# ROS-Waves and Prey-Predator Models

As mentioned in chap. 3.2.1 in leaves of *A. thaliana* treated with naphthalene ROS waves were observed that spread over the cell tissue with a temporal frequency of 20 minutes and a wavelength of several hundreds of micrometers (see Figure 62). Such a behavior is in line with wave-like closure and opening of stomata as observed in green plants under stress conditions. A simple explanation for the formation of waves is the relaxation of a nonequlibrium system that contains compounds that inhibit their own production (autoinihibition). The overreduction of the elec?tron transfer chain (ETC) can lead to the production of ROS as electron transfer is blocked and ^{3}Chl accumulates. ROS in turn oxidizes the ETC and an overreduced ETC is known to activate NPQ. So growth of electronic charge in the ETC forms ROS which inhibits the overreduction. Similarily all ROS triggered mechanisms that lead to the depletion of ROS on the molecular level might cause ROS waves with characteristic oscillation frequencies and intensity distributions as well as localizations delivering information on the underlaying mechanisms.

ROS waves can be described by prey-predator models based on rate equations. In a simplified approach, the basic prerequisite for any oscillating reaction demands for processes that are autocatalytic or auto- inhibited. If we look at ROS nearly all induced processes are autocatalytic or autoinhibited because they are nonlinear. Higher ROS level activates catalase. For example treatment of mature leaves of wheat plants with H2O2 was shown to activate leaf catalase (Sairam and Srivastava, 2000).The higher amount of catalase will reduce the H2O2 level and the reduced H2O2 level again reduces the catalase activity. Similarly a high concentration of excited singlet states in the light-harvesting complex can form singlet oxygen. The overall sequence of such reactions occurs as an oscillating chemical reaction as observed in simple prey-predator models like the fox and the rabbit as shown in Figure 75.

Figure 75. Fox and rabbit in a simplified prey-predator model.

Both species, fox and rabbit as shown in Figure 75 are autoinhibiting due to the coupling with the other species. The production of rabbits leads to more rabbits, however the reproduction rate is constant. More rabbits lead to the growth of foxes which inhibit the rabbit population. In dependence on the exact distribution of the reproduction and inhibition rates this can lead to oscillations.

To model the system we assume that the rabbit population *X* can reproduce according to the equation for the feeding of rabbits: *A* + *X —> 2X *by consumption of a constant food supply A. Rabbits can die according to natural death following an equation for the death of rabbits: *X —> B. *If we assume the rabbits to represent ROS then the first equation describes the production rate and the second the natural ROS scavenging. The fox population *Y* is fed by rabbits: *nX* + *Y —> 2Y* where a number of *n* consumed rabbits leads to a reproduction of a fox. This process is the most important one as it describes the autoinhibition of the rabbits by producing foxes. Also the fox might die due to natural death: *Y —> C.*

The fox might represent the catalase molecules which is activated due to a higher ROS level.

All these equations that are needed to describe the population of foxes and rabbits are characterized by certain rate constants according to the rate formalism presented by eq. 8 in chapter 1.3 and 1.4:

The exact representation of these equations describes the change of the rabbit *X* and fox population *Y* in time according to:

Solving these equations we will find that both, rabbit and fox population can follow an oscillating concentration in time as plot in Figure 76 which is the solution of the rate equation system shown above.

Figure 77 illustrates a time series of propagating ROS on naphthalene treated leaves of *Arabidopsis* that is strongest in the beginning (light areas on the leaf) and decays whereby in some areas the intensity reaches a local minimum and starts to grow again.

Figure 76. Population of rabbits (red) and foxes (green) as the solution of the equations shown above.

Figure 77. Spread of ROS waves in * A. thaliana* treated with naphthalene under continuous illumination. The temporal development of the sensor intensity (DCF, see Table 3) that is used to monitor ROS is shown in Figure 62.