Periodic patterns in biochemical reactions

Complexity in subnetworks of a peroxidase-oxidase reaction model

The peroxidase-oxidase (PO) reaction is a paradigmatic (bio)chemical system well suited to study the organization and stability of self-sustained oscillatory phases typically present in nonlinear systems. The PO reaction can be simulated by the state-of-the-art Bronnikova-Fedkina-Schaffer-Olsen model involving ten coupled ordinary differential equations. The complex and dynamically rich distribution of self-sustained oscillatory stability phases of this model was recently investigated in detail. However, would it be possible to understand aspects of such a complex model using much simpler models? Here, we investigate stability phases predicted by three simple four-variable subnetworks derived from the complete model. While stability diagrams for such subnetworks are found to be distorted compared to those of the complete model, we find them to surprisingly preserve significant features of the original model as well as from the experimental system, e.g., period-doubling and period-adding scenarios. In addition, return maps obtained from the subnetworks look very similar to maps obtained in the experimental system under different conditions. Finally, two of the three subnetwork models are found to exhibit quint points, i.e., recently reported singular points where five distinct stability phases coalesce. We also provide experimental evidence that such quint points are present in the PO reaction.

Effects of propagation delay in coupled oscillators under direct-indirect coupling: Theory and experiment

Propagation delay arises in a coupling channel due to the finite propagation speed of signals and the dispersive nature of the channel. In this paper, we study the effects of propagation delay that appears in the indirect coupling path of direct (diffusive)-indirect (environmental) coupled oscillators. In sharp contrast to the direct coupled oscillators where propagation delay induces amplitude death, we show that in the case of direct-indirect coupling, even a small propagation delay is conducive to an oscillatory behavior. It is well known that simultaneous application of direct and indirect coupling is the general mechanism for amplitude death. However, here we show that the presence of propagation delay hinders the death state and helps the revival of oscillation. We demonstrate our results by considering chaotic time-delayed oscillators and FitzHugh-Nagumo oscillators. We use linear stability analysis to derive the explicit conditions for the onset of oscillation from the death state. We also verify the robustness of our results in an electronic hardware level experiment. Our study reveals that the effect of time delay on the dynamics of coupled oscillators is coupling function dependent and, therefore, highly non-trivial.

Polar N-terminal Residues Conserved in Type 2 Secretion Pseudopilins Determine Subunit Targeting and Membrane Extraction Steps during Fibre Assembly

Bacterial type 2 secretion systems (T2SS), type 4 pili, and archaeal flagella assemble fibres from initially membrane-embedded pseudopilin and pilin subunits. Fibre subunits are made as precursors with positively charged N-terminal anchors, whose cleavage via the prepilin peptidase, essential for pilin membrane extraction and assembly, is followed by N-methylation of the mature (pseudo)pilin N terminus. The conserved Glu residue at position 5 (E5) of mature (pseudo)pilins is essential for assembly. Unlike T4 pilins, where E5 residue substitutions also abolish N-methylation, the E5A variant of T2SS pseudopilin PulG remains N-methylated but is affected in interaction with the T2SS component PulM. Here, biochemical and functional analyses showed that the PulM interaction defect only partly accounts for the PulG^E5A assembly defect. First, PulG^T2A variant, equally defective in PulM interaction, remained partially functional. Furthermore, pseudopilus assembly defect of pulG(E5A) mutant was stronger than that of the pulM deletion mutant. To understand the dominant effect of E5A mutation, we used molecular dynamics simulations of PulG^E5A, methylated PulG^WT (MePulG^WT), and MePulG^E5A variant in a model membrane. These simulations pointed to a key role for an intramolecular interaction between the pseudopilin N-terminal amine and E5 to limit polar interactions with membrane phospholipids. N-methylation of the N-terminal amine further limited its interactions with phospholipid head-groups to facilitate pseudopilin membrane escape. By binding to polar residues in the conserved N-terminal region of PulG, we propose that PulM acts as chaperone to promote pseudopilin recruitment and coordinate its membrane extraction with subsequent steps of the fibre assembly process.

Zinc(II)-regulation of hydrazone switch isomerization kinetics

The extra H-bond in a bipyridyl-functionalized hydrazone rotary switch slows down its Z→E isomerization rate by 2 orders of magnitude (k = (3.5 ± 0.2) × 10(-6) s(-1)). The coordination of Zn(2+) with the bipyridyl subgroup simultaneously 'unlocks' this H-bond and accelerates the isomerization rate by at least 6 orders of magnitude (k > 6.9 s(-1)). This coordination-regulated kinetic control could open the way to molecular timers that can be used in guiding temporal events.

Self-organization in living cells: networks of protein machines and nonequilibrium soft matter

Microscopic self-organization phenomena inside a living cell should not represent merely a reduced copy of self-organization in macroscopic systems. A cell is populated by active protein machines that communicate via small molecules diffusing through the cytoplasm. Mutual synchronization of machine cycles can spontaneously develop in such networks - an effect which is similar to coherent laser generation. On the other hand, an interplay between reactions, diffusion and phase transitions in biological soft matter may lead to the formation of stationary or traveling nonequilibrium nanoscale structures.

ENHANCEMENT AND RESTRICTION OF SYSTEM COORDINATION BY INTERACTION OF PATHWAYS

System coordination for a system with interaction of two pathways is investigated. Sufficient conditions for guaranteeing system coordination subject to any type, amplitude or period of external forcing are analytically derived. Effects of a pathway operating in the opposite direction on system coordination are examined in detail, and it is revealed that the pathway may enhance or restrict system coordination, depending on the values of kinetic parameters. It is concluded that increasing the complexity of enzymatic network by introducing interaction of pathways does not necessarily enhance system coordination. Numerical results using rectangular and sinusoidal forcing support the analytical results, and they quantitatively show how the system with interaction of two pathways maintain its coordination. When the sufficient conditions are satisfied, the system always develops to a finite stable (time-dependent) state under the forcing of any type, amplitude or period. When not, system coordination depends quantitatively on parameter values and the type, amplitude or period of external forcing. When two parameters are forced simultaneously, an additional factor, namely phase shifts between two forced parameters, also affects system coordination. It is shown that, unless the sufficient coordination conditions are maintained, external forcing may induce 'loss of coordination', resulting in the system having no biological functioning. The implications of the results for understanding biochemical coordination and for assessing possible consequences of modulating biochemical systems are discussed.

SUFFICIENT CONDITIONS FOR COORDINATION OF A FORCED BIOCHEMICAL SYSTEM WITH THE INTERPLAY OF ACTIVATION AND INHIBITION

A system of ordinary differential equations representing a biochemical system with the interplay of enzyme activation and inhibition is studied. Each term of the equations describes an enzymatic reaction and has an upper limit — the maximum activity of the enzyme. The sufficient conditions for guaranteeing coordination of the system subject to any type, period and amplitude of external forcing are analytically derived. Numerical analysis using three types of external signals, namely rectangular, sinusoidal and noisy signals, supports the analytical results. The sufficient conditions require kinetic parameter values (in particular, maximum enzyme activities) be related, implying system coordination requires enzymes in the system properly work together. It is shown that, when the sufficient conditions are satisfied, the system always develop to a stable (possibly time-dependent) state when it is subject to any type, period and amplitude of external forcing. When not, whether system coordination is destroyed depends quantitatively on the parameter values and the type, period and amplitude of external signals. Once system coordination is destroyed by external forcing, the system does not have any stable state on phase plane, and one of the species concentrations accumulates infinitely. Finally, I discuss the implications of the results for understanding the coordination of nonlinear enzyme-catalysed reaction systems with the interplay of activation and inhibition, and the possible consequences of modulating such systems.

Sufficient Conditions for Coordination of Coupled Nonlinear Biochemical Systems: Analysis of a Simple, Representative Example

Under conditions of stress and environmental fluctuations, how do coupled biochemical systems maintain the balance of metabolic fluxes? Using a model derived from a representative glycolysis example, this work derives sufficient coordination conditions for guaranteeing the balance of metabolic fluxes in the coupled systems subjected to any fluctuations. For diffusion-like coupling, it is explicitly shown that the sufficient conditions are the linear summation of individual uncoupled systems. For this case, coupling strength is not a key factor affecting the balance of metabolic fluxes, although it may affect the emergence of certain dynamic patterns. When the sufficient coordination conditions are satisfied, coupled systems always settle onto stable finite states, independently of the nature (type, period or amplitude) of external signals. When they are not, external signals may force the stable states of coupled systems to lose their coordination, resulting in the coupled systems having no stable finite states which is inconsistent with most normal biological functions. Numerical simulations support the analytical results. The generalization of this result for other coupled nonlinear biochemical systems is discussed. Finally, the maintenance of such biological coordination is discussed in the context of genetic engineering and environmental fluctuations.

Sustained self-organizing pH patterns in hydrogen peroxide driven aqueous redox systems

Many pattern developments in nature are believed to result from the interplay between self-activated (bio)chemical processes and the diffusive transport of constituents. Though the details are difficult to work out, the relevance of reaction-diffusion processes is widely accepted in many aspects of biological development. Due to their easier manipulation and control, aqueous phase chemical reactions are commonly preferred to probe the patterning capacity of reaction-diffusion processes. Nonetheless, sustained patterns of such a type were observed only in reactions involving oxyhalogen compounds. We report on halogen free solution chemistry systems which lead to stationary or oscillatory spatiotemporal pH patterns. They are based on the acid autocatalytic oxidation of sulfite ions by hydrogen peroxide in combination with two significantly different proton consuming feedback reactions. Besides the chemical novelty, yet experimentally and even theoretically undocumented pattern dynamics are uncovered. This success, based on a well-defined method, further paves the way to the discovery of stationary patterns in delicate biochemical reactions.

Protein self-organization: lessons from the min system

One of the most fundamental features of biological systems is probably their ability to self-organize in space and time on different scales. Despite many elaborate theoretical models of how molecular self-organization can come about, only a few experimental systems of biological origin have so far been rigorously described, due mostly to their inherent complexity. The most promising strategy of modern biophysics is thus to identify minimal biological systems showing self-organized emergent behavior. One of the best-understood examples of protein self-organization, which has recently been successfully reconstituted in vitro, is represented by the oscillations of the Min proteins in Escherichia coli. In this review, we summarize the current understanding of the mechanism of Min protein self-organization in vivo and in vitro. We discuss the potential of the Min oscillations to sense the geometry of the cell and suggest that spontaneous protein waves could be a general means of intracellular organization. We hypothesize that cooperative membrane binding and unbinding, e.g., as an energy-dependent switch, may act as an important regulatory mechanism for protein oscillations and pattern formation in the cell.

Spatial control of the energy metabolism of yeast cells through electrolytic generation of oxygen

The metabolic dynamics of yeast cells is controlled by electric pulses delivered through a spatially extended yeast cell/Au electrode interface. Concomitant with voltage pulses, oxygen is generated electrolytically at the electrode surface and delivered to the cells. The generation of oxygen was investigated in dependence of the applied voltage, width of the voltage pulses and temperature of the electrolytic solution. The local oxygen pulses at the electrodes lead to a transient activation of the aerobic energy metabolism of the yeast cells causing a perturbation in their energy balance. The effect of these local perturbations on the temporal dynamics of glycolysis in yeast cells is quantified in dependence of the energy state of cells.

Bursting Oscillations in the Revised Mechanism of the Hemin – Hydrogen Peroxide – Sulfite Oscillator

The reaction mechanism for the hemin-mediated oxidation of sulfite by hydrogen peroxide was reinvestigated. This has become necessary due to an erroneous stoichiometric factor used during a previous numerical analysis. A simple correction of the previous model failed to reproduce the experimentally observed bursting oscillations of the pH value. Therefore, we propose an extended mechanism which includes not only the autocatalytic production of H+ and pH-dependent equilibria of hemin species, but also the decomposition of hemin in media of high H2O2 concentration. The dynamic properties of this 7-variable reaction mechanism are in good agreement with previous experimental and numerical observations. A closer analysis reveals that the pH-dependent dimerisation equilibrium of hemin provides only a minor contribution to the onset of oscillations. Therefore, this equilibrium can be neglected yielding a 6-variable version of the revised 7-variable model, while maintaining the local bifurcation structure. The revised mechanisms are considered realistic models that describe the observed dynamical features of the hemin-containing pH oscillator.

Global self-organization of the cellular metabolic structure

BACKGROUND

Over many years, it has been assumed that enzymes work either in an isolated way, or organized in small catalytic groups. Several studies performed using "metabolic networks models" are helping to understand the degree of functional complexity that characterizes enzymatic dynamic systems. In a previous work, we used "dissipative metabolic networks" (DMNs) to show that enzymes can present a self-organized global functional structure, in which several sets of enzymes are always in an active state, whereas the rest of molecular catalytic sets exhibit dynamics of on-off changing states. We suggested that this kind of global metabolic dynamics might be a genuine and universal functional configuration of the cellular metabolic structure, common to all living cells. Later, a different group has shown experimentally that this kind of functional structure does, indeed, exist in several microorganisms.

METHODOLOGY/PRINCIPAL FINDINGS

Here we have analyzed around 2.500.000 different DMNs in order to investigate the underlying mechanism of this dynamic global configuration. The numerical analyses that we have performed show that this global configuration is an emergent property inherent to the cellular metabolic dynamics. Concretely, we have found that the existence of a high number of enzymatic subsystems belonging to the DMNs is the fundamental element for the spontaneous emergence of a functional reactive structure characterized by a metabolic core formed by several sets of enzymes always in an active state.

CONCLUSIONS/SIGNIFICANCE

This self-organized dynamic structure seems to be an intrinsic characteristic of metabolism, common to all living cellular organisms. To better understand cellular functionality, it will be crucial to structurally characterize these enzymatic self-organized global structures.

Designing an enzymatic oscillator: Bistability and feedback controlled oscillations with glucose oxidase in a continuous flow stirred tank reactor

The reaction of glucose with ferricyanide catalyzed by glucose oxidase from Aspergillus niger gives rise to a wide range of bistability as the flow rate is varied in a continuous flow stirred tank reactor. Oscillations in pH can be obtained by introducing a negative feedback on the autocatalytic production of H+ that drives the bistability. In our experiments, this feedback consists of an inflow of hydroxide ion at a rate that depends on [H+] in the reactor as k0[OH-]0[H+]/(K+[H+]). pH oscillations are found over a broad range of enzyme and ferricyanide concentrations, residence times (k0 (-1)), and feedback parameters. A simple mathematical model quantitatively accounts for the experimentally found oscillations.

Low frequency electromagnetic fields and the Belousov–Zhabotinsky reaction

Low frequency magnetic fields can influence biochemical reactions and consequently physiological rhythms and oscillations. To test this for a model reaction we used the chemical Belousov-Zhabotinsky (BZ) reaction, which is one of the simplest chemical oscillators. The oscillation frequency of the reaction was tracked optically by the absorption of blue light. Field treatment was carried out at room temperature in the middle of two Helmholtz coils. After starting the reaction, for 5 min the oscillations were monitored as control measurement, then during the next 10 min monitoring was with a magnetic field switched on, followed by a period of 5 min with the field switched off. A variety of exposure conditions have been tested: the frequency was varied between 5 and 1000 Hz, the field strength was varied up to 2.7 mT, different pulse shapes were used, the influence of the exposure temperature was tested, and the influence of the optimum exposure conditions (static magnetic field and the frequency of the dynamic field) as predicted by the ion parametric resonance (IPR) model has been measured. In conclusion, in no case any statistical significant influence of the magnetic treatment on the oscillation frequency of the BZ reaction could be detected (P > .05, t-test).

Photo-infrared pulsed bio-modulation (PIPBM): a novel mechanism for the enhancement of physiologically reparative responses

OBJECTIVE

The present manuscript describes the non-invasive, long-range, energy transport of a singular infrared pulsed laser device (IPLD) and the upstream components of the original action mechanism, designated photo-infrared pulsed bio-modulation (PIPBM).

BACKGROUND DATA

Major strides have been taken in recent years towards scientifically acceptable clinical applications of low-energy lasers. Nevertheless, challenges still abound. For instance, the range of potential target tissues for laser therapy in medicine has been, until now, limited by the optical penetration of the beam or to sites accessible by fiberoptics. In addition, much needs to be learned about the action mechanisms of pulsed lasers, which can induce unique biological effects.

METHODS

We present a review of the IPLD laser technology and the PIPBM mechanism.

RESULTS

The studies reviewed suggest that the PIPBM enhances physiologically reparative processes in a non-toxic and selective manner through the activation and modulation of chaotic dynamics in water. These, in turn, lead not only to local, but also long-distance (systemic) effects.

CONCLUSIONS

Though additional studies are necessary to fully explore the biological effects of the PIPBM induced by the IPLD, this mechanism may have multiple potential applications in medicine that are the subject of active current and future investigations.

Collapse of single stable states via a fractal attraction basin: analysis of a representative metabolic network

The impact of external forcing on an enzymatic reaction system with a single finite stable state is investigated. External forcing impacts on the system in two distinct ways: firstly, the reaction system undergoes a series of discontinuous changes in dynamical state. Secondly, a critical level of forcing exists, beyond which all finite states become unstable. It is shown that the results stem from the conditions for global stability of the system. Competition between the attractor for stable states and the unbounded states leads to a loss of integrity and the fractal fragmentation of the attraction basin for the finite state. The consequences of a fractal basin in this context are profound. Initial states which are infinitesimally close diverge to a finite and an unbounded state where only the finite state is consistent with biological functionality. Furthermore, above a critical forcing amplitude, the system does not converge to a finite state from any initial state, implying that there is no configuration of metabolite concentrations that is consistent with sustained evolution of the system. These results point to opportunities for constraining uncertainty in cell networks where nonlinear saturating kinetics form an important component.

Glycolytic oscillations and waves in an open spatial reactor: Impact of feedback regulation of phosphofructokinase

An open spatial reactor has been designed for the investigation of spatio-temporal dynamics of glycolysis. The reactor consists of a diffusive layer made of gel-fixed yeast extract which is in contact with a continuously stirred reservoir to supply this layer with substrates. The coupling between reaction and diffusion in the gel layer enables the formation of spatio-temporal patterns. Temporal oscillations of glycolysis are simply induced by feeding the yeast extract with sugar. Under properly chosen conditions, these oscillations sustain for more than 12 h. A necessary prerequisite for the generation of oscillations is that the ATP concentration in the feeding solution must be high enough to allow for negative feedback of phosphofructokinase. Otherwise, the interplay between ATP-consuming and ATP-producing reactions leads to an unfavorable low ATP/AMP ratio. The generation of travelling NADH-waves is observed in the diffusive layer, when feeding the yeast extract with substrates. Break-up of circular-shaped waves is repeatedly observed, resulting in the formation of rotating NADH-spirals.

Control of glycolytic oscillations by temperature

External control of oscillatory glycolysis in yeast extract has been performed by application of either homogeneous temperature oscillations or stationary, spatial temperature gradients. Entrainment of the glycolytic oscillations by the 1/2- and 1/3-harmonic, as well as the fundamental input frequency, could be observed. From the phase response curve to a single temperature pulse, a distinct sensitivity of NADH-oxidizing processes, compared with NAD-reducing processes, is visible. Determination of glycolytic intermediates shows that the feedback-regulated phosphofructokinase as well as the glyceraldehyde-3-phosphate dehydrogenase are the most temperature-sensitive steps of glycolysis. We also find strong concentration changes in ATP and AMP at varying temperatures and, accordingly, in the energy charge. Construction of a feedback loop for spatial control of temperature by means of a Peltier element allowed us to apply a temperature gradient to the yeast extract. With this setup it is possible to initiate traveling waves and to control the wave velocity.

Temperature dependency and temperature compensation in a model of yeast glycolytic oscillations

Temperature sensitivities and conditions for temperature compensation have been investigated in a model for yeast glycolytic oscillations. The model can quantitatively simulate the experimental observation that the period length of glycolytic oscillations decreases with increasing temperature. Temperature compensation is studied by using control coefficients describing the effect of rate constants on oscillatory frequencies. Temperature compensation of the oscillatory period is observed when the positive contributions to the sum of products between control coefficients and activation energies balance the corresponding sum of the negative contributions. The calculations suggest that by changing the activation energies for one or several of the processes, i.e. by mutations, it could be possible to obtain temperature compensation in the yeast glycolytic oscillator.

A model of phosphofructokinase and glycolytic oscillations in the pancreatic beta-cell

We have constructed a model of the upper part of the glycolysis in the pancreatic beta-cell. The model comprises the enzymatic reactions from glucokinase to glyceraldehyde-3-phosphate dehydrogenase (GAPD). Our results show, for a substantial part of the parameter space, an oscillatory behavior of the glycolysis for a large range of glucose concentrations. We show how the occurrence of oscillations depends on glucokinase, aldolase and/or GAPD activities, and how the oscillation period depends on the phosphofructokinase activity. We propose that the ratio of glucokinase and aldolase and/or GAPD activities are adequate as characteristics of the glucose responsiveness, rather than only the glucokinase activity. We also propose that the rapid equilibrium between different oligomeric forms of phosphofructokinase may reduce the oscillation period sensitivity to phosphofructokinase activity. Methodologically, we show that a satisfying description of phosphofructokinase kinetics can be achieved using the irreversible Hill equation with allosteric modifiers. We emphasize the use of parameter ranges rather than fixed values, and the use of operationally well-defined parameters in order for this methodology to be feasible. The theoretical results presented in this study apply to the study of insulin secretion mechanisms, since glycolytic oscillations have been proposed as a cause of oscillations in the ATP/ADP ratio which is linked to insulin secretion.

Calcium waves in agarose gel with cell organelles: implications of the velocity curvature relationship

Calcium oscillations and waves have been observed not only in several types of living cells but also in less complex systems of isolated cell organelles. Here we report the determination of apparent Ca2+ diffusion coefficients in a novel excitable medium of agarose gel with homogeneously distributed vesicles of skeletal sarcoplasmic reticulum. Spatiotemporal calcium patterns were visualized by confocal laser scanning fluorescence microscopy. To obtain characteristic parameters of the velocity curvature relationship, namely, apparent diffusion coefficient, velocity of plane calcium waves, and critical radius, positively and negatively curved wave fronts were analyzed. It is demonstrated that gel-immobilized cell organelles reveal features of an excitable medium. Apparent Ca2+ diffusion coefficients of the in vitro system, both in the absence or in the presence of mitochondria, were found to be higher than in cardiac myocytes and lower than in unbuffered agarose gel. Plane calcium waves propagated markedly slower in the in vitro system than in rat cardiac myocytes. Whereas mitochondria significantly reduced the apparent Ca2+ diffusion coefficient of the in vitro system, propagation velocity and critical size of calcium waves were found to be nearly unchanged. These results suggest that calcium wave propagation depends on the kinetics of calcium release rather than on diffusion.

Differential regulation of [Ca2+]i oscillations in mouse pancreatic islets by glucose, alpha-ketoisocaproic acid, glyceraldehyde and glycolytic intermediates

Glucose induces slow oscillations of the cytoplasmic Ca2+ concentration in pancreatic beta-cells. In order to elucidate the mechanisms responsible for the slow [Ca2+]i oscillations the effects of various nutrient insulin secretagogues on glucose-induced [Ca2+]i oscillations in intact mouse pancreatic islets and single beta-cells were studied. These were the glycolytic intermediates, glyceraldehyde and pyruvate, and the mitochondrial substrate, alpha-ketoisocaproic acid (KIC). Glucose, at a 10 or 15 mM concentration, induced the typical slow oscillations of [Ca2+]i (0.4 min(-1)). At higher glucose concentrations the frequency of these oscillations decreased further (0.2 min(-1)). Glyceraldehyde, an insulin secretagogue like glucose, did not cause slow oscillations of [Ca2+]i in the absence of glucose. However, it exhibited a synergistic action with glucose. Glyceraldehyde, at 3 or 10 mM concentration, induced slow [Ca2+]i oscillations at a substimulatory concentration of 5 mM glucose (0.3-0.4 min(-1)) and reduced the frequency of the glucose-induced [Ca2+]i oscillations at stimulatory concentrations of 10 or 15 mM glucose (0.2 min(-1)). KIC (5 or 10 mM) as well as pyruvate (10 mM), the end product of glycolysis, and its ester methyl pyruvate (10 mM), did not cause slow oscillations of [Ca2+]i in the absence of glucose. In contrast to glyceraldehyde, however, all three compounds were capable of preventing the slow [Ca2+]i oscillations induced by glucose. Mannoheptulose (2 mM), an inhibitor of glucokinase and glucose-induced insulin secretion, reversibly blocked any kind of [Ca2+]i oscillation and returned the [Ca2+]i to a basal level through its ability to inhibit glycolytic flux. It can be concluded therefore that only substrates which generate a glucokinase-mediated metabolic flux through glycolysis and produce glycolytic ATP can induce slow [Ca2+]i oscillations in pancreatic beta-cells.

Oscillations and bistability predicted by a model for a cyclical bienzymatic system involving the regulated isocitrate dehydrogenase reaction

We analyze the dynamics of a bienzymatic system consisting of isocitrate dehydrogenase (IDH, EC. 1.1.1.42), which transforms NADP+ into NADPH, and of diaphorase (DIA, EC 1.8.1.4), which catalyzes the reverse reaction. Experimental evidence as well as a theoretical model showed the possibility of a coexistence between two stable steady states in this reaction system G.M. Guidi et al. Biophys. J. 74 (1998) 1229-1240[, owing to the regulatory properties of IDH. Here we extend this analysis by considering the behavior of the model proposed for the IDH-DIA bienzymatic system in conditions where the system is open to an influx of its substrates isocitrate and NADP+ and to an efflux of all metabolic species. The analysis indicates that in addition to different modes of bistability (including mushrooms and isolas), sustained oscillations can be observed in such conditions. These results point to the isocitrate dehydrogenase reaction coupled to diaphorase as a suitable candidate for further experimental and theoretical studies of bistability and oscillations in biochemical systems. The results obtained in this particular bienzymatic system bear on other enzymatic systems possessing a cyclical nature, which are known to play significant roles in a variety of metabolic and cellular regulatory processes.

Sarcoplasmic reticulum vesicles embedded in agarose gel exhibit propagating calcium waves

In different cell types, activation of signal transduction pathways leads to the generation of calcium oscillations and/or waves. Due to this important impact for cellular function, calcium waves are the subject of intensive investigations. To study interactions of cell organelles with no influence of the cell membrane, sarcoplasmic reticulum (SR) vesicles and well-coupled mitochondria were reconstituted. For the first time, we demonstrate the generation and propagation of calcium waves in a suspension of sarcoplasmic reticulum vesicles, embedded in an agarose gel. The propagation dynamics resemble those of calcium waves in living cells. Moreover, the addition of well-coupled mitochondria leads to more pronounced and significantly faster propagating waves, demonstrating the importance of the mitochondrial Ca(2+) transport. The experimental and simulation results indicate the resemblance of the in vitro system to an excitable medium.

Diversity of temporal self-organized behaviors in a biochemical system

The numerical study of a glycolytic model formed by a system of three delay-differential equations revealed a notable richness of temporal structures which included the three main routes to chaos, as well as a multiplicity of stable coexisting states. The Feigenbaum, intermitency and quasiperiodicity routes to chaos can emerge in the biochemical oscillator. Moreover, different types of birhythmicity, trirhythmicity and hard excitation emerge in the phase space. For a single range of the control parameter it can be observed the coexistence of two quasiperiodicity routes to chaos, the coexistence of a stable steady state with a stable torus, and the coexistence of a strange attractor with different stable regimes such as chaos with different periodic regimes, chaos with bursting behavior, and chaos with torus. In most of the numerical studies, the biochemical oscillator has been considered under periodic input flux being the mean input flux rate 6 mM/h. On the other hand, several investigators have observed quasiperiodic time patterns and chaotic oscillations by monitoring the fluorescence of NADH in glycolyzing yeast under sinusoidal glucose input flux. Our numerical results match well with these experimental studies.

Reductionism and explanation in cell biology

It is likely to be impossible or very difficult to provide a detailed description of the molecular interactions underlying all cellular phenomena. However, methods and ways of thinking are now available or being developed that can deal better with the complexity and greater extension in space and time found at the level of the cell. This will lead to the identification of some components or groups of components as being of particular importance for a cellular phenomenon which can then be studied in detailed molecular terms. In other cases detailed molecular characterization may be replaced by a logical description of the process which emphasizes the information flow and processing rather than the nature of the individual components and their interactions. This may provide an adequate explanation for an appropriate understanding of the cellular phenomena involved.

Traveling waves in yeast extract and in cultures of Dictyostelium discoideum

Biological self-organization was investigated in a biochemical and a cellular system: yeast extract and cultures of the slime mold Dictyostelium discoideum. In both systems traveling reaction-diffusion waves occur in response to oscillatory reactions. Glycolytic degradation of sugar in a yeast extract leads to the spontaneous formation of NADH and proton waves. Manipulation of the adenine nucleotide pool by addition of purified plasma membrane ATPase favors the formation of both reaction-diffusion waves and phase waves. The results indicate that the energy charge has an important impact for the dynamics of glycolytic patterns. When affecting the lower part of glycolysis by pyruvate addition the frequency of wave generation was increased with concomitant formation of rotating NADH and proton spirals. During morphogenesis of the cellular system Dictyostelium discoideum, circular and spiral shaped aggregation patterns of motile amoeboid cells form in response to traveling cAMP waves. Velocity analysis of the cell movements reveals that the cAMP waves guide the cells towards the site of wave initiation along optimized trajectories. The minimization of aggregation paths is based on a mechanism exploiting general properties of excitation waves. The resulting aggregation territories are reminiscent of Voronoi diagrams.

Self-organizing molecular networks

Strong diffusional mixing and short delivery times typical for micrometer and sub-micrometer reaction volumes lead to a special situation where the turnover times of individual enzyme molecules become the largest characteristic time scale of the chemical kinetics. Under these conditions, populations of cross-regulating allosteric enzymes form molecular networks that exhibit various kinds of self-organized coherent collective dynamics.