Hybridizing rapidly exploring random trees and basin hopping yields an improved exploration of energy landscapes

The number of local minima of the potential energy landscape (PEL) of molecular systems generally grows exponentially with the number of degrees of freedom, so that a crucial property of PEL exploration algorithms is their ability to identify local minima, which are low lying and diverse. In this work, we present a new exploration algorithm, retaining the ability of basin hopping (BH) to identify local minima, and that of transition based rapidly exploring random trees (T‐RRT) to foster the exploration of yet unexplored regions. This ability is obtained by interleaving calls to the extension procedures of BH and T‐RRT, and we show tuning the balance between these two types of calls allows the algorithm to focus on low lying regions. Computational efficiency is obtained using state‐of‐the art data structures, in particular for searching approximate nearest neighbors in metric spaces. We present results for the BLN69, a protein model whose conformational space has dimension 207 and whose PEL has been studied exhaustively. On this system, we show that the propensity of our algorithm to explore low lying regions of the landscape significantly outperforms those of BH and T‐RRT. © 2015 Wiley Periodicals, Inc.     

Computational design of a single amino acid sequence that can switch between two distinct protein folds

The functions of many proteins are mediated by specific conformational changes, and therefore the ability to design primary sequences capable of secondary and tertiary changes is an important step toward the creation of novel functional proteins. To this end, we have developed an algorithm that can optimize a single amino acid sequence for multiple target structures. The algorithm consists of an outer loop, in which sequence space is sampled by a Monte Carlo search with simulated annealing, and an inner loop, in which the effect of a given mutation is evaluated on the various target structures by using the rotamer packing routine and composite energy function of the protein design software, RosettaDesign. We have experimentally tested the method by designing a peptide, Sw2, which can be switched from a 2Cys-2His zinc finger-like fold to a trimeric coiled-coil fold, depending upon the pH or the presence of transition metals. Physical characterization of Sw2 confirms that it is able to reversibly adopt each intended target fold.     

Protein structure predictions by parallel simulated annealing molecular dynamics using genetic crossover

We propose a conformational search method to find a global minimum energy structure for protein systems. The simulated annealing is a powerful method for local conformational search. On the other hand, the genetic crossover can search the global conformational space. Our method incorporates these attractive features of the simulated annealing and genetic crossover. In the previous works, we have been using the Monte Carlo algorithm for simulated annealing. In the present work, we use the molecular dynamics algorithm instead. To examine the effectiveness of our method, we compared our results with those of the normal simulated annealing molecular dynamics simulations by using an α-helical miniprotein. We used genetic two-point crossover here. The conformations, which have lower energy than those obtained from the conventional simulated annealing, were obtained.     

Exploring protein structure and dynamics under denaturing conditions by single-molecule FRET analysis

Proteins are highly complex biopolymers, exhibiting a substantial degree of structural variability in their properly folded, native state. In the presence of denaturants, this heterogeneity is greatly enhanced, and fluctuations take place among vast numbers of folded and unfolded conformations via many different pathways. To better understand protein folding it is necessary to explore the structural and energetic properties of the folded and unfolded polypeptide chain, as well as the trajectories along which the chain navigates through its multi-dimensional conformational energy landscape. In recent years, single-molecule fluorescence spectroscopy has been established as a powerful tool in this research area, as it allows one to monitor the structure and dynamics of individual polypeptide chains in real time with atomic scale resolution using F?rster resonance energy transfer (FRET). Consequently, time trajectories of folding transitions can be directly observed, including transient intermediates that may exist along these pathways. Here we illustrate the power of single-molecule fluorescence with our recent work on the structure and dynamics of the small enzyme RNase H in the presence of the chemical denaturant guanidinium chloride (GdmCl). For FRET analysis, a pair of fluorescent dyes was attached to the enzyme at specific locations. In order to observe conformational changes of individual protein molecules for up to several hundred seconds, the proteins were immobilized on nanostructured, polymer coated glass surfaces specially developed to have negligible interactions with folded and unfolded proteins. The single-molecule FRET analysis gave insight into structural changes of the unfolded polypeptide chain in response to varying the denaturant concentration, and the time traces revealed stepwise transitions in the FRET levels, reflecting conformational dynamics. Barriers in the free energy landscape of RNase H were estimated from the kinetics of the transitions.     

Can a physics‐based,all‐atom potential find a protein's native structure among misfolded structures? I. Large scale AMBER benchmarking

Recent work has shown that physics-based, all-atom energy functions (AMBER, CHARMM, OPLS-AA) and local minimization, when used in scoring, are able to discriminate among native and decoy structures. Yet, there have been only few instances reported of the successful use of physics based potentials in the actual refinement of protein models from a starting conformation to one that ends in structures, which are closer to the native state. An energy function that has a global minimum energy in the protein's native state and a good correlation between energy and native-likeness should be able to drive model structures closer to their native structure during a conformational search. Here, the possible reasons for the discrepancy between the scoring and refinement results for the case of AMBER potential are examined. When the conformational search via molecular dynamics is driven by the AMBER potential for a large set of 150 nonhomologous proteins and their associated decoys, often the native minimum does not appear to be the lowest free energy state. Ways of correcting the potential function in order to make it more suitable for protein model refinement are proposed.     

Modification and optimization of the united-residue (UNRES) potential energy function for canonical simulations. I. Temperature dependence of the effective energy function and tests of the optimization method with single training proteins

We report the modification and parametrization of the united-residue (UNRES) force field for energy-based protein structure prediction and protein folding simulations. We tested the approach on three training proteins separately: 1E0L (beta), 1GAB (alpha), and 1E0G (alpha + beta). Heretofore, the UNRES force field had been designed and parametrized to locate native-like structures of proteins as global minima of their effective potential energy surfaces, which largely neglected the conformational entropy because decoys composed of only lowest-energy conformations were used to optimize the force field. Recently, we developed a mesoscopic dynamics procedure for UNRES and applied it with success to simulate protein folding pathways. However, the force field turned out to be largely biased toward -helical structures in canonical simulations because the conformational entropy had been neglected in the parametrization. We applied the hierarchical optimization method, developed in our earlier work, to optimize the force field; in this method, the conformational space of a training protein is divided into levels, each corresponding to a certain degree of native-likeness. The levels are ordered according to increasing native-likeness; level 0 corresponds to structures with no native-like elements, and the highest level corresponds to the fully native-like structures. The aim of optimization is to achieve the order of the free energies of levels, decreasing as their native-likeness increases. The procedure is iterative, and decoys of the training protein(s) generated with the energy function parameters of the preceding iteration are used to optimize the force field in a current iteration. We applied the multiplexing replica-exchange molecular dynamics (MREMD) method, recently implemented in UNRES, to generate decoys; with this modification, conformational entropy is taken into account. Moreover, we optimized the free-energy gaps between levels at temperatures corresponding to a predominance of folded or unfolded structures, as well as to structures at the putative folding-transition temperature, changing the sign of the gaps at the transition temperature. This enabled us to obtain force fields characterized by a single peak in the heat capacity at the transition temperature. Furthermore, we introduced temperature dependence to the UNRES force field; this is consistent with the fact that it is a free-energy and not a potential energy function. beta     

Flexible ligand docking without parameter adjustment across four ligand–receptor complexes

Understanding molecular recognition is one of the fundamental problems in molecular biology. Computationally, molecular recognition is formulated as a docking problem. Ideally, a molecular docking algorithm should be computationally efficient, provide reasonably thorough search of conformational space, obtain solutions with reasonable consistency, and not require parameter adjustments. With these goals in mind, we developed DIVALI (Docking wIth eVolutionary AlgorIthms), a program which efficiently and reliably searches for the possible binding modes of a ligand within a fixed receptor. We use an AMBER-type potential function and search for good ligand conformations using a genetic algorithm (GA). We apply our system to study the docking of both rigid and flexible ligands in four different complexes. Our results indicate that it is possible to find diverse binding modes, including structures like the crystal structure, all with comparable potential function values. To achieve this, certain modifications to the standard GA recipe are essential. © 1995 John Wiley & Sons, Inc.     

Nonisomerizable non-retinal chromophores initiate light-induced conformational alterations in bacterioopsin.

The photoactivation of retinal proteins is usually interpreted in terms of C=C photoisomerization of the retinal moiety, which triggers appropriate conformational changes in the protein. In this work several dye molecules, characterized by a completely rigid structure in which no double-bond isomerization is possible, were incorporated into the binding site of bacteriorhodopsin (bR). Using a light-induced chemical reaction of a labeled EPR probe, it was observed that specific conformational alterations in the protein are induced following light absorption by the dye molecules occupying the binding site. The exact nature of these changes and their relationship to those occurring in the bR photocycle are still unclear. Nevertheless, their occurrence proves that C=C or C=NH(+) isomerization is not a prerequisite for protein conformational changes in a retinal protein. More generally, we show that conformational changes, leading to changes in reactivity, may be induced in proteins by optical excitation of simple nonisomerizable dyes located in the macromolecular matrix.     

Determination of an empirical energy function for protein conformational analysis by energy embedding

It is quite easy to propose an empirical potential for conformational analysis such that given crystal structures lie near local minima. What is much more difficult, is to devise a function such that the native structure lies near a relatively deep local minimum, at least in some neighborhood of the native in conformation space. An algorithm is presented for finding such a potential acting on proteins where each amino acid residue is represented by a single point. When the given structure is either an α-helical, β-strand, or hairpin bend segment of pancreatic trypsin inhibitor, the resulting potential function in each case possesses a deep minimum within 0.10 Å of the native conformation. The improved energy embedding algorithm locates a marginally better minimum in each case only 0.1–1.3 Å away from the respective native state. In other words, this potential function guides a conformational search toward structures very close to the native over a wide range of conformation space.     

Global Minimum Search and Bonding Analysis of Tl2Hx and Tl3Hy (x=0–6; y=0–5) Series

A remarkable distinction between boron and carbon hydrides lies in their extremely different bonding patterns and chemical reactivity, resulting in diverse areas of application. Particularly, carbon, characterized by classical two-center – two-electron bonds, gives rise to organic chemistry. In contrast, boron forms numerous exotic and non-intuitive compounds collectively called non-classical structures. It is reasonable to anticipate that other elements of Group 13 exhibit their own unusual bonding patterns; however, our knowledge of the hydride chemistry for other elements in Group 13 is much more limited, especially for the heaviest stable element, thallium. In this work, we performed a conformational analysis of Tl₂H_x and Tl₃H_y (x=0–6, y=0–5) series via Coalescence Kick global minimum search algorithm, DFT, and ab initio quantum chemistry methods; we investigated the bonding pattern using the AdNDP algorithm, thermodynamic stability, and stability toward electron detachment. All found global minimum structures are classified as non-classical structures featuring at least one multi-center bond.     

Docking of photosystem I subunit C using a constrained geometric simulation

The elucidation of assembly pathways of multi-subunit protein complexes is a problem of great interest in structural biology and biomolecular modeling. In this study, we use a new computer algorithm for the simulation of large-scale motion in proteins to dock the subunit PsaC onto Photosystem I. We find that a complicated docking pathway involving multiple conformational changes can be quickly simulated by actively targeting only a few residues at a time to their target positions. Simulations for two possible docking scenarios are explored, and experimental approaches to distinguish between them are discussed.     

A normal mode-based geometric simulation approach for exploring biologically relevant conformational transitions in proteins

A three-step approach for multiscale modeling of protein conformational changes is presented that incorporates information about preferred directions of protein motions into a geometric simulation algorithm. The first two steps are based on a rigid cluster normal-mode analysis (RCNMA). Low-frequency normal modes are used in the third step (NMSim) to extend the recently introduced idea of constrained geometric simulations of diffusive motions in proteins by biasing backbone motions of the protein, whereas side-chain motions are biased toward favorable rotamer states. The generated structures are iteratively corrected regarding steric clashes and stereochemical constraint violations. The approach allows performing three simulation types: unbiased exploration of conformational space; pathway generation by a targeted simulation; and radius of gyration-guided simulation. When applied to a data set of proteins with experimentally observed conformational changes, conformational variabilities are reproduced very well for 4 out of 5 proteins that show domain motions, with correlation coefficients r > 0.70 and as high as r = 0.92 in the case of adenylate kinase. In 7 out of 8 cases, NMSim simulations starting from unbound structures are able to sample conformations that are similar (root-mean-square deviation = 1.0-3.1 ?) to ligand bound conformations. An NMSim generated pathway of conformational change of adenylate kinase correctly describes the sequence of domain closing. The NMSim approach is a computationally efficient alternative to molecular dynamics simulations for conformational sampling of proteins. The generated conformations and pathways of conformational transitions can serve as input to docking approaches or as starting points for more sophisticated sampling techniques.     

Guided macro-mutation in a graded energy based genetic algorithm for protein structure prediction

Protein structure prediction is considered as one of the most challenging and computationally intractable combinatorial problem. Thus, the efficient modeling of convoluted search space, the clever use of energy functions, and more importantly, the use of effective sampling algorithms become crucial to address this problem. For protein structure modeling, an off-lattice model provides limited scopes to exercise and evaluate the algorithmic developments due to its astronomically large set of data-points. In contrast, an on-lattice model widens the scopes and permits studying the relatively larger proteins because of its finite set of data-points. In this work, we took the full advantage of an on-lattice model by using a face-centered-cube lattice that has the highest packing density with the maximum degree of freedom. We proposed a graded energy—strategically mixes the Miyazawa–Jernigan (MJ) energy with the hydrophobic-polar (HP) energy—based genetic algorithm (GA) for conformational search. In our application, we introduced a 2 × 2 HP energy guided macro-mutation operator within the GA to explore the best possible local changes exhaustively. Conversely, the 20 × 20 MJ energy model—the ultimate objective function of our GA that needs to be minimized—considers the impacts amongst the 20 different amino acids and allow searching the globally acceptable conformations. On a set of benchmark proteins, our proposed approach outperformed state-of-the-art approaches in terms of the free energy levels and the root-mean-square deviations.     

Site-specific Heterogeneity of Multi-domain Human Serum Albumin and its Origin: A Red Edge Excitation Shift Study†

Conformational heterogeneity is a defining characteristic of a protein and is vital in understanding its function and folding landscape. In the present work, we interrogated the presence of conformational heterogeneity in multi-domain human serum albumin in a domain-specific manner using red edge excitation shift (REES) in its native state and also monitored its variation along the unfolding transition. We also looked into the origin of such conformational heterogeneity by varying the solution viscosity. We observed (1) even in the native state, the heterogeneity and dynamics of the side chain exhibit varied behaviors depending on which domain of the multi-domain human serum albumin (HSA) is being examined. (2) When the protein is in the unfolded state, the extent of REES is rendered unimportant since there is a greater quantity of free water present, in addition to the disruption of the protein's structure. (3) While the rigid protein matrix provides the rigidity of domain-I and domain-III, the rigidity of domain-II is provided by water molecules, which indicates that the role of water molecules in providing the rigidity is significant. Overall, our results provide direct evidence of the rigidity and alternate side chain packing arrangement of protein core that varies domain-wise in multi-domain HSA.     

Structures and physical properties of gaseous metal cationized biological ions

Metal chelation can alter the activity of free biomolecules by modifying their structures or stabilizing higher energy tautomers. In recent years, mass spectrometric techniques have been used to investigate the effects of metal complexation with proteins, nucleobases and nucleotides, where small conformational changes can have significant physiological consequences. In particular, infrared multiple photon dissociation spectroscopy has emerged as an important tool for determining the structure and reactivity of gas-phase ions. Unlike other mass spectrometric approaches, this method is able to directly resolve structural isomers using characteristic vibrational signatures. Other activation and dissociation methods, such as blackbody infrared radiative dissociation or collision-induced dissociation can also reveal information about the thermochemistry and dissociative pathways of these biological ions. This information can then be used to provide information about the structures of the ionic complexes under study. In this article, we review the use of gas-phase techniques in characterizing metal-bound biomolecules. Particular attention will be given to our own contributions, which detail the ability of metal cations to disrupt nucleobase pairs, direct the self-assembly of nucleobase clusters and stabilize non-canonical isomers of amino acids.     

Disordered proteins and network disorder in network descriptions of protein structure, dynamics and function: hypotheses and a comprehensive review

During the last decade, network approaches became a powerful tool to describe protein structure and dynamics. Here we review the links between disordered proteins and the associated networks, and describe the consequences of local, mesoscopic and global network disorder on changes in protein structure and dynamics. We introduce a new classification of protein networks into 'cumulus-type', i.e., those similar to puffy (white) clouds, and 'stratus-type', i.e., those similar to flat, dense (dark) low-lying clouds, and relate these network types to protein disorder dynamics and to differences in energy transmission processes. In the first class, there is limited overlap between the modules, which implies higher rigidity of the individual units; there the conformational changes can be described by an 'energy transfer' mechanism. In the second class, the topology presents a compact structure with significant overlap between the modules; there the conformational changes can be described by 'multi-trajectories'; that is, multiple highly populated pathways. We further propose that disordered protein regions evolved to help other protein segments reach 'rarely visited' but functionally-related states. We also show the role of disorder in 'spatial games' of amino acids; highlight the effects of intrinsically disordered proteins (IDPs) on cellular networks and list some possible studies linking protein disorder and protein structure networks.     

Lattice models of peptide aggregation: evaluation of conformational search algorithms

We present a series of conformational search calculations on the aggregation of short peptide fragments that form fibrils similar to those seen in many protein mis-folding diseases. The proteins were represented by a face-centered cubic lattice model with the conformational energies calculated using the Miyazawa-Jernigan potential. The searches were performed using algorithms based on the Metropolis Monte Carlo method, including simulated annealing and replica exchange. We also present the results of searches using the tabu search method, an algorithm that has been used for many optimization problems, but has rarely been used in protein conformational searches. The replica exchange algorithm consistently found more stable structures then the other algorithms, and was particularly effective for the octamers and larger systems.     

Sampling protein conformations and pathways

Protein flexibility and rigidity can be analyzed using constraint theory, which views proteins as 3D networks of constraints involving covalent bonds and also including hydrophobic interactions and hydrogen bonds. This article describes an algorithm, ROCK (Rigidity Optimized Conformational Kinetics), which generates new conformations for these complex networks with many interlocked rings while maintaining the constraints. These new conformations are tracked for the flexible regions of a protein, while leaving the rigid regions undisturbed. An application to HIV protease demonstrates how large the flap motion can be. The algorithm is also used to generate conformational pathways between two distinct protein conformations. As an example, directed trajectories between the closed and the occluded conformations of the protein dihydrofolate reductase are determined.     

Fast and efficient in silico 3D screening: toward maximum computational efficiency of pharmacophore-based and shape-based approaches

In continuation of our recent studies on the quality of conformational models generated with CATALYST and OMEGA we present a large-scale survey focusing on the impact of conformational model quality and several screening parameters on pharmacophore-based and shape-based virtual high throughput screening (vHTS). Therefore, we collected known active compounds of CDK2, p38 MAPK, PPAR-gamma, and factor Xa and built a set of druglike decoys using ilib:diverse. Subsequently, we generated 3D structures using CORINA and also calculated conformational models for all compounds using CAESAR, CATALYST FAST, and OMEGA. A widespread set of 103 structure-based pharmacophore models was developed with LigandScout for virtual screening with CATALYST. The performance of both database search modes (FAST and BEST flexible database search) as well as the fit value calculation procedures (FAST and BEST fit) available in CATALYST were analyzed in terms of their ability to discriminate between active and inactive compounds and in terms of efficiency. Moreover, these results are put in direct comparison to the performance of the shape-based virtual screening platform ROCS. Our results prove that high enrichment rates are not necessarily in conflict with efficient vHTS settings: In most of the experiments, we obtained the highest yield of actives in the hit list when parameter sets for the fastest search algorithm were used.