Macroscopic fluctuations of the kinetic activity of alcohol dehydrogenase

Macroscopic fluctuations of liver alcohol dehydrogenase enzymic activity in complex reaction consisting in ethanol oxidation and butyraldehyde reduction were studied. It was found that maximal fluctuation amplitude was observed when the rates of both reactions were equal. Such dependence indicates connection between macroscopic fluctuations in alcohol dehydrogenase reaction and oscillations of relative affinity of the enzyme to oxidized and reduced coenzyme forms.     

Simulation of chemical oscillations in membranes

A computer simulation model has been developed to follow chemical oscillations in a membrane for immobilized enzyme systems. It is a discrete particle type model which follows the spatial and temporal fluctuations of the concentrations in a reaction involving two substrates. The parameters can be readily varied to allow dissipative structures to result from the sustained nonlinear reaction kinetics and to determine which parameters cause damping of the oscillations. The nature of the diffusion mechanism allows extension to more than one dimension.     

Dynamics of the latent periods of the avoidance response and its correlation with adaptive behavior in the rat

In the chamber with one-way avoidance, the latency of avoidance reaction was repeatedly evaluated every 30 s. Chronograms revealed clear minute latencies fluctuations. Some rats had a short (1-2.5 min) biorhythm period, others--a much longer one (10 min and more). The structure of rhythmic oscillations correlated with the ability of animals to relearning in the Y-maze. At slow oscillation process, the relearning was more difficult. d,l-amphetamine in a dose eliciting stereotype movements, impeded the relearning, and this coincided with prevailing of slow waves on chronograms.     

Synchronous reversible alterations in enzymatic activity (conformational fluctuations) in actomyosin and creatine kinase preparations.

The phenomenon of synchronism of oscillations of actomyosin and creatine kinase activity in the whole volume of the enzyme preparations was analysed. The synchronous "conformational oscillations" were observed in concentrated gels of actomyosin and in diluted actomyosin and creatine kinase solutions (ATP-creatine N-phosphotransferase, EC 2.7.3.2). The macromolecules of proteins studied may be in two or four conformational states differing enzymatic activity. Large fluctuations become possible in a range of conditions wherein two or four different states, or conformers, are equiprobable. The synchronization of conformational changes of separate macromolecules is maintained with energy derived, for instance, from some oxidative process or dilution of the solution, the process being displayed as conformational oscillations.     

Corresponding oscillations in neutrophil shape and filamentous actin content

Human neutrophils pretreated with 17-hydroxywortmannin responded to the chemotactic agonist formyl-Met-Leu-Phe with a transient doubling in filamentous actin content which was characterized by prominent oscillations. These oscillations closely matched transient oscillations in suspension turbidity measured in parallel. The experimental data could be simulated using A----B----C stochastic series kinetic models with an oscillating intermediate species (B), allowing quantitative comparison of the frequencies of the oscillations (0.092 +/- 0.006 and 0.094 +/- 0.004 Hz) and the overall reaction rate constants for actin mobilization and turbidity changes (0.11 +/- 0.02 and 0.14 +/- 0.03 s-1, respectively). The total cell volume remained constant, indicating that stimulus-induced extension of lamellipods reduces the body volume by an amount proportional to the mass displaced outward. Light scattering theory predicts that a decrease in body size decreases the turbidity and that fluctuations in body size due to lamellipod extension and retraction cycles like those exhibited by crawling neutrophils result in turbidity oscillations (lamellipods scatter very little by comparison to the cell body, and both aggregation and degranulation were absent). The experiments thus suggest that the cyclic variations in F-actin content are correlated with periodic fluctuations in lamellipod size. The available evidence appears to be consistent with the hypothesis that actin polymerization provides the main driving force for lamellipod extension and that depolymerization causes lamellipod retraction.     

Stochastic Oscillations Induced by Intrinsic Fluctuations in a Self-Repressing Gene

Biochemical reaction networks are subjected to large fluctuations attributable to small molecule numbers, yet underlie reliable biological functions. Thus, it is important to understand how regularity can emerge from noise. Here, we study the stochastic dynamics of a self-repressing gene with arbitrarily long or short response time. We find that when the mRNA and protein half-lives are approximately equal to the gene response time, fluctuations can induce relatively regular oscillations in the protein concentration. To gain insight into this phenomenon at the crossroads of determinism and stochasticity, we use an intermediate theoretical approach, based on a moment-closure approximation of the master equation, which allows us to take into account the binary character of gene activity. We thereby obtain differential equations that describe how nonlinearity can feed-back fluctuations into the mean-field equations to trigger oscillations. Finally, our results suggest that the self-repressing Hes1 gene circuit exploits this phenomenon to generate robust oscillations, inasmuch as its time constants satisfy precisely the conditions we have identified.     

稀释速率对高浓度酒精连续发酵过程振荡行为的影响

在一搅拌罐和三段管式反应器组成的组合反应器系统中,使用葡萄糖浓度为280g/L,添加5g/L酵母膏和3g/L蛋白胨的底物,在总稀释速率分别为0.032h^-1,0.024h^-1,0.017h^-1,0.012h^-1和0.006h^-1的条件下,考察了稀释速率对高浓度酒精发酵系统振荡行为的影响。结果表明,振荡行为在特定的稀释速率条件下呈现,进而基于数学上的分岔理论,分析了振荡行为发生的可能性及对应的稀释速率范围,并与实验结果进行了比较,在此基础上,讨论了振荡行为对酒精发酵过程的影响。     

Unmasking Chaotic Attributes in Time Series of Living Cell Populations

Background

Long-range oscillations of the mammalian cell proliferation rate are commonly observed both in vivo and in vitro. Such complicated dynamics are generally the result of a combination of stochastic events and deterministic regulation. Assessing the role, if any, of chaotic regulation is difficult. However, unmasking chaotic dynamics is essential for analysis of cellular processes related to proliferation rate, including metabolic activity, telomere homeostasis, gene expression, and tumor growth.

Methodology/Principal Findings

Using a simple, original, nonlinear method based on return maps, we previously found a geometrical deterministic structure coordinating such fluctuations in populations of various cell types. However, nonlinearity and determinism are only necessary conditions for chaos; they do not by themselves constitute a proof of chaotic dynamics. Therefore, we used the same analytical method to analyze the oscillations of four well-known, low-dimensional, chaotic oscillators, originally designed in diverse settings and all possibly well-adapted to model the fluctuations of cell populations: the Lorenz, Rössler, Verhulst and Duffing oscillators. All four systems also display this geometrical structure, coordinating the oscillations of one or two variables of the oscillator. No such structure could be observed in periodic or stochastic fluctuations.

Conclusion/Significance

Theoretical models predict various cell population dynamics, from stable through periodically oscillating to a chaotic regime. Periodic and stochastic fluctuations were first described long ago in various mammalian cells, but by contrast, chaotic regulation had not previously been evidenced. The findings with our nonlinear geometrical approach are entirely consistent with the notion that fluctuations of cell populations can be chaotically controlled.     

Parameter oscillations in a very high gravity medium continuous ethanol fermentation and their attenuation on a multistage packed column bioreactor system

The quasi-steady-states, marked by small fluctuations of residual glucose, ethanol, and biomass concentrations, and sustainable oscillations marked by big fluctuations of these monitored fermentation parameters were observed during the continuous ethanol fermentation of Saccharomyces cerevisiae when very high gravity media were fed and correspondingly high ethanol concentrations reached. A high ethanol concentration was shown to be one of the main factors that incited these oscillations, although the residual glucose level affected the patterns of these oscillations to some extent. The lag response of S. cerevisiae to high ethanol stress that causes the shifts of morphology, viability loss, and death of yeast cells is assumed to be one of the probable mechanisms behind these oscillations. It was predicted that the longer the delay of this response was, the longer the oscillation periods would be, which was validated by the experimental data and the comparison with the oscillatory behaviors reported for the ethanologen bacterium, Zymomonas mobilis. Furthermore, three tubular bioreactors in series were arranged to follow a stirred tank bioreactor to attenuate these oscillations. However, exaggerated oscillations were observed for the residual glucose, ethanol, and biomass concentrations measured in the broth from these tubular bioreactors. After the tubular reactors were packed with Intalox ceramic saddle packing, these oscillations were effectively attenuated and quasi-steady-states were observed during which there were very small fluctuations of residual glucose, ethanol, and biomass within the entire experimental run.     

Spontaneous lipid bilayer transmembrane electrical oscillations induced by concanavalin A-polysaccharide interaction

Potassium ion currents through bilayer lipid membranes were modified by the membrane-surface reaction of concanavalin A and the polysaccharides dextran and glycogen. Aggregative reaction with glycogen occasionally induced spontaneous periodic ion current fluctuations with cycle times of minutes and durations of over one hour. Different electrochemical characteristics were observed between large planar lipid membranes and filter paper supported membranes, providing an indication that the aqueous unstirred surface layer participates in the control of the surface aggregative event. Lipid chemical composition was implicated in the development of spontaneous oscillations.     

UNDAMPED OSCILLATIONS OF PYRIDINE NUCLEOTIDE AND OXYGEN TENSION IN CHEMOSTAT CULTURES OF KLEBSIELLA AEROGENES

Klebsiella aerogenes was grown in chemostat culture with the pH controlled to ±0.01 and temperature to ±0.1°C. The oxygen tension of the culture was regulated by changing the partial pressure of oxygen in the gas phase and recorded by means of an oxygen electrode. Reduced pyridine nucleotide was monitored continuously in the culture by means of direct fluorimetry. On applying an anaerobic shock to the culture, damped oscillations in pyridine nucleotide fluorescence were obtained. Further anaerobic shocks decreased the damping and eventually gave rise to undamped oscillations of a 2–3 min period which continued for several days. These oscillations were paralleled by oscillations of the same frequency in respiration rate. The amplitude of the oscillations in the respiration rate was equivalent to only 1% of the total steady-state respiration, whereas that of pyridine nucleotide oscillations was equivalent to 10% of the total aerobic/anaerobic fluorescence response. The oscillations ceased on interrupting the glucose feed but restarted on adding excess glucose to the culture. Addition of succinate also restarted the oscillations so that they appear not to be of glycolytic origin. The frequency of oscillations varied with growth rate and conditions. Oscillations of much lower frequency were obtained under limited-oxygen and anaerobic conditions than under fully aerobic conditions. Under glucose-limited conditions, fluctuations were found in adenosine triphosphate (ATP) content which were in phase with the pyridine nucleotide oscillations, but under nitrogen-limited growth conditions no such fluctuations in ATP were observed. The primary oscillating pathway could not be identified but the mechanism would appear to be quite different from that involved in oscillations observed in yeast cells. The synchronization of oscillations and observations of negative damping could be explained by a syntalysis effect.     

Night-day differences in the ultradian rhythmicity of plasma renin activity

During night-sleep, plasma renin activity displays periodic oscillations which are closely related to the alternation of REM-NREM sleep. To see whether this nocturnal rhythm persisted during the day-time, plasma renin activity was measured every 10 min for 24 hours in 4 human volunteers and in 4 others over a 10-h day-time period. To avoid the influence of repeated food intake which stimulates renin release, the subjects were on continuous enteral nutrition. Spectral analyses of the data revealed clear differences between the nocturnal and the diurnal PRA patterns. In subjects on enteral nutrition, sustained 100-min oscillations with strong spectral densities persisted during the night. They were closely related to REM-NREM cycles. During the day-time, however, the fluctuations were damped and less regular, and power spectra were split into 2 or 3 peaks without any predominant period. These results demonstrate that regular 100-min PRA oscillations could only be detected during night-sleep. The clear night-day differences suggest that the underlying oscillatory mechanisms may be weaker during day-time or may be counteracted by other physiological processes.     

Spontaneous firings of carnivorous aquatic Utricularia traps: temporal patterns and mechanical oscillations

Aquatic species of Utricularia are carnivorous plants living in environments poor in nutrients. Their trapping mechanism has fascinated generations of scientists and is still debated today. It was reported recently that Utricularia traps can fire spontaneously. We show here that these spontaneous firings follow an unexpected diversity of temporal patterns, from "metronomic" traps which fire at fixed time intervals to "random" patterns, displaying more scattered firing times. Some "bursting" traps even combine both aspects, with groups of fast regular firings separated by a variable amount of time. We propose a physical model to understand these very particular behaviors, showing that a trap of Utricularia accomplishes mechanical oscillations, based on continuous pumping and sudden opening of the trap door (buckling). We isolate the key parameters governing these oscillations and discuss the effect of their fluctuations.     

A quantum model for controlled enzymic reactions

A quantum model for the general enzymic reaction,E+S ⇌ ES → P, is presented, starting with the assumptions that any chemical substanceS, which may be a substrate for a particularE _(S)-enzyme is a microphysical system and any enzymeE-molecule, capable of interacting with anS-substrate is a “measuring system” which will “measure” one or more of theS-observables. According to the above assumptions a stochastic model of the reaction is constructed and a computer simulation of the steady state performed. The results thus obtained predicted fluctuations in the enzymic reaction rate, function of the substrate “perturbation”. On an experimental basis it is demonstrated that the irradiation of an enzymic substrate with low energies results in the inducement of a dose-dependent oscillatory behavior in the corresponding enzymic reaction rate. In the reaction type, the oscillations thus induced in theE-activity by the corresponding substrates are out-of-phase, realizing a biochemical discriminating net. Likewise, in an reaction type, the oscillations induced by the irradiatedS-substrate in the activities of the respective enzyme, realize a biochemical switching net.     

Parameters of voluntary effort correlates with functional state of the motor control system

The spectrum oscillations of a prolonged supported effort that was registered at isometric regimen in 3 age groups of healthy volunteers, were analyzed. Changes in distribution of spectral density of effort oscillations and distinction in distribution of spectral density as a reaction to fatigue in age groups, were shown. The revealed amplitude-frequency ranges of changes of spectral density of effort oscillations characterize activity of suprasegmental and segmental levels of motor control system fulfilling the voluntary movement control and the automatic regulation of posture. The correlates with functional state of motor control system are considered in the terms of voluntary and involuntary components of regulation. The substantial growth of activity in the central structures of motor control system in process of development of fatigue and the narrowing of the frequency range of activity of sub-cortical structures with age, were revealed.     

Recording of spontaneous oscillations in the procerebrum of terrestrial mollusk Helix in free behavior

Procerebrum is the central part of the olfactory system in terrestrial snails. Spontaneous rhythmic oscillations were described in this structure. The role of these oscillations in the mechanisms of odor perception and discrimination is unknown yet. Electrical activity of the Helix procerebrum was recorded in vivo. Changes in spontaneous rhythmic oscillations in response to olfactory stimulation were observed. Within the first 10 s after odor application (cineole) in low concentration, a statistically significant decrease in the frequency and increase in the amplitude of procerebrum oscillations were revealed in freely behaving animals. Timing of those changes corresponded to the time of defensive reaction realization of the tentacle withdrawal. The increase in the amplitude and a tendency to a decrease in the frequency of oscillations in response to odor application in high concentration were observed in time period 11-20 s, which corresponded to an increased duration of tentacle withdrawal. The results suggest an implicit relation of the amplitude and frequency of oscillations in odor perception and discrimination.     

About the effect of the amplitude of fluctuations on the coefficient of rubbing of the brownian oscillator in aqueous media

The methods of molecular dynamics and correlation functions of coordinates were applied to investigate molecular oscillations in water solution at a variation of the amplitude of fluctuations. It was established, that the amplitude of fluctuation exceeds the threshold value (in water of the order of 0.3-0.45 A), of the force of friction sharply increases, and the vibration mode changes to the mode of limited diffusion. The consistency of the results with the theory of M?ssbauer effect and the model of Brownian oscillator for conformational mobility in biopolymers is discussed.     

The adenylate kinase reaction acts as a frequency filter towards fluctuations of ATP utilization in the cell

The buffering ability of the adenylate kinase reaction with respect to the phosphate potential and efficiency of oxidative phosphorylation in the presence of a fluctuating load conductance were studied by computer simulations. Fluctuations of the load conductance, i.e., of the irreversible ATP-utilizing reactions in the cell, were generated by integrating an Ornstein-Uhlenbeck diffusion process. This real or colored noise was then injected into the set of differential equations describing the rate laws for the changes of the adenine nucleotide concentrations based on a simple nonequilibrium thermodynamic model of oxidative phosphorylation. Numerical integration of this system of stochastic differential equations allowed us to investigate the influence of different parameters on the performance of this energy converter. Probability density estimates revealed that the variance of the efficiency about its optimal value was significantly reduced by the adenylate kinase reaction. It was found that the buffering ability of this enzyme is restricted to a specific frequency domain of the fluctuations of the load conductance. This frequency filtering was confirmed by substituting the random fluctuations of the load conductance by simple sinusoidal perturbations. All these studies revealed that for each domain of frequencies of the load perturbations there exists an optimal activity of the adenylate kinase which minimizes deviations from optimal efficiency of oxidative phosphorylation.     

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.     

Problems associated with the study of cellular oscillations

Data from the article by Brodsky et al. (2000) have been examined in order to confirm that the fluctuations they report are not random but have a rhythmic basis, thereby verifying their conclusions regarding the existence of periodicity in protein synthesis. Reasons are outlined why oscillations should be expected in all cellular biochemical studies. Associated practical problems are briefly discussed together with comments on the validity and value of less rigorous methods of analysis. The subject of aliasing is raised as justification for doubting the validity of much published data, especially where periodicity has not been suspected. The existence of oscillations indicates the need for a thorough re-evaluation of our understanding of cell biochemistry.