Distribution of Proton Dissociation Constants
for Model Humic and Fulvic Acid Molecules
Before and After R
R Group Special Event
Yasemin B. Atalay
Environmental Engineer, PhD
[email protected]
October 5, 2010
Introduction
Analysis Before R
Analysis After R
More plotting options with R
Fun with R
2
The objective: Building a chemical equilibrium model with less degree of
freedom for metal binding to natural organic matter.
3
picture taken from JESS Manual.
Natural Organic Matter
Dissolved Organic Carbon histogram for an
average river water
0
10
20
30
40
50
60
70
80
90
100
Fulvic acid
Humic acid
Hydrophilic
acid
Carbohydrates
Carboxylic
acids
Amino acids
Hydrocarbons
Sutton, R. et al. Environmental Toxicology and Chemistry, Vol. 24, No. 8, pp. 1902–1911, 2005
Thurman, E. M. (1985). Organic geochemistry of natural waters, Martinus Nijhoff/Dr W. Junk Publishers.
4
Structures of hypothetical humic acid and fulvic acid molecules
Leonardite humic acid
1Buffle
et al., fulvic acid
Chelsea soil humic acid
2Stevenson
et al., humic acid
Suwannee river fulvic acid
1,2. Aiken, G. R.; McKnight, D. M.; Wershaw, R. L.; MacCarthy, P., Wiley, J.: New York, 1985.
5
Proton Binding to Organic Matter
= HA
Proton Binding
HA ↔ H+ + A{H + }[ A− ]
Ka =
[ HA]
-log10 (Ka) = pKa
pKa is an energy term representing the proton dissociation.
6
WHAM VI : Proton-Ligand Binding
(WHAM = Windermere Humic Aqueous Model)
OH
COOH
COOH
OH
OH
COOH
HO
COOH
- Discrete site model
- Only 8 proton dissociating groups
- Ion-binding groups positioned on the surface
7
Before R
Cumulative Probability Distribution of Sites
Cumulativ e Probability
Distribution of Site
s
Cumulative
Probability
Distribution
(cpd)
Plots
HA Molecules - Intrinsic pKAs
HA (Diallo M ole cule s)-Intrinsic pKAs
14
14
12
12
10
pKA
8
6
WHAM
Diallo 9
4
Diallo 8
Diallo6
Diallo 5
2
8
6
WHAM
Perdue-1
Perdue-2
Perdue-3
4
2
Diallo 4
0
0
0.0
0.0
0.2
0.4
0.6
0.8
0.2
1.0
0.4
0.6
0.8
1.0
Fraction less than (i/n+1)
Fraction less than (i/n+1)
FA - Intrinsic pKAs
14
12
Fraction pK
lessa than, (i/n+1)
pKA
10
10
8
6
4
WHAM
Leenheer a
Leenheer b
Leenheer c
2
8
0
0
0.2
0.4
0.6
Fraction lesspKA
than (i/n+1)
0.8
1
After R
Cumulative Probability Distribution Plot and use of stepfunction
Humic acid molecule
Cumulative distribution function
alcohol groups 10 & 11 are not considered.
WHAM carboxylic sites are more basic than the molecule.
9
After R
CPD Plots & Q-Q plots
Soil HA
1.0
+
+
+
+
+
+
+
+
+
++
+
+
+
+
++
+
+
+
+
+
+
+
+
+
+
+
+
++
F (pK s )
0.6
0.4
0.2
0.0
Molecules pK s
14
+
+
+
+
+
++
A
0.8
Aqueous HA
+
+
+
B
Aqueous FA
C
+
+
+
+
++
+
+
+
D
+
E
+
+
+
+
++
+
++
+
+
++
+
+
++
+
+
+
+
++
+
+
+
+
+
+
WHAM
+
+
+
Molecules
+
F
12
10
8
6
4
2
0
0
2
4
6
8 10 12 14
0
2
4
6
8 10 12 14
0
2
4
6
8 10 12 14
WHAM pKs
Advantages of qq plots;
- Sample sizes need not to be equal
- Distributional aspects ie. the shifts, outliers can be tested
10
Model Molecules vs. WHAM VI Model
12
10
pH
8
6
4
SRFA
Molecule constants
WHAM constants
WHAM VI
2
0
0
1
2
3
NaOH added (mM)
4
0
2 4 6 8 10 12 14
Charge density (meq/gC)
Variation in surface charge:
Charge density (meq / g C)
11
Atalay et al., Environ. Sci & Technol., 2009, 43 (10), pp 3626–3631.
More Plotting options with R
Tukey Mean Difference (TMD)
0
TMD plots the difference of the
quantiles against their average.
-1
The advantage of TMD plot over
qq-plot is te interpretation of
difference over zero line.
-2
Difference
1
2
Tukey Mean Difference
HA Molecules
0
2
4
6
8
10
12
14
Mean (pKA)
12
Fun with R:
∆D (mm)
20
Sea urchin growth modeled using quantile regression
10
A graph of quantile residuals using
boxplots around the median model
0
-10
60
A graph for presenting individual
growth with time in a population with:
D (mm)
50
40
- Histograms of size distribution with
time
- Quantile regressions for the median
and 5% / 95% percentiles,
30
20
10
0
0
1
2
3
4
t (years)
5
6
7
13
http://addictedtor.free.fr/graphiques/
6
Bird 131
4
4
2
2
0
0
0
4
8
12
Travel Time (s)
Histogra m of Y
0.5
0.4
Density
6
Responses per Second
Responses per Travel
Fun with R:
0.0
-3
16
-2
-1
0
1
2
3
Y
35
30
66
100
54.3
54.6
50
30.9
37
35.1
20.3
11.7
8.7
24.3
15.4
19.3
13.6
8.4
41
26.9
18.1
11.7
Rural
M ale
R ural
Female
Urban
M ale
U rban
Female
tooth length
71.1
150
0
0.2
0.1
200
50
0.3
25
20
15
10
A sc orbic ac id
Orange juice
5
0
0.5
0.5
1
1
2
2
Vitamin C dose (mg)
Cherry
Blueberry
z
Apple
y
Vanilla
x
Other
Boston C ream
14
http://www.stat.auckland.ac.nz/~paul/RGraphics/rgraphics.html
y
Thank
Q
u e s tioyou...
ns???
O n c e u p o n a t im e . . .
...
15
http://www.stat.auckland.ac.nz/~paul/RGraphics/rgraphics.html