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

The Electrome of a Parasitic Plant in a Putative State of Attention Increases the Energy of Low Band Frequency Waves: A Comparative Study with Neural Systems

Selective attention is an important cognitive phenomenon that allows organisms to flexibly engage with certain environmental cues or activities while ignoring others, permitting optimal behaviour. It has been proposed that selective attention can be present in many different animal species and, more recently, in plants. The phenomenon of attention in plants would be reflected in its electrophysiological activity, possibly being observable through electrophytographic (EPG) techniques. Former EPG time series obtained from the parasitic plant Cuscuta racemosa in a putative state of attention towards two different potential hosts, the suitable bean (Phaseolus vulgaris) and the unsuitable wheat (Triticum aestivum), were revisited. Here, we investigated the potential existence of different band frequencies (including low, delta, theta, mu, alpha, beta, and gamma waves) using a protocol adapted from neuroscientific research. Average band power (ABP) was used to analyse the energy distribution of each band frequency in the EPG signals, and time dispersion analysis of features (TDAF) was used to explore the variations in the energy of each band. Our findings indicated that most band waves were centred in the lower frequencies. We also observed that C. racemosa invested more energy in these low-frequency waves when suitable hosts were present. However, we also noted peaks of energy investment in all the band frequencies, which may be linked to extremely low oscillatory electrical signals in the entire tissue. Overall, the presence of suitable hosts induced a higher energy power, which supports the hypothesis of attention in plants. We further discuss and compare our results with generic neural systems.

The pH Signaling Transcription Factor PAC-3 Regulates Metabolic and Developmental Processes in Pathogenic Fungi

The zinc finger transcription factor PAC-3/RIM101/PacC has a defined role in the secretion of enzymes and proteins in response to ambient pH, and also contributes to the virulence of species. Herein we evaluated the role of PAC-3 in the regulation of Neurospora crassa genes, in a model that examined the plant-fungi interactions. N. crassa is a model fungal species capable of exhibiting dynamic responses to its environment by employing endophytic or phytopathogenic behavior according to a given circumstance. Since plant growth and productivity are highly affected by pH and phosphorus (P) acquisition, we sought to verify the impact that induction of a Δpac-3 mutation would have under limited and sufficient Pi availability, while ensuring that the targeted physiological adjustments mimicked ambient pH and nutritional conditions required for efficient fungal growth and development. Our results suggest direct regulatory functions for PAC-3 in cell wall biosynthesis, homeostasis, oxidation-reduction processes, hydrolase activity, transmembrane transport, and modulation of genes associated with fungal virulence. Pi-dependent modulation was observed mainly in genes encoding for transporter proteins or related to cell wall development, thereby advancing the current understanding regarding colonization and adaptation processes in response to challenging environments. We have also provided comprehensive evidence that suggests a role for PAC-3 as a global regulator in plant pathogenic fungi, thus presenting results that have the potential to be applied to various types of microbes, with diverse survival mechanisms.

Estimating the biophysical properties of neurons with intracellular calcium dynamics

We investigate the dynamics of a conductance-based neuron model coupled to a model of intracellular calcium uptake and release by the endoplasmic reticulum. The intracellular calcium dynamics occur on a time scale that is orders of magnitude slower than voltage spiking behavior. Coupling these mechanisms sets the stage for the appearance of chaotic dynamics, which we observe within certain ranges of model parameter values. We then explore the question of whether one can, using observed voltage data alone, estimate the states and parameters of the voltage plus calcium (V+Ca) dynamics model. We find the answer is negative. Indeed, we show that voltage plus another observed quantity must be known to allow the estimation to be accurate. We show that observing both the voltage time course V(t) and the intracellular Ca time course will permit accurate estimation, and from the estimated model state, accurate prediction after observations are completed. This sets the stage for how one will be able to use a more detailed model of V+Ca dynamics in neuron activity in the analysis of experimental data on individual neurons as well as functional networks in which the nodes (neurons) have these biophysical properties.

Automated analysis of calcium spiking profiles with CaSA software: two case studies from root-microbe symbioses

BACKGROUND

Repeated oscillations in intracellular calcium (Ca2+) concentration, known as Ca2+ spiking signals, have been described in plants for a limited number of cellular responses to biotic or abiotic stimuli and most notably the common symbiotic signaling pathway (CSSP) which mediates the recognition by their plant hosts of two endosymbiotic microbes, arbuscular mycorrhizal (AM) fungi and nitrogen fixing rhizobia. The detailed analysis of the complexity and variability of the Ca2+ spiking patterns which have been revealed in recent studies requires both extensive datasets and sophisticated statistical tools.

RESULTS

As a contribution, we have developed automated Ca2+ spiking analysis (CaSA) software that performs i) automated peak detection, ii) statistical analyses based on the detected peaks, iii) autocorrelation analysis of peak-to-peak intervals to highlight major traits in the spiking pattern.We have evaluated CaSA in two experimental studies. In the first, CaSA highlighted unpredicted differences in the spiking patterns induced in Medicago truncatula root epidermal cells by exudates of the AM fungus Gigaspora margarita as a function of the phosphate concentration in the growth medium of both host and fungus. In the second study we compared the spiking patterns triggered by either AM fungal or rhizobial symbiotic signals. CaSA revealed the existence of different patterns in signal periodicity, which are thought to contribute to the so-called Ca2+ signature.

CONCLUSIONS

We therefore propose CaSA as a useful tool for characterizing oscillatory biological phenomena such as Ca2+ spiking.

Towards the Physics of Calcium Signalling in Plants

Calcium is an abundant element with a wide variety of important roles within cells. Calcium ions are inter- and intra-cellular messengers that are involved in numerous signalling pathways. Fluctuating compartment-specific calcium ion concentrations can lead to localised and even plant-wide oscillations that can regulate downstream events. Understanding the mechanisms that give rise to these complex patterns that vary both in space and time can be challenging, even in cases for which individual components have been identified. Taking a systems biology approach, mathematical and computational techniques can be employed to produce models that recapitulate experimental observations and capture our current understanding of the system. Useful models make novel predictions that can be investigated and falsified experimentally. This review brings together recent work on the modelling of calcium signalling in plants, from the scale of ion channels through to plant-wide responses to external stimuli. Some in silico results that have informed later experiments are highlighted.

Dating in the dark: how roots respond to fungal signals to establish arbuscular mycorrhizal symbiosis

The arbuscular mycorrhizal symbiosis that involves most plants and Glomeromycota fungi is the result of a complex exchange of molecular information, which commences before the partners are in physical contact. On the one hand, plants release soluble factors, including strigolactones that activate both the metabolism and branching of the fungal partners. On the other hand, fungi use compounds that trigger the signaling transduction pathways that are required for the symbiotic modus of plant cells. Here we describe some of the recent discoveries regarding the fungal molecules involved in rhizospheric conversation, and the way in which they are perceived by their hosts. We conclude that similar signaling molecules may have different meanings, depending on the context. However, at the end, specificity must be maintained to ensure appropriate partners enter symbiosis.

Automated Bayesian model development for frequency detection in biological time series

Background

A first step in building a mathematical model of a biological system is often the analysis of the temporal behaviour of key quantities. Mathematical relationships between the time and frequency domain, such as Fourier Transforms and wavelets, are commonly used to extract information about the underlying signal from a given time series. This one-to-one mapping from time points to frequencies inherently assumes that both domains contain the complete knowledge of the system. However, for truncated, noisy time series with background trends this unique mapping breaks down and the question reduces to an inference problem of identifying the most probable frequencies.

Results

In this paper we build on the method of Bayesian Spectrum Analysis and demonstrate its advantages over conventional methods by applying it to a number of test cases, including two types of biological time series. Firstly, oscillations of calcium in plant root cells in response to microbial symbionts are non-stationary and noisy, posing challenges to data analysis. Secondly, circadian rhythms in gene expression measured over only two cycles highlights the problem of time series with limited length. The results show that the Bayesian frequency detection approach can provide useful results in specific areas where Fourier analysis can be uninformative or misleading. We demonstrate further benefits of the Bayesian approach for time series analysis, such as direct comparison of different hypotheses, inherent estimation of noise levels and parameter precision, and a flexible framework for modelling the data without pre-processing.

Conclusions

Modelling in systems biology often builds on the study of time-dependent phenomena. Fourier Transforms are a convenient tool for analysing the frequency domain of time series. However, there are well-known limitations of this method, such as the introduction of spurious frequencies when handling short and noisy time series, and the requirement for uniformly sampled data. Biological time series often deviate significantly from the requirements of optimality for Fourier transformation. In this paper we present an alternative approach based on Bayesian inference. We show the value of placing spectral analysis in the framework of Bayesian inference and demonstrate how model comparison can automate this procedure.

Asymmetric interaction and indeterminate fitness correlation between cooperative partners in the fig-fig wasp mutualism

Empirical observations have shown that cooperative partners can compete for common resources, but what factors determine whether partners cooperate or compete remain unclear. Using the reciprocal fig-fig wasp mutualism, we show that nonlinear amplification of interference competition between fig wasps-which limits the fig wasps' ability to use a common resource (i.e. female flowers)-keeps the common resource unsaturated, making cooperation locally stable. When interference competition was manually prevented, the fitness correlation between figs and fig wasps went from positive to negative. This indicates that genetic relatedness or reciprocal exchange between cooperative players, which could create spatial heterogeneity or self-restraint, was not sufficient to maintain stable cooperation. Moreover, our analysis of field-collected data shows that the fitness correlation between cooperative partners varies stochastically, and that the mainly positive fitness correlation observed during the warm season shifts to a negative correlation during the cold season owing to an increase in the initial oviposition efficiency of each fig wasp. This implies that the discriminative sanction of less-cooperative wasps (i.e. by decreasing the egg deposition efficiency per fig wasp) but reward to cooperative wasps by fig, a control of the initial value, will facilitate a stable mutualism. Our finding that asymmetric interaction leading to an indeterminate fitness interaction between symbiont (i.e. cooperative actors) and host (i.e. recipient) has the potential to explain why conflict has been empirically observed in both well-documented intraspecific and interspecific cooperation systems.

Mechanisms underlying beneficial plant-fungus interactions in mycorrhizal symbiosis

Mycorrhizal fungi are a heterogeneous group of diverse fungal taxa, associated with the roots of over 90% of all plant species. Recently, state-of-the-art molecular and genetic tools, coupled to high-throughput sequencing and advanced microscopy, have led to the genome and transcriptome analysis of several symbionts. Signalling pathways between plants and fungi have now been described and the identification of several novel nutrient transporters has revealed some of the cellular processes that underlie symbiosis. Thus, the contributions of each partner in a mycorrhizal association are starting to be unravelled. This new knowledge is now available for use in agricultural practices.