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1.
    
Dead‐end elimination (DEE) is a powerful theorem for selecting optimal protein side‐chain orientations from a large set of discrete conformations. The present work describes a new approach to dead‐end elimination that effectively splits conformational space into partitions to more efficiently eliminate dead‐ending rotamers. Split DEE makes it possible to complete protein design calculations that were previously intractable due to the combinatorial explosion of intermediate conformations generated during the convergence process. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 999–1009, 2000  相似文献   

2.
    
The search for the global minimum energy conformation (GMEC) of protein side chains is an important computational challenge in protein structure prediction and design. Using rotamer models, the problem is formulated as a NP‐hard optimization problem. Dead‐end elimination (DEE) methods combined with systematic A* search (DEE/A*) has proven useful, but may not be strong enough as we attempt to solve protein design problems where a large number of similar rotamers is eligible and the network of interactions between residues is dense. In this work, we present an exact solution method, named BroMAP (branch‐and‐bound rotamer optimization using MAP estimation), for such protein design problems. The design goal of BroMAP is to be able to expand smaller search trees than conventional branch‐and‐bound methods while performing only a moderate amount of computation in each node, thereby reducing the total running time. To achieve that, BroMAP attempts reduction of the problem size within each node through DEE and elimination by lower bounds from approximate maximum‐a‐posteriori (MAP) estimation. The lower bounds are also exploited in branching and subproblem selection for fast discovery of strong upper bounds. Our computational results show that BroMAP tends to be faster than DEE/A* for large protein design cases. BroMAP also solved cases that were not solved by DEE/A* within the maximum allowed time, and did not incur significant disadvantage for cases where DEE/A* performed well. Therefore, BroMAP is particularly applicable to large protein design problems where DEE/A* struggles and can also substitute for DEE/A* in general GMEC search. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009  相似文献   

3.
    
FASTER is a combinatorial optimization algorithm useful for finding low-energy side-chain configurations in side-chain placement and protein design calculations. We present two simple enhancements to FASTER that together improve the computational efficiency of these calculations by as much as two orders of magnitude with no loss of accuracy. Our results highlight the importance of choosing appropriate initial configurations, and show that efficiency can be improved by stringently limiting the number of positions that are allowed to relax in response to a perturbation. The changes we describe improve the quality of solutions found for large-scale designs, and allow them to be found in hours rather than days. The improved FASTER algorithm finds low-energy solutions more efficiently than common optimization schemes based on the dead-end elimination theorem and Monte Carlo. These advances have prompted investigations into new methods for force field parameterization and multiple state design.  相似文献   

4.
    
Multistate protein design is the task of predicting the amino acid sequence that is best suited to selectively and stably fold to one state out of a set of competing structures. Computationally, it entails solving a challenging optimization problem. Therefore, notwithstanding the increased interest in multistate design, the only implementations reported are based on either genetic algorithms or Monte Carlo methods. The dead-end elimination (DEE) theorem cannot be readily transfered to multistate design problems despite its successful application to single-state protein design. In this article we propose a variant of the standard DEE, called type-dependent DEE. Our method reduces the size of the conformational space of the multistate design problem, while provably preserving the minimal energy conformational assignment for any choice of amino acid sequence. Type-dependent DEE can therefore be used as a preprocessing step in any computational multistate design scheme. We demonstrate the applicability of type-dependent DEE on a set of multistate design problems and discuss its strength and limitations.  相似文献   

5.
    
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.  相似文献   

6.
    
Recent advances in protein design have demonstrated the effectiveness of optimization algorithms based on the dead-end elimination theorem. The algorithms solve the combinatorial problem of finding the optimal placement of side chains for a set of backbone coordinates. Although they are powerful tools, these algorithms have severe limitations when the number of side chain rotamers is large. This is due to the high-order time dependence of the aspect of the calculation that deals with rotamer doubles. We present three independent algorithmic enhancements that significantly increase the speed of the doubles computation. These methods work by using quantities that are inexpensive to compute as a basis for forecasting which expensive calculations are worthwhile. One of the methods, the comparison of extrema, is derived from analytical considerations, and the remaining two, the “magic-bullet” and the “qrs” and “quv” metrics, are based on empirical observation of the distribution of energies in the system. When used together, these methods effect an overall speed improvement of as much as a factor of 47, and for the doubles aspect of the calculation, a factor of 95. Together, these enhancements extend the envelope of inverse folding to larger proteins by making formerly intractable calculations attainable in reasonable computer time. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1505–1514, 1998  相似文献   

7.
    
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.  相似文献   

8.
    
Dead‐end elimination (DEE) has emerged as a powerful structure‐based, conformational search technique enabling computational protein redesign. Given a protein with n mutable residues, the DEE criteria guide the search toward identifying the sequence of amino acids with the global minimum energy conformation (GMEC). This approach does not restrict the number of permitted mutations and allows the identified GMEC to differ from the original sequence in up to n residues. In practice, redesigns containing a large number of mutations are often problematic when taken into the wet‐lab for creation via site‐directed mutagenesis. The large number of point mutations required for the redesigns makes the process difficult, and increases the risk of major unpredicted and undesirable conformational changes. Preselecting a limited subset of mutable residues is not a satisfactory solution because it is unclear how to select this set before the search has been performed. Therefore, the ideal approach is what we define as the κ‐restricted redesign problem in which any κ of the n residues are allowed to mutate. We introduce restricted dead‐end elimination (rDEE) as a solution of choice to efficiently identify the GMEC of the restricted redesign (the κGMEC). Whereas existing approaches require n‐choose‐κ individual runs to identify the κGMEC, the rDEE criteria can perform the redesign in a single search. We derive a number of extensions to rDEE and present a restricted form of the A* conformation search. We also demonstrate a 10‐fold speed‐up of rDEE over traditional DEE approaches on three different experimental systems. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010  相似文献   

9.
    
We have developed a process that significantly reduces the number of rotamers in computational protein design calculations. This process, which we call Vegas, results in dramatic computational performance increases when used with algorithms based on the dead-end elimination (DEE) theorem. Vegas estimates the energy of each rotamer at each position by fixing each rotamer in turn and utilizing various search algorithms to optimize the remaining positions. Algorithms used for this context specific optimization can include Monte Carlo, self-consistent mean field, and the evaluation of an expression that generates a lower bound energy for the fixed rotamer. Rotamers with energies above a user-defined cutoff value are eliminated. We found that using Vegas to preprocess rotamers significantly reduced the calculation time of subsequent DEE-based algorithms while retaining the global minimum energy conformation. For a full boundary design of a 51 amino acid fragment of engrailed homeodomain, the total calculation time was reduced by 12-fold.  相似文献   

10.
Proteins are flexible systems and commonly populate several functionally important states. To understand protein function, these states and their energies have to be identified. We introduce an algorithm that allows the determination of a gap-free list of the low energy states. This algorithm is based on the dead-end elimination (DEE) theorem and is termed X-DEE (extended DEE). X-DEE is applicable to discrete systems whose state energy can be formulated as pairwise interaction between sites and their intrinsic energies. In this article, the computational performance of X-DEE is analyzed and discussed. X-DEE is implemented to determine the lowest energy protonation states of proteins, a problem to which DEE has not been applied so far. We use X-DEE to calculate a list of low energy protonation states for two bacteriorhodopsin structures that represent the first proton transfer step of the bacteriorhodopsin photocycle.  相似文献   

11.
    
Molecular docking of small‐molecules is an important procedure for computer‐aided drug design. Modeling receptor side chain flexibility is often important or even crucial, as it allows the receptor to adopt new conformations as induced by ligand binding. However, the accurate and efficient incorporation of receptor side chain flexibility has proven to be a challenge due to the huge computational complexity required to adequately address this problem. Here we describe a new docking approach with a very fast, graph‐based optimization algorithm for assignment of the near‐optimal set of residue rotamers. We extensively validate our approach using the 40 DUD target benchmarks commonly used to assess virtual screening performance and demonstrate a large improvement using the developed side chain optimization over rigid receptor docking (average ROC AUC of 0.693 vs. 0.623). Compared to numerous benchmarks, the overall performance is better than nearly all other commonly used procedures. Furthermore, we provide a detailed analysis of the level of receptor flexibility observed in docking results for different classes of residues and elucidate potential avenues for further improvement. © 2013 Wiley Periodicals, Inc.  相似文献   

12.
    
We adapt a combinatorial optimization algorithm, extremal optimization (EO), for the search problem in computational protein design. This algorithm takes advantage of the knowledge of local energy information and systematically improves on the residues that have high local energies. Power-law probability distributions are used to select the backbone sites to be improved on and the rotamer choices to be changed to. We compare this method with simulated annealing (SA) and motivate and present an improved method, which we call reference energy extremal optimization (REEO). REEO uses reference energies to convert a problem with a structured local-energy profile to one with more random profile, and extremal optimization proves to be extremely efficient for the latter problem. We show in detail the large improvement we have achieved using REEO as compared to simulated annealing and discuss a number of other heuristics we have attempted to date.  相似文献   

13.
    
Designing proteins with novel protein/protein binding properties can be achieved by combining the tools that have been developed independently for protein docking and protein design. We describe here the sequence-independent generation of protein dimer orientations by protein docking for use as scaffolds in protein sequence design algorithms. To dock monomers into sequence-independent dimer conformations, we use a reduced representation in which the side chains are approximated by spheres with atomic radii derived from known C2 symmetry-related homodimers. The interfaces of C2-related homodimers are usually more hydrophobic and protein core-like than the interfaces of heterodimers; we parameterize the radii for docking against this feature to capture and recreate the spatial characteristics of a hydrophobic interface. A fast Fourier transform-based geometric recognition algorithm is used for docking the reduced representation protein models. The resulting docking algorithm successfully predicted the wild-type homodimer orientations in 65 out of 121 dimer test cases. The success rate increases to approximately 70% for the subset of molecules with large surface area burial in the interface relative to their chain length. Forty-five of the predictions exhibited less than 1 A C(alpha) RMSD compared to the native X-ray structures. The reduced protein representation therefore appears to be a reasonable approximation and can be used to position protein backbones in plausible orientations for homodimer design.  相似文献   

14.
Acrylate‐methylmethacrylate copolymers have been synthesized for nonlinear optical applications. Acrylate monomer units are characterized by the presence in the side chain of phenylbenzoxazole groups containing electron donor‐electron acceptor substituents. The phase behavior of all polymers has been investigated by DSC, X‐ray diffraction and polarizing microscopy: two of them exhibit liquid crystalline behavior of smectic type. For four polymers, nonlinear optical properties have been examined by second harmonic generation measurements on thin films (∼ 1 μm thickness) electrically poled by corona discharge. Second order susceptibility coefficients d33 and average relaxation times 〈τ〉, relative to the time stability of the chromophore poling, have been measured. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 603–608, 1999  相似文献   

15.
    
We present the Molecular Software Library (MSL), a C++ library for molecular modeling. MSL is a set of tools that supports a large variety of algorithms for the design, modeling, and analysis of macromolecules. Among the main features supported by the library are methods for applying geometric transformations and alignments, the implementation of a rich set of energy functions, side chain optimization, backbone manipulation, calculation of solvent accessible surface area, and other tools. MSL has a number of unique features, such as the ability of storing alternative atomic coordinates (for modeling) and multiple amino acid identities at the same backbone position (for design). It has a straightforward mechanism for extending its energy functions and can work with any type of molecules. Although the code base is large, MSL was created with ease of developing in mind. It allows the rapid implementation of simple tasks while fully supporting the creation of complex applications. Some of the potentialities of the software are demonstrated here with examples that show how to program complex and essential modeling tasks with few lines of code. MSL is an ongoing and evolving project, with new features and improvements being introduced regularly, but it is mature and suitable for production and has been used in numerous protein modeling and design projects. MSL is open‐source software, freely downloadable at http://msl‐libraries.org . We propose it as a common platform for the development of new molecular algorithms and to promote the distribution, sharing, and reutilization of computational methods. © 2012 Wiley Periodicals, Inc.  相似文献   

16.
    
The optimization for function in computational design requires the treatment of, often competing, multiple objectives. Current algorithms reduce the problem to a single objective optimization problem, with the consequent loss of relevant solutions. We present a procedure, based on a variant of a Pareto algorithm, to optimize various competing objectives in protein design that allows reducing in several orders of magnitude the search of the solution space. Our methodology maintains the diversity of solutions and provides an iterative way to incorporate automatic design methods in the design of functional proteins. We have applied our systematic procedure to design enzymes optimized for both catalysis and stability. However, this methodology can be applied to any computational chemistry application requiring multi-objective combinatorial optimization techniques.  相似文献   

17.
    
Styrene was polymerized with azobiscyanovaleric acid (ACVA) to obtain carboxy‐telechelic polystyrene. Our aim was to synthesize an oligostyrene with a molecular weight of about 2000 g/mol. Thus, styrene was polymerized at 90 °C, where t1/2ACVA is very short, and at very high initiator concentrations. In these conditions a new termination reaction appeared, known as the primary radical termination (PRT). At first, PRT was observed by a deviation from the simple kinetic law. Then, the constant of PRT was determined by several kinetic models to be more important than the constant of bimolecular termination. Finally, the PREDICI simulation program was used to confirm the predominance of PRT. This simulation program allowed the determination of the constant of primary radical deactivation krr and the influence of this reaction on the conversion rate. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 2740–2750, 2001  相似文献   

18.
    
Poly[(methyl acrylate)‐rotaxa‐(30‐crown‐10)] ( 5 ) and poly[(methyl methacrylate)‐rotaxa‐(30‐crown‐10)] ( 6 ) were synthesized by azobisisobutyronitrile‐initiated free‐radical bulk polymerizations of the respective monomers in the presence of 30‐crown‐10 ( 1 ; equimolar; 5 times the monomer mass). For 5 , 3.8 mass % (0.81 mol % with respect to the monomer) of the crown was incorporated versus 1.7 mass % (0.39 mol % with respect to the monomer) for 6 . Control reactions with 18‐crown‐6, which is to small to be threaded, showed that chain transfer to the crown ethers was detectable only for the acrylate but was relatively negligible and spectroscopically distinct. The threading yields were much higher with these systems than with polystyrene, most likely because of the greater compatibility of the crown ether with these polar monomers and polymers and the consequent ability to carry out the polymerizations homogeneously in the absence of added solvent; however, the threading process was still essentially statistical. Therefore, the polymerization of methacrylate monomers 8a – 8c based on tetraarylmethane moieties connected via diethyleneoxy or triethyleneoxy spacers was examined in the presence of 1 in the belief that the supramolecular semirotaxane monomer 9 formed statistically in situ could be captured more efficiently and produce higher threading yields, presumably of side‐chain polyrotaxanes, than the simple (meth)acrylate monomers. Azobisisobutyronitrile‐initiated polymerizations either neat or in toluene produced polyrotaxanes 10 with up to about 1.6 mass % and 2 mol % threaded crown ether, presumably trapped on the pendant stoppered side chains. Although primarily statistical in nature, the latter rotaxane syntheses afforded on a molar basis 3–7 times more efficient incorporation of 1 than styrene (0.33 mol %), methyl acrylate (0.81 mol %), or methyl methacrylate (0.39 mol %) monomers for the preparation of main‐chain polypseudorotaxanes and indeed even surpassed the 60‐crown‐20/polyacrylonitrile system (1.5 mol %). This was presumed to be due to the fact that the loss of the crown ether, once it was threaded onto the monomer to form 9 and the latter was polymerized, was either retarded (by the tetraphenylmethyl stopper in 10a ) or prevented completely [by tris(p‐t‐butylphenyl)phenylmethyl stoppers in 10b and 10c ]. © 2001 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 39: 1978–1993, 2001  相似文献   

19.
    
One of the main challenges in computational protein design (CPD) is the huge size of the protein sequence and conformational space that has to be computationally explored. Recently, we showed that state‐of‐the‐art combinatorial optimization technologies based on Cost Function Network (CFN) processing allow speeding up provable rigid backbone protein design methods by several orders of magnitudes. Building up on this, we improved and injected CFN technology into the well‐established CPD package Osprey to allow all Osprey CPD algorithms to benefit from associated speedups. Because Osprey fundamentally relies on the ability of to produce conformations in increasing order of energy, we defined new strategies combining CFN lower bounds, with new side‐chain positioning‐based branching scheme. Beyond the speedups obtained in the new ‐CFN combination, this novel branching scheme enables a much faster enumeration of suboptimal sequences, far beyond what is reachable without it. Together with the immediate and important speedups provided by CFN technology, these developments directly benefit to all the algorithms that previously relied on the DEE/ combination inside Osprey* and make it possible to solve larger CPD problems with provable algorithms. © 2016 Wiley Periodicals, Inc.  相似文献   

20.
    
π-Conjugated polymers are important materials for organic photovoltaics. While search for new backbone systems is central to the development of π-conjugated polymers, side-chain engineering is also imperative. Here, two benzodithiophene-thiazolothiazole copolymers, PSTz1 and POTz1, were synthesized, for which the side-chain placement was different. Due to less steric hindrance between the side chains, PSTz1 had a more coplanar backbone than POTz1. This led to significant differences in trend of the performance for the binary and ternary blend cells that used a fullerene (PC71BM) and/or non-fullerene (ITIC) as the acceptor materials. Whereas PSTz1 showed higher photovoltaic performance in the PC71BM-based cell, POTz1 showed higher performance in the ITIC-based cell. Furthermore, in the ternary blend cell, whereas increase in the PC71BM content improved the photovoltaic performance for the PSTz1 system, it was detrimental to the performance for the POTz1 system. These results could be a good guideline for maximizing the performance of organic photovoltaics.  相似文献   

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