A P system and a constructive membrane-inspired DNA algorithm for solving the Maximum Clique Problem

We present a P system with replicated rewriting to solve the Maximum Clique Problem for a graph. Strings representing cliques are built gradually. This involves the use of inhibitors that control the space of all generated solutions to the problem. Calculating the maximum clique for a graph is a highly relevant issue not only on purely computational grounds, but also because of its relationship to fundamental problems in genomics. We propose to implement the designed P system by means of a DNA algorithm. This algorithm is then compared with two standard papers that addressed the same problem and its DNA implementation in the past. This comparison is carried out on the basis of a series of computational and physical parameters. Our solution features a significantly lower cost in terms of time, the number and size of strands, as well as the simplicity of the biological implementation.     

NAS Grid Benchmarks: A Tool for Grid Space Exploration

We present a benchmark suite for computational Grids. It is based on the NAS Parallel Benchmarks (NPB) and is called NAS Grid Benchmark (NGB) in this paper. We present NGB as a data flow graph encapsulating an instance of an NPB code in each graph node, which communicates with other nodes by sending/receiving initialization data. These nodes may be mapped to the same or different Grid machines. Like NPB, NGB specifies several different classes (problem sizes). NGB also specifies the generic Grid services sufficient for running the suite. The implementor has the freedom to choose any Grid environment. We describe a reference implementation in Java, and present some scenarios for using NGB.     

基于质粒DNA匹配问题的分子算法

给定无向图,图的最小极大匹配问题是寻找每条边都不相邻的最大集中的最小者,这个问题是著名的NP-完全问题.1994年Adleman博士首次提出用DNA计算解决NP-完全问题,以编码的DNA序列为运算对象,通过分子生物学的运算操作解决复杂的数学难题,使得NP-完全问题的求解可能得到解决.提出了基于质粒DNA的无向图的最大匹配问题的DNA分子生物算法,通过限制性内切酶的酶切和凝胶电泳完成解的产生和最终接的分离,依据分子生物学的实验手段,算法是有效并且可行的.     

A CLIQUE algorithm using DNA computing techniques based on closed-circle DNA sequences

DNA computing has been applied in broad fields such as graph theory, finite state problems, and combinatorial problem. DNA computing approaches are more suitable used to solve many combinatorial problems because of the vast parallelism and high-density storage. The CLIQUE algorithm is one of the gird-based clustering techniques for spatial data. It is the combinatorial problem of the density cells. Therefore we utilize DNA computing using the closed-circle DNA sequences to execute the CLIQUE algorithm for the two-dimensional data. In our study, the process of clustering becomes a parallel bio-chemical reaction and the DNA sequences representing the marked cells can be combined to form a closed-circle DNA sequences. This strategy is a new application of DNA computing. Although the strategy is only for the two-dimensional data, it provides a new idea to consider the grids to be vertexes in a graph and transform the search problem into a combinatorial problem.     

DNA computing the Hamiltonian path problem

The directed Hamiltonian path (DHP) problem is one of the hard computational problems for which there is no practical algorithm on a conventional computer available. Many problems, including the traveling sales person problem and the longest path problem, can be translated into the DHP problem, which implies that an algorithm for DHP can also solve all the translated problems. To study the robustness of the laboratory protocol of the pioneering DNA computing for the DHP problem performed by Leonard Adleman (1994), we investigated how the graph size, multiplicity of the Hamiltonian paths, and the size of oligonucleotides that encode the vertices would affect the laboratory procedures. We applied Adleman's protocol with 18-mer oligonucleotide per node to a graph with 8 vertices and 14 edges containing two Hamiltonian paths (Adleman used 20-mer oligonucleotides for a graph with 7 nodes, 14 edges and one Hamiltonian path). We found that depending on the graph characteristics such as the number of short cycles, the oligonucleotide size, and the hybridization conditions that used to encode the graph, the protocol should be executed with different parameters from Adleman's.     

Parallel Clustering Algorithm for Large Data Sets with Applications in Bioinformatics

Large sets of bioinformatical data provide a challenge in time consumption while solving the cluster identification problem, and that is why a parallel algorithm is so needed for identifying dense clusters in a noisy background. Our algorithm works on a graph representation of the data set to be analyzed. It identifies clusters through the identification of densely intraconnected subgraphs. We have employed a minimum spanning tree (MST) representation of the graph and solve the cluster identification problem using this representation. The computational bottleneck of our algorithm is the construction of an MST of a graph, for which a parallel algorithm is employed. Our high-level strategy for the parallel MST construction algorithm is to first partition the graph, then construct MSTs for the partitioned subgraphs and auxiliary bipartite graphs based on the subgraphs, and finally merge these MSTs to derive an MST of the original graph. The computational results indicate that when running on 150 CPUs, our algorithm can solve a cluster identification problem on a data set with 1,000,000 data points almost 100 times faster than on single CPU, indicating that this program is capable of handling very large data clustering problems in an efficient manner. We have implemented the clustering algorithm as the software CLUMP.     

基于分子信标的DNA计算

DNA计算是解决一类难以计算问题的一种新方法,这种计算随着问题的增大可以呈指数增长．迄今为止,许多研究成果已经成功地提高了它的性能和增加了它的可行性,本文在基于表面的DNA计算中采用了分子信标编码策略,并对分子信标在与对应的补链杂交形成双链时的受力进行分析,给出3-SAT问题的另一种解法．这种方法比现有的方法更有效,更具发展前景．因为它具有编码简单;耗材底;操作时间短;技术先进等优点．本文尝试了分子生物学,光学和力学的结合．这一工作为DNA计算能解决NP一完全问题提供了更有力的依据．     

A computational study of liposome logic: towards cellular computing from the bottom up

In this paper we propose a new bottom-up approach to cellular computing, in which computational chemical processes are encapsulated within liposomes. This “liposome logic” approach (also called vesicle computing) makes use of supra-molecular chemistry constructs, e.g. protocells, chells, etc. as minimal cellular platforms to which logical functionality can be added. Modeling and simulations feature prominently in “top-down” synthetic biology, particularly in the specification, design and implementation of logic circuits through bacterial genome reengineering. The second contribution in this paper is the demonstration of a novel set of tools for the specification, modelling and analysis of “bottom-up” liposome logic. In particular, simulation and modelling techniques are used to analyse some example liposome logic designs, ranging from relatively simple NOT gates and NAND gates to SR-Latches, D Flip-Flops all the way to 3 bit ripple counters. The approach we propose consists of specifying, by means of P systems, gene regulatory network-like systems operating inside proto-membranes. This P systems specification can be automatically translated and executed through a multiscaled pipeline composed of dissipative particle dynamics (DPD) simulator and Gillespie’s stochastic simulation algorithm (SSA). Finally, model selection and analysis can be performed through a model checking phase. This is the first paper we are aware of that brings to bear formal specifications, DPD, SSA and model checking to the problem of modeling target computational functionality in protocells. Potential chemical routes for the laboratory implementation of these simulations are also discussed thus for the first time suggesting a potentially realistic physiochemical implementation for membrane computing from the bottom-up.     

Efficient extraction of mapping rules of atoms from enzymatic reaction data.

Many computational problems and methods have been proposed for analysis of biological pathways. Among them, this paper focuses on extraction of mapping rules of atoms from enzymatic reaction data, which is useful for drug design, simulation of tracer experiments, and consistency checking of pathway databases. Most of existing methods for this problem are based on maximal common subgraph algorithms. In this paper, we propose a novel approach based on graph partition and graph isomorphism. We show that this problem is NP-hard in general, but can be solved in polynomial time for wide classes of enzymatic reactions. We also present an O(n(1.5)) time algorithm for a special but fundamental class of reactions, where n is the maximum size of compounds appearing in a reaction. We develop practical polynomial-time algorithms in which the Morgan algorithm is used for computing the normal form of a graph, where it is known that the Morgan algorithm works correctly for most chemical structures. Computational experiments are performed for these practical algorithms using the chemical reaction data stored in the KEGG/LIGAND database. The results of computational experiments suggest that practical algorithms are useful in many cases.     

Three dimensional DNA structures in computing

We show that 3-dimensional graph structures can be used for solving computational problems with DNA molecules. Vertex building blocks consisting of k-armed (k = 3 or 4) branched junction molecules are used to form graphs. We present procedures for the 3-SAT and 3-vertex-colorability problems. Construction of one graph structure (in many copies) is sufficient to determine the solution to the problem. In our proposed procedure for 3-SAT, the number of steps required is equal to the number of variables in the formula. For the 3-vertex-colorability problem, the procedure requires a constant number of steps regardless of the size of the graph.     

Pairwise alignment of protein interaction networks.

With an ever-increasing amount of available data on protein-protein interaction (PPI) networks and research revealing that these networks evolve at a modular level, discovery of conserved patterns in these networks becomes an important problem. Although available data on protein-protein interactions is currently limited, recently developed algorithms have been shown to convey novel biological insights through employment of elegant mathematical models. The main challenge in aligning PPI networks is to define a graph theoretical measure of similarity between graph structures that captures underlying biological phenomena accurately. In this respect, modeling of conservation and divergence of interactions, as well as the interpretation of resulting alignments, are important design parameters. In this paper, we develop a framework for comprehensive alignment of PPI networks, which is inspired by duplication/divergence models that focus on understanding the evolution of protein interactions. We propose a mathematical model that extends the concepts of match, mismatch, and gap in sequence alignment to that of match, mismatch, and duplication in network alignment and evaluates similarity between graph structures through a scoring function that accounts for evolutionary events. By relying on evolutionary models, the proposed framework facilitates interpretation of resulting alignments in terms of not only conservation but also divergence of modularity in PPI networks. Furthermore, as in the case of sequence alignment, our model allows flexibility in adjusting parameters to quantify underlying evolutionary relationships. Based on the proposed model, we formulate PPI network alignment as an optimization problem and present fast algorithms to solve this problem. Detailed experimental results from an implementation of the proposed framework show that our algorithm is able to discover conserved interaction patterns very effectively, in terms of both accuracies and computational cost.     

Genetic code symmetry and efficient design of GC-constrained coding sequences

MOTIVATION: Cloning of long DNA sequences (40-60 bases) into phage display libraries using polymerase chain reaction (PCR) is a low efficiency process, in which PCR is used to incorporate a DNA insert, coding for a certain peptide, into the amplified sequence. The PCR efficiency in this process is strongly affected by the distribution of G-C bases in the amplified sequence. As any DNA insert coding for the target peptide may be attempted, there is a flexibility in choosing part of the amplified sequence. Since the number of inserts coding for the same peptide is exponential in the peptide length, a computational problem naturally arises--that of efficiently finding an insert, whose parameters are optimal for PCR cloning. RESULTS: The GC distribution requirements are formulated as a search problem. We developed an efficient, linear time 'one pass' algorithm for this problem. Interestingly, our algorithm strongly relies on an interesting symmetry, which we observed in the standard genetic code. Most non-standard genetic codes examined possess this symmetry as well, yet some do not. We generalize the search problem and consider the case of a non-standard, or arbitrary, genetic code where this symmetry does not necessary hold. We solve the generalized problem in polynomial, but nonlinear, time. AVAILABILITY: An implementation of the proposed algorithm is available upon request from the authors.     

Computing with DNA by operating on plasmids

A new method of computing using DNA plasmids is introduced and the potential advantages are listed. The new method is illustrated by reporting a laboratory computation of an instance of the NP-complete algorithmic problem of computing the cardinal number of a maximal independent subset of the vertex set of a graph. A circular DNA plasmid, specifically designed for this method of molecular computing, was constructed. This computational plasmid contains a specially inserted series of DNA sequence segments, each of which is bordered by a characteristic pair of restriction enzyme sites. For the computation reported here, the DNA sequence segments of this series were used to represent the vertices of the graph being investigated. By applying a scheme of enzymatic treatments to the computational plasmids, modified plasmids were generated from which the solution of the computational problem was selected. This new method of computing is applicable to a wide variety of algorithmic problems. Further computations in this style are in progress.     

An Eulerian path approach to global multiple alignment for DNA sequences.

With the rapid increase in the dataset of genome sequences, the multiple sequence alignment problem is increasingly important and frequently involves the alignment of a large number of sequences. Many heuristic algorithms have been proposed to improve the speed of computation and the quality of alignment. We introduce a novel approach that is fundamentally different from all currently available methods. Our motivation comes from the Eulerian method for fragment assembly in DNA sequencing that transforms all DNA fragments into a de Bruijn graph and then reduces sequence assembly to a Eulerian path problem. The paper focuses on global multiple alignment of DNA sequences, where entire sequences are aligned into one configuration. Our main result is an algorithm with almost linear computational speed with respect to the total size (number of letters) of sequences to be aligned. Five hundred simulated sequences (averaging 500 bases per sequence and as low as 70% pairwise identity) have been aligned within three minutes on a personal computer, and the quality of alignment is satisfactory. As a result, accurate and simultaneous alignment of thousands of long sequences within a reasonable amount of time becomes possible. Data from an Arabidopsis sequencing project is used to demonstrate the performance.     

An Efficient Algorithm for Mapping of Reads to a Genome Graph Using an Index Based on Hash Tables and Dynamic Programming

The problem of storage of the sequences of a number of closely related genomes and analysis of genome variations is considered. A genome graph with the structure of an acyclic directed graph is used to store matching sections of sequences and known variants. An algorithm for rapid mapping of reads to the genome graph is developed to align the individual nucleotide sequence fragments to the genome graph. The algorithm combines rapid searching using hash tables with the algorithm of dynamic programming and solves the problem of exponential growth in the number of paths on the graph. The implementation of the genome graph and the algorithm of the alignment of reads is developed. A comparison with the best-known programs with similar functionality is made.     

An efficient algorithm for DNA fragment assembly in MapReduce

Fragment assembly is one of the most important problems of sequence assembly. Algorithms for DNA fragment assembly using de Bruijn graph have been widely used. These algorithms require a large amount of memory and running time to build the de Bruijn graph. Another drawback of the conventional de Bruijn approach is the loss of information. To overcome these shortcomings, this paper proposes a parallel strategy to construct de Bruijin graph. Its main characteristic is to avoid the division of de Bruijin graph. A novel fragment assembly algorithm based on our parallel strategy is implemented in the MapReduce framework. The experimental results show that the parallel strategy can effectively improve the computational efficiency and remove the memory limitations of the assembly algorithm based on Euler superpath. This paper provides a useful attempt to the assembly of large-scale genome sequence using Cloud Computing.     

Communication and complexity in a GRN-based multicellular system for graph colouring

Artificial Genetic Regulatory Networks (GRNs) are interesting control models through their simplicity and versatility. They can be easily implemented, evolved and modified, and their similarity to their biological counterparts makes them interesting for simulations of life-like systems as well. These aspects suggest they may be perfect control systems for distributed computing in diverse situations, but to be usable for such applications the computational power and evolvability of GRNs need to be studied. In this research we propose a simple distributed system implementing GRNs to solve the well known NP-complete graph colouring problem. Every node (cell) of the graph to be coloured is controlled by an instance of the same GRN. All the cells communicate directly with their immediate neighbours in the graph so as to set up a good colouring. The quality of this colouring directs the evolution of the GRNs using a genetic algorithm. We then observe the quality of the colouring for two different graphs according to different communication protocols and the number of different proteins in the cell (a measure for the possible complexity of a GRN). Those two points, being the main scalability issues that any computational paradigm raises, will then be discussed.     

Reconstruction of DNA sequencing by hybridization

MOTIVATION: It is widely recognized that the hybridization process is prone to errors and that the future of DNA sequencing by hybridization is predicated on the ability to successfully cope with such errors. However, the occurrence of hybridization errors results in the computational difficulty of the reconstruction of DNA sequencing by hybridization. The reconstruction problem of DNA sequencing by hybridization with errors is a strongly NP-hard problem. So far the problem has not been solved well. RESULTS: In this paper, a new approach is presented to solve the reconstruction problem of DNA sequencing by hybridization, which realizes the computational part of the SBH experiment. The proposed algorithm accepts both the negative and positive errors. The computational experiments show that the algorithm behaves satisfactorily, especially for the case with k-tuple repetitions and positive errors.