of the degree to which the starting and ending points determine the path of evolution in fitness landscapes. Global measures of landscape roughness are good predictors of path divergence in all studied landscapes: the mean path divergence is greater in smooth landscapes than in rough ones. The model-derived and experimental landscapes are significantly smoother than random landscapes and resemble additive landscapes perturbed with moderate amounts of noise; thus, these landscapes are substantially robust to mutation. The model landscapes show a deficit of suboptimal peaks even compared with noisy additive landscapes with similar overall roughness. We suggest that smoothness and the substantial deficit of peaks in the fitness landscapes of protein evolution are fundamental consequences of the physics of protein folding.

Is evolution deterministic, hence predictable, or stochastic, that is unpredictable? What would happen if one could “replay the tape of evolution”: will the outcomes of evolution be completely different or is evolution so constrained that history will be repeated? Arguably, these questions are among the most intriguing and most difficult in evolutionary biology. In other words, the predictability of evolution depends on the fraction of the trajectories on fitness landscapes that are accessible for evolutionary exploration. Because direct experimental investigation of fitness landscapes is technically challenging, the available studies only explore a minuscule portion of the landscape for individual enzymes. We therefore sought to investigate the topography of fitness landscapes within the framework of a previously developed model of protein folding and evolution where fitness is equated with robustness to misfolding. We show that model-derived and experimental landscapes are significantly smoother than random landscapes and resemble moderately perturbed additive landscapes; thus, these landscapes are substantially robust to mutation. The model landscapes show a deficit of suboptimal peaks even compared with noisy additive landscapes with similar overall roughness. Thus, the smoothness and substantial deficit of peaks in fitness landscapes of protein evolution could be fundamental consequences of the physics of protein folding.

Comparison of translation loads for standard and alternative genetic codes

Background

The (almost) universality of the genetic code is one of the most intriguing properties of cellular life. Nevertheless, several variants of the standard genetic code have been observed, which differ in one or several of 64 codon assignments and occur mainly in mitochondrial genomes and in nuclear genomes of some bacterial and eukaryotic parasites. These variants are usually considered to be the result of non-adaptive evolution. It has been shown that the standard genetic code is preferential to randomly assembled codes for its ability to reduce the effects of errors in protein translation.

Results

Using a genotype-to-phenotype mapping based on a quantitative model of protein folding, we compare the standard genetic code to seven of its naturally occurring variants with respect to the fitness loss associated to mistranslation and mutation. These fitness losses are computed through computer simulations of protein evolution with mutations that are either neutral or lethal, and different mutation biases, which influence the balance between unfolding and misfolding stability. We show that the alternative codes may produce significantly different mutation and translation loads, particularly for genomes evolving with a rather large mutation bias. Most of the alternative genetic codes are found to be disadvantageous to the standard code, in agreement with the view that the change of genetic code is a mutationally driven event. Nevertheless, one of the studied alternative genetic codes is predicted to be preferable to the standard code for a broad range of mutation biases.

Conclusions

Our results show that, with one exception, the standard genetic code is generally better able to reduce the translation load than the naturally occurring variants studied here. Besides this exception, some of the other alternative genetic codes are predicted to be better adapted for extreme mutation biases. Hence, the fixation of alternative genetic codes might be a neutral or nearly-neutral event in the majority of the cases, but adaptation cannot be excluded for some of the studied cases.

Mutation bias favors protein folding stability in the evolution of small populations

Mutation bias in prokaryotes varies from extreme adenine and thymine (AT) in obligatory endosymbiotic or parasitic bacteria to extreme guanine and cytosine (GC), for instance in actinobacteria. GC mutation bias deeply influences the folding stability of proteins, making proteins on the average less hydrophobic and therefore less stable with respect to unfolding but also less susceptible to misfolding and aggregation. We study a model where proteins evolve subject to selection for folding stability under given mutation bias, population size, and neutrality. We find a non-neutral regime where, for any given population size, there is an optimal mutation bias that maximizes fitness. Interestingly, this optimal GC usage is small for small populations, large for intermediate populations and around 50% for large populations. This result is robust with respect to the definition of the fitness function and to the protein structures studied. Our model suggests that small populations evolving with small GC usage eventually accumulate a significant selective advantage over populations evolving without this bias. This provides a possible explanation to the observation that most species adopting obligatory intracellular lifestyles with a consequent reduction of effective population size shifted their mutation spectrum towards AT. The model also predicts that large GC usage is optimal for intermediate population size. To test these predictions we estimated the effective population sizes of bacterial species using the optimal codon usage coefficients computed by dos Reis et al. and the synonymous to non-synonymous substitution ratio computed by Daubin and Moran. We found that the population sizes estimated in these ways are significantly smaller for species with small and large GC usage compared to species with no bias, which supports our prediction.

Mutation bias favors protein folding stability in the evolution of small populations

Mutation bias in prokaryotes varies from extreme adenine and thymine (AT) in obligatory endosymbiotic or parasitic bacteria to extreme guanine and cytosine (GC), for instance in actinobacteria. GC mutation bias deeply influences the folding stability of proteins, making proteins on the average less hydrophobic and therefore less stable with respect to unfolding but also less susceptible to misfolding and aggregation. We study a model where proteins evolve subject to selection for folding stability under given mutation bias, population size, and neutrality. We find a non-neutral regime where, for any given population size, there is an optimal mutation bias that maximizes fitness. Interestingly, this optimal GC usage is small for small populations, large for intermediate populations and around 50% for large populations. This result is robust with respect to the definition of the fitness function and to the protein structures studied. Our model suggests that small populations evolving with small GC usage eventually accumulate a significant selective advantage over populations evolving without this bias. This provides a possible explanation to the observation that most species adopting obligatory intracellular lifestyles with a consequent reduction of effective population size shifted their mutation spectrum towards AT. The model also predicts that large GC usage is optimal for intermediate population size. To test these predictions we estimated the effective population sizes of bacterial species using the optimal codon usage coefficients computed by dos Reis et al. and the synonymous to non-synonymous substitution ratio computed by Daubin and Moran. We found that the population sizes estimated in these ways are significantly smaller for species with small and large GC usage compared to species with no bias, which supports our prediction.

Universal distribution of protein evolution rates as a consequence of protein folding physics

The hypothesis that folding robustness is the primary determinant of the evolution rate of proteins is explored using a coarse-grained off-lattice model. The simplicity of the model allows rapid computation of the folding probability of a sequence to any folded conformation. For each robust folder, the network of sequences that share its native structure is identified. The fitness of a sequence is postulated to be a simple function of the number of misfolded molecules that have to be produced to reach a characteristic protein abundance. After fixation probabilities of mutants are computed under a simple population dynamics model, a Markov chain on the fold network is constructed, and the fold-averaged evolution rate is computed. The distribution of the logarithm of the evolution rates across distinct networks exhibits a peak with a long tail on the low rate side and resembles the universal empirical distribution of the evolutionary rates more closely than either distribution resembles the log-normal distribution. The results suggest that the universal distribution of the evolutionary rates of protein-coding genes is a direct consequence of the basic physics of protein folding.

Determination, prediction, and understanding of structures, using the energy landscapes of chemical systems – Part II

In the past decade, new theoretical approaches have been developed to determine, predict and understand the struc-ture of chemical compounds. The central element of these methods has been the investigation of the energy landscape of chemical systems. Applications range from extended crystalline and amorphous compounds over clusters and molecular crystals to proteins. In this review, we are going to give an introduction to energy landscapes and methods for their investigation, together with a number of examples. These include structure prediction of extended and mo-lecular crystals, structure prediction and folding of proteins, structure analysis of zeolites, and structure determination of crystals from powder diffraction data.

Population-based local search for protein folding simulation in the MJ energy model and cubic lattices

We present experimental results on benchmark problems in 3D cubic lattice structures with the Miyazawa-Jernigan energy function for two local search procedures that utilise the pull-move set: (i) population-based local search (PLS) that traverses the energy landscape with greedy steps towards (potential) local minima followed by upward steps up to a certain level of the objective function; (ii) simulated annealing with a logarithmic cooling schedule (LSA). The parameter settings for PLS are derived from short LSA-runs executed in pre-processing and the procedure utilises tabu lists generated for each member of the population. In terms of the total number of energy function evaluations both methods perform equally well, however, PLS has the potential of being parallelised with an expected speed-up in the region of the population size. Furthermore, both methods require a significant smaller number of function evaluations when compared to Monte Carlo simulations with kink-jump moves.

Analysing the origin of long-range interactions in proteins using lattice models

BACKGROUND

Long-range communication is very common in proteins but the physical basis of this phenomenon remains unclear. In order to gain insight into this problem, we decided to explore whether long-range interactions exist in lattice models of proteins. Lattice models of proteins have proven to capture some of the basic properties of real proteins and, thus, can be used for elucidating general principles of protein stability and folding.

RESULTS

Using a computational version of double-mutant cycle analysis, we show that long-range interactions emerge in lattice models even though they are not an input feature of them. The coupling energy of both short- and long-range pairwise interactions is found to become more positive (destabilizing) in a linear fashion with increasing 'contact-frequency', an entropic term that corresponds to the fraction of states in the conformational ensemble of the sequence in which the pair of residues is in contact. A mathematical derivation of the linear dependence of the coupling energy on 'contact-frequency' is provided.

CONCLUSION

Our work shows how 'contact-frequency' should be taken into account in attempts to stabilize proteins by introducing (or stabilizing) contacts in the native state and/or through 'negative design' of non-native contacts.

Classifying proteinlike sequences in arbitrary lattice protein models using LatPack

Knowledge of a protein's three-dimensional native structure is vital in determining its chemical properties and functionality. However, experimental methods to determine structure are very costly and time-consuming. Computational approaches such as folding simulations and structure prediction algorithms are quicker and cheaper but lack consistent accuracy. This currently restricts extensive computational studies to abstract protein models. It is thus essential that simplifications induced by the models do not negate scientific value. Key to this is the use of thoroughly defined proteinlike sequences. In such cases abstract models can allow for the investigation of important biological questions. Here, we present a procedure to generate and classify proteinlike sequence data sets. Our LatPack tools and the approach in general are applicable to arbitrary lattice protein models. Identification is based on thermodynamic kinetic features and incorporates the sequential assembly of proteins by addressing cotranslational folding. We demonstrate the approach in the widely used unrestricted 3D-cubic HP-model. The resulting sequence set is the first large data set for this model exhibiting the proteinlike properties required. Our data tools are freely available and can be used to investigate protein-related problems.

Thermodynamics imprinting reveals differential binding of metals to alpha-synuclein: relevance to Parkinson's disease

The aggregation of alpha-synuclein is a hallmark feature of Parkinson's disease (PD) and other synucleinopathies. Metals are the significant etiological factors in PD, and their interaction with alpha-synuclein affect dramatically the kinetics of fibrillation in vitro and are proposed to play an important and potential neurodegenerative role in vivo. In the present study, we investigated the stoichiometry of binding of copper [Cu (II)] and iron [Fe (III)] with alpha-synuclein (wild recombinant type and A30P, A53T, E46K mutant forms) using isothermal titration calorimetry (ITC). alpha-Synuclein monomer (wild and mutant forms) titrated by Cu (II), showed two binding sites, with an apparent K(B) of 10(5)M and 10(4)M, respectively. But, alpha-synuclein (wild type and mutant forms) titrated with Fe (III) revealed a K(B) of 10(5)M with single binding site. The present investigation uncovers the detailed binding propensities between metals and alpha-synuclein and has biological implications in PD.

Functionality and the evolution of marginal stability in proteins: inferences from lattice simulations

It has been known for some time that many proteins are marginally stable. This has inspired several explanations. Having noted that the functionality of many enzymes is correlated with subunit motion, flexibility, or general disorder, some have suggested that marginally stable proteins should have an evolutionary advantage over proteins of differing stability. Others have suggested that stability and functionality are contradictory qualities, and that selection for both criteria results in marginally stable proteins, optimised to satisfy the competing design pressures. While these explanations are plausible, recent research simulating the evolution of model proteins has shown that selection for stability, ignoring any aspects of functionality, can result in marginally stable proteins because of the underlying makeup of protein sequence-space. We extend this research by simulating the evolution of proteins, using a computational protein model that equates functionality with binding and catalysis. In the model, marginal stability is not required for ligand-binding functionality and we observe no competing design pressures. The resulting proteins are marginally stable, again demonstrating that neutral evolution is sufficient for explaining marginal stability in observed proteins.

Divergence, recombination and retention of functionality during protein evolution

We have only a vague idea of precisely how protein sequences evolve in the context of protein structure and function. This is primarily because structural and functional contexts are not easily predictable from the primary sequence, and evaluating patterns of evolution at individual residue positions is also difficult. As a result of increasing biodiversity in genomics studies, progress is being made in detecting context-dependent variation in substitution processes, but it remains unclear exactly what context-dependent patterns we should be looking for. To address this, we have been simulating protein evolution in the context of structure and function using lattice models of proteins and ligands (or substrates). These simulations include thermodynamic features of protein stability and population dynamics. We refer to this approach as 'ab initio evolution' to emphasise the fact that the equilibrium details of fitness distributions arise from the physical principles of the system and not from any preconceived notions or arbitrary mathematical distributions. Here, we present results on the retention of functionality in homologous recombinants following population divergence. A central result is that protein structure characteristics can strongly influence recombinant functionality. Exceptional structures with many sequence options evolve quickly and tend to retain functionality--even in highly diverged recombinants. By contrast, the more common structures with fewer sequence options evolve more slowly, but the fitness of recombinants drops off rapidly as homologous proteins diverge. These results have implications for understanding viral evolution, speciation and directed evolutionary experiments. Our analysis of the divergence process can also guide improved methods for accurately approximating folding probabilities in more complex but realistic systems.

A protein evolution model with independent sites that reproduces site-specific amino acid distributions from the Protein Data Bank

BACKGROUND

Since thermodynamic stability is a global property of proteins that has to be conserved during evolution, the selective pressure at a given site of a protein sequence depends on the amino acids present at other sites. However, models of molecular evolution that aim at reconstructing the evolutionary history of macromolecules become computationally intractable if such correlations between sites are explicitly taken into account.

RESULTS

We introduce an evolutionary model with sites evolving independently under a global constraint on the conservation of structural stability. This model consists of a selection process, which depends on two hydrophobicity parameters that can be computed from protein sequences without any fit, and a mutation process for which we consider various models. It reproduces quantitatively the results of Structurally Constrained Neutral (SCN) simulations of protein evolution in which the stability of the native state is explicitly computed and conserved. We then compare the predicted site-specific amino acid distributions with those sampled from the Protein Data Bank (PDB). The parameters of the mutation model, whose number varies between zero and five, are fitted from the data. The mean correlation coefficient between predicted and observed site-specific amino acid distributions is larger than <r> = 0.70 for a mutation model with no free parameters and no genetic code. In contrast, considering only the mutation process with no selection yields a mean correlation coefficient of <r> = 0.56 with three fitted parameters. The mutation model that best fits the data takes into account increased mutation rate at CpG dinucleotides, yielding <r> = 0.90 with five parameters.

CONCLUSION

The effective selection process that we propose reproduces well amino acid distributions as observed in the protein sequences in the PDB. Its simplicity makes it very promising for likelihood calculations in phylogenetic studies. Interestingly, in this approach the mutation process influences the effective selection process, i.e. selection and mutation must be entangled in order to obtain effectively independent sites. This interdependence between mutation and selection reflects the deep influence that mutation has on the evolutionary process: The bias in the mutation influences the thermodynamic properties of the evolving proteins, in agreement with comparative studies of bacterial proteomes, and it also influences the rate of accepted mutations.

Viscous drag as the source of active site perturbation during protease translocation: insights into how inhibitory processes are controlled by serpin metastability

The native form of serine protease inhibitors (serpins) is kinetically trapped in a metastable state, which is thought to play a central role in the inhibitory mechanism. The initial binding complex between a serpin and a target protease undergoes a conformational change that forces the protease to translocate toward the opposite pole. Although structural determination of the final stable complex revealed a detailed mechanism of keeping the bound protease in an inactive conformation, it has remained unknown how the serpin exquisitely translocates a target protease with an acyl-linkage unhydrolyzed. We previously suggested that the acyl-linkage hydrolysis is strongly suppressed by active site perturbation during the protease translocation. Here, we address what induces the transient perturbation and how the serpin metastability contributes to the perturbation. Inhibitory activity of alpha1-antitrypsin (alpha1AT) toward elastase showed negative correlations with medium viscosity and Stokes radius of elastase moiety, indicating that viscous drag directly affects the protease translocation. Stopped-flow measurements revealed that the change in the inhibitory activity is primarily caused by the change in the translocation rate. The native stability of alpha1AT cavity mutants showed a negative correlation with the translocation rate but a positive correlation with the acyl-linkage hydrolysis rate, suggesting that the two kinetic steps are not independent but closely related. The degree of active site perturbation was probed by amino acid nucleophiles, supporting the view that the changes in the acyl-linkage hydrolysis rate are due to different perturbation states. These results suggest that the active site perturbation is caused by local imbalance between a pulling force driving protease translocation and a counteracting viscous drag force. The structural architecture of serpin metastability seems to be designed to ensure the active site perturbation by providing a sufficient pulling force, so the undesirable hydrolytic activity of protease is strongly suppressed during the translocation.

SELECTIVE ADVANTAGE OF RECOMBINATION IN EVOLVING PROTEIN POPULATIONS: A LATTICE MODEL STUDY

Recent research has attempted to clarify the contributions of several mutational processes, such as substitutions or homologous recombination. Simplistic, tractable protein models, which determine the compact native structure phenotype from the sequence genotype, are well-suited to such studies. In this paper, we use a lattice-protein model to examine the effects of point mutation and homologous recombination on evolving populations of proteins. We find that while the majority of mutation and recombination events are neutral or deleterious, recombination is far more likely to be beneficial. This results in a faster increase in fitness during evolution, although the final fitness level is not significantly changed. This transient advantage provides an evolutionary advantage to subpopulations that undergo recombination, allowing fixation of recombination to occur in the population.

Simulating protein evolution in sequence and structure space

Naturally occurring proteins comprise a special subset of all plausible sequences and structures selected through evolution. Simulating protein evolution with simplified and all-atom models has shed light on the evolutionary dynamics of protein populations, the nature of evolved sequences and structures, and the extent to which today's proteins are shaped by selection pressures on folding, structure and function. Extensive mapping of the native structure, stability and folding rate in sequence space using lattice proteins has revealed organizational principles of the sequence/structure map important for evolutionary dynamics. Evolutionary simulations with lattice proteins have highlighted the importance of fitness landscapes, evolutionary mechanisms, population dynamics and sequence space entropy in shaping the generic properties of proteins. Finally, evolutionary-like simulations with all-atom models, in particular computational protein design, have helped identify the dominant selection pressures on naturally occurring protein sequences and structures.

Looking at structure, stability, and evolution of proteins through the principal eigenvector of contact matrices and hydrophobicity profiles

We review and further develop an analytical model that describes how thermodynamic constraints on the stability of the native state influence protein evolution in a site-specific manner. To this end, we represent both protein sequences and protein structures as vectors: structures are represented by the principal eigenvector (PE) of the protein contact matrix, a quantity that resembles closely the effective connectivity of each site; sequences are represented through the "interactivity" of each amino acid type, using novel parameters that are correlated with hydropathy scales. These interactivity parameters are more strongly correlated than the other hydropathy scales that we examine with: (1) the change upon mutations of the unfolding free energy of proteins with two-states thermodynamics; (2) genomic properties as the genome-size and the genome-wide GC content; (3) the main eigenvectors of the substitution matrices. The evolutionary average of the interactivity vector correlates very strongly with the PE of a protein structure. Using this result, we derive an analytic expression for site-specific distributions of amino acids across protein families in the form of Boltzmann distributions whose "inverse temperature" is a function of the PE component. We show that our predictions are in agreement with site-specific amino acid distributions obtained from the Protein Data Bank, and we determine the mutational model that best fits the observed site-specific amino acid distributions. Interestingly, the optimal model almost minimizes the rate at which deleterious mutations are eliminated by natural selection.

Lack of self-averaging in neutral evolution of proteins

We simulate neutral evolution of proteins imposing conservation of the thermodynamic stability of the native state in the framework of an effective model of folding thermodynamics. This procedure generates evolutionary trajectories in sequence space which share two universal features for all of the examined proteins. First, the number of neutral mutations fluctuates broadly from one sequence to another, leading to a non-Poissonian substitution process. Second, the number of neutral mutations displays strong correlations along the trajectory, thus causing the breakdown of self-averaging of the resulting evolutionary substitution process.

Why are proteins so robust to site mutations?

There have been repeated observations that proteins are surprisingly robust to site mutations, enduring significant numbers of substitutions with little change in structure, stability, or function. These results are almost paradoxical in light of what is known about random heteropolymers and the sensitivity of their properties to seemingly trivial mutations. To address this discrepancy, the preservation of biological protein properties in the presence of mutation has been interpreted as indicating the independence of selective pressure on such properties. Such results also lead to the prediction that de novo protein design should be relatively easy, in contrast to what is observed. Here, we use a computational model with lattice proteins to demonstrate how this robustness can result from population dynamics during the evolutionary process. As a result, sequence plasticity may be a characteristic of evolutionarily derived proteins and not necessarily a property of designed proteins. This suggests that this robustness must be re-interpreted in evolutionary terms, and has consequences for our understanding of both in vivo and in vitro protein evolution.

Why are proteins marginally stable?

Most globular proteins are marginally stable regardless of size or activity. The most common interpretation is that proteins must be marginally stable in order to function, and so marginal stability represents the results of positive selection. We consider the issue of marginal stability directly using model proteins and the dynamical aspects of protein evolution in populations. We find that the marginal stability of proteins is an inherent property of proteins due to the high dimensionality of the sequence space, without regard to protein function. In this way, marginal stability can result from neutral, non-adaptive evolution. By allowing evolving protein sub-populations with different stability requirements for functionality to complete, we find that marginally stable populations of proteins tend to dominate. Our results show that functionalities consistent with marginal stability have a strong evolutionary advantage, and might arise because of the natural tendency of proteins towards marginal stability.

Prediction of contact maps with neural networks and correlated mutations

Contact maps of proteins are predicted with neural network-based methods, using as input codings of increasing complexity including evolutionary information, sequence conservation, correlated mutations and predicted secondary structures. Neural networks are trained on a data set comprising the contact maps of 173 non-homologous proteins as computed from their well resolved three-dimensional structures. Proteins are selected from the Protein Data Bank database provided that they align with at least 15 similar sequences in the corresponding families. The predictors are trained to learn the association rules between the covalent structure of each protein and its contact map with a standard back propagation algorithm and tested on the same protein set with a cross-validation procedure. Our results indicate that the method can assign protein contacts with an average accuracy of 0.21 and with an improvement over a random predictor of a factor >6, which is higher than that previously obtained with methods only based either on neural networks or on correlated mutations. Furthermore, filtering the network outputs with a procedure based on the residue coordination numbers, the accuracy of predictions increases up to 0.25 for all the proteins, with an 8-fold deviation from a random predictor. These scores are the highest reported so far for predicting protein contact maps.

Engineering delta 9-16:0-acyl carrier protein (ACP) desaturase specificity based on combinatorial saturation mutagenesis and logical redesign of the castor delta 9-18:0-ACP desaturase

Six amino acid locations in the soluble castor Delta(9)-18:0-acyl carrier protein (ACP) desaturase were identified that can affect substrate specificity. Combinatorial saturation mutagenesis of these six amino acids, in conjunction with selection, using an unsaturated fatty acid auxotroph system, led to the isolation of variants with up to 15-fold increased specific activity toward 16-carbon substrates. The most improved mutant, com2, contained two substitutions (T117R/G188L) common to five of the 19 complementing variants subjected to further analysis. These changes, when engineered into otherwise wild-type 18:0-ACP desaturase to make mutant 5.2, produced a 35-fold increase in specific activity with respect to 16-carbon substrates. Kinetic analysis revealed changes in both k(cat) and K(m) that result in an 82-fold improvement in specificity factor for 16-carbon substrate compared with wild-type enzyme. Improved substrate orientation apparently compensated for loss of binding energy that results from the loss of desolvation energy for 16-carbon substrates. Mutant 5.2 had specific activity for 16-carbon substrates 2 orders of magnitude higher than those of known natural 16-carbon specific desaturases. These data support the hypothesis that it should be possible to reengineer archetypal enzymes to achieve substrate specificities characteristic of recently evolved enzymes while retaining the desired stability and/or turnover characteristics of a parental paralog.

Evolution of functionality in lattice proteins

We study the evolution of protein functionality using a two-dimensional lattice model. The characteristics particular to evolution, such as population dynamics and early evolutionary trajectories, have a large effect on the distribution of observed structures. Only subtle differences are observed between the distribution of structures evolved for function and those evolved for their ability to form compact structures.

A statistical mechanical method to optimize energy functions for protein folding

We present a method for deriving energy functions for protein folding by maximizing the thermodynamic average of the overlap with the native state. The method has been tested by using the pairwise contact approximation of the energy function and generating alternative structures by threading sequences over a database of 1, 169 structures. With the derived energy function, most native structures: (i) have minimal energy and (ii) are thermodynamically rather stable, and (iii) the corresponding energy landscapes are smooth. Precisely, 92% of the 1,013 x-ray structures are stabilized. Most failures can be attributed to the neglect of interactions between chains forming polychain proteins and of interactions with cofactors. When these are considered, only nine cases remain unexplained. In contrast, 38% of NMR structures are not assigned properly.

The distribution of structures in evolving protein populations

Proteins exhibit a nonuniform distribution of structures. A number of models have been advanced to explain this observation by considering the distribution of designabilities, that is, the fraction of all sequences that could successfully fold into any particular structure. It has been postulated that more designable structures should be more common, although the exact nature of this relationship has not been addressed. We find that the nonuniform distribution of protein structures found in nature can be explained by the interplay of evolution and population dynamics with the designability distribution. The relative frequency of different structures has a greater-than-linear dependence on designability, making the distribution of observed protein structures more uneven than the distribution of designabilities. The distribution of structures is also affected by additional factors such as the topology of the sequence space and the similarity of other structures.

Neural networks predict protein folding and structure: artificial intelligence faces biomolecular complexity

In the genomic era DNA sequencing is increasing our knowledge of the molecular structure of genetic codes from bacteria to man at a hyperbolic rate. Billions of nucleotides and millions of aminoacids are already filling the electronic files of the data bases presently available, which contain a tremendous amount of information on the most biologically relevant macromolecules, such as DNA, RNA and proteins. The most urgent problem originates from the need to single out the relevant information amidst a wealth of general features. Intelligent tools are therefore needed to optimise the search. Data mining for sequence analysis in biotechnology has been substantially aided by the development of new powerful methods borrowed from the machine learning approach. In this paper we discuss the application of artificial feedforward neural networks to deal with some fundamental problems tied with the folding process and the structure-function relationship in proteins.

Designing potential energy functions for protein folding

By following a consistent line of physical reasoning, some fundamental understanding about the foldability of proteins has been achieved. In recent years, this has led to the development of a number of successful algorithms for optimizing potential energy functions for folding protein models. The differences between the folding mechanisms of simple, contact-based lattice proteins and more traditional, realistic protein models, however, still call for further development of the potentials in addition to the optimization approaches.