Oscillations and efficiency in glycolysis

We suggest that temporal oscillations of concentrations of intermediates in biochemical reaction systems may enhance the efficiency of free energy conversion (reduce dissipation) in those reactions. Experiments on glycolysis are used to estimate the Gibbs free energy changes along the glycolysis mechanism, and to postulate a construct for the glycolysis "machine" which involves: the PFK reaction as the primary oscillophor; the GAPDH reaction as a phase-shifting device; and the PK reaction with the property of intrinsic oscillatory response at resonance with the driving frequency. Analysis of a simple reaction mechanism with these postulated properties shows that the conversion of free energy from reactants to products is more efficient in an oscillatory than a steady state operation. The efficiency of free energy conversion in glycolysis from glucose + ADP to products + ATP is estimated to be increased by 5--10% due to oscillations. This may have been relevant for the evolutionary development of oscillations such as in glycolysis, especially in anaerobic cells.     

初始条件对高浓度乙醇连续发酵过程的影响及振荡行为提高发酵效率的机理分析

前期实验在稀释速率为0.027h-1的高浓度乙醇连续发酵过程中,发现了一种长周期、宽振幅的参数振荡现象。本实验进一步考察了不同稀释速率下的连续发酵过程,发现在稀释速率为0.04h-1条件下,也能出现类似的振荡现象;在稀释速率为0.027h-1或0.04h-1的条件下,改变系统的初始状态可以得到振荡和稳态两种不同的发酵过程。比较振荡和稳态过程的实验数据后,发现在稀释速率为0.04h-1的条件下,与稳态过程相比,振荡过程的平均残糖浓度降低了14.8%,平均乙醇浓度提高了12.6%,平均设备生产强度提高了12.3%。进一步分析表明:与稳态过程相比,振荡过程动力学行为不仅存在滞后,而且在相同残糖和乙醇浓度条件下,所对应的平均比生长速率提高了53.8%。     

Channel opening of gamma-aminobutyric acid receptor from rat brain: molecular mechanisms of the receptor responses

The function of gamma-aminobutyric acid (GABA) receptors, which mediate transmembrane chloride flux, can be studied by use of 36Cl- isotope tracer with membrane from mammalian brain by quench-flow technique, with reaction times that allow resolution of the receptor desensitization rates from the ion flux rates. The rates of chloride exchange into the vesicles in the absence and presence of GABA were characterized with membrane from rat cerebral cortex. Unspecific 36Cl- influx was completed in three phases of ca. 3% (t 1/2 = 0.6 s), 56% (t 1/2 = 82 s), and 41% (t 1/2 = 23 min). GABA-mediated, specific chloride exchange occurred with 6.5% of the total vesicular internal volume. The GABA-dependent 36Cl- influx proceeded in two phases, each progressively slowed by desensitization. The measurements supported the presence of two distinguishable active GABA receptors on the same membrane mediating chloride exchange into the vesicles with initial first-order rate constants of 9.5 s-1 and 2.3 s-1 and desensitizing with first-order rate constants of 21 s-1 and 1.4 s-1, respectively, at saturation. The half-response concentrations were similar for both receptors, 150 microM and 114 microM GABA for desensitization and 105 microM and 82 microM for chloride exchange, for the faster and slower desensitizing receptors, respectively. The two receptors were present in the activity ratio of ca. 4/1, similar to the ratio of "low-affinity" to "high-affinity" GABA sites found in ligand binding experiments. The desensitization rates have a different dependence on GABA concentration than the channel-opening equilibria.(ABSTRACT TRUNCATED AT 250 WORDS)     

Autonomously oscillating biochemical systems: parametric sensitivity of extrema and period

This work addresses sensitivity analysis of autonomously oscillating biochemical systems. Building on results from the engineering literature, a general analysis is presented which addresses key features of oscillatory trajectories, namely the period and local maximum or minimum values of species concentrations and reaction rates. A discussion of sensitivity invariants generalises results from steady-state sensitivity analysis to this context. The results are illustrated by the application to a model of a circadian oscillator.     

Effects of calcium buffers and calbindin-D28k upon histamine-induced calcium oscillations and calcium waves in HeLa cells

The effects of the artificial Ca(2+) buffers EGTA and BAPTA upon histamine-induced Ca(2+) oscillations and calcium waves were studied in HeLa cells. These events were also examined in HeLa cell lines transfected with the intracellular calcium-binding protein calbindin-D28k (CaBP; HeLa-CaBP) or the pCINeo vector alone (HeLa-pCINeo). High concentrations of the Ca(2+) indicators fluo-3 and fura-2 significantly influenced the oscillatory pattern of intracellular Ca(2+) in HeLa-pCINeo cells exposed to 1 microM histamine. Loading cells with low concentrations of the cell-permeant esters of the artificial Ca(2+)-buffers EGTA or BAPTA, resulted in fewer cells with a distinct "baseline" oscillatory pattern, and loading with higher concentrations of BAPTA almost completely abolished them. In HeLa-CaBP cells, stimulation with 1 microM histamine resulted in individual Ca(2+) spikes that had a flattened profile when compared to control cells; peak [Ca(2+)](i) was lowered, the rate of increase in [Ca(2+)](i) was slower and transients were prolonged. When compared to HeLa-pCINeo cells, loading with EGTA or BAPTA, or transfection of CaBP, significantly reduced the propagation velocity (by up to 60%) of Ca(2+) waves induced by exposure to 100 microM histamine. We conclude that intracellular Ca(2+) buffering exerts a significant influence on global Ca(2+) responses in HeLa cells and the propagation of Ca(2+) waves that underlie them. The relative effectiveness of different Ca(2+) buffers, including CaBP, appears to be particularly dependent upon the rapidity of their binding kinetics, with BAPTA being the most effective.     

Clinical assessment of rheumatic diseases using viscoelastic parameters for synovial fluid

For the first time it is clearly exhibited that synovial fluid (SF) is thixotropic. Although no hysteresis loops were observed for SF, not even at high shear rates, thixotropy may be exhibited by measuring the rate of recovery after extensive shearing. The rebuilding of the structure in a small-amplitude oscillatory state following the high-shear-rate state reveals the thixotropic behaviour. Five different viscoelastic parameters for various synovial fluids (SF) were obtained using oscillatory rheometry. It was also shown that for SF in the low frequency range, corresponding to a knee joint almost at rest, the shear loss modulus G" is greater than the shear storage modulus G', since the system is allowed to dissipate energy at rest. However, with movement, G' increases and eventually becomes greater than G" at a characteristic frequency above which the system has insufficient time to dissipate energy and hence responds as an elastic body. This functional behaviour, characteristic for normal SF, broke down in the SF of rheumatoid arthritis. It was also absent in the SF of knee joints with meniscus lesions and ligament defects.     

Oscillatory reaction of chondroitin sulfate induced by gradual introduction of calcium ion

Rhythm is an important dynamic behavior in biological systems. We have been studying oscillatory reactions of enzymes induced by gradual entry of substances through semipermeable membrane. Not only enzymes but also a few species of substance of living system have been elucidated to cause oscillatory reaction. Here we present the oscillatory reaction by chondroitin sulfate in a system of gradual entry of calcium ion. Introducing calcium ion through dialysis membrane into chondroitin sulfate solution induces an oscillation of free calcium ion concentration in chondroitin sulfate solution. Simultaneously, it is elucidated that oscillation of conformation occurs with permeation of calcium ion. In both measurements, oscillations with 25h period are obtained. The phases of oscillation, however, differ slightly from each other. From these results, it is suggested that autocatalysis exerts in the contraction of chondroitin sulfate conformation. These phenomena are very intriguing for elucidating oscillation in living system.     

Rates of structural fluctuations of lysozyme in the range of thermal unfolding transition

The hydrogen–deuterium exchange reaction for the tryptophan residues in lysozyme have been followed in 4.5M LiBr at pH 7.2 in the temperature range of the unfolding transition by measuring the transmittance change at 293 nm. The exchange reaction proceeded in three phases at low temperature for native protein. The first and the second phases were ascribed to the H-D exchange reactions of three relatively exposed tryptophan residues on the molecular surface. The third phase corresponded to the H-D exchange reaction of the three tryptophan residues buried in the interior of the molecule. The H-D exchange reaction proceeded in two phases near the melting temperature and in a single phase at high temperature, where almost all molecules are unfolded. The H-D exchange of three tryptophan residues buried in folded molecules was caused by fluctuation between the folded and unfolded structure of the protein molecule. The rates of such a fluctuation were determined from the rates of the exchange reaction at various temperatures. These rates agreed very well with those determined from the temperature-jump method. This means that a protein molecule in solution fluctuates between the N- and D-states at every temperature within the transition region, where the N-form is the tightly folded native structure and the D-form the randomly coiled chain. From measurements of thermal unfolding of ester-108-lysozyme and the binding constant of (NAG)₃ to ester-108-lysozyme, it was found that almost all cross-linked molecules are in the folded state near 50°C and pH 7.2 in 4.5M LiBr, where intact molecules are unfolded. We also studied the H-D exchange reaction of ester-108-lysozyme. In the temperature region of 43–50°C, about 70% of the exchangeable tryptophan residues of ester-108-lysozyme were exchanged within 1 s immediately after the mixing of D₂O, in spite of the fact that almost all molecules are in the folded state. This was considered the premelting of the surface of a corss-linked molecule.     

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.     

Stability analysis of an artificial biomolecular oscillator with non-cooperative regulatory interactions

Oscillators are essential to fuel autonomous behaviours in molecular systems. Artificial oscillators built with programmable biological molecules such as DNA and RNA are generally easy to build and tune, and can serve as timers for biological computation and regulation. We describe a new artificial nucleic acid biochemical reaction network, and we demonstrate its capacity to exhibit oscillatory solutions. This network can be built in vitro using nucleic acids and three bacteriophage enzymes, and has the potential to be implemented in cells. Numerical simulations suggest that oscillations occur in a realistic range of reaction rates and concentrations.     

Oscillatory behavior of Saccharomyces cerevisiae in continuous culture: II. Analysis of cell synchronization and metabolism

Sustained oscillations of biomass, ethanol, and ammonium concentrations, specific growth rate, and specific uptake rates of ethanol, ammonium, and oxygen were found in continuous cultures of Saccharomyces cerevisiae under controlled dissolved oxygen (DO), pH, and temperature conditions. The period of oscillations was approximately 2.5-3 h at a pH of 5.5 and 2-2.5 h at a pH of 6.5. Oscillations were observed only under conditions of low carbon (glucose below the minimum detectable level), nitrogen nutrient (ammonium concentration varied between 0.00001 and 0.0015M), and ethanol concentration (0.002-0.085 g/L) in the bioreactor.The oscillatory behavior at pH 5.5 was also characterized by partially synchronized cell growth and reproduction. Not only did the total percentage of budding cells oscillate with the same period as observed for the global biomass and nutrient concentrations, but the peaks in the individual subpopulations of initial budding, middle budding, and late budding cells appeared sequentially during the oscillation period. This provides strong evidence of the hypothesis that variations in metabolism during different periods in the cell cycle of a partially synchronized cell population are responsible for the observed oscillatory bioreactor behavior.The specific nutrient uptake rates for ammonium and oxygen as well as the net specific ethanol uptake rate oscillated with the same period as the biomass oscillations. These results show a dramatic increase in the ammonium and oxygen consumption rates prior to the initial budding of the synchronized subpopulation and a decrease in these rates during the late budding phase. At a pH of 5.5, the late budding phase is characterized by high specific ethanol productivity; however, the ethanol productivity lags the late budding phase at a pH pf 6.5. The observed time-varying metabolism in the oscillatory operating regime appears to be the result of the metabolic changes which occur during the cell cycle. Models which can predict the oscillatory biomass concentration and nutrient levels in this regime must be capable of predicting the concentrations and metabolic rates of the subpopulations as well.     

Seasonal differences in the effects of oscillatory and uni‐directional flow on the growth and nitrate‐uptake rates of juvenile Laminaria digitata (Phaeophyceae)

The influence of oscillatory versus unidirectional flow on the growth and nitrate‐uptake rates of juvenile kelp, Laminaria digitata, was determined seasonally in experimental treatments that simulated as closely as possible natural environmental conditions. In winter, regardless of flow condition (oscillatory and unidirectional) or water velocity, no influence of water motion was observed on the growth rate of L. digitata. In summer, when ambient nitrate concentrations were low, increased water motion enhanced macroalgal growth, which is assumed to be related to an increase in the rate of supply of nutrients to the blade surface. Nitrate‐uptake rates were significantly influenced by water motion and season. Lowest nitrate‐uptake rates were observed for velocities <5 cm · s^?1 and nitrate‐uptake rates increased by 20%–50% under oscillatory motion compared to unidirectional flow at the same average speed. These data further suggested that the diffusion boundary layer played a significant role in influencing nitrate‐uptake rates. However, while increased nitrate‐uptake in oscillatory flow was clear, this was not reflected in growth rates and further work is required to understand the disconnection of nitrate‐uptake and growth by L. digitata in oscillatory flow. The data obtained support those from related field‐based studies, which suggest that in summer, when insufficient nitrogen is available in the water to saturate metabolic demand, the growth rate of kelps will be influenced by water motion restricting mass transfer of nitrogen.     

A minimally parametrized branching process explaining plateau phase of qPCR amplification

Quantitative polymerase chain reaction (qPCR) is a commonly used molecular biology technique for measuring the concentration of a target nucleic acid sequence in a sample. The whole qPCR amplification process usually consists of an exponential, a linear and a plateau phase. In qPCR experiments, amplification curves of samples with different template concentrations often, even though not always, have the same plateau height. The biological theory for this phenomenon is that the plateau height is determined by reaction kinetics. Does it mean that the target concentration has no effect on the final plateau height? We proposed a branching process based on Michaelis–Menten kinetics. Our model can describe all phases of qPCR amplification despite its simplicity (it depends on only one parameter). We theoretically showed, through almost sure convergence, that amplification curves will eventually plateau at finite values in any experiment, under any condition. We conclude that the plateau height is largely determined by reaction kinetics but could also be affected by the template concentration. This is in accordance with the current biological theory.

     

Dynamics of a biochemical system with multiple oscillatory domains as a clue for multiple modes of neuronal oscillations

We analyze the behavior of a two-variable biochemical model in conditions where it admits multiple oscillatory domains in parameter space. The model represents an autocatalytic enzyme reaction with input of substrate both from a constant source and from non-linear recycling of product into substrate. This system was previously studied for birhythmicity, i.e. the coexistence between two stable periodic regimes (Moran and Goldbeter 1984), and for multithreshold excitability (Moran and Goldbeter 1985). When two distinct oscillatory domains obtain as a function of the substrate injection rate, the system is capable of exhibiting two markedly different modes of oscillations for slightly different values of this control parameter. Phase plane analysis shows how the multiplicity of oscillatory domains depends on the parameters that govern the underlying biochemical mechanism of product recycling. We analyze the response of the model to various kinds of transient perturbations and to periodic changes in the substrate input that bring the system through the two ranges of oscillatory behavior. The results provide a qualitative explanation for experimental observations (Jahnsen and Llinas 1984b) related to the occurrence of two different modes of oscillations in thalamic neurones.     

Dynamics of Sparsely Connected Networks of Excitatory and Inhibitory Spiking Neurons

The dynamics of networks of sparsely connected excitatory and inhibitory integrate-and-fire neurons are studied analytically. The analysis reveals a rich repertoire of states, including synchronous states in which neurons fire regularly; asynchronous states with stationary global activity and very irregular individual cell activity; and states in which the global activity oscillates but individual cells fire irregularly, typically at rates lower than the global oscillation frequency. The network can switch between these states, provided the external frequency, or the balance between excitation and inhibition, is varied. Two types of network oscillations are observed. In the fast oscillatory state, the network frequency is almost fully controlled by the synaptic time scale. In the slow oscillatory state, the network frequency depends mostly on the membrane time constant. Finite size effects in the asynchronous state are also discussed.     

Numerical integration of a stochastic model for the Volterra-Lotka reaction

Time-integration of the master equation governing the birth-and-death model of the Volterra-Lotka reaction is carried out for three different initial conditions, with the results:

1. Fluctuations destroy the deterministic steady state in a manner quantitatively predicted from a cumulant expansion;
2. The sustained oscillatory behavior predicted by the deterministic model degenerated after 1/4 cycle in the stochastic model;
3. It is possible to select initial distributions such that the asymptotic distribution is a spike at the origin of the plane of reactants.

     

Circuit analysis of the oscillatory state in glycolysis

The oscillatory state of glycolysis in yeast extracts has been analysed by methods known from electronic circuit studies. The time course of the reactions are calculated by the method of least squares from experimentally determined sets of the concentrations of most of the metabolites. The dynamics of the glycolytic network of reactions can then be represented in terms of flow versus driving force (current versus voltage in the corresponding electronic circuit). The analysis of the dynamics leads to the conclusion that glycolysis is switched on and off in a pulsed manner during the oscillatory state. The resulting pulsed flow cannot only be measured with glycolytic end products, like carbon dioxide or ethanol, but can also readily be demonstrated by diagrams of reaction rates of single enzymic steps even in the initial stages of the glycolytic sequence. An analytic method widely applied to electronic circuits also proved to be useful in the study of the dynamics of a complex enzymic network.     

Instantaneous flux control analysis for biochemical systems.

Linear sensitivity analysis of steady-state control of enzymic systems has been extended to non-steady states yielding sensitivity coefficients which provide non-intuitive insights into the behavior of the system and the sites of metabolic control, and which are quantitative counterparts to traditional qualitative concepts. Because this information is provided in a readily understood format, these coefficients serve as convenient indices of metabolic control. This treatment was applied to a simple test system, consisting of two enzymes and one non-enzymatic reaction, which exhibits oscillatory behavior. The results indicate that oscillations in the concentrations of the intermediate metabolites are regulated almost exclusively by the second enzyme. Control of the flux through the pathway is apportioned equally among the three reactions during periods of low net flux, but it is due almost exclusively to the second enzyme during periods of high net flux.     

Effects of the Intracellular Ca Ion Concentration upon the Excitability of the Muscle Fiber Membrane of a Barnacle

The membrane excitability and contraction were examined in single barnacle muscle fibers with different internal Ca⁺⁺ concentrations by using buffer solutions made up with EGTA and Ca-gluconate in various proportions. During the passage of dc currents the membrane shows all-or-none spike potentials for internal Ca⁺⁺ concentrations below about 8 x 10^-8 M, oscillatory potential changes in the range between 8 x 10^-8 to 5 x 10^-7 M, but neither oscillatory nor spike potentials were seen for concentrations above 5 x 10^-7 M. All-or-none spike potentials were suppressed when the internal Mg⁺⁺ concentration exceeded 5 mM. The suppression threshold of the internal Ca⁺⁺ concentration for the Sr spike is much higher than that for the Ca spike. The threshold concentration of internal Ca⁺⁺ for contraction was about 8 x 10^-7 M.