Evolutionary-inspired probabilistic search for enhancing sampling of local minima in the protein energy surface

<p>Abstract</p> <p>Background</p> <p>Despite computational challenges, elucidating conformations that a protein system assumes under physiologic conditions for the purpose of biological activity is a central problem in computational structural biology. While these conformations are associated with low energies in the energy surface that underlies the protein conformational space, few existing conformational search algorithms focus on explicitly sampling low-energy local minima in the protein energy surface.</p> <p>Methods</p> <p>This work proposes a novel probabilistic search framework, PLOW, that explicitly samples low-energy local minima in the protein energy surface. The framework combines algorithmic ingredients from evolutionary computation and computational structural biology to effectively explore the subspace of local minima. A greedy local search maps a conformation sampled in conformational space to a nearby local minimum. A perturbation move jumps out of a local minimum to obtain a new starting conformation for the greedy local search. The process repeats in an iterative fashion, resulting in a trajectory-based exploration of the subspace of local minima.</p> <p>Results and conclusions</p> <p>The analysis of PLOW's performance shows that, by navigating only the subspace of local minima, PLOW is able to sample conformations near a protein's native structure, either more effectively or as well as state-of-the-art methods that focus on reproducing the native structure for a protein system. Analysis of the actual subspace of local minima shows that PLOW samples this subspace more effectively that a naive sampling approach. Additional theoretical analysis reveals that the perturbation function employed by PLOW is key to its ability to sample a diverse set of low-energy conformations. This analysis also suggests directions for further research and novel applications for the proposed framework.</p

OPT-GAN: Black-Box Global Optimization via Generative Adversarial Nets

Black-box optimization (BBO) algorithms are concerned with finding the best solutions for problems with missing analytical details. Most classical methods for such problems are based on strong and fixed a priori assumptions, such as Gaussianity. However, the complex real-world problems, especially when the global optimum is desired, could be very far from the a priori assumptions because of their diversities, causing unexpected obstacles to these methods. In this study, we propose a generative adversarial net-based broad-spectrum global optimizer (OPT-GAN) which estimates the distribution of optimum gradually, with strategies to balance exploration-exploitation trade-off. It has potential to better adapt to the regularity and structure of diversified landscapes than other methods with fixed prior, e.g. Gaussian assumption or separability. Experiments conducted on BBO benchmarking problems and several other benchmarks with diversified landscapes exhibit that OPT-GAN outperforms other traditional and neural net-based BBO algorithms.Comment: M. Lu and S. Ning contribute equally. Submitted to IEEE transactions on Neural Networks and Learning System

Development of an evolutionary algorithm for crystal structure prediction

Die vorliegende Dissertation befasst sich mit der theoretischen Vorhersage neuer Materialien. Ein evolutionärer Algorithmus, der zur Lösung dieses globalen Optimierungsproblems Konzepte der natürlichen Evolution imitiert, wurde entwickelt und ist als Programmpaket EVO frei verfügbar. EVO findet zuverlässig sowohl bekannte als auch neuartige Kristallstrukturen. Beispielsweise wurden die Strukturen von Germaniumnitrofluorid, einer neue Borschicht und mit dem gekreuzten Graphen einer bisher unbekannte Kohlenstoffstruktur gefunden. Ferner wurde in der Arbeit gezeigt, dass das reine Auffinden solcher Strukturen der erste Teil einer erfolgreichen Vorhersage ist. Weitere aufwendige Berechnungen sind nötig, die Aufschluss über die Stabilität der hypothetischen Struktur geben und Aussagen über zu erwartende Materialeigenschaften liefern

A global optimization approach for searching low energy conformations of proteins

De novo protein structure prediction and understanding the protein folding mechanism is an outstanding challenge of Biological Physics. Relying on the thermodynamic hypothesis of protein folding it is expected that the native state of a protein can be found out if the global minimum of the free energy surface is found. To understand the energy landscape or the free energy surface is challenging. The structure and dynamics of proteins are the manifestations of the underlying potential energy surface. Here the potential energy function stands on a framework of all-atom representation and uses purely physics-based interactions. For the solvated proteins the effective free energy is defined as an implicit solvation model which includes the solvation free energy, along with a standard all-atom biomolecular forcefield. A major challenge is to search for the global minimum on this effective free energy surface. In this work the Minima Hopping Algorithm (MHOP) to find global minima on potential energy surfaces has been used for protein structure prediction or in general finding the lowest energy conformations of proteins. Here proteins have been studied both in vacuo and in the aqueous medium. For short peptides starting from a completely extended conformation we could find conformational minima which are very close to the experimentally observed structures

Preventing premature convergence and proving the optimality in evolutionary algorithms

http://ea2013.inria.fr//proceedings.pdfInternational audienceEvolutionary Algorithms (EA) usually carry out an efficient exploration of the search-space, but get often trapped in local minima and do not prove the optimality of the solution. Interval-based techniques, on the other hand, yield a numerical proof of optimality of the solution. However, they may fail to converge within a reasonable time due to their inability to quickly compute a good approximation of the global minimum and their exponential complexity. The contribution of this paper is a hybrid algorithm called Charibde in which a particular EA, Differential Evolution, cooperates with a Branch and Bound algorithm endowed with interval propagation techniques. It prevents premature convergence toward local optima and outperforms both deterministic and stochastic existing approaches. We demonstrate its efficiency on a benchmark of highly multimodal problems, for which we provide previously unknown global minima and certification of optimality

From RNA folding to inverse folding: a computational study: Folding and design of RNA molecules

Since the discovery of the structure of DNA in the early 1953s and its double-chained complement of information hinting at its means of replication, biologists have recognized the strong connection between molecular structure and function. In the past two decades, there has been a surge of research on an ever-growing class of RNA molecules that are non-coding but whose various folded structures allow a diverse array of vital functions. From the well-known splicing and modification of ribosomal RNA, non-coding RNAs (ncRNAs) are now known to be intimately involved in possibly every stage of DNA translation and protein transcription, as well as RNA signalling and gene regulation processes. Despite the rapid development and declining cost of modern molecular methods, they typically can only describe ncRNA's structural conformations in vitro, which differ from their in vivo counterparts. Moreover, it is estimated that only a tiny fraction of known ncRNAs has been documented experimentally, often at a high cost. There is thus a growing realization that computational methods must play a central role in the analysis of ncRNAs. Not only do computational approaches hold the promise of rapidly characterizing many ncRNAs yet to be described, but there is also the hope that by understanding the rules that determine their structure, we will gain better insight into their function and design. Many studies revealed that the ncRNA functions are performed by high-level structures that often depend on their low-level structures, such as the secondary structure. This thesis studies the computational folding mechanism and inverse folding of ncRNAs at the secondary level. In this thesis, we describe the development of two bioinformatic tools that have the potential to improve our understanding of RNA secondary structure. These tools are as follows: (1) RAFFT for efficient prediction of pseudoknot-free RNA folding pathways using the fast Fourier transform (FFT)}; (2) aRNAque, an evolutionary algorithm inspired by Lévy flights for RNA inverse folding with or without pseudoknot (A secondary structure that often poses difficulties for bio-computational detection). The first tool, RAFFT, implements a novel heuristic to predict RNA secondary structure formation pathways that has two components: (i) a folding algorithm and (ii) a kinetic ansatz. When considering the best prediction in the ensemble of 50 secondary structures predicted by RAFFT, its performance matches the recent deep-learning-based structure prediction methods. RAFFT also acts as a folding kinetic ansatz, which we tested on two RNAs: the CFSE and a classic bi-stable sequence. In both test cases, fewer structures were required to reproduce the full kinetics, whereas known methods (such as Treekin) required a sample of 20,000 structures and more. The second tool, aRNAque, implements an evolutionary algorithm (EA) inspired by the Lévy flight, allowing both local global search and which supports pseudoknotted target structures. The number of point mutations at every step of aRNAque's EA is drawn from a Zipf distribution. Therefore, our proposed method increases the diversity of designed RNA sequences and reduces the average number of evaluations of the evolutionary algorithm. The overall performance showed improved empirical results compared to existing tools through intensive benchmarks on both pseudoknotted and pseudoknot-free datasets. In conclusion, we highlight some promising extensions of the versatile RAFFT method to RNA-RNA interaction studies. We also provide an outlook on both tools' implications in studying evolutionary dynamics