Reaction kinetics of a two-photon excitation microparticle based immunoassay--from modelling to practice

Real time observation of reaction kinetics is one of the key features of the newly developed microparticle based two-photon excitation fluorescence immunoassay system (TPX). By observing binding reactions at the surface of individual microparticles during the incubation of an assay, the binding constants of an assay become apparent. This paper describes the use of the new system in quantifying the reaction parameters of human thyroid stimulating hormone (hTSH) assay. A mechanistic reaction model for the assay is presented. The reaction model is further shown to precisely predict the behaviour of the assay kinetics over a wide range of analyte concentrations.     

A database-based approach for predicting coupled cascade reaction kinetics in polymers: application to oxidative degradation kinetics of high-performance polymers

Coupled cascade reactions forming complex reaction networks can be commonly found in polymerisation reactions and other reactions involving radical intermediates. Predicting the mechanism and kinetics of such reactions requires proper modelling of complex reaction networks. This becomes particularly difficult when coupled cascade reactions occur in polymeric systems containing different types of residues. Here, we propose a residue-based database approach to model such reactions in polymers, with the aid of a visual interface developed here. We demonstrate this approach by predicting the oxidative degradation kinetics of high-performance polymers (HPPs). First, we show that residue-based reaction database can be linked to construct the whole reaction network. For this purpose, we developed a database for oxidation reactions of commonly occurring residues in industrially important HPPs. Then we implement a visual interface which takes inputs from a user about residues in a polymer of interest and subsequently link appropriate databases to build reaction network. Finally, this program executes numerical integration of rate equations in the back-end. Application of this approach and the developed program is demonstrated by studying the oxidative degradation kinetics of three well-known HPPs- PMR-15, HFPE-30 and PMR-II, where the computations took less than a minute in a conventional desktop computer.     

Calibration of bioaffinity assays using kinetic data

Bioaffinity assays are usually calibrated by using a set of standard measurements fitted to a simple empirical model. In this paper, a new calibration approach based on mechanistic model of reaction kinetics is presented. When the calibration assay is known in terms of reaction mechanism, incubation time, initial concentration, and rate constants, one can back-calculate concentrations of unknown samples measured in a nonequilibrium time point. This paper describes a calculation method of unknown sample concentrations based on kinetically measured single calibration assay point. The theoretical results are verified by two common in-vitro diagnostic assays.     

Hybrid dynamic modeling of Escherichia coli central metabolic network combining Michaelis–Menten and approximate kinetic equations

The construction of dynamic metabolic models at reaction network level requires the use of mechanistic enzymatic rate equations that comprise a large number of parameters. The lack of knowledge on these equations and the difficulty in the experimental identification of their associated parameters, represent nowadays the limiting factor in the construction of such models. In this study, we compare four alternative modeling approaches based on Michaelis–Menten kinetics for the bi-molecular reactions and different types of simplified rate equations for the remaining reactions (generalized mass action, convenience kinetics, lin-log and power-law). Using the mechanistic model for Escherichia coli central carbon metabolism as a benchmark, we investigate the alternative modeling approaches through comparative simulations analyses. The good dynamic behavior and the powerful predictive capabilities obtained using the hybrid model composed of Michaelis–Menten and the approximate lin-log kinetics indicate that this is a possible suitable approach to model complex large-scale networks where the exact rate laws are unknown.     

Something from nothing: bridging the gap between constraint-based and kinetic modelling

Two divergent modelling methodologies have been adopted to increase our understanding of metabolism and its regulation. Constraint-based modelling highlights the optimal path through a stoichiometric network within certain physicochemical constraints. Such an approach requires minimal biological data to make quantitative inferences about network behaviour; however, constraint-based modelling is unable to give an insight into cellular substrate concentrations. In contrast, kinetic modelling aims to characterize fully the mechanics of each enzymatic reaction. This approach suffers because parameterizing mechanistic models is both costly and time-consuming. In this paper, we outline a method for developing a kinetic model for a metabolic network, based solely on the knowledge of reaction stoichiometries. Fluxes through the system, estimated by flux balance analysis, are allowed to vary dynamically according to linlog kinetics. Elasticities are estimated from stoichiometric considerations. When compared to a popular branched model of yeast glycolysis, we observe an excellent agreement between the real and approximate models, despite the absence of (and indeed the requirement for) experimental data for kinetic constants. Moreover, using this particular methodology affords us analytical forms for steady state determination, stability analyses and studies of dynamical behaviour.     

Theoretical assessments of errors in rapid immunoassays-how critical is the exact timing and reagent concentrations?

The reliability of rapid immunoassay is a concern due to an incomplete incubation to a non-equilibrium state and is susceptible to different error factors causing variance. The most critical point in the process should be found in order to improve the accuracy, and reproducibility of immunoassays, and enhance the system robustness. In this paper, the behavior of rapid assays is predicted by simulations using mechanistic assay model, based on antibody-analyte binding reaction kinetics. This antibody-analyte binding reaction kinetics model was constructed for a generic three-component (immunometric) assay and the parameters were chosen to be those of a known surface binding assay. The effects of the exact incubation timing and the initial reagent concentrations were studied focusing on the early phase of incubation, the non-equilibrium state. The magnitudes of errors in the input parameters were estimated using knowledge from practical immunoassays. According to simulations, inaccurate incubation timing adds error in the results at very short incubation times, especially in low analyte concentrations. The inaccurate reagent concentrations increase variance at short incubation times, as well. The error decreases rapidly after the first few minutes of incubation.     

Timescale analysis of rule-based biochemical reaction networks

The flow of information within a cell is governed by a series of protein–protein interactions that can be described as a reaction network. Mathematical models of biochemical reaction networks can be constructed by repetitively applying specific rules that define how reactants interact and what new species are formed on reaction. To aid in understanding the underlying biochemistry, timescale analysis is one method developed to prune the size of the reaction network. In this work, we extend the methods associated with timescale analysis to reaction rules instead of the species contained within the network. To illustrate this approach, we applied timescale analysis to a simple receptor–ligand binding model and a rule‐based model of interleukin‐12 (IL‐12) signaling in naïve CD4+ T cells. The IL‐12 signaling pathway includes multiple protein–protein interactions that collectively transmit information; however, the level of mechanistic detail sufficient to capture the observed dynamics has not been justified based on the available data. The analysis correctly predicted that reactions associated with Janus Kinase 2 and Tyrosine Kinase 2 binding to their corresponding receptor exist at a pseudo‐equilibrium. By contrast, reactions associated with ligand binding and receptor turnover regulate cellular response to IL‐12. An empirical Bayesian approach was used to estimate the uncertainty in the timescales. This approach complements existing rank‐ and flux‐based methods that can be used to interrogate complex reaction networks. Ultimately, timescale analysis of rule‐based models is a computational tool that can be used to reveal the biochemical steps that regulate signaling dynamics. © 2011 American Institute of Chemical Engineers Biotechnol. Prog., 2012     

Enzymatic synthesis of amoxicillin: avoiding limitations of the mechanistic approach for reaction kinetics

A recurrent doubt that occurs to the enzyme‐kinetics modeler is, When should I stop adding parameters to my mechanistic model in order to fit a non‐conventional behavior? This problem becomes more and more involving when the complexity of the reaction network increases. This work intends to show how the use of artificial neural networks may circumvent the need of including an overwhelming number of parameters in the rate equations obtained through the classical, mechanistic approach. We focus on the synthesis of amoxicillin by the reaction of p‐OH‐phenylglycine methyl ester and 6‐aminopenicillanic acid, catalyzed by penicillin G acylase immobilized on glyoxyl‐agarose, at 25°C and pH 6.5. The reaction was carried on a batch reactor. Three kinetic models of this system were compared: a mechanistic, a semi‐empiric, and a hybrid–neural network (NN). A semi‐empiric, simplified model with a reasonable number of parameters was initially built‐up. It was able to portray many typical process conditions. However, it either underestimated or overestimated the rate of synthesis of amoxicillin when substrates' concentrations were low. A more complex, full‐scale mechanistic model that could span all operational conditions was intractable for all practical purposes. Finally, a hybrid model, that coupled artificial neural networks (NN) to mass‐balance equations was established, that succeeded in representing all situations of interest. Particularly, the NN could predict with accuracy reaction rates for conditions where the semi‐empiric model failed, namely, at low substrate concentrations, a situation that would occur, for instance, at the end of a fed‐batch industrial process. © 2002 Wiley Periodicals, Inc. Biotechnol Bioeng 80: 622–631, 2002.     

Signalling Network Construction for Modelling Plant Defence Response

Plant defence signalling response against various pathogens, including viruses, is a complex phenomenon. In resistant interaction a plant cell perceives the pathogen signal, transduces it within the cell and performs a reprogramming of the cell metabolism leading to the pathogen replication arrest. This work focuses on signalling pathways crucial for the plant defence response, i.e., the salicylic acid, jasmonic acid and ethylene signal transduction pathways, in the Arabidopsis thaliana model plant. The initial signalling network topology was constructed manually by defining the representation formalism, encoding the information from public databases and literature, and composing a pathway diagram. The manually constructed network structure consists of 175 components and 387 reactions. In order to complement the network topology with possibly missing relations, a new approach to automated information extraction from biological literature was developed. This approach, named Bio3graph, allows for automated extraction of biological relations from the literature, resulting in a set of (component1, reaction, component2) triplets and composing a graph structure which can be visualised, compared to the manually constructed topology and examined by the experts. Using a plant defence response vocabulary of components and reaction types, Bio3graph was applied to a set of 9,586 relevant full text articles, resulting in 137 newly detected reactions between the components. Finally, the manually constructed topology and the new reactions were merged to form a network structure consisting of 175 components and 524 reactions. The resulting pathway diagram of plant defence signalling represents a valuable source for further computational modelling and interpretation of omics data. The developed Bio3graph approach, implemented as an executable language processing and graph visualisation workflow, is publically available at http://ropot.ijs.si/bio3graph/and can be utilised for modelling other biological systems, given that an adequate vocabulary is provided.     

Kinetics and mechanism of the cutinase-catalyzed transesterification of oils in AOT reversed micellar system

The kinetics of the enzymatic transesterification between a mixture of triglycerides (oils) and methanol for biodiesel production in a bis(2-ethylhexyl) sodium sulfosuccinate (AOT)/isooctane reversed micellar system, using recombinant cutinase from Fusarium solani pisi as a catalyst, was investigated. In order to describe the results that were obtained, a mechanistic scheme was proposed, based on the literature and on the experimental data. This scheme includes the following reaction steps: the formation of the active enzyme–substrate complex, the addition of an alcohol molecule to the complex followed by the separation of a molecule of the fatty acid alkyl ester and a glycerol moiety, and release of the active enzyme. Enzyme inhibition and deactivation effects due to methanol and glycerol were incorporated in the model. This kinetic model was fitted to the concentration profiles of the fatty acid methyl esters (the components of biodiesel), tri-, di- and monoglycerides, obtained for a 24 h transesterification reaction performed in a stirred batch reactor under different reaction conditions of enzyme and initial substrates concentration.     

Dynamic modelling of the PI3K/MTOR signalling network uncovers biphasic dependence of mTORC1 activity on the mTORC2 subunit SIN1

The PI3K/MTOR signalling network regulates a broad array of critical cellular processes, including cell growth, metabolism and autophagy. The mechanistic target of rapamycin (MTOR) kinase functions as a core catalytic subunit in two physically and functionally distinct complexes mTORC1 and mTORC2, which also share other common components including MLST8 (also known as GβL) and DEPTOR. Despite intensive research, how mTORC1 and 2 assembly and activity are coordinated, and how they are functionally linked remain to be fully characterized. This is due in part to the complex network wiring, featuring multiple feedback loops and intricate post-translational modifications. Here, we integrate predictive network modelling, in vitro experiments and -omics data analysis to elucidate the emergent dynamic behaviour of the PI3K/MTOR network. We construct new mechanistic models that encapsulate critical mechanistic details, including mTORC1/2 coordination by MLST8 (de)ubiquitination and the Akt-to-mTORC2 positive feedback loop. Model simulations validated by experimental studies revealed a previously unknown biphasic, threshold-gated dependence of mTORC1 activity on the key mTORC2 subunit SIN1, which is robust against cell-to-cell variation in protein expression. In addition, our integrative analysis demonstrates that ubiquitination of MLST8, which is reversed by OTUD7B, is regulated by IRS1/2. Our results further support the essential role of MLST8 in enabling both mTORC1 and 2’s activity and suggest MLST8 as a viable therapeutic target in breast cancer. Overall, our study reports a new mechanistic model of PI3K/MTOR signalling incorporating MLST8-mediated mTORC1/2 formation and unveils a novel regulatory linkage between mTORC1 and mTORC2.     

Investigating Differential Dynamics of the MAPK Signaling Cascade Using a Multi-Parametric Global Sensitivity Analysis

Cell growth critically depends on signalling pathways whose regulation is the focus of intense research. Without utilizing a priori knowledge of the relative importance of pathway components, we have applied in silico computational methods to the EGF-induced MAPK cascade. Specifically, we systematically perturbed the entire parameter space, including initial conditions, using a Monte Carlo approach, and investigate which protein components or kinetic reaction steps contribute to the differentiation of ERK responses. The model, based on previous work by Brightman and Fell (2000), is composed of 28 reactions, 27 protein molecules, and 48 parameters from both mass action and Michaelis-Menten kinetics. Our multi-parametric systems analysis confirms that Raf inactivation is one of the key steps regulating ERK responses to be either transient or sustained. Furthermore, the results of amplitude-differential ERK phosphorylations within the transient case are mainly attributed to the balance between activation and inactivation of Ras while duration-differential ERK responses for the sustained case are, in addition to Ras, markedly affected by dephospho-/phosphorylation of both MEK and ERK. Our sub-module perturbations showed that MEK and ERK''s contribution to this differential ERK activation originates from fluctuations in intermediate pathway module components such as Ras and Raf, implicating a cooperative regulatory mode among the key components. The initial protein concentrations of corresponding reactions such as Ras, GAP, and Raf also influence the distinct signalling outputs of ERK activation. We then compare these results with those obtained from a single-parametric perturbation approach using an overall state sensitivity (OSS) analysis. The OSS findings indicate a more pronounced role of ERK''s inhibitory feedback effect on catalysing the dissociation of the SOS complex. Both approaches reveal the presence of multiple specific reactions involved in the distinct dynamics of ERK responses and the cell fate decisions they trigger. This work adds a mechanistic insight of the contribution of key pathway components, thus may support the identification of biomarkers for pharmaceutical drug discovery processes.     

Enzyme-catalyzed and binding reaction kinetics determined by titration calorimetry

BackgroundIsothermal calorimetry allows monitoring of reaction rates via direct measurement of the rate of heat produced by the reaction. Calorimetry is one of very few techniques that can be used to measure rates without taking a derivative of the primary data. Because heat is a universal indicator of chemical reactions, calorimetry can be used to measure kinetics in opaque solutions, suspensions, and multiple phase systems and does not require chemical labeling. The only significant limitation of calorimetry for kinetic measurements is that the time constant of the reaction must be greater than the time constant of the calorimeter which can range from a few seconds to a few minutes. Calorimetry has the unique ability to provide both kinetic and thermodynamic data.Scope of reviewThis article describes the calorimetric methodology for determining reaction kinetics and reviews examples from recent literature that demonstrate applications of titration calorimetry to determine kinetics of enzyme-catalyzed and ligand binding reactions.Major conclusionsA complete model for the temperature dependence of enzyme activity is presented. A previous method commonly used for blank corrections in determinations of equilibrium constants and enthalpy changes for binding reactions is shown to be subject to significant systematic error.General significanceMethods for determination of the kinetics of enzyme-catalyzed reactions and for simultaneous determination of thermodynamics and kinetics of ligand binding reactions are reviewed. This article is part of a Special Issue entitled Microcalorimetry in the BioSciences — Principles and Applications, edited by Fadi Bou-Abdallah.     

A population balance model of enzymatic lysis of microbial cells

A model is proposed for enzymatic lysis of microbial cells based on number balances over the distribution of cell-wall mass in a population of cells. Analytical solutions to the population balance equations were obtained by the method of characteristics for simple reaction kinetics. The model has been used to analyze the following cases of lysis in a nonhomogeneous cell population: wall hydrolysis with cell rupture and product release, the effect of a distribution of lysis rates, and lysis of two-layer cell walls. Rate expressions for the reactions of lysis can be derived from bulk-phase experiments; the distributions of cell size and product content can be measured independently by flow cytometric techniques. The population model also provides an explanation for the initial lag seen in lysis kinetics for virtually any initial distribution. The model demonstrates patterns of lysis and product recovery for heterogeneous populations of cells and also applies to the more general problem of soluble-enzyme reactions with heterogeneous solid substrates.     

Abnormal Behavior in Cascading Dynamics with Node Weight

Considering a preferential selection mechanism of load destination, we introduce a new method to quantify initial load distribution and subsequently construct a simple cascading model. By attacking the node with the highest load, we investigate the cascading dynamics in some synthetic networks. Surprisingly, we observe that for several networks of different structural patterns, a counterintuitive phenomenon emerges if the highest load attack is applied to the system, i.e., investing more resources to protect every node in a network inversely makes the whole network more vulnerable. We explain this ability paradox by analyzing the micro-structural components of the underlying network and therefore reveals how specific structural patterns may influence the cascading dynamics. We discover that the robustness of the network oscillates as the capacity of each node increases. The conclusion of the paper may shed lights on future investigations to avoid the demonstrated ability paradox and subsequent cascading failures in real-world networks.     

A Kinetic Analysis of Coupled (or Auxiliary) Enzyme Reactions

As a case study, we consider a coupled (or auxiliary) enzyme assay of two reactions obeying the Michaelis–Menten mechanism. The coupled reaction consists of a single-substrate, single-enzyme non-observable reaction followed by another single-substrate, single-enzyme observable reaction (indicator reaction). In this assay, the product of the non-observable reaction is the substrate of the indicator reaction. A mathematical analysis of the reaction kinetics is performed, and it is found that after an initial fast transient, the coupled reaction is described by a pair of interacting Michaelis–Menten equations. Moreover, we show that when the indicator reaction is fast, the quasi-steady-state dynamics are governed by three fast variables and one slow variable. Timescales that approximate the respective lengths of the indicator and non-observable reactions, as well as conditions for the validity of the Michaelis–Menten equations, are derived. The theory can be extended to deal with more complex sequences of enzyme-catalyzed reactions.     

A mathematical modelling framework for understanding chemorepulsive signal transduction in Dictyostelium

Chemorepulsion is the process by which an organism or a cell moves in the direction of decreasing chemical concentration. While a few experimental studies have been performed, no mathematical models exist for this process. In this paper we have modelled gradient sensing, the first subprocess of chemorepulsion, in Dictyostelium discoideum-a well characterized model eukaryotic system. We take the first steps towards achieving a comprehensive mechanistic understanding of chemorepulsion in this system. We have used, as a basis, the biochemical network of the Keizer-Gunnink et al. (2007) to develop the mathematical modelling framework. This network describes the underlying pathways of chemorepellent gradient sensing in D. discoideum. Working within this modelling framework we address whether the postulated interactions of the pathways and species in this network can lead to a chemorepulsive response. We also analyse the possible role of additional regulatory effects (such as additional receptor regulation of enzymes in this network) and if this is necessary to achieve this behaviour. Thus we have investigated the receptor regulation of important enzymes and feedback effects in the network. This modelling framework generates important insights into and testable predictions regarding the role of key components and feedback loops in regulating chemorepulsive gradient sensing, and what factors might be important for generating a chemorepulsive response; it serves as a first step towards a comprehensive mechanistic understanding of this process.     

The complex kinetics of auxin-binding to a particulate fraction from tobacco-pith callus

The kinetics of binding of 1-naphthylacetic acid to particulate fractions from tobacco-pith callus were studied. This binding site does not bind auxin at 0° C. Binding experiments performed at 25° C demonstrated an apparent K _a of approx. 6.5·10⁶ M^-1. A filtration method was developed in order to study non-equilibrium kinetics of this binding. Dissociation of the complex of auxin and binding site indicates the presence of at least two binding components with dissociation rate constants (k _off) of 6.1·10^-3 min^-1 and 6.0·10^-2 min^-1. This binding behaviour was not independent, indicating that the binding of auxin to the particulate fractions was more complex than binding of one hormone molecule to one binding site. This complexity was further confirmed by experiments in which the initial velocity of complex formation was measured. A model was worked out into which our data fit without contradictions. It involves the binding of four hormone molecules to one receptor molecule.     

Application of a new method of nonlinear dynamical system identification to biochemical problems

The system identification method for a variety of nonlinear dynamic models is elaborated. The problem of identification of an original nonlinear model presented as a system of ordinary differential equations in the Cauchy explicit form with a polynomial right part reduces to the solution of the system of linear equations for the constants of the dynamical model. In other words, to construct an integral model of the complex system (phenomenon), it is enough to collect some data array characterizing the time-course of dynamical parameters of the system. Collection of such a data array has always been a problem. However difficulties emerging are, as a rule, not principal and may be overcome almost without exception. The potentialities of the method under discussion are demonstrated by the example of the test problem of multiparametric nonlinear oscillator identification. The identification method proposed may be applied to the study of different biological systems and in particular the enzyme kinetics of complex biochemical reactions.