DAMPED SINUSOIDAL OSCILLATIONS OF CYTOPLASMIC REDUCED PYRIDINE NUCLEOTIDE IN YEAST CELLS

The yeast metabolic cycle: insights into the life of a eukaryotic cell

The budding yeast Saccharomyces cerevisiae undergoes robust oscillations in oxygen consumption during continuous growth under nutrient-limited conditions. Comprehensive microarray studies reveal that more than half of the yeast genome is expressed periodically as a function of these respiratory oscillations, thereby specifying an extensively orchestrated program responsible for regulating numerous cellular outputs. Here, we summarize the logic of the yeast metabolic cycle (YMC) and highlight additional cellular processes that are predicted to be compartmentalized in time. Certain principles of temporal orchestration as seen during the YMC might be conserved across other biological cycles.

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.

Metabolic cycles as an underlying basis of biological oscillations

The evolutionary origins of periodic phenomena in biology, such as the circadian cycle, the hibernation cycle and the sleep-wake cycle, remain a mystery. We discuss the concept of temporal compartmentalization of metabolism that takes place during such cycles, and suggest that cyclic changes in a cell's metabolic state might be a fundamental driving force for such biological oscillations.

The temporal architecture of eukaryotic growth

Coherence of the time structure of growing organisms depends on a metronome-like orchestration. In a continuously perfused culture of Saccharomyces cerevisiae the redox state of the cell shows a temperature-compensated oscillation manifest in respiratory cycles, which are measured by continuous and non-invasive electrodes of probes such as dissolved oxygen and probes such as fluorometric NAD(P)H. Although the entire transcriptome exhibits low-amplitude oscillatory behaviour, transcripts involved in the vast majority of metabolism, stress response, cellular structure, protein turnover, mRNA turnover, and DNA synthesis are amongst the top oscillators and their orchestration occurs by an intricate network of transcriptional regulators. Therefore cellular auto-dynamism is a function of a large ensemble of excitable intracellular components of that self-organized temporally and spatially that encompasses mitochondrial, nuclear, transcriptional and metabolic dynamics, coupled by cellular redox state.

Logic of the yeast metabolic cycle: temporal compartmentalization of cellular processes

Budding yeast grown under continuous, nutrient-limited conditions exhibit robust, highly periodic cycles in the form of respiratory bursts. Microarray studies reveal that over half of the yeast genome is expressed periodically during these metabolic cycles. Genes encoding proteins having a common function exhibit similar temporal expression patterns, and genes specifying functions associated with energy and metabolism tend to be expressed with exceptionally robust periodicity. Essential cellular and metabolic events occur in synchrony with the metabolic cycle, demonstrating that key processes in a simple eukaryotic cell are compartmentalized in time.

The evolution of molecular biology into systems biology

Systems analysis has historically been performed in many areas of biology, including ecology, developmental biology and immunology. More recently, the genomics revolution has catapulted molecular biology into the realm of systems biology. In unicellular organisms and well-defined cell lines of higher organisms, systems approaches are making definitive strides toward scientific understanding and biotechnological applications. We argue here that two distinct lines of inquiry in molecular biology have converged to form contemporary systems biology.

Yeast glycolytic oscillations that are not controlled by a single oscillophore: a new definition of oscillophore strength

Biochemical oscillations, such as glycolytic oscillations, are often believed to be caused by a single so-called 'oscillophore'. The main characteristics of yeast glycolytic oscillations, such as frequency and amplitude, are however controlled by several enzymes. In this paper, we develop a method to quantify to which extent any enzyme determines the occurrence of oscillations. Principles extrapolated from metabolic control analysis are applied to calculate the control exerted by individual enzymes on the real and imaginary parts of the eigenvalues of the Jacobian matrix. We propose that the control exerted by an enzyme on the real part of the smallest eigenvalue, in terms of absolute value, quantifies to which extent that enzyme contributes to the emergence of instability. Likewise the control exerted by an enzyme on the imaginary part of complex eigenvalues may serve to quantify the extent to which that enzyme contributes to the tendency of the system to oscillate. The method was applied both to a core model and to a realistic model of yeast glycolytic oscillations. Both the control over stability and the control over oscillatory tendency were distributed among several enzymes, of which glucose transport, pyruvate decarboxylase and ATP utilization were the most important. The distributions of control were different for stability and oscillatory tendency, showing that control of instability does not imply control of oscillatory tendency nor vice versa. The control coefficients summed up to 1, suggesting the existence of a new summation theorem. These results constitute proof that glycolytic oscillations in yeast are not caused by a single oscillophore and provide a new, subtle, definition for the oscillophore strength of an enzyme.

Simulated complex dynamics of glycolysis in the protozoan parasite Trypanosoma brucei

Glycolysis in Trypanosoma brucei was modeled using a reaction transport simulator and tested for possible complex dynamics. The glycolytic model is multi-compartmentalized and accounts for the exchange of metabolites between the glycosomes, cytosol, mitochondrion and the host medium. The model is used to examine the effects of a range of culture medium concentrations of oxygen on the glycolysis of T. brucei. Our results are in good agreement with steady-state experiments. We also find that under aerobic conditions, increasing the activity of glycerol-3-phosphate dehydrogenase induces complex dynamics in the system. We report the presence of three distinct types of these dynamics. Varying the oxygen concentration in the medium can induce the transition between these dynamics.

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.

The rhythm of yeast

Although yeast are unicellular and comparatively simple organisms, they have a sense of time which is not related to reproduction cycles. The glycolytic pathway exhibits oscillatory behaviour, i.e. the metabolite concentrations oscillate around phosphofructokinase. The frequency of these oscillations is about 1 min when using intact cells. Also a yeast cell extract can oscillate, though with a lower frequency. With intact cells the macroscopic oscillations can only be observed when most of the cells oscillate in concert. Transient oscillations can be observed upon simultaneous induction; sustained oscillations require an active synchronisation mechanism. Such an active synchronisation mechanism, which involves acetaldehyde as a signalling compound, operates under certain conditions. How common these oscillations are in the absence of a synchronisation mechanism is an open question. Under aerobic conditions an oscillatory metabolism can also be observed, but with a much lower frequency than the glycolytic oscillations. The frequency is between one and several hours. These oscillations are partly related to the reproductive cycle, i.e. the budding index also oscillates; however, under some conditions they are unrelated to the reproductive cycle, i.e. the budding index is constant. These oscillations also have an active synchronisation mechanism, which involves hydrogen sulfide as a synchronising agent. Oscillations with a frequency of days can be observed with yeast colonies on plates. Here the oscillations have a synchronisation mechanism which uses ammonia as a synchronising agent.

Respiratory oscillations in yeast: mitochondrial reactive oxygen species, apoptosis and time; a hypothesis

Oscillatory metabolic activities occur more widely than is generally realised; detectability requires observation over extended times of single yeast cells or synchrony of individuals to provide a coherent population. Where oscillations in intracellular metabolite concentrations are observed, the phenomenon has been ascribed to sloppy control, energetic optimisation, signalling, temporal compartmentation of incompatible reactions, or timekeeping functions. Here we emphasise the consequences of respiratory oscillations as a source of mitochondrially generated reactive O(2) metabolites. Temporal co-ordination of intracellular activities necessitates a time base. This is provided by an ultradian clock, and one result of its long-term operation is cyclic energisation of mitochondria, and thereby the generation of deleterious free radical species. Our hypothesis is that unrepaired cellular constituents and components (especially mitochondria) eventually lead to cellular senescence and apoptosis when a finite number of respiratory cycles has occurred.

In-situ-fluorescence-probes: a useful tool for non-invasive bioprocess monitoring

Optical sensors appear to be very promising for different applications in modern biotechnology. They offer the possibility to interface all the well known optical analysis techniques to bioprocesses via fiber optical cables. Thus, high sophisticated and sensitive optical analysis techniques can be coupled to a bioprocess via these light signal transporting fibers. A wide variety of sensor types for application in biotechnology has been described. Normally these sensors are non-invasive and the response times are nearly instantaneous. In particular, the use of glass fiber technology makes these sensors small, robust and reduces their costs.

Control analysis for autonomously oscillating biochemical networks

It has hitherto not been possible to analyze the control of oscillatory dynamic cellular processes in other than qualitative ways. The control coefficients, used in metabolic control analyses of steady states, cannot be applied directly to dynamic systems. We here illustrate a way out of this limitation that uses Fourier transforms to convert the time domain into the stationary frequency domain, and then analyses the control of limit cycle oscillations. In addition to the already known summation theorems for frequency and amplitude, we reveal summation theorems that apply to the control of average value, waveform, and phase differences of the oscillations. The approach is made fully operational in an analysis of yeast glycolytic oscillations. It follows an experimental approach, sampling from the model output and using discrete Fourier transforms of this data set. It quantifies the control of various aspects of the oscillations by the external glucose concentration and by various internal molecular processes. We show that the control of various oscillatory properties is distributed over the system enzymes in ways that differ among those properties. The models that are described in this paper can be accessed on http://jjj.biochem.sun.ac.za.

The modelling of a primitive 'sustainable' conservative cell

The simple sustainable or 'eternal' cell model, assuming preservation of all proteins, is designed as a building block, a primitive element upon which one can build more complete functional cell models of various types, representing various species. In the modelling we emphasize the electrophysiological aspects, in part because these are a well-developed component of cell models and because membrane potentials and their fluctuations have been generally omitted from metabolically oriented cell models in the past. Fluctuations in membrane potential deserve heightened consideration because probably all cells have negative intracellular potentials and most cells demonstrate electrical activity with vesicular extrusion, receptor occupancy, as well as with stimulated excitation resulting in regenerative depolarization. The emphasis is on the balances of mass, charge, and of chemical species while accounting for substrate uptake, metabolism and metabolite loss from the cell. By starting with a primitive representation we emphasize the conservation ideas. As more advanced models are generated they must adhere to the same basic principles as are required for the most primitive incomplete model.

Control of glycolytic dynamics by hexose transport in Saccharomyces cerevisiae

It is becoming accepted that steady-state fluxes are not necessarily controlled by single rate-limiting steps. This leaves open the issue whether cellular dynamics are controlled by single pacemaker enzymes, as has often been proposed. This paper shows that yeast sugar transport has substantial but not complete control of the frequency of glycolytic oscillations. Addition of maltose, a competitive inhibitor of glucose transport, reduced both average glucose consumption flux and frequency of glycolytic oscillations. Assuming a single kinetic component and a symmetrical carrier, a frequency control coefficient of between 0.4 and 0.6 and an average-flux control coefficient of between 0.6 and 0.9 were calculated for hexose transport activity. In a second approach, mannose was used as the carbon and free-energy source, and the dependencies on the extracellular mannose concentration of the transport activity, of the frequency of oscillations, and of the average flux were compared. In this case the frequency control coefficient and the average-flux control coefficient of hexose transport activity amounted to 0.7 and 0.9, respectively. From these results, we conclude that 1) transport is highly important for the dynamics of glycolysis, 2) most but not all control resides in glucose transport, and 3) there should at least be one step other than transport with substantial control.

Circadian and ultradian clock-controlled rhythms in unicellular microorganisms

The time structure of a biological system is at least as intricate as its spatial structure. Whereas we have detailed information about the latter, our understanding of the former is still rudimentary. As techniques for monitoring intracellular processes continuously in single cells become more refined, it becomes increasingly evident that periodic behaviour abounds in all time domains. Circadian timekeeping dominates in natural environments. Here the free-running period is about 24 h. Circadian rhythms in eukaryotes and prokaryotes allow predictive matching of intracellular states with environmental changes during the daily cycles. Unicellular organisms provide excellent systems for the study of these phenomena, which pervade all higher life forms. Intracellular timekeeping is essential. The presence of a temperature-compensated oscillator provides such a timer. The coupled outputs (epigenetic oscillations) of this ultradian clock constitute a special class of ultradian rhythm. These are undamped and endogenously driven by a device which shows biochemical properties characteristic of transcriptional and translational elements. Energy-yielding processes, protein turnover, motility and the timing of the cell-division cycle processes are all controlled by the ultradian clock. Different periods characterize different species, and this indicates a genetic determinant. Periods range from 30 min to 4 h. Mechanisms of clock control are being elucidated; it is becoming evident that many different control circuits can provide these functions.

Is segmentation generic?

When two populations of cells within a tissue mass differ from one another in magnitude or type of intercellular adhesions, a boundary can form within the tissue, across which cells will fail to mix. This phenomenon may occur regardless of the identity of the molecules that mediate cell adhesion. If, in addition, a choice between the two adhesive states is regulated by a molecule the concentration of which is periodic in space, or in time, then alternating bands of non-mixing tissue, or segments, can form. But temporal or spatial periodicities in concentration will tend to arise for any molecule that is positively autoregulatory. It is therefore proposed that segmentation is a 'generic' property of metazoan organisms, and that metamerism would be expected to have emerged numerous times during evolution. A simple model of segmentation, based solely on differential adhesion and periodic regulation of adhesion, can account for segment properties as disparate as those seen in long and short germ band insects, and for diverse experimental results on boundary regeneration in the chick hind brain and the insect cuticle. It is suggested that the complex, multicomponent segment-forming systems found in contemporary organisms (e.g., Drosophila) are the products of evolutionary recruitment of molecular cues such as homeobox gene products, that increase the reliability and stability of metameric patterns originally templated by generic self-organizing properties of tissues.

An allometric interpretation of the spatio-temporal organization of molecular and cellular processes

Different levels of organization distinguished by characteristics spatial dimensions, Ec, and relaxation times, Tr, of biological processes ranging from electron transport in energy transduction to growth of microbial and plant cells, are shown to be related through a relation that may be interpreted as allometric and characterized by two different slopes. Processes, at levels of organization occurring in spatial dimensions of micrometers and relaxing in the order of minutes, delimit a 'transition point' between the two curves, that we interpret as a limit for the emergence of macroscopic coherence. The characteristic spatial dimension, Ec, and the relaxation time, Tr, contain dynamical information about the processes occurring at a given level of organization. When a steady state of a biological process at a certain level of organization becomes unstable, the system undergoes a transition to another level of organization. To exemplify the appearance of macroscopic order at levels of organization further from the 'transition point' we present in this report various experimental systems involving many levels of organization allometrically related that exhibit different kinds of self-organized behavior, i.e. bi-stability, oscillations, changes in (a)symmetry.

Mutations in phosphofructokinases alter the control characteristics of glycolysis in vivo in Saccharomyces cerevisiae

Ethanol and CO2 production from glucose by non-proliferating suspensions of aerobically-grown, glucose-derepressed wild-type Saccharomyces cerevisiae is inhibited by O2; monitoring by mass spectrometry provides a direct method for measurement of the Pasteur effect. Under aerobic conditions, that part of the CO2 evolved equivalent to the O2 consumed, is produced by respiration: subtraction of this respiratory CO2 from the total gives CO2 produced by aerobic glycolysis. Pasteur quotients (anaerobic CO2/aerobic glycolytic CO2) were within the range 1.2 to 3.0. The Pasteur effect was not observed in the presence of carbonyl cyanide m-chlorophenylhydrazone, an uncoupler of mitochondrial energy metabolism, or in a rho degree cytoplasmic petite mutant. A 'non-allosteric' mutant with an altered regulatory subunit of phosphofructokinase showed no Pasteur effect. Strains bearing a nonsense mutation pfk1 in the catalytic subunit of soluble phosphofructokinase (PFKI) also showed no Pasteur effect; the residual fermentative activity of this strain was dependent on PFKII, the particulate phosphofructokinase. A double mutant lacking both PFKI and glucose-6-phosphate dehydrogenase showed similar characteristics to those of the single pfk1 mutant; this indicates that the hexose monophosphate shunt is not acting to bypass the phosphofructokinase block. A 'hyper-allosteric' mutant altered in the regulatory subunit encoded by the gene PFK2 showed characteristics of glucose fermentation and ethanol oxidation very similar to those of wild-type organisms. These results indicate that either of the two phosphofructokinases can carry out glycolysis.

The occurrence and functions of ultradian rhythms

Ultradian oscillations with periods between 5 min and 4 h have been described in cell-free extracts, single-celled eukaryotes, cultured cells and embryos. Whereas some of these potentially oscillatory systems (e.g. glycolysis) may only exhibit this type of behaviour rarely if at all in vivo, other ultradian oscillators in lower eukaryotes are rhythms and probably have timekeeping functions. Rhythms with ultradian periods of 10 min to 20 h in oxygen consumption and carbon dioxide production have also been studied in endotherm animals: these rhythms may be modified by variations of environmental parameters and by circadian and infradian synchronizers. Interspecies and interstrain differences strongly suggest that these rhythms are endogenous and have a genetic origin. We suggest that the temporal organization of biochemical and physiological processes facilitates optimization of thermodynamic maintenance of the organism within the random fluctuations of its physicochemical environment and contributes to genetic selection.

Clock mutations alter developmental timing in Drosophila

The developmental time of period mutants in Drosophila melanogaster was monitored under different environmental conditions. We observed that the pers mutants, which have short 19 h circadian cycles, develop faster from eggs to adult than the wild-type: perL mutants, which have long 28 h circadian rhythms, complete development more slowly than the wild-type. These results suggest that endogenous timers may be involved in regulating the development time of D. melanogaster.

Temperature-compensated oscillations in respiration and cellular protein content in synchronous cultures of Acanthamoeba castellanii

Synchronous cultures of the soil amoeba Acanthamoeba castellanii, established by a selection procedure, show significant oscillations of respiration and total cell protein. There was little difference between the period of these oscillations, which averaged 76 min, although the five incubation temperatures used varied between 20 degrees C and 30 degrees C and the cell division time increased from 7.8 to 16 hr. The phase of these oscillations also corresponded approximately at all incubation temperatures. Similar observations made over the whole division cycle at three temperatures indicated that similar oscillations occurred, with a constant period of 65 min, although these data were too variable to show this unequivocally. Control (asynchronous) cultures show that the oscillations are not a consequence of metabolic perturbation produced by the centrifugal selection procedure. It is suggested that these temperature-compensated epigenetic oscillations serve a dual role in cell cycle and circadian timekeeping and that cell cycle time is quantized.

Circadian rhythm mutations in Drosophila melanogaster affect short-term fluctuations in the male's courtship song

Courtship song in Drosophila is produced by the male's wing vibration and consists of pulses of tone produced at intervals of approximately 34 msec in D. melanogaster and 48 msec in D. simulans. We have observed that the intervals between these pulses are not constant but fluctuate rhythmically with periods of approximately 1 min in D. melanogaster and 0.5 min in D. simulans. In D. melanogaster, three allelic per mutations have been isolated which affect the periodicity of the circadian oscillators affecting both eclosion and locomotor activity [Konopka, R. & Benzer S. (1971) Proc. Natl. Acad. Sci. USA 68, 2112-2116]. Each of the per alleles--pers, which shortens the circadian period, perI, which lengthens it, and perO, which abolishes it--strikingly affects the 60-sec song rhythm in a parallel fashion. Therefore, both circadian rhythms and a very short, noncircadian oscillation appear to be influenced by the same gene.

Computer-aided biochemical system analysis in open systems with environment simulation

A computer-aided arrangement is described which allows kinetic and regulative studies with enzymes, organelles and cells in an open system. This is demonstrated with some simple examples.

Estimation of Fermentation Biomass Concentration by Measuring Culture Fluorescence

The fluorescence of a fermentation culture was studied for its application as an estimator of biomass concentration. The measurement was obtained by irradiating the culture with ultraviolet light (366 nm) through a glass window and detecting fluorescent light at the window surface at 460 nm. It was estimated that over one-half of the fluorescent material was intercellular reduced nicotinamide adenine dinucleotide, with the remainder being reduced nicotinamide adenine dinucleotide phosphate and other unidentified intercellular and extracellular fluorophores. The culture fluorescence was found to be a function of biomass concentration, together with environmental factors, which presumably act at the cellular metabolic level to modify intercellular reduced nicotinamide adenine dinucleotide pools (e.g., dissolved oxygen tension, energy substrate concentration, and inhibitors). When these environmental conditions were controlled, a linear relationship was obtained between the log of the biomass concentration and the log of the fluorescence. Under these conditions, this relationship has considerable potential as a method to provide real-time biomass concentration estimates for process control and optimization since the fluorescence data is obtained on line. When environmental conditions are variable, the fluorescence data may be a sensitive index of overall culture activity because of its dependence on intercellular reduced nicotinamide adenine dinucleotide reserves and metabolic rates. This index may provide information about the period of maximum specific productivity for a specific microbial product.

Quantized generation time in mammalian cells as an expression of the cellular clock

The distribution of possible generation times in mammalian cells does not appear to be continous within the limits of range for each cell type; rather, generation time is quantized in multiples of 3-4 hr. Synchronous cultures of Chinese hamster V79 cells were prepared using manual and automated methods to select and stage mitotic cells. Using synchronous cultures and time-lapse video tape microscopy, it was possible to show that generation times within a population of mitotically selected cells normally disperse in a quantized fashion, with intervals of 3-4 hr occurring between bursts in division. In addition, at temperatures above 37 degrees, V79 cells have a 7.5-8.5 hr modal cell cycle, while at temperatures from 36.5 degrees to 33.5 degrees the modal cell cycle is 11-12 hr long. A survey of the synchrony literature reveals that the tendency to preferred generation times holds between cell lines. The distribution of modal generation times from a variety of different cell types forms a series with a similar interval but with a greater range of values than that observed here for V79 cells. To satisfy the published data and the work presented here, I propose a subcycle, Gq, which has a traverse time equal to the period of the clock. The period appears to be fixed at close to the same value in all mammalian somatic cells. The timekeeping mechanism appears to be temperature compensated, since the time required to traverse Gq is constant at temperatures between 34 degrees and 39 degrees. It is suggested that cell cycle time increases at lower temperatures, lower serum concentration, and high cell densitite because the number of rounds of traverse through Gq increases.

Circadian rhythms in neurospora: spatial differences in pyridine nucleotide levels

A growing colony of a mutant strain of Neurospora crassa had two morphologically distinct areas which were formed as a result of a rhythmic spore-forming (conidiation) process. The total pyridine nucleotide content of these two areas was the same, but the levels of NADH, NADPH, and NADP were lower in the conidiating area, while the NAD level was higher. These biochemical differences in the adjacent areas of a single colony were only found in newly formed areas, and were not a permanent record. It is not known whether these pyridine nucleotide changes are a result of the conidiation process, or whether they are tied more directly to some underlying metabolic oscillation. However, it is speculated that the changes in the levels of these key coenzymes could have far-reaching effects on many areas of metabolism.

Dissipative structures for an allosteric model. Application to glycolytic oscillations

An allosteric model of an open monosubstrate enzyme reaction is analyzed for the case where the enzyme, containing two protomers, is activated by the product. It is shown that this system can lead to instabilities beyond which a new state organized in time or in space (dissipative structure) can be reached. The conditions for both types of instabilities are presented and the occurrence of a temporal structure, consisting of a limit cycle behavior, is determined numerically as a function of the important parameters involved in the system. Sustained oscillations in the product and substrate concentrations are shown to occur for acceptable values of the allosteric and kinetic constants; moreover, they seem to be favored by substrate activation. The model is applied to phosphofructokinase, which is the enzyme chiefly responsible for glycolytic oscillations and which presents the same pattern of regulation as the allosteric enzyme appearing in the model. A qualitative and quantitative agreement is obtained with the experimental observations concerning glycolytic self-oscillations.