Modeling of stoma

While formaldehyde diffused into plant cells through the stoma, it suffered a series of obstruction or resistance of diffusion. Subsequently, a range of complex chemical reactions activated when the formaldehyde in cell diffused intercellular space. By analyzing the process, the molecule of formaldehyde diffused into cell through the stoma, we found the reason is the mass transport caused by the uneven distribution of formaldehyde density. Therefore, the formaldehyde molecular diffusion velocity distribution meets the maxwell speed distribution function in normal temperature conditions. That means the number of formaldehyde encountered the unit leaf area within per unit time along the x-axis direction were obtained by the below equation.

(1)

where the vx, vy and vz are the components of velocity of the gas molecules on the x-axis, y-axis and z-axis, respectively. is the gas molecule maxwell speed distribution function. Ω is the number of gas molecule diffused into unit leaf areawithin per unit time. S, t is the leaf area and time, respectively. In equation , the n stands for the number of formaldehyde in air, m for molecular weight of HCHO, k for boltzmann constant and T for temperature. From Equ.1, we got:

(2)

We knew that the average velocity of gas molecule in temperature T can be shown as:

(3)

substitute into Equ.2, we got:

(4)

Molecular mass of the formaldehyde from high concentration along the direction of diffusion of low concentration within the unit leaf area per unit time can be described by:

(5)

where Ωb and Ωa stand for the number of gas molecules inside stoma and outside stoma. △ρ for the density difference. We also assumed that the temperature and humidity are constants. The stomatal conductance (Gs) can be defined which the molecular mass diffused into plant within the unit leaf area and per unit time.

(6)

According to hydrodynamics, the compressible gas exits the continuity equation showed below if the temperature and humidity remain unchanged.

(7)

where C stands for concentration. The unit of MC/St is μmol HCHO•m^–2•s^–1, stands for the nubmer of formaldehyde absorbed by the plant within the unit leaf area and per unit time. Substitute into Equ.6:

(8)

We assumed parameter P stands for the net absorption rate for plant leaf:

(9)

The P indicated the absorbing ability of formaldehyde. In our project, we assume P is a constant. η is the ratio of formaldehyde used in the reaction. Noted that if η=0, it means all the gases absorbed in plant do not participate in any chemical reaction. If η=1, it means all the gases participated in the chemical reaction and were absorbed by those reaction. Substitute into Equ.8, we obtained:

(10)

where C stands for the concentration difference inside (Ci) and outside (Ca) stoma. Therefore, Equ.10 is the relationship between stomatal conductance and net absorption rate of plant leaf, concentration difference inside and outside stoma when the temperature and humidity remain unchanged. It indicated that plant leaf stomatal conductance and net HCHO absorption rate is proportional and inversely proportional to the concentration difference.

Results

Since changing the parameter P, we plotted the situations and the diagram was shown in Fig.1.

Fig.1 The relationship between stomatal conductance and the concentration difference of air formaldehyde for differ P.

As all the information above concerned, we realized that since the absorption radio η maintains the constant and by enhancing the absorption radio of formaldehyde, the net absorption rate P would be significant increased. It has been proved (Wang, Noguchi et al. 2014) that, the gene AtAHA2 which was transferred into plant cell, can significantly increase the stomata opening. From that, the absorption rate of formaldehyde would be increased. Therefore, the gene AtAHA2 is a key component to intensify the net absorption rate P. From Fig.1, we also found that the larger P, the greater stomatal conductance Gs. Thus, we will clone the stomatal regulation gene, AtAHA2, to the expression vector and transfer into plant cell in the future.

Link to other modeling

Reference

Wang, Y., K. Noguchi, N. Ono, S. Inoue, I. Terashima and T. Kinoshita (2014). "Overexpression of plasma membrane H+-ATPase in guard cells promotes light-induced stomatal opening and enhances plant growth." Proc Natl Acad Sci U S A 111(1): 533-538.