Mechanism of protection of peroxidase activity by oscillatory dynamics.

The peroxidase-oxidase reaction is known to involve reactive oxygen species as intermediates. These intermediates inactivate many types of biomolecules, including peroxidase itself. Previously, we have shown that oscillatory dynamics in the peroxidase-oxidase reaction seem to protect the enzyme from inactivation. It was suggested that this is due to a lower average concentration of reactive oxygen species in the oscillatory state compared to the steady state. Here, we studied the peroxidase-oxidase reaction with either 4-hydroxybenzoic acid or melatonin as cofactors. We show that the protective effect of oscillatory dynamics is present in both cases. We also found that the enzyme degradation depends on the concentration of the cofactor and on the pH of the reaction mixture. We simulated the oscillatory behaviour, including the oscillation/steady state bistability observed experimentally, using a detailed reaction scheme. The computational results confirm the hypothesis that protection is due to lower average concentrations of superoxide radical during oscillations. They also show that the shape of the oscillations changes with increasing cofactor concentration resulting in a further decrease in the average concentration of radicals. We therefore hypothesize that the protective effect of oscillatory dynamics is a general effect in this system.     

Concerted simulations reveal how peroxidase compound III formation results in cellular oscillations

A major problem in mathematical modeling of the dynamics of complex biological systems is the frequent lack of knowledge of kinetic parameters. Here, we apply Brownian dynamics simulations, based on protein three-dimensional structures, to estimate a previously undetermined kinetic parameter, which is then used in biochemical network simulations. The peroxidase-oxidase reaction involves many elementary steps and displays oscillatory dynamics important for immune response. Brownian dynamics simulations were performed for three different peroxidases to estimate the rate constant for one of the elementary steps crucial for oscillations in the peroxidase-oxidase reaction, the association of superoxide with peroxidase. Computed second-order rate constants agree well with available experimental data and permit prediction of rate constants at physiological conditions. The simulations show that electrostatic interactions depress the rate of superoxide association with myeloperoxidase, bringing it into the range necessary for oscillatory behavior in activated neutrophils. Such negative electrostatic steering of enzyme-substrate association presents a novel control mechanism and lies in sharp contrast to the electrostatically-steered fast association of superoxide and Cu/Zn superoxide dismutase, which is also simulated here. The results demonstrate the potential of an integrated and concerted application of structure-based simulations and biochemical network simulations in cellular systems biology.     

Mechanism of melatonin-induced oscillations in the peroxidase-oxidase reaction

Melatonin induces oscillations in the peroxidase-oxidase (PO) reaction catalyzed by horseradish peroxidase. We present here studies of the effect of pH, enzyme concentration, and concentration of melatonin on the oscillation frequency. We also present a mechanistic model to explain the experimentally observed changes in oscillation frequency. Using the data obtained here we are able to predict that oscillations will also occur in the PO reaction catalyzed by myeloperoxidase. Myeloperoxidase is an important protein in activated neutrophils and we provide evidence that the oscillations of NAD(P)H, superoxide and hydrogen peroxide in these cells may involve this enzyme. Thus, our experimental system can be considered a model system for the nonrespiratory oxygen metabolism in activated neutrophils and other similar cells participating in the defence against invading pathogens.     

Hydrogen/deuterium isotope effect in the oscillating peroxidase-oxidase reaction.

The oscillatory peroxidase-oxidase reaction has been investigated by using NADH deuterated in the nicotinamide 4-A position. A considerable kinetic hydrogen/deuterium isotope effect on the oscillatory behavior was revealed, which may provide an additional valuable tool for mechanistic studies and for discriminating between various mechanistic models of the peroxidase-oxidase reaction. Particularly, this effect manifests in different oscillation frequencies. A sequence of simple and aperiodic oscillations was found between two stable steady states.     

Melatonin activates the peroxidase-oxidase reaction and promotes oscillations.

We have studied the peroxidase-oxidase reaction with NADH and O2 as substrates and melatonin as a cofactor in a semibatch reactor. We show for the first time that melatonin is an activator of the reaction catalyzed by enzymes from both plant and animal sources. Furthermore, melatonin promotes oscillatory dynamics in the pH range from 5 to 6. The frequency of the oscillations depends on the pH such that an increase in pH was accompanied by a decrease in frequency. Conversely, an increase in the flow rate of NADH or an increase in the average concentration of NADH resulted in an increase in oscillation frequency. Complex dynamics were not observed with melatonin as a cofactor. These results are discussed in relation to observations of oscillatory dynamics and the function of melatonin and peroxidase in activated neutrophils.     

Computer simulation of sustained oscillations in peroxidase-oxidase reaction

A system of differential equations of second order exhibiting transitional behaviour and sustained oscillations has been obtained for a complete scheme of the peroxidase-oxidase reaction. The concentrations of hydrogen peroxide and of hydrogen donor radicals are slow variables of the system. The most essential reactions responsible for oscillations have been selected. Analysis of the system in phase plane and in parameter space has been carried out. The dependence of oscillation period and amplitude on the parameter values has been investigated.     

A model of the oscillatory metabolism of activated neutrophils

We present a two-compartment model to explain the oscillatory behavior observed experimentally in activated neutrophils. Our model is based mainly on the peroxidase-oxidase reaction catalyzed by myeloperoxidase with melatonin as a cofactor and NADPH oxidase, a major protein in the phagosome membrane of the leukocyte. The model predicts that after activation of a neutrophil, an increase in the activity of the hexose monophosphate shunt and the delivery of myeloperoxidase into the phagosome results in oscillations in oxygen and NAD(P)H concentration. The period of oscillation changes from >200 s to 10-30 s. The model is consistent with previously reported oscillations in cell metabolism and oxidant production. Key features and predictions of the model were confirmed experimentally. The requirement of the hexose monophosphate pathway for 10 s oscillations was verified using 6-aminonicotinamide and dexamethasone, which are inhibitors of glucose-6-phosphate dehydrogenase. The role of the NADPH oxidase in promoting oscillations was confirmed by dose-response studies of the effect of diphenylene iodonium, an inhibitor of the NADPH oxidase. Moreover, the model predicted an increase in the amplitude of NADPH oscillations in the presence of melatonin, which was confirmed experimentally. Successful computer modeling of complex chemical dynamics within cells and their chemical perturbation will enhance our ability to identify new antiinflammatory compounds.     

Slight phenotypic variation in predators and prey causes complex predator-prey oscillations

Predator-prey oscillations are expected to show a 1/4-phase lag between predator and prey. However, observed dynamics of natural or experimental predator-prey systems are often more complex. A striking but hardly studied example are sudden interruptions of classic 1/4-lag cycles with periods of antiphase oscillations, or periods without any regular predator-prey oscillations. These interruptions occur for a limited time before the system reverts to regular 1/4-lag oscillations, thus yielding intermittent cycles. Reasons for this behaviour are often difficult to reveal in experimental systems. Here we test the hypothesis that such complex dynamical behaviour may result from minor trait variation and trait adaptation in both the prey and predator, causing recurrent small changes in attack rates that may be hard to capture by empirical measurements. Using a model structure where the degree of trait variation in the predator can be explicitly controlled, we show that a very limited amount of adaptation resulting in 10–15% temporal variation in attack rates is already sufficient to generate these intermittent dynamics. Such minor variation may be present in experimental predator-prey systems, and may explain disruptions in regular 1/4-lag oscillations.     

Spatio-temporal dynamics of glycolysis in cell layers. A mathematical model

Glycolytic oscillations occur in many cell types and have been intensively studied in yeast. Recent experimental and theoretical research has been focussed on the oscillatory dynamics and the synchronisation mechanism in stirred yeast cell suspensions. Here we are interested in the spatio-temporal organisation of glycolysis in cell layers. To this end we study a grid of a few thousand compartments each containing a cell. The intracellular dynamics is described by a core model of glycolysis. The compartments can exchange metabolites via diffusion. The conditions for oscillatory dynamics in a single compartment are investigated by bifurcation analysis. The spatio-temporal behaviour of the cell layer is studied by simulations. The model predicts the propagation of repetitive wave fronts induced by a substrate gradient. The formation of these waves crucially depends on the diffusive exchange of the reaction product between cells. Depending on the kinetic parameters complex spatio-temporal behaviour such as periodic termination of waves can arise. In these cases the cellular oscillation characteristics depend on the location of the cell in the array.     

The oscillating peroxidase-oxidase reaction in an open system. Analysis of the reaction mechanism.

1. The oscillations in the peroxidase-oxidase reaction in an open system with NADH as the hydrogen donor are caused by the reaction starting and stopping at critical concentrations of the substrates O2 and NADH. The existence of such critical concentrations is typical of branched chain reactions. 2. The critical concentrations of O2 and NADH that determine the initiation of the reaction are mutually dependent. 3. The branching reactions that determine these critical concentrations involve compounds I and II. 4. Superoxide may be involved in the branching reactions by reacting with NADH and ferriperoxidase. At pH 5.1 the rate constant for the latter reaction is determined as 1.5 . 10(5) M-1 . s-1, whereas for the former reaction only an upper limit for the rate constant of 3.5 . 10(4) M-1 . s-1 could be estimated. These relatively low rate constants suggest that alternative branching reactions may also be involved.     

Bistability and oscillations in the Huang-Ferrell model of MAPK signaling

Physicochemical models of signaling pathways are characterized by high levels of structural and parametric uncertainty, reflecting both incomplete knowledge about signal transduction and the intrinsic variability of cellular processes. As a result, these models try to predict the dynamics of systems with tens or even hundreds of free parameters. At this level of uncertainty, model analysis should emphasize statistics of systems-level properties, rather than the detailed structure of solutions or boundaries separating different dynamic regimes. Based on the combination of random parameter search and continuation algorithms, we developed a methodology for the statistical analysis of mechanistic signaling models. In applying it to the well-studied MAPK cascade model, we discovered a large region of oscillations and explained their emergence from single-stage bistability. The surprising abundance of strongly nonlinear (oscillatory and bistable) input/output maps revealed by our analysis may be one of the reasons why the MAPK cascade in vivo is embedded in more complex regulatory structures. We argue that this type of analysis should accompany nonlinear multiparameter studies of stationary as well as transient features in network dynamics.     

Distribution of carbon isotopes ((13)C/(12)C) in cells and temporal organization of cellular processes]

Recent studies on fractionation of carbon isotopes in biological systems are reviewed. It follows that direct experimental proofs have been obtained that 1) basic fractionation of carbon isotopes in the cell is related to isotope effect in pyruvate decarboxylation; 2) fractionation of carbon isotopes in the above reaction in vivo proceeds with exhausting substrate pool. The latter provides natural relationship between metabolites isotope distribution and sequence of their synthesis in the cell cycle, or with the temporal organization of cellular metabolism. The non-steady and periodic pattern of pyruvate decarboxylation due to the exhausting substrate pool well agrees with the existing notions on reciprocal oscillations in the cell glycolytic chain. Experimental data are presented corroborating indirectly the existence of oscillations in bacterial cells. Earlier proposed model of the mechanism of carbon isotope fractionation based on the above principles can be used for analysing changes in isotopic characteristics of the organisms and interpreting their relations with metabolic processes.     

Stable long-period cycling and complex dynamics in a single-locus fertility model with genomic imprinting

Although long-period population size cycles and chaotic fluctuations in abundance are common in ecological models, such dynamics are uncommon in simple population-genetic models where convergence to a fixed equilibrium is most typical. When genotype-frequency cycling does occur, it is most often due to frequency-dependent selection that results from individual or species interactions. In this paper, we demonstrate that fertility selection and genomic imprinting are sufficient to generate a Hopf bifurcation and complex genotype-frequency cycling in a single-locus population-genetic model. Previous studies have shown that on its own, fertility selection can yield stable two-cycles but not long-period cycling characteristic of a Hopf bifurcation. Genomic imprinting, a molecular mechanism by which the expression of an allele depends on the sex of the donating parent, allows fitness matrices to be nonsymmetric, and this additional flexibility is crucial to the complex dynamics we observe in this fertility selection model. Additionally, we find under certain conditions that stable oscillations and a stable equilibrium point can coexist. These dynamics are characteristic of a Chenciner (generalized Hopf) bifurcation. We believe this model to be the simplest population-genetic model with such dynamics.     

Stable and transient periodic oscillations in a mathematical model for CTL response to HTLV-I infection

The cytotoxic T lymphocyte (CTL) response to the infection of CD4+ T cells by human T cell leukemia virus type I (HTLV-I) has previously been modelled using standard response functions, with relatively simple dynamical outcomes. In this paper, we investigate the consequences of a more general CTL response and show that a sigmoidal response function gives rise to complex behaviours previously unobserved. Multiple equilibria are shown to exist and none of the equilibria is a global attractor during the chronic infection phase. Coexistence of local attractors with their own basin of attractions is the norm. In addition, both stable and unstable periodic oscillations can be created through Hopf bifurcations. We show that transient periodic oscillations occur when a saddle-type periodic solution exists. As a consequence, transient periodic oscillations can be robust and observable. Implications of our findings to the dynamics of CTL response to HTLV-I infections in vivo and pathogenesis of HAM/TSP are discussed.     

Experimental Assessment of the Sensitiveness of an Electrochemical Oscillator towards Chemical Perturbations

In this study we address the problem of the response of a (electro)chemical oscillator towards chemical perturbations of different magnitudes. The chemical perturbation was achieved by addition of distinct amounts of trifluoromethanesulfonate (TFMSA), a rather stable and non-specifically adsorbing anion, and the system under investigation was the methanol electro-oxidation reaction under both stationary and oscillatory regimes. Increasing the anion concentration resulted in a decrease in the reaction rates of methanol oxidation and a general decrease in the parameter window where oscillations occurred. Furthermore, the addition of TFMSA was found to decrease the induction period and the total duration of oscillations. The mechanism underlying these observations was derived mathematically and revealed that inhibition in the methanol oxidation through blockage of active sites was found to further accelerate the intrinsic non-stationarity of the unperturbed system. Altogether, the presented results are among the few concerning the experimental assessment of the sensitiveness of an oscillator towards chemical perturbations. The universal nature of the complex chemical oscillator investigated here might be used for reference when studying the dynamics of other less accessible perturbed networks of (bio)chemical reactions.     

Dynamics of a biological fixed film for phenol degradation in a fluidized-bed bioreactor

Experimental and modeling studies were conducted to analyze the dynamic response behavior of a phenol-oxidizing fixed film using a differential, fluidized-bed bioreactor in a recycle loop with a well-mixed reservoir. With the bioreactor at steady state, a pulse of phenol was added to perturb the system, and the phenol concentration was monitored continuously until steady state was again achieved.The experimental dynamics were compared with a dynamic mathematical model based on diffusion and reaction within the biofilm, liquid mixing, and biofilm growth. Constant-pH experiments could be adequately described using an unstructured, double-Monod kinetic expression with substrate inhibition by phenol.However, in dynamic experiments without pH control, the pH of the liquid phase dropped, and damped oscillations were observed in the phenol concentration and reaction rate trajectories. Oscillatory solutions could not be induced in the model, even when product inhibition was included, and a linear stability analysis did not reveal tendencies toward instability. The cause of the experimental oscillations remains unknown.     

Heterogeneity of glycolytic oscillatory behaviour in individual yeast cells

There are many examples of oscillations in biological systems and one of the most investigated is glycolytic oscillations in yeast. These oscillations have been studied since the 1950s in dense, synchronized populations and in cell-free extracts, but it has for long been unknown whether a high cell density is a requirement for oscillations to be induced, or if individual cells can oscillate also in isolation without synchronization. Here we present an experimental method and a detailed kinetic model for studying glycolytic oscillations in individual, isolated yeast cells and compare them to previously reported studies of single-cell oscillations. The importance of single-cell studies of this phenomenon and relevant future research questions are also discussed.     

In vivo conditions induce faithful encoding of stimuli by reducing nonlinear synchronization in vestibular sensory neurons

Previous studies have shown that neurons within the vestibular nuclei (VN) can faithfully encode the time course of sensory input through changes in firing rate in vivo. However, studies performed in vitro have shown that these same VN neurons often display nonlinear synchronization (i.e. phase locking) in their spiking activity to the local maxima of sensory input, thereby severely limiting their capacity for faithful encoding of said input through changes in firing rate. We investigated this apparent discrepancy by studying the effects of in vivo conditions on VN neuron activity in vitro using a simple, physiologically based, model of cellular dynamics. We found that membrane potential oscillations were evoked both in response to step and zap current injection for a wide range of channel conductance values. These oscillations gave rise to a resonance in the spiking activity that causes synchronization to sinusoidal current injection at frequencies below 25 Hz. We hypothesized that the apparent discrepancy between VN response dynamics measured in in vitro conditions (i.e., consistent with our modeling results) and the dynamics measured in vivo conditions could be explained by an increase in trial-to-trial variability under in vivo vs. in vitro conditions. Accordingly, we mimicked more physiologically realistic conditions in our model by introducing a noise current to match the levels of resting discharge variability seen in vivo as quantified by the coefficient of variation (CV). While low noise intensities corresponding to CV values in the range 0.04-0.24 only eliminated synchronization for low (<8 Hz) frequency stimulation but not high (>12 Hz) frequency stimulation, higher noise intensities corresponding to CV values in the range 0.5-0.7 almost completely eliminated synchronization for all frequencies. Our results thus predict that, under natural (i.e. in vivo) conditions, the vestibular system uses increased variability to promote fidelity of encoding by single neurons. This prediction can be tested experimentally in vitro.     

Beyond Bt resistance of pests in the context of population dynamical complexity

Complexity in ecological systems often prevents long-term predictions about changes in population size and properties of the population dynamics. Mathematical modeling of such complex system behaviors can provide a rough idea of scenarios of the population dynamics. We use the reaction–diffusion model [Medvinsky, A.B., Morozov, A.Y., Velkov, V.V., Li, B.-L., Sokolov, M.S., Malchow, H., 2004. Modeling the invasion of recessive Bt-resistant insects: an impact on transgenic plants. J. Theor. Biol. 231, 121–127] to study the impact of pests resistant to toxins produced by genetically modified plants on the dynamics of the plant–insect system. Using genetically modified crops is an effective pest management tool for world-wide growers. However, there is a concern that pests may develop resistance to Bt toxins, which are a product of Bacillus thuringiensis genes introduced into genetically modified Bt plants. We show by computer simulations that the Bt plant–Bt-resistant insect dynamics resulting from the invasion of the Bt-resistant pests leads to variety of complex changes in the plant–insect biomass, which underlie the dependence of the Bt plant biomass on the duration of the insect reproduction period. We demonstrate that the plant and insect biomass can undergo both regular and irregular oscillations. We show that the character of such oscillations essentially depends on local insect fluxes resulting from inhomogeneous spatial distributions of the insects. In order to characterize the insect diffusion fluxes we introduce a new parameter, the diffusion number Dn. We show that the dependence between a value of Dn and regularity/irregularity of the plant–insect biomass oscillations is governed by a region in the model parameter space. In one of the regions the growth of the value of the diffusion number correlates with the transformation of regular oscillations into irregular ones, while in the neighboring region of the model parameter space the dependence between the character of the plant–insect oscillations and the value of the diffusion number Dn is more complex. The oscillations are irregular if the values of Dn are between 0.05 and 0.25. On either side of this interval the plant–insect oscillations are regular. The complex character of the response of the Bt crop–pest system to the invasion of Bt-resistant insects can lead to significant complications in attempts to regulate the system dynamics.