Thermodynamic studies of binary and ternary complexes of pig heart lactate dehydrogenase.

The thermodynamics of the reaction catalyzed by pig heart muscle lactate dehydrogenase (LDH; EC1.1.1,27) have been studied in 0,2 M potassium phosphate buffer, pH 7, over the temperature range of 10 to 35 degrees C by using oxamate and oxalate to simulate the corresponding reactions of the substrates pyruvate and lactate, respectively. The various complexes formed are characterized by Gibbs free energies, enthalpies, and entropies. The Gibbs free energies were determined by equilibrium dialysis investigations, fluorescence titrations, and ultraviolet difference spectroscopy, while the reaction enthalpies stem from direct calorimetric measurements, Formulas are given for both the temperature dependence of the equilibrium constants and the variation with temperature of the enthalpies involved in the four reactions between LDH and NADH or NAD, LDH-NADH and oxamate, and LDH-NAD and oxalate. All reactions show a marked negative temperature coefficient, deltacp, of the binding enthalpies indicating partial refolding to be associated with binary and ternary complex formation. This interpretation appears very probable in view of recent x-ray crystallographic studies on lactate dehydrogenase from dogfish, which demonstrate a volume decrease to occur on binding of oxamate to the LDH-NADH complex. The validity of the thermodynamic parameters, as derived with substrate analogues, for the actual catalytic reaction, gains strong support from the agreement between the sum of the heats involved in the four intermediary reactions reported in this study and direct determinations of the overall enthalpy associated with the catalytic process published in the literature.     

Kinetic constraints for formation of steady states in biochemical networks

The constraint-based analysis has emerged as a useful tool for analysis of biochemical networks. This work introduces the concept of kinetic constraints. It is shown that maximal reaction rates are appropriate constraints only for isolated enzymatic reactions. For biochemical networks, it is revealed that constraints for formation of a steady state require specific relationships between maximal reaction rates of all enzymes. The constraints for a branched network are significantly different from those for a cyclic network. Moreover, the constraints do not require Michaelis-Menten constants for most enzymes, and they only require the constants for the enzymes at the branching or cyclic point. Reversibility of reactions at system boundary or branching point may significantly impact on kinetic constraints. When enzymes are regulated, regulations may impose severe kinetic constraints for the formation of steady states. As the complexity of a network increases, kinetic constraints become more severe. In addition, it is demonstrated that kinetic constraints for networks with co-regulation can be analyzed using the approach. In general, co-regulation enhances the constraints and therefore larger fluctuations in fluxes can be accommodated in the networks with co-regulation. As a first example of the application, we derive the kinetic constraints for an actual network that describes sucrose accumulation in the sugar cane culm, and confirm their validity using numerical simulations.     

Calculating activation energies for temperature compensation in circadian rhythms

Many biological species possess a circadian clock, which helps them anticipate daily variations in the environment. In the absence of external stimuli, the rhythm persists autonomously with a period of approximately 24 h. However, single pulses of light, nutrients, chemicals or temperature can shift the clock phase. In the case of light- and temperature-cycles, this allows entrainment of the clock to cycles of exactly 24 h. Circadian clocks have the remarkable property of temperature compensation, that is, the period of the circadian rhythm remains relatively constant within a physiological range of temperatures. For several organisms, temperature-regulated processes within the circadian clock have been identified in recent years. However, how these processes contribute to temperature compensation is not fully understood. Here, we theoretically investigate temperature compensation in general oscillatory systems. It is known that every oscillator can be locally temperature compensated around a reference temperature, if reactions are appropriately balanced. A balancing is always possible if the control coefficient with respect to the oscillation period of at least one reaction in the oscillator network is positive. However, for global temperature compensation, the whole physiological temperature range is relevant. Here, we use an approach which leads to an optimization problem subject to the local balancing principle. We use this approach to analyse different circadian clock models proposed in the literature and calculate activation energies that lead to temperature compensation.     

Characteristic reaction paths of biochemical reaction systems with time scale separation

A technique has been developed for characterizing the in vivo behavior of key enzymes from intermediate measurements. The technique is based on the identification of characteristic reaction paths, and it depends on the time scale separation characteristics of the systems. It is shown that useful information can be obtained from the phase plots of properly selected intermediate pairs or combinations which typically show process insensitive algebraic relations approached on time scales short compared to those of most practical interest. These characteristic reaction paths provide useful global measures of enzyme activity. The mathematical basis of reaction path analysis is investigated using linear transformation techniques. General theorems are developed predicting the existence of characteristic reaction paths as asymptotic limits whenever there is effective time scale separation. These limits are reached when fast reactions are relaxed, and available evidence suggests that these conditions will occur for the majority of reaction networks.     

Self-stabilization of neuronal networks

Between the extreme views concerning ontogenesis (genetic vs. environmental determination), we use a moderate approach: a somehow pre-established neuronal model network reacts to activity deviations (reflecting input to be compensated), and stabilizes itself during a complex feed-back process. Morphogenesis is based on an algorithm formalizing the compensation theory of synaptogenesis (Wolff and Wagner 1983). This algorithm is applied to randomly connected McCulloch-Pitts networks that are able to maintain oscillations of their activity patterns over time. The algorithm can lead to networks which are morphogenetically stable but preserve self-maintained oscillations in activity. This is in contrast to most of the current models of synaptogenesis and synaptic modification based on Hebbian rules of plasticity. Hebbian networks are morphogenetically unstable without additional assumptions. The effects of compensation on structural and functional properties of the networks are described. It is concluded that the compensation theory of synaptogenesis can account for the development of morphogenetically stable neuronal networks out of randomly connected networks via selective stabilization and elimination of synapses.The logic of the compensation algorithm is based on experimental results. The present paper shows that the compensation theory can not only predict the behavior of synaptic populations (Wagner and Wolff, in preparation), but it can also describe the behavior of neurons interconnected in a network, with the resulting additional system properties. The neuronal interactions-leading to equilibrium in certain cases-are a self-organizing process in the sense that all decisions are performed on the individual cell level without knowing the overall network situation or goal.     

The Validity of Quasi-Steady-State Approximations in Discrete Stochastic Simulations

In biochemical networks, reactions often occur on disparate timescales and can be characterized as either fast or slow. The quasi-steady-state approximation (QSSA) utilizes timescale separation to project models of biochemical networks onto lower-dimensional slow manifolds. As a result, fast elementary reactions are not modeled explicitly, and their effect is captured by nonelementary reaction-rate functions (e.g., Hill functions). The accuracy of the QSSA applied to deterministic systems depends on how well timescales are separated. Recently, it has been proposed to use the nonelementary rate functions obtained via the deterministic QSSA to define propensity functions in stochastic simulations of biochemical networks. In this approach, termed the stochastic QSSA, fast reactions that are part of nonelementary reactions are not simulated, greatly reducing computation time. However, it is unclear when the stochastic QSSA provides an accurate approximation of the original stochastic simulation. We show that, unlike the deterministic QSSA, the validity of the stochastic QSSA does not follow from timescale separation alone, but also depends on the sensitivity of the nonelementary reaction rate functions to changes in the slow species. The stochastic QSSA becomes more accurate when this sensitivity is small. Different types of QSSAs result in nonelementary functions with different sensitivities, and the total QSSA results in less sensitive functions than the standard or the prefactor QSSA. We prove that, as a result, the stochastic QSSA becomes more accurate when nonelementary reaction functions are obtained using the total QSSA. Our work provides an apparently novel condition for the validity of the QSSA in stochastic simulations of biochemical reaction networks with disparate timescales.     

Effect of regulatory mechanism on hyperbolic reaction network properties

The notion that the regulated and flux-controlling enzyme in a metabolic network need not correspond suggests that the purpose of regulation may not be flux homeostasis under all physiological circumstances. Additionally, the fact that diversity in the function of intact metabolic networks exists suggests that in addition to time constant separation, other kinetic structure/regulatory mechanism patterns exist. In order to compliment and expand prior work on identifying kinetic structure-property relationships in networks, the present work explores in a general way how the control, dynamic, and energetic properties of metabolic networks depend on operating point, kinetic structure, and regulatory mechanism. The basic feature of trade-offs between properties is illustrated and used as a basis for indicating how particular subsets of structure, regulatory mechanism, and operating point emphasize certain properties that can be associated with a physiological function. Examples of scavenging trace metabolites and amphibolite coordination are proposed. Microstructure logic in terms of turnover number distributions as well as a potential mixed polynomial network analysis approach are also discussed.     

The Validity of Quasi-Steady-State Approximations in Discrete Stochastic Simulations

In biochemical networks, reactions often occur on disparate timescales and can be characterized as either fast or slow. The quasi-steady-state approximation (QSSA) utilizes timescale separation to project models of biochemical networks onto lower-dimensional slow manifolds. As a result, fast elementary reactions are not modeled explicitly, and their effect is captured by nonelementary reaction-rate functions (e.g., Hill functions). The accuracy of the QSSA applied to deterministic systems depends on how well timescales are separated. Recently, it has been proposed to use the nonelementary rate functions obtained via the deterministic QSSA to define propensity functions in stochastic simulations of biochemical networks. In this approach, termed the stochastic QSSA, fast reactions that are part of nonelementary reactions are not simulated, greatly reducing computation time. However, it is unclear when the stochastic QSSA provides an accurate approximation of the original stochastic simulation. We show that, unlike the deterministic QSSA, the validity of the stochastic QSSA does not follow from timescale separation alone, but also depends on the sensitivity of the nonelementary reaction rate functions to changes in the slow species. The stochastic QSSA becomes more accurate when this sensitivity is small. Different types of QSSAs result in nonelementary functions with different sensitivities, and the total QSSA results in less sensitive functions than the standard or the prefactor QSSA. We prove that, as a result, the stochastic QSSA becomes more accurate when nonelementary reaction functions are obtained using the total QSSA. Our work provides an apparently novel condition for the validity of the QSSA in stochastic simulations of biochemical reaction networks with disparate timescales.     

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.     

The isokinetic relationship. VII. Statistical analyses and examples for unimolecular reaction systems

The existence of the isokinctic relationship (IKR), also called the ‘compensation effect’, is examined for unimolecular reaction series. A statistical analysis on the bases of a common point of intersection of the Arrhenius plots is given. This method is performed using three experimcntal examples. They exhibit highly precise IKRs, showing that this relationship is not necessarily an artefact based on measurement errors. The isokinetic tempcrature, T_iso, of a reaction series is significantly higher in an excess of a mono- atomic inert gas than in gas phase reactions without the inert gas or for reactions in condensed phase. The isokinetic temperature seems to correspond to energy quanta available in the system which can be found in the vibrational spectra of the system.     

Four-dimensional visualisation and analysis of protein-protein interaction networks

Protein-protein interaction networks are typically built with interactions collated from many experiments. These networks are thus composite and show all interactions that are currently known to occur in a cell. However, these representations are static and ignore the constant changes in protein-protein interactions. Here we present software for the generation and analysis of dynamic, four-dimensional (4-D) protein interaction networks. In this, time-course-derived abundance data are mapped onto three-dimensional networks to generate network movies. These networks can be navigated, manipulated and queried in real time. Two types of dynamic networks can be generated: a 4-D network that maps expression data onto protein nodes and one that employs 'real-time rendering' by which protein nodes and their interactions appear and disappear in association with temporal changes in expression data. We illustrate the utility of this software by the analysis of singlish interface date hub interactions during the yeast cell cycle. In this, we show that proteins MLC1 and YPT52 show strict temporal control of when their interaction partners are expressed. Since these proteins have one and two interaction interfaces, respectively, it suggests that temporal control of gene expression may be used to limit competition at the interaction interfaces of some hub proteins. The software and movies of the 4-D networks are available at http://www.systemsbiology.org.au/downloads_geomi.html.     

Dynamic modeling of complex biological systems: a link between metabolic and macroscopic description

In this study, a class of dynamic models based on metabolic reaction pathways is analyzed, showing that systems with complex intracellular reaction networks can be represented by macroscopic reactions relating extracellular components only. Based on rigorous assumptions, the model reduction procedure is systematic and allows an equivalent 'input-output' representation of the system to be derived. The procedure is illustrated with a few examples.     

Kinetic and thermodynamic parameters for oxygen binding to the allosteric states of Panulirus interruptus hemocyanin

The temperature dependence of the oxygen binding equilibria and kinetics of Panulirus interruptus hemocyanin has been analyzed within the context of the two-state allosteric model. Oxygenation of the T-state is characterized by a more negative value of DeltaH than that of the R-state; therefore, cooperative effects in oxygen binding to P. interruptus hemocyanin are thermodynamically governed by favorable entropy changes. The allosteric transition in the unliganded derivative shows an enthalpy-entropy compensation effect. The activation enthalpies for oxygenation and deoxygenation of the T-state are larger than those for the R-state, while the activation entropies are favorable for the T-state and unfavorable for the R-state. Thus, the activation free energies for oxygen binding to the T- and R-states are similar, while for the deoxygenation reaction DeltaG++ is smaller for the T-state. The analysis reported confirms the applicability of the Monod-Wyman-Changeux two-state allosteric model to P. interruptus hemocyanin and yields a complete thermodynamic characterization of oxygen binding under both equilibrium and dynamic regimes.     

Sequence-Dependent Biophysical Modeling of DNA Amplification

A theoretical framework for prediction of the dynamic evolution of chemical species in DNA amplification reactions, for any specified sequence and operating conditions, is reported. Using the polymerase chain reaction (PCR) as an example, we developed a sequence- and temperature-dependent kinetic model for DNA amplification using first-principles biophysical modeling of DNA hybridization and polymerization. We compare this kinetic model with prior PCR models and discuss the features of our model that are essential for quantitative prediction of DNA amplification efficiency for arbitrary sequences and operating conditions. Using this model, the kinetics of PCR is analyzed. The ability of the model to distinguish between the dynamic evolution of distinct DNA sequences in DNA amplification reactions is demonstrated. The kinetic model is solved for a typical PCR temperature protocol to motivate the need for optimization of the dynamic operating conditions of DNA amplification reactions. It is shown that amplification efficiency is affected by dynamic processes that are not accurately represented in the simplified models of DNA amplification that form the basis of conventional temperature cycling protocols. Based on this analysis, a modified temperature protocol that improves PCR efficiency is suggested. Use of this sequence-dependent kinetic model in a control theoretic framework to determine the optimal dynamic operating conditions of DNA amplification reactions, for any specified amplification objective, is discussed.