Reconstructing biochemical pathways from time course data

Time series data on biochemical reactions reveal transient behavior, away from chemical equilibrium, and contain information on the dynamic interactions among reacting components. However, this information can be difficult to extract using conventional analysis techniques. We present a new method to infer biochemical pathway mechanisms from time course data using a global nonlinear modeling technique to identify the elementary reaction steps which constitute the pathway. The method involves the generation of a complete dictionary of polynomial basis functions based on the law of mass action. Using these basis functions, there are two approaches to model construction, namely the general to specific and the specific to general approach. We demonstrate that our new methodology reconstructs the chemical reaction steps and connectivity of the glycolytic pathway of Lactococcus lactis from time course experimental data.     

Classification of chemical compounds to support complex queries in a pathway database

Data quality in biological databases has become a topic of great discussion. To provide high quality data and to deal with the vast amount of biochemical data, annotators and curators need to be supported by software that carries out part of their work in an (semi-) automatic manner. The detection of errors and inconsistencies is a part that requires the knowledge of domain experts, thus in most cases it is done manually, making it very expensive and time-consuming. This paper presents two tools to partially support the curation of data on biochemical pathways. The tool enables the automatic classification of chemical compounds based on their respective SMILES strings. Such classification allows the querying and visualization of biochemical reactions at different levels of abstraction, according to the level of detail at which the reaction participants are described. Chemical compounds can be classified in a flexible manner based on different criteria. The support of the process of data curation is provided by facilitating the detection of compounds that are identified as different but that are actually the same. This is also used to identify similar reactions and, in turn, pathways.     

Three steady state situation in an open chemical reaction system. I

In an isothermal continuously stirred tank reactor (open chemical reaction system) fed by sulphuric acid solutions of bromate, bromide and cerium)(III) bistability (three steady state situation) is experimentally observed. This remarkable behavior, based on the instability of one steady state, has important consequences for the understanding of excitability and biochemical control mechanisms. The mass-balance equations for the reactor and the chemical mechanism of the reaction are combined into a simple mathematical model. The behavior of the resulting nonlinear differential equations is examined analytically and by a graphical integration procedure (method of isoclines). Using realistic kinetic data, the model shows the same behavior as observed in the experiment.     

A Stronger Necessary Condition for the Multistationarity of Chemical Reaction Networks

Biochemical reaction networks grow bigger and bigger, fed by the high-throughput data provided by biologists and bred in open repositories of models allowing merging and evolution. Nevertheless, since the available data is still very far from permitting the identification of the increasing number of kinetic parameters of such models, the necessity of structural analyses for describing the dynamics of chemical networks appears stronger every day. Using the structural information, notably from the stoichiometric matrix, of a biochemical reaction system, we state a more strict version of the famous Thomas’ necessary condition for multistationarity. In particular, the obvious cases where Thomas’ condition was trivially satisfied, mutual inhibition due to a multimolecular reaction and mutual activation due to a reversible reaction, can now easily be ruled out. This more strict condition shall not be seen as some version of Thomas’ circuit functionality for the continuous case but rather as related and complementary to the whole domain of the structural analysis of (bio)chemical reaction systems, as pioneered by the chemical reaction network theory.     

Hammerhead redux: Does the new structure fit the old biochemical data?

The cleavage rates of 78 hammerhead ribozymes containing structurally conservative chemical modifications were collected from the literature and compared to the recently determined crystal structure of the Schistosoma mansoni hammerhead. With only a few exceptions, the biochemical data were consistent with the structure, indicating that the new structure closely resembles the transition state of the reaction. Since all the biochemical data were collected on minimal hammerheads that have a very different structure, the minimal hammerhead must be dynamic and occasionally adopt the quite different extended structure in order to cleave.     

Efficient parametric analysis of the chemical master equation through model order reduction

ABSTRACT: BACKGROUND: Stochastic biochemical reaction networks are commonly modelled by the chemical master equation, and can be simulated as first order linear differential equations through a finite state projection. Due to the very high state space dimension of these equations, numerical simulations are computationally expensive. This is a particular problem for analysis tasks requiring repeated simulations for different parameter values. Such tasks are computationally expensive to the point of infeasibility with the chemical master equation. RESULTS: In this article, we apply parametric model order reduction techniques in order to construct accurate low-dimensional parametric models of the chemical master equation. These surrogate models can be used in various parametric analysis task such as identifiability analysis, parameter estimation, or sensitivity analysis. As biological examples, we consider two models for gene regulation networks, a bistable switch and a network displaying stochastic oscillations. CONCLUSIONS: The results show that the parametric model reduction yields efficient models of stochastic biochemical reaction networks, and that these models can be useful for systems biology applications involving parametric analysis problems such as parameter exploration, optimization, estimation or sensitivity analysis.     

Application of multivariate resolution methods to the study of biochemical and biophysical processes

Multivariate resolution methods make up a set of mathematical tools that may be applied to the analysis and interpretation of spectroscopic data recorded when monitoring a physical or chemical process with multichannel detectors. The goal of resolution methods is the recovery of chemical and/or physical information from the experimental data. Such data include, for example, the number of intermediates present in a reaction, the rate or equilibrium constants, and the spectra for each one of those intermediates. Multivariate resolution methods have been shown to be useful for the study of biophysical and biochemical processes such as folding/unfolding of proteins or nucleic acids. The present article reviews the most frequently used resolution methods, the limitations on their use, and their latest applications in protein and nucleic acid research.     

Translated Chemical Reaction Networks

Many biochemical and industrial applications involve complicated networks of simultaneously occurring chemical reactions. Under the assumption of mass action kinetics, the dynamics of these chemical reaction networks are governed by systems of polynomial ordinary differential equations. The steady states of these mass action systems have been analyzed via a variety of techniques, including stoichiometric network analysis, deficiency theory, and algebraic techniques (e.g., Gröbner bases). In this paper, we present a novel method for characterizing the steady states of mass action systems. Our method explicitly links a network’s capacity to permit a particular class of steady states, called toric steady states, to topological properties of a generalized network called a translated chemical reaction network. These networks share their reaction vectors with their source network but are permitted to have different complex stoichiometries and different network topologies. We apply the results to examples drawn from the biochemical literature.     

Plant-Mediated Synthesis and Applications of Iron Nanoparticles

Nanoscale iron particles have attracted substantial interest due to their unique physical and chemical properties. Over the years, various physical and chemical methods have been developed to synthesize these nanostructures which are usually expensive and potentially harmful to human health and the environment. Synthesis of iron nanoparticles (INPs) by using plant extract is now of great interest in order to develop a novel and sustainable approach toward green chemistry. In this method the chemical compounds and organic solvents are replaced with phytochemicals and aqueous matrixes, respectively. Similar to any chemical and biochemical reaction, factors such as reaction temperature, concentration of iron precursor, concentration of leaf extract, and reaction time have critical effects on the reaction yield. This review focuses on the novel approaches used for green synthesis of INPs by using plant resources. The currently available statistics including the factors affecting the synthesis process and potential applications of the fabricated nanoparticles are discussed. Recommendations are also given for areas of future research in order to improve the production process.     

Mesoscopic biochemical basis of isogenetic inheritance and canalization: stochasticity, nonlinearity, and emergent landscape

Biochemical reaction systems in mesoscopic volume, under sustained environmental chemical gradient(s), can have multiple stochastic attractors. Two distinct mechanisms are known for their origins: (a) Stochastic single-molecule events, such as gene expression, with slow gene on-off dynamics; and (b) nonlinear networks with feedbacks. These two mechanisms yield different volume dependence for the sojourn time of an attractor. As in the classic Arrhenius theory for temperature dependent transition rates, a landscape perspective provides a natural framework for the system's behavior. However, due to the nonequilibrium nature of the open chemical systems, the landscape, and the attractors it represents, are all themselves emergent properties of complex, mesoscopic dynamics. In terms of the landscape, we show a generalization of Kramers' approach is possible to provide a rate theory. The emergence of attractors is a form of self-organization in the mesoscopic system; stochastic attractors in biochemical systems such as gene regulation and cellular signaling are naturally inheritable via cell division. Delbrück-Gillespie's mesoscopic reaction system theory, therefore, provides a biochemical basis for spontaneous isogenetic switching and canalization.     

Memory switches in chemical reaction space

Just as complex electronic circuits are built from simple Boolean gates, diverse biological functions, including signal transduction, differentiation, and stress response, frequently use biochemical switches as a functional module. A relatively small number of such switches have been described in the literature, and these exhibit considerable diversity in chemical topology. We asked if biochemical switches are indeed rare and if there are common chemical motifs and family relationships among such switches. We performed a systematic exploration of chemical reaction space by generating all possible stoichiometrically valid chemical configurations up to 3 molecules and 6 reactions and up to 4 molecules and 3 reactions. We used Monte Carlo sampling of parameter space for each such configuration to generate specific models and checked each model for switching properties. We found nearly 4,500 reaction topologies, or about 10% of our tested configurations, that demonstrate switching behavior. Commonly accepted topological features such as feedback were poor predictors of bistability, and we identified new reaction motifs that were likely to be found in switches. Furthermore, the discovered switches were related in that most of the larger configurations were derived from smaller ones by addition of one or more reactions. To explore even larger configurations, we developed two tools: the “bistabilizer,” which converts almost-bistable systems into bistable ones, and frequent motif mining, which helps rank untested configurations. Both of these tools increased the coverage of our library of bistable systems. Thus, our systematic exploration of chemical reaction space has produced a valuable resource for investigating the key signaling motif of bistability.     

Reactions of vitamin A with acceptors of electrons. Interactions with iodine and the formation of iodide

1. The reactions of retinol and retinoic acid with iodine were investigated since knowledge of the chemical reactions of vitamin A with acceptors of electrons may shed light on its biochemical mode of action. 2. Colloidal retinol, but not retinoic acid, reacts with iodine to yield a blue-green complex that rapidly decomposes, giving iodide and an unknown species with lambda(max.) at 870mmu. 3. In addition, both retinol and retinoic acid reduce iodine to iodide by a reaction that does not involve an intermediate coloured complex; this reaction appears to yield unstable carbonium ion derivatives of the vitamin. 4. The presence of water greatly facilitates the production of iodide from vitamin A and iodine. 5. Possible chemical pathways involved in these reactions are discussed. 6. It is suggested that the chemical properties of retinol and retinoic acid that underlie their biochemical behaviour might be apparent only when the molecules are at a lipid-water interface, and that vitamin A might be expected to react with a number of different electron acceptors in vivo.     

Role of ribosomal protein L27 in peptidyl transfer

The current view of ribosomal peptidyl transfer is that the ribosome is a ribozyme and that ribosomal proteins are not involved in catalysis of the chemical reaction. This view is largely based on the first crystal structures of bacterial large ribosomal subunits that did not show any protein components near the peptidyl transferase center (PTC). Recent crystallographic data on the full 70S ribosome from Thermus thermophilus, however, show that ribosomal protein L27 extends with its N-terminus into the PTC in accordance with independent biochemical data, thus raising the question of whether the ribozyme picture is strictly valid. We have carried out extensive computer simulations of the peptidyl transfer reaction in the T. thermophilus ribosome to address the role of L27. The results show a reaction rate similar to that obtained in earlier simulations of the Haloarcula marismortui reaction. Furthermore, deletion of L27 is predicted to only give a minor rate reduction, in agreement with biochemical data, suggesting that the ribozyme view is indeed valid. The N-terminus of L27 is predicted to interact with the A76 phosphate group of the A-site tRNA, thereby explaining the observed impairment of A-site substrate binding for ribosomes lacking L27. Simulations are also reported for the reaction with puromycin, an A-site tRNA analogue which lacks the A76 phosphate group. The calculated energetics shows that this substrate can cause a downward p K a shift of L27 and that the reaction proceeds faster with the L27 N-terminus deprotonated, in contrast to the situation with aminoacyl-tRNA substrates. These results could explain the observed differences in pH dependence between the puromycin and C-puromycin reactions, where the former reaction has been seen to depend on an additional ionizing group besides the attacking amine, and our model predicts this ionizing group to be the N-terminal amine of L27.     

Exploring the diversity of complex metabolic networks

MOTIVATION: Metabolism, the network of chemical reactions that make life possible, is one of the most complex processes in nature. We describe here the development of a computational approach for the identification of every possible biochemical reaction from a given set of enzyme reaction rules that allows the de novo synthesis of metabolic pathways composed of these reactions, and the evaluation of these novel pathways with respect to their thermodynamic properties. RESULTS: We applied this framework to the analysis of the aromatic amino acid pathways and discovered almost 75,000 novel biochemical routes from chorismate to phenylalanine, more than 350,000 from chorismate to tyrosine, but only 13 from chorismate to tryptophan. Thermodynamic analysis of these pathways suggests that the native pathways are thermodynamically more favorable than the alternative possible pathways. The pathways generated involve compounds that exist in biological databases, as well as compounds that exist in chemical databases and novel compounds, suggesting novel biochemical routes for these compounds and the existence of biochemical compounds that remain to be discovered or synthesized through enzyme and pathway engineering. AVAILABILITY: Framework will be available via web interface at http://systemsbiology.northwestern.edu/BNICE (site under construction). CONTACT: vassily@northwestern.edu or broadbelt@northwestern.edu SUPPLEMENTARY INFORMATION: http://systemsbiology.northwestern.edu/BNICE/publications.     

Phenomenon of Life: Between Equilibrium and Non-Linearity

A model of ordering applicable to biological evolution is presented. It is shown that a steady state (more precisely approaching to a steady state) system of irreversible processes, under conditions of disproportionation of entropy, produces a lower-entropy product, that is, ordering. The ordering is defined as restricting of degrees of freedom: freedom of motion, interactions etc. The model differs from previous ones in that it relates the ordering to processes running not far from equilibrium, described in the linear field of non-equilibrium thermodynamics. It is shown that a system, which includes adenosine triphosphate (ATP) to adenosine diphosphate (ADP) conversion meets the demands of the physical model: it provides energy maintaining steady state conditions, and hydrolysis of ATP proceeding with consumption of water can be tightly conjugated with the most important reactions of synthesis of organic polymers (peptides, nucleotide chains etc.), which proceed with release of water. For these and other reasons ATP seems to be a key molecule of prebiotic evolution. It is argued that the elementary chemical reaction proceeding under control of an enzyme is not necessarily far from equilibrium. The experimental evidence supporting this idea, is presented. It is based on isotope data. Carbon isotope distribution in biochemical systems reveals regularity, which is inherent to steady state systems of chemical reactions, proceeding not far from equilibrium. In living organisms this feature appears at the statistical level, as many completely irreversible and non-linear processes occur in organisms. However not-far-from-equilibrium reactions are inherent to biochemical systems as a matter of principle. They are reconcilable with biochemical behavior. Extant organisms are highly evolved entities which, however, show in their basis the same features, as the simplest chemical systems must have had been involved in the origin of life. Some consequences following from the model, which may be significant for understanding the origin of life and the mechanism of biological evolution, are pointed out.     

Coupling of conformational folding and disulfide-bond reactions in oxidative folding of proteins

The oxidative folding of proteins consists of conformational folding and disulfide-bond reactions. These two processes are coupled significantly in folding-coupled regeneration steps, in which a single chemical reaction (the "forward" reaction) converts a conformationally unstable precursor species into a conformationally stable, disulfide-protected successor species. Two limiting-case mechanisms for folding-coupled regeneration steps are described. In the folded-precursor mechanism, the precursor species is preferentially folded at the moment of the forward reaction. The (transient) native structure increases the effective concentrations of the reactive thiol and disulfide groups, thus favoring the forward reaction. By contrast, in the quasi-stochastic mechanism, the forward reaction occurs quasi-stochastically in an unfolded precursor; i.e., reactive groups encounter each other with a probability determined primarily by loop entropy, albeit modified by conformational biases in the unfolded state. The resulting successor species is initially unfolded, and its folding competes with backward chemical reactions to the unfolded precursors. The folded-precursor and quasi-stochastic mechanisms may be distinguished experimentally by the dependence of their kinetics on factors affecting the rates of thiol--disulfide exchange and conformational (un)folding. Experimental data and structural and biochemical arguments suggest that the quasi-stochastic mechanism is more plausible than the folded-precursor mechanism for most proteins.     

Thermodynamics of stoichiometric biochemical networks in living systems far from equilibrium

The principles of thermodynamics apply to both equilibrium and nonequilibrium biochemical systems. The mathematical machinery of the classic thermodynamics, however, mainly applies to systems in equilibrium. We introduce a thermodynamic formalism for the study of metabolic biochemical reaction (open, nonlinear) networks in both time-dependent and time-independent nonequilibrium states. Classical concepts in equilibrium thermodynamics-enthalpy, entropy, and Gibbs free energy of biochemical reaction systems-are generalized to nonequilibrium settings. Chemical motive force, heat dissipation rate, and entropy production (creation) rate, key concepts in nonequilibrium systems, are introduced. Dynamic equations for the thermodynamic quantities are presented in terms of the key observables of a biochemical network: stoichiometric matrix Q, reaction fluxes J, and chemical potentials of species mu without evoking empirical rate laws. Energy conservation and the Second Law are established for steady-state and dynamic biochemical networks. The theory provides the physiochemical basis for analyzing large-scale metabolic networks in living organisms.     

Comparison of estimation capabilities of response surface methodology (RSM) with artificial neural network (ANN) in lipase-catalyzed synthesis of palm-based wax ester

Background  

Wax esters are important ingredients in cosmetics, pharmaceuticals, lubricants and other chemical industries due to their excellent wetting property. Since the naturally occurring wax esters are expensive and scarce, these esters can be produced by enzymatic alcoholysis of vegetable oils. In an enzymatic reaction, study on modeling and optimization of the reaction system to increase the efficiency of the process is very important. The classical method of optimization involves varying one parameter at a time that ignores the combined interactions between physicochemical parameters. RSM is one of the most popular techniques used for optimization of chemical and biochemical processes and ANNs are powerful and flexible tools that are well suited to modeling biochemical processes.     

Hyperdigraph-theoretic analysis of the EGFR signaling network: initial steps leading to GTP:Ras complex formation.

We construct an algebraic-combinatorial model of the SOS compartment of the EGFR biochemical network. A Petri net is used to construct an initial representation of the biochemical decision making network, which in turn defines a hyperdigraph. We observe that the linear algebraic structure of each hyperdigraph admits a canonical set of algebraic-combinatorial invariants that correspond to the information flow conservation laws governing a molecular kinetic reaction network. The linear algebraic structure of the hyperdigraph and its sets of invariants can be generalized to define a discrete algebraic-geometric structure, which is referred to as an oriented matroid. Oriented matroids define a polyhedral optimization geometry that is used to determine optimal subpaths that span the nullspace of a set of kinetic chemical reaction equations. Sets of constrained submodular path optimizations on the hyperdigraph are objectively obtained as a spanning tree of minimum cycle paths. This complete set of subcircuits is used to identify the network pinch points and invariant flow subpaths. We demonstrate that this family of minimal circuits also characteristically identifies additional significant biochemical reaction pattern features. We use the SOS Compartment A of the EGFR biochemical pathway to develop and demonstrate the application of our algebraic-combinatorial mathematical modeling methodology.     

Structural insights into intermediate steps in the Sir2 deacetylation reaction

Sirtuin enzymes comprise a unique class of NAD(+)-dependent protein deacetylases. Although structures of many sirtuin complexes have been determined, structural resolution of intermediate chemical steps are needed to understand the deacetylation mechanism. We report crystal structures of the bacterial sirtuin, Sir2Tm, in complex with an S-alkylamidate intermediate, analogous to the naturally occurring O-alkylamidate intermediate, and a Sir2Tm ternary complex containing a dissociated NAD(+) analog and acetylated peptide. The structures and biochemical studies reveal critical roles for the invariant active site histidine in positioning the reaction intermediate, and for a conserved phenylalanine residue in shielding reaction intermediates from base exchange with nicotinamide. The new structural and biochemical studies provide key mechanistic insight into intermediate steps of the Sir2 deacetylation reaction.