A combined steepest descent and genetic algorithm (SD/GA) approach for the optimization of solvation parameters

An accurate solvation model is essential for computer modeling of protein folding and other biomolecular self-assembly processes. Compared to explicit solvent models, implicit solvent models, such as the Poisson-Boltzmann (PB) with solvent accessible surface area model (PB/SA), offer a much faster speed—the most compelling reason for the popularity of these implicit solvent models. Since these implicit solvent models typically use empirical parameters, such as atomic radii and the surface tensions, an optimal fit of these parameters is crucial for the final accuracy of properties such as solvation free energy and folding free energy. In this paper, we proposed a combined approach, namely SD/GA, which takes the advantage of both local optimization with the steepest descent (SD), and global optimization with the genetic algorithm (GA), for parameters optimization in multi-dimensional space. The SD/GA method is then applied to the optimization of solvation parameters in the non-polar cavity term of the PB/SA model. The results show that the newly optimized parameters from SD/GA not only increase the accuracy in the solvation free energies for ～200 organic molecules, but also significantly improve the free energy landscape of a β-hairpin folding. The current SD/GA method can be readily applied to other multi-dimensional parameter space optimization as well.     

The Genetic Algorithm and the Conformational Search of Polypeptides and Proteins

Abstract

The genetic algorithm is a technique of function optimization derived from the principles of evolutionary theory. We have adapted it to perform conformational search on polypeptides and proteins. The algorithm was first tested on several small polypeptides and the 46 amino acid protein crambin under the AMBER potential energy function. The probable global minimum conformations of the polypeptides were located 90% of the time and a non-native conformation of crambin was located that was 150kcal/mol lower in potential energy than the minimized crystal structure conformation. Next, we used a knowledge-based potential function to predict the structures of melittin, pancreatic polypeptide, and crambin. A 2.31 Å ΔRMS conformation of melittin and a 5.33 Å ΔRMS conformation of pancreatic polypeptide were located by genetic algorithm-based conformational search under the knowledge-based potential function. Although the ΔRMS of pancreatic polypeptide was somewhat high, most of the secondary structure was correct. The secondary structure of crambin was predicted correctly, but the potential failed to promote packing interactions. Finally, we tested the packing aspects of our potential function by attempting to predict the tertiary structure of cytochrome b ₅₆₂ given correct secondary structure as a constraint. The final predicted conformation of cytochrome b ₅₆₂ was an almost completely extended continuous helix which indicated that the knowledge-based potential was useless for tertiary structure prediction. This work serves as a warning against testing potential functions designed for tertiary structure prediction on small proteins.     

Multiscale simulations of protein folding: application to formation of secondary structures

A multiscale simulation method of protein folding is proposed, using atomic representation of protein and solvent, combing genetic algorithms to determine the key protein structures from a global view, with molecular dynamic simulations to reveal the local folding pathways, thus providing an integrated landscape of protein folding. The method is found to be superior to previously investigated global search algorithms or dynamic simulations alone. For secondary structure formation of a selected peptide, RN24, the structures and dynamics produced by this method agree well with corresponding experimental results. Three most populated conformations are observed, including hairpin, β-sheet and α-helix. The energetic barriers separating these three structures are comparable to the kinetic energy of the atoms of the peptide, implying that the transition between these states can be easily triggered by kinetic perturbations, mainly through electrostatic interactions between charged atoms. Transitions between α-helix and β-sheet should jump over at least two energy barriers and may stay in the energetic trap of hairpin. It is proposed that the structure of proteins should be jointly governed by thermodynamic and dynamic factors; free energy is not the exclusive dominant for stability of proteins.     

The design of a peptide sequence to inhibit HIV replication: a search algorithm combining Monte Carlo and self-consistent mean field techniques

We developed a search algorithm combining Monte Carlo (MC) and self-consistent mean field techniques to evolve a peptide sequence that has good binding capability to the anticodon stem and loop (ASL) of human lysine tRNA species, tRNA^Lys3, with the ultimate purpose of breaking the replication cycle of human immunodeficiency virus-1. The starting point is the 15-amino-acid sequence, RVTHHAFLGAHRTVG, found experimentally by Agris and co-workers to bind selectively to hypermodified tRNA^Lys3. The peptide backbone conformation is determined via atomistic simulation of the peptide-ASL^Lys3 complex and then held fixed throughout the search. The proportion of amino acids of various types (hydrophobic, polar, charged, etc.) is varied to mimic different peptide hydration properties. Three different sets of hydration properties were examined in the search algorithm to see how this affects evolution to the best-binding peptide sequences. Certain amino acids are commonly found at fixed sites for all three hydration states, some necessary for binding affinity and some necessary for binding specificity. Analysis of the binding structure and the various contributions to the binding energy shows that: 1) two hydrophilic residues (asparagine at site 11 and the cysteine at site 12) “recognize” the ASL^Lys3 due to the VDW energy, and thereby contribute to its binding specificity and 2) the positively charged arginines at sites 4 and 13 preferentially attract the negatively charged sugar rings and the phosphate linkages, and thereby contribute to the binding affinity.     

广西柿种质资源果实性状多样性分析与模糊综合评价

为进一步揭示广西柿种质资源信息,运用多样性分析和模糊综合评价法对不同生态气候区的柿种质资源果实性状进行研究和评价。结果表明:不同柿种质的果实性状存在丰富的多样性。86份柿种质的模糊综合评价指数FCI值在1.849～3.947之间,平均2.835。根据FCI取值范围将所调查的柿种质分成5个等级,FCI值最高的第5级种质数量最少,占所调查种质的3.49%;FCI值最低的第1级种质数量最多,占所调查种质的48.84%。月柿、牛心柿、大方柿、京柿、鸡心柿、小方柿和火柿等柿品种及一些实生单株的模糊综合评价指数较高,它们的果实综合性状表现较优,建议作为优良品种和单株加以开发和利用。部分单个性状比较优良的实生单株虽不适合于直接推广种植,但可作为柿品种改良的资源加以利用。     

Application of Artificial Bee Colony Algorithm to Maximum Likelihood DOA Estimation

Maximum Likelihood (ML) method has an excellent performance for Direction-Of-Arrival (DOA) estimation, but a multidimensional nonlinear solution search is required which complicates the computation and prevents the method from practical use. To reduce the high computational burden of ML method and make it more suitable to engineering applications, we apply the Artificial Bee Colony (ABC) algorithm to maximize the likelihood function for DOA estimation. As a recently proposed bio-inspired computing algorithm, ABC algorithm is originally used to optimize multivariable functions by imitating the behavior of bee colony finding excellent nectar sources in the nature environment. It offers an excellent alternative to the conventional methods in ML-DOA estimation. The performance of ABC-based ML and other popular meta-heuristic-based ML methods for DOA estimation are compared for various scenarios of convergence, Signal-to-Noise Ratio (SNR), and number of iterations. The computation loads of ABC-based ML and the conventional ML methods for DOA estimation are also investigated. Simulation results demonstrate that the proposed ABC based method is more efficient in computation and statistical performance than other ML-based DOA estimation methods.     

Optimization-driven identification of genetic perturbations accelerates the convergence of model parameters in ensemble modeling of metabolic networks

The ensemble modeling (EM) approach has shown promise in capturing kinetic and regulatory effects in the modeling of metabolic networks. Efficacy of the EM procedure relies on the identification of model parameterizations that adequately describe all observed metabolic phenotypes upon perturbation. In this study, we propose an optimization-based algorithm for the systematic identification of genetic/enzyme perturbations to maximally reduce the number of models retained in the ensemble after each round of model screening. The key premise here is to design perturbations that will maximally scatter the predicted steady-state fluxes over the ensemble parameterizations. We demonstrate the applicability of this procedure for an Escherichia coli metabolic model of central metabolism by successively identifying single, double, and triple enzyme perturbations that cause the maximum degree of flux separation between models in the ensemble. Results revealed that optimal perturbations are not always located close to reaction(s) whose fluxes are measured, especially when multiple perturbations are considered. In addition, there appears to be a maximum number of simultaneous perturbations beyond which no appreciable increase in the divergence of flux predictions is achieved. Overall, this study provides a systematic way of optimally designing genetic perturbations for populating the ensemble of models with relevant model parameterizations.