Identifying the species of copper that are toxic to plant roots in alkaline nutrient solutions
Peng Wang1,2,, Neal W. Menzies2, Yi-min Wang1, Dong-Mei Zhou1,*, Fang-Jie Zhao3, and Peter M. Kopittke2
Supporting Data
The GCS computer program
The GCS model combines a classic electrostatic Gouy-Chapman theory and ion binding (Stern model), and is discussed in detail by Kinraide [1], Yermiyahu and Kinraide [2], and Kinraide and Wang [3]. The GCS model incorporates the intrinsic surface charge density (σ0; this is the surface charge density in the absence of solute ion binding) of a membrane, the ion composition of the bathing medium, and ion binding to the membrane. The Gouy-Chapman portion of the model is expressed in this equation:
σ 2 = 2εrεRTΣI [IZ]b(exp[-ZIFψ0o/(RT)]–1) Equation 1
where σ is the charge density on the membrane surface expressed in coulombs per square meter (C m-2); 2εr ε0 RT = 0.00345 at 250C for bulk-phase concentrations of IZ expressed in M (εr is the dielectric constant for water, ε0 is the permittivity of a vacuum, R is the gas constant and T is temperature). [IZ]b is the concentration of ion IZ (the ith ion) in the bulk-phase medium; Zi is the charge on ion IZ; F is the Faraday constant.
The value for σ depends in part on σ0, but also includes the effects of ions binding to the cell surface (the Stern modification takes this binding into account). For the Stern portion, the membrane surfaces were assumed to be composed of two classes of binding sites: one negatively charged (R–) and one neutral (P0). Ions may bind according to the reactions R- + IZ RIZ – 1 and P0 + IZ PIZ for which the binding constants KR,I (= [RIZ – 1]/([R-][IZ]0)) and KP,I (= [PIZ]/([P0][IZ]0)) are needed. [R-], [P0], [RIZ – 1], and [PIZ] denote CM surface densities in mol m-2, and [IZ]0 (= [IZ]exp[-ZiFψ0o/(RT)], a Boltzmann Equation) denotes the concentration in M of an unbound ion at the CM surface. F/(RT) = 1/25.7 at 250C for ψ0o expressed in mV. The contingent σ can be expressed as the sum of the products of the surface density of each species and the charge of each species all times F:
σ = (-[R -] + ΣRI (Z - 1)[RIZ – 1] + ΣPI Z[PI Z])F Equation 2
The computation of σ by Equation 2 requires both binding constants and ψ0o. To compute ψ0o, trial values were assigned to it, and σ in Equations 1 and 2 were computed until the values for σ from the two equations converged. In order to do that, values of KR,I, KP,I, RT and PT must be known in order to computer the variables in Equation 2. RT is an alternative expression of σ0. The parameters of GCS model for calculating bacterial surface potential in this study were estimated based on the measured values of z potentials. Knowledge of ψ0o enables the calculation of ion activities at the cell surface according to the Nernst equation ({IZ}0o ={IZ}bexp[-ZFψ0o/(RT)]). The parameters for roots of wheat used in this study were derived from the Standard GCS parameters (column 2 in Table 3 in Kinraide and Wang (2010)). The updated calculation software can be available from the authors.
Table S1. Concentrations of Cu, Ca, and Na in the bulk solution for all treatments. The values for relative root elongation (RRE) are the average of two measurements.
Treatment / pH / [Ca]Bulk(mM) / [Na]Bulk
(mM) / [Cu]Bulk
(µM) / {Cu2+}b
(µM) / y0
(mV) / {Cu2+}0
(µM) / {CuCO30}
(µM) / RRE /
Experiment 1
1 / 4.50 / 0.25 / 0.00 / 0.00 / 0.00 / -34.6 / 0.00 / 0.00 / 100.0
2 / 4.50 / 0.25 / 0.00 / 1.00 / 0.88 / -34.6 / 13.08 / 0.00 / 47.7
3 / 4.50 / 1.00 / 0.00 / 0.00 / 0.00 / -26.1 / 0.00 / 0.00 / 99.9
4 / 4.50 / 1.00 / 0.00 / 1.25 / 0.99 / -26.0 / 7.48 / 0.00 / 63.3
5 / 4.50 / 4.00 / 0.00 / 0.00 / 0.00 / -15.1 / 0.00 / 0.00 / 100.0
6 / 4.50 / 4.00 / 0.00 / 1.50 / 0.98 / -15.1 / 3.18 / 0.00 / 86.8
7 / 5.00 / 0.25 / 0.00 / 0.00 / 0.00 / -46.8 / 0.00 / 0.00 / 100.0
8 / 5.00 / 0.25 / 0.00 / 1.00 / 0.88 / -46.8 / 33.77 / 0.00 / 37.2
9 / 5.00 / 1.00 / 0.00 / 0.00 / 0.00 / -33.7 / 0.00 / 0.00 / 100.0
10 / 5.00 / 1.00 / 0.00 / 1.25 / 0.99 / -33.5 / 13.41 / 0.00 / 49.1
11 / 5.00 / 4.00 / 0.00 / 0.00 / 0.00 / -19.0 / 0.00 / 0.00 / 100.0
12 / 5.00 / 4.00 / 0.00 / 1.50 / 0.98 / -19.0 / 4.31 / 0.00 / 98.5
13 / 5.50 / 0.25 / 0.00 / 0.00 / 0.00 / -52.2 / 0.00 / 0.00 / 100.0
14 / 5.50 / 0.25 / 0.00 / 0.75 / 0.66 / -52.2 / 38.44 / 0.00 / 27.4
15 / 5.50 / 1.00 / 0.00 / 0.00 / 0.00 / -36.6 / 0.00 / 0.00 / 100.0
16 / 5.50 / 1.00 / 0.00 / 1.00 / 0.79 / -36.4 / 13.44 / 0.00 / 56.4
17 / 5.50 / 4.00 / 0.00 / 0.00 / 0.00 / -20.4 / 0.00 / 0.00 / 100.0
18 / 5.50 / 4.00 / 0.00 / 1.25 / 0.82 / -20.4 / 4.00 / 0.00 / 67.6
19 / 6.00 / 0.25 / 0.02 / 0.00 / 0.00 / -54.1 / 0.00 / 0.00 / 100.0
20 / 6.00 / 0.25 / 0.02 / 0.75 / 0.66 / -54.1 / 44.07 / 0.00 / 37.4
21 / 6.00 / 1.00 / 0.02 / 0.00 / 0.00 / -37.6 / 0.00 / 0.00 / 99.9
22 / 6.00 / 1.00 / 0.02 / 1.00 / 0.78 / -37.4 / 14.38 / 0.00 / 52.8
23 / 6.00 / 4.00 / 0.02 / 0.00 / 0.00 / -20.9 / 0.00 / 0.00 / 100.0
24 / 6.00 / 4.00 / 0.02 / 1.25 / 0.81 / -20.9 / 4.12 / 0.00 / 57.5
25 / 6.50 / 0.25 / 0.05 / 0.00 / 0.00 / -54.7 / 0.00 / 0.00 / 100.0
26 / 6.50 / 0.25 / 0.05 / 0.75 / 0.63 / -54.7 / 44.70 / 0.01 / 39.4
27 / 6.50 / 1.00 / 0.05 / 0.00 / 0.00 / -37.9 / 0.00 / 0.00 / 100.1
28 / 6.50 / 1.00 / 0.05 / 1.00 / 0.76 / -37.7 / 14.29 / 0.01 / 55.1
29 / 6.50 / 4.00 / 0.05 / 0.00 / 0.00 / -21.0 / 0.00 / 0.00 / 100.0
30 / 6.50 / 4.00 / 0.05 / 1.25 / 0.79 / -21.0 / 4.06 / 0.01 / 46.5
31 / 7.00 / 0.25 / 0.14 / 0.75 / 0.54 / -54.8 / 38.60 / 0.07 / 46.3
32 / 7.00 / 1.00 / 0.14 / 0.00 / 0.00 / -37.9 / 0.00 / 0.00 / 99.9
33 / 7.00 / 1.00 / 0.14 / 1.00 / 0.66 / -37.8 / 12.45 / 0.08 / 54.0
34 / 7.00 / 4.00 / 0.15 / 0.00 / 0.00 / -21.1 / 0.00 / 0.00 / 100.0
35 / 7.00 / 4.00 / 0.15 / 1.25 / 0.70 / -21.1 / 3.60 / 0.09 / 57.2
36 / 7.25 / 0.25 / 0.20 / 0.00 / 0.00 / -54.7 / 0.00 / 0.00 / 100.0
37 / 7.25 / 0.25 / 0.20 / 1.00 / 0.57 / -54.7 / 40.08 / 0.22 / 46.0
38 / 7.25 / 1.00 / 0.22 / 0.00 / 0.00 / -37.9 / 0.00 / 0.00 / 100.0
39 / 7.25 / 1.00 / 0.22 / 1.25 / 0.66 / -37.7 / 12.42 / 0.26 / 48.2
40 / 7.25 / 4.00 / 0.21 / 0.00 / 0.00 / -21.1 / 0.00 / 0.00 / 100.0
41 / 7.25 / 4.00 / 0.21 / 1.50 / 0.69 / -21.1 / 3.56 / 0.27 / 45.1
42 / 7.50 / 0.25 / 0.26 / 0.00 / 0.00 / -54.8 / 0.00 / 0.00 / 100.0
43 / 7.50 / 0.25 / 0.26 / 1.00 / 0.35 / -54.8 / 25.12 / 0.44 / 40.1
44 / 7.50 / 1.00 / 0.25 / 0.00 / 0.00 / -37.9 / 0.00 / 0.00 / 100.1
45 / 7.50 / 1.00 / 0.25 / 1.25 / 0.42 / -37.8 / 7.97 / 0.53 / 40.3
46 / 7.50 / 4.00 / 0.26 / 0.00 / 0.00 / -21.1 / 0.00 / 0.00 / 100.0
47 / 7.50 / 4.00 / 0.26 / 1.50 / 0.46 / -21.1 / 2.38 / 0.58 / 34.4
48 / 7.75 / 0.25 / 0.35 / 0.00 / 0.00 / -54.8 / 0.00 / 0.00 / 100.0
49 / 7.75 / 0.25 / 0.35 / 1.00 / 0.17 / -54.8 / 11.95 / 0.66 / 42.5
50 / 7.75 / 1.00 / 0.30 / 0.00 / 0.00 / -37.9 / 0.00 / 0.00 / 100.1
51 / 7.75 / 1.00 / 0.29 / 1.25 / 0.20 / -37.8 / 3.88 / 0.81 / 38.8
52 / 7.75 / 4.00 / 0.32 / 0.00 / 0.00 / -21.1 / 0.00 / 0.00 / 100.0
53 / 7.75 / 4.00 / 0.32 / 1.50 / 0.23 / -21.1 / 1.21 / 0.92 / 34.8
54 / 8.00 / 0.25 / 0.34 / 0.00 / 0.00 / -55.0 / 0.00 / 0.00 / 100.0
55 / 8.00 / 0.25 / 0.34 / 1.00 / 0.06 / -55.0 / 4.65 / 0.81 / 44.9
56 / 8.00 / 1.00 / 0.34 / 0.00 / 0.00 / -37.9 / 0.00 / 0.00 / 100.0
57 / 8.00 / 1.00 / 0.39 / 1.25 / 0.08 / -37.8 / 1.51 / 1.00 / 33.1
58 / 8.00 / 4.00 / 0.33 / 0.00 / 0.00 / -21.1 / 0.00 / 0.00 / 100.0
59 / 8.00 / 4.00 / 0.33 / 1.50 / 0.09 / -21.1 / 0.48 / 1.17 / 26.8
60 / 8.25 / 0.25 / 0.57 / 0.00 / 0.00 / -54.8 / 0.00 / 0.00 / 100.0
61 / 8.25 / 0.25 / 0.57 / 1.00 / 0.02 / -54.8 / 1.58 / 0.87 / 40.4
62 / 8.25 / 1.00 / 0.37 / 0.00 / 0.00 / -37.9 / 0.00 / 0.00 / 100.1
63 / 8.25 / 1.00 / 0.36 / 0.00 / 0.00 / -37.8 / 0.00 / 0.00 / 100.0
64 / 8.25 / 1.00 / 0.36 / 1.25 / 0.03 / -37.8 / 0.52 / 1.09 / 32.5
65 / 8.25 / 4.00 / 0.52 / 0.00 / 0.00 / -21.1 / 0.00 / 0.00 / 100.0
66 / 8.25 / 4.00 / 0.52 / 1.50 / 0.03 / -21.1 / 0.17 / 1.29 / 26.6
Experiment 2
67 / 7.50 / 0.50 / 0.21 / 0.00 / 0.00 / -46.6 / 0.00 / 0.00 / 100.0
68 / 7.50 / 0.50 / 0.21 / 0.19 / 0.06 / -46.6 / 2.40 / 0.08 / 74.8
69 / 7.50 / 8.00 / 0.22 / 0.00 / 0.00 / -13.2 / 0.00 / 0.00 / 100.0
70 / 7.50 / 8.00 / 0.24 / 0.22 / 0.06 / -13.2 / 0.18 / 0.08 / 65.4
71 / 7.75 / 0.50 / 0.24 / 0.00 / 0.00 / -46.6 / 0.00 / 0.00 / 99.9
72 / 7.75 / 0.50 / 0.28 / 0.39 / 0.07 / -46.5 / 2.44 / 0.26 / 51.0
73 / 7.75 / 8.00 / 0.24 / 0.00 / 0.00 / -13.2 / 0.00 / 0.00 / 100.0
74 / 7.75 / 8.00 / 0.26 / 0.43 / 0.07 / -13.2 / 0.18 / 0.26 / 57.5
75 / 8.00 / 0.50 / 0.30 / 0.00 / 0.00 / -46.6 / 0.00 / 0.00 / 100.0
76 / 8.00 / 0.50 / 0.27 / 1.00 / 0.06 / -46.4 / 2.39 / 0.80 / 35.5
77 / 8.00 / 8.00 / 0.32 / 0.00 / 0.00 / -13.2 / 0.00 / 0.00 / 100.1
78 / 8.00 / 8.00 / 0.41 / 1.05 / 0.06 / -13.2 / 0.18 / 0.81 / 33.5
79 / 8.25 / 0.50 / 0.31 / 0.00 / 0.00 / -46.6 / 0.00 / 0.00 / 100.0
80 / 8.25 / 0.50 / 0.32 / 2.88 / 0.06 / -46.3 / 2.33 / 2.51 / 18.8
81 / 8.25 / 8.00 / 0.32 / 0.00 / 0.00 / -13.2 / 0.00 / 0.00 / 100.0
82 / 8.25 / 8.00 / 0.34 / 2.97 / 0.06 / -13.2 / 0.18 / 2.53 / 21.5
Experiment 3
83 / 8.00 / 0.25 / 0.33 / 0.00 / 0.00 / -55.2 / 0.00 / 0.00 / 100.0
84 / 8.00 / 0.25 / 0.33 / 0.75 / 0.05 / -55.0 / 3.51 / 0.60 / 43.2
85 / 8.00 / 0.25 / 0.33 / 1.48 / 0.10 / -54.8 / 6.82 / 1.19 / 32.6
86 / 8.00 / 0.50 / 0.33 / 0.00 / 0.00 / -46.5 / 0.00 / 0.00 / 100.0
87 / 8.00 / 0.50 / 0.31 / 0.75 / 0.05 / -46.5 / 1.79 / 0.60 / 44.8
88 / 8.00 / 0.50 / 0.32 / 1.49 / 0.10 / -46.3 / 3.53 / 1.20 / 34.2
89 / 8.00 / 1.00 / 0.34 / 0.00 / 0.00 / -37.9 / 0.00 / 0.00 / 100.0
90 / 8.00 / 1.00 / 0.32 / 0.76 / 0.05 / -37.8 / 0.92 / 0.60 / 43.1
91 / 8.00 / 1.00 / 0.32 / 1.50 / 0.10 / -37.8 / 1.82 / 1.20 / 36.3
92 / 8.00 / 2.00 / 0.35 / 0.00 / 0.00 / -29.4 / 0.00 / 0.00 / 100.0
93 / 8.00 / 2.00 / 0.35 / 0.77 / 0.05 / -29.3 / 0.48 / 0.61 / 43.5
94 / 8.00 / 2.00 / 0.34 / 1.52 / 0.10 / -29.3 / 0.94 / 1.20 / 29.4
95 / 8.00 / 4.00 / 0.35 / 0.00 / 0.00 / -21.1 / 0.00 / 0.00 / 100.1
96 / 8.00 / 4.00 / 0.34 / 0.78 / 0.05 / -21.1 / 0.25 / 0.61 / 43.9
97 / 8.00 / 4.00 / 0.34 / 1.54 / 0.10 / -21.1 / 0.50 / 1.20 / 32.0
98 / 8.00 / 8.00 / 0.35 / 0.00 / 0.00 / -13.2 / 0.00 / 0.00 / 100.0
99 / 8.00 / 8.00 / 0.33 / 0.79 / 0.05 / -13.2 / 0.14 / 0.61 / 41.1
100 / 8.00 / 8.00 / 0.33 / 1.57 / 0.10 / -13.2 / 0.27 / 1.20 / 31.1
101 / 8.00 / 10.00 / 0.34 / 0.00 / 0.00 / -10.8 / 0.00 / 0.00 / 100.0
102 / 8.00 / 10.00 / 0.33 / 0.80 / 0.05 / -10.8 / 0.11 / 0.61 / 39.1
103 / 8.00 / 10.00 / 0.35 / 1.58 / 0.10 / -10.8 / 0.22 / 1.20 / 29.3
Figure S1. Speciation of Cu as function of pH in solution containing a total of 1.0 µM Cu(NO3)2 and 1.0 mM Ca(NO3)2. The speciation was modelled using the equilibrium constants (Table 1) of WHAM (A), NIST (B) and IUPAC [C] in equilibrium with atmospheric CO2 (pCO2 = 10–3.5 atm). Only the five most abundant species are presented.