Supplemental Material
Atomistic modeling of peptide adsorption on
rutile (100) in the presence of water and of
contamination by low molecular weight
alcohols
Wenke Friedrichs and Walter Langel*,
Institut für Biochemie, Universität Greifswald, Felix Haussdorf-Straße 4, 17487 Greifswald,
Germany
In this supplemental material, we describe the calculation of the anisotropic permittivity
of rutile in our force field model and give a list of the molecular dynamics runs evaluated in this
work. An additional figure shows the contaminated surface from top.
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The permittivity ε of an isotropic liquid is in general evaluated from the fluctuation of the total
dipole moment of the simulation cell (cf. [1]) according to the following relation for the total

 2
M2  M





polarization: P   0  (  1)  E ext   p  Eloc 
 Eloc (S1). Here, ε0, M , and V
3 V  kB  T
are the dielectric constant of the vacuum, the total dipole moment and the volume of the
simulation cell, respectively. It was shown in ([2, 3]) that the ration of local to external electric
fields,
E loc
 1, when Ewald summation methods are applied. The polarizability αp is a scalar,
E ext

which does not depend on the direction of Eext relative to the sample and which is calculated

from the fluctuation of M .
The rutile permittivity is strongly anisotropic, with
 //
parallel to z being about twice as
high as   vertical to it in the experiment [4] (Tab 2). αp becomes a tensor, which is diagonal,
if the z-axis is parallel to c.
Returning to the derivation of (S1), it is shown here that the direction dependent
polarization tensor may be calculated from the three components Mx,y,z of the fluctuating total
dipole of the cell. This vector is in equilibrium given by (q partition function with derivatives

qx,y,z with respect to reduced energy E/kbT, H Hamilton function,  i dipole moment of molecule
i):
 k B  T  q 
 




H  i  E




E


x
 qx 
  i  exp   k  T 


k B  T  q 
1  
i
B

 1
M
  
   qy 
 
q 
E y 
q  
 H  i  E 
 q z T
 exp   k  T 
 k B  T  q 
i
B




E z

T
 
 
 H  i  E 
 H  i  E 
k B  T  q
; q k  
; k  x, y, z
q   exp  
   ik  exp  
k B  T 
E k
k B  T 
i
i


 
 H  i  E 
  ik  exp   k  T  q
i
B


Mk 
 k
 
q
 H  E
 exp   k  iT 
i
B


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In the anisotropic case, we get for linear dependence of polarization P on electric field E:
 Px

 E x
 Py


P   E   
 E x
 P
 z
 E x

Px
E y
Py
E y
Pz
E y

 Px



 E x
P


x
    Py
   Py   
E z     E x
P
Pz   z   Pz


 E x
E z 

Px
E z
Py



  E x    xx
   E y     yx
E z    
E

Pz   z   zx

E z 
Px
E y
Py
Px
E z
Py
E y
Pz
E y
 xy  xz   E x 
  
 yy  yz    E y 
 zy  zz   E z 
with
 P 
 M

1
k 
 kl   k   
  k  T V 

E
V


E
l T
B
 l T 
qkl  q q k ql
1

  M kl  M k  M l
2
kB  T V
q

according to quotient rule with
 
 H  i  E 
k B  T    k B  T  q 
;

    ik   il  exp  
q kl  


E l 
E k
k

T
i
B



 
 H  i  E 

 ik   il  exp  


k

T
q kl
i
B



 Mk  Ml


q
 H  i  E 
 exp   k  T 
i
B


In a molecular dynamics calculation, the averages M k
are taken by summing up
over the molecular dipole components in the total simulation cell. M k  M l
is the average of

the products of the components of M in directions k and l for each time step. < ..> means
averaging (here over about 1 ns NVE run).
In case of a general anisotropic system, we obtain
 Mx Mx  Mx  Mx

1
 My Mx  My  Mx
p 
V  kB T 
 Mz Mx  Mz  Mx

Mx My  Mx  My
My My  My  My
Mz My  Mz  My
M x  M z  M x  M z 
My Mz  My  Mz 

M z  M z  M z  M z 
After diagonalization of αp by a matrix Dα, we obtain permittivity values along the main axes
 x

0
0

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0
y
0
0

1
1
0   1   D   p  D1  1 
0
0
 z 
3
 x

 0
 0

0
y
0
0 

0 .
 z 
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For isotropic systems such as liquid water, the polarizability is a scalar, which is
independent of the field direction, and our general formula reduces to the well known
expression cited at the beginning. For the field for example parallel to x, we obtain

Mx Mx  Mx  Mx
V  kB T


1 Mx Mx  My My  Mz Mz  Mx  Mx  My  My  Mz  Mz

3
V  kB T
 


1 M M  M  M

3
V  kB T
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

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Cell contents, issue
Cell size / nm³
Single Ti and O atoms, test of
force field parameters
Bulk rutile; lattice constant,
bulk modulus and permittivity
3.0 x 3.0 x 3.0
Stoichiometric surface (i),
Hydroxylated (ii)
3.6752 x 3.8467 x 5.89
5.9722 x 4.7344 x 5.91
300, free
300, free
z
z
1
10
6918, bulk
13437, bulk
Contaminated (iv)
5.9722 x 5.918 x 6.042
300, free
z
10
13188, bulk
on
14.7008 x 14.795 x 9.0
300,
controlled
--
2
rigid
14.7008 x 14.795 x 9.0
300,
controlled
--
2
Contact
angle
on
physisorbed butanol with
chemisorbed methanol and
hydroxylation (iv), cf. Fig 2
Contact
angle
on
physisorbed pentanol with
chemisorbed methanol and
hydroxylation (iv), cf. Fig 2
14.7008 x 14.795 x 12.0
300,
controlled
--
1.5
4734
Initially cubic
(5.4639 nm)³
4734,
Initially cubic
(5.4639 nm)³
2744,
initially tetrahedral
(5.0 nm)² x 3.0 nm
14.7008 x 14.795 x 12.0
300,
controlled
--
1.5
TiOBP1 on hydroxylated
surfaces (ii),
ARG1/ 9 contacts
TiOBP1 on rutile, top
contaminated (iv), bottom
hydroxylated (ii),
contact to
5.9722 x 4.7344 x 4.01
300, free
z
5.9722 x 5.918 x 5.983
300, free
z
2.297 x 2.297 x 2.96
(+/- 10 %)
T/K
Barostat
Time water
in
/ ns
molecules
direction
Bulk properties of TiO2
Hydroxyle
groups
/ nm²
carbon molecules
/ nm²
--
--
--
--
--
--
200-600
controlled
x, y, z
1
--
--
--
-1.01 H+
1.88 OH1.60 OH-
---
Water properties (structure and mobility)
2.89 physisorbed pentanol
0.67 chemisorbed methanol
Contact angles
Spreading of water
stoichiometric TiO2 (i)
Contact angle
methanol (iii)
on
--
--
--
0-4.53 methanol with fixed
C atoms
1.57 OH-
0.15-3.84
physisorbed butanol
0.60 chemisorbed methanol
2744,
initially tetrahedral
(5.0 nm)² x 3.0 nm
1.57 OH-
0.11-3.58
physisorbed pentanol
0.60 chemisorbed methanol
10
8028, bulk
1.01 H+
1.88 OH-
--
10
14760, bulk
1.60 OH-
2.80 physisorbed pentanol
0.67 chemisorbed methanol
Peptide adsorption
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ARG1/ 11, N terminus
(periodic in +z)
TiOBP1 on contaminated
surfaces (iv)
ARG 3, GLN 12 (CTC) side
chain adsorption
TiOBP2 on hydroxylated
surface (ii), no contact
TiOBP2 on contaminated
surface (iv),
hydrophobic adsorption via
PHE and TRP
minTBP in water
minTBP on hydroxylated
surface (ii), contacts
ARG, ASP, backbone
minTBP on contaminated
surface (iv),
adsorption of ARG 1 on
surface and LEU on PEN
5.9722 x 5.918 x 7.95
300, free
z
110
19674, bulk
1.60 OH--
2.89 physisorbed pentanol
(both sides)
0.67 chemisorbed methanol
5.9722 x 4.7344 x 3.92
300, free
z
10
7755, bulk,
--
5.9722 x 5.918 x 5.934
300, free
z
85
12663, bulk
1.01 H+
1.88 OH1.60 OH-
3.0 x 3.0 x 3.0
5.9722 x 5.918 x 6.89
300, free
300, free
x, y, z
z
25
10
7022, bulk
16023, bulk
-1.01 H+
1.88 OH-
---
5.9722 x 5.918 x 6.05
300, free
z
74
13056, bulk
1.60 OH--
2.89 physisorbed pentanol
(both sides)
0.67 chemisorbed methanol
2.89 physisorbed pentanol
(both sides)
0.67 chemisorbed methanol
Table SI1: Parameters for molecular dynamics runs used in the present work. Surface types see text:
(i) stoichiometric, (ii) hydroxylated, (iii) with physisorbed methanol, and (iv) with chemisorbed methanol and additionally physisorbed butanol or
pentanol. H+: Protonated bridging atoms, OH- singly coordinated hydroxyl groups on surface Ti.
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Fig SI1: View of the contaminated surface from top. The pentanol molecules (blue), which
were homogeneously distributed at the beginning, have clustered and leave gaps for water
freely accessing the TiO2 surface (grey). The TiOBP1 molecule in this frame had α-helical
structure (red) and did not enter the gaps.
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References
[1] M. Neumann, Molecular Physics 50, 841 (1983).
[2] P. Höchtl, S. Boresch, W. Bitomsky, and O. Steinhauser, Journal of Chemical Physics 109,
4927 (1998).
[3] D. J. Price, and C. L. Brooks III, Journal of Chemical Physics 121, 10096 (2004).
[4] M. E. Tobar, J. Krupka, E. Nicolay Ivanov, and R. A. Woode, Journal of Applied Physics 83,
1604 (1998).
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