Coarse-grained models of protein folding: toy models or predictive tools?

Coarse-grained models are emerging as a practical alternative to all-atom simulations for the characterization of protein folding mechanisms over long time scales. While a decade ago minimalist toy models were mainly designed to test general hypotheses on the principles regulating protein folding, the latest coarse-grained models are increasingly realistic and can be used to characterize quantitatively the detailed folding mechanism of specific proteins. The ability of such models to reproduce the essential features of folding dynamics suggests that each single atomic degree of freedom is not by itself particularly relevant to folding and supports a statistical mechanical approach to characterize folding transitions. When combined with more refined models and with experimental studies, the systematic investigation of protein systems and complexes using coarse-grained models can advance our theoretical understanding of the actual organizing principles that emerge from the complex network of interactions among protein atomic constituents.     

Translational diffusion and intrinsic viscosity of globular proteins. Theoretical predictions using hydrated hydrodynamic models. Application to BPTI.

In this paper, we present a way to make hydrodynamic models of globular proteins, including the hydration shell associated with them in aqueous solutions. Theoretical calculations using these models are made in order to determine the hydrodynamic properties of these proteins, employing rigorous and approximate methods of calculation. These will be applied to the bovine pancreatic trypsin inhibitor, BPTI. Several hydrodynamic models are constructed: the A-model for the unhydrated protein BPTI and a set of H-models for hydrated protein with different hydration degrees. Theoretical results for the translational diffusion coefficient Dt and the intrinsic viscosity [eta] are obtained from different models. From the analysis of the A-model and hydrodynamic properties, there is not a clear assignation of an ellipsoidal shape to this protein molecule. An amount of approximately 0.5 g H2O/g protein could be assigned to the BPTI.     

What are the dielectric “constants” of proteins and how to validate electrostatic models?

Implicit models for evaluation of electrostatic energies in proteins include dielectric constants that represent effect of the protein environment. Unfortunately, the results obtained by such models are very sensitive to the value used for the dielectric constant. Furthermore, the factors that determine the optimal value of these constants are far from being obvious. This review considers the meaning of the protein dielectric constants and the ways to determine their optimal values. It is pointed out that typical benchmarks for validation of electrostatic models cannot discriminate between consistent and inconsistent models. In particular, the observed pK(a) values of surface groups can be reproduced correctly by models with entirely incorrect physical features. Thus, we introduce a discriminative benchmark that only includes residues whose pK(a) values are shifted significantly from their values in water. We also use the semimacroscopic version of the protein dipole Langevin dipole (PDLD/S) formulation to generate a series of models that move gradually from microscopic to fully macroscopic models. These include the linear response version of the PDLD/S models, Poisson Boltzmann (PB)-type models, and Tanford Kirkwwod (TK)-type models. Using our different models and the discriminative benchmark, we show that the protein dielectric constant, epsilon(p), is not a universal constant but simply a parameter that depends on the model used. It is also shown in agreement with our previous works that epsilon(p) represents the factors that are not considered explicitly. The use of a discriminative benchmark appears to help not only in identifying nonphysical models but also in analyzing effects that are not reproduced in an accurate way by consistent models. These include the effect of water penetration and the effect of the protein reorganization. Finally, we show that the optimal dielectric constant for self-energies is not the optimal constant for charge-charge interactions.     

Estimating amino acid substitution models for metazoan evolutionary studies

Amino acid substitution models represent the substitution rates among amino acids during the evolution of protein sequences. The models are a prerequisite for maximum likelihood or Bayesian methods to analyse the phylogenetic relationships among species based on their protein sequences. Estimating amino acid substitution models requires large protein datasets and intensive computation. In this paper, we presented the estimation of both time-reversible model (Q.met) and time non-reversible model (NQ.met) for multicellular animals (Metazoa). Analyses showed that the Q.met and NQ.met models were significantly better than existing models in analysing metazoan protein sequences. Moreover, the time non-reversible model NQ.met enables us to reconstruct the rooted phylogenetic tree for Metazoa. We recommend researchers to employ the Q.met and NQ.met models in analysing metazoan protein sequences.     

Critical evaluation of simple network models of protein dynamics and their comparison with crystallographic B-factors

In recent years, elastic network models (ENM) have been widely used to describe low-frequency collective motions in proteins. These models are often validated and calibrated by fitting mean-square atomic displacements estimated from x-ray crystallography (B-factors). We show that a proper calibration procedure must account for the rigid-body motion and constraints imposed by the crystalline environment on the protein. These fundamental aspects of protein dynamics in crystals are often ignored in currently used ENMs, leading to potentially erroneous network parameters. Here we develop an ENM that properly takes the rigid-body motion and crystalline constraints into account. Its application to the crystallographic B-factors reveals that they are dominated by rigid-body motion and thus are poorly suited for the calibration of models for internal protein dynamics. Furthermore, the translation libration screw (TLS) model that treats proteins as rigid bodies is considerably more successful in interpreting the experimental B-factors than ENMs. This conclusion is reached on the basis of a comparative study of various models of protein dynamics. To evaluate their performance, we used a data set of 330 protein structures that combined the sets previously used in the literature to test and validate different models. We further propose an extended TLS model that treats the bulk of the protein as a rigid body while allowing for flexibility of chain ends. This model outperforms other simple models of protein dynamics in interpreting the crystallographic B-factors.     

CONFOLD: Residue‐residue contact‐guided ab initio protein folding

Predicted protein residue–residue contacts can be used to build three‐dimensional models and consequently to predict protein folds from scratch. A considerable amount of effort is currently being spent to improve contact prediction accuracy, whereas few methods are available to construct protein tertiary structures from predicted contacts. Here, we present an ab initio protein folding method to build three‐dimensional models using predicted contacts and secondary structures. Our method first translates contacts and secondary structures into distance, dihedral angle, and hydrogen bond restraints according to a set of new conversion rules, and then provides these restraints as input for a distance geometry algorithm to build tertiary structure models. The initially reconstructed models are used to regenerate a set of physically realistic contact restraints and detect secondary structure patterns, which are then used to reconstruct final structural models. This unique two‐stage modeling approach of integrating contacts and secondary structures improves the quality and accuracy of structural models and in particular generates better β‐sheets than other algorithms. We validate our method on two standard benchmark datasets using true contacts and secondary structures. Our method improves TM‐score of reconstructed protein models by 45% and 42% over the existing method on the two datasets, respectively. On the dataset for benchmarking reconstructions methods with predicted contacts and secondary structures, the average TM‐score of best models reconstructed by our method is 0.59, 5.5% higher than the existing method. The CONFOLD web server is available at http://protein.rnet.missouri.edu/confold/ . Proteins 2015; 83:1436–1449. © 2015 Wiley Periodicals, Inc.     

MODBASE, a database of annotated comparative protein structure models

MODBASE (http://guitar.rockefeller.edu/modbase) is a relational database of annotated comparative protein structure models for all available protein sequences matched to at least one known protein structure. The models are calculated by MODPIPE, an automated modeling pipeline that relies on PSI-BLAST, IMPALA and MODELLER. MODBASE uses the MySQL relational database management system for flexible and efficient querying, and the MODVIEW Netscape plugin for viewing and manipulating multiple sequences and structures. It is updated regularly to reflect the growth of the protein sequence and structure databases, as well as improvements in the software for calculating the models. For ease of access, MODBASE is organized into different datasets. The largest dataset contains models for domains in 304 517 out of 539 171 unique protein sequences in the complete TrEMBL database (23 March 2001); only models based on significant alignments (PSI-BLAST E-value < 10^–4) and models assessed to have the correct fold are included. Other datasets include models for target selection and structure-based annotation by the New York Structural Genomics Research Consortium, models for prediction of genes in the Drosophila melanogaster genome, models for structure determination of several ribosomal particles and models calculated by the MODWEB comparative modeling web server.     

Efficient incorporation of protein flexibility and dynamics into molecular docking simulations

Flexibility and dynamics are protein characteristics that are essential for the process of molecular recognition. Conformational changes in the protein that are coupled to ligand binding are described by the biophysical models of induced fit and conformational selection. Different concepts that incorporate protein flexibility into protein-ligand docking within the context of these two models are reviewed. Several computational studies that discuss the validity and possible limitations of such approaches will be presented. Finally, different approaches that incorporate protein dynamics, e.g., configurational entropy, and solvation effects into docking will be highlighted.     

Knowledge-based model building of proteins: concepts and examples.

We describe how to build protein models from structural templates. Methods to identify structural similarities between proteins in cases of significant, moderate to low, or virtually absent sequence similarity are discussed. The detection and evaluation of structural relationships is emphasized as a central aspect of protein modeling, distinct from the more technical aspects of model building. Computational techniques to generate and complement comparative protein models are also reviewed. Two examples, P-selectin and gp39, are presented to illustrate the derivation of protein model structures and their use in experimental studies.     

Computational protein design is a challenge for implicit solvation models

Increasingly complex schemes for representing solvent effects in an implicit fashion are being used in computational analyses of biological macromolecules. These schemes speed up the calculations by orders of magnitude and are assumed to compromise little on essential features of the solvation phenomenon. In this work we examine this assumption. Five implicit solvation models, a surface area-based empirical model, two models that approximate the generalized Born treatment and a finite difference Poisson-Boltzmann method are challenged in situations differing from those where these models were calibrated. These situations are encountered in automatic protein design procedures, whose job is to select sequences, which stabilize a given protein 3D structure, from a large number of alternatives. To this end we evaluate the energetic cost of burying amino acids in thousands of environments with different solvent exposures belonging, respectively, to decoys built with random sequences and to native protein crystal structures. In addition we perform actual sequence design calculations. Except for the crudest surface area-based procedure, all the tested models tend to favor the burial of polar amino acids in the protein interior over nonpolar ones, a behavior that leads to poor performance in protein design calculations. We show, on the other hand, that three of the examined models are nonetheless capable of discriminating between the native fold and many nonnative alternatives, a test commonly used to validate force fields. It is concluded that protein design is a particularly challenging test for implicit solvation models because it requires accurate estimates of the solvation contribution of individual residues. This contrasts with native recognition, which depends less on solvation and more on other nonbonded contributions.     

Artificial beta-sheets: chemical models of beta-sheets

Chemical models provide tools with which to simplify and study complicated biological systems. Forces and chemical processes that govern the structure, function, and interactions of a biomacromolecule can be explored with a simple, easy-to-study synthetic molecule. Chemical models of beta-sheet structures have helped to elucidate the factors influencing protein structures and functions. Chemical models that mimic beta-sheet quaternary structure and interactions are emerging as valuable tools with which to better understand and control protein recognition and protein aggregation.     

Deep generative modeling for protein design

Deep learning approaches have produced substantial breakthroughs in fields such as image classification and natural language processing and are making rapid inroads in the area of protein design. Many generative models of proteins have been developed that encompass all known protein sequences, model specific protein families, or extrapolate the dynamics of individual proteins. Those generative models can learn protein representations that are often more informative of protein structure and function than hand-engineered features. Furthermore, they can be used to quickly propose millions of novel proteins that resemble the native counterparts in terms of expression level, stability, or other attributes. The protein design process can further be guided by discriminative oracles to select candidates with the highest probability of having the desired properties. In this review, we discuss five classes of generative models that have been most successful at modeling proteins and provide a framework for model guided protein design.     

Novel machine learning approaches revolutionize protein knowledge

Breakthrough methods in machine learning (ML), protein structure prediction, and novel ultrafast structural aligners are revolutionizing structural biology. Obtaining accurate models of proteins and annotating their functions on a large scale is no longer limited by time and resources. The most recent method to be top ranked by the Critical Assessment of Structure Prediction (CASP) assessment, AlphaFold 2 (AF2), is capable of building structural models with an accuracy comparable to that of experimental structures. Annotations of 3D models are keeping pace with the deposition of the structures due to advancements in protein language models (pLMs) and structural aligners that help validate these transferred annotations. In this review we describe how recent developments in ML for protein science are making large-scale structural bioinformatics available to the general scientific community.     

Simple but predictive protein models

The traditional approach to computational biophysics studies of molecular systems is brute force molecular dynamics simulations under the conditions of interest. The disadvantages of this approach are that the time and length scales that are accessible to computer simulations often do not reach biologically relevant scales. An alternative approach, which we call intuitive modeling, is hypothesis-driven and based on tailoring simplified protein models to the systems of interest. Using intuitive modeling, the length and time scales that can be achieved using simplified protein models exceed those of traditional molecular-dynamic simulations. Here, we describe several recent studies that signify the predictive power of simplified protein models within the intuitive-modeling approach.     

Interpretable pairwise distillations for generative protein sequence models

Many different types of generative models for protein sequences have been proposed in literature. Their uses include the prediction of mutational effects, protein design and the prediction of structural properties. Neural network (NN) architectures have shown great performances, commonly attributed to the capacity to extract non-trivial higher-order interactions from the data. In this work, we analyze two different NN models and assess how close they are to simple pairwise distributions, which have been used in the past for similar problems. We present an approach for extracting pairwise models from more complex ones using an energy-based modeling framework. We show that for the tested models the extracted pairwise models can replicate the energies of the original models and are also close in performance in tasks like mutational effect prediction. In addition, we show that even simpler, factorized models often come close in performance to the original models.     

Studies of folding and misfolding using simplified models

Computer simulations are as vital to our studies of biological systems as experiments. They bridge and rationalize experimental observations, extend the experimental "field of view", which is often limited to a specific time or length scale, and, most importantly, provide novel insights into biological systems, offering hypotheses about yet-to-be uncovered phenomena. These hypotheses spur further experimental discoveries. Simplified molecular models have a special place in the field of computational biology. Branded as less accurate than all-atom protein models, they have offered what all-atom molecular dynamics simulations could not--the resolution of the length and time scales of biological phenomena. Not only have simplified models proven to be accurate in explaining or reproducing several biological phenomena, they have also offered a novel multiscale computational strategy for accessing a broad range of time and length scales upon integration with traditional all-atom simulations. Recent computer simulations of simplified models have shaken or advanced the established understanding of biological phenomena. It was demonstrated that simplified models can be as accurate as traditional molecular dynamics approaches in identifying native conformations of proteins. Their application to protein structure prediction yielded phenomenal accuracy in recapitulating native protein conformations. New studies that utilize the synergy of simplified protein models with all-atom models and experiments yielded novel insights into complex biological processes, such as protein folding, aggregation and the formation of large protein complexes.     

Deducing Underlying Mechanisms from Protein Recruitment Data

By using fluorescent labelling techniques, the distribution and dynamics of proteins can be measured within living cells, allowing to study in vivo the response of cells to a triggering event, such as DNA damage. In order to evaluate the reaction rate constants and to identify the proteins and reactions that are essential for the investigated process, mechanistic models are used, which often contain many proteins and associated parameters and are therefore underdetermined by the data. In order to establish criteria for assessing the significance of a model, we present here a systematic investigation of the information that can be reliably deduced from protein recruitment data, assuming that the complete set of reactions that affect the data of the considered protein species is not known. To this purpose, we study in detail models where one or two proteins that influence each other are recruited to a substrate. We show that in many cases the kind of interaction between the proteins can be deduced by analyzing the shape of the recruitment curves of one protein. Furthermore, we discuss in general in which cases it is possible to discriminate between different models and in which cases it is impossible based on the data. Finally, we argue that if different models fit experimental data equally well, conducting experiments with different protein concentrations would allow discrimination between the alternative models in many cases.     

Applying PyRosetta molecular energies to separate properly oriented protein models from mirror models,obtained from contact maps

Reconstructing protein structure based on contact maps leads to two types of models: properly oriented models and mirror models. This is due to the fact that contact maps do not include information on protein chirality. Therefore, both types of model orientations share the same contact map and are geometrically allowed. In this work, we verified the hypothesis that some of the energy terms calculated by PyRosetta could be useful to distinguish between properly oriented and mirror models. We studied 440 models of all-alpha protein domains reconstructed manually from their contact maps, where 50 % of the models were properly oriented and 50 % had mirror orientation. We showed that dihedral angles and energy terms, based on the probability of specific geometrical arrangement of the residues, differed significantly for properly oriented and mirror models.     

Application of docking methodologies to modeled proteins

Protein docking is essential for structural characterization of protein interactions. Besides providing the structure of protein complexes, modeling of proteins and their complexes is important for understanding the fundamental principles and specific aspects of protein interactions. The accuracy of protein modeling, in general, is still less than that of the experimental approaches. Thus, it is important to investigate the applicability of docking techniques to modeled proteins. We present new comprehensive benchmark sets of protein models for the development and validation of protein docking, as well as a systematic assessment of free and template-based docking techniques on these sets. As opposed to previous studies, the benchmark sets reflect the real case modeling/docking scenario where the accuracy of the models is assessed by the modeling procedure, without reference to the native structure (which would be unknown in practical applications). We also expanded the analysis to include docking of protein pairs where proteins have different structural accuracy. The results show that, in general, the template-based docking is less sensitive to the structural inaccuracies of the models than the free docking. The near-native docking poses generated by the template-based approach, typically, also have higher ranks than those produces by the free docking (although the free docking is indispensable in modeling the multiplicity of protein interactions in a crowded cellular environment). The results show that docking techniques are applicable to protein models in a broad range of modeling accuracy. The study provides clear guidelines for practical applications of docking to protein models.