Browse
Submit Data
Databases
API
Help

Dataset Information

19 Views

0 Connections

0 Citations

0 Reanalyses

0 Downloads

Omics score: 0

Nonlinear time series analysis of nodulation factor induced calcium oscillations: evidence for deterministic chaos?

ABSTRACT: Legume plants form beneficial symbiotic interactions with nitrogen fixing bacteria (called rhizobia), with the rhizobia being accommodated in unique structures on the roots of the host plant. The legume/rhizobial symbiosis is responsible for a significant proportion of the global biologically available nitrogen. The initiation of this symbiosis is governed by a characteristic calcium oscillation within the plant root hair cells and this signal is activated by the rhizobia. Recent analyses on calcium time series data have suggested that stochastic effects have a large role to play in defining the nature of the oscillations. The use of multiple nonlinear time series techniques, however, suggests an alternative interpretation, namely deterministic chaos. We provide an extensive, nonlinear time series analysis on the nature of this calcium oscillation response. We build up evidence through a series of techniques that test for determinism, quantify linear and nonlinear components, and measure the local divergence of the system. Chaos is common in nature and it seems plausible that properties of chaotic dynamics might be exploited by biological systems to control processes within the cell. Systems possessing chaotic control mechanisms are more robust in the sense that the enhanced flexibility allows more rapid response to environmental changes with less energetic costs. The desired behaviour could be most efficiently targeted in this manner, supporting some intriguing speculations about nonlinear mechanisms in biological signaling.

SUBMITTER: Hazledine S

PROVIDER: S-EPMC2722092 | biostudies-literature |

REPOSITORIES: biostudies-literature

ACCESS DATA

Json Xml

Similar Datasets

A deterministic model predicts the properties of stochastic calcium oscillations in airway smooth muscle cells.

Project description:The inositol trisphosphate receptor ([Formula: see text]) is one of the most important cellular components responsible for oscillations in the cytoplasmic calcium concentration. Over the past decade, two major questions about the [Formula: see text] have arisen. Firstly, how best should the [Formula: see text] be modeled? In other words, what fundamental properties of the [Formula: see text] allow it to perform its function, and what are their quantitative properties? Secondly, although calcium oscillations are caused by the stochastic opening and closing of small numbers of [Formula: see text], is it possible for a deterministic model to be a reliable predictor of calcium behavior? Here, we answer these two questions, using airway smooth muscle cells (ASMC) as a specific example. Firstly, we show that periodic calcium waves in ASMC, as well as the statistics of calcium puffs in other cell types, can be quantitatively reproduced by a two-state model of the [Formula: see text], and thus the behavior of the [Formula: see text] is essentially determined by its modal structure. The structure within each mode is irrelevant for function. Secondly, we show that, although calcium waves in ASMC are generated by a stochastic mechanism, [Formula: see text] stochasticity is not essential for a qualitative prediction of how oscillation frequency depends on model parameters, and thus deterministic [Formula: see text] models demonstrate the same level of predictive capability as do stochastic models. We conclude that, firstly, calcium dynamics can be accurately modeled using simplified [Formula: see text] models, and, secondly, to obtain qualitative predictions of how oscillation frequency depends on parameters it is sufficient to use a deterministic model.

| S-EPMC4133161 | biostudies-literature

Inference for nonlinear epidemiological models using genealogies and time series.

Project description:Phylodynamics - the field aiming to quantitatively integrate the ecological and evolutionary dynamics of rapidly evolving populations like those of RNA viruses - increasingly relies upon coalescent approaches to infer past population dynamics from reconstructed genealogies. As sequence data have become more abundant, these approaches are beginning to be used on populations undergoing rapid and rather complex dynamics. In such cases, the simple demographic models that current phylodynamic methods employ can be limiting. First, these models are not ideal for yielding biological insight into the processes that drive the dynamics of the populations of interest. Second, these models differ in form from mechanistic and often stochastic population dynamic models that are currently widely used when fitting models to time series data. As such, their use does not allow for both genealogical data and time series data to be considered in tandem when conducting inference. Here, we present a flexible statistical framework for phylodynamic inference that goes beyond these current limitations. The framework we present employs a recently developed method known as particle MCMC to fit stochastic, nonlinear mechanistic models for complex population dynamics to gene genealogies and time series data in a Bayesian framework. We demonstrate our approach using a nonlinear Susceptible-Infected-Recovered (SIR) model for the transmission dynamics of an infectious disease and show through simulations that it provides accurate estimates of past disease dynamics and key epidemiological parameters from genealogies with or without accompanying time series data.

| S-EPMC3161897 | biostudies-literature

Detecting causality from nonlinear dynamics with short-term time series.

Project description:Quantifying causality between variables from observed time series data is of great importance in various disciplines but also a challenging task, especially when the observed data are short. Unlike the conventional methods, we find it possible to detect causality only with very short time series data, based on embedding theory of an attractor for nonlinear dynamics. Specifically, we first show that measuring the smoothness of a cross map between two observed variables can be used to detect a causal relation. Then, we provide a very effective algorithm to computationally evaluate the smoothness of the cross map, or "Cross Map Smoothness" (CMS), and thus to infer the causality, which can achieve high accuracy even with very short time series data. Analysis of both mathematical models from various benchmarks and real data from biological systems validates our method.

| S-EPMC5376982 | biostudies-literature

A unified nonlinear stochastic time series analysis for climate science.

Project description:Earth's orbit and axial tilt imprint a strong seasonal cycle on climatological data. Climate variability is typically viewed in terms of fluctuations in the seasonal cycle induced by higher frequency processes. We can interpret this as a competition between the orbitally enforced monthly stability and the fluctuations/noise induced by weather. Here we introduce a new time-series method that determines these contributions from monthly-averaged data. We find that the spatio-temporal distribution of the monthly stability and the magnitude of the noise reveal key fingerprints of several important climate phenomena, including the evolution of the Arctic sea ice cover, the El Nio Southern Oscillation (ENSO), the Atlantic Nio and the Indian Dipole Mode. In analogy with the classical destabilising influence of the ice-albedo feedback on summertime sea ice, we find that during some time interval of the season a destabilising process operates in all of these climate phenomena. The interaction between the destabilisation and the accumulation of noise, which we term the memory effect, underlies phase locking to the seasonal cycle and the statistical nature of seasonal predictability.

| S-EPMC5347016 | biostudies-literature

Nonlinear dynamics and chaos in an optomechanical beam.

Project description:Optical nonlinearities, such as thermo-optic mechanisms and free-carrier dispersion, are often considered unwelcome effects in silicon-based resonators and, more specifically, optomechanical cavities, since they affect, for instance, the relative detuning between an optical resonance and the excitation laser. Here, we exploit these nonlinearities and their intercoupling with the mechanical degrees of freedom of a silicon optomechanical nanobeam to unveil a rich set of fundamentally different complex dynamics. By smoothly changing the parameters of the excitation laser we demonstrate accurate control to activate two- and four-dimensional limit cycles, a period-doubling route and a six-dimensional chaos. In addition, by scanning the laser parameters in opposite senses we demonstrate bistability and hysteresis between two- and four-dimensional limit cycles, between different coherent mechanical states and between four-dimensional limit cycles and chaos. Our findings open new routes towards exploiting silicon-based optomechanical photonic crystals as a versatile building block to be used in neurocomputational networks and for chaos-based applications.

| S-EPMC5394270 | biostudies-literature

Time-series transcriptomics and proteomics reveal alternative modes to decode p53 oscillations

Project description:Transcription factors (TFs) can relay signals through temporal alterations in their levels. The cell stress responsive TF p53 exhibits different dynamics depending on the type of stress, which influence the magnitude and dynamics of expression of its target genes and subsequent cellular outcomes. The mechanisms decoding p53 dynamics into levels and dynamics of RNA and protein of its targets remain unclear. We systematically quantified p53 target mRNA and protein levels over time under two p53 dynamical regimes – oscillatory and sustained – using RNA-seq and quantitative mass spectrometry. We categorized the mRNA dynamical patterns arising from oscillatory or sustained p53 expression, as well as the corresponding protein dynamics. We found that in both cases oscillatory dynamics allowed for the greatest variety of dynamical patterns of the downstream species. Target proteins from a wide range of functional categories were induced under both p53 dynamic conditions, with induction levels being overall higher under sustained dynamics. Mathematical modeling combined with analysis of empirical data revealed three mechanisms of decoding p53 dynamics: adjustment of mRNA and protein degradation rates, adjustment of activation thresholds for expression of mRNA and corresponding protein levels, and usage of coherent and incoherent feed-forward loop motifs in generating exclusive responses to p53 oscillatory or sustained dynamics, respectively. Our results highlight the diversity of mechanisms that decode complex TF dynamics into dynamical patterns of mRNA and proteins.

2022-02-11 | PXD027030 | Pride

Identifying Temporally Regulated Root Nodulation Biomarkers Using Time Series Gene Co-Expression Network Analysis.

Project description:Root nodulation results from a symbiotic relationship between a plant host and Rhizobium bacteria. Synchronized gene expression patterns over the course of rhizobial infection result in activation of pathways that are unique but overlapping with the highly conserved pathways that enable mycorrhizal symbiosis. We performed RNA sequencing of 30 Medicago truncatula root maturation zone samples at five distinct time points. These samples included plants inoculated with Sinorhizobium medicae and control plants that did not receive any Rhizobium. Following gene expression quantification, we identified 1,758 differentially expressed genes at various time points. We constructed a gene co-expression network (GCN) from the same data and identified link community modules (LCMs) that were comprised entirely of differentially expressed genes at specific time points post-inoculation. One LCM included genes that were up-regulated at 24 h following inoculation, suggesting an activation of allergen family genes and carbohydrate-binding gene products in response to Rhizobium. We also identified two LCMs that were comprised entirely of genes that were down regulated at 24 and 48 h post-inoculation. The identity of the genes in these modules suggest that down-regulating specific genes at 24 h may result in decreased jasmonic acid production with an increase in cytokinin production. At 48 h, coordinated down-regulation of a specific set of genes involved in lipid biosynthesis may play a role in nodulation. We show that GCN-LCM analysis is an effective method to preliminarily identify polygenic candidate biomarkers of root nodulation and develop hypotheses for future discovery.

| S-EPMC6836625 | biostudies-literature

Detecting and quantifying causal associations in large nonlinear time series datasets.

Project description:Identifying causal relationships and quantifying their strength from observational time series data are key problems in disciplines dealing with complex dynamical systems such as the Earth system or the human body. Data-driven causal inference in such systems is challenging since datasets are often high dimensional and nonlinear with limited sample sizes. Here, we introduce a novel method that flexibly combines linear or nonlinear conditional independence tests with a causal discovery algorithm to estimate causal networks from large-scale time series datasets. We validate the method on time series of well-understood physical mechanisms in the climate system and the human heart and using large-scale synthetic datasets mimicking the typical properties of real-world data. The experiments demonstrate that our method outperforms state-of-the-art techniques in detection power, which opens up entirely new possibilities to discover and quantify causal networks from time series across a range of research fields.

| S-EPMC6881151 | biostudies-literature

Qubit-mediated deterministic nonlinear gates for quantum oscillators.

Project description:Quantum nonlinear operations for harmonic oscillator systems play a key role in the development of analog quantum simulators and computers. Since strong highly nonlinear operations are often unavailable in the existing physical systems, it is a common practice to approximate them by using conditional measurement-induced methods. The conditional approach has several drawbacks, the most severe of which is the exponentially decreasing success rate of the strong and complex nonlinear operations. We show that by using a suitable two level system sequentially interacting with the oscillator, it is possible to resolve these issues and implement a nonlinear operation both nearly deterministically and nearly perfectly. We explicitly demonstrate the approach by constructing self-Kerr and cross-Kerr couplings in a realistic situation, which require a feasible dispersive coupling between the two-level system and the oscillator.

| S-EPMC5599512 | biostudies-literature

The Fourier decomposition method for nonlinear and non-stationary time series analysis.

Project description:for many decades, there has been a general perception in the literature that Fourier methods are not suitable for the analysis of nonlinear and non-stationary data. In this paper, we propose a novel and adaptive Fourier decomposition method (FDM), based on the Fourier theory, and demonstrate its efficacy for the analysis of nonlinear and non-stationary time series. The proposed FDM decomposes any data into a small number of 'Fourier intrinsic band functions' (FIBFs). The FDM presents a generalized Fourier expansion with variable amplitudes and variable frequencies of a time series by the Fourier method itself. We propose an idea of zero-phase filter bank-based multivariate FDM (MFDM), for the analysis of multivariate nonlinear and non-stationary time series, using the FDM. We also present an algorithm to obtain cut-off frequencies for MFDM. The proposed MFDM generates a finite number of band-limited multivariate FIBFs (MFIBFs). The MFDM preserves some intrinsic physical properties of the multivariate data, such as scale alignment, trend and instantaneous frequency. The proposed methods provide a time-frequency-energy (TFE) distribution that reveals the intrinsic structure of a data. Numerical computations and simulations have been carried out and comparison is made with the empirical mode decomposition algorithms.

| S-EPMC5378250 | biostudies-literature

OmicsDI is part of the ELIXIR infrastructure

OmicsDI is an Elixir interoperability service. Learn more ›

Tweets

OmicsDI Databases

PRIDE
PeptideAtlas
MassIVE
JPOST Repository
Physiome Model Repository

EGA
EVA
ENA
LINCS
PAXDB
Cell Collective

MetaboLights
Metabolomics Workbench
MetabolomeExpress
GNPS
BioModels
FAIRDOMHub

ArrayExpress
dbGaP
ExpressionAtlas
GEO
NODE

Information

Databases
Help
API
Contact us
Code on GitHub
Terms of use
Submit Data