Models Of Biochemical Systems Research Articles

Examination of enzyme and metabolic activity in yeast expressing mutant alleles of triose phosphate isomerase (578.1)

Glycolysis is a highly conserved metabolic pathway by which the enzymatic breakdown of glucose occurs to yield energy in the form of ATP. Our research focuses on a mutation in an enzyme involved in glycolysis called triose phosphate isomerase (TPI). This enzyme converts DHAP to G3P in glycolysis. Importantly, mutations in TPI are associated with a human neurodegenerative disease called TPI deficiency and the pathology of TPI deficiency is still poorly understood. In order to study the effects of the TPI deficiency causing mutations on cellular processes we will use the yeast, Saccharomyces cerevisiae, as a biochemical model system for glycolysis, which is highly conserved between eukaryotes. S cerevisiae, when cultured without shaking, will rely heavily on the fermentation for energy production. We hypothesized that if the mutations that cause TPI deficiency resulted in reduced pyruvate production through glycolysis, then we would see a corresponding drop in carbon dioxide and ethanol production through fermentation. In addition, we examined redox activity due to cellular respiration with an alamar blue assay with shaking cultures. In addition, the activity of each TPI mutant allele was assessed by a spectrophotometric assay. Overall, we found that indeed some, but not all of the TPI mutants exhibited altered isomerase activity which affected metabolic output.

Stochastic Hybrid Automata with delayed transitions to model biochemical systems with delays

To study the effects of a delayed immune-response on the growth of an immunogenic neoplasm we introduce Stochastic Hybrid Automata with delayed transitions as a representation of hybrid biochemical systems with delays. These transitions abstractly model unknown dynamics for which a constant duration can be estimated, i.e. a delay. These automata are inspired by standard Stochastic Hybrid Automata, and their semantics is given in terms of Piecewise Deterministic Markov Processes. The approach is general and can be applied to systems where (i) components at low concentrations are modeled discretely (so to retain their intrinsic stochastic fluctuations), (ii) abundant component, e.g., chemical signals, are well approximated by mean-field equations (so to simulate them efficiently) and (iii) missing components are abstracted with delays. Via simulations we show in our application that interesting delay-induced phenomena arise, whose quantification is possible in this new quantitative framework.

An inverse small molecule screen to design a chemically defined medium supporting long-term growth of Drosophila cell lines.

Drosophila cell culture is used as a model system with multiple applications including the identification of new therapeutic targets in screens, the study of conserved signal transduction pathway mechanisms, and as an expression system for recombinant proteins. However, in vitro methods for Drosophila cell and organ cultures are relatively undeveloped. To characterize the minimal requirements for long-term maintenance of Drosophila cell lines, we developed an inverse screening strategy to identify small molecules and synergies stimulating proliferation in a chemically defined medium. In this chemical-genetics approach, a compound-protein interaction database is used to systematically score genetic targets on a screen-wide scale to extract further information about cell growth. In the pilot screen, we focused on two well-characterized cell lines, Clone 8 (Cl.8) and Schneider 2 (S2). Validated factors were investigated for their ability to maintain cell growth over multiple passages in the chemically defined medium (CDM). The polyamine spermidine proved to be the critical component that enables the CDM to support long-term maintenance of Cl.8 cells. Spermidine supplementation upregulates DNA synthesis for Cl.8 and S2 cells and increases MAPK signaling for Cl.8 cells. The CDM also supports the long-term growth of Kc167 cells. Our target scoring approach validated the importance of polyamines, with enrichment for multiple polyamine ontologies found for both cell lines. Future iterations of the screen will enable the identification of compound combinations optimized for specific applications-maintenance and generation of new cell lines or the production and purification of recombinant proteins-thus increasing the versatility of Drosophila cell culture as both a genetic and biochemical model system. Our cumulative target scoring approach improves on traditional chemical-genetics methods and is extensible to biological processes in other species.

A novel X-ray diffractometer for studies of liquid–liquid interfaces

The study of liquid-liquid interfaces with X-ray scattering methods requires special instrumental considerations. A dedicated liquid surface diffractometer employing a tilting double-crystal monochromator in Bragg geometry has been designed. This diffractometer allows reflectivity and grazing-incidence scattering measurements of an immobile mechanically completely decoupled liquid sample, providing high mechanical stability. The available energy range is from 6.4 to 29.4 keV, covering many important absorption edges. The instrument provides access in momentum space out to 2.54 Å(-1) in the surface normal and out to 14.8 Å(-1) in the in-plane direction at 29.4 keV. Owing to its modular design the diffractometer is also suitable for heavy apparatus such as vacuum chambers. The instrument performance is described and examples of X-ray reflectivity studies performed under in situ electrochemical control and on biochemical model systems are given.

Markov chain aggregation and its applications to combinatorial reaction networks

We consider a continuous-time Markov chain (CTMC) whose state space is partitioned into aggregates, and each aggregate is assigned a probability measure. A sufficient condition for defining a CTMC over the aggregates is presented as a variant of weak lumpability, which also characterizes that the measure over the original process can be recovered from that of the aggregated one. We show how the applicability of de-aggregation depends on the initial distribution. The application section is devoted to illustrate how the developed theory aids in reducing CTMC models of biochemical systems particularly in connection to protein-protein interactions. We assume that the model is written by a biologist in form of site-graph-rewrite rules. Site-graph-rewrite rules compactly express that, often, only a local context of a protein (instead of a full molecular species) needs to be in a certain configuration in order to trigger a reaction event. This observation leads to suitable aggregate Markov chains with smaller state spaces, thereby providing sufficient reduction in computational complexity. This is further exemplified in two case studies: simple unbounded polymerization and early EGFR/insulin crosstalk.

Stochastic modelling of biochemical systems of multi-step reactions using a simplified two-variable model

BackgroundA fundamental issue in systems biology is how to design simplified mathematical models for describing the dynamics of complex biochemical reaction systems. Among them, a key question is how to use simplified reactions to describe the chemical events of multi-step reactions that are ubiquitous in biochemistry and biophysics. To address this issue, a widely used approach in literature is to use one-step reaction to represent the multi-step chemical events. In recent years, a number of modelling methods have been designed to improve the accuracy of the one-step reaction method, including the use of reactions with time delay. However, our recent research results suggested that there are still deviations between the dynamics of delayed reactions and that of the multi-step reactions. Therefore, more sophisticated modelling methods are needed to accurately describe the complex biological systems in an efficient way.ResultsThis work designs a two-variable model to simplify chemical events of multi-step reactions. In addition to the total molecule number of a species, we first introduce a new concept regarding the location of molecules in the multi-step reactions, which is the second variable to represent the system dynamics. Then we propose a simulation algorithm to compute the probability for the firing of the last step reaction in the multi-step events. This probability function is evaluated using a deterministic model of ordinary differential equations and a stochastic model in the framework of the stochastic simulation algorithm. The efficiency of the proposed two-variable model is demonstrated by the realization of mRNA degradation process based on the experimentally measured data.ConclusionsNumerical results suggest that the proposed new two-variable model produces predictions that match the multi-step chemical reactions very well. The successful realization of the mRNA degradation dynamics indicates that the proposed method is a promising approach to reduce the complexity of biological systems.

Iodine-starch clathrate complexes under the impact of a low-frequency acoustic field

The results from research on the kinetics of destruction of clathrate complexes (amyloidine, amylopectoiodine and iodinol) in low-frequency acoustic waves from 5 to 25 Hz are presented. Features of the transfer of energy from low-frequency acoustic oscillations are determined. The ability of systems containing biologically active clathrate structures to interact in resonance with external acoustic stimuli according to the energy state of the active part of iodine-containing compexes is confirmed. In the first approximation, such compounds can be regarded as model biochemical systems.

Eigenvalues of Jacobian Matrices Report on Steps of Metabolic Reprogramming in a Complex Plant-Environment Interaction

Mathematical modeling of biochemical systems aims at improving the knowledge about complex regulatory networks. The experimental high-throughput measurement of levels of biochemical components, like metabolites and proteins, has become an integral part for characterization of biological systems. Yet, strategies of mathematical modeling to functionally integrate resulting data sets is still challenging. In plant biology, regulatory strategies that determine the metabolic output of metabolism as a response to changes in environmental conditions are hardly traceable by intuition. Mathematical modeling has been shown to be a promising approach to address such problems of plant-environment interaction promoting the comprehensive understanding of plant biochemistry and physiology. In this context, we recently published an inversely calculated solution for first-order partial derivatives, i.e. the Jacobian matrix, from experimental high-throughput data of a plant biochemical model system. Here, we present a biomathematical strategy, comprising 1) the inverse calculation of a biochemical Jacobian; 2) the characterization of the associated eigenvalues and 3) the interpretation of the results with respect to biochemical regulation. Deriving the real parts of eigenvalues provides information about the stability of solutions of inverse calculations. We found that shifts of the eigenvalue real part distributions occur together with metabolic shifts induced by short-term and long-term exposure to low temperature. This indicates the suitability of mathematical Jacobian characterization for recognizing perturbations in the metabolic homeostasis of plant metabolism. Together with our previously published results on inverse Jacobian calculation this represents a comprehensive strategy of mathematical modeling for the analysis of complex biochemical systems and plant-environment interactions from the molecular to the ecosystems level.

Simplifying Stochastic Mathematical Models of Biochemical Systems

Stochastic modeling of biochemical reactions taking place at the cellular level has become the subject of intense research in recent years. Molecular interactions in a single cell exhibit random fluctuations. These fluctuations may be significant when small populations of some reacting species are present and then a stochastic description of the cellular dynamics is required. Often, the biochemically reacting systems encountered in applications consist of many species interacting through many reaction channels. Also, the dynamics of such systems is typically non-linear and presents multiple time-scales. Consequently, the stochastic mathematical models of biochemical systems can be quite complex and their analysis challenging. In this paper, we present a method to reduce a stochastic continuous model of well-stirred biochemical systems, the Chemical Langevin Equation, while preserving the overall behavior of the system. Several tests of our method on models of practical interest gave excellent results.

From time series to biological network regulations: an evolutionary approach

In this paper we present a new methodology, based on genetic algorithms and multiple linear regression, for discovering regulation mechanisms responsible for observed time series in biological networks. The modeling framework employed is called Metabolic P systems; they are deterministic and time-discrete dynamical systems proposed as an effective alternative to ordinary differential equations for modeling biochemical systems. Our methodology is here successfully applied to the mitotic oscillator in early amphibian embryos. Starting from the time series of substances involved in this system, we are able to reconstruct an MP system reproducing the observed dynamics, where the regulatory components were discovered by our evolutionary methodology. In particular, genetic algorithms are used as a variable selection technique to identify the best representation of any regulation function in terms of some given primitive functions.

Post-Trapping Derivatization of Radical-Derived EPR-Silent Adducts: Application to Free Radical Detection by HPLC/UV in Chemical, Biochemical, and Biological Systems and Comparison with EPR Spectroscopy

Free radicals are conventionally detected by electron paramagnetic resonance (EPR) spectroscopy after being trapped as spin adducts. Albeit this technique has demonstrated utmost efficacy in studying free radicals, its application to biological settings is intrinsically hampered by the inevitable bioreduction of radical-derived paramagnetic adducts. Herein, we describe a reliable technique to detect and quantify free radical metabolites, wherein reduced alkyl- and phenyl-5,5-dimethyl-1-pyrroline N-oxide (DMPO) adducts are converted into ultrastable N-naphthoate esters. To mimic the ubiquitous in vivo microenvironment, bioreductants, exogenous thiols, and sodium borohydride were studied. Nitroxyl reduction was confirmed using EPR and triphenyltetrazolium chloride. The formation of the N-naphthoyloxy derivatives was established by liquid chromatography/mass spectrometry (LC/MS). The derivatives were chromatographed using a binary eluent. HPLC and internal standards were synthesized using Grignard addition. The labeled DMPO adduct is (1) fluorescent, (2) stable as opposed to nitroxyl radical adducts, (3) biologically relevant, and (4) excellently chromatographed. Applications encompassed chemical, biochemical, and biological model systems generating C-centered radicals. Different levels of phenyl radicals produced in situ from whole blood were successfully determined. The method is readily applicable to the detection of hydroxyl radical. Analogously, DMPO, the spin trap, could be detected with extreme sensitivity suitable for in vivo applications. The developed method proved to be a viable alternative to EPR, where for the first time the reductive loss of paramagnetic signals of DMPO-trapped free radicals is transformed into fluorescence emission. We believe the proposed methodology could represent a valuable tool to probe free radical metabolites in vivo using DMPO, the least toxic spin trap.

Engineered Troponin C Constructs Correct Disease-related Cardiac Myofilament Calcium Sensitivity

Aberrant myofilament Ca(2+) sensitivity is commonly observed with multiple cardiac diseases, especially familial cardiomyopathies. Although the etiology of the cardiomyopathies remains unclear, improving cardiac muscle Ca(2+) sensitivity through either pharmacological or genetic approaches shows promise of alleviating the disease-related symptoms. Due to its central role as the Ca(2+) sensor for cardiac muscle contraction, troponin C (TnC) stands out as an obvious and versatile target to reset disease-associated myofilament Ca(2+) sensitivity back to normal. To test the hypothesis that aberrant myofilament Ca(2+) sensitivity and its related function can be corrected through rationally engineered TnC constructs, three thin filament protein modifications representing different proteins (troponin I or troponin T), modifications (missense mutation, deletion, or truncation), and disease subtypes (familial or acquired) were studied. A fluorescent TnC was utilized to measure Ca(2+) binding to TnC in the physiologically relevant biochemical model system of reconstituted thin filaments. Consistent with the pathophysiology, the restrictive cardiomyopathy mutation, troponin I R192H, and ischemia-induced truncation of troponin I (residues 1-192) increased the Ca(2+) sensitivity of TnC on the thin filament, whereas the dilated cardiomyopathy mutation, troponin T ΔK210, decreased the Ca(2+) sensitivity of TnC on the thin filament. Rationally engineered TnC constructs corrected the abnormal Ca(2+) sensitivities of the thin filament, reconstituted actomyosin ATPase activity, and force generation in skinned trabeculae. Thus, the present study provides a novel and versatile therapeutic strategy to restore diseased cardiac muscle Ca(2+) sensitivity.

An adaptive stepsize method for the chemical Langevin equation

Mathematical and computational modeling are key tools in analyzing important biological processes in cells and living organisms. In particular, stochastic models are essential to accurately describe the cellular dynamics, when the assumption of the thermodynamic limit can no longer be applied. However, stochastic models are computationally much more challenging than the traditional deterministic models. Moreover, many biochemical systems arising in applications have multiple time-scales, which lead to mathematical stiffness. In this paper we investigate the numerical solution of a stochastic continuous model of well-stirred biochemical systems, the chemical Langevin equation. The chemical Langevin equation is a stochastic differential equation with multiplicative, non-commutative noise. We propose an adaptive stepsize algorithm for approximating the solution of models of biochemical systems in the Langevin regime, with small noise, based on estimates of the local error. The underlying numerical method is the Milstein scheme. The proposed adaptive method is tested on several examples arising in applications and it is shown to have improved efficiency and accuracy compared to the existing fixed stepsize schemes.

Antioxidant activity of hydroxy derivatives of coumarin

The inhibition efficiency (antioxidant activity) of hydroxy derivatives of coumarin, such as esculetin, dicumarol, and fraxetin, was studied in the methemalbumin-H2O2-tetramethylbenzidine (TMB) pseudoperoxidase system at 20 degrees C in a buffered physiological solution (pH 7.4) containing 6% DMF and 0.25% DMSO. The inhibitor's efficiency was quantitatively characterized by the inhibition constants (K(i), microM) and the inhibition degree (%). The K(i) values for esculetin, dicumarol, and fraxetin were 9.5, 15, and 26 microM, respectively. Esculetin and fraxetin inhibited pseudoperoxidase oxidation of TMB in a noncompetitive manner; dicumarol, in a mixed manner. The inhibiting activity ofesculetin in peroxidase-catalyzed TMB oxidation at pH 6.4 is characterized by a K(i) value equal to 1.15 microM, and the inhibition process is competitive. Esculetin was found to be the most effective antioxidant of plant origin among all derivatives previously studied in model biochemical systems.

Smoldyn on Graphics Processing Units: Massively Parallel Brownian Dynamics Simulations

Space is a very important aspect in the simulation of biochemical systems; recently, the need for simulation algorithms able to cope with space is becoming more and more compelling. Complex and detailed models of biochemical systems need to deal with the movement of single molecules and particles, taking into consideration localized fluctuations, transportation phenomena, and diffusion. A common drawback of spatial models lies in their complexity: models can become very large, and their simulation could be time consuming, especially if we want to capture the systems behavior in a reliable way using stochastic methods in conjunction with a high spatial resolution. In order to deliver the promise done by systems biology to be able to understand a system as whole, we need to scale up the size of models we are able to simulate, moving from sequential to parallel simulation algorithms. In this paper, we analyze Smoldyn, a widely diffused algorithm for stochastic simulation of chemical reactions with spatial resolution and single molecule detail, and we propose an alternative, innovative implementation that exploits the parallelism of Graphics Processing Units (GPUs). The implementation executes the most computational demanding steps (computation of diffusion, unimolecular, and bimolecular reaction, as well as the most common cases of molecule-surface interaction) on the GPU, computing them in parallel on each molecule of the system. The implementation offers good speed-ups and real time, high quality graphics output

Assays for RNA synthesis and replication by the hepatitis C virus

At least six major genotypes of Hepatitis C virus (HCV) cause liver diseases worldwide. The efficacy rates with current standard of care are about 50% against genotype 1, the most prevalent strain in the United States, Europe and Japan. Therefore more effective pan-genotypic therapies are needed. HCV RNA replication provides a number of validated targets for virus-specific and potentially pan-genotypic inhibitors. In vitro assays capturing the different steps of RNA synthesis are needed not only to identify new inhibitors, but also to examine their mechanisms of action. This review attempts to provide a comprehensive summary of the biochemical, cell-based and animal model systems to assess HCV polymerase activity and HCV RNA replication that should be useful for both basic research and applied studies.

Complexity reduction preserving dynamical behavior of biochemical networks

The complexity of biochemical systems, stemming from both the large number of components and the intricate interactions between these components, may hinder us in understanding the behavior of these systems. Therefore, effective methods are required to capture their key components and interactions. Here, we present a novel and efficient reduction method to simplify mathematical models of biochemical systems. Our method is based on the exploration of the so-called admissible region, that is the set of parameters for which the mathematical model yields some required output. From the shape of the admissible region, parameters that are really required in generating the output of the system can be identified and hence retained in the model, whereas the rest is removed.To describe the idea, first the admissible region of a very small artificial network with only three nodes and three parameters is determined. Despite its simplicity, this network reveals all the basic ingredients of our reduction method. The method is then applied to an epidermal growth factor receptor (EGFR) network model. It turns out that only about 34% of the network components are required to yield the correct response to the epidermal growth factor (EGF) that was measured in the experiments, whereas the rest could be considered as redundant for this purpose. Furthermore, it is shown that parameter sensitivity on its own is not a reliable tool for model reduction, because highly sensitive parameters are not always retained, whereas slightly sensitive parameters are not always removable.

HPLC Determination of 5,5-Dimethyl-1-Pyrroline N-Oxide Free Radical-Derived Adducts After Derivatization of the Electron Paramagnetic Resonance-Silent Species: Application To Chemical and Biochemical Model Systems

HPLC Determination of 5,5-Dimethyl-1-Pyrroline N-Oxide Free Radical-Derived Adducts After Derivatization of the Electron Paramagnetic Resonance-Silent Species: Application To Chemical and Biochemical Model Systems

SBRML- A Markup Language for Encoding Systems Biology Results

Abstract Background: The wide acceptance of Systems Biology Markup Language (SBML) as standard format for models of biochemical systems makes it possible to build, share, evaluate and develop biochemical models cooperatively. However, there is currently no standard format for encoding the results of computational analyses of systems biology models. To address this issue, we present here the Systems Biology Results Markup Language (SBRML), an XML-based format for representing systems biology results. SBRML provides a means of representing computational simulation results as well as encoding experimental data in the context of a particular model. Methods & Results: SBRML is based on XML and is specified through the XML Schema language. SBRML Object Model (SBRML-OM) was first developed using the Universal Modelling Language (UML), and a Model-Driven Architecture (MDA) approach was then used to derive the corresponding XML Schema semi-automatically with the help of mapping rules for classes and associations. SBRML can be used to describe any type of systems biology results, the model that is used to generate the results, the ontology terms that link all the terms/vocabularies used to an external ontology sources, the operation (e.g. time course, steady state etc.) that is performed on the model and a flexible means for encoding the results of the operation. SBRML associates a model with several data sets. Each data set consists of a series of values associated with model variables, and their corresponding parameter values. It provides a flexible way of indexing both simulation results and experimental data to model parameter values which supports both spreadsheet-like data or multidimensional data cubes. Some of its major uses are: associating experimental results with models for passing to analysis tools, sharing and archiving of model simulations and recording the results of analysis for validation, archiving or comparison. Conclusions: SBRML is a software-neutral language intended to allow any type of systems biology results to be represented. Standardization of systems biology results format will bring obvious benefits in terms of storage and retrieval, but will also benefit any program that needs to read data in the context of a biochemical model. Application areas are enzyme kinetics data, microarray gene expression data, and various types of simulation results. We will soon release a library (in various programming languages) for reading and writing SBRML documents.

The efficiency of reactant site sampling in network-free simulation of rule-based models for biochemical systems

Rule-based models, which are typically formulated to represent cell signaling systems, can now be simulated via various network-free simulation methods. In a network-free method, reaction rates are calculated for rules that characterize molecular interactions, and these rule rates, which each correspond to the cumulative rate of all reactions implied by a rule, are used to perform a stochastic simulation of reaction kinetics. Network-free methods, which can be viewed as generalizations of Gillespie's method, are so named because these methods do not require that a list of individual reactions implied by a set of rules be explicitly generated, which is a requirement of other methods for simulating rule-based models. This requirement is impractical for rule sets that imply large reaction networks (i.e. long lists of individual reactions), as reaction network generation is expensive. Here, we compare the network-free simulation methods implemented in RuleMonkey and NFsim, general-purpose software tools for simulating rule-based models encoded in the BioNetGen language. The method implemented in NFsim uses rejection sampling to correct overestimates of rule rates, which introduces null events (i.e. time steps that do not change the state of the system being simulated). The method implemented in RuleMonkey uses iterative updates to track rule rates exactly, which avoids null events. To ensure a fair comparison of the two methods, we developed implementations of the rejection and rejection-free methods specific to a particular class of kinetic models for multivalent ligand–receptor interactions. These implementations were written with the intention of making them as much alike as possible, minimizing the contribution of irrelevant coding differences to efficiency differences. Simulation results show that performance of the rejection method is equal to or better than that of the rejection-free method over wide parameter ranges. However, when parameter values are such that ligand-induced aggregation of receptors yields a large connected receptor cluster, the rejection-free method is more efficient.