In this paper, a fuzzy hierarchical optimization framework is proposed for identifying potential antiviral targets for treating severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection in the heart. The proposed framework comprises four objectives for evaluating the elimination of viral biomass growth and the minimization of side effects during treatment. In the application of the framework, Dulbecco's modified eagle medium (DMEM) and Ham's medium were used as uptake nutrients on an antiviral target discovery platform. The prediction results from the framework reveal that most of the antiviral enzymes in the aforementioned media are involved in fatty acid metabolism and amino acid metabolism. However, six enzymes involved in cholesterol biosynthesis in Ham's medium and three enzymes involved in glycolysis in DMEM are unable to eliminate the growth of the SARS-CoV-2 biomass. Three enzymes involved in glycolysis, namely BPGM, GAPDH, and ENO1, in DMEM combine with the supplemental uptake of L-cysteine to increase the cell viability grade and metabolic deviation grade. Moreover, six enzymes involved in cholesterol biosynthesis reduce and fail to reduce viral biomass growth in a culture medium if a cholesterol uptake reaction does not occur and occurs in this medium, respectively.

The liver is a vital organ involving in various major metabolic functions in human body. MicroRNA-122 (miR-122) plays an important role in the regulation of liver metabolism, but its intrinsic physiological functions require further clarification. This study integrated the genome-scale metabolic model of hepatocytes and mouse experimental data with germline deletion of Mir122a (Mir122a-/-) to infer Warburg-like effects. Elevated expression of MiR-122a target genes in Mir122a-/-mice, especially those encoding for metabolic enzymes, was applied to analyze the flux distributions of the genome-scale metabolic model in normal and deficient states. By definition of the similarity ratio, we compared the flux fold change of the genome-scale metabolic model computational results and metabolomic profiling data measured through a liquid-chromatography with mass spectrometer, respectively, for hepatocytes of 2-month-old mice in normal and deficient states. The Ddc gene demonstrated the highest similarity ratio of 95% to the biological hypothesis of the Warburg effect, and similarity of 75% to the experimental observation. We also used 2, 6, and 11 months of mir-122 knockout mice liver cell to examined the expression pattern of DDC in the knockout mice livers to show upregulated profiles of DDC from the data. Furthermore, through a bioinformatics (LINCS program) prediction, BTK inhibitors and withaferin A could downregulate DDC expression, suggesting that such drugs could potentially alter the early events of metabolomics of liver cancer cells.

MOTIVATION: Mathematical modeling and optimization have been used for detecting enzyme targets in human metabolic disorders. Such optimal drug design methods are generally differentiated as two stages, identification and decision-making, to find optimal targets. We developed a unified method named fuzzy equal metabolic adjustment to formulate an optimal enzyme target design problem for drug discovery. The optimization framework combines the identification of enzyme targets and a decision-making strategy simultaneously. The objectives of this algorithm include evaluations of the therapeutic effect of target enzymes, the adverse effects of drugs and the minimum effective dose (MED). RESULTS: An existing generalized mass action system model of human uric acid (UA) metabolism was used to formulate the fuzzy optimization method for detecting two types of enzymopathies: hyperuricemia caused by phosphoribosylpyrophosphate synthetase (PRPPS) overactivity and Lesch-Nyhan syndrome. The fuzzy objectives were set so that the concentrations of the metabolites were as close as possible to the healthy levels. The target design included a diet control of ribose-5-phospahate (R5P). The diet control of R5P served as an extra remedy to reduce phosphate uptake entering the purine metabolic pathway, so that we could obtain a more satisfactory treatment than obtained for those without a diet control. Moreover, enhancing UA excretion resulted in an effective treatment of hyperuricemia caused by PRPPS overactivity. This result correlates with using probenecid and benbromazone, which are uricosuric agents present in current clinical medications. By contrast, the Lesch-Nyhan syndrome required at least three enzyme targets to cure hyperuricemia.

The crisp and fuzzy optimization approaches were introduced to design an optimal temperature control policy for a batch process of simultaneous saccharification and cofermentation (SSCF) to produce ethanol from lignocellulose using the enzymes and the recombinant strain Saccharomyces yeast 1400 (pLNH33). The goal of the optimal design herein is to find the optimal temperature, initial lignocellulosic concentration, and fermentation time that maximize the ethanol productivity under the constraints of follow-up separation specifications. The interactive crisp and fuzzy optimization methods towards were respectively applied to solve the trade-off optimization problems in order to obtain a compromised design. The fuzzy goal attainment approach can more flexibly obtain a comprehensive design in comparison to the crisp optimization. Both crisp and fuzzy optimization could be efficiently solved by hybrid differential evolution.

BACKGROUND: Determining the parameters of a mathematical model from quantitative measurements is the main bottleneck of modelling biological systems. Parameter values can be estimated from steady-state data or from dynamic data. The nature of suitable data for these two types of estimation is rather different. For instance, estimations of parameter values in pathway models, such as kinetic orders, rate constants, flux control coefficients or elasticities, from steady-state data are generally based on experiments that measure how a biochemical system responds to small perturbations around the steady state. In contrast, parameter estimation from dynamic data requires time series measurements for all dependent variables. Almost no literature has so far discussed the combined use of both steady-state and transient data for estimating parameter values of biochemical systems. RESULTS: In this study we introduce a constrained optimization method for estimating parameter values of biochemical pathway models using steady-state information and transient measurements. The constraints are derived from the flux connectivity relationships of the system at the steady state. Two case studies demonstrate the estimation results with and without flux connectivity constraints. The unconstrained optimal estimates from dynamic data may fit the experiments well, but they do not necessarily maintain the connectivity relationships. As a consequence, individual fluxes may be misrepresented, which may cause problems in later extrapolations. By contrast, the constrained estimation accounting for flux connectivity information reduces this misrepresentation and thereby yields improved model parameters. CONCLUSION: The method combines transient metabolic profiles and steady-state information and leads to the formulation of an inverse parameter estimation task as a constrained optimization problem. Parameter estimation and model selection are simultaneously carried out on the constrained optimization problem and yield realistic model parameters that are more likely to hold up in extrapolations with the model.

BACKGROUND: Protein-protein interactions (PPIs) are critical to every aspect of biological processes. Expansion of all PPIs from a set of given queries often results in a complex PPI network lacking spatiotemporal consideration. Moreover, the reliability of available PPI resources, which consist of low- and high-throughput data, for network construction remains a significant challenge. Even though a number of software tools are available to facilitate PPI network analysis, an integrated tool is crucial to alleviate the burden on querying across multiple web servers and software tools. RESULTS: We have constructed an integrated web service, POINeT, to simplify the process of PPI searching, analysis, and visualization. POINeT merges PPI and tissue-specific expression data from multiple resources. The tissue-specific PPIs and the numbers of research papers supporting the PPIs can be filtered with user-adjustable threshold values and are dynamically updated in the viewer. The network constructed in POINeT can be readily analyzed with, for example, the built-in centrality calculation module and an integrated network viewer. Nodes in global networks can also be ranked and filtered using various network analysis formulas, i.e., centralities. To prioritize the sub-network, we developed a ranking filtered method (S3) to uncover potential novel mediators in the midbody network. Several examples are provided to illustrate the functionality of POINeT. The network constructed from four schizophrenia risk markers suggests that EXOC4 might be a novel marker for this disease. Finally, a liver-specific PPI network has been filtered with adult and fetal liver expression profiles. CONCLUSION: The functionalities provided by POINeT are highly improved compared to previous version of POINT. POINeT enables the identification and ranking of potential novel genes involved in a sub-network. Combining with tissue-specific gene expression profiles, PPIs specific to selected tissues can be revealed. The straightforward interface of POINeT makes PPI search and analysis just a few clicks away. The modular design permits further functional enhancement without hampering the simplicity. POINeT is available at (http://poinet.bioinformatics.tw/).

The inference of genetic regulatory networks from time-course data is one of the main challenges in systems biology. The ultimate goal of inferred model is to obtain the expressions quantitatively comprehending every detail and principle of biological systems. This study introduces a multiobjective optimization approach to infer a realizable S-system structure for genetic regulatory networks. The work of inference is to minimize simultaneously the concentration error, slope error and interaction measure in order to find a suitable S-system model structure and its corresponding model parameters. Hybrid differential evolution is applied to solve the epsiv-constrained problem, which is converted from the multiobjective optimization problem, for minimizing the interaction measure with subject to the expectation constraints for the concentration and slope error criteria. This approach could avoid assigning a suitable penalty weight for sum of magnitude of kinetic orders for the penalty problem in order to prune the model structure.

MOTIVATION: The inference of biochemical networks, such as gene regulatory networks, protein-protein interaction networks, and metabolic pathway networks, from time-course data is one of the main challenges in systems biology. The ultimate goal of inferred modeling is to obtain expressions that quantitatively understand every detail and principle of biological systems. To infer a realizable S-system structure, most articles have applied sums of magnitude of kinetic orders as a penalty term in the fitness evaluation. How to tune a penalty weight to yield a realizable model structure is the main issue for the inverse problem. No guideline has been published for tuning a suitable penalty weight to infer a suitable model structure of biochemical networks. RESULTS: We introduce an interactive inference algorithm to infer a realizable S-system structure for biochemical networks. The inference problem is formulated as a multiobjective optimization problem to minimize simultaneously the concentration error, slope error and interaction measure in order to find a suitable S-system model structure and its corresponding model parameters. The multiobjective optimization problem is solved by the epsilon-constraint method to minimize the interaction measure subject to the expectation constraints for the concentration and slope error criteria. The theorems serve to guarantee the minimum solution for the epsilon-constrained problem to achieve the minimum interaction network for the inference problem. The approach could avoid assigning a penalty weight for sums of magnitude of kinetic orders.

BACKGROUND: The rapid growth of protein-protein interaction (PPI) data has led to the emergence of PPI network analysis. Despite advances in high-throughput techniques, the interactomes of several model organisms are still far from complete. Therefore, it is desirable to expand these interactomes with ortholog-based and other methods. RESULTS: Orthologous pairs of 18 eukaryotic species were expanded and merged with experimental PPI datasets. The contributions of interologs from each species were evaluated. The expanded orthologous pairs enable the inference of interologs for various species. For example, more than 32,000 human interactions can be predicted. The same dataset has also been applied to the prediction of host-pathogen interactions. PPIs between P. falciparum calmodulin and several H. sapiens proteins are predicted, and these interactions may contribute to the maintenance of host cell Ca2+ concentration. Using comparisons with Bayesian and structure-based approaches, interactions between putative HSP40 homologs of P. falciparum and the H. sapiens TNF receptor associated factor family are revealed, suggesting a role for these interactions in the interference of the human immune response to P. falciparum. CONCLUSION: The PPI datasets are available from POINT http://point.bioinformatics.tw/ and POINeT http://poinet.bioinformatics.tw/. Further development of methods to predict host-pathogen interactions should incorporate multiple approaches in order to improve sensitivity, and should facilitate the identification of targets for drug discovery and design.

Abstract Motivation: Modern experimental biology is moving away from analyses of single elements to whole-organism measurements. Such measured time-course data contain a wealth of information about the structure and dynamic of the pathway or network. The dynamic modeling of the whole systems is formulated as a reverse problem that requires a well-suited mathematical model and a very efficient computational method to identify the model structure and parameters. Numerical integration for differential equations and finding global parameter values are still two major challenges in this field of the parameter estimation of nonlinear dynamic biological systems. Results: We compare three techniques of parameter estimation for nonlinear dynamic biological systems. In the proposed scheme, the modified collocation method is applied to convert the differential equations to the system of algebraic equations. The observed time-course data are then substituted into the algebraic system equations to decouple system interactions in order to obtain the approximate model profiles. Hybrid differential evolution (HDE) with population size of five is able to find a global solution. The method is not only suited for parameter estimation but also can be applied for structure identification. The solution obtained by HDE is then used as the starting point for a local search method to yield the refined estimates. Availability: The algorithm, implemented by Compaq Visual Fortran Professional Edition 6.6, and the supplements are available at http://www.che.ccu.edu.tw/~bioproc/index-english.html/. IMSL Math/Library is a commercial library included in Compaq Visual Fortran Professional Edition. Contact: [email protected]

In this paper, we introduce hybrid differential evolution with a multiplier updating method to solve constrained optimization problems. An adaptive scheme for penalty parameters is involved in the proposed algorithm so that smaller penalty parameters can be used and does not affect the final search results. Computational examples reveal that nearly identical minimum solutions can be obtained using the proposed algorithm even under wide variation of the initial penalty parameters.

Plant scheduling and planning are two of the most important decision-making problems in manufacturing industry. In general, these two decision-making problems are complex, due to the features of combinatorial nature for production-strategy selection and coupling properties for constrained requirements. In this paper, we have developed two general mixed-integer nonlinear programming models to formulate the scheduling and planning problems. In order to obtain a global solution, mixed-integer hybrid differential evolution with a multiplier updating method is introduced to solve both constrained problems. The proposed method can use parameters to obtain a feasible solution as compared with the penalty function approach.

Hybrid differential evolution is applied to estimate the kinetic model parameters of batch fermentation for ethanol and glycerol production using Saccharomyces diastaticus LORRE 316. In this study, we consider the worst observed error for all experiments as an objective function so that the parameter estimation problem becomes a min-max estimation problem. Several methods have been employed to solve the min-max estimation problem for comparison. The proposed method can use a small population size to obtain a more satisfactory solution as compared from these computations. In order to validate the kinetic model, we have carried out the fedbatch experiments with an optimal feed rate. The experimental data can fit the computed results satisfactorily.

A hybrid method of evolutionary algorithms, called mixed-integer hybrid differential evolution (MIHDE), is proposed in this study. In the hybrid method, a mixed coding is used to represent the continuous and discrete variables. A rounding operation in the mutation is introduced to handle the integer variables so that the method is not only used to solve mixed-integer nonlinear optimization problems, but also used to solve the real or integer nonlinear optimization problems. The accelerated phase and migrating phase are implemented in MIHDE. These two phases acted as a balancing operator are used to explore the search space and to exploit the best solution. Both examples of mechanical design are tested by the MIHDE. The computation results demonstrate that the MIHDE is superior to other methods in terms of solution quality and robustness property.