Dynamic simulation and metabolic re-design of a branched pathway using linlog kinetics

This paper presents a new mathematical framework for modeling of in vivo dynamics and for metabolic re-design: the linlog approach. This approach is an extension of metabolic control analysis (MCA), valid for large changes of enzyme and metabolite levels. Furthermore, the presented framework combines MCA with kinetic modeling, thereby also combining the merits of both approaches. The linlog framework includes general expressions giving the steady-state fluxes and metabolite concentrations as a function of enzyme levels and extracellular concentrations, and a metabolic design equation that allows direct calculation of required enzyme levels for a desired steady state when control and response coefficients are available. Expressions giving control coefficients as a function of the enzyme levels are also derived. The validity of the linlog approximation in metabolic modeling is demonstrated by application of linlog kinetics to a branched pathway with moiety conservation, reversible reactions and allosteric interactions. Results show that the linlog approximation is able to describe the non-linear dynamics of this pathway very well for concentration changes up to a factor 20. Also the metabolic design equation was tested successfully.     

Automated oncogene detection in complex protein networks with applications to the MAPK signal transduction pathway

Activation of the extracellular signal-regulated kinases (ERK1/2; p42/p44 mitogen-activated protein kinase (MAPK)) is one of the most extensively studied signaling pathways not least because it occurs downstream of oncogenic RAS. Here, we take advantage of the wealth of experimental data available on the canonical RAS/RAF/MEK/ERK pathway of Bhalla et al. to test the utility of a newly developed nonlinear analysis algorithm designed to predict likelihood of cellular transformation. By using ERK phosphorylation as an "output signal", the method analyzes experimentally determined kinetic data and predicts putative oncogenes and tumor suppressor gene products impacting the RAS/MAPK module using a purely theoretical approach. This analysis identified several modifiers of ERK/MAPK activation described previously. In addition, several novel enzymes are identified which are not previously described to affect ERK/MAPK phosphorylation. Importantly, the nonlinear analysis enables a ranking of modifiers of MAPK activation predicting their relative importance in RAS-dependent oncogenesis. The results are compared with a linearized analysis based on sensitivity analysis about the steady state or metabolic control analysis (MCA). The results are favorable, pointing to the utility of first-order sensitivity analysis and MCA in the analysis of complex signaling networks for oncogenes.     

Optimal re-design of primary metabolism in Escherichia coli using linlog kinetics

This paper examines the validity of the linlog approach, which was recently developed in our laboratory, by comparison of two different kinetic models for the metabolic network of Escherichia coli. The first model is a complete mechanistic model; the second is an approximative model in which linlog kinetics are applied. The parameters of the linlog model (elasticities) are derived from the mechanistic model. Three different optimization cases are examined. In all cases, the objective is to calculate the enzyme levels that maximize a certain flux while keeping the total amount of enzyme constant and preventing large changes of metabolite concentrations. For an average variation of metabolite levels of 10% and individual changes of a factor 2, the predicted enzyme levels, metabolite concentrations and fluxes of both models are highly similar. This similarity holds for changes in enzyme level of a factor 4-6 and for changes in fluxes up to a factor 6. In all three cases, the predicted optimal enzyme levels could neither have been found by intuition-based approaches, nor on basis of flux control coefficients. This demonstrates that kinetic models are essential tools in Metabolic Engineering. In this respect, the linlog approach is a valuable extension of MCA, since it allows construction of kinetic models, based on MCA parameters, that can be used for constrained optimization problems and are valid for large changes of metabolite and enzyme levels.     

Steady-state analysis of metabolic pathways: comparing the double modulation method and the lin-log approach

The increasing interest in studying enzyme kinetics under in vivo conditions requires practical methods to estimate control parameters from experimental data. In contrast to currently established approaches of dynamic modelling, this paper addresses the steady-state analysis of metabolic pathways. Within the framework of metabolic control analysis (MCA), elasticity coefficients are used to describe the control properties of a local enzyme reaction. The double modulation method is one of the first experimental approaches to estimate elasticity coefficients from measurements of steady-state flux rates and metabolite concentrations. We propose a generalized form of the double modulation method and compare it to the recently developed linear-logarithmic approach.     

Recognition of N-Glycoforms in Human Chorionic Gonadotropin by Monoclonal Antibodies and Their Interaction Motifs

The glycosylation of human chorionic gonadotropin (hCG) plays an important role in reproductive tumors. Detecting hCG N-glycosylation alteration may significantly improve the diagnostic accuracy and sensitivity of related cancers. However, developing an immunoassay directly against the N-linked oligosaccharides is unlikely because of the heterogeneity and low immunogenicity of carbohydrates. Here, we report a hydrogen/deuterium exchange and MS approach to investigate the effect of N-glycosylation on the binding of antibodies against different hCG glycoforms. Hyperglycosylated hCG was purified from the urine of invasive mole patients, and the structure of its N-linked oligosaccharides was confirmed to be more branched by MS. The binding kinetics of the anti-hCG antibodies MCA329 and MCA1024 against hCG and hyperglycosylated hCG were compared using biolayer interferometry. The binding affinity of MCA1024 changed significantly in response to the alteration of hCG N-linked oligosaccharides. Hydrogen/deuterium exchange-MS reveals that the peptide β65–83 of the hCG β subunit is the epitope for MCA1024. Site-specific N-glycosylation analysis suggests that N-linked oligosaccharides at Asn-13 and Asn-30 on the β subunit affect the binding affinity of MCA1024. These results prove that some antibodies are sensitive to the structural change of N-linked oligosaccharides, whereas others are not affected by N-glycosylation. It is promising to improve glycoprotein biomarker-based cancer diagnostics by developing combined immunoassays that can determine the level of protein and measure the degree of N-glycosylation simultaneously.     

Optimization-based metabolic control analysis

In this work, a novel optimization-based metabolic control analysis (OMCA) method is introduced for reducing data requirement for metabolic control analysis (MCA). It is postulated that using the optimal control approach, the fluxes in a metabolic network are correlated to metabolite concentrations and enzyme activities as a state-feedback control system that is optimal with respect to a homeostasis objective. It is then shown that the optimal feedback gains are directly related to the elasticity coefficients (ECs) of MCA. This approach requires determination of the relative "importance" of metabolites and fluxes for the system, which is possible with significantly reduced experimental data, as compared with typical MCA requirements. The OMCA approach is applied to a top-down control model of glycolysis in hepatocytes. It is statistically demonstrated that the OMCA model is capable of predicting the ECs observed experimentally with few exceptions. Further, an OMCA-based model reconciliation study shows that the modification of four assumed stoichiometric coefficients in the model can explain most of the discrepancies, with the exception of elasticities with respect to the NADH/NAD ratio.     

A design criterion for symmetric model discrimination based on flexible nominal sets

Experimental design applications for discriminating between models have been hampered by the assumption to know beforehand which model is the true one, which is counter to the very aim of the experiment. Previous approaches to alleviate this requirement were either symmetrizations of asymmetric techniques, or Bayesian, minimax, and sequential approaches. Here we present a genuinely symmetric criterion based on a linearized distance between mean-value surfaces and the newly introduced tool of flexible nominal sets. We demonstrate the computational efficiency of the approach using the proposed criterion and provide a Monte-Carlo evaluation of its discrimination performance on the basis of the likelihood ratio. An application for a pair of competing models in enzyme kinetics is given.     

Novel kinetics, behaviour and cell-type specificity of CD157-mediated tyrosine kinase signalling

CD157, a recently characterized leukocyte surface antigen, has recently been shown to induce tyrosine phosphorylation of a 130-kDa protein (p130) when cross-linked with its antibody (ligand). We have further investigated the detailed kinetics, behaviour and cell-type specificity of this CD157-stimulated p130 phosphorylation. We demonstrate that CD157-mediated p130 phosphorylation is ligand independent in recombinant CD157-expressing CHO, MCA102 and COS-7 cells but is ligand dependent in HL-60-differentiated monocytes (mHL-60) having enhanced CD157 expression. This p130 phosphorylation is activated only at lower temperatures (0-4 degrees C) in MCA102, COS-7 and mHL-60 cells but is temperature insensitive in CHO cells. We further demonstrate that the CHO/CD157 cell clones have approximately 22-28% slower rates of proliferation than that of a CHO/mock clone. But the MCA102 cell proliferation remains unaffected by CD157 expression. We postulate that the difference in the temperature sensitivity of p130 phosphorylation can be responsible for the discrepancy in the rates of MCA102/CD157 and CHO/CD157 cell proliferation.     

Lymphocytes generated by in vivo priming and in vitro sensitization demonstrate therapeutic efficacy against a murine tumor that lacks apparent immunogenicity

The adoptive transfer of sensitized lymphocytes is an effective means to mediate the regression of established tumors. However, successful therapy can only be demonstrated in animal models where tumors are intrinsically immunogenic, capable of eliciting systemic immunity. To explore the potential of this therapeutic approach to tumors of less immunogenicity, we have selected and used a murine tumor, MCA 102, for the current study because all attempts to immunize syngeneic mice failed. We report here that inoculation of mice with a mixture of tumor cells and a bacterial adjuvant, Corynebacterium parvum led to the production of sensitized, but not fully functional, lymphocytes in the draining lymph nodes (LN). These cells, termed pre-effector cells, could nevertheless further differentiate to acquire full immunologic function by an established in vitro sensitization culture method. In adoptive immunotherapy experiments, transfer of as few as 1.5 X 10(7) in vitro sensitized cells not only reduced established pulmonary MCA 102 metastases but also prolonged survival and cured tumors in a majority of the treated animals. In order to elicit pre-effector cells in vivo, inoculation with both tumor cells and C. parvum was essential. Although a broad range of numbers of MCA 102 tumor cells appeared to be effective, generation of pre-effector cells was dependent on the dose of C. parvum. We have found that a C. parvum dose of 25 micrograms was optimal, whereas higher doses of the adjuvant had suppressive effects. Analysis of the kinetics of their appearance revealed that the generation of pre-effector cells was transient. They were detectable 7 days after in vivo priming followed by a rapid decline. Furthermore, pre-effector cells were detected only in the regional draining LN. No reactivity was demonstrable in the spleen, mesenteric LN, PBL, or bone marrow. Taken together, these results expand the scope of immunotherapy by demonstrating the feasibility of manipulating a limited and obscure immune response to the MCA 102 tumor for therapeutic efficacy.     

Optimization of bioreactor using metabolic control analysis approach

A new methodology based on a metabolic control analysis (MCA) approach is developed for the optimization of continuous cascade bioreactor system. A general framework for representation of a cascade bioreactor system consisting of a large number of reactors as a single network is proposed. The kinetic and transport processes occurring in the system are represented as a reaction network with appropriate stoichiometry. Such representation of the bioreactor systems makes it amenable to the direct application of the MCA approach. The process sensitivity information is extracted using MCA methodology in the form of flux and concentration control coefficients. The process sensitivity information is shown to be a useful guide for determining the choice of decision variables for the purpose of optimization. A generalized problem of optimization of the bioreactor is formulated in which the decision variables are the operating conditions and kinetic parameters. The gradient of the objective function to be maximized with respect to all decision variables is obtained in the form of response coefficients. This gradient information can be used in any gradient-based optimization algorithm. The efficiency of the proposed technique is demonstrated with two examples taken from literature: biotransformation of crotonobetaine and alcohol fermentation in cascade bioreactor system.     

Control of directed cell migration in vivo by membrane-to-cortex attachment

Cell shape and motility are primarily controlled by cellular mechanics. The attachment of the plasma membrane to the underlying actomyosin cortex has been proposed to be important for cellular processes involving membrane deformation. However, little is known about the actual function of membrane-to-cortex attachment (MCA) in cell protrusion formation and migration, in particular in the context of the developing embryo. Here, we use a multidisciplinary approach to study MCA in zebrafish mesoderm and endoderm (mesendoderm) germ layer progenitor cells, which migrate using a combination of different protrusion types, namely, lamellipodia, filopodia, and blebs, during zebrafish gastrulation. By interfering with the activity of molecules linking the cortex to the membrane and measuring resulting changes in MCA by atomic force microscopy, we show that reducing MCA in mesendoderm progenitors increases the proportion of cellular blebs and reduces the directionality of cell migration. We propose that MCA is a key parameter controlling the relative proportions of different cell protrusion types in mesendoderm progenitors, and thus is key in controlling directed migration during gastrulation.     

A generalized numerical approach to steady-state enzyme kinetics: Applications to protein kinase inhibition

A generalized numerical treatment of steady-state enzyme kinetics is presented. This new approach relies on automatic computer derivation of the underlying mathematical model (a system of simultaneous nonlinear algebraic equations) from a symbolic representation of the reaction mechanism (a system of biochemical equations) provided by the researcher. The method allows experimental biochemists to analyze initial-rate enzyme kinetic data, under the steady-state approximation, without having to use any mathematical equations. An illustrative example is based on the inhibition kinetics of p56^lck kinase by an ATP competitive inhibitor. A computer implementation of the new method, in the modified software package DYNAFIT [Kuzmi?, P. (1996) Anal. Biochem. 237, 260–273], is freely available to all academic researchers.     

Clonal expansion of adult rat hepatic stem cell lines by suppression of asymmetric cell kinetics (SACK)

Adult stem cells have potential use for several biomedical applications, including cell replacement therapy, gene therapy, and tissue engineering. However, such applications have been limited due to difficulties encountered in expanding functional adult stem cells. We have developed a new approach to the problem of adult stem cell expansion based on the suppression of asymmetric cell kinetics (SACK). We postulated that asymmetric cell kinetics, required for adult stem cell function, were a major barrier to their expansion in culture. As such, conversion of adult stem cells from asymmetric cell kinetics to symmetric cell kinetics would promote their exponential expansion and longterm propagation in culture. The purine nucleoside xanthosine (Xs), which promotes guanine ribonucleotide biosynthesis, can be used to reversibly convert cells from asymmetric cell kinetics to symmetric cell kinetics. We used Xs supplementation to derive clonal epithelial cell lines from adult rat liver that have properties of adult hepatic stem cells. The properties of two Xs-derived cell lines, Lig-8 and Lig-13, are described in detail and compared to properties of adult rat hepatic cell lines derived without Xs supplementation. The Xs-derived cell lines exhibit Xs-dependent asymmetric cell kinetics and Xs-dependent expression of mature hepatic differentiation markers. Interestingly, Lig-8 cells produce progeny with properties consistent with hepatocyte differentiation, while Lig-13 progeny cells have properties consistent with bile duct epithelium differentiation. A stable adult cholangiocyte stem cell line has not been previously described. Consistent with the principles of their derivation, the SACK-derived hepatic cell lines exhibit neither senescence nor tumorigenic properties, and their differentiation properties are stable after longterm culture. These characteristics of SACK-derived stem cell lines underscore asymmetric cell kinetics as an essential adult stem cell property with potential to be the basis for a general approach to expansion and propagation of diverse adult stem cells.     

The condition for pseudo-first-order kinetics in enzymatic reactions is independent of the initial enzyme concentration

The linearization of the Michaelis-Menten reaction by pseudo-first-order kinetics is revised. A phase-plane analysis allows the derivation of a new condition for its validity that is directly linked to the reaction efficiency, and contrary to widely established knowledge, is independent of the initial enzyme concentration.     

Microbial metabolism as an evolutionary response: the cybernetic approach to modeling

The growth and metabolic capabilities of microorganisms depend on their interactions with the culture medium. Many media contain two or more key substrates, and an organism may have different preferences for the components. Microorganisms adjust their preferences according to the prevailing conditions so as to favor their own survival. Cybernetic modeling describes this evolutionary strategy by defining a goal that an organism tries to attain optimally at all times. The goal is often, but not always, maximization of growth, and it may require the cells to manipulate their metabolic processes in response to changing environmental conditions. The cybernetic approach overcomes some of the limitations of metabolic control analysis (MCA), but it does not substitute MCA. Here we review the development of the cybernetic modeling of microbial metabolism, how it may be combined with MCA, and what improvements are needed to make it a viable technique for industrial fermentation processes.     

Fermentation analysis by clustering

To supervise, stabilize and optimize antibiotic fermentations in the industrial scale expert systems are presently worked out. For the knowledge acquisition various classifiers are tested using a set of 27 nourseothricin fermentation runs. Two methods are applied: optimal clustering by help of minimum variance criterion and hierarchical clustering by help of dendrograms. The fermentations are classified with respect to the specific material costs as well as the product formation kinetics.List of Symbols a kg/m³ initial value of linearized product kinetics - b kg/(m³ · h) slope of linearized product kinetics - B binary variable (value 0 or 1) - C DM/kg specific costs - d distance - m number of samples - p kg/m³ product concentration - pO₂ % dissolved oxygen concentration - t h fermentation time - T h initial time of linearized product kinetics - n number of fermentation runs     

Mechanistic information on some inorganic and bioinorganic reactions from volume profile analysis

The value of the application of hydrostatic pressure as a variable in kinetics investigations designed to elucidate mechanisms of some inorganic and bioinorganic reactions is reviewed and appraised. This is accomplished by charting the development of this experimental approach that leads to the derivation of the volume of activation for an individual reaction, and in many cases to the establishment of a volume profile for an overall reaction. A selection of recent investigations in which volume profiles together with other information have been pivotal in understanding the relevant reaction mechanism is presented. Reactions highlighted are water exchange on both fully hydrated cations or on partially complexed aqua ions, transition metal complex formation, reactions of nitric oxide with a wide variety of iron complexes or iron-containing proteins, and potential oxidative catalysis employing hydrogen peroxide. Recent advances in theoretical calculations regarding solvent exchange on various ions, and particularly on lithium ions and beryllium ions are described.     

Constraint-based metabolic control analysis for rational strain engineering

The advancements in genome editing techniques over the past years have rekindled interest in rational metabolic engineering strategies. While Metabolic Control Analysis (MCA) is a well-established method for quantifying the effects of metabolic engineering interventions on flows in metabolic networks and metabolite concentrations, it does not consider the physiological limitations of the cellular environment and metabolic engineering design constraints. We report here a constraint-based framework, Network Response Analysis (NRA), for rational genetic strain design. NRA is cast as a Mixed-Integer Linear Programming problem that integrates MCA, Thermodynamically-based Flux Analysis (TFA), biologically relevant constraints, as well as genome editing restrictions into a comprehensive platform for identifying metabolic engineering targets. We show that the NRA formulation and its core constraints are equivalent to the ones of Flux Balance Analysis (FBA) and TFA, which allows it to be used for a wide range of optimization criteria and with various physiological constraints. We also show how the parametrization and introduction of biological constraints enhance the NRA formulation compared to the classical MCA approach, and we demonstrate its features and its ability to generate multiple alternative optimal strategies given several user-defined boundaries and objectives. In summary, NRA is a sophisticated alternative to classical MCA for rational metabolic engineering that accommodates the incorporation of physiological data at metabolic flux, metabolite concentration, and enzyme expression levels.     

A dynamical approach to chemical kinetics: Mass-action laws as generalized Riccati equations

It is shown how the fundamental laws of chemical kinetics for either open or closed systems with an arbitrarily large number of reactants can be represented as a system of Riccati-like differential equations. Through the use of a concise tensor notation, it is shown when and how the differential system is exactly reducible to linear form, a reduction without approximation that parallels the well-known similar reduction of a single simle Riccati equation. An example is worked out to show how open kinetics can lead to oscillatory chemical concentrations of the Change-Higgins type. The biologically central problem of great chemical speciation is discussed from the viewpoint of Gibbs ensemble theory within the linearized kinetics and, approximately, within the starting nonlinear kinetics where it is shown roughly how to estimate, from an overall temperature-like parameter characterizing the whole system, mean chemical levels and mean frequencies of oscillation, and where a gross oscillation of the total mass is estimated in terms of an anharmonic oscillator whose general structure is fixed from the structure of the chemical kinetic laws.