In computational metabolic design, it is often necessary to modify the original constraint-based metabolic networks to lead to growth-coupled production, where cell growth forces target metabolite production. However, in genome-scale models, finding strategies to simultaneously delete and add genes to induce growth-coupled production is challenging. This is particularly true when heavy computation is necessary due to numerous gene deletions and additions. In this study, we mathematically defined related problems, proved NP-hardness and/or NP-completeness, and developed an algorithm named RatGene that (1) automatically integrates multiple constraint-based metabolic networks, (2) identifies gene deletion-addition strategies by a growth-to-production ratio-based approach, and (3) eliminates redundant gene additions and deletions. The results of computational experiments demonstrated that the RatGene-based approach can significantly improve the success ratio for identifying the strategies for growth-coupled production. RatGene can facilitate a more rational approach to computational metabolic design for the production of useful substances using microorganisms by concurrently considering both gene deletions and additions.

When simulating metabolite productions with genome-scale constraint-based metabolic models, gene deletion strategies are necessary to achieve growth-coupled production, which means cell growth and target metabolite production occur simultaneously. Since obtaining gene deletion strategies for large genome-scale models suffers from significant computational time, it is necessary to develop methods to mitigate this computational burden. In this study, we introduce a novel framework for computing gene deletion strategies. The proposed framework first mines related databases to extract prior information about gene deletions for growth-coupled production. It then integrates the extracted information with downstream algorithms to narrow down the algorithmic search space, resulting in highly efficient calculations on genome-scale models. Computational experiment results demonstrated that our framework can compute stoichiometrically feasible gene deletion strategies for numerous target metabolites, showcasing a noteworthy improvement in computational efficiency. Specifically, our framework achieves an average 6.1-fold acceleration in computational speed compared to existing methods while maintaining a respectable success rate.

In genome-scale constraint-based metabolic models, gene deletion strategies are crucial for achieving growth-coupled production, where cell growth and target metabolite production are simultaneously achieved. While computational methods for calculating gene deletions have been widely explored and have contributed to gene deletion strategy databases, current approaches remain computationally demanding and have yet to fully leverage emerging data-driven paradigms, such as machine learning, for more efficient strain design. Therefore, it is necessary to propose a fundamental framework for this objective. In this study, we first formulate the problem of gene deletion strategy prediction and then propose a framework for predicting gene deletion strategies for growth-coupled production in genome-scale metabolic models. The proposed framework leverages deep learning algorithms to learn and integrate sequential gene and metabolite data representation, enabling the automatic gene deletion strategy prediction. Computational experiment results demonstrate the feasibility of the proposed framework, showing substantial improvements over baseline methods. Specifically, the proposed framework achieves a 14.69%, 22.52%, and 13.03% increase in overall accuracy across three metabolic models of different scales under study, while maintaining balanced precision and recall in predicting gene deletion statuses.

When simulating genome-scale metabolite production using constraint-based metabolic networks, it is often necessary to find gene deletion strategies which lead to growth-coupled production, which means that target metabolites are produced when cell growth is maximized. Existing methods are effective when the number of gene deletions is relatively small, but when the number of required gene deletions exceeds approximately 1% of whole genes, the time required for the calculation is often unfeasible. Therefore, a complementing algorithm that is effective even when the required number of gene deletions is approximately 1% to 5% of whole genes would be helpful because the number of deletable genes in a strain is increasing with advances in genetic engineering technology. In this study, the author developed an algorithm, TrimGdel, which first computes a strategy with many gene deletions that results in growth-coupled production and then gradually reduces the number of gene deletions while ensuring the original production rate and growth rate. The results of the computer experiments showed that TrimGdel can calculate stoichiometrically feasible gene deletion strategies, especially those whose sizes are 1 to 5% of whole genes, which lead to growth-coupled production of many target metabolites, which include useful vitamins such as biotin and pantothenate, for which existing methods could not.

Growth-coupled production, in which cell growth forces the production of target metabolites, plays an essential role in the production of substances by microorganisms. The strains are first designed using computational simulation and then validated by biological experiments. In the simulations, gene-deletion strategies are often necessary because many metabolites are not produced in the natural state of the microorganisms. However, such information is not available for many metabolites owing to the requirement of heavy computation, especially when many gene deletions are required for genome-scale models. A database for such information will be helpful. However, developing such a database is not straightforward because heavy computation and the existence of replaceable genes render difficulty in efficient enumeration. In this study, the author developed efficient methods for enumerating minimal and maximal gene-deletion strategies and a web-based database system. MetNetComp provides information on 1) a total of 85,611 gene-deletion strategies excluding apparent duplicate counting for replaceable genes for 1,735 target metabolites, 11 constraint-based models, and 10 species; 2) necessary substrates and products in the process; and 3) reaction rates that can be used for visualization. MetNetComp is helpful for strain design and for new research paradigms using machine learning.

As one of the few irreversible protein posttranslational modifications, proteolytic cleavage is involved in nearly all aspects of cellular activities, ranging from gene regulation to cell life-cycle regulation. Among the various protease-specific types of proteolytic cleavage, cleavages by casapses/granzyme B are considered as essential in the initiation and execution of programmed cell death and inflammation processes. Although a number of substrates for both types of proteolytic cleavage have been experimentally identified, the complete repertoire of caspases and granzyme B substrates remains to be fully characterized. To tackle this issue and complement experimental efforts for substrate identification, systematic bioinformatics studies of known cleavage sites provide important insights into caspase/granzyme B substrate specificity, and facilitate the discovery of novel substrates. In this article, we review and benchmark 12 state-of-the-art sequence-based bioinformatics approaches and tools for caspases/granzyme B cleavage prediction. We evaluate and compare these methods in terms of their input/output, algorithms used, prediction performance, validation methods and software availability and utility. In addition, we construct independent data sets consisting of caspases/granzyme B substrates from different species and accordingly assess the predictive power of these different predictors for the identification of cleavage sites. We find that the prediction results are highly variable among different predictors. Furthermore, we experimentally validate the predictions of a case study by performing caspase cleavage assay. We anticipate that this comprehensive review and survey analysis will provide an insightful resource for biologists and bioinformaticians who are interested in using and/or developing tools for caspase/granzyme B cleavage prediction.

We present a simple linear-time algorithm for computing the topological centroid and the canonical form of a plane graph. Although the targets are restricted to plane graphs, it is much simpler than the linear-time algorithm by Hopcroft and Wong for determination of the canonical form and isomorphism of planar graphs. By utilizing a modified centroid for outerplanar graphs, we present a linear-time algorithm for a geometric version of the maximum common connected edge subgraph (MCCES) problem for the special case in which input geometric graphs have outerplanar structures, MCCES can be obtained by deleting at most a constant number of edges from each input graph, and both the maximum degree and the maximum face degree are bounded by constants.

The tree inclusion problem is, given two node-labeled trees P and T (the "pattern tree" and the "text tree"), to locate every minimal subtree in T (if any) that can be obtained by applying a sequence of node insertion operations to P. Although the ordered tree inclusion problem is solvable in polynomial time, the unordered tree inclusion problem is NP-hard. The currently fastest algorithm for the latter is from 1995 and runs in O(poly(m,n) * 2^{2d}) = O^*(2^{2d}) time, where m and n are the sizes of the pattern and text trees, respectively, and d is the maximum outdegree of the pattern tree. Here, we develop a new algorithm that improves the exponent 2d to d by considering a particular type of ancestor-descendant relationships and applying dynamic programming, thus reducing the time complexity to O^*(2^d). We then study restricted variants of the unordered tree inclusion problem where the number of occurrences of different node labels and/or the input trees' heights are bounded. We show that although the problem remains NP-hard in many such cases, it can be solved in polynomial time for c = 2 and in O^*(1.8^d) time for c = 3 if the leaves of P are distinctly labeled and each label occurs at most c times in T. We also present a randomized O^*(1.883^d)-time algorithm for the case that the heights of P and T are one and two, respectively.

BACKGROUND: Constraint-based metabolic flux analysis of knockout strategies is an efficient method to simulate the production of useful metabolites in microbes. Owing to the recent development of technologies for artificial DNA synthesis, it may become important in the near future to mathematically design minimum metabolic networks to simulate metabolite production. RESULTS: We have developed a computational method where parsimonious metabolic flux distribution is computed for designated constraints on growth and production rates which are represented by grids. When the growth rate of this obtained parsimonious metabolic network is maximized, higher production rates compared to those noted using existing methods are observed for many target metabolites. The set of reactions used in this parsimonious flux distribution consists of reactions included in the original genome scale model iAF1260. The computational experiments show that the grid size affects the obtained production rates. Under the conditions that the growth rate is maximized and the minimum cases of flux variability analysis are considered, the developed method produced more than 90% of metabolites, while the existing methods produced less than 50%. Mathematical explanations using examples are provided to demonstrate potential reasons for the ability of the proposed algorithm to identify design strategies that the existing methods could not identify. CONCLUSION: We developed an efficient method for computing the design of minimum metabolic networks by using constraint-based flux balance analysis to simulate the production of useful metabolites. The source code is freely available, and is implemented in MATLAB and COBRA toolbox.

In metabolic network modification, we newly add enzymes or/and knock-out genes to maximize the biomass production with minimum side-effect. Although this problem has been studied for various problem settings via mathematical models including flux balance analysis, elementary mode, and Boolean models, some important problem settings still remain to be studied. In this paper, we consider the Boolean Reaction Modification (BRM) problem, where a host metabolic network and a reference metabolic network are given in the Boolean model. The host network initially produces some toxic compounds and cannot produce some necessary compounds, but the reference network can produce the necessary compounds, and we should minimize the total number of removed reactions from the host network and added reactions from the reference network so that the toxic compounds are not producible, but the necessary compounds are producible in the resulting host network. We developed integer linear programming (ILP)-based methods for BRM, and compared them with OptStrain and SimOptStrain. The results show that our method performed better for reducing the total number of added and removed reactions, while OptStrain and SimOptStrain performed better for optimizing the production of the target compound. Our developed software is freely available at "http://sunflower.kuicr.kyoto-u.ac.jp/~rogi/solBRM/solBRM.html ".

This article studies the parameterized complexity of the unification problem with associative, commutative, or associative-commutative functions with respect to the parameter “number of variables”. It is shown that if every variable occurs only once then both of the associative and associative-commutative unification problems can be solved in polynomial time, but that in the general case, both problems are W[1]-hard even when one of the two input terms is variable-free. For commutative unification, an algorithm whose time complexity depends exponentially on the number of variables is presented; moreover, if a certain conjecture is true then the special case where one input term is variable-free belongs to FPT. Some related results are also derived for a natural generalization of the classic string and tree edit distance problems that allows variables.

Selection of influential genes using gene expression data from normal and disease samples is an important topic in bioinformatics. In this paper, we propose a novel computational method for the problem, which combines gene expression patterns from normal and disease samples with a mathematical model of metabolic networks. This method seeks a set of k genes knockout of which drives the state of the metabolic network towards that in the disease samples. We adopt a Boolean model of metabolic networks and formulate the problem as a maximization problem under an integer linear programming framework. We applied the proposed method to selection of influential genes using gene expression data from normal samples and disease (head and neck cancer) samples. The result suggests that the proposed method can select more biologically relevant genes than an existing P-value based ranking method can.

In this paper, we have extended the concept of unordered tree inclusion to take the costs of insertions and substitutions into account. The resulting algorithm, MinCostIncl, has the same time complexity as the original algorithm of [4] for unordered tree inclusion (O(22Dmn)). Computational experiments on a large synthetic dataset as well as real datasets showed that our proposed algorithm is fast and scalable. Source codes of the implemented algorithms are available upon request.

This paper considers the problem of identifying all locations of subtrees in a large tree or in a large collection of trees that are similar to a specified pattern tree, where all trees are assumed to be rooted and node-labeled. The tree edit distance is a widely-used measure of tree (dis-)similarity, but is NP-hard to compute for unordered trees. To cope with this issue, we propose a new similarity measure which extends the concept of unordered tree inclusion by taking the costs of insertion and substitution operations on the pattern tree into account, and present an algorithm for computing it. Our algorithm has the same time complexity as the original one for unordered tree inclusion, i.e., it runs in O(|T1∥T2|) time, where T1and T2denote the pattern tree and the text tree, respectively, when the maximum outdegree of T1is bounded by a constant. Our experimental evaluation using synthetic and real datasets confirms that the proposed algorithm is fast and scalable and very useful for bibliographic matching, which is a typical entity resolution problem for tree-structured data. Furthermore, we extend our algorithm to also allow a constant number of deletion operations on T1while still running in O(|T1∥T2|) time.

MOTIVATION: Metabolic pathways are complex systems of chemical reactions taking place in every living cell to degrade substrates and synthesize molecules needed for life. Modeling the robustness of these networks with respect to the dysfunction of one or several reactions is important to understand the basic principles of biological network organization, and to identify new drug targets. While several approaches have been proposed for that purpose, they are computationally too intensive to analyze large networks, and do not properly handle reversible reactions. RESULTS: We propose a new model-the flux balance impact degree-to model the robustness of large metabolic networks with respect to gene knock-out. We formulate the computation of the impact of one or several reaction blocking as linear programs, and propose efficient strategies to solve them. We show that the proposed method better predicts the phenotypic impact of single gene deletions on Escherichia coli than existing methods. AVAILABILITY: https://sunflower.kuicr.kyoto-u.ac.jp/∼tyoyo/fbid/index.html

In this paper, we study the problem of finding a periodic attractor of a Boolean network (BN), which arises in computational systems biology and is known to be NP-hard. Since a general case is quite hard to solve, we consider special but biologically important subclasses of BNs. For finding an attractor of period 2 of a BN consisting of n OR functions of positive literals, we present a polynomial time algorithm. For finding an attractor of period 2 of a BN consisting of n AND/OR functions of literals, we present an O(1:985(n)) time algorithm. For finding an attractor of a fixed period of a BN consisting of n nested canalyzing functions and having constant treewidth w, we present an O(n(2p(w+1))poly(n)) time algorithm.

The tree edit distance is one of the most widely used measures for comparison of tree structured data and has been used for analysis of RNA secondary structures, glycan structures, and vascular trees. However, it is known that the tree edit distance problem is NP-hard for unordered trees while it is polynomial time solvable for ordered trees. We have recently proposed a clique-based method for computing the tree edit distance between unordered trees in which each instance of the tree edit distance problem is transformed into an instance of the maximum vertex weighted clique problem and then an existing clique algorithm is applied. In this paper, we propose an improved clique-based method. Different from our previous method, the improved method is basically a dynamic programming algorithm that repeatedly solves instances of the maximum vertex weighted clique problem as sub-problems. Other heuristic techniques, which do not violate the optimality of the solution, are also introduced. When applied to comparison of large glycan structures, our improved method showed significant speed-up in most cases.

BACKGROUND: Measuring similarities between tree structured data is important for analysis of RNA secondary structures, phylogenetic trees, glycan structures, and vascular trees. The edit distance is one of the most widely used measures for comparison of tree structured data. However, it is known that computation of the edit distance for rooted unordered trees is NP-hard. Furthermore, there is almost no available software tool that can compute the exact edit distance for unordered trees. RESULTS: In this paper, we present a practical method for computing the edit distance between rooted unordered trees. In this method, the edit distance problem for unordered trees is transformed into the maximum clique problem and then efficient solvers for the maximum clique problem are applied. We applied the proposed method to similar structure search for glycan structures. The result suggests that our proposed method can efficiently compute the edit distance for moderate size unordered trees. It also suggests that the proposed method has the accuracy comparative to those by the edit distance for ordered trees and by an existing method for glycan search. CONCLUSIONS: The proposed method is simple but useful for computation of the edit distance between unordered trees. The object code is available upon request.

In this paper, we study control problems of Boolean Networks (BNs) and Probabilistic Boolean Networks (PBNs). For BN CONTROL, by applying external control, we propose to derive the network to the desired state within a few time steps. For PBN CONTROL, we propose to find a control sequence such that the network will terminate in the desired state with a maximum probability. Also, we propose to minimize the maximum cost of the terminal state to which the network will enter. Integer linear programming and dynamic programming in conjunction with hard constraints are then employed to solve the above problems. Numerical experiments are given to demonstrate the effectiveness of our algorithms. We also present a hardness result suggesting that PBN CONTROL is harder than BN CONTROL.

Robustness is one of the important features of living organisms. For example, many organisms have strong adaptability to environmental changes and many organisms can live even if some of their genes are mutated. Besides, it is considered that cancer cells are very robust and thus cancers are difficult to treat. Therefore, it is important to identify origins of robustness in various kinds of organisms.Though several methods have been proposed for measuring robustness in metabolic networks or signal transduction networks, most methods require large computation time or are not guaranteed to output optimal solutions.In this paper, we formalized the problem as an integer program, where an objective function is to minimize the number of reactions to be inactivated so that at least one of the target compounds cannot be synthesized. In order to cope with cycles and reversible reactions, we developed a novel integer programming formalization method using a feedback vertex set (FVS). When applied to an E. coli metabolic network consisting of Glycolysis/Glyconeogenesis, Citrate cycle and Pentose phosphate pathway obtained from KEGG database, we could find an optimal set of enzymes to be inactivated several times faster than a naive method.

BACKGROUND: Subcellular location prediction of proteins is an important and well-studied problem in bioinformatics. This is a problem of predicting which part in a cell a given protein is transported to, where an amino acid sequence of the protein is given as an input. This problem is becoming more important since information on subcellular location is helpful for annotation of proteins and genes and the number of complete genomes is rapidly increasing. Since existing predictors are based on various heuristics, it is important to develop a simple method with high prediction accuracies. RESULTS: In this paper, we propose a novel and general predicting method by combining techniques for sequence alignment and feature vectors based on amino acid composition. We implemented this method with support vector machines on plant data sets extracted from the TargetP database. Through fivefold cross validation tests, the obtained overall accuracies and average MCC were 0.9096 and 0.8655 respectively. We also applied our method to other datasets including that of WoLF PSORT. CONCLUSION: Although there is a predictor which uses the information of gene ontology and yields higher accuracy than ours, our accuracies are higher than existing predictors which use only sequence information. Since such information as gene ontology can be obtained only for known proteins, our predictor is considered to be useful for subcellular location prediction of newly-discovered proteins. Furthermore, the idea of combination of alignment and amino acid frequency is novel and general so that it may be applied to other problems in bioinformatics. Our method for plant is also implemented as a web-system and available on http://sunflower.kuicr.kyoto-u.ac.jp/~tamura/slpfa.html.