Supplemental Material for
“Study of Lysozyme Mobility and Binding Free Energy during Adsorption
on a Graphene Surface”
C. Masato Nakano,1,a) Heng Ma,2,a) and Tao Wei,2,*
1
Flintridge Preparatory School, La Canada Flintridge, CA 91011, USA
2
Dan F. Smith Department of Chemical Engineering, Lamar University, Beaumont, TX 77710,
USA
MD Simulation
The lysozyme was placed far away from the surface (around 0.9 nm) with negligible surfaceprotein interactions as shown in Fig. S1. Atoms were kept inside the box by inserting another
restraining layer of graphene sheet, which resulted in an 8.5-nm water slab to ensure sufficient
space for the protein’s free rotation inside the cell. Two vacuum slabs of 2.0 nm were also
inserted, with one at the bottom and one at the top of the cell, to remove the interactions
between atoms inside the cell and their images along the Z-direction. The simulations were
started with the relaxation of water molecules by energy minimization and a short-run of MD
(30 ns) at 300 K, keeping all lysozyme atoms’ positions fixed. Then production runs were
carried out in the NVT ensemble at 300 K for 200 ns without any constraint of lysozyme atoms.
FIG. S1. A snapshot of the initial configuration (10.315×10.635×12.500 nm3): graphene, (cyan) on the X-Y plane
(the Z-axis is normal to the plane), Cl- counterions (magenta), water (silver), protein’s first hydration shell1 (orange)
and protein with the secondary structures identified with the method of structural identification (STRIDE)2.
Secondary Structure Evolution
To investigate the structural deformation, we calculated the protein’s secondary structures as a
function of time by using the 200-ns trajectory of MD simulation. Secondary structures were
identified by using the method of structural identification (STRIDE)2. Fig. S2 shows the
secondary structures as a function of time. By monitoring the secondary structures for the
whole trajectory, we observed that β-sheet domains maintained their structural stability,
whereas parts of the structures of α-helix domains were disturbed. Our results are consistent
with previous simulations1,3 and experiments4 in that adsorption can induce the formation of βsheet while losing α-helix structures under the surface effects. However, our single-trajectory
MD simulation cannot simulate β-sheet propagation due to the big computational load in fullatom simulation.
FIG. S2. Secondary Structure Evolution.
Adsorption Kinetics
Protein adsorption kinetics was monitored by measuring the minimum distance between
the protein atoms and the surface atoms. Fig. S3 shows the protein-surface minimum distance,
d, as a function of time, t. Protein starts to approach the surface at around 1.2 ns and is finally
adsorbed on the surface at 20 ns.
FIG. S3.
Protein-surface’s shortest distance (d) as a function of time (t).
Diffusivity during Adsorption
The lateral diffusion coefficients (𝒟) are calculated with mean square displacement on the
X-Y plane5 parallel to the graphene surface, at different times. Our simulation also reveals that
the profiles of both diffusivity (see Fig. S4) and asphericity (see Fig. 2) show an increase at
around 110 ns, indicating the correlation between the diffusivity and protein structural
fluctuations upon adsorption.
FIG. S 4. Lysozyme lateral diffusion coefficients (D) at different times. The first data point is calculated with the
trajectories of 1.2-15 ns while the others are sampled every 20 ns.
Molecular Mechanics/Poisson-Boltzmann Surface Area (MM/PBSA)
The protein-protein binding free energy (∆𝐺𝑏𝑖𝑛𝑑𝑖𝑛𝑔 ) of A + B → AB is the free energy
difference between the complex (AB) and the sum of the free energies of the individual proteins
(A and B) in an aqueous environment as
∆𝐺
𝑏𝑖𝑛𝑑𝑖𝑛𝑔
𝐴𝐵
𝐴
𝐵
= 𝐺𝑎𝑞𝑢
− 𝐺𝑎𝑞𝑢
− 𝐺𝑎𝑞𝑢
(1)
where A represents the graphene surface; B stands for the lysozyme; and ∆𝐺𝑏𝑖𝑛𝑑𝑖𝑛𝑔 is
calculated with the thermodynamic cycle shown in Fig. S 5.
FIG. S5. Thermodynamic cycle to calculate the binding free energy of the graphene surface (A) and lysozyme (B).
The corresponding binding free energy is expressed as
∆𝐺
𝑏𝑖𝑛𝑑𝑖𝑛𝑔
𝐴
𝐵
𝐴𝐵
= ∆𝐺𝑔𝑎𝑠 − ∆𝐺𝑠𝑜𝑙
− ∆𝐺𝑠𝑜𝑙
+ ∆𝐺𝑠𝑜𝑙
∆𝐺𝑔𝑎𝑠 = (∆ ⟨𝐸𝑖𝑛𝑡𝑟𝑎 ⟩ + ∆⟨𝐸𝐿𝐽 ⟩ + ∆⟨𝐸𝑐𝑜𝑢𝑙 ⟩) − 𝑇⟨∆𝑆𝑀𝑀 ⟩
(2)
(3)
𝑖
𝑖
𝑖
∆𝐺𝑠𝑜𝑙
= ∆𝐺𝑝𝑜𝑙𝑎𝑟
+ ∆𝐺𝑛𝑜𝑛𝑝𝑜𝑙𝑎𝑟
, 𝑖 = 𝐴, 𝐵 𝑜𝑟 𝐴𝐵
(4)
𝑖
∆𝐺𝑛𝑜𝑛𝑝𝑜𝑙𝑎𝑟
= 𝛾𝑖 < 𝑆𝐴𝑆𝐴i > , 𝑖 = 𝐴, 𝐵 𝑜𝑟 𝐴
(5)
𝐴𝐵
𝐴
𝐵
∆𝐺𝑝𝑜𝑙𝑎𝑟 = ∆𝐺𝑝𝑜𝑙𝑎𝑟
− ∆𝐺𝑝𝑜𝑙𝑎𝑟
− ∆𝐺𝑝𝑜𝑙𝑎𝑟
(6)
𝐴𝐵
𝐴
𝐵
∆𝐺𝑛𝑜𝑛𝑝𝑜𝑙𝑎𝑟 = ∆𝐺𝑛𝑜𝑛𝑝𝑜𝑙𝑎𝑟
− ∆𝐺𝑛𝑜𝑛𝑝𝑜𝑙𝑎𝑟
− ∆𝐺𝑛𝑜𝑛𝑝𝑜𝑙𝑎𝑟
(7)
where the symbol  represents an average over configurations. The binding free energy for the
AB complex in the gas phase, ∆𝐺𝑔𝑎𝑠 in Eq. (4), consists of contributions from the averaged
changes in: intra-molecular interactions (Eintra), inter-molecular interactions made up of
Lennard-Jones (ELJ) and Coulombic (Ecoul) potentials, and the entropy contribution (SMM), all
three of which were computed with molecular mechanics. We followed the practice of previous
research works6 by ignoring the entropy (SMM) contribution due to its inaccuracy and debatable
𝑖
contribution to free energy. The total solvation free energy (∆𝐺𝑠𝑜𝑙
) for component i (i = A, B,
𝑖
𝑖
or AB) comprises both polar (∆𝐺𝑝𝑜𝑙𝑎𝑟
) and nonpolar (∆𝐺𝑛𝑜𝑛𝑝𝑜𝑙𝑎𝑟
) contributions (Eq. (4)).
𝑖
∆𝐺𝑝𝑜𝑙𝑎𝑟
is the energy required to transfer the ith component from the gas phase of a low
dielectric constant (𝜀 = 1) to the solution phase of a high dielectric constant (𝜀 = 80), which
is calculated by solving Poisson-Boltzmann equations in implicit continuum medium with a
grid spacing of 0.5 Å. Due to the zero-charge of graphene atoms, the graphene surface electric
𝐴
solvation free energy, ∆𝐺𝑠𝑜𝑙
, is equal to zero. Therefore, the exact value of the graphene
dielectric constant does not affect the binding free energy computation. In our calculation, the
dielectric constant of graphene was approximated as 2.0, which is close to the experimental
𝑖
value (=2.4) 7. The nonpolar contribution (∆𝐺𝑛𝑜𝑛𝑝𝑜𝑙𝑎𝑟
) in Eq. (7) is estimated from the solvent
accessible surface area (SASA) using the surface tension: 𝛾 = 2.77 kJ mol−1 nm−2 for
protein 8 and 𝛾 = 32.99 kJ mol−1 nm−2 for graphene surface9. A probe with the radius of 0.14
nm was used to identify the dielectric boundary in the SASA calculation. ∆𝐺𝑝𝑜𝑙𝑎𝑟 and
∆𝐺𝑛𝑜𝑛𝑝𝑜𝑙𝑎𝑟 as shown in Eq. (7) and (8) represent the itemized energy terms for the electrostatic
and nonpolar solvation free energy, respectively, between the protein-surface complex and the
two component parts (protein and surface). We ignored the ions in our calculations. It should
be noted that, to reduce our computational cost, we performed the MM/PBSA calculation with
configurations from a single solvation MD simulation for the whole complex, rather than three
separate ones for each individual component (surface for A and protein for B) plus the complex.
Accordingly, the change in the intra-molecular potential in the gas phase was ignored.
Movies from Molecular Dynamics Simulation
The QuickTime movie files, S1.mov and S2.mov, show the atomic trajectory of the
protein’s initial landing (1.2-20 ns) from the side view and top view taken from the molecular
dynamics simulation. The QuickTime movie files, S3.mov shows the atomic trajectory of the
protein’s the landing (80-100 ns) from the top view. In the movies, the protein’s secondary
structure is colored according to the same criteria as that in Fig. S1, and the hydration water
molecules inside protein’s first hydration shell are colored orange. The counterions are shown
in magenta. We can observe that the protein has large diffusivity on the surface both at the
initial and final stages.
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