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The Cell Model
Stefan Trapp
Department of Environmental Engineering
Technical University of Denmark
2,4-D
Glyphosate
Pymetrozine
Metsulfuron-methyl
PCP
So what do they have in common?
Pirimicarb
Some well known pesticides
This was actually a question to the audience 2,4-D
acid pKa at 3.0
Glyphosate
acid pKa at 0.5, 2.6, 5.9,
base pKa at 10 Pymetrozine
base pKa at 3.8
Metsulfuron-methyl
acid pKa at 4.1
PCP
acid pKa at 4.5
All these pesticides are ionizable
some are acids (rosa), some are bases (blue), some are both
Pirimicarb
base pKa at 4.5
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1 3 5 7 9 11 13
pH
Fra
cti
on
s
neutral ion
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1 3 5 7 9 11 13
pH
Fra
cti
on
s
neutral ion
Metsulfuron-methyl
acid, pKa = 4.41
Trimethoprim
base, pKa = 7.2
Impact of pH on speciation of ionics
(Weak) acids are ionic at high pH and bases at low pH
)(101
1apKpHinf
ni ff 1and
Processes for ionic compounds
Ionic compounds undergo extra effects:
► Ionizable compounds dissociate.
► They occur in (at least) two species (neutral and ion).
► Concentration ratios of these species change with pH.
► Ions are much more polar than the neutral molecules.
► Membrane permeabilities of ions are small.
► Ions are attracted or repelled by electrical fields.
2
Systemic Pesticides
Herbicidal action is supported when the chemical is distributed via
phloem (to all growing parts of the plants, incl. roots).
The phloem has a high pH (ca. pH 8), and weak acids accumulate in
that. That’s why systemic herbicides are typically weak acids.
Insecticides must hit the damaging insect. Aphids and wgiteflies suck
from the phloem and drink from the xylem, mites eat the whole cell.
Thus, intracellular distribution matters.
Fungi often attack via xylem (a dead pipe). Fungicides are good if
present xylem (acidic, pH 5.5). That’s could be the reason why some
fungicides are weak bases.
Kleier’s model considers the flow in
xylem (apoplast, pH 5.5) and
phloem (symplast pH 8).
Phloem transport is due to the “ion
trap” (weak acids) or to slow
permeability (neutral, polar
substances).
Kleier model (1988) available from
Stefan Trapp (on request).
Kleier's model for
phloem transport
The REACH chemicals
143 000 chemicals pre-registered at the European
Chemical Agency ECHA for REACH. Hereof:
Source: Based on a random sample of 1511 chemicals analyzed by
Antonio Franco et alii
Cell Model
and intracellular localization
Thanks to Prof. RW Horobin
for this sketch of a cell
Typical structure of an eukaryotic cell
(seen from the perspective of a neutral compound)
Lipids
The neutral compound “sees”
only aqueous and lipid phases
Water
BCF regressions for neutral compounds
BCF: bioconcentration factor for whole organisms
Process
Partitioning into aqueous and
lipid phase (described by Kow).
Basic equation
BCF = W + L x KOW
Example
70.0log85.0log OWKBCF
"Traditional" BCF regressions predict uptake into the whole organism
and consider aqueous and lipid phase.
BCF fish (Veith et al. 1979):
3
Thanks to media
photobucket
Structure of a Plant Cell
Organelles
Cell wall
Plasma membrane
Cytoplasm
Vacuole
Nucleus
Mitochondria
Chloroplast
ER + Golgi
Thanks fsu edu
Structure of an Animal Cell
Organelles
Plasma membrane
Cytoplasm
Lysosomes
Nucleus
Mitochondria
ER + Golgi
Typical structure of an eukaryotic cell
seen from the perspective of an ionic compound
cytosol
membrane
lipids
nucleus
lysosomes
(cell wall)
pH 8
pH 7 to
7.4
pH 5
pH 6.5
+20
-70
mV
-160
mV
mitochondrium
Outside
apoplast
Cytosol Vacuoles
H+ e-
pH 5-7 pH 7.5
pH
5-6
- 0.1 V
Charge at membranes by proton transport
ATP
Membrane
Neutral molecules adsorb often to lipids
4
Bioaccumulation of a weak acid
(2,4-D, pKa ~ 3)
1 RH 1 RH 1 RH
100 RH
neutral
ionic 100 R- 10 000 R- 100 R-
pH 5
Cytosol pH 7 Vacuole
pH 5
outside
Example: BCF of 2,4-D at pH 5 Cell model for ionic compounds
Processes: Transport across membranes neutral/ionic, dissociation in/outside,
lipophilic partitioning, electrical attraction, metabolism, pumps.
Each organelle is described by one differential equation. Dynamic matrix solution.
Proteins
)(1
,,
N
iioiNii eaae
NPJ
)( ,, inonnn aaPJ
Underlying equations
Fick’s 1st Law, flux of neutral molecules n
Nernst-Planck-equation, flux of ions i
i = inside
o = outside
J = flux
P = Permeability, f(log D)
N = Nernst potential
z = valency
E = electrical potential
F = Faraday constant
R = gas constant
T = Temperature
a = chemical activity
B = bulk capacity
C = concentration
RT
zEFN
CBa
Nernst-potential eN
activity a and concentration C
activity a times bulk capacity B gives concentration C
where B describes partitioning to lipids, proteins etc.
)( ,, inonnn aaPJ )(1
,,
N
iionoionNionion eaae
NPJ
How to find activity a ?
Activity a (mol m-3 or kg m-3) is the driving force for diffusion (and toxicity; and
reaction).
f effective fraction (n is neutral, ion is ion, W is water, L is lipids, K is adsorption, g
is activity coefficient), and analogue for fd:
ionionion
pKapHi
nnn
tnnKWKW
Cafgggg //10//
1/
)(
Steady-state concentration ratio (partition coefficient, BCF)
BCFeNePfPf
eNPfPf
C
CNN
ioniionnin
N
ionoionnon
ot
it
)1/(
)1/(
,,
,,
,
,
(t is total, i is inside, o is outside)
cmmmcmocccocc JAJAJAJA
dt
dm,,,,
cmmmcmm JAJA
dt
dm,,
change of mass in the cytoplasm mc = + flux from outside – flux to outside
– flux to mitochondria + flux from mitochondria
change of mass in the mitochondria mm =
+ flux to mitochondria – flux to cytoplasm
Mass balance Cell Model
etc. for lysosomes, chloroplasts, nucleus ...
This yields several parallel 2 x 2 matrices which are solved analytically.
N
FishiNiFishnn
WiNiWnn
W
Fish
ee
NPP
e
NPP
a
a
,,
,,
1
1
proteinsKKK
LipidsWaterB proteins
i
iOWi
n
nOWn
i
i
n
nbiota
g
g
g
g
,,
Uptake capacity B describes partitioning into water, lipids and proteins
capacityulkctivitybiota BaC _
and this replaces the BCF
Bioconcentration factor electrolytes
activity ratio in flux equilibrium ≠ 1 and f(pH)
5
Permeability P of unstirred boundary layer and biomembrane
outside inside
Membrane
Dx = 50 nm
lipid layer
Dx ≈ 30 mm
aqueos layer
Dx ≈ 0.4 mm
cell wall
boundary
layer or
cell wall
Daqua≈ 2 x 10-9 m2/s
Dcell wall ≈ 10-10 m2/s
K = 1
ebiomembranaqua
total
PP
P11
1
D≈ 10-14 m2/s
K = KOW
7.6loglog OWebiomembran KPUse:
P cellwall= 2.5x10-4 m/s and/or Paqua = Daqua/Dx
Two resistances in series
Permeability P of biomembrane
for neutral and ionic molecules
x
DKP
D
where
P = permeability (m/s)
D = diffusion coefficient ca. 10-14m2/s,
K = partition coefficient from water into the membrane ≈ KOW (L/L)
x = membrane thickness ≈ 50 nm
It follows that P ≈ 10-14/(50x10-9) m/s x KOW = 2x10-7 x KOW
log(2x10-7) = -6.7 → log P = log KOW - 6.7
log Kow ion is about 3.5 log units lower than log Kow neutral.
Permeability P ion is 3162times slower than P neutral.
Governing equation
-1.0
0.0
1.0
2.0
3 4 5 6 7 8 9
log
BC
F
external pHcell model water weed 2,4-D
ricinus 3,5-D barley 2,4-D
external pH
measured data from Briggs,
Rigitano, De Carvalho et al.
The ion trap high-lighted
neutral in + ionized not out
→ activity inside changes with pH
high pH
low pH BCF of 2,4-D
pKa = 2.98
N
FishiNiFishnn
WiNiWnn
W
Fish
ee
NPP
e
NPP
a
a
,,
,,
1
1
Alternative: Activity concept
Activity a (mol m-3 or kg m-3) is the driving force for diffusion (and toxicity; and
reaction). It relates to cponcentration by
Activity nomenklatura where B is bulk capacity (m3/m3), is fraction neutral or
ionized , for biota:
CBa
Bi
iOWBi
Bn
nOWBn
B
Bi
Bi
Bn
Bn
BB
KKLWB
,
,,
,
,,
,
,
,
,
g
g
g
g
More see Trapp, Mackay, Franco 2010, Env Sci Technol.
The cell model is still programmed in old nomenklatura.
BN
BiNiBnn
WiNiWnn
BBt B
ee
NPP
e
NPP
BaBCF
,,
,,
,
1
1
The activity concept makes calculations for multi-species compounds much
simpler - once you have it in your head!
Cell Organelle Properties
Cytosol Vacuole Phloem Xylem
% volume ca. 10 ca. 1 50-90 30-46 %
pH inside 7.4 5.5 8 4.5-5.5
outside
soil,
apoplast cytosol cytosol cytosol
lipid 0.05 0.05 0 0 g/g
water 0.95 0.95 1 1 g/g
Ion strength 0.3 0.3 0.3 0.01 mol
E
-0.12
to outside
+0.02
to cytosol
0
to cytosol -0.1
+0.12 to
cytosol
6
Results of the cell model - Acids
Acids external pH 5
- ion trap -
Acids external pH 7
2 3 4 5 6 7 8 9 10
0
2
4-1.0
0.0
1.0
2.0
3.0
log BCF
pKa
log Kow
0
1
2
3
4
2 3 4 5 6 7 8 9 10
0
2
4-1.0
0.0
1.0
2.0
3.0
log BCF
pKa
log Kow
0
1
2
3
4
Chemical Equilibrium to water – log BCF plants
Results of the cell model - Bases
Bases external pH 5
- opposite ion trap -
Bases external pH 9
- ion trap
2 3 4 5 6 7 8 9 10
0
2
4-1.0
0.0
1.0
2.0
3.0
log BCF
pKa
log Kow
0
1
2
3
4
Chemical Equilibrium to water – log BCF plants
2 3 4 5 6 7 8 9 10
0
2
4-1.0
0.0
1.0
2.0
3.0
log BCF
pKa
log Kow
0
1
2
3
4
Application
Bioconcentration (fish) of weak electrolytes at pH 7
log BCF = 0.63 log D - 0.18
R2 = 0.80
-1
1
3
5
-1 1 3 5 7
log D
log
BC
F
2 3 4 5 6 7 8 9
10
11
12
13
14
-11
357
-1
0
1
2
3
4
5
6
log BCF
pKalog Kow
Weak bases
empirical
Predicted BCF
(Cell model)
The slope log BCF vs log D is
less for cations - because polar
cations also accumulate due to
electrical attraction!
log BCF = 0.24 log D + 0.87
R2 = 0.34
-1
0
1
2
3
-4 -2 0 2 4
log D
log
BC
F
Strong bases
empirical
Fu et al. 2009, ETaC
Prediction of Intracellular
Localization
with the cell model
Intracellular Localization
Ionizable compounds (acids, bases, amphoteres) can
concentrate in selected cell organelles, due to pH effects and
electrical attraction.
This selective accumulation is known as "intracellular localization"
(ICL).
ICL is widely used in biological staining and medicine (drug design).
Predicted ICL by the Cell Model
Chemical groups considered
Weak acids (pka from 4 to 7)
Strong acids (anions, pKa < 3)
Weak bases (pka from 6 to 10)
Cations with delocalized charge and
strong bases (cations, pKa > 10)
hydro- and lipophilic (log KOW <0 to >4)
7
Weak acids (pka from 4 to 7)
● ion trap effect pKa 4-7, external pH < 7
● go mostly into cytosol (pH 7.4) and into mitochondria (pH 8)
● more uptake with lower outside-pH
Observed for pesticides: phloem mobility (pH 8)
ICL of weak acids
z = -1 z = 0
pH 2 4 6 8 pH
mitochondria
pH 8
-1.0
0.0
1.0
2.0
3 4 5 6 7 8 9
log
BC
F
external pHcell model water weed 2,4-D
ricinus 3,5-D barley 2,4-D
external pH
measured data from Briggs,
Rigitano, De Carvalho et al.
The ion trap highlighted
neutral in
ionized not out
high pH
low pH
BCF of 2,4-D, pKa = 2.98
ICL of weak bases
Weak bases (pka from 6 to 10)
● ion trap effect in
acidic lysosomes and vacuoles
● more uptake with high outside-pH
► Uptake into vacuoles
may lead to detoxification!
Observed
● plant alkaloids stored in vacuoles
Observed in medicine
● delayed effect of alkaline psychopharmaka
● mutual interaction of weak bases
Many pharmaceuticals
are weak bases!
(Manallack 2009)
Predicted ICL of bivalent weak bases
quinine, base pKa 8.1, 5.1
acid pKa 11.8
pH
+2 +1 0 -1
Bivalent weak bases (pka from 4 to 10)
● good uptake if lipophilic (log Kow > 4)
● strong ion trap with pKa > 6
● good accumulation in acidic vesicles
(vacuoles, lysosomes)
Medical use:
● anti-malaria drugs
(targeting lysosomes)
quinine, chloroquine
pH 4 6 8 10 12 pH
ICL of cations with delocalized charge
Delocalized charge
→ weak dipole of cation
→ cation not hydrophilic
→ similar log D of neutral mol. and ion
→ similar membrane permeability
→ no ion trap
→ no effect of pH differences
→ electrical attraction most relevant
● attraction by mitochondria (E -160 mV) and chloroplasts (?)
Medical use: staining of mitochondria, anti-tumor drugs
Similar: strong lipophilic cations
example Rhodamine 123
charge is delocalized
Summary: Predictions of preferred ICL
polar
anions weak acids pKa 5-7, z ≥-2
weak acids pKa 6-8
lipophilic cations
bases with delocalized charge
weak bases, z = +1 or +2
lipophilic,
neutrals
zwitterionic compounds (membranes), z = -1,+1
lipophilic compounds
8
Applications of the Cell Model
Ironically, though originally developed for pesticide design, the model
was rarely used for that purpose, but got popular in medical drug
design. Only now (2015) it was used for pesticide design.
Recently, we used it for pharmaceuticals, too (antibiotics).
Application of the new theory in medicine
To my surprise, our models
are widely applied in medicine
and pharmacology, too.
2000
2015
Screen-shot of the Cell Model
Chemical data input (yellow) Result for Cytosol (dark blue), vacuole (light blue),
phloem (pink) and xylem (green).
9
Data input for cell organelles Concentration versus time (scroll down)
It's a free software The rest is math and calculations - better don't touch
Questions? Intermezzo
Carles Hurtado demonstrates ACD/i-lab
10
5 Standard Modell
for Ionic Compounds
Standard Model for Ionics
diffusive
equilibrium
flux with water
The standard model for ionics
uses the same fluxes and
processes as the models for
neutral compounds
but the concentration ratios
(RCF, LCF, KRW etc.) of plant
cells to soil, water, xylem are
replaced
and calculated with the
cell model.
Dynamic Plant Uptake Model for Ionics Existing models for neutral molecules can be modified for ionics
by replacing the partition coefficients (Koc, RCF, LCF, KRW usw).
Soil-plant model
Tipping Buckets for soil
Cascade model for plants
Cell model
for BCF, RCF, LCF
“Standard Model” for ionics
RRR
RWR
SWS
R
R CkCKM
QCK
M
Q
dt
dC
LLL
LLA
LLA
L
LR
RWL
L CkCMK
mLgAC
M
gAC
KM
Q
dt
dC
31000
FFF
FAF
FAir
F
FR
RWF
FF CkCKM
gAC
M
gAC
KM
Q
dt
dC
1000
from Cell Model into Standard Model
Modifications for Ionics - replace partition coefficients
Trapp S. Bioaccumulation of polar and ionizable compounds in
plants.
in: J. Devillers, Ed.: Ecotoxicology Modeling. Springer,
Dordrecht, 2009.
Describes the fundamentals of the plant uptake models for
ionisable substances
Standard Model Cell Model
Fluxes and Processes as before – partition coefficients from cell model
11
Dynamic Model left side: cell model; right side: Bckets/ Cascade model Fundamental critics of the Model for Ionics
We work now several years on the plant uptake model for ionics.
Problem is a general issue:
Experiments like model results show very high variability (more by
Trine Eggen)
Is a model with so many input parameters (highly variable, plant
and site specific) useful at all?
Doesn't it lead to very high uncertainty of predictions?
Dedicated experiments for calibration and validation are also
missing and are difficult to do!
... but would be needed so much.
Questions
?
DTU Environment
