A homology/ab initio hybrid algorithm for sampling near‐native protein conformations

One of the major challenges for protein tertiary structure prediction strategies is the quality of conformational sampling algorithms, which can effectively and readily search the protein fold space to generate near‐native conformations. In an effort to advance the field by making the best use of available homology as well as fold recognition approaches along with ab initio folding methods, we have developed Bhageerath‐H Strgen, a homology/ab initio hybrid algorithm for protein conformational sampling. The methodology is tested on the benchmark CASP9 dataset of 116 targets. In 93% of the cases, a structure with TM‐score ≥ 0.5 is generated in the pool of decoys. Further, the performance of Bhageerath‐H Strgen was seen to be efficient in comparison with different decoy generation methods. The algorithm is web enabled as Bhageerath‐H Strgen web tool which is made freely accessible for protein decoy generation ( http://www.scfbio‐iitd.res.in/software/Bhageerath‐HStrgen1.jsp ). © 2013 Wiley Periodicals, Inc.     

Enhanced sampling method in molecular simulations using genetic algorithm for biomolecular systems

We propose a molecular simulation method using genetic algorithm (GA) for biomolecular systems to obtain ensemble averages efficiently. In this method, we incorporate the genetic crossover, which is one of the operations of GA, to any simulation method such as conventional molecular dynamics (MD), Monte Carlo, and other simulation methods. The genetic crossover proposes candidate conformations by exchanging parts of conformations of a target molecule between a pair of conformations during the simulation. If the candidate conformations are accepted, the simulation resumes from the accepted ones. While conventional simulations are based on local update of conformations, the genetic crossover introduces global update of conformations. As an example of the present approach, we incorporated genetic crossover to MD simulations. We tested the validity of the method by calculating ensemble averages and the sampling efficiency by using two kinds of peptides, ALA3 and (AAQAA)₃. The results show that for ALA3 system, the distribution probabilities of backbone dihedral angles are in good agreement with those of the conventional MD and replica-exchange MD simulations. In the case of (AAQAA)₃ system, our method showed lower structural correlation of α-helix structures than the other two methods and more flexibility in the backbone ψ angles than the conventional MD simulation. These results suggest that our method gives more efficient conformational sampling than conventional simulation methods based on local update of conformations. © 2018 Wiley Periodicals, Inc.     

A fast method for large‐scale De Novo peptide and miniprotein structure prediction

Although peptides have many biological and biomedical implications, an accurate method predicting their equilibrium structural ensembles from amino acid sequences and suitable for large‐scale experiments is still missing. We introduce a new approach—PEP‐FOLD—to the de novo prediction of peptides and miniproteins. It first predicts, in the terms of a Hidden Markov Model‐derived structural alphabet, a limited number of local conformations at each position of the structure. It then performs their assembly using a greedy procedure driven by a coarse‐grained energy score. On a benchmark of 52 peptides with 9–23 amino acids, PEP‐FOLD generates lowest‐energy conformations within 2.8 and 2.3 Å Cα root‐mean‐square deviation from the full nuclear magnetic resonance structures (NMR) and the NMR rigid cores, respectively, outperforming previous approaches. For 13 miniproteins with 27–49 amino acids, PEP‐FOLD reaches an accuracy of 3.6 and 4.6 Å Cα root‐mean‐square deviation for the most‐native and lowest‐energy conformations, using the nonflexible regions identified by NMR. PEP‐FOLD simulations are fast—a few minutes only—opening therefore, the door to in silico large‐scale rational design of new bioactive peptides and miniproteins. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

A Cyanine Photooxidation/β‐Elimination Sequence Enables Near‐infrared Uncaging of Aryl Amine Payloads

Uncaging strategies that use near‐infrared wavelengths can enable the highly targeted delivery of biomolecules in complex settings. Many methods, including an approach we developed using cyanine photooxidation, are limited to phenol‐containing payloads. Given the critical role of amines in diverse biological processes, we sought to use cyanine photooxidation to initiate the release of aryl amines. Heptamethine cyanines substituted with an aryl amine at the C4′ position undergo only inefficient release, likely due electronic factors. We then pursued the hypothesis that the carbonyl products derived from cyanine photooxidation could undergo efficient β‐elimination. After examining both symmetrical and unsymmetrical scaffolds, we identify a merocyanine substituted with indolenine and coumarin heterocycles that undergoes efficient photooxidation and aniline uncaging. In total, these studies provide a new scheme—cyanine photooxidation followed by β‐elimination—through which to design photocages with efficient uncaging properties.     

Collision‐free poisson motion planning in ultra high‐dimensional molecular conformation spaces

The function of protein, RNA, and DNA is modulated by fast, dynamic exchanges between three‐dimensional conformations. Conformational sampling of biomolecules with exact and nullspace inverse kinematics, using rotatable bonds as revolute joints and noncovalent interactions as holonomic constraints, can accurately characterize these native ensembles. However, sampling biomolecules remains challenging owing to their ultra‐high dimensional configuration spaces, and the requirement to avoid (self‐) collisions, which results in low acceptance rates. Here, we present two novel mechanisms to overcome these limitations. First, we introduce temporary constraints between near‐colliding links. The resulting constraint varieties instantaneously redirect the search for collision‐free conformations, and couple motions between distant parts of the linkage. Second, we adapt a randomized Poisson‐disk motion planner, which prevents local oversampling and widens the search, to ultra‐high dimensions. Tests on several model systems show that the sampling acceptance rate can increase from 16% to 70%, and that the conformational coverage in loop modeling measured as average closeness to existing loop conformations doubled. Correlated protein motions identified with our algorithm agree with those from MD simulations. © 2018 Wiley Periodicals, Inc.     

Folding Lattice HP Model of Proteins Using the Bond‐Fluctuation Model

In this paper, we find ‘good’ amino acid sequences that fold to a desired “target” structure as a ground state conformation of lowest accessible free energy using the modified bond‐fluctuation lattice model. In our protein lattice model, bond lengths are set to vary between one and √2 in three dimensions. Our results agree well with the native state energies E_N. Comparisons with the “putative native state” (PNS) energy E_PNS and the “hydrophobic zippers” (HZ) energy E_HZ are made. For every sequence, the global energy minimum is found to have multiple degeneracy of conformations, which is the same result as for the constraint‐based hydrophobic core construction (CHCC) method. The interior conformations of the ground states are also discussed.     

Effective protein conformational sampling based on predicted torsion angles

Protein structure prediction is a long‐standing problem in molecular biology. Due to lack of an accurate energy function, it is often difficult to know whether the sampling algorithm or the energy function is the most important factor for failure of locating near‐native conformations of proteins. This article examines the size dependence of sampling effectiveness by using a perfect “energy function”: the root‐mean‐squared distance from the target native structure. Using protein targets up to 460 residues from critical assessment of structure prediction techniques (CASP11, 2014), we show that the accuracy of near native structures sampled is relatively independent of protein sizes but strongly depends on the errors of predicted torsion angles. Even with 40% out‐of‐range angle prediction, 2 Å or less near‐native conformation can be sampled. The result supports that the poor energy function is one of the bottlenecks of structure prediction and predicted torsion angles are useful for overcoming the bottleneck by restricting the sampling space in the absence of a perfect energy function. © 2015 Wiley Periodicals, Inc.     

Pattern recognition in the prediction of protein structure. II. Chain conformation from a probability-directed search procedure

A procedure that finds the most probable conformational states of a protein chain is described. Single-residue conformations are represented in terms of four conformational states, α, ?, α*, and ?*. The conformation of the entire chain is represented by a sequence of single-residue conformational states; the distinct conformations in this representation are called “chain-states.” The first article in this series described a procedure that computes tripeptide conformational probabilities from the amino acid sequence using pattern recognition techniques. The procedure described in this article uses the tripeptide probabilities to estimate the probabilities of the chain-states. The chain-state probability estimator is a product of conditional and marginal probabilities (obtained from the tripeptide probabilities), with a penalty factor to eliminate conformations containing α-helices and ?-strands of excessive length. The probability estimator considers short-range conformational information, medium-range sequence information and some simple long-range information (through the restrictions on helix and strand lengths). Energy minimization calculations can be carried out in the region of conformational space corresponding to a particular chain-state. By selecting the most probable chain-states, the search can be focused on the most probable, or “important,” regions of the conformational space. These energy calculations are described in the third article of the series. The complete procedure described by the three articles is called PRISM, for pattern recognition-based importance sampling minimization.     

LEAP: Highly accurate prediction of protein loop conformations by integrating coarse‐grained sampling and optimized energy scores with all‐atom refinement of backbone and side chains

Prediction of protein loop conformations without any prior knowledge (ab initio prediction) is an unsolved problem. Its solution will significantly impact protein homology and template‐based modeling as well as ab initio protein‐structure prediction. Here, we developed a coarse‐grained, optimized scoring function for initial sampling and ranking of loop decoys. The resulting decoys are then further optimized in backbone and side‐chain conformations and ranked by all‐atom energy scoring functions. The final integrated technique called loop prediction by energy‐assisted protocol achieved a median value of 2.1 Å root mean square deviation (RMSD) for 325 12‐residue test loops and 2.0 Å RMSD for 45 12‐residue loops from critical assessment of structure‐prediction techniques (CASP) 10 target proteins with native core structures (backbone and side chains). If all side‐chain conformations in protein cores were predicted in the absence of the target loop, loop‐prediction accuracy only reduces slightly (0.2 Å difference in RMSD for 12‐residue loops in the CASP target proteins). The accuracy obtained is about 1 Å RMSD or more improvement over other methods we tested. The executable file for a Linux system is freely available for academic users at http://sparks‐lab.org . © 2013 Wiley Periodicals, Inc.     

A new route for the synthesis of phosphate esters: 2,2′‐[benzene‐1,2‐diylbis(oxy)]bis(5,5‐dimethyl‐1,3,2‐dioxaphosphinane) 2,2′‐dioxide

Podand‐type ligands are an interesting class of acyclic ligands which can form host–guest complexes with many transition metals and can undergo conformational changes. Organic phosphates are components of many biological molecules. A new route for the synthesis of phosphate esters with a retained six‐membered ring has been used to prepare 2,2′‐[benzene‐1,2‐diylbis(oxy)]bis(5,5‐dimethyl‐1,3,2‐dioxaphosphinane) 2,2′‐dioxide, C₆H₄{O[cyclo‐P(O)OCH₂CMe₂CH₂O]}₂ or C₁₆H₂₄O₈P₂, (1), 2‐[(2′‐hydroxybiphenyl‐2‐yl)oxy]‐5,5‐dimethyl‐1,3,2‐dioxaphosphinane 2‐oxide, [cyclo‐P(O)OCH₂CMe₂CH₂O](2,2′‐OC₆H₄–C₆H₄OH), (2), and oxybis(5,5‐dimethyl‐1,3,2‐dioxaphosphinane) 2,2′‐dioxide, O[cyclo‐P(O)OCH₂CMe₂CH₂O]₂, (3). Compound (1) is novel, whereas the results for compounds (2) and (3) have been reported previously, but we record here our results for compound (3), which we find are more precise and accurate than those currently reported in the literature. In (1), two cyclo‐P(O)OCH₂CMe₂CH₂O groups are linked through a catechol group. The conformations about the two catechol O atoms are quite different, viz. one C—C—O—P torsion angle is −169.11 (11)° and indicates a trans arrangement, whereas the other C—C—O—P torsion angle is 92.48 (16)°, showing a gauche conformation. Both six‐membered POCCCO rings have good chair‐shape conformations. In both the trans and gauche conformations, the catechol O atoms are in the axial sites and the short P=O bonds are equatorially bound.     

Adaptive partitioning by local density‐peaks: An efficient density‐based clustering algorithm for analyzing molecular dynamics trajectories

We present an efficient density‐based adaptive‐resolution clustering method APLoD for analyzing large‐scale molecular dynamics (MD) trajectories. APLoD performs the k‐nearest‐neighbors search to estimate the density of MD conformations in a local fashion, which can group MD conformations in the same high‐density region into a cluster. APLoD greatly improves the popular density peaks algorithm by reducing the running time and the memory usage by 2–3 orders of magnitude for systems ranging from alanine dipeptide to a 370‐residue Maltose‐binding protein. In addition, we demonstrate that APLoD can produce clusters with various sizes that are adaptive to the underlying density (i.e., larger clusters at low‐density regions, while smaller clusters at high‐density regions), which is a clear advantage over other popular clustering algorithms including k‐centers and k‐medoids. We anticipate that APLoD can be widely applied to split ultra‐large MD datasets containing millions of conformations for subsequent construction of Markov State Models. © 2016 Wiley Periodicals, Inc.     

Independence of photoproduct formation on DNA conformation.

Abstract— In an ethanolic solution native T7 DNA can undergo conformational transitions from the B conformation (0% ethanol) to the C-like (60% w/w ethanol) and the A (80% w/w ethanol) conformations. We have investigated the formation of three classes of thymine-derived photoproducts in T7 DNA irradiated (280 nm) in the B, C-like, and A conformations, which were monitored by circular dichroism measurements. We find that the predominant class of thymine-derived photoproducts in any conformational state is cyclobutyl dipyrimidines. While the ‘spore product,’ 5-thyminyl-5,6-dihydrothymine, which belongs to another class of photoproductsf does form in native DNA in the A conformation, its yield in denatured DNA at 80% ethanol is the same as that in native DNA. The yield of pyrimidine adduct, a third photoproduct class, is a maximum at 50–60% ethanol. This effect of ethanol is probably not due to the ethanol-induced C-like conformation, however, since pyrimidine adduct formation is not enhanced when T7 DNA is irradiated in the C conformation in 6 M CsCl or in intact phage. We conclude from these and other data in the literature that the degree of hydration rather than the conformational state is the critical factor in determining which of the photoproducts will form in native DNA.     

Error analysis and efficient sampling in Markovian state models for molecular dynamics

In previous work, we described a Markovian state model (MSM) for analyzing molecular-dynamics trajectories, which involved grouping conformations into states and estimating the transition probabilities between states. In this paper, we analyze the errors in this model caused by finite sampling. We give different methods with various approximations to determine the precision of the reported mean first passage times. These approximations are validated on an 87 state toy Markovian system. In addition, we propose an efficient and practical sampling algorithm that uses these error calculations to build a MSM that has the same precision in mean first passage time values but requires an order of magnitude fewer samples. We also show how these methods can be scaled to large systems using sparse matrix methods.     

Enhanced Wang Landau sampling of adsorbed protein conformations

Using computer simulations to model the folding of proteins into their native states is computationally expensive due to the extraordinarily low degeneracy of the ground state. In this paper, we develop an efficient way to sample these folded conformations using Wang Landau sampling coupled with the configurational bias method (which uses an unphysical "temperature" that lies between the collapse and folding transition temperatures of the protein). This method speeds up the folding process by roughly an order of magnitude over existing algorithms for the sequences studied. We apply this method to study the adsorption of intrinsically disordered hydrophobic polar protein fragments on a hydrophobic surface. We find that these fragments, which are unstructured in the bulk, acquire secondary structure upon adsorption onto a strong hydrophobic surface. Apparently, the presence of a hydrophobic surface allows these random coil fragments to fold by providing hydrophobic contacts that were lost in protein fragmentation.     

Receptor‐Bound Conformation of Cilengitide Better Represented by Its Solution‐State Structure than the Solid‐State Structure

The X‐ray crystal and NMR spectroscopic structures of the peptide drug candidate Cilengitide (cyclo(RGDf(NMe)Val)) in various solvents are obtained and compared in addition to the integrin receptor bound conformation. The NMR‐based solution structures exhibit conformations closely resembling the X‐ray structure of Cilengitide bound to the head group of integrin αvβ3. In contrast, the structure of pure Cilengitide recrystallized from methanol reveals a different conformation controlled by the lattice forces of the crystal packing. Molecular modeling studies of the various ligand structures docked to the αvβ3 integrin revealed that utilization of the solid‐state conformation of Cilengitide leads—unlike the solution‐based structures—to a mismatch of the ligand–receptor interactions compared with the experimentally determined structure of the protein–ligand complex. Such discrepancies between solution and crystal conformations of ligands can be misleading during the structure‐based lead optimization process and should thus be taken carefully into account in ligand orientated drug design.     

A comparative study of two polymorphs of L‐aspartic acid hydrochloride

Two polymorphs of L‐aspartic acid hydrochloride, C₄H₈NO₄⁺·Cl⁻, were obtained from the same aqueous solution. Their crystal structures have been determined from single‐crystal data collected at 100 K. The crystal structures revealed three‐ and two‐dimensional hydrogen‐bonding networks for the triclinic and orthorhombic polymorphs, respectively. The cations and anions are connected to one another via N—H...Cl and O—H...Cl interactions and form alternating cation–anion layer‐like structures. The two polymorphs share common structural features; however, the conformations of the L‐aspartate cations and the crystal packings are different. Furthermore, the molecular packing of the orthorhombic polymorph contains more interesting interactions which seems to be a favourable factor for more efficient charge transfer within the crystal.     

Focused grid‐based resampling for protein docking and mapping

The fast Fourier transform (FFT) sampling algorithm has been used with success in application to protein‐protein docking and for protein mapping, the latter docking a variety of small organic molecules for the identification of binding hot spots on the target protein. Here we explore the local rather than global usage of the FFT sampling approach in docking applications. If the global FFT based search yields a near‐native cluster of docked structures for a protein complex, then focused resampling of the cluster generally leads to a substantial increase in the number of conformations close to the native structure. In protein mapping, focused resampling of the selected hot spot regions generally reveals further hot spots that, while not as strong as the primary hot spots, also contribute to ligand binding. The detection of additional ligand binding regions is shown by the improved overlap between hot spots and bound ligands. © 2016 Wiley Periodicals, Inc.     

Constrained proper sampling of conformations of transition state ensemble of protein folding

Characterizing the conformations of protein in the transition state ensemble (TSE) is important for studying protein folding. A promising approach pioneered by Vendruscolo et al. [Nature (London) 409, 641 (2001)] to study TSE is to generate conformations that satisfy all constraints imposed by the experimentally measured φ values that provide information about the native likeness of the transition states. Fai?sca et al. [J. Chem. Phys. 129, 095108 (2008)] generated conformations of TSE based on the criterion that, starting from a TS conformation, the probabilities of folding and unfolding are about equal through Markov Chain Monte Carlo (MCMC) simulations. In this study, we use the technique of constrained sequential Monte Carlo method [Lin et al., J. Chem. Phys. 129, 094101 (2008); Zhang et al. Proteins 66, 61 (2007)] to generate TSE conformations of acylphosphatase of 98 residues that satisfy the φ-value constraints, as well as the criterion that each conformation has a folding probability of 0.5 by Monte Carlo simulations. We adopt a two stage process and first generate 5000 contact maps satisfying the φ-value constraints. Each contact map is then used to generate 1000 properly weighted conformations. After clustering similar conformations, we obtain a set of properly weighted samples of 4185 candidate clusters. Representative conformation of each of these cluster is then selected and 50 runs of Markov chain Monte Carlo (MCMC) simulation are carried using a regrowth move set. We then select a subset of 1501 conformations that have equal probabilities to fold and to unfold as the set of TSE. These 1501 samples characterize well the distribution of transition state ensemble conformations of acylphosphatase. Compared with previous studies, our approach can access much wider conformational space and can objectively generate conformations that satisfy the φ-value constraints and the criterion of 0.5 folding probability without bias. In contrast to previous studies, our results show that transition state conformations are very diverse and are far from nativelike when measured in cartesian root-mean-square deviation (cRMSD): the average cRMSD between TSE conformations and the native structure is 9.4 A? for this short protein, instead of 6 A? reported in previous studies. In addition, we found that the average fraction of native contacts in the TSE is 0.37, with enrichment in native-like β-sheets and a shortage of long range contacts, suggesting such contacts form at a later stage of folding. We further calculate the first passage time of folding of TSE conformations through calculation of physical time associated with the regrowth moves in MCMC simulation through mapping such moves to a Markovian state model, whose transition time was obtained by Langevin dynamics simulations. Our results indicate that despite the large structural diversity of the TSE, they are characterized by similar folding time. Our approach is general and can be used to study TSE in other macromolecules.