The American experiment
Student of
Predictions based on a model
The aim of the modelling side is to predict the nature of the signal based on the reponse time observed in the experiment.
Roots and mycorrhizae architecture
Predictions based on literature
Material and Methods
Quantification of root architecture
Description experimental setup
Quantification of root traits (SmartRoot)
Modelling root and mycorrhizae architecture
Description of CRootBox
Description of the root classes in the model in R
Experimental design in R language
(Post processing of crootbox)
Using the simulation results of the roots architecture implemented with mycorrhizae from CRootBox program, we was able to estimate with R the contact time between the two radical system with a fixed distance. We assume that the growth rate and the density of mycorrhizea are high enougth so that the contact happens always between mycorrhizea and not between real roots of the plants.
To do that, we positionned the two root systems in the XZ-plane leading to the representation of the experimental montage. After loading the files, we applied a translation along the X axis to one of the two root systems. This translation corresponds to the distance between the two collars of the plants. Notice that we applied an other translation, this time to both root systems, so that no segment has a negative x coordinate. This will greatly simplify the next step consisting in represent the 2D space by matrices. By ploting with a different color for the different root types, we possibly can check our assumption that contacts happen between mycorrhizea (remenber that mycorrhizea correspond to type 20 and type 50).
(graphique avec les 2 systèmes racinaires)
We divided the experimental space in a grid composed by cells characterized by a size depending on the distance between the collars of the two plants divided by 10. The idea is to increase the precision when the distance between the plants is short. For each root system we developped a matrix containing for each cell the number of root's segments it contains. After, we overlapped the two matrices in order to see if there is contact. If a same cell contains segments in the two matrices, we assume there is a mycorrhizea association. It is highly likely that two segments in the same cell are not really in contact but, when closed of each other, mycorrhizea can connect thanks to chemiotropism, justifying the assumption.
Compare the two matrices thus allows to find the cells where there is contact. From this information, we look in those cells for the youngest segment from each plant. The age of the older of the two correspond to the minimal time needed for what we consider as a contact. The minimum of the results obtained for the different cells is our estimation of the time needed for a mycorrhizea association between the two plants.
Modelling signal transfer in the environment
Describe the diffusion model
We kept the space discretization into cells like seen before. For both plants, we made a 3D array with two dimensions for the XZ space and a third dimension for the time. The time is discretized so that we have one time layer per day. We consider one plant emetting a signal and the other plant able to receive the sigal. For the emitting plant, the array contains the number of emetting segments in each cell. We consider that all root segments exudate if they are at most 3 days old. For the receiving plant, the cells contain a 1 if there is at least one root segment, and a 0 if there is not. A layer contain more 1 if it correspond to an advanced time value.
To verify that a chemical-type signal can be sent from a root of plant A to the root of plant B a two-dimensional numerical diffusion and reaction model has been created. The numerical model has been solved according to the explicit finite difference method on the software RStudio©. (((Time and space have been discretized respectively in steps of 1 day and in steps of 1 cm))). The model includes three 3-dimensional arrays that we will call respectively A, B and C. A and B characterize places of space and time where roots are present and are the result of the post-processing. Has characterized the transmitting roots and B any kind of roots. If a root exists in a place of the matrix this one registers at its coordinate the value 1 otherwise the value is 0. C characterizes the concentration in molecules signals in every point of the space and with each step of time. The signal is transmitted when the term product of the matrices B and C is non-zero, which is equivalent to saying that the signal is transmitted when a receiving root or a receiver mycorhize is located in (ti, xi, yi) and that the molecule concentration in (ti, xi, yi) is greater than 1 / 100,000 units of concentration / cm 2. Since the type of exudate is unknown, it has been arbitrarily considered at first approach that a root emits a unit of molecular concentration per day per square centimeter and that the quantity required for detecting the signal must be at least 1/100 000 times the concentration emitted. If the emission rate and the concentration required for detecting the compound are known, the model can take it into account for more realistic modeling.
Results
Roots architecture
Figure 1 = Root architecture
Mycorrhizae
Figure 2 = Root architecture + mycorrhizae
Diffusion of exudates
figure 3 = evolution of the signal
We calculated the response time based on three diffusion values ranging from 0.0018 cm² / day to 0.18 cm² / day to cover a wide range of possible values for the diffusion in a unknown homogeneous medium for unknown substances. Values less than 0.0018 have not been calculated because below this value the model calculated that the roots touch each other before the chemical signal has been transmitted, in fact the root contact seems to be established in the modeling after 28 days. With a diffusion coefficient of 0.18 which is the maximum estimated value, the signal is transmitted after 11 days. We can therefore exclude the possibility that the change of direction of the roots of the experiment is caused by the transmission of a chemical signal because it could not reach the root segment before the change of direction.
Discussion
Limits of the experimental systems
Crosstalk between the model and the experiment
In the model, we considered that the plants were enought separeted so that there is no direct contact between their roots in the period of time taken into account. Each contact is thus due to mycorrhize From the data we got, it seems that the growth rate of mycorrhizea is so low that
mprovement of the diffusion model. The model created seems robust on the scale of phenomena studied. Plausible results are observed for all scales of values analyzed. The most obvious improvement is the determination of the parameters. Indeed the diffusion coefficients, the rate of production of signal molecules and the concentration necessary for detection have been chosen arbitrarily and must be adapted to the medium, the signal and the types of roots studied. Only one type of plant has been analyzed by modeling, even if the results are similar before any type of plant should be run the model with different root phenotype In order to validate this assumption. More differentiation of roots in the root-collecting model could be used to characterize the signal transmission time for each type of root and thus improve the specificity of the results that remain in this very general model.
Improvement of the diffusion model
The model created seems robust on the scale of phenomena studied. Plausible results are observed for all scales of values analyzed. The most obvious improvement is the determination of the parameters. Indeed the diffusion coefficients, the rate of production of signal molecules and the concentration necessary for detection have been chosen arbitrarily and must be adapted to the medium, the signal and the types of roots studied. Only one type of plant has been analyzed by modeling, even if the results are a priori similar for any type of plant, the mode should be run with different root phenotype in order to validate this assumption. More differentiation in the model of the collecting roots could be used to characterize the signal transmission time for each type of root and thus improve the specificity of the results that remain very general in this model.
Conclusions