Protein topology and stability define the space of allowed sequences

Sequence-dependent and -independent information in a combined random energy model for protein folding and coding

Random energy models (REMs) provide a simple description of the energy landscapes that guide protein folding and evolution. The requirement of a large energy gap between the native structure and unfolded conformations, considered necessary for cooperative, protein-like, folding behavior, indicates that proteins differ markedly from random heteropolymers. It has been suggested, therefore, that natural selection might have acted to choose nonrandom amino acid sequences satisfying this particular condition, implying that a large fraction of possible, unselected random sequences, would not fold to any structure. From an informational perspective, however, this scenario could indicate that protein structures, regarded as messages to be transmitted through a communication channel, would not be efficiently encoded in amino acid sequences, regarded as the communication channel for this transmission, since a large fraction of possible channel states would not be used. Here, we use a combined REM for conformations and sequences, with previously estimated parameters for natural proteins, to explore an alternative possibility in which the appropriate shape of the landscape results mainly from the deviation from randomness of possible native structures instead of sequences. We observe that this situation emerges naturally if the distribution of conformational energies happens to arise from two independent contributions corresponding to sequence-dependent and -independent terms. This construction is consistent with the hypothesis of a protein burial folding code, with native structures being determined by a modest amount of sequence-dependent atomic burial information with sequence-independent constraints imposed by unspecific hydrogen bond formation. More generally, an appropriate combination of sequence-dependent and -independent information accommodates the possibility of an efficient structural encoding with the main physical requirement for folding, providing possible insight not only on the folding process but also on several aspects sequence evolution such as neutral networks, conformational coverage, and de novo gene emergence.

Stepwise introduction of stabilizing mutations reveals nonlinear additive effects in de novo TIM barrels

Over the past decades, the TIM-barrel fold has served as a model system for the exploration of how changes in protein sequences affect their structural, stability, and functional characteristics, and moreover, how this information can be leveraged to design proteins from the ground up. After numerous attempts to design de novo proteins with this specific fold, sTIM11 was the first validated de novo design of an idealized four-fold symmetric TIM barrel. Subsequent efforts to enhance the stability of this initial design resulted in the development of DeNovoTIMs, a family of de novo TIM barrels with various stabilizing mutations. In this study, we present an investigation into the biophysical and thermodynamic effects upon introducing a varying number of stabilizing mutations per quarter along the sequence of a four-fold symmetric TIM barrel. We compared the base design DeNovoTIM0 without any stabilizing mutations with variants containing mutations in one, two, three, and all four quarters-designated TIM1q, TIM2q, TIM3q, and DeNovoTIM6, respectively. This analysis revealed a stepwise and nonlinear change in the thermodynamic properties that correlated with the number of mutated quarters, suggesting positive nonadditive effects. To shed light on the significance of the location of stabilized quarters, we engineered two variants of TIM2q which contain the same number of mutations but positioned in different quarter locations. Characterization of these TIM2q variants revealed that the mutations exhibit varying effects on the overall protein stability, contingent upon the specific region in which they are introduced. These findings emphasize that the amount and location of stabilized interfaces among the four quarters play a crucial role in shaping the conformational stability of these four-fold symmetric TIM barrels. Analysis of de novo proteins, as described in this study, enhances our understanding of how sequence variations can finely modulate stability in both naturally occurring and computationally designed proteins.

Protein folding rate evolution upon mutations

Despite the spectacular success of cutting-edge protein fold prediction methods, many critical questions remain unanswered, including why proteins can reach their native state in a biologically reasonable time. A satisfactory answer to this simple question could shed light on the slowest folding rate of proteins as well as how mutations-amino-acid substitutions and/or post-translational modifications-might affect it. Preliminary results indicate that (i) Anfinsen's dogma validity ensures that proteins reach their native state on a reasonable timescale regardless of their sequence or length, and (ii) it is feasible to determine the evolution of protein folding rates without accounting for epistasis effects or the mutational trajectories between the starting and target sequences. These results have direct implications for evolutionary biology because they lay the groundwork for a better understanding of why, and to what extent, mutations-a crucial element of evolution and a factor influencing it-affect protein evolvability. Furthermore, they may spur significant progress in our efforts to solve crucial structural biology problems, such as how a sequence encodes its folding.

Constrained Layer Assignment for the Protein Burial Folding Code Accounting for Chain Connectivity

The connection between protein sequences and tertiary structures has intrigued investigators for decades. A plausible hypothesis for the coding scheme postulates that atomic burial information obtainable from the sequence could be sufficient for structural determination when combined to sequence-independent constraints. Accordingly, folding simulations using native burial information expressed by atomic central distances, discretized into a small number L of equiprobable burial layers, have indeed been successful in reaching and distinguishing the native structure of several globular proteins. Attempted predictions of layers from sequence, however, turned out to be insufficiently accurate for most proteins. Here we explore the possibility that a nonuniform assignment of layers, which is intended to account for constraints imposed by chain connectivity, might provide a more efficient burial encoding of tertiary structures. We consider the condition that adjacent C_α-atoms along the sequence cannot occupy nonadjacent layers, in which case the information required to specify sequences of burials would be smaller. It is shown that appropriate folding behavior can still be observed in this explicitly more constrained scenario with a structure-dependent assignment intended to produce the thinnest possible layers still compatible with the imposed burial constraint. This thinnest assignment turns out to be sufficiently restrictive for the observed examples and provides appropriately thinner layers or, equivalently, a larger number of layers, for examples previously observed to indeed require more restrictive constraints when compared to counterparts of similar size, as well as the appropriate increase in number of layers for larger proteins. Implications for the general understanding of the protein folding code are discussed.

Key aspects of the past 30 years of protein design

Proteins are the workhorse of life. They are the building infrastructure of living systems; they are the most efficient molecular machines known, and their enzymatic activity is still unmatched in versatility by any artificial system. Perhaps proteins' most remarkable feature is their modularity. The large amount of information required to specify each protein's function is analogically encoded with an alphabet of just ∼20 letters. The protein folding problem is how to encode all such information in a sequence of 20 letters. In this review, we go through the last 30 years of research to summarize the state of the art and highlight some applications related to fundamental problems of protein evolution.

About the Protein Space Vastness

An accurate estimation of the Protein Space size, in light of the factors that govern it, is a long-standing problem and of paramount importance in evolutionary biology, since it determines the nature of protein evolvability. A simple analysis will enable us to, firstly, reduce an unrealistic Protein Space size of ~ 10¹³⁰ sequences, for a 100-residues polypeptide chain, to ~ 10⁹ functional proteins and, secondly, estimate a robust average-mutation rate per amino acid (ξ ~ 1.23) and infer from it, in light of the protein marginal stability, that only a fraction of the sequence will be available at any one time for a functional protein to evolve. Although this result does not solve the Protein Space vastness problem frames it in a more rational one and illustrates the impact of the marginal stability on protein evolvability.

Exploring the sequence fitness landscape of a bridge between protein folds

Most foldable protein sequences adopt only a single native fold. Recent protein design studies have, however, created protein sequences which fold into different structures apon changes of environment, or single point mutation, the best characterized example being the switch between the folds of the GA and GB binding domains of streptococcal protein G. To obtain further insight into the design of sequences which can switch folds, we have used a computational model for the fitness landscape of a single fold, built from the observed sequence variation of protein homologues. We have recently shown that such coevolutionary models can be used to design novel foldable sequences. By appropriately combining two of these models to describe the joint fitness landscape of GA and GB, we are able to describe the propensity of a given sequence for each of the two folds. We have successfully tested the combined model against the known series of designed GA/GB hybrids. Using Monte Carlo simulations on this landscape, we are able to identify pathways of mutations connecting the two folds. In the absence of a requirement for domain stability, the most frequent paths go via sequences in which neither domain is stably folded, reminiscent of the propensity for certain intrinsically disordered proteins to fold into different structures according to context. Even if the folded state is required to be stable, we find that there is nonetheless still a wide range of sequences which are close to the transition region and therefore likely fold switches, consistent with recent estimates that fold switching may be more widespread than had been thought.

Comparison of Rosetta flexible-backbone computational protein design methods on binding interactions

Computational design of binding sites in proteins remains difficult, in part due to limitations in our current ability to sample backbone conformations that enable precise and accurate geometric positioning of side chains during sequence design. Here we present a benchmark framework for comparison between flexible-backbone design methods applied to binding interactions. We quantify the ability of different flexible backbone design methods in the widely used protein design software Rosetta to recapitulate observed protein sequence profiles assumed to represent functional protein/protein and protein/small molecule binding interactions. The CoupledMoves method, which combines backbone flexibility and sequence exploration into a single acceptance step during the sampling trajectory, better recapitulates observed sequence profiles than the BackrubEnsemble and FastDesign methods, which separate backbone flexibility and sequence design into separate acceptance steps during the sampling trajectory. Flexible-backbone design with the CoupledMoves method is a powerful strategy for reducing sequence space to generate targeted libraries for experimental screening and selection.

Superfunneled Energy Landscape of Protein Evolution Unifies the Principles of Protein Evolution, Folding, and Design

Evolution is essential for shaping the biological functions. Darwin proposed the selection as the driving force for evolution upon mutations. While mutations are clear, the quantification of the selection force is still challenging. In this study, we identified and quantified both thermodynamic stability and kinetic accessibility as the selection forces for protein evolution. The protein evolution can be viewed and quantified as a trajectory moving along a superfunneled energy landscape with a line attractor at the bottom. The resulting evolved sequences and structures show strong protein characteristics including the hydrophobic core, high designability, and fast folding. The evolution principle uncovered here is validated on real proteins and sheds light on the protein design.

Combining Rosetta with molecular dynamics (MD): A benchmark of the MD-based ensemble protein design

Computational protein design is a set of procedures for computing amino acid sequences that will fold into a specified structure. Rosetta Design, a commonly used software for protein design, allows for the effective identification of sequences compatible with a given backbone structure, while molecular dynamics (MD) simulations can thoroughly sample near-native conformations. We benchmarked a procedure in which Rosetta design is started on MD-derived structural ensembles and showed that such a combined approach generates 20-30% more diverse sequences than currently available methods with only a slight increase in computation time. Importantly, the increase in diversity is achieved without a loss in the quality of the designed sequences assessed by their resemblance to natural sequences. We demonstrate that the MD-based procedure is also applicable to de novo design tasks started from backbone structures without any sequence information. In addition, we implemented a protocol that can be used to assess the stability of designed models and to select the best candidates for experimental validation. In sum our results demonstrate that the MD ensemble-based flexible backbone design can be a viable method for protein design, especially for tasks that require a large pool of diverse sequences.

Cooperative "folding transition" in the sequence space facilitates function-driven evolution of protein families

In the protein sequence space, natural proteins form clusters of families which are characterized by their unique native folds whereas the great majority of random polypeptides are neither clustered nor foldable to unique structures. Since a given polypeptide can be either foldable or unfoldable, a kind of "folding transition" is expected at the boundary of a protein family in the sequence space. By Monte Carlo simulations of a statistical mechanical model of protein sequence alignment that coherently incorporates both short-range and long-range interactions as well as variable-length insertions to reproduce the statistics of the multiple sequence alignment of a given protein family, we demonstrate the existence of such transition between natural-like sequences and random sequences in the sequence subspaces for 15 domain families of various folds. The transition was found to be highly cooperative and two-state-like. Furthermore, enforcing or suppressing consensus residues on a few of the well-conserved sites enhanced or diminished, respectively, the natural-like pattern formation over the entire sequence. In most families, the key sites included ligand binding sites. These results suggest some selective pressure on the key residues, such as ligand binding activity, may cooperatively facilitate the emergence of a protein family during evolution. From a more practical aspect, the present results highlight an essential role of long-range effects in precisely defining protein families, which are absent in conventional sequence models.

How Many Protein Sequences Fold to a Given Structure? A Coevolutionary Analysis

Quantifying the relationship between protein sequence and structure is key to understanding the protein universe. A fundamental measure of this relationship is the total number of amino acid sequences that can fold to a target protein structure, known as the "sequence capacity," which has been suggested as a proxy for how designable a given protein fold is. Although sequence capacity has been extensively studied using lattice models and theory, numerical estimates for real protein structures are currently lacking. In this work, we have quantitatively estimated the sequence capacity of 10 proteins with a variety of different structures using a statistical model based on residue-residue co-evolution to capture the variation of sequences from the same protein family. Remarkably, we find that even for the smallest protein folds, such as the WW domain, the number of foldable sequences is extremely large, exceeding the Avogadro constant. In agreement with earlier theoretical work, the calculated sequence capacity is positively correlated with the size of the protein, or better, the density of contacts. This allows the absolute sequence capacity of a given protein to be approximately predicted from its structure. On the other hand, the relative sequence capacity, i.e., normalized by the total number of possible sequences, is an extremely tiny number and is strongly anti-correlated with the protein length. Thus, although there may be more foldable sequences for larger proteins, it will be much harder to find them. Lastly, we have correlated the evolutionary age of proteins in the CATH database with their sequence capacity as predicted by our model. The results suggest a trade-off between the opposing requirements of high designability and the likelihood of a novel fold emerging by chance.

Tertiary alphabet for the observable protein structural universe

Here, we systematically decompose the known protein structural universe into its basic elements, which we dub tertiary structural motifs (TERMs). A TERM is a compact backbone fragment that captures the secondary, tertiary, and quaternary environments around a given residue, comprising one or more disjoint segments (three on average). We seek the set of universal TERMs that capture all structure in the Protein Data Bank (PDB), finding remarkable degeneracy. Only ∼600 TERMs are sufficient to describe 50% of the PDB at sub-Angstrom resolution. However, more rare geometries also exist, and the overall structural coverage grows logarithmically with the number of TERMs. We go on to show that universal TERMs provide an effective mapping between sequence and structure. We demonstrate that TERM-based statistics alone are sufficient to recapitulate close-to-native sequences given either NMR or X-ray backbones. Furthermore, sequence variability predicted from TERM data agrees closely with evolutionary variation. Finally, locations of TERMs in protein chains can be predicted from sequence alone based on sequence signatures emergent from TERM instances in the PDB. For multisegment motifs, this method identifies spatially adjacent fragments that are not contiguous in sequence-a major bottleneck in structure prediction. Although all TERMs recur in diverse proteins, some appear specialized for certain functions, such as interface formation, metal coordination, or even water binding. Structural biology has benefited greatly from previously observed degeneracies in structure. The decomposition of the known structural universe into a finite set of compact TERMs offers exciting opportunities toward better understanding, design, and prediction of protein structure.

Comparing three stochastic search algorithms for computational protein design: Monte Carlo, replica exchange Monte Carlo, and a multistart, steepest-descent heuristic

Computational protein design depends on an energy function and an algorithm to search the sequence/conformation space. We compare three stochastic search algorithms: a heuristic, Monte Carlo (MC), and a Replica Exchange Monte Carlo method (REMC). The heuristic performs a steepest-descent minimization starting from thousands of random starting points. The methods are applied to nine test proteins from three structural families, with a fixed backbone structure, a molecular mechanics energy function, and with 1, 5, 10, 20, 30, or all amino acids allowed to mutate. Results are compared to an exact, "Cost Function Network" method that identifies the global minimum energy conformation (GMEC) in favorable cases. The designed sequences accurately reproduce experimental sequences in the hydrophobic core. The heuristic and REMC agree closely and reproduce the GMEC when it is known, with a few exceptions. Plain MC performs well for most cases, occasionally departing from the GMEC by 3-4 kcal/mol. With REMC, the diversity of the sequences sampled agrees with exact enumeration where the latter is possible: up to 2 kcal/mol above the GMEC. Beyond, room temperature replicas sample sequences up to 10 kcal/mol above the GMEC, providing thermal averages and a solution to the inverse protein folding problem. © 2016 Wiley Periodicals, Inc.

Identification of fibrillogenic regions in human triosephosphate isomerase

Background. Amyloid secondary structure relies on the intermolecular assembly of polypeptide chains through main-chain interaction. According to this, all proteins have the potential to form amyloid structure, nevertheless, in nature only few proteins aggregate into toxic or functional amyloids. Structural characteristics differ greatly among amyloid proteins reported, so it has been difficult to link the fibrillogenic propensity with structural topology. However, there are ubiquitous topologies not represented in the amyloidome that could be considered as amyloid-resistant attributable to structural features, such is the case of TIM barrel topology.

Methods. This work was aimed to study the fibrillogenic propensity of human triosephosphate isomerase (HsTPI) as a model of TIM barrels. In order to do so, aggregation of HsTPI was evaluated under native-like and destabilizing conditions. Fibrillogenic regions were identified by bioinformatics approaches, protein fragmentation and peptide aggregation.

Results. We identified four fibrillogenic regions in the HsTPI corresponding to the β3, β6, β7 y α8 of the TIM barrel. From these, the β3-strand region (residues 59–66) was highly fibrillogenic. In aggregation assays, HsTPI under native-like conditions led to amorphous assemblies while under partially denaturing conditions (urea 3.2 M) formed more structured aggregates. This slightly structured aggregates exhibited residual cross-β structure, as demonstrated by the recognition of the WO1 antibody and ATR-FTIR analysis.

Discussion. Despite the fibrillogenic regions present in HsTPI, the enzyme maintained under native-favoring conditions displayed low fibrillogenic propensity. This amyloid-resistance can be attributed to the three-dimensional arrangement of the protein, where β-strands, susceptible to aggregation, are protected in the core of the molecule. Destabilization of the protein structure may expose inner regions promoting β-aggregation, as well as the formation of hydrophobic disordered aggregates. Being this last pathway kinetically favored over the thermodynamically more stable fibril aggregation pathway.

Information and redundancy in the burial folding code of globular proteins within a wide range of shapes and sizes

Recent ab initio folding simulations for a limited number of small proteins have corroborated a previous suggestion that atomic burial information obtainable from sequence could be sufficient for tertiary structure determination when combined to sequence-independent geometrical constraints. Here, we use simulations parameterized by native burials to investigate the required amount of information in a diverse set of globular proteins comprising different structural classes and a wide size range. Burial information is provided by a potential term pushing each atom towards one among a small number L of equiprobable concentric layers. An upper bound for the required information is provided by the minimal number of layers L(min) still compatible with correct folding behavior. We obtain L(min) between 3 and 5 for seven small to medium proteins with 50 ≤ Nr ≤ 110 residues while for a larger protein with Nr = 141 we find that L ≥ 6 is required to maintain native stability. We additionally estimate the usable redundancy for a given L ≥ L(min) from the burial entropy associated to the largest folding-compatible fraction of "superfluous" atoms, for which the burial term can be turned off or target layers can be chosen randomly. The estimated redundancy for small proteins with L = 4 is close to 0.8. Our results are consistent with the above-average quality of burial predictions used in previous simulations and indicate that the fraction of approachable proteins could increase significantly with even a mild, plausible, improvement on sequence-dependent burial prediction or on sequence-independent constraints that augment the detectable redundancy during simulations.

Logistic regression models to predict solvent accessible residues using sequence- and homology-based qualitative and quantitative descriptors applied to a domain-complete X-ray structure learning set

A working example of relative solvent accessibility (RSA) prediction for proteins is presented. Novel logistic regression models with various qualitative descriptors that include amino acid type and quantitative descriptors that include 20- and six-term sequence entropy have been built and validated. A domain-complete learning set of over 1300 proteins is used to fit initial models with various sequence homology descriptors as well as query residue qualitative descriptors. Homology descriptors are derived from BLASTp sequence alignments, whereas the RSA values are determined directly from the crystal structure. The logistic regression models are fitted using dichotomous responses indicating buried or accessible solvent, with binary classifications obtained from the RSA values. The fitted models determine binary predictions of residue solvent accessibility with accuracies comparable to other less computationally intensive methods using the standard RSA threshold criteria 20 and 25% as solvent accessible. When an additional non-homology descriptor describing Lobanov-Galzitskaya residue disorder propensity is included, incremental improvements in accuracy are achieved with 25% threshold accuracies of 76.12 and 74.79% for the Manesh-215 and CASP(8+9) test sets, respectively. Moreover, the described software and the accompanying learning and validation sets allow students and researchers to explore the utility of RSA prediction with simple, physically intuitive models in any number of related applications.

Computational protein design quantifies structural constraints on amino acid covariation

Amino acid covariation, where the identities of amino acids at different sequence positions are correlated, is a hallmark of naturally occurring proteins. This covariation can arise from multiple factors, including selective pressures for maintaining protein structure, requirements imposed by a specific function, or from phylogenetic sampling bias. Here we employed flexible backbone computational protein design to quantify the extent to which protein structure has constrained amino acid covariation for 40 diverse protein domains. We find significant similarities between the amino acid covariation in alignments of natural protein sequences and sequences optimized for their structures by computational protein design methods. These results indicate that the structural constraints imposed by protein architecture play a dominant role in shaping amino acid covariation and that computational protein design methods can capture these effects. We also find that the similarity between natural and designed covariation is sensitive to the magnitude and mechanism of backbone flexibility used in computational protein design. Our results thus highlight the necessity of including backbone flexibility to correctly model precise details of correlated amino acid changes and give insights into the pressures underlying these correlations.

Proteins generally fold into specific three-dimensional structures to perform their cellular functions, and the presence of misfolded proteins is often deleterious for cellular and organismal fitness. For these reasons, maintenance of protein structure is thought to be one of the major fitness pressures acting on proteins. Consequently, the sequences of today's naturally occurring proteins contain signatures reflecting the constraints imposed by protein structure. Here we test the ability of computational protein design methods to recapitulate and explain these signatures. We focus on the physical basis of evolutionary pressures that act on interactions between amino acids in folded proteins, which are critical in determining protein structure and function. Such pressures can be observed from the appearance of amino acid covariation, where the amino acids at certain positions in protein sequences are correlated with each other. We find similar patterns of amino acid covariation in natural sequences and sequences optimized for their structures using computational protein design, demonstrating the importance of structural constraints in protein molecular evolution and providing insights into the structural mechanisms leading to covariation. In addition, these results characterize the ability of computational methods to model the precise details of correlated amino acid changes, which is critical for engineering new proteins with useful functions beyond those seen in nature.

Tethering preferences of domain families co-occurring in multi-domain proteins

Genomic data of several organisms have revealed the presence of a vast repertoire of multi-domain proteins. The role played by individual domains in a multi-domain protein has a profound influence on the overall function of the protein. In the present analysis an attempt has been made to better understand the tethering preferences of domain families that occur in multi-domain proteins. The analysis has been carried out on an exhaustive dataset of 2 961 898 sequences of proteins from 930 organisms, where 741 274 proteins are comprised of at least two domain families. For every domain family, the number of other domain families with which it co-occurs within a protein in this dataset has been enumerated and is referred to as the tethering number of the domain family. It was found that, in the general dataset, the AAA ATPase family and the family of Ser/Thr kinases have the highest tethering numbers of 450 and 444 respectively. Further analysis reveals significant correlation between the number of members in a family and its tethering number. Positive correlation was also observed for the extent of a sequence and functional diversity within a family and the tethering numbers of domain families. Domain families that are present ubiquitously in diverse organisms tend to have large tethering numbers, while organism/kingdom-specific families have low tethering numbers. Thus, the analysis uncovers how domain families recombine and evolve to give rise to multi-domain proteins.

Mining tertiary structural motifs for assessment of designability

The observation of a limited secondary-structural alphabet in native proteins, with significant sequence preferences, has profoundly influenced the fields of protein design and structure prediction (Simons, Kooperberg, Huang, & Baker, 1997; Verschueren et al., 2011). In the era of structural genomics, as the size of the structural dataset continues to grow rapidly, it is becoming possible to extend this analysis to tertiary structural motifs and their sequences. For a hypothetical tertiary motif, the rate of its utilization in natural proteins may be used to assess its designability-the ease with which the motif can be realized with natural amino acids. This requires a structural similarity search methodology, which rather than looking for global topological agreement (more appropriate for categorization of full proteins or domains), identifies detailed geometric matches. In this chapter, we introduce such a method, called MaDCaT, and demonstrate its use by assessing the designability landscapes of two tertiary structural motifs. We also show that such analysis can establish structure/sequence links by providing the sequence constraints necessary to encode designable motifs. As logical extension of their secondary-structure counterparts, tertiary structural preferences will likely prove extremely useful in de novo protein design and structure prediction.

De novo automated design of small RNA circuits for engineering synthetic riboregulation in living cells

A grand challenge in synthetic biology is to use our current knowledge of RNA science to perform the automatic engineering of completely synthetic sequences encoding functional RNAs in living cells. We report here a fully automated design methodology and experimental validation of synthetic RNA interaction circuits working in a cellular environment. The computational algorithm, based on a physicochemical model, produces novel RNA sequences by exploring the space of possible sequences compatible with predefined structures. We tested our methodology in Escherichia coli by designing several positive riboregulators with diverse structures and interaction models, suggesting that only the energy of formation and the activation energy (free energy barrier to overcome for initiating the hybridization reaction) are sufficient criteria to engineer RNA interaction and regulation in bacteria. The designed sequences exhibit nonsignificant similarity to any known noncoding RNA sequence. Our riboregulatory devices work independently and in combination with transcription regulation to create complex logic circuits. Our results demonstrate that a computational methodology based on first-principles can be used to engineer interacting RNAs with allosteric behavior in living cells.

Information-theoretic analysis and prediction of protein atomic burials: on the search for an informational intermediate between sequence and structure

MOTIVATION

It has been recently suggested that atomic burials, as expressed by molecular central distances, contain sufficient information to determine the tertiary structure of small globular proteins. A possible approach to structural determination from sequence could therefore involve a sequence-to-burial intermediate prediction step whose accuracy, however, is theoretically limited by the mutual information between these two variables. We use a non-redundant set of globular protein structures to estimate the mutual information between local amino acid sequence and atomic burials. Discretizing central distances of or atoms in equiprobable burial levels, we estimate relevant mutual information measures that are compared with actual predictions obtained from a Naive Bayesian Classifier (NBC) and a Hidden Markov Model (HMM).

RESULTS

Mutual information density for 20 amino acids and two or three burial levels were estimated to be roughly 15% of the unconditional burial entropy density. Lower estimates for the mutual information between local amino acid sequence and burial of a single residue indicated an increase in mutual information with the number of burial levels up to at least five or six levels. Prediction schemes were found to efficiently extract the available burial information from local sequence. Lower estimates for the mutual information involving single burials are consistently approached by predictions from the NBC and actually surpassed by predictions from the HMM. Near-optimal prediction for the HMM is indicated by the agreement between its density of prediction information and the corresponding density of mutual information between input and output representations.

AVAILABILITY

The dataset of protein structures and the prediction implementations are available at http://www.btc.unb.br/ (in 'Software').

Quantifying protein modularity and evolvability: a comparison of different techniques

Modularity increases evolvability by reducing constraints on adaptation and by allowing preexisting parts to function in new contexts for novel uses. Protein evolution provides an excellent context to study the causes and consequences of biological modularity. In order to address such questions, however, an index for protein modularity is necessary. This paper proposes a simple index for protein modularity-"module density"-which is the number of evolutionarily independent modules that compose a protein divided by the number of amino acids in the protein. The decomposition of proteins into constituent modules can be accomplished by either of two classes of methods. The first class of methods relies on "suppositional" criteria to assign amino acids to modules, whereas the second class of methods relies on "coevolutionary" criteria for this task. One simple and practical method from the first class consists of approximating the number of modules in a protein as the number of regular secondary structure elements (i.e., helices and sheets). Methods based on coevolutionary criteria require more elaborate data, but they have the advantage of being able to specify modules without prior assumptions about why they exist. Given the increasing availability of datasets sampling protein mutational spectra (e.g., from comparative genomics, experimental evolution, and computational prediction), methods based on coevolutionary criteria will likely become more promising in the near future. The ability to meaningfully quantify protein modularity via simple indices has the potential to aid future efforts to understand protein evolutionary rate determinants, improve molecular evolution models and engineer novel proteins.

Analytic markovian rates for generalized protein structure evolution

A general understanding of the complex phenomenon of protein evolution requires the accurate description of the constraints that define the sub-space of proteins with mutations that do not appreciably reduce the fitness of the organism. Such constraints can have multiple origins, in this work we present a model for constrained evolutionary trajectories represented by a Markovian process throughout a set of protein-like structures artificially constructed to be topological intermediates between the structure of two natural occurring proteins. The number and type of intermediate steps defines how constrained the total evolutionary process is. By using a coarse-grained representation for the protein structures, we derive an analytic formulation of the transition rates between each of the intermediate structures. The results indicate that compact structures with a high number of hydrogen bonds are more probable and have a higher likelihood to arise during evolution. Knowledge of the transition rates allows for the study of complex evolutionary pathways represented by trajectories through a set of intermediate structures.

Systematic assessment of accuracy of comparative model of proteins belonging to different structural fold classes

In the absence of experimental structures, comparative modeling continues to be the chosen method for retrieving structural information on target proteins. However, models lack the accuracy of experimental structures. Alignment error and structural divergence (between target and template) influence model accuracy the most. Here, we examine the potential additional impact of backbone geometry, as our previous studies have suggested that the structural class (all-α, αβ, all-β) of a protein may influence the accuracy of its model. In the twilight zone (sequence identity ≤ 30%) and at a similar level of target-template divergence, the accuracy of protein models does indeed follow the trend all-α > αβ > all-β. This is mainly because the alignment accuracy follows the same trend (all-α > αβ > all-β), with backbone geometry playing only a minor role. Differences in the diversity of sequences belonging to different structural classes leads to the observed accuracy differences, thus enabling the accuracy of alignments/models to be estimated a priori in a class-dependent manner. This study provides a systematic description of and quantifies the structural class-dependent effect in comparative modeling. The study also suggests that datasets for large-scale sequence/structure analyses should have equal representations of different structural classes to avoid class-dependent bias.

Thermodynamics of protein folding: a random matrix formulation

The process of protein folding from an unfolded state to a biologically active, folded conformation is governed by many parameters, e.g. the sequence of amino acids, intermolecular interactions, the solvent, temperature and chaperon molecules. Our study, based on random matrix modeling of the interactions, shows, however, that the evolution of the statistical measures, e.g. Gibbs free energy, heat capacity, and entropy, is single parametric. The information can explain the selection of specific folding pathways from an infinite number of possible ways as well as other folding characteristics observed in computer simulation studies.

Probing designability via a generalized model of helical bundle geometry

Because the space of folded protein structures is highly degenerate, with recurring secondary and tertiary motifs, methods for representing protein structure in terms of collective physically relevant coordinates are of great interest. By collapsing structural diversity to a handful of parameters, such methods can be used to delineate the space of designable structures (i.e., conformations that can be stabilized with a large number of sequences)-a crucial task for de novo protein design. We first demonstrate this on natural α-helical coiled coils using the Crick parameterization. We show that over 95% of known coiled-coil structures are within  1-Å C(α) root mean square deviation of a Crick-ideal backbone. Derived parameters show that natural geometric space of coiled coils is highly restricted and can be represented by "allowed" conformations amidst a potential continuum of conformers. Allowed structures have (1) restricted axial offsets between helices, which differ starkly between parallel and anti-parallel structures; (2) preferred superhelical radii, which depend linearly on the oligomerization state; (3) pronounced radius-dependent a- and d-position amino acid propensities; and (4) discrete angles of rotation of helices about their axes, which are surprisingly independent of oligomerization state or orientation. In all, we estimate the space of designable coiled-coil structures to be reduced at least 160-fold relative to the space of geometrically feasible structures. To extend the benefits of structural parameterization to other systems, we developed a general mathematical framework for parameterizing arbitrary helical structures, which reduces to the Crick parameterization as a special case. The method is successfully validated on a set of non-coiled-coil helical bundles, frequent in channels and transporter proteins, which show significant helix bending but not supercoiling. Programs for coiled-coil parameter fitting and structure generation are provided via a web interface at http://www.gevorggrigoryan.com/cccp/, and code for generalized helical parameterization is available upon request.

Design of multispecific protein sequences using probabilistic graphical modeling

In nature, proteins partake in numerous protein- protein interactions that mediate their functions. Moreover, proteins have been shown to be physically stable in multiple structures, induced by cellular conditions, small ligands, or covalent modifications. Understanding how protein sequences achieve this structural promiscuity at the atomic level is a fundamental step in the drug design pipeline and a critical question in protein physics. One way to investigate this subject is to computationally predict protein sequences that are compatible with multiple states, i.e., multiple target structures or binding to distinct partners. The goal of engineering such proteins has been termed multispecific protein design. We develop a novel computational framework to efficiently and accurately perform multispecific protein design. This framework utilizes recent advances in probabilistic graphical modeling to predict sequences with low energies in multiple target states. Furthermore, it is also geared to specifically yield positional amino acid probability profiles compatible with these target states. Such profiles can be used as input to randomly bias high-throughput experimental sequence screening techniques, such as phage display, thus providing an alternative avenue for elucidating the multispecificity of natural proteins and the synthesis of novel proteins with specific functionalities. We prove the utility of such multispecific design techniques in better recovering amino acid sequence diversities similar to those resulting from millions of years of evolution. We then compare the approaches of prediction of low energy ensembles and of amino acid profiles and demonstrate their complementarity in providing more robust predictions for protein design.

Projection of gene-protein networks to the functional space of the proteome and its application to analysis of organism complexity

We consider the problem of biological complexity via a projection of protein-coding genes of complex organisms onto the functional space of the proteome. The latter can be defined as a set of all functions committed by proteins of an organism. Alternative splicing (AS) allows an organism to generate diverse mature RNA transcripts from a single mRNA strand and thus it could be one of the key mechanisms of increasing of functional complexity of the organism's proteome and a driving force of biological evolution. Thus, the projection of transcription units (TU) and alternative splice-variant (SV) forms onto proteome functional space could generate new types of relational networks (e.g. SV-protein function networks, SFN) and lead to discoveries of novel evolutionarily conservative functional modules. Such types of networks might provide new reliable characteristics of organism complexity and a better understanding of the evolutionary integration and plasticity of interconnection of genome-transcriptome-proteome functions.

Computational protein design as a tool for fold recognition

Computationally designed protein sequences have been proposed as a basis to perform fold recognition and homology searching. To investigate this possibility, an automated procedure is used to completely redesign 24 SH3 proteins and 22 SH2 proteins. We use the experimental backbone coordinates as fixed templates in the folded state and a molecular mechanics model to compute the pairwise interaction energies between all sidechain types and conformations. Energy calculations are done with the Proteins@Home volunteer computing platform. A heuristic algorithm is then used to scan the sequence and conformational space for optimal solutions. We produced 200,000-450,000 sequences for each backbone template. The designed sequences ressemble moderately-distant, natural homologues of the initial templates, according to their identity scores and their similarity with respect to the Pfam sets of SH2 and SH3 domains. Standard homology detection tools document their native-like character: the Conserved Domain Database recognizes 61% (52%) of our low-energy sequences as SH3 (SH2) domains; the SUPERFAMILY, Hidden-Markov Model library recognizes 81% (84%). Conversely, position specific scoring matrices (PSSMs) derived from our designed sequences can be used to detect natural homologues in sequence databases. Within SwissProt, a set of natural SH3 PSSMs detects 772 SH3 domains, for example; our designed PSSMs detect 67% of these, plus one additional sequence and two false positives. If six amino acids involved in substrate binding (a selective pressure not accounted for in our design) are reset to their experimental types, then 77% of the experimental SH3 domains are detected. Results for the SH2 domains are similar. Several directions to improve the method further are discussed.

A sequence-compatible amount of native burial information is sufficient for determining the structure of small globular proteins

Protein tertiary structures are known to be encoded in amino acid sequences, but the problem of structure prediction from sequence continues to be a challenge. With this question in mind, recent simulations have shown that atomic burials, as expressed by atom distances to the molecular geometrical center, are sufficiently informative for determining native conformations of small globular proteins. Here we use a simple computational experiment to estimate the amount of this required burial information and find it to be surprisingly small, actually comparable with the stringent limit imposed by sequence statistics. Atomic burials appear to satisfy, therefore, minimal requirements for a putative dominating property in the folding code because they provide an amount of information sufficiently large for structural determination but, at the same time, sufficiently small to be encodable in sequences. In a simple analogy with human communication, atomic burials could correspond to the actual "language" encoded in the amino acid "script" from which the complexity of native conformations is recovered during the folding process.

Multi-constraint computational design suggests that native sequences of germline antibody H3 loops are nearly optimal for conformational flexibility

The limited size of the germline antibody repertoire has to recognize a far larger number of potential antigens. The ability of a single antibody to bind multiple ligands due to conformational flexibility in the antigen-binding site can significantly enlarge the repertoire. Among the six complementarity determining regions (CDRs) that generally comprise the binding site, the CDR H3 loop is particularly variable. Computational protein design studies showed that predicted low energy sequences compatible with a given backbone structure often have considerable similarity to the corresponding native sequences of naturally occurring proteins, indicating that native protein sequences are close to optimal for their structures. Here, we take a step forward to determine whether conformational flexibility, believed to play a key functional role in germline antibodies, is also central in shaping their native sequence. In particular, we use a multi-constraint computational design strategy, along with the Rosetta scoring function, to propose that the native sequences of CDR H3 loops from germline antibodies are nearly optimal for conformational flexibility. Moreover, we find that antibody maturation may lead to sequences with a higher degree of optimization for a single conformation, while disfavoring sequences that are intrinsically flexible. In addition, this computational strategy allows us to predict mutations in the CDR H3 loop to stabilize the antigen-bound conformation, a computational mimic of affinity maturation, that may increase antigen binding affinity by preorganizing the antigen binding loop. In vivo affinity maturation data are consistent with our predictions. The method described here can be useful to design antibodies with higher selectivity and affinity by reducing conformational diversity.

A search for energy minimized sequences of proteins

In this paper, we present numerical evidence that supports the notion of minimization in the sequence space of proteins for a target conformation. We use the conformations of the real proteins in the Protein Data Bank (PDB) and present computationally efficient methods to identify the sequences with minimum energy. We use edge-weighted connectivity graph for ranking the residue sites with reduced amino acid alphabet and then use continuous optimization to obtain the energy-minimizing sequences. Our methods enable the computation of a lower bound as well as a tight upper bound for the energy of a given conformation. We validate our results by using three different inter-residue energy matrices for five proteins from protein data bank (PDB), and by comparing our energy-minimizing sequences with 80 million diverse sequences that are generated based on different considerations in each case. When we submitted some of our chosen energy-minimizing sequences to Basic Local Alignment Search Tool (BLAST), we obtained some sequences from non-redundant protein sequence database that are similar to ours with an E-value of the order of 10^-7. In summary, we conclude that proteins show a trend towards minimizing energy in the sequence space but do not seem to adopt the global energy-minimizing sequence. The reason for this could be either that the existing energy matrices are not able to accurately represent the inter-residue interactions in the context of the protein environment or that Nature does not push the optimization in the sequence space, once it is able to perform the function.

Prediction of protein-protein interface sequence diversity using flexible backbone computational protein design

A major challenge in computational protein design is to identify functional sequences as top predictions. One reason for design failures is conformational plasticity, as proteins frequently change their conformation in response to mutations. To advance protein design, here we describe a method employing flexible backbone ensembles to predict sequences tolerated for a protein-protein interface. We show that the predictions are enriched in functional proteins when compared to a phage display screen quantitatively mapping the energy landscape for the interaction between human growth hormone and its receptor. Our model for structural plasticity is inspired by coupled side chain-backbone "backrub" motions observed in high-resolution protein crystal structures. Although the modeled structural changes are subtle, our results on predicting sequence plasticity suggest that backrub sampling may capture a sizable fraction of localized conformational changes that occur in proteins. The described method has implications for predicting sequence libraries to enable challenging protein engineering problems.

Relationship between energy distribution and fold stability: Insights from molecular dynamics simulations of native and mutant proteins

Most proteins must fold to a well-defined structure with a minimal stability to perform their function. Here we use a simple, molecular dynamics-based, energy decomposition approach to map the principal energetic interactions in a set of proteins representative of different folds. This work involves the all-atom simulation and analysis of the native structures and mutants of five different proteins representative of an all-alpha (yACPB, Protein A), all-beta (SH3), and a mixed alpha/beta fold (Proteins G and L). Given a certain structure, a native sequence and a set of mutants, we show that our model discriminates the ability of a mutation to yield a more or less stable protein, in agreement with experimental data, catching the principal energetic determinants of protein stabilization. Our approach identifies the interaction determinants responsible to define a fold and shows that mutations can either modulate the strength of pair-wise coupling between residues important for folding, or modify the profile of the principal interactions. Furthermore, we address the question of how to evaluate the fitness of a sequence to a given structure by comparing the information contained in the energy map, which recapitulates the chemistry of the sequence, to that contained in the contact map, which recapitulates the fold topology. The results show that the better fit between the energetic properties of the sequence and the fold topology corresponds to a higher stabilization of the protein. We discuss the relevance of these observations to the analysis of protein designability and to the rational evolution of new sequences.

Testing the Coulomb/Accessible Surface Area solvent model for protein stability, ligand binding, and protein design

Background

Protein structure prediction and computational protein design require efficient yet sufficiently accurate descriptions of aqueous solvent. We continue to evaluate the performance of the Coulomb/Accessible Surface Area (CASA) implicit solvent model, in combination with the Charmm19 molecular mechanics force field. We test a set of model parameters optimized earlier, and we also carry out a new optimization in this work, using as a target a set of experimental stability changes for single point mutations of various proteins and peptides. The optimization procedure is general, and could be used with other force fields. The computation of stability changes requires a model for the unfolded state of the protein. In our approach, this state is represented by tripeptide structures of the sequence Ala-X-Ala for each amino acid type X. We followed an iterative optimization scheme which, at each cycle, optimizes the solvation parameters and a set of tripeptide structures for the unfolded state. This protocol uses a set of 140 experimental stability mutations and a large set of tripeptide conformations to find the best tripeptide structures and solvation parameters.

Results

Using the optimized parameters, we obtain a mean unsigned error of 2.28 kcal/mol for the stability mutations. The performance of the CASA model is assessed by two further applications: (i) calculation of protein-ligand binding affinities and (ii) computational protein design. For these two applications, the previous parameters and the ones optimized here give a similar performance. For ligand binding, we obtain reasonable agreement with a set of 55 experimental mutation data, with a mean unsigned error of 1.76 kcal/mol with the new parameters and 1.47 kcal/mol with the earlier ones. We show that the optimized CASA model is not inferior to the Generalized Born/Surface Area (GB/SA) model for the prediction of these binding affinities. Likewise, the new parameters perform well for the design of 8 SH3 domain proteins where an average of 32.8% sequence identity relative to the native sequences was achieved. Further, it was shown that the computed sequences have the character of naturally-occuring homologues of the native sequences.

Conclusion

Overall, the two CASA variants explored here perform very well for a wide variety of applications. Both variants provide an efficient solvent treatment for the computational engineering of ligands and proteins.

Protein domain prediction

Domains are considered to be the building blocks of protein structures. A protein can contain a single domain or multiple domains, each one typically associated with a specific function. The combination of domains determines the function of the protein, its subcellular localization and the interactions it is involved in. Determining the domain structure of a protein is important for multiple reasons, including protein function analysis and structure prediction. This chapter reviews the different approaches for domain prediction and discusses lessons learned from the application of these methods.

Computationally mapping sequence space to understand evolutionary protein engineering

Evolutionary protein engineering has been dramatically successful, producing a wide variety of new proteins with altered stability, binding affinity, and enzymatic activity. However, the success of such procedures is often unreliable, and the impact of the choice of protein, engineering goal, and evolutionary procedure is not well understood. We have created a framework for understanding aspects of the protein engineering process by computationally mapping regions of feasible sequence space for three small proteins using structure-based design protocols. We then tested the ability of different evolutionary search strategies to explore these sequence spaces. The results point to a non-intuitive relationship between the error-prone PCR mutation rate and the number of rounds of replication. The evolutionary relationships among feasible sequences reveal hub-like sequences that serve as particularly fruitful starting sequences for evolutionary search. Moreover, genetic recombination procedures were examined, and tradeoffs relating sequence diversity and search efficiency were identified. This framework allows us to consider the impact of protein structure on the allowed sequence space and therefore on the challenges that each protein presents to error-prone PCR and genetic recombination procedures.

Recognizing protein-protein interfaces with empirical potentials and reduced amino acid alphabets

Background

In structural genomics, an important goal is the detection and classification of protein–protein interactions, given the structures of the interacting partners. We have developed empirical energy functions to identify native structures of protein–protein complexes among sets of decoy structures. To understand the role of amino acid diversity, we parameterized a series of functions, using a hierarchy of amino acid alphabets of increasing complexity, with 2, 3, 4, 6, and 20 amino acid groups. Compared to previous work, we used the simplest possible functional form, with residue–residue interactions and a stepwise distance-dependence. We used increased computational ressources, however, constructing 290,000 decoys for 219 protein–protein complexes, with a realistic docking protocol where the protein partners are flexible and interact through a molecular mechanics energy function. The energy parameters were optimized to correctly assign as many native complexes as possible. To resolve the multiple minimum problem in parameter space, over 64000 starting parameter guesses were tried for each energy function. The optimized functions were tested by cross validation on subsets of our native and decoy structures, by blind tests on series of native and decoy structures available on the Web, and on models for 13 complexes submitted to the CAPRI structure prediction experiment.

Results

Performance is similar to several other statistical potentials of the same complexity. For example, the CAPRI target structure is correctly ranked ahead of 90% of its decoys in 6 cases out of 13. The hierarchy of amino acid alphabets leads to a coherent hierarchy of energy functions, with qualitatively similar parameters for similar amino acid types at all levels. Most remarkably, the performance with six amino acid classes is equivalent to that of the most detailed, 20-class energy function.

Conclusion

This suggests that six carefully chosen amino acid classes are sufficient to encode specificity in protein–protein interactions, and provide a starting point to develop more complicated energy functions.

The network of sequence flow between protein structures

Sequence-structure relationships in proteins are highly asymmetric because many sequences fold into relatively few structures. What is the number of sequences that fold into a particular protein structure? Is it possible to switch between stable protein folds by point mutations? To address these questions, we compute a directed graph of sequences and structures of proteins, which is based on 2,060 experimentally determined protein shapes from the Protein Data Bank. The directed graph is highly connected at native energies with "sinks" that attract many sequences from other folds. The sinks are rich in beta-sheets. The number of sequences that transition between folds is significantly smaller than the number of sequences retained by their fold. The sequence flow into a particular protein shape from other proteins correlates with the number of sequences that matches this shape in empirically determined genomes. Properties of strongly connected components of the graph are correlated with protein length and secondary structure.

Computational sidechain placement and protein mutagenesis with implicit solvent models

Structure prediction and computational protein design should benefit from accurate solvent models. We have applied implicit solvent models to two problems that are central to this area. First, we performed sidechain placement for 29 proteins, using a solvent model that combines a screened Coulomb term with an Accessible Surface Area term (CASA model). With optimized parameters, the prediction quality is comparable with earlier work that omitted electrostatics and solvation altogether. Second, we computed the stability changes associated with point mutations involving ionized sidechains. For over 1000 mutations, including many fully or partly buried positions, we compared CASA and two generalized Born models (GB) with a more accurate model, which solves the Poisson equation of continuum electrostatics numerically. CASA predicts the correct sign and order of magnitude of the stability change for 81% of the mutations, compared to 97% with the best GB. We also considered 140 mutations for which experimental data are available. Comparing to experiment requires additional assumptions about the unfolded protein structure, protein relaxation in response to the mutations, and contributions from the hydrophobic effect. With a simple, commonly-used unfolded state model, the mean unsigned error is 2.1 kcal/mol with both CASA and the best GB. Overall, the electrostatic model is not important for sidechain placement; CASA and GB are equivalent for surface mutations, while GB is far superior for fully or partly buried positions. Thus, for problems like protein design that involve all these aspects, the most recent GB models represent an important step forward. Along with the recent discovery of efficient, pairwise implementations of GB, this will open new possibilities for the computational engineering of proteins.

Novel enzymes through design and evolution

The generation of enzymes with new catalytic activities remains a major challenge. So far, several different strategies have been developed to tackle this problem, including site-directed mutagenesis, random mutagenesis (directed evolution), antibody catalysis, computational redesign, and de novo methods. Using these techniques, a broad array of novel enzymes has been created (aldolases, decarboxylases, dehydratases, isomerases, oxidases, reductases, and others), although their low efficiencies (10 to 100 M(-1) s(-l)) compared to those of the best natural enzymes (10(6) to 10(8) M(-1) s(-1)) remains a significant concern. Whereas rational design might be the most promising and versatile approach to generating new activities, directed evolution seems to be the best way to optimize the catalytic properties of novel enzymes. Indeed, impressive successes in enzyme engineering have resulted from a combination of rational and random design.

Packing regularities in biological structures relate to their dynamics

The high packing density inside proteins leads to certain geometric regularities and also is one of the most important contributors to the high extent of cooperativity manifested by proteins in their cohesive domain motions. The orientations between neighboring nonbonded residues in proteins substantially follow the similar geometric regularities, regardless of whether the residues are on the surface or buried, a direct result of hydrophobicity forces. These orientations are relatively fixed and correspond closely to small deformations from those of the face-centered cubic lattice, which is the way in which identical spheres pack at the highest density. Packing density also is related to the extent of conservation of residues, and we show this relationship for residue packing densities by averaging over a large sample or residue packings. There are three regimes: (1) over a broad range of packing densities the relationship between sequence entropy and inverse packing density is nearly linear, (2) over a limited range of low packing densities the sequence entropy is nearly constant, and (3) at extremely low packing densities the sequence entropy is highly variable. These packing results provide important justification for the simple elastic network models that have been shown for a large number of proteins to represent protein dynamics so successfully, even when the models are extremely coarse grained. Elastic network models for polymeric chains are simple and could be combined with these protein elastic networks to represent partially denatured parts of proteins. Finally, we show results of applications of the elastic network model to study the functional motions of the ribosome, based on its known structure. These results indicate expected correlations among its components for the step-wise processing steps in protein synthesis, and suggest ways to use these elastic network models to develop more detailed mechanisms, an important possibility because most experiments yield only static structures.

Direct correlation between proteins' folding rates and their amino acid compositions: An ab initio folding rate prediction

Discovering the mechanism of protein folding, in molecular biology, is a great challenge. A key step to this end is to find factors that correlate with protein folding rates. Over the past few years, many empirical parameters, such as contact order, long-range order, total contact distance, secondary structure contents, have been developed to reflect the correlation between folding rates and protein tertiary or secondary structures. However, the correlation between proteins' folding rates and their amino acid compositions has not been explored. In the present work, we examined systematically the correlation between proteins' folding rates and their amino acid compositions for two-state and multistate folders and found that different amino acids contributed differently to the folding progress. The relation between the amino acids' molecular weight and degeneracy and the folding rates was examined, and the role of hydrophobicity in the protein folding process was also inspected. As a consequence, a new indicator called composition index was derived, which takes no structure factors into account and is merely determined by the amino acid composition of a protein. Such an indicator is found to be highly correlated with the protein's folding rate (r > 0.7). From the results of this work, three points of concluding remarks are evident. (1) Two-state folders and multistate folders have different rate-determining amino acids. (2) The main determining information of a protein's folding rate is largely reflected in its amino acid composition. (3) Composition index may be the best predictor for an ab initio protein folding rate prediction directly from protein sequence from the standpoint of practical application.