Modelling chronotaxicity of cellular energy metabolism to facilitate the identification of altered metabolic states

Glycolytic oscillations under periodic drivings

In many living organisms displaying circadian rhythms, the intake of energy often occurs in a periodic manner. Glycolysis is a prototypical biochemical reaction that exhibits a self-sustained oscillation under continuous injection of glucose. Here we study the effect of periodic injection of glucose on the glycolytic oscillation from a dynamical systems perspective. In particular, we employ Goldbeter's allosteric model of phosphofructokinase as a model system for glycolytic oscillations, and explore the effect of periodic substrate influx of varying frequencies and amplitudes by building the phase diagrams of Lyapunov exponents and oscillatory periods. When the frequency of driving is tuned around the harmonic and sub/super-harmonic conditions of the natural frequency, the system is entrained to a frequency-locked state, forming an entrainment band that broadens with an increasing amplitude of driving. On the other hand, if the amplitude is substantial, the system may transition, albeit infrequent, to a chaotic state which defies prediction of dynamical behaviour. Our study offers in-depth understandings into the controllability of glycolytic oscillation as well as explaining physical underpinnings that enable the synchronous oscillations among a dense population of cells.

Metabolic Oscillations and Glycolytic Phenotypes of Cancer Cells

Cancer cells show several metabolic phenotypes depending on the cancer types and the microenvironments in tumor tissues. The glycolytic phenotype is one of the hallmarks of cancer cells and is considered to be one of the crucial features of malignant cancers. Here, we show glycolytic oscillations in the concentrations of metabolites in the glycolytic pathway in two types of cancer cells, HeLa cervical cancer cells and DU145 prostate cancer cells, and in two types of cellular morphologies, spheroids and monolayers. Autofluorescence from nicotinamide adenine dinucleotide (NADH) in cells was used for monitoring the glycolytic oscillations at the single-cell level. The frequencies of NADH oscillations were different among the cellular types and morphologies, indicating that more glycolytic cancer cells tended to exhibit oscillations with higher frequencies than less glycolytic cells. A mathematical model for glycolytic oscillations in cancer cells reproduced the experimental results quantitatively, confirming that the higher frequencies of oscillations were due to the higher activities of glycolytic enzymes. Thus, glycolytic oscillations are expected as a medical indicator to evaluate the malignancy of cancer cells with glycolytic phenotypes.

Oscillations and Dynamic Symbiosis in Cellular Metabolism in Cancer

The grade of malignancy differs among cancer cell types, yet it remains the burden of genetic studies to understand the reasons behind this observation. Metabolic studies of cancer, based on the Warburg effect or aerobic glycolysis, have also not provided any clarity. Instead, the significance of oxidative phosphorylation (OXPHOS) has been found to play critical roles in aggressive cancer cells. In this perspective, metabolic symbiosis is addressed as one of the ultimate causes of the grade of cancer malignancy. Metabolic symbiosis gives rise to metabolic heterogeneities which enable cancer cells to acquire greater opportunities for proliferation and metastasis in tumor microenvironments. This study introduces a real-time new imaging technique to visualize metabolic symbiosis between cancer-associated fibroblasts (CAFs) and cancer cells based on the metabolic oscillations in these cells. The causality of cellular oscillations in cancer cells and CAFs, connected through lactate transport, is a key point for the development of this novel technique.

Modeling Cell Energy Metabolism as Weighted Networks of Non-autonomous Oscillators

Networks of oscillating processes are a common occurrence in living systems. This is as true as anywhere in the energy metabolism of individual cells. Exchanges of molecules and common regulation operate throughout the metabolic processes of glycolysis and oxidative phosphorylation, making the consideration of each of these as a network a natural step. Oscillations are similarly ubiquitous within these processes, and the frequencies of these oscillations are never truly constant. These features make this system an ideal example with which to discuss an alternative approach to modeling living systems, which focuses on their thermodynamically open, oscillating, non-linear and non-autonomous nature. We implement this approach in developing a model of non-autonomous Kuramoto oscillators in two all-to-all weighted networks coupled to one another, and themselves driven by non-autonomous oscillators. Each component represents a metabolic process, the networks acting as the glycolytic and oxidative phosphorylative processes, and the drivers as glucose and oxygen supply. We analyse the effect of these features on the synchronization dynamics within the model, and present a comparison between this model, experimental data on the glycolysis of HeLa cells, and a comparatively mainstream model of this experiment. In the former, we find that the introduction of oscillator networks significantly increases the proportion of the model's parameter space that features some form of synchronization, indicating a greater ability of the processes to resist external perturbations, a crucial behavior in biological settings. For the latter, we analyse the oscillations of the experiment, finding a characteristic frequency of 0.01–0.02 Hz. We further demonstrate that an output of the model comparable to the measurements of the experiment oscillates in a manner similar to the measured data, achieving this with fewer parameters and greater flexibility than the comparable model.

Extracellular ionic fluxes suggest the basis for cellular life at the 1/f ridge of extended criticality

The criticality hypothesis states that a system may be poised in a critical state at the boundary between different types of dynamics. Previous studies have suggested that criticality has been evolutionarily selected, and examples have been found in cortical cell cultures and in the human nervous system. However, no one has yet reported a single- or multi-cell ensemble that was investigated ex vivo and found to be in the critical state. Here, the precise 1/f noise was found for pollen tube cells of optimum growth and for the physiological ("healthy") state of blood cells. We show that the multi-scale processes that arise from the so-called critical phenomena can be a fundamental property of a living cell. Our results reveal that cell life is conducted at the border between order and disorder, and that the dynamics themselves drive a system towards a critical state. Moreover, a temperature-driven re-entrant state transition, manifest in the form of a Lorentz resonance, was found in the fluctuation amplitude of the extracellular ionic fluxes for the ensemble of elongating pollen tubes of Nicotiana tabacum L. or Hyacintus orientalis L. Since this system is fine-tuned for rapid expansion to reach the ovule at a critical temperature which results in fertilisation, the core nature of criticality (long-range coherence) offers an explanation for its potential in cell growth. We suggest that the autonomous organisation of expansive growth is accomplished by self-organised criticality, which is an orchestrated instability that occurs in an evolving cell.

In-vivo correlations between skin metabolic oscillations and vasomotion in wild-type mice and in a model of oxidative stress

Arterioles in the cutaneous microcirculation frequently display an oscillatory phenomenon defined vasomotion, consistent with periodic diameter variations in the micro-vessels associated with particular physiological or abnormal conditions. The cellular mechanisms underlying vasomotion and its physiological role have not been completely elucidated. Various mechanisms were demonstrated, based on cell Ca²⁺ oscillations determined by the activity of channels in the plasma membrane or sarcoplasmic reticulum of vascular cells. However, the possible engagement in vasomotion of cell metabolic oscillations of mitochondrial or glycolytic origin has been poorly explored. Metabolic oscillations associated with the production of ATP energy were previously described in cells, while limited studies have investigated these fluctuations in-vivo. Here, we characterised a low-frequency metabolic oscillator (MO-1) in skin from live wild-type and Nrf2^−/− mice, by combination of fluorescence spectroscopy and wavelet transform processing technique. Furthermore, the relationships between metabolic and microvascular oscillators were examined during phenylephrine-induced vasoconstriction. We found a significant interaction between MO-1 and the endothelial EDHF vasomotor mechanism that was reduced in the presence of oxidative stress (Nrf2^−/− mice). Our findings suggest indirectly that metabolic oscillations may be involved in the mechanisms underlying endothelium-mediated skin vasomotion, which might be altered in the presence of metabolic disturbance.

Nonautonomous driving induces stability in network of identical oscillators

Nonautonomous driving of an oscillator has been shown to enlarge the Arnold tongue in parameter space, but little is known about the analogous effect for a network of oscillators. To test the hypothesis that deterministic nonautonomous perturbation is a good candidate for stabilizing complex dynamics, we consider a network of identical phase oscillators driven by an oscillator with a slowly time-varying frequency. We investigate both the short- and long-term stability of the synchronous solutions of this nonautonomous system. For attractive couplings we show that the region of stability grows as the amplitude of the frequency modulation is increased, through the birth of an intermittent synchronization regime. For repulsive couplings, we propose a control strategy to stabilize the dynamics by altering very slightly the network topology. We also show how, without changing the topology, time-variability in the driving frequency can itself stabilize the dynamics. As a byproduct of the analysis, we observe chimeralike states. We conclude that time-variability-induced stability phenomena are also present in networks, reinforcing the idea that this is a quite realistic scenario for living systems to use in maintaining their functioning in the face of ongoing perturbations.

Stabilization of dynamics of oscillatory systems by nonautonomous perturbation

Synchronization and stability under periodic oscillatory driving are well understood, but little is known about the effects of aperiodic driving, despite its abundance in nature. Here, we consider oscillators subject to driving with slowly varying frequency, and investigate both short-term and long-term stability properties. For a phase oscillator, we find that, counterintuitively, such variation is guaranteed to enlarge the Arnold tongue in parameter space. Using analytical and numerical methods that provide information on time-variable dynamical properties, we find that the growth of the Arnold tongue is specifically due to the growth of a region of intermittent synchronization where trajectories alternate between short-term stability and short-term neutral stability, giving rise to stability on average. We also present examples of higher-dimensional nonlinear oscillators where a similar stabilization phenomenon is numerically observed. Our findings help support the case that in general, deterministic nonautonomous perturbation is a very good candidate for stabilizing complex dynamics.

Biological Oscillators in Nanonetworks-Opportunities and Challenges

One of the major issues in molecular communication-based nanonetworks is the provision and maintenance of a common time knowledge. To stay true to the definition of molecular communication, biological oscillators are the potential solutions to achieve that goal as they generate oscillations through periodic fluctuations in the concentrations of molecules. Through the lens of a communication systems engineer, the scope of this survey is to explicitly classify, for the first time, existing biological oscillators based on whether they are found in nature or not, to discuss, in a tutorial fashion, the main principles that govern the oscillations in each oscillator, and to analyze oscillator parameters that are most relevant to communication engineer researchers. In addition, the survey highlights and addresses the key open research issues pertaining to several physical aspects of the oscillators and the adoption and implementation of the oscillators to nanonetworks. Moreover, key research directions are discussed.

Oscillatory signatures underlie growth regimes in Arabidopsis pollen tubes: computational methods to estimate tip location, periodicity, and synchronization in growing cells

Oscillations in pollen tubes have been reported for many cellular processes, including growth, extracellular ion fluxes, and cytosolic ion concentrations. However, there is a shortage of quantitative methods to measure and characterize the different dynamic regimes observed. Herein, a suite of open-source computational methods and original algorithms were integrated into an automated analysis pipeline that we employed to characterize specific oscillatory signatures in pollen tubes of Arabidopsis thaliana (Col-0). Importantly, it enabled us to detect and quantify a Ca2+ spiking behaviour upon growth arrest and synchronized oscillations involving growth, extracellular H+ fluxes, and cytosolic Ca2+, providing the basis for novel hypotheses. Our computational approach includes a new tip detection method with subpixel resolution using linear regression, showing improved ability to detect oscillations when compared to currently available methods. We named this data analysis pipeline 'Computational Heuristics for Understanding Kymographs and aNalysis of Oscillations Relying on Regression and Improved Statistics', or CHUKNORRIS. It can integrate diverse data types (imaging, electrophysiology), extract quantitative and time-explicit estimates of oscillatory characteristics from isolated time series (period and amplitude) or pairs (phase relationships and delays), and evaluate their synchronization state. Here, its performance is tested with ratiometric and single channel kymographs, ion flux data, and growth rate analysis.

Oscillatory signatures underlie growth regimes in Arabidopsis pollen tubes: computational methods to estimate tip location, periodicity, and synchronization in growing cells

Oscillations in pollen tubes have been reported for many cellular processes, including growth, extracellular ion fluxes, and cytosolic ion concentrations. However, there is a shortage of quantitative methods to measure and characterize the different dynamic regimes observed. Herein, a suite of open-source computational methods and original algorithms were integrated into an automated analysis pipeline that we employed to characterize specific oscillatory signatures in pollen tubes of Arabidopsis thaliana (Col-0). Importantly, it enabled us to detect and quantify a Ca2+ spiking behaviour upon growth arrest and synchronized oscillations involving growth, extracellular H+ fluxes, and cytosolic Ca2+, providing the basis for novel hypotheses. Our computational approach includes a new tip detection method with subpixel resolution using linear regression, showing improved ability to detect oscillations when compared to currently available methods. We named this data analysis pipeline 'Computational Heuristics for Understanding Kymographs and aNalysis of Oscillations Relying on Regression and Improved Statistics', or CHUKNORRIS. It can integrate diverse data types (imaging, electrophysiology), extract quantitative and time-explicit estimates of oscillatory characteristics from isolated time series (period and amplitude) or pairs (phase relationships and delays), and evaluate their synchronization state. Here, its performance is tested with ratiometric and single channel kymographs, ion flux data, and growth rate analysis.