View source for PACS/Plant response to stress & Biological Networks

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==''Context'' ==
Global agriculture is facing a serious threat from climate change that compromises
global food security and impacts the ecosystem services and biodiversity. 
High temperatures affect plant development at the level of seed germination which represents the first step of plant establishment and also reduce the plant growth by affecting the shoot net assimilation rates and thus the total dry weight of the plant (Bita et al 2013). It is the first climatic factor capping yields on a global scale for wheat (Lobell et al 2007) and rice (Peng et al 2004). Projections predict a 9-15% decrease in the production of major cereals by 2020 (Hisas et al. 2011). Climate change will increase the negative effect on crop productivity not only due to heat waves, i.e. an increase of several degrees over the seasonal temperature for a sustained period of days (IPCC 2014), but also by exacerbating broad-spectrum stresses such as drought, cold, salinity, flood, submergence and pests (Kole et al 2015). Moreover, recent studies have revealed that the response of plants to combinations of two or more stress conditions is unique and cannot be directly extrapolated from the response of plants to each of the different stresses applied individually. Indeed the responses to the combined stresses are complex and largely controlled by different, and sometimes opposing, signaling pathways that may interact and inhibit each other (Suzuki et al 2014). 

We have designed the project PACS that will delve into the use of plant activity and signatures as stress sensor with regard to climate changes.

==''Plant responses to Multi-Stress'' ==
Although genetic engineering (Mittler et  al 2010) and agro-ecology (Dufumier 2015) constitute the main topics of work to increase the resilience of crops to climate change, development of real time plant stress sensor is a strategic alternative for insuring a predictive and dynamic management of crop plants under field conditions. Since the first report (Burdon-Sanderson 1872), bioelectric activity during development and adaptation of plants to environmental changes became increasingly recognized and studied (Gorovich et al 2012, Baluska & Mancuso 2009, Shabala et al. 2009). Plant bioelectric activity, but also chemical, thermal & hydraulic responses, can be recorded locally or globally in short- and long-term. They represent a systemic and integrative response of the plant to environmental stimuli. 

====''Chemical signals''====
Chemistry represents the most frequently discussed signals in plants, underlining their importance in plant stress response(s) (Huber & Bauerle 2016). 
However, despite their indispensability in plant stress/defense response initiation, it is still questionable whether chemicals are exclusively a short-distance stress signal and their propagation speeds are slow in comparison with hydraulic and/or electrical signals. Volatiles are also widely discussed in the literature as a systemic long-distance signal both between and within plants in response to herbivore or pathogen attacks. They are a good mechanism for long-distance signaling since they can induce systemic defense responses in distant parts of plants but within hours (Howe and Jander, 2008).

====''Hydraulic signals''====
Water is the connecting medium between plant organs and is responsible for nutrient exchange and maintenance of metabolic processes, making water an excellent medium for fast information exchange. Water in plants is transported under tension along the soil–plant–air continuum (Zimmermann, 1983) due to an increasing water potential difference, largely determined by the soil water availability and the vapor pressure deficit (Comstock, 2002). In most climates, the driest (most negative) component in the soil–plant–air continuum is the atmosphere and the least negative the soil, causing the water to be pulled through the plant to the leaves (Steudle, 2001). In light of hydraulic signal transmission, this same pathway is utilized and integrated with adjacent living cells. Hydraulic signals orchestrate the physiological behavior of plants on a daily basis, through the regulation of cell expansion rates (Westgate and Boyer, 1984; Tang and Boyer, 2002, 2003) which are mainly controlled by the cell’s turgor pressure (Taiz, 1984) and fluctuate with a decrease in soil water status, an increase in evaporation demand (Bouchabke et al., 2006).

====''Electric signals''====
Acceptance of electric signaling in plants has been somewhat reticent (Davies, 1987, 2004 and see below), although interest in this phenomenon has been increasing over the last twenty years, as is reflected by a recent spate of reviews (e.g., Davies, 2006; Fromm, 2006; Trębacz et al., 2006; Fromm and Lautner, 2007, Hedrich et al. 2016, Huber and Laueberle 2016). Amongst the numerous physiological consequences of action potential or variation potential passage, the rapid movements featured by specialized plants have received most attention; snapping of traps in Venus flytraps (Dionaea muscipula) (Haberland, 1890), falling leaves in Mimosa (Mimosa pudica) (Applewhite, 1972). In addition to these dramatic and amazing examples though, electrical signalling appears to occur in all plants. Nowadays, electrical signals in plants are established as a rapidly propagated signal in response to both biotic and abiotic stimuli (Maffei and Bossi, 2006, Huber and Bauerle 2016, Hedrich et al. 2016), and are defined as an ion imbalance across the plasma membrane leading to a voltage transient. The voltage transient’s shape is dependent on the stimulus type and the resulting ion fluxes. In general, three different kinds of electrical signals are recognized in plants: action potentials (APs), slow wave potentials (SWPs), also called variation potentials (VPs), and system potentials (SPs).

==''Multi-aspect network modeling'' ==
Beyond the analysis of the signals emitted by the plant, an expected extension from the analysed stress response output may consist in building a model for the whole plant. Coupling the thermal, electric, hydrodynamic and chemical phenomena, the methodology would involve a nodal-type network and should allow for steady, pseudo-unsteady & unsteady simulations. Owing to an Onsager type force-flux approach, an elementary building block trying to mimic the behaviour of a (group of) similar plant cell(s) can first be designed then connected to others to form a network. The inputs/outputs and local features of this building block would be e.g.: chemical composition (like Ca++ concentration), temperature T, electro-chemical potential μ, local sap mass flow-rate and variation of the pressure P. 

====''The Lechatelier-Braun principle''====
According to the Lechatelier-Braun principle all the thermodynamic potentials are connected.
For instance, the hydraulic and electric responses of plant are known to be highly correlated (Mancuso 1999) revealing the underlying coupling between  <math>P</math> and <math>\mu</math>. 
Similar observations of coupling between <math>\mu</math> and  <math>T</math> have been reported from vegetal thermoelectric responses. All these thermodynamic-type analyses (cf. also e.g. Demirel & Sandler 2002, or Qian & Beard 2005) would benefit from a description of the energetic & material fluxes in order to build up solid knowledge about a plant metabolism. The dynamics energy budget 􏰀(DEB􏰁) theory is the most popular non-species-specific theory of this kind. However, this now quite standard modeling of biochemical networks neglects the spatial structure and the complex transport and allocation processes in the organism.

====''A spatio-temporal nodal approach''====
Coupling the thermal, electric, hydrodynamic and chemical phenomena, the methodology would involve a nodal-type network and should allow for steady, pseudo-unsteady & unsteady simulations. Owing to an Onsager type force-flux approach, an elementary building block trying to mimic the behaviour of a (group of) similar plant (biological) cell(s) can first be designed then connected to others to form a network. More specifically, the inputs/outputs and local features of this building block would be e.g.: chemical composition (like <math>Ca^{++}</math> concentration), temperature <math>T</math>, electro-chemical potential <math>\mu</math>, local sap mass flow-rate and variation of the pressure <math>P</math>. 
The figure below illustrates the envisaged structure for the elementary building block and the way the blocks can be (physically) connected:  generalized fluxes <math>X_i </math>and generalized input and output potentials <math>\mu_j^{in}</math> and  <math>\mu_j^{out}</math> are inter-connected through a (locally linearized) Onsager-type approach.

[[File:Pacs.png|330 px]]

To fix ideas, each building block of the above kind (the numerical elementary cell) can be connected to other cells of the same type. A locally linearized relationship between the column vector  <math>{\bf X}</math> and the vector of potential output/input differences <math>{\large \mu}</math> can be proposed, thank to the introduction of the Onsager matrix <math>{\bf Z}</math>, <math>{\bf X}= {\bf Z}{\large \mu}</math>. The coefficient of the matrix <math>{\bf Z} </math> can depend on <math>{\bf X}</math> and <math>{\large \mu}</math> (their local value, and possibly their temporal gradient or history).

===''Expected Validations and Outcomes''===
Since the approach is quite versatile, more complex non-homogeneous structures and topologies may also be analyzed, and help possibly encompassing the role of the spatial biological cells distribution for the plant response to stress. Possibly anisotropic, discontinuous transport and thermoelectric properties may also be included, hence mimicking the sharp interface between cells of different kinds. Notice that the numerical strategy is able to enforce the fluxes (of energy, matter, species) continuity at the local (nodal) scale, and at any time. This aspect is of paramount importance, enforcing the compatibility of the numerical modeling with physical first-principles.

The aim would be to be able to validate the network modeling against the observed data obtained from experiments,. Once thoroughly validated, one should be able to extrapolate the modeling to situations where no data can be measured (because e.g. of too high spatial and/or temporal resolution requirements), or difficult to measure properties. To our knowledge, this would be the very first spatio-temporal network-based thermodynamic-type modeling of the whole plant, in order to reproduce the plant response to different kinds of simultaneous (and hence interacting) stresses.

== ''Participants'' ==
François Bouteau, Delphine Bonnin,  [https://www.researchgate.net/profile/Hayat_El-Maarouf-Bouteau Hayat El-Maarouf-Bouteau], Patrice Meimoun, [https://www6.rennes.inra.fr/umreva/Annuaire/INFlux/E.-Le-Deunff Erwan Le Deunff], Eric Herbert, Christophe Goupil, Yves D'Angelo.