Predicting scheme of RNA folding structure including pseudoknots

The prediction of RNA structure with pseudoknots is a nondeterministic polynomial-time hard (NP-hard) problem; according to minimum free energy models and computational methods, we investigate the RNA-pseudoknotted structure. Our paper presents an efficient algorithm for predicting RNA structure with pseudoknots, and the algorithm takes O([Formula: see text]) time and O([Formula: see text]) space, the experimental tests in Rfam10.1 and PseudoBase indicate that the algorithm is more effective and precise. The predicting accuracy, the time complexity and space complexity outperform existing algorithms, such as Maximum Weight Matching (MWM) algorithm, PKNOTS algorithm and Inner Limiting Layer (ILM) algorithm, and the algorithm can predict arbitrary pseudoknots. And there exists a [Formula: see text] ([Formula: see text]) polynomial time approximation scheme in searching maximum number of stackings, and we give the proof of the approximation scheme in RNA-pseudoknotted structure. We have improved several types of pseudoknots considered in RNA folding structure, and analyze their possible transitions between types of pseudoknots.

The paper further investigates the computational problem and complexity of predicting Ribonucleic Acid structure in order to find a way to optimize the Ribonucleic Acid pseudoknotted structure in electronics engineering. We investigate the Ribonucleic Acid pseudoknotted structure based on thermal dynamic model, computational methods and models with minimum free energy are adopted to predict Ribonucleic Acid structure. The contribution of this paper is to obtain an efficient algorithm for finding RNA pseudoknotted structure. Compared with other algorithms, the heuristic algorithm takes O(n3) time and O(n2) space. The experimental test in PseudoBase shows that the algorithm is more effective and exact than other algorithms, and the algorithm can predict arbitrary pseudoknots.

Over the last few years, many optimization algorithms have been developed to predict the optimal secondary structure of ribonucleic acid (RNA) with “minimum free energy” (MFE). These algorithms are either inspired by dynamic programming or by meta-heuristic techniques. RNA participates in several biological activities in the organism. These activities involve protein synthesis, understanding the functional behavior of RNA molecules, coding, decoding and gene expression, carrier of transferring genetic information, formation of protein, catalyst in biomedical reactions and structural molecule in cellular organelles, transcription, etc. Beside the said activities, the major role of RNA is in developing new drugs and understanding several diseases occurred due to genetic disorder and viruses. For the above said activities, it is required to predict the correct RNA secondary structure having minimum free energy with desired prediction accuracy. This paper presents a meta-heuristic optimization algorithm to obtain the optimal secondary structure of RNA with required functionality and requires less time than the others in the literature. The performance of the proposed algorithm is checked with different existing state-of-the-art techniques. It is found that the proposed algorithm gives better results against the other techniques.

Determination of Ribonucleic Acid structure is challenging, in order to optimize the RNA pseudoknotted structure,the paper investigates the computational problem and complexity of predicting RNA structure. A new computational method and model with minimum free energy are adopted to predict RNA structure. The main contribution of the paper is to achieves an efficient approximation algorithm for finding RNA pseudoknotted structure and nested structures. We have compared with other algorithms in time complexity and space complexity, the approximation algorithm takes O(n3) time and O(n2) space,where n is the length of the RNA sequences. The experimental tests for a large database of RNA show that the algorithm is more exact and effective than the algorithms, the algorithm can predict arbitrary pseudoknots, and improve the a predicting accuracy.

Ribonucleic acid (RNA) is a polymeric nucleic acid that is crucial for cellular function, regulating gene expression and encoding/decoding protein/DNA molecules. Recent discoveries of diverse functionality in non-coding RNAs have led to unprecedented demand for RNA 3D structure determination. With current technology, general, accurate prediction of 3D structures for large RNAs from the sequence remains computationally intractable. One of the principal challenges arises from the conformational flexibility of RNA, especially in loop/junction regions, which results in a rugged energy landscape. Several strategies exist to overcome this challenge, including incorporation of efficient experimental information and coarse-grained (CG) modeling to improve computational sampling of the structural ensemble. A second challenge is the inclusion of naturally modified derivatives of canonical RNA nucleotides in structure analysis. Most RNA prediction strategies rely upon the canonical nucleotides (adenine (A), uracil (U), guanine (G), and cytosine (C)), ignoring the effects of modified nucleotides on the structure and system dynamics. In general, RNA molecules contain rigid and flexible structural elements, which can be probed using efficient selective 2'-hydroxyl analyzed by primer extension (SHAPE) experiments. SHAPE experiments selectively modify flexible RNA nucleotides and can be processed to produce a characteristic reactivity profile for an RNA molecule that contains structural information. Incorporation of efficient experimental information, such as SHAPE, in predicting RNA 3D structure is highly desirable for overcoming the current knowledge gap between RNA sequence and 3D structure. In the first project, we introduce a physics-based model, the 3D structure-SHAPE relationship (3DSSR) model, to predict the SHAPE reactivity from the structure and show how this model may be used to sieve SHAPE-compatible structures from a pool of low-energy decoys and refine our predictions. In the second project, we compare 3DSSR performance to that of a convolutional neural network (CNN) trained on the SHAPE data and RNA structures, showing that 3DSSR outperforms the CNN given the limited data available. In the third project, we further improve the 3DSSR model, gaining deeper insights into the SHAPE reaction and biases. In the fourth project, we explore the theory underpinning the iterative simulated CG RNA folding model (IsRNA). In establishing the underlying mechanics driving the success of the model, we were able to clarify and improve the parameterization method while expanding the model interpretation, which should broaden application of the method to other biopolymers, such as protein. We found that the parameterization method follows statistical mechanics principles but also has a Bayesian interpretation. Further, we found that the parameterization process can benefit from application of the principle of maximum entropy, which improves simulation and parameterization efficiency. In the fifth project, we investigate the impact of nucleotide modification on the structure and configurational ensemble of RNA molecules using free energy calculations. By applying modifications to a common RNA hairpin, we estimate the impact on the stability of the structural ensemble, identifying specific interactions that drive changes to the potential of mean force (PMF) and showing the context and modification-dependence of the variable alterations to the structure stability.

Ribonucleic Acid (RNA) has important structural and functional roles in the cell and plays roles in many stages of protein synthesis. The structure of RNA largely determines its function. Current physical methods for structure determination are time-consuming and expensive, thus the methods for the computational prediction of structure are necessary. Various algorithms that have been used for RNA structure prediction based in minimum free energy include dynamic programming (DP) and meta heuristic algorithms. One of the most recent meta heuristic algorithms is Musician's behavior-inspired harmony search (HS) algorithm that has been successful in numerous complex optimization problems. This paper builds on the previous work of the harmony search algorithm (HSRNAFold) which was used to find the RNA secondary structure with minimum free energy. In this paper, the accuracy of prediction is compared to the dynamic programming technique RNAFold. The results show that HSRNAFold is able to predict more accurate structures than RNAFold for all test sequences.

One of polymeric biological molecules called ribonucleic acid (RNA) is involved in diverse biological roles in regulation of gene expression. Generally, secondary structures of RNA determine their functions in living organisms. In medical field, various structures of synthetic RNAs are much needed at present. Recently, an RNA design tool has been developed to identify optimal RNA sequences for the desired interacting RNAs based on Genetic Algorithm (GA). In an attempt to improve the design tool, we applied Artificial Bee Colony (ABC) algorithm, which can outperform several population-based methods including GA. To achieve this goal, we developed an ABC-based RNA design tool and employed this tool to design 6 different interacting RNA models. The design performance from ABC-based tool for all models were compared with that from the existing GA-based tool. It was found that the ABC-based tool and the GA-based tools equally perform in all 6 models. Both tools can achieve the fitness score above 0.996. Although the ABC-based tool could be used to design interacting RNA more reliably, it seems to require more design time, especially in the models with larger RNA length. Thus, with further improvement, this tool shall be a promising tool for designing synthetic RNA devices for biomedical applications.

Modeling of RNA secondary structures using two-way quantum finite automata

We present the first polynomial-time approximation scheme (PTAS), i.e., (1+e)-approximation algorithm for any constant e> 0, for the planar group Steiner tree problem (in which each group lies on a boundary of a face). This result improves on the best previous approximation factor of O(logn (loglogn)O(1)). We achieve this result via a novel and powerful technique called spanner bootstrapping, which allows one to bootstrap from a superconstant approximation factor (even superpolynomial in the input size) all the way down to a PTAS. This is in contrast with the popular existing approach for planar PTASs of constructing light-weight spanners in one iteration, which notably requires a constant-factor approximate solution to start from. Spanner bootstrapping removes one of the main barriers for designing PTASs for problems which have no known constant-factor approximation (even on planar graphs), and thus can be used to obtain PTASs for several difficult-to-approximate problems. Our second major contribution required for the planar group Steiner tree PTAS is a spanner construction, which reduces the graph to have total weight within a factor of the optimal solution while approximately preserving the optimal solution. This is particularly challenging because group Steiner tree requires deciding which terminal in each group to connect by the tree, making it much harder than recent previous approaches to construct spanners for planar TSP by Klein [SIAM J. Computing 2008], subset TSP by Klein [STOC 2006], Steiner tree by Borradaile, Klein, and Mathieu [ACM Trans. Algorithms 2009], and Steiner forest by Bateni, Hajiaghayi, and Marx [J. ACM 2011] (and its improvement to an efficient PTAS by Eisenstat, Klein, and Mathieu [SODA 2012]. The main conceptual contribution here is realizing that selecting which terminals may be relevant is essentially a complicated prize-collecting process: we have to carefully weigh the cost and benefits of reaching or avoiding certain terminals in the spanner. Via a sequence of involved prize-collecting procedures, we can construct a spanner that reaches a set of terminals that is sufficient for an almost-optimal solution. Our PTAS for planar group Steiner tree implies the first PTAS for geometric Euclidean group Steiner tree with obstacles, as well as a (2+)-approximation algorithm for group TSP with obstacles, improving over the best previous constant-factor approximation algorithms. By contrast, we show that planar group Steiner forest, a slight generalization of planar group Steiner tree, is APX-hard on planar graphs of treewidth 3, even if the groups are pairwise disjoint and every group is a vertex or an edge.

PurposeThe purpose of this paper is to find the best approximation algorithm for solving the more general case of single‐supplier multi‐retailer capacitated economic lot‐sizing (SM‐CELS) problem in deterministic inventory theory, which is the non‐deterministic polynomial (NP)‐hard problem.Design/methodology/approachSince few theoretical results have been published on polynomial time approximation algorithms for SM‐CELS problems, this paper develops a fully polynomial time approximation scheme (FPTAS) for the problem with monotone production and holding‐backlogging cost functions. First the optimal solution of a rounded problem is presented as the approximate solution and its straightforward dynamic‐programming (DP) algorithm. Then the straightforward DP algorithm is converted into an FPTAS by exploiting combinatorial properties of the recursive function.FindingsAn FPTAS is designed for the SM‐CELS problem with monotone cost functions, which is the strongest polynomial time approximation result.Research limitations/implicationsThe main limitation is that the supplier only manufactures without holding any products when the model is applied.Practical implicationsThe paper presents the best result for the SM‐CELS problem in deterministic inventory theory.Originality/valueThe LP‐rounding technique, an effective approach to design approximation algorithms for NP‐hard problems, is successfully applied to the SM‐CELS problem in this paper.

A faster FPTAS for knapsack problem with cardinality constraint

The role of ribonucleic acid (RNA) in biology continues to grow, but insight into important aspects of RNA behavior is lacking, such as dynamic structural ensembles in different environments, how flexibility is coupled to function, and how function might be modulated by small molecule binding. In the case of proteins, much progress in these areas has been made by complementing experiments with atomistic simulations, but RNA simulation methods and force fields are less mature. It remains challenging to generate stable RNA simulations, even for small systems where well-defined, thermostable structures have been established by experiments. Many different aspects of RNA energetics have been adjusted in force fields, seeking improvements that are transferable across a variety of RNA structural motifs. In this work, the role of weak CH···O interactions is explored, which are ubiquitous in RNA structure but have received less attention in RNA force field development. By comparing data extracted from high-resolution RNA crystal structures to energy profiles from quantum mechanics and force field calculations, it is shown that CH···O interactions are overly repulsive in the widely used Amber RNA force fields. A simple, targeted adjustment of CH···O repulsion that leaves the remainder of the force field unchanged was developed. Then, the standard and modified force fields were tested using molecular dynamics (MD) simulations with explicit water and salt, amassing over 300 μs of data for multiple RNA systems containing important features such as the presence of loops, base stacking interactions as well as canonical and noncanonical base pairing. In this work and others, standard force fields lead to reproducible unfolding of the NMR-based structures. Including a targeted CH···O adjustment in an otherwise identical protocol dramatically improves the outcome, leading to stable simulations for all RNA systems tested.

The structure of RiboNucleic Acid (RNA) has the potential to be altered by a Single Nucleotide Polymorphism (SNP). Disease-associated SNPs mapping to non-coding regions of the genome that are transcribed into RiboNucleic Acid (RNA) can potentially affect cellular regulation (and cause disease) by altering the structure of the transcript. We performed a large-scale meta-analysis of Selective 2'-Hydroxyl Acylation analyzed by Primer Extension (SHAPE) data, which probes the structure of RNA. We found that several single point mutations exist that significantly disrupt RNA secondary structure in the five transcripts we analyzed. Thus, every RNA that is transcribed has the potential to be a “RiboSNitch;” where a SNP causes a large conformational change that alters regulatory function. Predicting the SNPs that will have the largest effect on RNA structure remains a contemporary computational challenge. We therefore benchmarked the most popular RNA structure prediction algorithms for their ability to identify mutations that maximally affect structure. We also evaluated metrics for rank ordering the extent of the structural change. Although no single algorithm/metric combination dramatically outperformed the others, small differences in AUC (Area Under the Curve) values reveal that certain approaches do provide better agreement with experiment. The experimental data we analyzed nonetheless show that multiple single point mutations exist in all RNA transcripts that significantly disrupt structure in agreement with the predictions.

We consider the problem of scheduling with renewable speed-up resources. Given m identical machines, n jobs and c different discrete resources, the task is to schedule each job non-preemptively onto one of the machines so as to minimize the makespan. In our problem, a job has its original processing time, which could be reduced by utilizing one of the resources. As resources are different, the amount of the time reduced for each job is different depending on the resource it uses. Once a resource is being used by one job, it can not be used simultaneously by any other job until this job is finished, hence the scheduler should take into account the job-to-machine assignment together with the resource-to-job assignment. We observe that, the classical unrelated machine scheduling problem is actually a special case of our problem when m=c, i.e., the number of resources equals the number of machines. Extending the techniques for the unrelated machine scheduling, we give a 2-approximation algorithm when both m and c are part of the input. We then consider two special cases for the problem, with m or c being a constant, and derive PTASes (Polynomial Time Approximation Schemes) respectively. We also establish the relationship between the two parameters m and c, through which we are able to transform the PTAS for the case when m is constant to the case when c is a constant. The relationship between the two parameters reveals the structure within the problem, and may be of independent interest.

#NFA refers to the problem of counting the words of length n accepted by a non-deterministic finite automaton. #NFA is #P-hard, and although fully-polynomial-time randomized approximation schemes (FPRAS) exist, they are all impractical. The first FPRAS for #NFA had a running time of Õ(n 17 m 17 ε -14 łog(δ -1 )), where m is the number of states in the automaton, δ ∈ (0,1] is the confidence parameter, and ε > 0 is the tolerance parameter (typically smaller than 1). The current best FPRAS achieved a significant improvement in the time complexity relative to the first FPRAS and obtained FPRAS with time complexity Õ((n 10 m 2 + n 6 m 3 )ε -4 łog 2 (δ -1 )). The complexity of the improved FPRAS is still too intimidating to attempt any practical implementation. In this paper, we pursue the quest for practical FPRAS for #NFA by presenting a new algorithm with a time complexity of O(n 2 m 3 łog(nm)ε -2 łog(δ -1 )). Observe that evaluating whether a word of length n is accepted by an NFA has a time complexity of O(nm 2 ). Therefore, our proposed FPRAS achieves sub-quadratic complexity with respect to membership checks.