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

The role of promiscuous molecular recognition in the evolution of RNase-based self-incompatibility in plants

How do biological networks evolve and expand? We study these questions in the context of the plant collaborative-non-self recognition self-incompatibility system. Self-incompatibility evolved to avoid self-fertilization among hermaphroditic plants. It relies on specific molecular recognition between highly diverse proteins of two families: female and male determinants, such that the combination of genes an individual possesses determines its mating partners. Though highly polymorphic, previous models struggled to pinpoint the evolutionary trajectories by which new specificities evolved. Here, we construct a novel theoretical framework, that crucially affords interaction promiscuity and multiple distinct partners per protein, as is seen in empirical findings disregarded by previous models. We demonstrate spontaneous self-organization of the population into distinct "classes" with full between-class compatibility and a dynamic long-term balance between class emergence and decay. Our work highlights the importance of molecular recognition promiscuity to network evolvability. Promiscuity was found in additional systems suggesting that our framework could be more broadly applicable.

In silico design of misfolding resistant proteins: the role of structural similarity of a competing conformational ensemble in the optimization of frustration

Most state-of-the-art in silico design methods fail due to misfolding of designed sequences to a conformation other than the target. Thus, a method to design misfolding resistant proteins will provide a better understanding of the misfolding phenomenon and will also increase the success rate of in silico design methods. In this work, we optimize the conformational ensemble to be selected for negative design purposes based on the similarity of the conformational ensemble to the target. Five ensembles with different degrees of similarity to the target are created and destabilized and the target is stabilized while designing sequences using mean field theory and Monte Carlo simulation methods. The results suggest that the degree of similarity of the non-native conformations to the target plays a prominent role in designing misfolding resistant protein sequences. The design procedures that destabilize the conformational ensemble with moderate similarity to the target have proven to be more promising. Incorporation of either highly similar or highly dissimilar conformations to the target conformation into the non-native ensemble to be destabilized may lead to sequences with a higher misfolding propensity. This will significantly reduce the conformational space to be considered in any protein design procedure. Interestingly, the results suggest that a sequence with higher frustration in the target structure does not necessarily lead to a misfold prone sequence. A successful design method may purposefully choose a frustrated sequence in the target conformation if that sequence is even more frustrated in the competing non-native conformations.

Supertertiary protein structure affects an allosteric network

Protein function can be allosterically regulated by changes in structure or dynamics. PDZ domains are classic examples for studies of allostery in single protein domains. However, PDZ domains are often found in multidomain proteins; in particular, PDZ3 is located in a supramodule containing three domains. The allosteric network in PDZ3 has never been studied in the presence of the adjacent domains. Here we map the allosteric network for a PDZ3:ligand complex, both in isolation and in the context of a supramodule. We demonstrate that the allosteric network is highly dependent on this supertertiary structure, with broad implications for studies of allostery in single domains.

The notion that protein function is allosterically regulated by structural or dynamic changes in proteins has been extensively investigated in several protein domains in isolation. In particular, PDZ domains have represented a paradigm for these studies, despite providing conflicting results. Furthermore, it is still unknown how the association between protein domains in supramodules, consitituting so-called supertertiary structures, affects allosteric networks. Here, we experimentally mapped the allosteric network in a PDZ:ligand complex, both in isolation and in the context of a supramodular structure, and show that allosteric networks in a PDZ domain are highly dependent on the supertertiary structure in which they are present. This striking sensitivity of allosteric networks to the presence of adjacent protein domains is likely a common property of supertertiary structures in proteins. Our findings have general implications for prediction of allosteric networks from primary and tertiary structures and for quantitative descriptions of allostery.

Double-mutant cycles: new directions and applications

Double-mutant cycle (DMC) analysis is a powerful approach for detecting and quantifying the energetics of both direct and long-range interactions in proteins and other chemical systems. It can also be used to unravel higher-order interactions (e.g. three-body effects) that lead to cooperativity in protein folding and function. In this review, we describe new applications of DMC analysis based on advances in native mass spectrometry and high-throughput methods such as next generation sequencing and protein complementation assays. These developments have facilitated carrying out high-throughput DMC analysis, which can be used to characterize increasingly higher-order interactions and very large interaction networks in proteins. Such studies have provided insights into the extent of cooperativity (epistasis) in protein structures. High-throughput DMC studies have also been used to validate correlated mutation analysis and can provide restraints for protein docking.

How Often Do Protein Genes Navigate Valleys of Low Fitness?

To escape from local fitness peaks, a population must navigate across valleys of low fitness. How these transitions occur, and what role they play in adaptation, have been subjects of active interest in evolutionary genetics for almost a century. However, to our knowledge, this problem has never been addressed directly by considering the evolution of a gene, or group of genes, as a whole, including the complex effects of fitness interactions among multiple loci. Here, we use a precise model of protein fitness to compute the probability P ( s , Δ t ) that an allele, randomly sampled from a population at time t, has crossed a fitness valley of depth s during an interval t - Δ t , t in the immediate past. We study populations of model genes evolving under equilibrium conditions consistent with those in mammalian mitochondria. From this data, we estimate that genes encoding small protein motifs navigate fitness valleys of depth 2 N s ≳ 30 with probability P ≳ 0 . 1 on a time scale of human evolution, where N is the (mitochondrial) effective population size. The results are consistent with recent findings for Watson⁻Crick switching in mammalian mitochondrial tRNA molecules.

Correlating topology and thermodynamics to predict protein structure sensitivity to point mutations

The relation between distribution of hydrophobic amino acids along with protein chains and their structure is far from being completely understood. No reliable method allowsab initioprediction of the folded structure from this distribution of physicochemical properties, even when they are highly degenerated by considering only two classes: hydrophobic and polar. Establishment of long-range hydrophobic three dimension (3D) contacts is essential for the formation of the nucleus, a key process in the early steps of protein folding. Thus, a large number of 3D simulation studies were developed to challenge this issue. They are nowadays evaluated in a specific chapter of the molecular modeling competition, Critical Assessment of Protein Structure Prediction. We present here a simulation of the early steps of the folding process for 850 proteins, performed in a discrete 3D space, which results in peaks in the predicted distribution of intra-chain noncovalent contacts. The residues located at these peak positions tend to be buried in the core of the protein and are expected to correspond to critical positions in the sequence, important both for folding and structural (or similarly, energetic in the thermodynamic hypothesis) stability. The degree of stabilization or destabilization due to a point mutation at the critical positions involved in numerous contacts is estimated from the calculated folding free energy difference between mutated and native structures. The results show that these critical positions are not tolerant towards mutation. This simulation of the noncovalent contacts only needs a sequence as input, and this paper proposes a validation of the method by comparison with the prediction of stability by well-established programs.

Did α-Synuclein and Glucocerebrosidase Coevolve? Implications for Parkinson's Disease

Mutations in the GBA1 gene are associated with increased risk of Parkinson's disease, and the protein produced by the gene, glucocerebrosidase, interacts with α-synuclein, the protein at the center of the disease etiology. One possibility is that the mutations disrupt a beneficial interaction between the proteins, and a beneficial interaction would imply that the proteins have coevolved. To explore this possibility, a correlated mutation analysis has been performed for all 72 vertebrate species where complete sequences of α-synuclein and glucocerebrosidase are known. The most highly correlated pair of residue variations is α-synuclein A53T and glucocerebrosidase G115E. Intriguingly, the A53T mutation is a Parkinson's disease risk factor in humans, suggesting the pathology associated with this mutation and interaction with glucocerebrosidase might be connected. Correlations with β-synuclein are also evaluated. To assess the impact of lowered species number on accuracy, intra and inter-chain correlations are also calculated for hemoglobin, using mutual information Z-value and direct coupling analyses.

Biophysics of protein evolution and evolutionary protein biophysics

The study of molecular evolution at the level of protein-coding genes often entails comparing large datasets of sequences to infer their evolutionary relationships. Despite the importance of a protein's structure and conformational dynamics to its function and thus its fitness, common phylogenetic methods embody minimal biophysical knowledge of proteins. To underscore the biophysical constraints on natural selection, we survey effects of protein mutations, highlighting the physical basis for marginal stability of natural globular proteins and how requirement for kinetic stability and avoidance of misfolding and misinteractions might have affected protein evolution. The biophysical underpinnings of these effects have been addressed by models with an explicit coarse-grained spatial representation of the polypeptide chain. Sequence-structure mappings based on such models are powerful conceptual tools that rationalize mutational robustness, evolvability, epistasis, promiscuous function performed by 'hidden' conformational states, resolution of adaptive conflicts and conformational switches in the evolution from one protein fold to another. Recently, protein biophysics has been applied to derive more accurate evolutionary accounts of sequence data. Methods have also been developed to exploit sequence-based evolutionary information to predict biophysical behaviours of proteins. The success of these approaches demonstrates a deep synergy between the fields of protein biophysics and protein evolution.

Detecting selection on protein stability through statistical mechanical models of folding and evolution

The properties of biomolecules depend both on physics and on the evolutionary process that formed them. These two points of view produce a powerful synergism. Physics sets the stage and the constraints that molecular evolution has to obey, and evolutionary theory helps in rationalizing the physical properties of biomolecules, including protein folding thermodynamics. To complete the parallelism, protein thermodynamics is founded on the statistical mechanics in the space of protein structures, and molecular evolution can be viewed as statistical mechanics in the space of protein sequences. In this review, we will integrate both points of view, applying them to detecting selection on the stability of the folded state of proteins. We will start discussing positive design, which strengthens the stability of the folded against the unfolded state of proteins. Positive design justifies why statistical potentials for protein folding can be obtained from the frequencies of structural motifs. Stability against unfolding is easier to achieve for longer proteins. On the contrary, negative design, which consists in destabilizing frequently formed misfolded conformations, is more difficult to achieve for longer proteins. The folding rate can be enhanced by strengthening short-range native interactions, but this requirement contrasts with negative design, and evolution has to trade-off between them. Finally, selection can accelerate functional movements by favoring low frequency normal modes of the dynamics of the native state that strongly correlate with the functional conformation change.

A firefly-inspired method for protein structure prediction in lattice models

We introduce a Firefly-inspired algorithmic approach for protein structure prediction over two different lattice models in three-dimensional space. In particular, we consider three-dimensional cubic and three-dimensional face-centred-cubic (FCC) lattices. The underlying energy models are the Hydrophobic-Polar (H-P) model, the Miyazawa–Jernigan (M-J) model and a related matrix model. The implementation of our approach is tested on ten H-P benchmark problems of a length of 48 and ten M-J benchmark problems of a length ranging from 48 until 61. The key complexity parameter we investigate is the total number of objective function evaluations required to achieve the optimum energy values for the H-P model or competitive results in comparison to published values for the M-J model. For H-P instances and cubic lattices, where data for comparison are available, we obtain an average speed-up over eight instances of 2.1, leaving out two extreme values (otherwise, 8.8). For six M-J instances, data for comparison are available for cubic lattices and runs with a population size of 100, where, a priori, the minimum free energy is a termination criterion. The average speed-up over four instances is 1.2 (leaving out two extreme values, otherwise 1.1), which is achieved for a population size of only eight instances. The present study is a test case with initial results for ad hoc parameter settings, with the aim of justifying future research on larger instances within lattice model settings, eventually leading to the ultimate goal of implementations for off-lattice models.

Detecting selection for negative design in proteins through an improved model of the misfolded state

Proteins that need to be structured in their native state must be stable both against the unfolded ensemble and against incorrectly folded (misfolded) conformations with low free energy. Positive design targets the first type of stability by strengthening native interactions. The second type of stability is achieved by destabilizing interactions that occur frequently in the misfolded ensemble, a strategy called negative design. Here, we investigate negative design adopting a statistical mechanical model of the misfolded ensemble, which improves the usual Gaussian approximation by taking into account the third moment of the energy distribution and contact correlations. Applying this model, we detect and quantify selection for negative design in most natural proteins, and we analytically design protein sequences that are stable both against unfolding and against misfolding.

On the characterization and software implementation of general protein lattice models

models of proteins have been widely used as a practical means to computationally investigate general properties of the system. In lattice models any sterically feasible conformation is represented as a self-avoiding walk on a lattice, and residue types are limited in number. So far, only two- or three-dimensional lattices have been used. The inspection of the neighborhood of alpha carbons in the core of real proteins reveals that also lattices with higher coordination numbers, possibly in higher dimensional spaces, can be adopted. In this paper, a new general parametric lattice model for simplified protein conformations is proposed and investigated. It is shown how the supporting software can be consistently designed to let algorithms that operate on protein structures be implemented in a lattice-agnostic way. The necessary theoretical foundations are developed and organically presented, pinpointing the role of the concept of main directions in lattice-agnostic model handling. Subsequently, the model features across dimensions and lattice types are explored in tests performed on benchmark protein sequences, using a Python implementation. Simulations give insights on the use of square and triangular lattices in a range of dimensions. The trend of potential minimum for sequences of different lengths, varying the lattice dimension, is uncovered. Moreover, an extensive quantitative characterization of the usage of the so-called "move types" is reported for the first time. The proposed general framework for the development of lattice models is simple yet complete, and an object-oriented architecture can be proficiently employed for the supporting software, by designing ad-hoc classes. The proposed framework represents a new general viewpoint that potentially subsumes a number of solutions previously studied. The adoption of the described model pushes to look at protein structure issues from a more general and essential perspective, making computational investigations over simplified models more straightforward as well.

Comparative modeling and protein-like features of hydrophobic-polar models on a two-dimensional lattice

Lattice models of proteins have been extensively used to study protein thermodynamics, folding dynamics, and evolution. Our study considers two different hydrophobic-polar (HP) models on the 2D square lattice: the purely HP model and a model where a compactness-favoring term is added. We exhaustively enumerate all the possible structures in our models and perform the study of their corresponding folds, HP arrangements in space and shapes. The two models considered differ greatly in their numbers of structures, folds, arrangements, and shapes. Despite their differences, both lattice models have distinctive protein-like features: (1) Shapes are compact in both models, especially when a compactness-favoring energy term is added. (2) The residue composition is independent of the chain length and is very close to 50% hydrophobic in both models, as we observe in real proteins. (3) Comparative modeling works well in both models, particularly in the more compact one. The fact that our models show protein-like features suggests that lattice models incorporate the fundamental physical principles of proteins. Our study supports the use of lattice models to study questions about proteins that require exactness and extensive calculations, such as protein design and evolution, which are often too complex and computationally demanding to be addressed with more detailed models.

Evidence of the participation of remote residues in the catalytic activity of Co-type nitrile hydratase from Pseudomonas putida

Active sites may be regarded as layers of residues, whereby the residues that interact directly with substrate also interact with residues in a second shell and these in turn interact with residues in a third shell. These residues in the second and third layers may have distinct roles in maintaining the essential chemical properties of the first-shell catalytic residues, particularly their spatial arrangement relative to the substrate binding pocket, and their electrostatic and dynamic properties. The extent to which these remote residues participate in catalysis and precisely how they affect first-shell residues remains unexplored. To improve our understanding of the roles of second- and third-shell residues in catalysis, we used THEMATICS to identify residues in the second and third shells of the Co-type nitrile hydratase from Pseudomonas putida (ppNHase) that may be important for catalysis. Five of these predicted residues, and three additional, conserved residues that were not predicted, have been conservatively mutated, and their effects have been studied both kinetically and structurally. The eight residues have no direct contact with the active site metal ion or bound substrate. These results demonstrate that three of the predicted second-shell residues (α-Asp164, β-Glu56, and β-His147) and one predicted third-shell residue (β-His71) have significant effects on the catalytic efficiency of the enzyme. One of the predicted residues (α-Glu168) and the three residues not predicted (α-Arg170, α-Tyr171, and β-Tyr215) do not have any significant effects on the catalytic efficiency of the enzyme.

Roles of non-native hydrogen-bonding interaction in helix-coil transition of a single polypeptide as revealed by comparison between Gō-like and non-Gō models

To explore the role of non-native interactions in the helix-coil transition, a detailed comparison between a Gō-like model and a non-Gō model has been performed via lattice Monte Carlo simulations. Only native hydrogen bonding interactions occur in the Gō-like model, and the non-native ones with sequence interval more than 4 is also included into the non-Gō model. Some significant differences between the results from those two models have been found. The non-native hydrogen bonds were found most populated at temperature around the helix-coil transition. The rearrangement of non-native hydrogen bonds into native ones in the formation of alpha-helix leads to the increase of susceptibility of chain conformation, and even two peaks of susceptibility of radius of gyration versus temperature exist in the case of non-Gō model for a non-short peptide, while just a single peak exists in the case of Gō model for a single polypeptide chain with various chain lengths. The non-native hydrogen bonds have complicated the temperature-dependence of Zimm-Bragg nucleation constant. The increase of relative probability of non-native hydrogen bonding for long polypeptide chains leads to non-monotonous chain length effect on the transition temperature.

Correlated mutations: a hallmark of phenotypic amino acid substitutions

Point mutations resulting in the substitution of a single amino acid can cause severe functional consequences, but can also be completely harmless. Understanding what determines the phenotypical impact is important both for planning targeted mutation experiments in the laboratory and for analyzing naturally occurring mutations found in patients. Common wisdom suggests using the extent of evolutionary conservation of a residue or a sequence motif as an indicator of its functional importance and thus vulnerability in case of mutation. In this work, we put forward the hypothesis that in addition to conservation, co-evolution of residues in a protein influences the likelihood of a residue to be functionally important and thus associated with disease. While the basic idea of a relation between co-evolution and functional sites has been explored before, we have conducted the first systematic and comprehensive analysis of point mutations causing disease in humans with respect to correlated mutations. We included 14,211 distinct positions with known disease-causing point mutations in 1,153 human proteins in our analysis. Our data show that (1) correlated positions are significantly more likely to be disease-associated than expected by chance, and that (2) this signal cannot be explained by conservation patterns of individual sequence positions. Although correlated residues have primarily been used to predict contact sites, our data are in agreement with previous observations that (3) many such correlations do not relate to physical contacts between amino acid residues. Access to our analysis results are provided at http://webclu.bio.wzw.tum.de/~pagel/supplements/correlated-positions/.

Point mutations (i.e., changes of a single sequence element) can have a severe impact on protein function. Many diseases are caused by such minute defects. On the other hand, the majority of such mutations does not lead to noticeable effects. Although previous research has revealed important aspects that influence or predict the chance of a mutation to cause disease, much remains to be learned before we fully understand this complex problem. In our work, we use the observation that sometimes certain positions in a protein mutate in an apparently correlated fashion and analyze this correlation with respect to mutation vulnerability. Our results show that positions exhibiting evolutionary correlation are significantly more likely to be vulnerable to mutation than average positions. On one hand, our data further support the concept of correlated positions to not only be associated with protein contacts but also functional sites and/or disease positions (as introduced by others). On the other hand, this could be useful to further improve the understanding and prediction of the consequences of mutations. Our work is the first to attempt a large-scale quantitation of this relationship.

Detection of native-state nonadditivity in double mutant cycles via hydrogen exchange

Proteins have evolved to exploit long-range structural and dynamic effects as a means of regulating function. Understanding communication between sites in proteins is therefore vital to our comprehension of such phenomena as allostery, catalysis, and ligand binding/ejection. Double mutant cycle analysis has long been used to determine the existence of communication between pairs of sites, proximal or distal, in proteins. Typically, nonadditivity (or "thermodynamic coupling") is measured from global transitions in concert with a single probe. Here, we have applied the atomic resolution of NMR in tandem with native-state hydrogen exchange (HX) to probe the structure/energy landscape for information transduction between a large number of distal sites in a protein. Considering the event of amide proton exchange as an energetically quantifiable structural perturbation, m n-dimensional cycles can be constructed from mutation of n-1 residues, where m is the number of residues for which HX data is available. Thus, efficient mapping of a large number of couplings is made possible. We have applied this technique to one additive and two nonadditive double mutant cycles in a model system, eglin c. We find heterogeneity of HX-monitored couplings for each cycle, yet averaging results in strong agreement with traditionally measured values. Furthermore, long-range couplings observed at locally exchanging residues indicate that the basis for communication can occur within the native state ensemble, a conclusion not apparent from traditional measurements. We propose that higher-order couplings can be obtained and show that such couplings provide a mechanistic basis for understanding lower-order couplings via "spheres of perturbation". The method is presented as an additional tool for identifying a large number of couplings with greater coverage of the protein of interest.

Evolvability and single-genotype fluctuation in phenotypic properties: a simple heteropolymer model

Experiment showed that the response of a genotype to mutation, i.e., the magnitude of mutational change in a phenotypic property, can be correlated with the extent of phenotypic fluctuation among genetic clones. To address a possible statistical mechanical basis for such phenomena at the protein level, we consider a simple hydrophobic-polar lattice protein-chain model with an exhaustive mapping between sequence (genotype) and conformational (phenotype) spaces. Using squared end-to-end distance, R(N)(2), as an example conformational property, we study how the thermal fluctuation of a sequence's R(N)(2) may be predictive of the changes in the Boltzmann average R(N)(2) caused by single-point mutations on that sequence. We found that sequences with the same ground-state (R(N)(2))(0) exhibit a funnel-like organization under conditions favorable to chain collapse or folding: fluctuation (standard deviation sigma) of R(N)(2) tends to increase with mutational distance from a prototype sequence whose R(N)(2) deviates little from its (R(N)(2))(0). In general, large mutational decreases in R(N)(2) or in sigma are only possible for some, though not all, sequences with large sigma values. This finding suggests that single-genotype phenotypic fluctuation is a necessary, though not sufficient, indicator of evolvability toward genotypes with less phenotypic fluctuations.

Reducing phylogenetic bias in correlated mutation analysis

Correlated mutation analysis (CMA) is a sequence-based approach for ab initio protein contact map prediction. The basis of this approach is the observed correlation between mutations in interacting amino acid residues. These correlations are often estimated by either calculating the Pearson's correlation coefficient (PCC) or the mutual information (MI) between columns in a multiple sequence alignment (MSA) of the protein of interest and its homologs. A major challenge of CMA is to filter out the background noise originating from phylogenetic relatedness between sequences included in the MSA. Recently, a procedure to reduce this background noise was demonstrated to improve an MI-based predictor. Herein, we tested whether a similar approach can also improve the performance of the classical PCC-based method. Indeed, performance improvements were achieved for all four major SCOP classes. Furthermore, the results reveal that the improved PCC-based method is superior to MI-based methods for proteins having MSAs of up to 100 sequences.

Trade-off between positive and negative design of protein stability: from lattice models to real proteins

Two different strategies for stabilizing proteins are (i) positive design in which the native state is stabilized and (ii) negative design in which competing non-native conformations are destabilized. Here, the circumstances under which one strategy might be favored over the other are explored in the case of lattice models of proteins and then generalized and discussed with regard to real proteins. The balance between positive and negative design of proteins is found to be determined by their average "contact-frequency", a property that corresponds to the fraction of states in the conformational ensemble of the sequence in which a pair of residues is in contact. Lattice model proteins with a high average contact-frequency are found to use negative design more than model proteins with a low average contact-frequency. A mathematical derivation of this result indicates that it is general and likely to hold also for real proteins. Comparison of the results of correlated mutation analysis for real proteins with typical contact-frequencies to those of proteins likely to have high contact-frequencies (such as disordered proteins and proteins that are dependent on chaperonins for their folding) indicates that the latter tend to have stronger interactions between residues that are not in contact in their native conformation. Hence, our work indicates that negative design is employed when insufficient stabilization is achieved via positive design owing to high contact-frequencies.

Liaison amid disorder: non-native interactions may underpin long-range coupling in proteins

A lattice-model study of double-mutant cycles published in BMC Structural Biology underscores how interactions in non-native conformations can lead to thermodynamic coupling between distant residues in globular proteins, adding to recent advances in delineating the often crucial roles played by disordered conformational ensembles in protein behavior.