Redesigning metabolic networks using mathematical programming

The design of new generation bioprocessing plants is increasingly dependent on the design of process-compatible microorganisms. The latter, whether through genetic or physiological manipulations, can be greatly assisted by metabolic engineering. An emerging powerful tool in metabolic engineering research is computer-assisted cell design using mathematical programming. In this work, the problem of optimizing cellular metabolic networks has been formulated as a Mixed Integer Nonlinear Programming (MINLP) model. The model can assist genetic engineers to identify which cellular enzymes should be modified, and the new levels of activity required to produce an optimal network. Results are presented from the tricarboxylic acid cycle in Dictyostelium discoideum. Copyright 1998 John Wiley & Sons, Inc.     

A mathematical model of iron metabolism

A mathematical model of iron metabolism is presented. It comprises the following iron pools within the body: transferrin-bound iron in the plasma, iron in circulating red cells and their bone marrow precursors, iron in mucosal, parenchymal and reticuloendothelial cells. The control exerted by a hormone, called erythropoietin, on bone marrow utilization of iron for hemoglobin synthesis is taken into account. The model so obtained consists of a system of functional differential equations of retarded type. Most model parameters can be estimated from radiotracer experiments, others can be measured and numerical values can be assigned to the remaining ones making few reasonable assumptions according to the available physiological knowledge. Iron metabolism behavior under different therapeutical treatments was simulated. Model predictions were compared to experimental data collected in clinical routine.This work has been partially supported by C.N.R. (Italy) through grants N. 80.01227.07 and N. 81.00888.07     

A mathematical model of glutathione metabolism

Background and hypothesis

Based on neurochemical and genetic evidence, we suggest that both prevention and treatment of multiple addictions, such as dependence to alcohol, nicotine and glucose, should involve a biphasic approach. Thus, acute treatment should consist of preferential blocking of postsynaptic Nucleus Accumbens (NAc) dopamine receptors (D1-D5), whereas long term activation of the mesolimbic dopaminergic system should involve activation and/or release of Dopamine (DA) at the NAc site. Failure to do so will result in abnormal mood, behavior and potential suicide ideation. Individuals possessing a paucity of serotonergic and/or dopaminergic receptors, and an increased rate of synaptic DA catabolism due to high catabolic genotype of the COMT gene, are predisposed to self-medicating any substance or behavior that will activate DA release, including alcohol, opiates, psychostimulants, nicotine, gambling, sex, and even excessive internet gaming. Acute utilization of these substances and/or stimulatory behaviors induces a feeling of well being. Unfortunately, sustained and prolonged abuse leads to a toxic" pseudo feeling" of well being resulting in tolerance and disease or discomfort. Thus, a reduced number of DA receptors, due to carrying the DRD2 A1 allelic genotype, results in excessive craving behavior; whereas a normal or sufficient amount of DA receptors results in low craving behavior. In terms of preventing substance abuse, one goal would be to induce a proliferation of DA D2 receptors in genetically prone individuals. While in vivo experiments using a typical D2 receptor agonist induce down regulation, experiments in vitro have shown that constant stimulation of the DA receptor system via a known D2 agonist results in significant proliferation of D2 receptors in spite of genetic antecedents. In essence, D2 receptor stimulation signals negative feedback mechanisms in the mesolimbic system to induce mRNA expression causing proliferation of D2 receptors.

Proposal and conclusion

The authors propose that D2 receptor stimulation can be accomplished via the use of Synapatmine?, a natural but therapeutic nutraceutical formulation that potentially induces DA release, causing the same induction of D2-directed mRNA and thus proliferation of D2 receptors in the human. This proliferation of D2 receptors in turn will induce the attenuation of craving behavior. In fact as mentioned earlier, this model has been proven in research showing DNA-directed compensatory overexpression (a form of gene therapy) of the DRD2 receptors, resulting in a significant reduction in alcohol craving behavior in alcohol preferring rodents. Utilizing natural dopaminergic repletion therapy to promote long term dopaminergic activation will ultimately lead to a common, safe and effective modality to treat Reward Deficiency Syndrome (RDS) behaviors including Substance Use Disorders (SUD), Attention Deficit Hyperactivity Disorder (ADHD), Obesity and other reward deficient aberrant behaviors. This concept is further supported by the more comprehensive understanding of the role of dopamine in the NAc as a "wanting" messenger in the meso-limbic DA system.     

Medium term planning of biopharmaceutical manufacture using mathematical programming

Regulatory pressures and capacity constraints are forcing the biopharmaceutical industry to consider employing multiproduct manufacturing facilities running on a campaign basis. The need for such flexible and cost-effective manufacture poses a significant challenge for planning and scheduling. This paper reviews the problem of planning and scheduling of biopharmaceutical manufacture and presents a methodology for the planning of multiproduct biopharmaceutical manufacturing facilities. The problem is formulated as a mixed integer linear program (MILP) to represent the relevant decisions required within the planning process and is tested on two typical biopharmaceutical industry planning problems. The proposed formulation is compared with an industrial rule based approach, which it outperforms in terms of profitability. The results indicate that the developed formulation offers an effective representation of the planning problem and would be a useful decision tool for manufacturers in the biopharmaceutical industry particularly at times of limited manufacturing capacity.     

Analysis of pathological defects in methionine metabolism using a simple mathematical model

Derangements in methionine metabolism are a hallmark of cancers and homocystinuria, an inborn error of metabolism. In this study, the metabolic consequences of the pathological changes associated with the key pathway enzymes, methionine adenosyl transferase (MAT), glycine N-methyl transferase (GNMT) and cystathionine beta-synthase (CBS) as well as an activation of polyamine metabolism, were analyzed using a simple mathematical model describing methionine metabolism in liver. The model predicts that the mere loss of allosteric regulation of CBS by adenosylmethionine (AdoMet) leads to an increase in homocysteine concentration. This is consistent with the experimental data on the corresponding genetic defects, which specifically impair allosteric activation but not basal enzyme activity. Application of the characteristics of transformed hepatocytes to our model, i.e., substitution of the MAT I/III isozyme by MAT II, loss of GNMT activity and activation of polyamine biosynthesis, leads to the prediction of a significantly different dependence of methionine metabolism on methionine concentrations. The theoretical predictions were found to be in good agreement with experimental data obtained with the human hepatoma cell line, HepG2.     

A mechanobiological mathematical model of liver metabolism

The liver plays a complex role in metabolism and detoxification, and better tools are needed to understand its function and to develop liver-targeted therapies. In this study, we establish a mechanobiological model of liver transport and hepatocyte biology to elucidate the metabolism of urea and albumin, the production/detoxification of ammonia, and consumption of oxygen and nutrients. Since hepatocellular shear stress (SS) can influence the enzymatic activities of liver, the effect of SS on the urea and albumin synthesis are empirically modeled through the mechanotransduction mechanisms. The results demonstrate that the rheology and dynamics of the sinusoid flow can significantly affect liver metabolism. We show that perfusate rheology and blood hematocrit can affect urea and albumin production by changing hepatocyte mechanosensitive metabolism. The model can also simulate enzymatic diseases of the liver such as hyperammonemia I, hyperammonemia II, hyperarginemia, citrollinemia, and argininosuccinicaciduria, which disrupt the urea metabolism and ammonia detoxification. The model is also able to predict how aggregate cultures of hepatocytes differ from single cell cultures. We conclude that in vitro perfusable devices for the study of liver metabolism or personalized medicine should be designed with similar morphology and fluid dynamics as patient liver tissue. This robust model can be adapted to any type of hepatocyte culture to determine how hepatocyte viability, functionality, and metabolism are influenced by liver pathologies and environmental conditions.     

Identifying responsive modules by mathematical programming: an application to budding yeast cell cycle

High-throughput biological data offer an unprecedented opportunity to fully characterize biological processes. However, how to extract meaningful biological information from these datasets is a significant challenge. Recently, pathway-based analysis has gained much progress in identifying biomarkers for some phenotypes. Nevertheless, these so-called pathway-based methods are mainly individual-gene-based or molecule-complex-based analyses. In this paper, we developed a novel module-based method to reveal causal or dependent relations between network modules and biological phenotypes by integrating both gene expression data and protein-protein interaction network. Specifically, we first formulated the identification problem of the responsive modules underlying biological phenotypes as a mathematical programming model by exploiting phenotype difference, which can also be viewed as a multi-classification problem. Then, we applied it to study cell-cycle process of budding yeast from microarray data based on our biological experiments, and identified important phenotype- and transition-based responsive modules for different stages of cell-cycle process. The resulting responsive modules provide new insight into the regulation mechanisms of cell-cycle process from a network viewpoint. Moreover, the identification of transition modules provides a new way to study dynamical processes at a functional module level. In particular, we found that the dysfunction of a well-known module and two new modules may directly result in cell cycle arresting at S phase. In addition to our biological experiments, the identified responsive modules were also validated by two independent datasets on budding yeast cell cycle.     

A mathematical programming approach for gene selection and tissue classification

MOTIVATION: Extracting useful information from expression levels of thousands of genes generated with microarray technology needs a variety of analytical techniques. Mathematical programming approaches for classification analysis outperform parametric methods when the data depart from assumptions underlying these methods. Therefore, a mathematical programming approach is developed for gene selection and tissue classification using gene expression profiles. RESULTS: A new mixed integer programming model is formulated for this purpose. The mixed integer programming model simultaneously selects genes and constructs a classification model to classify two groups of tissue samples as accurately as possible. Very encouraging results were obtained with two data sets from the literature as examples. These results show that the mathematical programming approach can rival or outperform traditional classification methods.     

Developmental programming of skeletal muscle phenotype/metabolism

Skeletal muscle is a highly dynamic and malleable tissue that is able to adapt to different stimuli placed upon it, both during gestation and after birth, ultimately resulting in anatomical changes to muscle fibre composition. Variation in nutrient supply throughout gestation is common, whether in livestock or in the human. The specific effects of maternal nutrition on foetal development are at the forefront of scientific research. However, results describing how different maternal feeding strategies affect skeletal muscle fibre development in the offspring are not fully consistent, even where the same time windows during gestation have been examined. The aim of this study is to determine the effects of increased maternal nutrition (above the recommended levels) on the Musculus semitendinosus phenotype of progeny. In all, 24 pregnant sows were assigned to one of four feeding regimes during gestation; T1 (control group): 30 MJ digestible energy per day (MJ DE/day) throughout gestation, T2: same as that for T1 but increased to 60 MJ DE/day from 25 to 50 days of gestation (dg), T3: same as that for T1 but increased to 60 MJ DE/day from 50 to 80 dg, T4: same as that for T1 but increased nutrition to 60 MJ DE/day from 25 to 80 dg. Light- and heavy-weight littermate pairs of the same sex were selected at birth and individually fed to slaughter (c. 158 days). Histochemical and immunohistochemical staining were used to identify the predominantly oxidative (deep) and less oxidative (superficial) regions of the M. semitendinosus, and to determine total fibre number and proportions of fibre types. The results demonstrate that increased maternal nutrition alters skeletal muscle phenotype in the offspring by changing fibre-type proportions, leading to an increased oxidative capacity due to an increase in Type IIA fibres. No change in total muscle area, total muscle fibre number, or fibre cross-sectional area is observed. The precise molecular mechanism(s) by which these findings occur is being investigated.     

HEMETβ: improvement of hepatocyte metabolism mathematical model

This article describes hepatocyte metabolism mathematical model (HEMETβ), which is an improved version of HEMET, an effective and versatile virtual cell model based on hepatic cell metabolism. HEMET is based on a set of non-linear differential equations, implemented in Simulink®, which describes the biochemical reactions and energetic cell state, and completely mimics the principal metabolic pathways in hepatic cells. The cell energy function and modular structure are the core of this model. HEMETβ as HEMET model describes hepatic cellular metabolism in standard conditions (cell culture in a plastic multi-well placed in an incubator at 37°C with 5% of CO₂) and with excess substrates concentration. The main improvements in HEMETβ are the introductions of Michaelis–Menten models for reversible reactions and enzymatic inhibition. In addition, we eliminated hard non-linearities and modelled cell proliferation and every single aminoacid degradation pathway. All these innovations, combined with a user-friendly aspect, allow researchers to create new cell types and validate new experimental protocols just varying ‘peripheral’ pathways or model inputs.     

Controlling genetic variability by mathematical programming in a selection scheme on an open-pollinated population in Eucalyptus globulus

A model using integer quadratic mathematical programming has been developed to control the inbreeding level (or genetic diversity) through group coancestry in a selection programme for a forestry population structured in terms of maternal families coming from different locations. A method to calculate the average group coancestry between- and within-families for these open-pollinated populations is also proposed. This model has been applied to data from a breeding programme of Australian Eucalyptus globulus. The strategy proved to be effective as reductions of up to 50% for the group coancestry of the selected individuals were reached with a loss of only 5% of the maximum attainable selection differential (corresponding to truncation selection). Received: 14 October 1999 / Accepted: 26 July 2000     

Interactions in the metabolism of polyunsaturated fatty acids: analysis by a simple mathematical model

Interactions in the metabolism of polyunsaturated fatty acids have been simulated in a simple model system. In the development of this system it was assumed that simple competitive inhibition occurs between parent acids as they are transformed (via dehydrogenation and chain lengthening) to their derivative acids. Numerical solutions of this model system give the composition of the tissue pool of polyunsaturated acids as a function of the proportion of the parent acids in the diet. Experimental data have been analyzed in the light of relations generated by the model system and the parallels observed substantiate the assumptions postulated in the development of the model system.     

Insights into pathological mechanisms and interventions revealed by analyzing a mathematical model for cone metabolism

This work analyzes a mathematical model for the metabolic dynamics of a cone photoreceptor, which is the first model to account for energy generation from fatty acids oxidation of shed photoreceptor outer segments (POS). Multiple parameter bifurcation analysis shows that joint variations in external glucose, the efficiency of glucose transporter 1 (GLUT1), lipid utilization for POS renewal, and oxidation of fatty acids affect the cone’s metabolic vitality and its capability to adapt under glucose-deficient conditions. The analysis further reveals that when glucose is scarce, cone viability cannot be sustained by only fueling energy production in the mitochondria, but it also requires supporting anabolic processes to create lipids necessary for cell maintenance and repair. In silico experiments are used to investigate how the duration of glucose deprivation impacts the cell without and with a potential GLUT1 or oxidation of fatty acids intervention as well as a dual intervention. The results show that for prolonged duration of glucose deprivation, the cone metabolic system does not recover with higher oxidation of fatty acids and requires greater effectiveness of GLUT1 to recover. Finally, time-varying global sensitivity analysis (GSA) is applied to assess the sensitivity of the model outputs of interest to changes and uncertainty in the parameters at specific times. The results reveal a critical temporal window where there would be more flexibility for interventions to rescue a cone cell from the detrimental consequences of glucose shortage.