Adaptive bi-level programming for optimal gene knockouts for targeted overproduction under phenotypic constraints

Multi-parametric programming based algorithms for the global solution of bi-level mixed-integer linear and quadratic programming problems

Genome-scale metabolic models have lead to the development of computational methods to understand the underlying mechanism about the metabolism of an organism. With the foundation of Flux balance analysis (FBA), optimization methods are developed to suggest optimal knockout strategies to achieve the maximum production of the target metabolite of interest including industrial and pharmaceutical chemicals. Many of these existing methods employ bi-level optimization formulations to maximize the production of the desired biochemical at the outer-level while the organism still maintains living modeled as the inner-level optimization model, for example, by maximizing biomass production yield under the constraints imposed by gene knockouts as in the well-known OptKnock. OptKnock always selects the most optimistic flux for the production of the desired biochemical under the maximum biomass condition although the actual flux can be less than this maximum. This is because optimal knockout strategies derived in such a bi-level optimization framework may heavily depend on the closeness and robustness of the inner-level optimization model in capturing actual cell survival states. By examining the non-uniqueness of the surviving mutants from the inner-level optimization model and the fact that there may be a non-cooperative environment between the inner-level and outer-level decision makers, the suggested mutants produced by OptKnock may be different from the actual knockout strategies in practice. In order to prevent these limitations of the optimistic OptKnock, we propose a modification of it through a novel pessimistic bi-level optimization perspective. We compute pessimistic knockout solutions and compare with those from OptKnock on a core E. coli metabolic network, and observe that the solutions through pessimistic view are more reliable and perform better. For future research, we believe that the proposed pessimistic bi-level optimization model will lead to more practical and robust knockout strategies.

In this paper, we propose an alternate modified solution procedure based on fuzzy goal programming (FGP) approach for solving bi-level multiobjective linear fractional programming problems (BL-MOLFPPs) with some major modifications in the algorithm suggested by Abo-Sinna and Baky (2010). The proposed modified technique is simpler and requires less computational works than that of earlier technique. In the formulation of FGP models, each objective function (at both the levels - leader's level and follower's level) as well as control variables (of leader's level) are transformed into fuzzy goals with modified membership functions. Then FGP approach is used for achieving the highest degree of each of membership goals. To avoid decision deadlock situations and difficulties associated with bi-level programming problems, solution preferences by decision makers (at leader's and follower's levels) are not taken into account in proposed algorithm. A comparative analysis is also carried out with numerical example in order to show efficiency of proposed algorithm over earlier technique.

A solution to bi/tri-level programming problems using particle swarm optimization

Designing metabolic engineering strategies with genome-scale metabolic flux modeling Jiun Y Yen,1,2 Imen Tanniche,1 Amanda K Fisher,1–3 Glenda E Gillaspy,2 David R Bevan,2,3 Ryan S Senger,1 1Department of Biological Systems Engineering, 2Department of Biochemistry, 3Genomics, Bioinformatics, and Computational Biology Interdisciplinary Program, Virginia Tech, Blacksburg, VA, USA Abstract: New in silico tools that make use of genome-scale metabolic flux modeling are improving the design of metabolic engineering strategies. This review highlights the latest developments in this area, explains the interface between these in silico tools and the experimental implementation tools of metabolic engineers, and provides a way forward so that in silico predictions can better mimic reality and more experimental methods can be considered in simulation studies. The several methodologies for solving genome-scale models (eg, flux balance analysis [FBA], parsimonious FBA, flux variability analysis, and minimization of metabolic adjustment) all have unique advantages and applications. There are two basic approaches to designing metabolic engineering strategies in silico, and both have demonstrated success in the literature. The first involves: 1) making a genetic manipulation in a model; 2) testing for improved performance through simulation; and 3) iterating the process. The second approach has been used in more recently designed in silico tools and involves: 1) comparing metabolic flux profiles of a wild-type and ideally engineered state and 2) designing engineering strategies based on the differences in these flux profiles. Improvements in genome-scale modeling are anticipated in areas such as the inclusion of all relevant cellular machinery, the ability to understand and anticipate the results of combinatorial enrichment experiments, and constructing dynamic and flexible biomass equations that can respond to environmental and genetic manipulations. Keywords: genome-scale modeling, genome-scale modeling, flux balance analysis, flux variability analysis, minimization of metabolic adjustment, metabolic bottleneck, pathway optimization

Comparison of Resilience against Genetic Perturbations in Microbial Metabolism

In this paper, the triangular fuzzy bilevel programming problem (TFBLPP) is investigated. We transformed TBFLPP to interval fuzzy bilevel linear programming problem by using nearest interval approximation. In the next step, three problem were obtained that by solving them solution TBFLPP obtained.

Multi-objective linear bi-level multi-follower programming problem (MOBLMFPP) is a special case of two level hierarchical programming problems in which the second level hierarchy includes multiple followers. This paper presents an alternate method based on fuzzy goal programming approach for the solution of multi-objective linear bi-level multi-follower programming (MOLBMFP) problem in which there is no sharing of information among followers. In the proposed FGP model formulation, each of objective functions of each level (leader and follower's level of MOLBMFPP) as well as decision variables at each level are characterised into fuzzy goals. Suitable linear membership functions are defined for each objective function and decision variables. Then minimising the sum of the negative deviational variables of both levels, the highest membership value of each of fuzzy goals is obtained. Existence of compromise optimal solution for MOLBMFPP is established in context of proposed approach. A numerical example is illustrated in support of proposed methodology. A comparative analysis is also carried out in order to show efficiency of proposed method over earlier method for the solution of MOLBMFPP.

A global optimization algorithm for solving the bi-level linear fractional programming problem

This paper considers bilevel linear programming with fuzzy random variables. Through the introduction of a novel optimisation model that is to minimise the absolute deviation of degree of possibility and necessity that each fuzzy goal is fulfilled, the original bilevel programming problems with fuzzy random variables can be transformed into deterministic bilevel fractional programming problems. It is shown that the extended Stackelberg solutions can be obtained by solving the transformed bilevel linear programming problem through the combined use of the variable transformation method and the Kth best algorithm. A numerical example of bilevel purchase problem for food retailing is provided to illustrate the usefulness of the proposed methods.

By handling the travel cost function artfully, the authors formulate the transportation mixed network design problem (MNDP) as a mixed-integer, nonlinear bilevel programming problem, in which the lower-level problem, comparing with that of conventional bilevel DNDP models, is not a side constrained user equilibrium assignment problem, but a standard user equilibrium assignment problem. Then, the bilevel programming model for MNDP is reformulated as a continuous version of bilevel programming problem by the continuation method. By virtue of the optimal-value function, the lower-level assignment problem can be expressed as a nonlinear equality constraint. Therefore, the bilevel programming model for MNDP can be transformed into an equivalent single-level optimization problem. By exploring the inherent nature of the MNDP, the optimal-value function for the lower-level equilibrium assignment problem is proved to be continuously differentiable and its functional value and gradient can be obtained efficiently. Thus, a continuously differentiable but still nonconvex optimization formulation of the MNDP is created, and then a locally convergent algorithm is proposed by applying penalty function method. The inner loop of solving the subproblem is mainly to implement an all-or-nothing assignment. Finally, a small-scale transportation network and a large-scale network are presented to verify the proposed model and algorithm.

For a long time, the bilevel programming problem has essentially been considered as a special case of mathematical programs with equilibrium constraints, in particular when the so-called KKT reformulation is in question. Recently though, this widespread believe was shown to be false in general. In this paper, other aspects of the difference between both problems are revealed as we consider the KKT approach for the nonsmooth bilevel program. It turns out that the new inclusion (constraint) which appears as a consequence of the partial subdifferential of the lower-level Lagrangian (PSLLL) places the KKT reformulation of the nonsmooth bilevel program in a new class of mathematical program with both set-valued and complementarity constraints. While highlighting some new features of this problem, we attempt here to establish close links with the standard optimistic bilevel program. Moreover, we discuss possible natural extensions for C-, M-, and S-stationarity concepts. Most of the results rely on a coderivati...

This paper represents the bi-level linear programming problem in an imprecise and uncertain mixed environment. The aim of this paper is to introduce coefficients of leader and the follower’s objective function and the constraints as the fuzzy random variable. To determine the optimal value of the leader and follower’s objectives a new methodology is developed for bi-level linear programming model in the presence of fuzzy random variable. A numerical example is solved to demonstrate the methodology.

Gene deletion and overexpression are critical technologies for designing or improving the metabolic flux distribution of microbes. Some algorithms including flux balance analysis (FBA) and minimization of metabolic adjustment (MOMA) predict a flux distribution from a stoichiometric matrix in the mutants in which some metabolic genes are deleted or non-functional, but there are few algorithms that predict how a broad range of genetic modifications, such as over- and underexpression of metabolic genes, alters the phenotypes of the mutants at the metabolic flux level. To overcome such existing limitations, we develop a novel algorithm that predicts the flux distribution of the mutants with a broad range of genetic modification, based on elementary mode analysis. It is denoted as genetic modification of flux (GMF), which couples two algorithms that we have developed: modified control effective flux (mCEF) and enzyme control flux (ECF). mCEF is proposed based on CEF to estimate the gene expression patterns in genetically modified mutants in terms of specific biological functions. GMF is demonstrated to predict the flux distribution of not only gene deletion mutants, but also the mutants with underexpressed and overexpressed genes in Escherichia coli and Corynebacterium glutamicum. This achieves breakthrough in the a priori flux prediction of a broad range of genetically modified mutants. Supplementary file and programs are available at Bioinformatics online or http://www.cadlive.jp.

This article considers bilevel linear programming problems where the coefficients of the objective functions and the constraints in the problem are given as fuzzy parameters. Stackelberg problems and Stackelberg solutions under fuzziness have not been fully discussed so far. New Stackelberg solution concepts under fuzziness, called possibilistic Stackelberg solutions , are proposed by incorporating possibility theory into Stackelberg solutions in non-fuzzy environments. This paper shows some theoretical properties and theorems on the formulated fuzzy bilevel programming problems. It is shown that the proposed possibilistic Stackelberg solutions are obtained by using linear or nonlinear programming techniques. The effectiveness of the proposed models is demonstrated by numerical experiments using transportation problems where the upper-level decision maker is a buyer and the lower-level one is a supplier.