/
permeability.R
64 lines (54 loc) · 4.25 KB
/
permeability.R
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
####################################################################################################################
# Function calculating cell permeability and protonated fraction of fomesafen
####################################################################################################################
# INPUT : pH : pH of the medium
# pKa : pKa of the toxicant (fomesafen)
# R : algal cell radius (in meter)
# OUTPUT: return a list Papp : apparent cellular permeability (m/h)
# Conc_AH : protonated fomesafen concentration at pH 6.8 (mol / m^3)
# Pm and Pbl : membrane and boundary layer permeability (m/h)
# Pm_Pbl_ratio : Ratio of Pm to Pbl
permeability <- function(pH, pKa, R) {
if(is.null(pH) || is.null(pKa) || is.null(R))
stop("all arguments must be inputted")
if ( !is.numeric(pH) || (!is.numeric(pKa)) || (!is.numeric(R)) )
stop("all arguments should be numeric")
if ( pH < 0 || pH > 14 || pKa < 0 || pKa > 14 )
stop("pH and pKa should be between 0 and 14")
# Computing the concentration of the protonated fomesafen species using the Henderson-Hasselbalch equation
A_AH_ratio <- 10^(pH - pKa) # Ratio of unprotonated to protonated species
F_AH <- 1-(A_AH_ratio/(1+A_AH_ratio)) # Fraction of protonated molecule (no units)
Prop_AH <- F_AH * 100 # proportion of protonated molecule (%)
Conc_AH <- Conc*F_AH # Initial concentration of protonated fomesafen in the culture medium (mol/m^3)
Conc_AH
# Calculation of fomesafen permeability
Kow_exp <- 2.90 # Octanol water partition coefficient from Experimental database match (Tomlin, 1994)
# Kow_model <- 3.41 # Octanol water partition coefficient (KOWWIN v1.67 estimates)
Pm_cm <- 10^1.11*log10(Kow_exp) - 0.6 # (cm/s) Empiricial equation of lipid bilayer permeability of non-electrolyte : log Pm = s log (kow) + b, where s = 1.11 and b = -0.67 for the solutes with MW > 50 Da (Walter and Gutknecht, 1986)
Pm <- Pm_cm /100 # (m/s)
# Calculating the diffusion coefficient of fomesafen
# kb <- 1.38064852E-23 # Boltzmann's constant (J/K) (or Kg m^2 s-2 K-1)
# T <- 25 + 273 # Temperature (K)
# n <- 0.89 # Absolute or dynamic viscosity of water at 25 °•C (N s / m^2) (or: Kg m s-2 s m-2 = Kg s-1 m-1)
# R_fomesafen <- 1E-12 # Hydrodynamic radii (m)
# D <- (kb * T) / (6 * pi * n * R_fomesafen) # Diffusion coefficient of fomesafen (m^2/s)
# D
# Calculating the diffusion coefficient of fomesafen with the empirical equation of Hayduk and Laudie (1974)
cP <- 0.8937 # viscosity of water at 25 C (centipoise) (Haynes et al., 2016)
Vm <- 278.7 # molar volume (cm^3/mol) (LookChem website)
Dcm <- (13.3E-05) / ((cP ^ -1.14) * (Vm ^ 0.589)) # Diffusion coefficient in cm^2/s (Hayduk and Laudie, 1974)
D <- Dcm/1E+04 # Diffusion coefficient (m^2/s)
# Caclulating the the overall permeability of fomesafen in the boundary layer and the cell membrane
R # Cell radius
L <- R # Boundary layer thickness (m) equals to cell radius (Wolf-Gladrow and Riebesell, 1997; Lavoie et al, 2018)
Pbl <- D/L # Permeability of the boundary layer (m s-1)
Papp <- 1/(1/Pm + 1/Pbl) # Apparent permeability of the membrane plus that of the boundary layer (m s-1) (Missner and Pohl, 2009)
Pm_Pbl_ratio <- Pm/Pbl # Ratio Pm/Pbl, ratio of membrane permeability to boundary layer permeability
# Converting the seconds in hours for all relevant parameters
D1 <- D * 60 * 60 # D (m^2/h)
Pbl_1 <- D1/L # Permeability of BL (m/h)
Pm1 <- Pm * 60 * 60 # Permeability of membrane (m/h)
Papp1 <- (1/(1/Pm1 + 1/Pbl_1)) # Papp (in m/h)
return(list(Papp1=Papp1, Conc_AH=Conc_AH, Pm=Pm, Pbl=Pbl, Pm_Pbl_ratio=Pm_Pbl_ratio))
}
##################################################################################################