beta-Barrel transmembrane proteins: Geometric modelling, detection of transmembrane region, and structural properties

The location of the membrane lipid bilayer relative to a transmembrane protein structure is important in protein engineering. Since it is not present on the determined structures, it is essential to automatically define the membrane embedded protein region in order to test mutation effects or to design potential drugs. beta-Barrel transmembrane proteins, present in nature as outer membrane proteins (OMPs), comprise one of the two transmembrane protein fold classes. Lately, the number of their determined structures has increased and this enables the implementation and evaluation of structure-based annotation methods and their more comprehensive study. In this paper, we propose two new algorithms for (i) the geometric modelling of beta-barrels and (ii) the detection of the transmembrane region of a beta-barrel transmembrane protein. The geometric modelling algorithm combines a non-linear least square minimization method and a genetic algorithm in order to find the characteristics (axis, radius) of a shape with axial symmetry which best models a beta-barrel. The transmembrane region is detected by profiling the external residues of the beta-barrel along its axis in terms of hydrophobicity and existence of aromatic and charged residues. TbB-Tool implements these algorithms and is available in . A non-redundant set of 22 OMPs is used in order to evaluate the algorithms implemented and the results are very satisfying. In addition, we quantify the abundance of all amino acids and the average hydrophobicity for external and internal beta-stranded residues along the axis of beta-barrel, thus confirming and extending other researchers' results.     

PharmID: pharmacophore identification using Gibbs sampling

The binding of a small molecule to a protein is inherently a 3D matching problem. As crystal structures are not available for most drug targets, there is a need to be able to infer from bioassay data the key binding features of small molecules and their disposition in space, the pharmacophore. Fingerprints of 3D features and a modification of Gibbs sampling to align a set of known flexible ligands, where all compounds are active, are used to discern possible pharmacophores. A clique detection method is used to map the features back onto the binding conformations. The complete algorithm is described in detail, and it is shown that the method can find common superimposition for several test data sets. The method reproduces answers very close to the crystal structure and literature pharmacophores in the examples presented. The basic algorithm is relatively fast and can easily deal with up to 100 compounds and tens of thousands of conformations. The algorithm is also able to handle multiple binding mode problems, which means it can superimpose molecules within the same data set according to two different sets of binding features. We demonstrate the successful use of this algorithm for multiple binding modes for a set of D2 and D4 ligands.     

The minimized dead-end elimination criterion and its application to protein redesign in a hybrid scoring and search algorithm for computing partition functions over molecular ensembles

One of the main challenges for protein redesign is the efficient evaluation of a combinatorial number of candidate structures. The modeling of protein flexibility, typically by using a rotamer library of commonly-observed low-energy side-chain conformations, further increases the complexity of the redesign problem. A dominant algorithm for protein redesign is dead-end elimination (DEE), which prunes the majority of candidate conformations by eliminating rigid rotamers that provably are not part of the global minimum energy conformation (GMEC). The identified GMEC consists of rigid rotamers (i.e., rotamers that have not been energy-minimized) and is thus referred to as the rigid-GMEC. As a postprocessing step, the conformations that survive DEE may be energy-minimized. When energy minimization is performed after pruning with DEE, the combined protein design process becomes heuristic, and is no longer provably accurate: a conformation that is pruned using rigid-rotamer energies may subsequently minimize to a lower energy than the rigid-GMEC. That is, the rigid-GMEC and the conformation with the lowest energy among all energy-minimized conformations (the minimized-GMEC) are likely to be different. While the traditional DEE algorithm succeeds in not pruning rotamers that are part of the rigid-GMEC, it makes no guarantees regarding the identification of the minimized-GMEC. In this paper we derive a novel, provable, and efficient DEE-like algorithm, called minimized-DEE (MinDEE), that guarantees that rotamers belonging to the minimized-GMEC will not be pruned, while still pruning a combinatorial number of conformations. We show that MinDEE is useful not only in identifying the minimized-GMEC, but also as a filter in an ensemble-based scoring and search algorithm for protein redesign that exploits energy-minimized conformations. We compare our results both to our previous computational predictions of protein designs and to biological activity assays of predicted protein mutants. Our provable and efficient minimized-DEE algorithm is applicable in protein redesign, protein-ligand binding prediction, and computer-aided drug design.     

Conformational sampling by self-organization

A new stochastic algorithm for conformational sampling is described. The algorithm generates molecular conformations that are consistent with a set of geometric constraints, which include interatomic distance bounds and chiral volumes derived from the molecular connectivity table. The algorithm repeatedly selects individual geometric constraints at random and updates the respective atomic coordinates toward satisfying the chosen constraint. When compared to a conventional distance geometry algorithm based on the same set of geometric constraints, our method is faster and generates conformations that are more diverse and more energetically favorable.     

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.     

Genetic algorithms for protein conformation sampling and optimization in a discrete backbone dihedral angle space

We have investigated protein conformation sampling and optimization based on the genetic algorithm and discrete main chain dihedral state model. An efficient approach combining the genetic algorithm with local minimization and with a niche technique based on the sharing function is proposed. Using two different types of potential energy functions, a Go-type potential function and a knowledge-based pairwise potential energy function, and a test set containing small proteins of varying sizes and secondary structure compositions, we demonstrated the importance of local minimization and population diversity in protein conformation optimization with genetic algorithms. Some general properties of the sampled conformations such as their native-likeness and the influences of including side-chains 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.     

Loop closure via bond scaling and relaxation

We describe, test, and apply a new computational algorithm for generating protein loop conformations subject to distance and secondary structure constraints. The algorithm is based upon initial scaling and subsequent relaxation of covalent bond lengths. The scaling-relaxation procedure needs no additional energy terms and can be readily incorporated into existing molecular modeling packages. The algorithm uses an all-atom energy function from the outset in a straightforward way so that about 60% of the generated loop conformations are free of severe distortions of covalent bond lengths and angles. An extensive application to the major loop conformations of TFIIIA-type zinc fingers (Zif268 and ADR1) is presented, as well as preliminary calculations on hypervariable loops of two immunoglobulins (MCPC603 and Bence-Jones). © 1993 John Wiley & Sons, Inc.     

Efficient approximate all-atom solvent accessible surface area method parameterized for folded and denatured protein conformations

Continuing advances in computer hardware and software are permitting atomic-resolution molecular simulations for longer time scales and on larger systems. Despite these advances, routinely performing atomistic simulations with explicit water for even small proteins, which reach the folding time of such proteins, remains intractable for the foreseeable future. An implicit approximation of the solvent environment using a solvent accessible surface area (SASA) term in a molecular mechanics potential function allows exclusion of the explicit water molecules in protein simulations. This reduces the number of particles by approximately an order of magnitude. We present a fast and acceptably accurate approximate all-atom SASA method parameterized using a set of folded and heat-denatured conformations of globular proteins. The parameters are shown to be transferable to folded and heat-denatured conformations for another set of proteins. Calculation of the approximate SASA and the associated derivatives with respect to atomic positions for a 4644 atom protein requires only 1/11th the CPU time required for calculation of the nonbonded interactions for this system. On a per atom basis, this algorithm is three times faster than the fastest previously published approximate SASA method and achieves the same level of accuracy.     

Heuristic-based tabu search algorithm for folding two-dimensional AB off-lattice model proteins

The protein structure prediction problem is a classical NP hard problem in bioinformatics. The lack of an effective global optimization method is the key obstacle in solving this problem. As one of the global optimization algorithms, tabu search (TS) algorithm has been successfully applied in many optimization problems. We define the new neighborhood conformation, tabu object and acceptance criteria of current conformation based on the original TS algorithm and put forward an improved TS algorithm. By integrating the heuristic initialization mechanism, the heuristic conformation updating mechanism, and the gradient method into the improved TS algorithm, a heuristic-based tabu search (HTS) algorithm is presented for predicting the two-dimensional (2D) protein folding structure in AB off-lattice model which consists of hydrophobic (A) and hydrophilic (B) monomers. The tabu search minimization leads to the basins of local minima, near which a local search mechanism is then proposed to further search for lower-energy conformations. To test the performance of the proposed algorithm, experiments are performed on four Fibonacci sequences and two real protein sequences. The experimental results show that the proposed algorithm has found the lowest-energy conformations so far for three shorter Fibonacci sequences and renewed the results for the longest one, as well as two real protein sequences, demonstrating that the HTS algorithm is quite promising in finding the ground states for AB off-lattice model proteins.     

Stochastic protein folding simulation in the three-dimensional HP-model

We present results from three-dimensional protein folding simulations in the HP-model on ten benchmark problems. The simulations are executed by a simulated annealing-based algorithm with a time-dependent cooling schedule. The neighbourhood relation is determined by the pull-move set. The results provide experimental evidence that the maximum depth D of local minima of the underlying energy landscape can be upper bounded by D相似文献   

Conformational searching using a population-based incremental learning algorithm

A new population-based incremental learning algorithm for conformational searching of molecules is presented. This algorithm is particularly effective at determining, by relatively small number of energy minimizations, global energy minima of large flexible molecules. The algorithm is also able to find a large set of low energy conformations of more rigid small molecules. The performance of the algorithm is relation to other algorithm is examined via the test molecules: C(18) H(38) , C(39)H(80) , cycloheptadecane and a set of five drug-like molecules.     

The ellipsoid algorithm as a method for the determination of polypeptide conformations from experimental distance constraints and energy minimization

A new method for constrained nonlinear optimization known as the ellipsoid algorithm is evaluated as a means of determining and refining the conformations of peptides. Advantages of the ellipsoid algorithm over conventional optimization methods include that it avoids many local minima that other methods would be trapped by, and that it is sometimes able to find optimum solutions in which the constraints are satisfied exactly. The dihedral angles about single bonds were used as variables to keep the dimensionality low (the rate of convergence decreases rapidly with increasing dimensionality of the problem). The method is evaluated on problems involving distance constraints, and for minimization of conformational energy functions. In an initial application, conformations consistent with an experimental set of NMR distance constraints were obtained in a problem involving 48 variable dihedral angles.     

Peptide backbone reconstruction using dead-end elimination and a knowledge-based forcefield

A novel, yet simple and automated, protocol for reconstruction of complete peptide backbones from C(alpha) coordinates only is described, validated, and benchmarked. The described method collates a set of possible backbone conformations for each set of residue triads from a structural library derived from the PDB. The optimal permutation of these three residue segments of backbone conformations is determined using the dead-end elimination (DEE) algorithm. Putative conformations are evaluated using a pairwise-additive knowledge-based forcefield term and a fragment overlap term. The protocol described in this report is able to restore the full backbone coordinates to within 0.2-0.6 A of the actual crystal structure from C(alpha) coordinates only. In addition, it is insensitive to errors in the input C(alpha) coordinates with RMSDs of 3.0 A, and this is illustrated through application to deliberately distorted C(alpha) traces. The entire process, as described, is rapid, requiring of the order of a few minutes for a typical protein on a typical desktop PC. Approximations enable this to be reduced to a few seconds, although this is at the expense of prediction accuracy. This compares very favorably to previously published methods, being sufficiently fast for general use and being one of the most accurate methods. Because the method is not restricted to the reconstruction from only C(alpha) coordinates, reconstruction based on C(beta) coordinates is also demonstrated.     

Calculation of hydration free energy for a solute with many atomic sites using the RISM theory: A robust and efficient algorithm

We have developed an algorithm for solving the reference interaction site model (RISM) equations for water near a solute molecule with many atomic sites (interaction sites). It is a hybrid of the Newton–Raphson and Picard methods and is judiciously constructed. Various considerations are given so that the computer time can be saved as much as possible. The robustness and high efficiency of the algorithm has been demonstrated for calculating hydration free energies of Met-enkephalin (a peptide with 75 sites) with different conformations. The Jacobian matrix is treated as part of the input data, and it has been found that the same matrix can be used for a considerably large set of different conformations of the solute molecule. © 1997 John Wiley & Sons, Inc. J Comput Chem 18: 1320–1326, 1997     

Nanobody‐Enabled Reverse Pharmacology on G‐Protein‐Coupled Receptors

The conformational complexity of transmembrane signaling of G‐protein‐coupled receptors (GPCRs) is a central hurdle for the design of screens for receptor agonists. In their basal states, GPCRs have lower affinities for agonists compared to their G‐protein‐bound active state conformations. Moreover, different agonists can stabilize distinct active receptor conformations and do not uniformly activate all cellular signaling pathways linked to a given receptor (agonist bias). Comparative fragment screens were performed on a β₂‐adrenoreceptor–nanobody fusion locked in its active‐state conformation by a G‐protein‐mimicking nanobody, and the same receptor in its basal‐state conformation. This simple biophysical assay allowed the identification and ranking of multiple novel agonists and permitted classification of the efficacy of each hit in agonist, antagonist, or inverse agonist categories, thereby opening doors to nanobody‐enabled reverse pharmacology.     

Exact rotamer optimization for protein design

Computational methods play a central role in the rational design of novel proteins. The present work describes a new hybrid exact rotamer optimization (HERO) method that builds on previous dead-end elimination algorithms to yield dramatic performance enhancements. Measured on experimentally validated physical models, these improvements make it possible to perform previously intractable designs of entire protein core, surface, or boundary regions. Computational demonstrations include a full core design of the variable domains of the light and heavy chains of catalytic antibody 48G7 FAB with 74 residues and 10(128) conformations, a full core/boundary design of the beta1 domain of protein G with 25 residues and 10(53) conformations, and a full surface design of the beta1 domain of protein G with 27 residues and 10(60) conformations. In addition, a full sequence design of the beta1 domain of protein G is used to demonstrate the strong dependence of algorithm performance on the exact form of the potential function and the fidelity of the rotamer library. These results emphasize that search algorithm performance for protein design can only be meaningfully evaluated on physical models that have been subjected to experimental scrutiny. The new algorithm greatly facilitates ongoing efforts to engineer increasingly complex protein features.     

Generic shapes for the conformation analysis of macrocyclic structures

A new algorithm for the systematic generation of conformations of macrocyclic systems is presented. The procedure is based on the concept of generic shapes that are found in such structures. These shapes are characterized by a selection of harmonics which occur in an approximate Fourier representation of the atomic coordinates of the rings. Following a fixed protocol, a limited set of in-plane and out-of-plane circular harmonics is used to define an ensemble of generic ring shapes. These generic shapes are used as start structures for energy minimizations by a given force-field method. To account for the possibility of having several final conformations originating from the same generic shape, the corresponding initial structure is taken several times and subjected to a randomization step before minimization. The resulting conformations that fall within a preset low-energy band are collected and screened for duplicates and enantiomers. The efficiency of this procedure (ratio between the number of accepted conformations and the total number of energy minimizations) depends on the flexibility of the macrocyclic system. The efficiency is generally quite high for very flexible rings. According to the proposed protocol, the number of generic shapes used as start structures grows as the square of N(lnN), where N is the ring size. The algorithm lends itself to conformational analyses of medium-size and large rings as well as of loops spanned between fixed structural units.     

Kinetics of cooperative protein folding involving two separate conformational families

The master equation that describes the kinetics of protein folding is solved numerically for a portion of Staphylococcal Protein A by a Laplace transformation. The calculations are carried out with 50 local-minimum conformations belonging to two conformational families. The master equation allows for transitions among all the 50 conformations in the evolution toward the final folded equilibrium distribution of conformations. It is concluded that the native protein folds in a fast cooperative process. The global energy minimum of a native protein can be reached after a sufficiently long folding time regardless of the initial state and the existence of a large number of local energy minima. Conformations representing non-native states of the protein can transform to the native state even if they do not belong to the native conformational family. Given a starting conformation, the protein molecule can fold to its final conformation through different paths. Finally, when the folding reaches the equilibrium distribution, the protein molecule adopts a set of conformations in which the global minimum has the largest average probability.     

Coarse-Grained Molecular Dynamics Study based on TorchMD

The coarse grained (CG) model implements the molecular dynamics simulation by simplifying atom properties and interaction between them. Despite losing certain detailed information, the CG model is still the first-thought option to study the large molecule in long time scale with less computing resource. The deep learning model mainly mimics the human studying process to handle the network input as the image to achieve a good classification and regression result. In this work, the TorchMD, a MD framework combining the CG model and deep learning model, is applied to study the protein folding process. In 3D collective variable (CV) space, the modified find density peaks algorithm is applied to cluster the conformations from the TorchMD CG simulation. The center conformation in different states is searched. And the boundary conformations between clusters are assigned. The string algorithm is applied to study the path between two states, which are compared with the end conformations from all atoms simulations. The result shows that the main phenomenon of protein folding with TorchMD CG model is the same as the all-atom simulations, but with a less simulating time scale. The workflow in this work provides another option to study the protein folding and other relative processes with the deep learning CG model.