Effect of hydrophobic groups on adsorption of arginine-based amino acids to solid surfaces in water

We calculate the free energies of adsorption between a solid wall and various arginine derivatives in water using molecular dynamics simulations. We vary the hydrophobic group size of the amino acids in two ways and the hydrophilicity of the solid wall in five ways. The free energy of adsorption decreases by increasing the hydrophilicity of the solid wall, regardless of the size of the hydrophobic group. Amino acids with small hydrophobic groups are adsorbed on the solid wall with the strongest hydrophilicity, but the free energy of the amino acids with large hydrophobic groups is relatively small. The free energy of adsorption in benzene solvent is increased by increasing the hydrophilicity of the solid wall; however, analogous to results in water solvent, it is independent of the size of the hydrophobic group. We attribute these differences in free energy to the effect of solvent molecules localized on the solid wall. Thus, these results may modulate peptide adsorption on a solid surface by the size of the peptide’s hydrophobic groups.

Sensitive detection of metals based on the affinity and specificity of aptamers is an active field of research in environmental monitoring and medical diagnosis [2].In medicine, the concentrations of various metals in vivo can be used as biomarkers, measurable indicators of biological conditions.For example, titanium and its alloys see use in the production of many medical implants, such as artificial bones and joints.Recent studies suggest that titanium-based implants exhibit wear and corrosion in physiological environments, releasing titanium particles into the surrounding tissues and blood.Because titanium is highly insoluble and can lead to tissue injury, researchers need accurate and facile measurements of the titanium concentration in blood.However, precise measurements require technical equipment, which makes routine monitoring difficult [33].Using aptamers in blood tests would enable the concentration of various metals in blood, such as titanium, to be measured at a low cost.This would solve the problems associated with conventional testing methods.Thus, it is necessary to develop aptamers with specific and high affinity for various metals.
Sano et al. identified a peptide TBP-1 (RKLPDAPGMHTW) that specifically binds to Ti by using phage display and suggested that RKLPDA (minTBP-1) in the peptide sequence is pertinent to binding to the Ti surface.Initial studies on the binding affinity suggest that minTBP-1 has affinities for Ti, Si, and Ag; but not for Au, Cr, Pt, Sn, Zn, Cu, and Fe [41].Regarding the roles of amino acid residues in the minTBP-1 sequence, alanine substitution experiments suggest that mutation of a neutral proline in the sequence decreases these affinities; in contrast, mutation of a charged lysine in the sequence increases them [42].Skelton et al. obtained similar results using molecular dynamics simulations.They suggested that changes in the flexibility of minTBP-1 (due to mutations of proline) and changes in the stability of the molecular structure in the adsorbed state (due to mutations of lysine) are pertinent factors.Furthermore, the interactions of the charged residues in the sequence-Arg, Asp, and Lys-with the water layers structured on the TiO 2 surface drive the initial stage of adsorption of minTBP-1 [43].These results suggest the importance of interfacial water layers in interactions between peptides and TiO 2 surfaces.
Schneider et al. performed molecular dynamics simulations to analyze the adsorption of minTBP-1 on TiO 2 and SiO 2 surfaces [44].Sultan et al. suggested that peptide structures and sequences are pertinent to binding affinity, and evaluated various titanium-binding peptides Ti-1 (QPYL-FATDSLIK) and Ti-2 (GHTHYHAVRTQT) from the standpoint of entropy and enthalpy.These two peptide sequences differ substantially in terms of the overall balance between hydrophobic and charged residues.Hydropathy scores indicate that Ti-1 has stronger hydrophobicity.However, quartz crystal microbalance experiments show that these two peptides have similar binding affinities for the TiO 2 surface.Molecular dynamics simulations suggest that Ti-1 is an entropically driven binder, with no strong anchor residues, whereas Ti-2 is an enthalpically guided binder, featuring a high number of periodically spaced anchor residues along the chain length [45].
Although many studies have been published on the interactions between biomolecules and inorganic surfaces, researchers still do not fully understand why particular peptides have specific binding affinities for inorganic surfaces.
By elucidating the fundamentals of specific recognition between peptides and inorganic surfaces, novel peptide aptamers can be rationally designed on the basis of the properties of the target inorganic surfaces, which will reduce research and development costs.Therefore, it is necessary to understand how the properties of peptides, which are determined by their steric structures and amino acid sequences, affect their interactions with inorganic surfaces and how one can tailor these properties to modulate affinity.
We focused on hydrophobic groups in amino acids to understand their affinity for solid walls.We used virtual amino acid molecules based on arginine.In physiological environments, metal surfaces are oxidized and positively or negatively charged [46].Assuming a negatively charged metal solid surface, we simulated virtual solid walls with downward dipole moments on the surface.We performed molecular dynamics simulations to evaluate changes in the adsorption states of amino acids and changes in the magnitude of the dipole moments by calculating the free energy.

Computational details
Figure 1 shows the structures of the virtual amino acids based on arginine used in this study.The amino acid derivatives consist of a hydrophobic carbon chain with an amine that is bonded to the carboxy group of the main chain of arginine, thus constituting an amide bond.The number of carbon atoms in the hydrophobic chain is 1 and 16.We named two carbon atoms in the amino acids.Carbon atoms at the end of the hydrophobic carbon chain are called C 1 , and carbons bonded with three hydrogen atoms are called C 2 .Figure 2 shows the system used in the simulation and the definition of the reaction coordinate.Figure 2a shows the simulation system.The solid wall consists of one virtual atom based on FCC's crystal structure.The orientation of the surface where the virtual molecules adsorb is the (111) plane.We prepared a supercell volume, 39.0 Å×29.4 Å×300 Å.For solvent molecules, we used 5000 water molecules.The number of virtual molecules was one.We used periodic boundary conditions in all directions.Figure 2b shows the schematic diagram of the reaction path.We employed a difference of the z-coordinate between the surface of the solid wall and the center of mass of the amino acid.
We determined the partial atomic charge of the amino acids by fitting the electron density calculated from optimized structures using the restrained electrostatic potential method.All electronic structure calculations were carried out on the basis of the density functional theory using Gaussian 16 [47].We used B3LYP [48] functionals as the exchange-correlation functionals.Moreover, the 6-31G** basis set was used for all atoms.We used harmonic oscillators for the bond, angle, and dihedral potentials.The SPC/E [49] model was used for water molecules and the general amber force field [50] for the amino acid.We evaluated interaction parameters between various atoms using the Lorentz-Berthelot mixing rule.We set the Coulomb and Lennard-Jones potential cutoffs at 10 Å and the dipole potential cutoff at 15 Å.The particle-particle-particle-mesh methods [51] were used to calculate the distance beyond the cutoff distance of the Coulomb potential.We constrained the bond lengths and bond angles of the water molecules by the SHAKE [52] method.
To maintain the structure of the solid wall, we used a harmonic oscillator potential between virtual atoms in the unit cell (Fig. 2): where r is the distance to atoms, r 0 is the equilibrium distance between two atoms (4.08 Å), and K is a constant (500 kcal/mol/Å 2 ).Assuming a negatively charged surface, all atoms in the outermost layers were assigned downward (1) Harmonic = K r − r 0 2 dipole moments in the simulation.We changed the magnitude of the dipole moment (D) to 0.0 eÅ, 0.5 eÅ, 1.0 eÅ, 1.5 eÅ, and 2.0 eÅ.To represent the electric field on the solid wall by this dipole moment, the charges of all the atoms constituting the solid wall were assumed to be zero.We set the parameters ε and σ of the virtual atoms of the solid walls to appropriate values to prevent solvent molecules from entering the solid wall.
We carried out molecular dynamics simulations with LAMMPS [53].In the initial state, virtual molecules were placed at a distance of 10 Å from the solid wall surface to its center of mass, and water molecules were randomly placed in the region of 25-100 Å from the solid wall surface.We set the time step for the numerical integration to 1 fs.We calculated the free energy using the umbrella sampling method [54] and the weighted histogram analysis method [55,56].In this study, the reaction coordinates were defined as the distance from the solid wall surface (z w ) to the center of gravity of the amino acid (z p ), as shown in Fig. 2b.We varied the reaction coordinates from 4.8 to 22.8 Å in increments of 1.0 Å up to the bulk solvent.To control the reaction coordinates, a harmonic potential was imposed to constrain only the distance in the z-direction, leaving the amino acids free to move in the xy direction.
At the first step of the simulation, to create a stable state constrained by the harmonic potential, we set the spring constant for the harmonic potential to control the reaction coordinate to 1000 kcal/mol/Å 2 and calculated 200 ps in the NVT ensemble at a temperature of 300 K.Then, we changed the spring constant to 100 kcal/mol/Å 2 , and ran the simulation for 200 ps.After obtaining the equilibrium state, we set the spring constant for the harmonic potential to control the reaction coordinate to 1 kcal/mol/Å 2 and performed the calculation for 1 ns for sampling.To confirm that the sampling time is sufficiently long, the free energies for n = 1, D = 0 e Å were compared with those calculated with a sampling time of 200 ps and 1 ns.Both calculation results are in general agreement, which indicates that the calculations in this study converge at a few 100 ps.Therefore, 1 ns is sufficiently long as a sampling time.

Results and discussion
First, we will discuss the adsorption free energy.The free energy at each reaction coordinate is shown in Fig. 3. Figure 3a shows the free energy of the amino acid with n = 1, and Fig. 3b shows the free energy of the amino acid with n = 16.The red line indicates results in the case of D = 0 eÅ, the green line those for D = 0.5 eÅ, the blue line those for D = 1.0 eÅ, the purple line those for D = 1.5 eÅ, and the black line those for D = 2.0 eÅ.The free energy at z = 22.8 Å was set to 0, where the amino acid was sufficiently far from the solid wall to ignore the interaction between the amino acid and the solid wall.The horizontal axis shows the reaction path of the amino acid.For n = 1, the free energy curve can be divided into two types.One type can be seen when the dipole moment is 0 eÅ, 0.5 eÅ, and 1 eÅ.In this type, the stable point is located where the distance parameter is 5 Å.However, for dipole moments of 1.5 eÅ and 2.0 eÅ, there is an adsorption point near 7 Å (the local stable state in 2.0 eÅ).These different adsorption points indicate that the adsorption state may change with the magnitude of the dipole moment.Even when n is 16, the free energy curve can be divided into two parts.One is the type with adsorption points in the region near 5 Å, as in the case of n = 1 (D = 0 eÅ, 0.5 eÅ, 1.0 eÅ), and the other is the type with adsorption points in the area farthest from the wall (D = 1.5 eÅ, 2.0 eÅ). Figure 4 shows the magnitude of the free energy of the adsorbed state at each dipole for the amino acid with n = 1 and n = 16.When the dipole is 0 eÅ, the adsorption energy increases in proportion to the number of carbons in the virtual molecule.However, as the dipole increases, the magnitude of the adsorption free energy of the virtual molecule with n = 16 becomes smaller than that of the amino acids with n = 1.This indicates that the decrease in the magnitude of the free energy is dependent on the size of the hydrophobic component of the amino acid.However, the rate of increase in adsorption free energy of n = 16 amino acids with the sizeable hydrophobic component is more significant than that of the n = 1 amino acid.This indicates that the adsorption on the solid wall can be regulated by adjusting the size of the hydrophobic component.
Next, we discuss adsorption geometry.We focus on the difference of the stable structure and the magnitude of the dipole moment.Figure 5 shows the probability distribution of two carbon atoms.Figure 5a  On the other hand, for D = 2 eÅ, the carbon atoms are more than about 2 Å away from the solid wall, indicating that the molecule is not adsorbed on the solid wall.We also show the schematic diagram of the adsorption structure at n = 1 in Fig. 6. Figure 6a indicates that the molecule is parallel to the solid wall (D = 0 eÅ), and Fig. 6b indicates that the molecule is perpendicular to the solid wall (D = 2 eÅ).As shown in Fig. 6a, when the dipole moment of the solid wall is zero, because the molecule is adsorbed on the solid wall via the non-Coulombic interaction, atoms that compose the molecule are adsorbed in a state where the distance between them and the solid wall becomes small.However, in the case of the D = 2 eÅ, the dipole interacts strongly with charged atoms such as oxygen in water and nitrogen in the molecule.As a result, carbon atoms, which have fewer charges, are inhibited by water to close the solid wall.This fact indicates that the adsorption of amino acids on solid walls in water is likely to be determined by the magnitude of the interaction between the solid surface and water molecules and charged sites such as nitrogen atoms, i.e., the size of the surface dipole, and the length of the carbon chain with which these interactions are small.

Conclusions
We focused on the effect of hydrophobic groups in amino acid molecules to obtain fundamental insight into modulating the peptide binding affinity to solid walls.We modeled amino acids with different-sized hydrophobic groups based on arginine, a polar amino acid with a high affinity for inorganic surfaces.To investigate the effect of the difference of the surface dipole on the adsorption free energy, we simulated a solid wall with a downward dipole moment on the surface.We performed molecular dynamics simulations to evaluate the change in the adsorption state of amino acids and the free energy due to the difference in the dipole moment on the solid wall.As the dipole moment of the solid surface was increased, the free energy of the amino acid adsorption decreased regardless of the size of the hydrophobic group.Still, the increasing rate of the free energy of the n = 1 amino acid was more significant than that of the n = 16 amino acid.As a result, when the magnitude of the dipole moment is greater than 1 eÅ, the free energy of the amino acid with a large hydrophobic group will be smaller than that of an amino acid with a small hydrophobic group.This result suggests that the adsorption state may be controlled by the size of the hydrophobic group.Next, we focused on the adsorption geometry of the amino acid.In the case of n = 1, when D is smaller than 1 eÅ, the amino acid is adsorbed parallel to the solid wall.However, when D is higher than 1.5 eÅ, the amino acid is adsorbed perpendicular to the solid wall.This difference is caused by the Coulombic interaction between water molecules and the solid wall.This fact indicates that the adsorption of amino acids on solid walls in water is likely to be determined by the magnitude of the interaction between the solid surface and water molecules and charged sites such as nitrogen atoms, i.e., the size of the surface dipole, and the length of the carbon chain for which these interactions are small.

Fig. 1
Fig. 1 Chemical structures of molecules used in this study: a n = 1; b n = 16

Fig. 2
Fig. 2 Simulation systems and wall structures used in this study: a simulation system; b reaction pathway

Fig. 3 16 Fig. 4 Fig. 5
Fig. 3 Free energy diagram along the reaction path: a n = 1; b n = 16 Figure4shows the magnitude of the free energy of the adsorbed state at each dipole for the amino acid with n = 1 and n = 16.When the dipole is 0 eÅ, the adsorption energy increases in proportion to the number of carbons in the virtual molecule.However, as the dipole increases, the magnitude of the adsorption free energy of the virtual molecule with n = 16 becomes smaller than that of the amino acids with n = 1.This indicates that the decrease in the magnitude of the free energy is dependent on the size of the hydrophobic component of the amino acid.However, the rate of increase in adsorption free energy of n = 16 amino acids with the sizeable hydrophobic component is more significant than that of the n = 1 amino acid.This indicates that the adsorption on the solid wall can be regulated by adjusting the size of the hydrophobic component.Next, we discuss adsorption geometry.We focus on the difference of the stable structure and the magnitude of the dipole moment.Figure5shows the probability distribution of two carbon atoms.Figure5aindicates results of n = 1, and Fig. 5b indicates results of n = 16.We defined the distance between carbon atom C 1 at the bonded end of the side chain of arginine and the solid wall and the distance between the free terminus carbon atom C 2 at the end of the hydrophobic component of the amino acid and the solid wall as parameters as shown in Fig. 1.The horizontal axis shows the parameters defined above and the vertical axis represents the probability distribution.Purple lines indicate results of C 1 and red lines indicate results of C 2 .Moreover, solid lines indicate results of D = 0 eÅ and dashed lines indicate results of D = 2 eÅ.In the case of n = 1, comparing the case of D = 0 eÅ with the case of D = 2 eÅ, we can see that the position of C 2 does not change, but the position of C 1 differs significantly.This indicates that when D is equal to 0 eÅ, the molecule is parallel to the solid wall, while when D is equal to 2 eÅ, the molecule is perpendicular to the solid wall.In

Fig. 6
Fig. 6 Schematic illustration of the adsorbed amino acid on the solid wall: a stable structure for n = 1, D = 0 eÅ; b local minimum structure for n = 1, D = 2 eÅ