Incorporation of enzyme concentrations into FBA and identification of optimal metabolic pathways

Current State, Challenges, and Opportunities in Genome-Scale Resource Allocation Models: A Mathematical Perspective

Stoichiometric genome-scale metabolic models (generally abbreviated GSM, GSMM, or GEM) have had many applications in exploring phenotypes and guiding metabolic engineering interventions. Nevertheless, these models and predictions thereof can become limited as they do not directly account for protein cost, enzyme kinetics, and cell surface or volume proteome limitations. Lack of such mechanistic detail could lead to overly optimistic predictions and engineered strains. Initial efforts to correct these deficiencies were by the application of precursor tools for GSMs, such as flux balance analysis with molecular crowding. In the past decade, several frameworks have been introduced to incorporate proteome-related limitations using a genome-scale stoichiometric model as the reconstruction basis, which herein are called resource allocation models (RAMs). This review provides a broad overview of representative or commonly used existing RAM frameworks. This review discusses increasingly complex models, beginning with stoichiometric models to precursor to RAM frameworks to existing RAM frameworks. RAM frameworks are broadly divided into two categories: coarse-grained and fine-grained, with different strengths and challenges. Discussion includes pinpointing their utility, data needs, highlighting framework strengths and limitations, and appropriateness to various research endeavors, largely through contrasting their mathematical frameworks. Finally, promising future applications of RAMs are discussed.

A control theoretic three timescale model for analyzing energy management in mammalian cancer cells

Interaction among different pathways, such as metabolic, signaling and gene regulatory networks, of cellular system is responsible to maintain homeostasis in a mammalian cell. Malfunctioning of this cooperation may lead to many complex diseases, such as cancer and type 2 diabetes. Timescale differences among these pathways make their integration a daunting task. Metabolic, signaling and gene regulatory networks have three different timescales, such as, ultrafast, fast and slow respectively. The article deals with this problem by developing a support vector regression (SVR) based three timescale model with the application of genetic algorithm based nonlinear controller. The proposed model can successfully capture the nonlinear transient dynamics and regulations of such integrated biochemical pathway under consideration. Besides, the model is quite capable of predicting the effects of certain drug targets for many types of complex diseases. Here, energy and cell proliferation management of mammalian cancer cells have been explored and analyzed with the help of the proposed novel approach. Previous investigations including in silico/in vivo/in vitro experiments have validated the results (the regulations of glucose transporter 1 (glut1), hexokinase (HK), and hypoxia-inducible factor-1 α (HIF-1 α ) among others, and the switching of pyruvate kinase (M2 isoform) between dimer and tetramer) generated by this model proving its effectiveness. Subsequently, the model predicts the effects of six selected drug targets, such as, the deactivation of transketolase and glucose-6-phosphate isomerase among others, in the case of mammalian malignant cells in terms of growth, proliferation, fermentation, and energy supply in the form of adenosine triphosphate (ATP).

Metabolic pathway engineering: Perspectives and applications

BACKGROUND

Metabolic engineering aims at contriving microbes as biocatalysts for enhanced and cost-effective production of countless secondary metabolites. These secondary metabolites can be treated as the resources of industrial chemicals, pharmaceuticals and fuels. Plants are also crucial targets for metabolic engineers to produce necessary secondary metabolites. Metabolic engineering of both microorganism and plants also contributes towards drug discovery. In order to implement advanced metabolic engineering techniques efficiently, metabolic engineers should have detailed knowledge about cell physiology and metabolism. Principle behind methodologies: Genome-scale mathematical models of integrated metabolic, signal transduction, gene regulatory and protein-protein interaction networks along with experimental validation can provide such knowledge in this context. Incorporation of omics data into these models is crucial in the case of drug discovery. Inverse metabolic engineering and metabolic control analysis (MCA) can help in developing such models. Artificial intelligence methodology can also be applied for efficient and accurate metabolic engineering.

CONCLUSION

In this review, we discuss, at the beginning, the perspectives of metabolic engineering and its application on microorganism and plant leading to drug discovery. At the end, we elaborate why inverse metabolic engineering and MCA are closely related to modern metabolic engineering. In addition, some crucial steps ensuring efficient and optimal metabolic engineering strategies have been discussed. Moreover, we explore the use of genomics data for the activation of silent metabolic clusters and how it can be integrated with metabolic engineering. Finally, we exhibit a few applications of artificial intelligence to metabolic engineering.

A comparative review of computational methods for pathway perturbation analysis: dynamical and topological perspectives

Stem cells offer great promise within the field of regenerative medicine but despite encouraging results, the large scale use of stem cells for therapeutic applications still faces challenges when it comes to controlling signaling pathway responses with respect to environmental perturbations.

Exploring the Altered Dynamics of Mammalian Central Carbon Metabolic Pathway in Cancer Cells: A Classical Control Theoretic Approach

BACKGROUND

In contrast with normal cells, most of the cancer cells depend on aerobic glycolysis for energy production in the form of adenosine triphosphate (ATP) bypassing mitochondrial oxidative phosphorylation. Moreover, compared to normal cells, cancer cells exhibit higher consumption of glucose with higher production of lactate. Again, higher rate of glycolysis provides the necessary glycolytic intermediary precursors for DNA, protein and lipid synthesis to maintain high active proliferation of the tumor cells. In this scenario, classical control theory based approach may be useful to explore the altered dynamics of the cancer cells. Since the dynamics of the cancer cells is different from that of the normal cells, understanding their dynamics may lead to development of novel therapeutic strategies.

METHOD

We have developed a model based on the state space equations of classical control theory along with an order reduction technique to mimic the actual dynamic behavior of mammalian central carbon metabolic (CCM) pathway in normal cells. Here, we have modified Michaelis Menten kinetic equation to incorporate feedback mechanism along with perturbations and cross talks associated with a metabolic pathway. Furthermore, we have perturbed the proposed model to reduce the mitochondrial oxidative phosphorylation. Thereafter, we have connected proportional-integral (PI) controller(s) with the model for tuning it to behave like the CCM pathway of a cancer cell. This methodology allows one to track the altered dynamics mediated by different enzymes.

RESULTS AND DISCUSSIONS

The proposed model successfully mimics all the probable dynamics of the CCM pathway in normal cells. Moreover, experimental results demonstrate that in cancer cells, a coordination among enzymes catalyzing pentose phosphate pathway and intermediate glycolytic enzymes along with switching of pyruvate kinase (M2 isoform) plays an important role to maintain their altered dynamics.

A model of an integrated immune system pathway in Homo sapiens and its interaction with superantigen producing expression regulatory pathway in Staphylococcus aureus: comparing behavior of pathogen perturbed and unperturbed pathway

Response of an immune system to a pathogen attack depends on the balance between the host immune defense and the virulence of the pathogen. Investigation of molecular interactions between the proteins of a host and a pathogen helps in identifying the pathogenic proteins. It is necessary to understand the dynamics of a normally behaved host system to evaluate the capacity of its immune system upon pathogen attack. In this study, we have compared the behavior of an unperturbed and pathogen perturbed host system. Moreover, we have developed a formalism under Flux Balance Analysis (FBA) for the optimization of conflicting objective functions. We have constructed an integrated pathway system, which includes Staphylococcal Superantigen (SAg) expression regulatory pathway and TCR signaling pathway of Homo sapiens. We have implemented the method on this pathway system and observed the behavior of host signaling molecules upon pathogen attack. The entire study has been divided into six different cases, based on the perturbed/unperturbed conditions. In other words, we have investigated unperturbed and pathogen perturbed human TCR signaling pathway, with different combinations of optimization of concentrations of regulatory and signaling molecules. One of these cases has aimed at finding out whether minimization of the toxin production in a pathogen leads to the change in the concentration levels of the proteins coded by TCR signaling pathway genes in the infected host. Based on the computed results, we have hypothesized that the balance between TCR signaling inhibitory and stimulatory molecules can keep TCR signaling system into resting/stimulating state, depending upon the perturbation. The proposed integrated host-pathogen interaction pathway model has accurately reflected the experimental evidences, which we have used for validation purpose. The significance of this kind of investigation lies in revealing the susceptible interaction points that can take back the Staphylococcal Enterotoxin (SE)-challenged system within the range of normal behavior.

An optimization rule for in silico identification of targeted overproduction in metabolic pathways

In an extension of previous work, here we introduce a second-order optimization method for determining optimal paths from the substrate to a target product of a metabolic network, through which the amount of the target is maximum. An objective function for the said purpose, along with certain linear constraints, is considered and minimized. The basis vectors spanning the null space of the stoichiometric matrix, depicting the metabolic network, are computed, and their convex combinations satisfying the constraints are considered as flux vectors. A set of other constraints, incorporating weighting coefficients corresponding to the enzymes in the pathway, are considered. These weighting coefficients appear in the objective function to be minimized. During minimization, the values of these weighting coefficients are estimated and learned. These values, on minimization, represent an optimal pathway, depicting optimal enzyme concentrations, leading to overproduction of the target. The results on various networks demonstrate the usefulness of the methodology in the domain of metabolic engineering. A comparison with the standard gradient descent and the extreme pathway analysis technique is also performed. Unlike the gradient descent method, the present method, being independent of the learning parameter, exhibits improved results.

Modeling the optimal central carbon metabolic pathways under feedback inhibition using flux balance analysis

Metabolism is a complex process for energy production for cellular activity. It consists of a cascade of reactions that form a highly branched network in which the product of one reaction is the reactant of the next reaction. Metabolic pathways efficiently produce maximal amount of biomass while maintaining a steady-state behavior. The steady-state activity of such biochemical pathways necessarily incorporates feedback inhibition of the enzymes. This observation motivates us to incorporate feedback inhibition for modeling the optimal activity of metabolic pathways using flux balance analysis (FBA). We demonstrate the effectiveness of the methodology on a synthetic pathway with and without feedback inhibition. Similarly, for the first time, the Central Carbon Metabolic (CCM) pathways of Saccharomyces cerevisiae and Homo sapiens have been modeled and compared based on the above understanding. The optimal pathway, which maximizes the amount of the target product(s), is selected from all those obtained by the proposed method. For this, we have observed the concentration of the product inhibited enzymes of CCM pathway and its influence on its corresponding metabolite/substrate. We have also studied the concentration of the enzymes which are responsible for the synthesis of target products. We further hypothesize that an optimal pathway would opt for higher flux rate reactions. In light of these observations, we can say that an optimal pathway should have lower enzyme concentration and higher flux rates. Finally, we demonstrate the superiority of the proposed method by comparing it with the extreme pathway analysis.

Kinetic modelling of plant metabolic pathways

This paper provides a review of kinetic modelling of plant metabolic pathways as a tool for analysing their control and regulation. An overview of different modelling strategies is presented, starting with those approaches that only require a knowledge of the network stoichiometry; these are referred to as structural. Flux-balance analysis, metabolic flux analysis using isotope labelling, and elementary mode analysis are briefly mentioned as three representative examples. The main focus of this paper, however, is a discussion of kinetic modelling, which requires, in addition to the stoichiometry, a knowledge of the kinetic properties of the constituent pathway enzymes. The different types of kinetic modelling analysis, namely time-course simulation, steady-state analysis, and metabolic control analysis, are explained in some detail. An overview is presented of strategies for obtaining model parameters, as well as software tools available for simulation of such models. The kinetic modelling approach is exemplified with discussion of three models from the general plant physiology literature. With the aid of kinetic modelling it is possible to perform a control analysis of a plant metabolic system, to identify potential targets for biotechnological manipulation, as well as to ascertain the regulatory importance of different enzymes (including isoforms of the same enzyme) in a pathway. Finally, a framework is presented for extending metabolic models to the whole-plant scale by linking biochemical reactions with diffusion and advective flow through the phloem. Future challenges include explicit modelling of subcellular compartments, as well as the integration of kinetic models on the different levels of the cellular and organizational hierarchy.

Two-stage flux balance analysis of metabolic networks for drug target identification

Background

Efficient identification of drug targets is one of major challenges for drug discovery and drug development. Traditional approaches to drug target identification include literature search-based target prioritization and in vitro binding assays which are both time-consuming and labor intensive. Computational integration of different knowledge sources is a more effective alternative. Wealth of omics data generated from genomic, proteomic and metabolomic techniques changes the way researchers view drug targets and provides unprecedent opportunities for drug target identification.

Results

In this paper, we develop a method based on flux balance analysis (FBA) of metabolic networks to identify potential drug targets. This method consists of two linear programming (LP) models, which first finds the steady optimal fluxes of reactions and the mass flows of metabolites in the pathologic state and then determines the fluxes and mass flows in the medication state with the minimal side effect caused by the medication. Drug targets are identified by comparing the fluxes of reactions in both states and examining the change of reaction fluxes. We give an illustrative example to show that the drug target identification problem can be solved effectively by our method, then apply it to a hyperuricemia-related purine metabolic pathway. Known drug targets for hyperuricemia are correctly identified by our two-stage FBA method, and the side effects of these targets are also taken into account. A number of other promising drug targets are found to be both effective and safe.

Conclusions

Our method is an efficient procedure for drug target identification through flux balance analysis of large-scale metabolic networks. It can generate testable predictions, provide insights into drug action mechanisms and guide experimental design of drug discovery.

Manipulating the steady state of metabolic pathways

Metabolic pathways show the complex interactions among enzymes that transform chemical compounds. The state of a metabolic pathway can be expressed as a vector, which denotes the yield of the compounds or the flux in that pathway at a given time. The steady state is a state that remains unchanged over time. Altering the state of the metabolism is very important for many applications such as biomedicine, biofuels, food industry, and cosmetics. The goal of the enzymatic target identification problem is to identify the set of enzymes whose knockouts lead the metabolism to a state that is close to a given goal state. Given that the size of the search space is exponential in the number of enzymes, the target identification problem is very computationally intensive. We develop efficient algorithms to solve the enzymatic target identification problem in this paper. Unlike existing algorithms, our method works for a broad set of metabolic network models. We measure the effect of the knockouts of a set of enzymes as a function of the deviation of the steady state of the pathway after their knockouts from the goal state. We develop two algorithms to find the enzyme set with minimal deviation from the goal state. The first one is a traversal approach that explores possible solutions in a systematic way using a branch and bound method. The second one uses genetic algorithms to derive good solutions from a set of alternative solutions iteratively. Unlike the former one, this one can run for very large pathways. Our experiments show that our algorithms' results follow those obtained in vitro in the literature from a number of applications. They also show that the traversal method is a good approximation of the exhaustive search algorithm and it is up to 11 times faster than the exhaustive one. This algorithm runs efficiently for pathways with up to 30 enzymes. For large pathways, our genetic algorithm can find good solutions in less than 10 minutes.