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Plants respond to almost any kind of external stimulus with transients in their cytoplasmic free calcium concentration ([Ca2+]c). A huge variety of kinetics recorded by optical techniques has been reported in the past. This variety has been credited the specificity needed to explain how information about incoming stimuli is evaluated by the organism and turned into the right physiological responses which provide advantages for survival and reproduction. A physiological response often takes place away from the site of stimulation. This requires cell-to-cell communication. Hence, responding cells are not necessarily directly stimulated but rather receive an indirect stimulus via cell-to-cell communication. It appears unlikely that the ‘[Ca2+]c signature’ in the primarily stimulated cell is conveyed over long distances via cell-to-cell communication from the ‘receptor cells’ to the ‘effector cells’. Here, a novel aspect is highlighted to explain the variety of [Ca2+] kinetics seen by integrating methods of [Ca2+]c recording. Plants can generally be seen as cellular automata with specific morphology and capable for cell-to-cell communication. Just a few rules are needed to demonstrate how waves of [Ca2+]c-increases percolate through the organism and thereby deliver a broad variety of ‘signatures’. Modelling intercellular signalling may be a possible way to find explanations for different kinds of signal transmission, signal amplification, wave formation, oscillations and stimulus-response coupling. The basic examples presented here show that care has to be taken when interpreting cellular ‘[Ca2+]c signatures’ recorded by optical techniques which integrate over a big number of cells or even whole plants.
In the past three decades the cytoplasmic free calcium [Ca2+]c in plants has been credited with central roles in ion transport, signal perception, signal transduction and physiological response.1,2,3 Changes in cytoplasmic free calcium ([Ca2+]c) occur with any external stimulus, be it biotic or abiotic. It has been hypothesized many times that amplitude and duration of the cellular [Ca2+] signal and its subcellular location may determine what specific subset of calcium dependent proteins (i.e., the ‘calcium receptors’) are responding (i.e., activated or de-activated) on cellular level. “However, the focus on intracelluar mechanisms might have led […] away from physiology”.4 Therefore, a glance at the whole, namely intercellular signalling, may be worthwhile.
Any physiological ‘whole plant’-responses like changes in growth and development, organ movement, metabolic shifts or pathogen defence will need some sort of cell-to-cell communication and systemic spread of signals. This communication is coupled with directed transport of ions,5,6 or phytohormones,7–9 with hydraulic signals10 or with the release and spread of reactive oxygen species (ROS) or nitrogen monoxide (NO).11 The best studied, the most effective and fastest cell-to-cell communication in plants is electrical signalling, in vascular plants, via vascular tissue.12–14 This in turn is always tightly coupled with transients in [Ca2+]c. Action potentials (APs) and other fast membrane potential transients are accompanied by changes in [Ca2+]c due to the abundance of depolarisation-activated cation channels.
Electrical signals on cellular level can spread over tissues, organs and the whole organism and thereby transport information and elicit responses at locations far away from the point of initial stimulation. Most prominent examples are Mimosa pudica and the venus fly trap Dionaea muscipula.15,16 All plants can propagate and spread signals via cell-to-cell communication. In particular electrical signalling has been observed in many diverse plant species from macroalgae like Chara to vascular plants like Arabidopsis, Tobacco and maize and even shrubs and trees like willow and poplar.12,13,17,18
Different optical techniques were developed to measure and image [Ca2+]c in plants.19 On cellular level fluorescence techniques using synthetic Ca2+ dyes like Indo or Fura20,21 or recombinant indicators like pericams or cameleons22 are most frequently used. Luminescence techniques using recombinant photoproteins like aequorin and obelin are used to measure [Ca2+]c more globally, on whole organ or whole plant level.23 The latter technique has been used to also demonstrate the migration (percolation) of the [Ca2+]c-signal through organs.24,25 All these optical techniques showed that each stimulus elicits a specific [Ca2+]c response (e.g., reference 26).
The big diversity of [Ca2+]c responses recorded on cellular and on whole-plant level led to the so-called ‘signature hypothesis’.27–29 This hypothesis has been questioned3,30 and despite well-founded doubts it is still conveyed.31
Here, another aspect is highlighted to explain the broad variety and complexity of [Ca2+]c kinetics seen in intact higher plants when measured by means of integrating optical techniques:
For simplicity reasons just a few general assumptions (rules) are made to model plants as conglomerations of cells with a competence for cell-to-cell communication. Each cell can respond to an external stimulus, giving a typical [Ca2+]c signal and can hand down this signal to neighboring cells, leading to signal percolation and spreading throughout the organism. This delivers a possible answer to the question: How does local and specific stimulation determine the overall [Ca2+]c response recorded from a whole plant?
#1. The kinetic of [Ca2+]c in a single cell after stimulation or excitation is well defined.
#2. A cell is either in an excited state or not (binary state behavior).
#3. A cell switches into an excited state when it is stimulated or when one of its neighboring cells has switched into an excited state.
#4. A cell is not excitable (i.e., in a refractory period) as long as it is still excited.
Assumption #1 means that a single-cell [Ca2+]c kinetic elicited by a certain stimulus can be described by a sum of exponentials (example Eq. 1, Fig. 1). Thereby, the kinetic is quantified by a minimum of five independent free parameters (Ca0, a1, a2, τE, τR).
Assumption #2 means that an excited state is defined by the cytoplasmic calcium concentration which exceeds a certain (excitation-) level, E-level = [Ca2+]E. Cells with [Ca2+]c below [Ca2+]E are called ‘not excited’.
Assumption #3 means that a stimulus received from a cell is transmitted to its neighboring cells. The speed of this transmission depends on the kinetics of the [Ca2+]c increase i.e., the time constant τE (see Eq. 1) and on [Ca2+]E (Fig. 2).
Assumption #4 means that a cell is not excitable as long as its [Ca2+]c level is still not below [Ca2+]E. This determines a refractory period (mainly given by τR) which is needed to form a wave of excitation.
A stimulated cell may undergo a rapid change in membrane potential which is sometimes called “action potential” (AP) or “transient potential” (TP). This transient is accompanied by a [Ca2+]c spike with a fast rise and a slow recovery of [Ca2+]c to its previous level. The kinetics of the AP and of the [Ca2+]c changes however are not necessarily identical (Thiel et al. 1997).
The two-cell system. A cellular excitation can be transmitted to neighboring cells (assumption #3). With a simple two cell system this means that a [Ca2+]c signal elicited by a stimulus in one cell is received by the other one. This event is shown in Figure 2. When the [Ca2+]c in the stimulated cell (black trace) exceeds a certain level [Ca2+]E (i.e., ≈400 nM; red line) then the neighboring cell switches into the excited state as well (blue trace). The time Δt (i.e., ≈5) between the stimulus of the first cell (at t = 50) and the response in the second cell is defined by [Ca2+]E, the amplitude of the [Ca2+]c spike and the time constant τE (Eq. 1). The observed [Ca2+]c transient of the whole system then is the mean of the two individual [Ca2+]c traces. The velocity V of signal transmission from cell to cell (wavefront) through the tissue is then given by Δt and the dimension (r) of the cell (Eq. 2):
The four-cell system. Figure 3 shows the responses in the 4-cell system when a border cell is stimulated. The overall signal received (Fig. 3C bold trace) does not differ very much from that of a single cell (Fig. 3C gray trace). The main difference is in the raising part of the curve. The whole system seems to response more slowly.
The sixteen-cell system. The model can be expanded to a system with an increased number of individual cells. As a next step a 16-cell system is chosen as this is still easy to study. Here, the fact becomes obvious that the shape of the system and the location of the stimulus determine the overall signal. Figure 4A gives the compact version (4 × 4 cell system) with excitation in the middle of the system. Figure 4B, in contrast, shows the system where the exciting stimulus is transmitted like through a chain of dominos. The overall response of the 16-cell system in the ‘domino-configuration’ (Fig. 4D green trace) is remarkably different from of a single cell response (gray trace).
From here on it is easy to imagine that finally with increasing cell numbers a stimulus will cause independent [Ca2+]c-waves propagating from the location of stimulation onwards through the whole plant.
The 225-cell system. Consequently, a much bigger number of cells allows to study responses from systems with different configurations:
The ‘domino’-configuration. If we have 225 cells in the domino configuration analogous to Figure 4B then a wave-front of excited states would propagate through the system after the first cell has been stimulated. In the overall signal (Fig. 5B and blue trace) this would result in a constantly elevated [Ca2+]c level as long as the wave is still propagating through the system. Now, this response gives no clue anymore on what happens on cellular level (compare blue trace with gray trace in Fig. 5B).
The avalanche configuration. In an avalanche configuration it is assumed that every excited cell stimulates two neighboring cells. Thus the number of excited cells is exponentially increasing (avalanche reaction). Even here (Fig. 5B, red trace), the system response is clearly different from that when all cells are responding simultaneously (gray trace).
225 cells in the ‘young-seedling’ configuration. An avalanche configuration as mentioned above would require a fractal morphology. This is realized in only few plant species such as ferns (e.g., male fern Dryopteris filix-mas). Thus, this example remains more academic.
However, the 225 cells in Figure 5A can be arranged in a pattern which is similar to that of a seedling (Fig. 6). Here four different events are demonstrated (Fig. 6A–D) just to see what happens when the seedling is stimulated in four different ways:
The different kinetics resulting from the different events are shown in Figure 6E.
When the root tip is excited, the overall signal starts to climb up the root resulting in a domino effect (compare Fig. 6E at 100 < t < 150 with Fig. 5B blue trace), then, in the hypocotyl, an avalanche effect occurs (compare Fig. 6E at 150 < t < 250 with Fig. 5B red trace) amplifying the signal and resulting in an additional bump at t = 220 before the signal spreads into the coteledons and ceases (at t > 300). So, even biphasic responses—not seen in the single-cell signal (Fig. 1)—occur. Thus, the recorded overall signal is dependent on the configuration of the system and on the site of initial stimulation.
Based on the assumption that (electrical) cell-to-cell communication is accompanied by a cell-to-cell percolation of [Ca2+]c signals and vice versa, a basic model has been developed here that mimics the overall [Ca2+]c response in whole plants such as recorded by a luminometer from luminescent aequorin-expressing plants or by brightfield fluorescence ratios from whole plants or organs expressing calcium-specific probes. On the one hand, the above model shows that the whole-system-response does not differ significantly from the single-cell-response (Figs. 2–4) when
On the other hand, however, the overall signal is very different from the single-cell signal, when
Thus, it becomes obvious that in some cases a kinetic analysis of a whole-system-signal will not allow conclusions on the response (the ‘signature’) in a single cell. And vice versa: the single cell response does not provide clues about the whole system's response. If the primary stimulus defines the signature of the cellular [Ca2+]c signal then this signature does not necessarily appear in the neigbouring ‘secondary’ cells which receive the message via cell-to-cell communication. In fact, several parameters, like shape/morphology of the plant, the location of the primary stimulus or the primary receptor, and the kind of cell-to-cell interaction have to be considered, before specific conclusions can be drawn.
Here only two-dimensional objects have been modelled for convenience. But, it is easy to deduce from the above examples that the kinetics of a recorded overall [Ca2+]c signal become even more complicated when
In particular the latter points (5 and 6) show that in complex biological systems like plants, signal events may form their own routes depending on the underlying signal transmission mode.
The models presented here are no ‘cellular automata’ by definition [for exact definition see Wolfram32 and his website (www.stephenwolfram.com/publications/books/ca-reprint/)] since the systems discussed here are very limited in their number of cells. However, ‘cellular automata’ in a broader sense may be favourable tools for modelling complexity, self organisation and even nonlinear dynamics.33–35
The examples presented here are not based on assumptions about the time scale and the molecular mechanisms underlying cell-to-cell communication. Therefore, they are open for further refinements in order to simulate observed events and concrete mechanisms.
The models have been developed as Excel spreadsheets using Micosoft-Excel 2002. The Excel files can be obtained from the author on request. (www.zbm.uni-kiel.de/agplieth/).
I thank Hartmut Kaiser (Botanical Institute, University Kiel) for critically reading the manuscript. The author received financial support from the DFG and the federal state of Schleswig-Holstein.
Previously published online: www.landesbioscience.com/journals/psb/article/10717