Continuous oscillations in a cell-free extract of S. carlsbergensis

Metabolic Reprogramming is a Hallmark of Metabolism Itself

The reprogramming of metabolism has been identified as one of the hallmarks of cancer. It is becoming more and more frequent to connect other diseases with metabolic reprogramming. This article aims to argue that metabolic reprogramming is not driven by disease but instead is the main hallmark of metabolism, based on its dynamic behavior that allows it to continuously adapt to changes in the internal and external conditions.

Modeling the dynamic behavior of biochemical regulatory networks

Strategies for modeling the complex dynamical behavior of gene/protein regulatory networks have evolved over the last 50 years as both the knowledge of these molecular control systems and the power of computing resources have increased. Here, we review a number of common modeling approaches, including Boolean (logical) models, systems of piecewise-linear or fully non-linear ordinary differential equations, and stochastic models (including hybrid deterministic/stochastic approaches). We discuss the pro's and con's of each approach, to help novice modelers choose a modeling strategy suitable to their problem, based on the type and bounty of available experimental information. We illustrate different modeling strategies in terms of some abstract network motifs, and in the specific context of cell cycle regulation.

The rehabilitation of irreversible processes and dissipative structures' 50th anniversary

In 2017, Ilya Prigogine would have been 100 years of age. As for any human being, this centenary is a notable event. For him, as a scientist, 2017 was also above all the 50th anniversary of dissipative structures It was indeed in 1967 that for the first time he used this denomination at the occasion of an important scientific event and in publications. The attribution of this qualification for self-organized behaviours of matter only possible far from equilibrium coincided with the outcome of a research effort of more than 25 years. Centred in thermodynamics and statistical physics on the role played by irreversible processes in the physical evolution of matter, the aim of this research is clear from the outset of his scientific career. With visionary personal intuition and iron-willed determination, it was pursued. The road to success had been long and sinuous, but finally it led to what he called the rehabilitation of irreversible processes The progresses that stand out as major landmarks of this endeavour that imposed a U-turn with respect to conceptions of classical physics deeply rooted since the nineteenth century will be described. This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (Part 1)'.

Computational analysis of the oscillatory behavior at the translation level induced by mRNA levels oscillations due to finite intracellular resources

Recent studies have demonstrated how the competition for the finite pool of available gene expression factors has important effect on fundamental gene expression aspects. In this study, based on a whole-cell model simulation of translation in S. cerevisiae, we evaluate for the first time the expected effect of mRNA levels fluctuations on translation due to the finite pool of ribosomes. We show that fluctuations of a single gene or a group of genes mRNA levels induce periodic behavior in all S. cerevisiae translation factors and aspects: the ribosomal densities and the translation rates of all S. cerevisiae mRNAs oscillate. We numerically measure the oscillation amplitudes demonstrating that fluctuations of endogenous and heterologous genes can cause a significant fluctuation of up to 50% in the steady-state translation rates of the rest of the genes. Furthermore, we demonstrate by synonymous mutations that oscillating the levels of mRNAs that experience high ribosomal occupancy (e.g. ribosomal “traffic jam”) induces the largest impact on the translation of the S. cerevisiae genome.

The results reported here should provide novel insights and principles related to the design of synthetic gene expression circuits and related to the evolutionary constraints shaping gene expression of endogenous genes.

Each cell contains a limited number of macromolecules and factors that participate in the gene expression process. These expression resources are shared between the different molecules that encode the genetic code, resulting in non-trivial couplings and competitions between the different gene expression stages. Such competitions should be considered when analyzing the cellular economy of the cell, the genome evolution, and the design of synthetic expression circuits. Here we study the effect of couplings and competitions for ribosomes by performing a whole-cell simulation of translation of S. cerevisiae, with parameters estimated from experimental data. We demonstrate that by periodically changing the mRNA levels of a single gene (endogenous or heterologous) or a set of genes, the translation of all S. cerevisiae genes are affected in a periodic manner. We numerically estimate the exact impact of the mRNA levels periodicity on the translation process dynamics, as well as on the dynamics of the free ribosomal pool and the way it is affected by parameters such as the codon composition of the oscillating gene, its initiation rate and mRNA levels. Furthermore, we show that the codon compositions of synthetically highly expressed heterologous genes that are expected to oscillate must be carefully considered. For example, synonymous mutations resulting in “traffic jams” of ribosomes along the fluctuated mRNAs may cause significant fluctuations of up to 50% in the steady-state translation rates of all genes.

Circadian clocks in human red blood cells

Circadian (~24 hour) clocks are fundamentally important for coordinated physiology in organisms as diverse as cyanobacteria and humans. All current models of the clockwork in eukaryotic cells are based on transcription-translation feedback loops. Non-transcriptional mechanisms in the clockwork have been difficult to study in mammalian systems. We circumvented these problems by developing novel assays using human red blood cells (RBCs), which have no nucleus (or DNA), and therefore cannot perform transcription. Our results show that transcription is, in fact, not required for circadian oscillations in humans, and that non-transcriptional events appear sufficient to sustain cellular circadian rhythms. Using RBCs, we found that peroxiredoxins, highly conserved antioxidant proteins, undergo ~24 hour redox cycles, which persist for many days under constant conditions (i.e. in the absence of external cues). Moreover, these rhythms are entrainable (i.e. tunable by environmental stimuli), and temperature-compensated, both key features of circadian rhythms. We anticipate our findings will facilitate more sophisticated cellular clock models, highlighting the interdependency of transcriptional and non-transcriptional oscillations in potentially all eukaryotic cells.

Phase reversal in the Selkov model with inhomogeneous influx

The dynamical reaction-diffusion Selkov system as a model describing the complex traveling wave behavior is presented. The approximate amplitude-phase solution allows us to extract the base properties of the biochemical distributed system, which determines such patterns. It is shown that this relatively simple model could describe qualitatively the main features of the glycolysis waves observed in the experiments.

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.

Simple and complex spatiotemporal structures in a glycolytic allosteric enzyme model

Pattern formation in glycolysis is studied with a classical reaction-diffusion allosteric enzyme model. It is found that, similar to recent experimental reports in the yeast extracts, a small magnitude local perturbation can induce transient target waves in a two dimensional oscillatory medium. An above threshold stimulation generates target waves which eventually evolve into spatiotemporal chaos upon collisions with the boundary or other wave activities. Detailed simulation studies show that the studied simple glycolytic reaction-diffusion model can support three types of spatiotemporal behaviors which are independent of the boundary conditions: (1) a spatially uniform stable steady state, (2) periodic global oscillations and (3) spatiotemporal chaos.

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.

Sustained oscillations in glycolysis: an experimental and theoretical study of chaotic and complex periodic behavior and of quenching of simple oscillations

We report sustained oscillations in glycolysis conducted in an open system (a continuous-flow, stirred tank reactor; CSTR) with inflow of yeast extract as well as glucose. Depending on the operating conditions, we observe simple or complex periodic oscillations or chaos. We report the response of the system to instantaneous additions of small amounts of several substrates as functions of the amount added and the phase of the addition. We simulate oscillations and perturbations by a kinetic model based on the mechanism of glycolysis in a CSTR. We find that the response to particular perturbations forms an efficient tool for elucidating the mechanism of biochemical oscillations.

A constant of temporal structure in the human hierarchy and other systems

The levels that compose biological hierarchies each have their own energetic, spatial and temporal structure. Indeed, it is the discontinuity in energy relationships between levels, as well as the similarity of sub-systems that support them, that permits levels to be defined. In this paper, the temporal structure of living hierarchies, in particular that pertaining to Human society, is examined. Consideration is given to the period defining the lifespan of entities at each level and to a periodic event considered fundamental to the maintenance of that level. The ratio between the duration of these two periods is found to be approximately 2.5 x 10(4). A similar relationship is found when lower, non-living levels of molecules and atoms are considered. This suggests that there is a constant factor of amplification between analogous periodic events at successive levels of the Human hierarchy.

Field-induced instabilities in two-component systems: the cell-free glycolytic system

The effects of weak static electric field on a cell-free glycolytic system, which is known to exhibit oscillatory behavior, have been studied using an allosteric model (due to Goldbeter and Lefever). Linear stability analysis is used to determine the change in the nature of stability and the consequent appearance of dissipative structures, due to the electric field. The results show that for this system all the necessary conditions for a field induced instability are satisfied. An order of magnitude calculation of the field strength shows that field strength in the range 10-100 V/cm is required to produce observable change in the system's behavior.

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.