Dynamics of moisture diffusion and adsorption in plant cuticles including the role of cellulose

Food production must increase significantly to sustain a growing global population. Reducing plant water loss may help achieve this goal and is especially relevant in a time of climate change. The plant cuticle defends leaves against drought, and so understanding water movement through the cuticle could help future proof our crops and better understand native ecology. Here, via mathematical modelling, we identify mechanistic properties of water movement in cuticles. We model water sorption in astomatous isolated cuticles, utilising three separate pathways of cellulose, aqueous pores and lipophilic. The model compares well to data both over time and humidity gradients. Sensitivity analysis shows that the grouping of parameters influencing plant species variations has the largest effect on sorption, those influencing cellulose are very influential, and aqueous pores less so but still relevant. Cellulose plays a significant role in diffusion and adsorption in the cuticle and the cuticle surfaces.

PPs are removed (referred to as cutin) in purple, the large nonlinear increase in sorption at high humidities is no longer present and the sorption increases linearly. The large nonlinear increase in the PP curve can clearly be seen at high humidities, indicating PPs are the reason for this trend. We fitted 1 the data 2 using y = a b x/(1 + a x) + c d x/(1 − c x), where y is the percentage moisture adsorption per dry weight and x is the water activity or RH/100%, with parameters shown in Supplementary Table 1.
Supplementary The experimental data over a time of 10 minutes, as shown in Fig. 2, was shown in the original text 2 as uncorrected for water sorption by the vessel or basket holding the sample that is also being weighted and can also adsorb water. We have corrected for the vessel here by fitting two Langmuir isotherms (see equation (9)), then the sample minus the vessel, to produce the weight of water in the cuticle, ∆w(t), at 57%RH, with an R-squared value better than 99%, as follows: where t here is time in minutes. The original work 2 did not provide error bars, and the two sets of data points, for the sample data not corrected for by the vessel and the data for the vessel, were not conducted at matching relative humidities, hence we are only able to produce a fitted curve, not individual data points. Supplementary

Supplementary Note 2: Additional Model Description
Here we describe additional equations, included in the model, as shown in Supplementary Equations (2)-(8) and the modelling constants in Supplementary Table 3. The parameters Γ S and β are calculated as follows: The constant Γ S , described in Supplementary Equation (2), is described elsewhere, 4 γ is defined in Supplementary Equation (4), and here the maximum pore radius, r max A , is limited by relative humidity, H. The constant β , as described in Supplementary Equation (3), is formulated utilising equation (9) and Supplementary Equation (2), simplifying and rearranging. To calculate the binding of water to cellulose, k 2 , as described in Supplementary Table 3, on the surface of the cuticle as a function of humidity, H, we utilise the following equation to find W C , where W C is the weight of water adsorbed per gram of dry solid as a fraction, H is the relative humidity as a fraction or water activity, K 1 is the number of strong binding sites and equal to 0.05, K 2 is the attraction of these sites and equal to 7.43, and K 3 is related to the water activity of the solid and equal to 0.907. 5 All parameters are dimensionless and a surf scales the outside surface, as there is less cellulose 6, 7 on the outside surface (see Supplementary Table 3).

Supplementary Note 3: Conversion of Concentration to Weight
To convert the final solution from a concentration to a weight in mg, including the adsorbed water, the following equations are applied. The initial condition is removed from the solution, as the initial condition is equivalent to the dry weight, to produce where c w is the concentration of water without the initial condition, c is the concentration of free water and solution to the model, and c min is the initial condition.
The experimental data are given as the difference between the wet weight, at a given relative humidity, and dry weight over time; therefore to convert the concentration to the total weight in mg, the following equation is utilised. The first integral is considered over space (resulting in a solution at each point in time), and the second is a cumulative integral over time, and the first three terms are ions in the cuticle, adsorbed in aqueous pores and adsorbed in cellulose, and the cumulative integral term is the ions adsorbed to cellulose at the two cuticle surfaces, where ∆w(t) is the weight increase over dry weight in mg, M w is the molecular weight of water, f is the value 10 3 and converts g to mg or kg to g, n is the total number of cuticle discs used in the experiment, t final is the final experimental time and is 10 minutes here, A CM is the area of one cuticle disc, z is the thickness of the cuticle, Γ A is the adsorption of water to the aqueous pores, Γ C is the adsorption of water to cellulose, Γ SC is the saturated concentration of water adsorbed in cellulose, r A is the aqueous pore radius, t is time and k 1 and k 2 are the rate constants for binding to cellulose on the cuticle surfaces. The formulation of the area for the moles adsorbed per aqueous pore, using Γ A , is based on the circumference of the aqueous pore that is circular in cross-section.
To convert ∆w to a percentage increase over the dry weight at the end time, we utilise the following: where %moisture content per DW is the percentage gain of water content over the dry weight, DW is the total dry weight and t final is 6 hours here. The resultant change in weight, ∆w(t), is a vector and can be seen in Fig. 2, while the % moisture content per DW is a scalar at each RH and can be seen in Fig. 1. Mass water in cuticle -mg Exp data k = 1e-10 k = 5e-10 k = 1e-09 k = 2.5e-09 k = 5e-09 k = 7e-09 k = 1e-08

Supplementary
Supplementary Figure