Self-Assembled Monolayers of an Azobenzene Derivative on Silica

Nov 23, 2015 - The capability of the photoresponsive isomerization of azobenzene derivatives in self-assembled monolayer (SAM) surfaces to control pro...
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Self-Assembled Monolayers of an Azobenzene Derivative on Silica and Their Interactions with Lysozyme Tao Wei,*,† Md. Symon Jahan Sajib,† Mohammadreza Samieegohar,† Heng Ma,† and Katherine Shing*,‡ †

Dan F. Smith Department of Chemical Engineering, Lamar University, Beaumont, Texas 77710, United States Mork Family Department of Chemical Engineering and Materials Science, University of Southern California, Los Angeles, California 90089, United States

‡

ABSTRACT: The capability of the photoresponsive isomerization of azobenzene derivatives in self-assembled monolayer (SAM) surfaces to control protein adsorption behavior has very promising applications in antifouling materials and biotechnology. In this study, we performed an atomistic molecular dynamics (MD) simulation in combination with free-energy calculations to study the morphology of azobenzene-terminated SAMs (Azo-SAMs) grafted on a silica substrate and their interactions with lysozyme. Results show that the Azo-SAM surface morphology and the terminal benzene rings’ packing are highly correlated with the surface density and the isomer state. Higher surface coverage and the trans-isomer state lead to a more ordered polycrystalline backbone as well as more ordered local packing of benzene rings. On the Azo-SAM surface, water retains a high interfacial diffusivity, whereas the adsorbed lysozyme is found to have extremely low mobility but a relative stable secondary structure. The moderate desorption free energy (∼60 kT) from the trans-Azo-SAM surface was estimated by using both the nonequilibrium-theorem-based Jarzynski’s equality and equilibrium umbrella sampling.

1. INTRODUCTION Azobenzene (C6H5NNH5C6) trans- and cis- reversible isomerization can be controlled by alternative photoillumination between ultraviolet and (blue) visible light or external (thermal or electric) stimuli.1,2 The stimuli-responsive reversible switching of azobezene enables the conversion of the external energy input (light, thermal or electric energy) to mechanical work at the molecular level. This unique property of azobenzene derivatives has attracted extensive studies on the fabrication of molecular devices with a photomechanical effect and specific molecular structures. Examples include high-density data storage,3,4 liquid crystals,5,6 molecular machines,7 and switchable biomaterials.8 Published experimental studies revealed that the yield of photoisomerization is much higher on SAM surfaces3,4 than in the solution phase. In addition, the cis-isomer has a longer lifetime in SAMs than in bulk solution.3,4 The self-assembling monolayers of azobenzene derivatives (Azo-SAMs) can form highly ordered crystallized domain structures, leading to cooperative lightinduced movements.3,4 Experimental studies rationalized that intermolecular interactions from adjacent neighbors play a key role in the surface supermolecular packing structure and collective motions.3,4 Tien et al. explored the collective switching process of the terminal-thiol-functionalized azobiphenyl film tethered on a Au(111) substrate at different surface coverages by incorporating a NN twisting-angle-dependent random switching function for trans and cis-isomers9,10 in their molecular dynamics simulations. However, the azo-moieties’ interactions and packing structures in SAMs have not been sufficiently explored at the molecular level. © 2015 American Chemical Society

Despite intensive interest in the applications of Azo-SAMs in biological systems1,2,11 for decades in areas such as the control of DNA hybridization12,13 and drug release in hydrogels,2,14 the interactions between proteins and azobenzene derivatives are still not well understood. A wide range of behavior has been reported. For instance, recent experiments15 on poly(ether sulfone) (PES) membranes terminated with azobenzene derivatives show that azo-molecules have moderate antibiofouling functionalities (e.g., resistant to protein adsorption). On the other hand, reversible protein adsorption was achieved on films made from photoazobezene−SiO2 nanoparticle composites where the wettability changes16 with the isomer state conversion. Also, in contrast to the antibiofouling functionality, conformationally flexible azo-polymers have been reported to immobilize biomolecules (such as immunoglobulin G (IgG), bacterial protease, and F-actin aggregates) without losing their bioactivity by deforming the surface along the contour of the biomolecule under photoirradiation with blue-wavelength light.17−21 Understanding protein adsorption behavior and protein− surface interactions is key to the development of biocompatible materials22 and biotechnologies such as protein chips,23 molecular printing,17 drug delivery,22 and biofuel cells.24 Previous experimental and theoretical studies demonstrated that protein adsorption behavior is affected by a combination of many factors, Received: September 26, 2015 Revised: November 16, 2015 Published: November 23, 2015 13543

DOI: 10.1021/acs.langmuir.5b03603 Langmuir 2015, 31, 13543−13552

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Langmuir such as the surface charge distribution,25 morphology,26,27 roughness,28 surface tension,29 buffer ions,30 and protein surface heterogeneity in charge and hydrophobicity.31,32 Among those factors, electrostatic interactions25,29 and water-mediated hydrophobic and hydration forces29,33 have been found to be most important. Our recent study29 illustrated that the dehydration of a hydrophobic surface provides a driving force for protein adsorption, whereas protein dehydration serves as a barrier force. Because of the possible strong driving forces as well as the slow rotational motion near the surface, a protein can display various adsorption orientations of local minimum energy.34 The structure and rigidity of the surface also strongly affect protein diffusivity. On rigid and hydrophobic surfaces such as graphene29 and crystallized polyethylene,26 protein is found to have high mobility close to that in bulk diffusion, during its initial interactions with the surface. In this work, we first employed molecular dynamics simulations (MD) to examine the structures and interactions of alkylazobenzene derivative SAM surfaces on a silica substrate with different surface coverage densities and the isomer states (trans- vs cis-). We investigated the magnitude and range of anisotropic interactions of the π−π stacked intermolecular benzene rings, which are known to be responsible for collective movement. We further explored the interactions between a small protein (lysozyme) and the Azo-SAM surface by using a steered molecular dynamics (SMD)35 simulation combined with free-energy computations. Our results yield insights into the azobenzene moieties’ molecular-scale packing structure and provide a quantification of the interactions between protein and azobenzene derivatives via the computation of desorption free energies. A fundamental understanding of protein adsorption behavior and protein−surface interactions will pave the way for more applications of azobenzene polymers in biological systems and biotechnology in the future. The rest of the article is organized as follows: section 2 provides details of the implementation of molecular dynamics simulations and the binding free energy computations; section 3 discusses our simulation results; and the article then concludes with a summary in section 4.

Figure 1. Unit cells of α-cristobalite (101) surface modified by azobenzene chains (from left to right: trans-isomer of 50% coverage (Trans50%), cis-isomer of 50% coverage (Cis50%), and trans-isomer of 25% coverage (Trans25%)).

Nonbonded interactions between a protein and the surface consist of Lennard-Jones (LJ) and coulombic interactions. The LJ potential parameters of Si and O atoms for the α-cristobalite (101) surface and their partial charges were taken from the literature.37,38 The force field potential parameters of azobenzene groups were also adopted from literature reports.39,40 The OPLSAA force field41 was used for the alkane chain link and lysozyme. For the water model, we chose TIP4P.42 The particle mesh Ewald (PME) summation43 was utilized to calculate the longrange electrostatic interactions, with a cutoff distance of 1.2 nm for the separation of the direct and reciprocal space. A spherical cutoff at 1.2 nm was imposed on LJ interactions. The long-range dispersion effect on energy and pressure was also included. For the preparation of the lysozyme initial structure, we used a crystal structure (1HWA) from the Protein Data Bank (http:// www.ncbi.nlm.nih.gov/). Amino acids histidine (His), arginine (Arg), and lysine (Lys) were protonated, whereas glutamate (Glu) and aspartate (Asp) were deprotonated, resulting in a net charge of +8e that corresponds to the experimental conditions at pH 7. The N and C termini were capped uncharged. The simulation system is shown in Figure 2 where lysozyme was initially placed far away from the surface (minimum protein− surface distance ≈ 1.2 nm) with negligible surface−protein interactions (Eps ≈ 0 kT). Any water molecule within 0.3 nm of the lysozyme was removed. The system was neutralized by adding 8 Cl− ions. The box size for both Trans50% (74 067 atoms) and Cis50% (72 489 total atoms) is 8.547 × 7.965 × 12.500 nm3, and for Trans25% (70 914 atoms), the size is 8.547 × 7.965 × 12.000 nm3. A periodic boundary condition was applied to the system only along the X and Y directions. Therefore, the interaction between the simulation box and its periodic images along the Z direction was effectively removed. It is noteworthy that special care needs to be taken in the surface modeling in MD simulations to avoid introducing an artifact surface dipole moment and electric field44 due to the 3D periodicity of the simulation box. The design of the substrate surface in our simulations eliminated this issue and yielded realistic results for water and protein interfacial behavior on the surface. Water molecules and lysozyme were kept inside the box by inserting a restraining layer of repulsive Lennard-Jones artificial atoms at fixed positions sufficiently far (8.2 nm) from the top of

2. METHODS Parallel MD was performed with the Gromacs (version 4.6.5) simulation package36 supported with MPI on supercomputer clusters in the NVT ensemble. A total of about 1.0 million CPU hours were consumed for this whole project, including the simulations of SAM surfaces, protein adsorption, and desorption free energy computations. 2.1. Molecular Dynamics Simulations. The dynamic equations were integrated by using the leapfrog algorithm with a time step of 1 fs. The system was maintained at a temperature of 300 K with a Nosé−Hoover thermostat. Each azobenzene group was connected to a hydroxylated α-cristobalite (101) surface Si atom with an alkyl spacer, −(CH2)20, as shown in Figure 1. The substrate surface was constructed by cleaving an α-cristobalite unit cell along the (101) direction with a thickness of 1.624 nm and then periodically expanded. The positions of atoms in the bottom layer of the α-cristobalite (101) surface were fixed, and others were completely mobile during the simulation. Our study focused on three SAM surfaces: trans-Azo of 50% coverage (Trans50%), cis-Azo of 50% coverage (Cis50%), and trans-Azo of 25% coverage (Trans25%). Here, 50% coverage means that 50% of available surface Si atoms are connected to a grafted chain (Figure 1). For both Trans50% and Cis50%, the surface density is 2.35 chain/nm2, whereas Trans25% corresponds to a surface density of 1.18 chain/nm2. 13544

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given temperature. If the pulling process is reversible, then W(z) can be evaluated by W (z ) =

the Azo-SAM surface so that the protein can rotate inside the cell without being affected by the top restraining layer. A vacuum slab of 2.0 nm thickness was also inserted at the bottom of the water box. The lysozyme adsorption simulations were started with the relaxation of water molecules through energy minimization and a short run of MD (30 ns) at 300 K, keeping the lysozyme fixed at its original position. Then production runs were carried out in the NVT ensemble at 300 K using a 1 fs time step without any constraint of lysozyme atoms for 300 ns. 2.2. Desorption Free Energy Calculation. The protein desorption free energy (ΔA) is defined as the difference in Helmholtz free energy between the initial state (i.e., protein on the SAMs (Asurface)) and the final state (i.e., protein in the bulk water bulk phase (Abulk)):

f (z ) d z

ΔA ≈ ⟨W ⟩ −

(4)

β (⟨W 2⟩ − ⟨W ⟩2 ) 2

(5)

In this study, we approximated ⟨W⟩ by the average of N pulling experiments. Therefore, eq 5 becomes 1 ΔA ≈ N

N

β ∑ Wi − 2(N − 1) i=1

⎛ 1 ∑ ⎜⎜Wi − N i=1 ⎝ N

⎞2 ∑ Wi ⎟⎟ ⎠ i=1 N

(6)

(1)

A simpler approximation of eq 5 is to retain only the leading term:

In this work, ΔA was calculated using two complementary methods. The first is a combination of nonequilibrium steered molecular dynamics (SMD)35 simulations and free-energy computation based on the Jarzynski equality45 as follows 1 ΔA = − ln⟨exp( −βW )⟩ β (2)

ΔA ≈ ⟨W ⟩ ≈

1 N

N

∑ Wi i=1

(7)

The result based on eq 7 is designated as the mean work (MW) estimate. In terms of Wi, the full Jarzynski equality (JE) in eq 2 is expressed as

where β is equal to 1/(kBT), kB is the Boltzmann constant, and T is temperature. W is the work (regardless of reversibility), and the brackets denote an ensemble average with respect to the initial state overall processes (again, regardless of reversibility). The second method is based on the equilibrium approach of umbrella sampling.46 In SMD, the lysozyme was detached from the surface at constant velocity, v, along the direction perpendicular to the Azo-SAM surface (i.e., the Z direction). The external pulling forces, f(t), at the protein’s center of mass (COM) is given by the following equation f (t ) = k[(Zcom(0) + vt ) − Zcom(t )]

z

Appropriate choices of the force constant (k) and the pulling velocity (v) are critical to the ΔA estimation.47,48 To minimize the fluctuations along different trajectories, a finite-size force constant is needed;48 however, if the force constant is too large, then the free-energy landscape cannot be scanned with enough resolution. A lower pulling velocity (v) relieves the hysteresis effect49 and provides an estimate of the nonequilibrium force closer to the equilibrium value50 but at the expense of increased computation time. On the basis of the previous work of Hung et al.,50 we performed a systematic investigation of a range of values of v and k. Balancing the computational load and signal resolution, we chose k = 6000 kJ mol−1 Å−2 and v = 0.25 nm/ns. In principle, the Jarzynski equality as follows yields ΔA directly, provided that the sampling of the nonequilibrium work, W, is sufficiently complete. However, direct sampling of W generally suffers from slow convergence. Under certain conditions or for fortuitous reasons, a Taylor expansion of eq 2 up to second order as the fluctuation−dissipation (FD) estimation (eq 5) may yield better results than the full expression when the sampling for W is incomplete.

Figure 2. Snapshot of the initial configuration of lysozyme adsorption on Trans50% SAMs. (Note that the Z axis is normal to the surface.)

ΔA = Abulk − A surface

∫0

ΔA ≈

−1 1 ln[ β N

N

∑ exp(−βWi )] i=1

(8)

The results for the three nonequilibrium estimation methods (MW, FD, and JE) were based on N = 36 pulling experiments. In the equilibrium approach, we computed ΔA by employing the method of weighted histogram analysis (WHAM)51 to estimate the potential of mean force (PMF) using the probability histograms generated from a series of umbrella sampling simulations. Umbrella sampling was implemented by dividing the space above the protein adsorption position into 37 windows with a uniform gap distance of 0.5 Å along the Z axis. In each umbrella simulation window, an equilibrium MD simulation was conducted for 10 ns of relaxation. During the relaxation period, protein was constrained to its original place in the center of a window with a harmonic potential represented by

(3)

where k is the force constant, v is the pulling velocity, and Zcom(t) and Zcom(0) are z-axis coordinates of the protein’s COM at times t and t = 0, respectively. Different final configurations of 300 ns of equilibrium protein adsorption MD simulations were used as the initial configurations for the pulling simulations. Also, different random seeds were adopted to generate various initial velocities based on the Boltzmann distribution at the

ui(Zi) = 13545

1 k′(Zcom − Zi)2 2

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Figure 3. (a) Snapshots of the equilibrated solvated Trans50% SAM surface on the X−Z plane (Z axis perpendicular to the surface) and (b) the corresponding density profile for the alkyl linkage, two azobenzene benzene rings (Azo1 and Azo2), and water; Z = 0 corresponds to the bottom of the solid substrate.

Figure 4. (a) Snapshots of the equilibrated solvated Cis50% SAM surface on the X−Z plane (Z axis perpendicular to the surface) and (b) the corresponding density profile for the alkyl linkage, two azobenzene benzene rings (Azo1 and Azo2), and water.

where k′ is the force constant, Zcom is the Z coordinate of the protein’s center of the mass, Zi is the center position of the ith window, and ui (Zi) is the corresponding harmonic potential. We chose k′ = 1400 kJ mol−1 Å−2, which allows for fluctuations of an appropriate magnitude to ensure sufficient overlap and hence enough sampling in each window. A total of 37 independent sets of MD trajectories were created in the umbrella sampling. The biased probabilities obtained from the analysis of umbrella sampling trajectories were then properly renormalized by using the well-established protocol of WHAM to construct the PMF profile51 and estimate the protein desorption free energy.

interactions of the substrate silica surface from the protein. Because the azobenzene group is at the end of each chain, terminal benzene ring Azo1 is exposed to the aqueous environment. Water permeates the Azo-SAM film only superficially, barely penetrating beyond the position of the second benzene ring (Azo2). This implies that the Azo-SAM layer is extremely hydrophobic. For comparison, we also simulated the Azo-SAM surface where the azo group is in the cis-isomer state in water at the same high surface coverage density of 2.35 chain/nm2. The profiles in Figure 4(a) show that the morphology of cis-Azo-SAM is very similar to that of trans-Azo-SAM: alkyl chains tilting on the silica surface to form an ordered polycrystalline structure. The density profiles in Figure 4(b) show that the cis-azobenzene groups constitute the outermost layer of the film in contact with bulk water. The density peak of the terminal benzene ring (Azo1) is lower and broader in cis-Azo-SAM than in trans-Azo-SAM. A very slight decrease is observed in the film thickness (1.69 vs 1.71 nm), which is expected because of the more extended configuration of the trans- form of the azo group. The very limited extent of water penetration indicates that cis-Azo-SAM is equally hydrophobic. To examine the effect of surface density, we reduced the number of chains by half for the trans-Azo-SAM surface. At this low surface coverage (1.18 chain/nm2), the chains adopted a disordered packing structure (Figure 5(a)), with local segregation resulting in the formation of cavities (Figure 5(b)). Consequently, water is able to permeate the cavities and wet the substrate. (See the water density profile in Figure 5(c), with a peak very near the substrate surface.) In contrast to the highsurface-density case where the two benzene rings (Azo1 and Azo2) are exclusively located near the surface, these are now

3. RESULTS AND DISCUSSION 3.1. Azo-SAM Surface. trans-Azobenzene is thermodynamically more stable than cis-azobenzene, dominating the equilibrium states. We compared the packing structures at different isomer states and surface coverage densities. The solvated structure of the Trans50% SAM surface with a high surface coverage density (2.35 chain/nm2) was equilibrated for 100 ns in aqueous solution after relaxation in vacuum for 50 ns. The alkyl chains form ordered polycrystalline packing structures with a tilt on the silica surface as shown in Figure 3(a). Similar highly ordered structures were also observed in an experimental study3 of thiolated azobiphenyl SAMs on the Au surface with a surface coverage density of 3.46 chain/nm2. Figure 3(b) compares the density distribution of the alkyl spacer, two benzene rings (Azo1 and Azo2), and water in the simulated Azo-SAM. The Azo-SAM film thickness is estimated by using the onset position of the alkyl chain density profile and the peak position of the terminal benzene rings (Azo1 and Azo2). Azo1 is the outermost terminal group of a chain (Figure 1). For the Trans50% Azo-SAM, the thickness is around 1.71 nm, which can effectively screen the 13546

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Figure 5. Snapshots of the equilibrated solvated Trans25% SAM surface on the X−Z plane (Z axis perpendicular to the surface) ((a) top view and (b) side view) and (c) density profiles for the alkyl linkage, two azobenzene benzene rings (Azo1 and Azo2), and water.

indicates that π−π stacking is strongly favored. In Figure 6(d), the high-surface-density trans-Azo-SAM profile shows a much slower decay compared to the other two cases with a nonrandom distribution persisting beyond 2.5 nm. Interestingly, the highdensity cis- curve and the low-density trans-SAM curves show high degrees of resemblance, probably indicating that both are less able to enforce order than the high-density trans- case. 3.2. Water Diffusion in the Azo-SAM Surface. Water diffusive behavior at the Azo-SAM interface was monitored by solving the diffusion equation subject to absorbing boundary conditions with the MD trajectories.55 The boundaries were selected at the SAM surface interface area, where water density varies from 90% of the bulk water density to 0% for the highdensity Azo-SAM layers (3.2 nm < Z < 3.987 nm for Trans50% and 3.2 nm < Z < 3.992 nm for Cis50% in Figure 4). For the low-density Azo-SAM layer, the boundaries are 3.2 nm < Z < 3.503 nm in Figure 5, where the water density drops from 90% of the bulk value to about 20% of the bulk value. The diffusivity components (Dxx, Dyy, and Dzz) were calculated using the autocorrelation functions as follows

much more uniformly distributed throughout the surface layer as shown by the density profiles in Figure 5(c). According to the consistent criteria used to measure the film thickness, the Trans25% SAM thickness decreased to ∼1.29 nm as shown in Figure 5(c). Our results are consistent with numerous previous experimental and theoretical studies52−54 in revealing that the phase morphologies of SAMs are dependent on the surface coverage density. A recent simulation study9,10 also demonstrated the disordered packing of Azo-SAM at a low surface coverage density (1.73 chain/nm2) on the Au(111) substrate surface. A previous experimental (scanning tunneling microscopy (STM)) study of Azo-SAMs3 attributed the cooperative motion in these systems to the important role of benzene rings’ π−π interactions. In this work, we examine the packing of terminal benzene rings (Azo1). The snapshots in Figure 6(a−c) of the top view of the surface show that the terminal benzene rings of transAzo-SAM of high surface coverage (Trans50%) form a locally ordered packing structure. For trans-Azo-SAM of low coverage (Trans25%) and cis-Azo-SAM (Cis50%), benzene rings are more disordered. To quantify this, we use the order parameter, S, defined by

Dxx = limτ→∞

⟨Δx(τ )2 ⟩{a , b}

2

S(r ) =

3 cos (θ(r )) − 1 2

2τP(τ )

, with a similar equation for Dyy (11)

(10)

P(τ ) =

where r is the radial distribution distance of the terminal benzene rings (Azo1) and θ is the averaged angle defined with the normal vectors of benzene rings at r (Figure 6(d)). S = 1 corresponds to completely ordered packing, and S = 0 represents a random structure. For all three surfaces (Trans50%, Trans25%, and Cis50%), a strong and sharp peak was observed at around 0.34 nm, which matches the strong π−π stacking distance and

Dzz =

1 T

T

∑ t=1

N (t , t + τ ) N (t )

ln(L ·⟨Ψn(z(t ))ψn*(z(0))⟩) −

13547

(12)

2

( nLπ ) t

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Figure 6. Top views of the top layer of Azo-SAM ((a) Trans50%, (b) Trans25%, and (c) Cis50%) and (d) order parameter S as a function of radial distance r.

Ψn(z) =

⎛ nπ (z − a) ⎞ 2/L sin⎜ ⎟ ⎝ ⎠ L

enforce π−π stacking, resulting in a greater resistance to water mobility. At the low-density trans-Azo-SAM/water interface, water diffusion coefficients are much larger, approaching the bulk value, despite the deep penetration of water into the Azo-SAM layer. This is most likely due to the presence of cavities inside the Azo-SAM (Figure 5(a)). On the Trans25% surface, both +xx and +yy are observed to be slightly larger than +zz . 3.3. Lysozyme Adsorption Behavior and Lysozyme− Azo-SAM Interactions. Azobenzene-terminated SAMs have many potential applications where the manipulation of protein adsorption behavior15−21 is needed. Desorption free energy is a central property governing adsorption behavior. Our recent study56 of lipid A bilayers showed consistently that the water permeation free energy is highly dependent on the packing morphology and the flexibility of the hydrocarbon acyl chains. In this study, we employed full-atom MD simulations in combination with free-energy computation to investigate the adsorption of lysozyme on the high-density trans-Azo-SAM surface (Trans50%). Two sets of computations were performed. In the first set of calculations, the lysozyme adsorption behavior on Azo-SAM was monitored with MD simulations. The lysozyme secondary structure and diffusion coefficient were calculated. In the second set of calculations, the lysozyme desorption free energy (from Azo-SAM) was estimated with SMD starting with the final configurations taken from the adsorption MD trajectory. 3.3.1. Lysozyme Adsorption on the trans-Azo-SAM Surface. During the adsorption simulation, the lysozyme molecule was initially away from the surface with negligible protein−surface interactions. The lysozyme molecule diffused toward the surface

(14)

where a and b are the boundary positions; L (= b − a) is the water slab thickness; T is the total number of time steps averaged over; N(t) represents the total number of water molecules over time (t); and τ is the autocorrelation function time step. Table 1 lists Table 1. Water Interfacial Diffusion Coefficients (10−5 cm2/s) Trans50% Cis50% Trans25%

+xx

+yy

+zz

0.788 1.96 3.41

1.07 1.99 3.60

0.487 0.672 1.65

results for water interfacial diffusion coefficient components (+xx , +yy , and +zz ) for the surfaces of Trans50%, Cis50%, and Trans25%. At the azobenzene−water interface, water molecules were observed to have relatively large mobility (+xx and +yy ), within an order of magnitude of the bulk value (5.0 × 10−5 cm2/s), estimated for the TIP4P water model. The relatively high water interfacial diffusivities also imply that the terminal azobenzene groups did not substantially affect the water mobility despite the compact packing of the Azo-SAM surface. At the high-density trans-Azo-SAM/water interface, water diffusion coefficients exhibit some anisotropic behavior in the X−Y plane (i.e., +yy > +xx ). This observation is consistent with the alkylbackbone-ordered polycrystalline structure. Water diffusion coefficients for trans-Azo-SAM are lower than for cis-Azo-SAM, presumably because the trans- conformation is more able to 13548

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obtained by the four different estimation methods described in section 2.2. In Figure 8(b), the vertical axis shows ΔA as a function of the position of the lysozyme center of mass, Zcom. Here, ΔA corresponds to the free-energy change when the lysozyme desorbs from its equilibrium position at Zcom ≈ 3.7 nm to various larger values of Zcom. From the equilibrium estimation approach of umbrella sampling (US), ΔA is ∼60kT. Theoretically, the Jarzynski equality (JE) requires infinite trajectory sampling.45 As expected from the second law of thermodynamics, although the nonequilibrium approaches yields a straightforward estimation of ΔA based on a limited number of trajectory samples, regardless of the estimation methods (eq 6, 7, or 8), in general it overestimates ΔA compared to the conventional equilibrium technique of umbrella sampling, provided, of course, that the latter is adequately sampled. Indeed, Figure 8(b) shows that the three nonequilibrium methods (MW, FD, and JE) yield ΔA values higher than those corresponding to umbrella sampling. Although it is not possible to definitely state that the US results are superior to the other estimates, we at least observe that the US curve exhibits a realistic plateau at Zcom > 5.2 nm, where the lysozyme is sufficiently far from the surface that any further increase in Zcom should not incur an additional free-energy penalty. We note that none of the three nonequilibrium estimates exhibit a similar plateau, implying that with N = 36 and the parameters for k and v chosen here that the nonequilibrium techniques yield insufficient sampling for calculating ΔA. To obtain more insight into the protein−surface interactions, we analyzed the averaged Lennard-Jones (LJ), electrostatics (Elect), and the sum of both LJ and Elect (Total) potential energies between protein and the SAM surface by summing over all configurations in each of the different umbrella sampling windows. As shown in Figure 8(c), the total averaged protein− surface interaction energy for protein desorption is around 110kT when the lysozyme molecule is near the surface, gradually decreasing to zero when the lysozyme is far from the surface. The protein−surface LJ interaction is dominant and attractive, whereas the protein−surface electrostatic interaction is repulsive. It should be noted that during the umbrella sampling simulations the protein is relaxed in different windows of displacement distance by constraining the protein center of mass with weak harmonic potentials, allowing for enough fluctuations to yield probabilities overlapping in the histogram. The large fluctuations in the protein−surface interaction terms observed, as shown in Figure 8(c), are mainly due to protein rotations around its center of mass. We further computed the mean force acting on the lysozyme molecule by taking the negative derivative of the desorption free energy with respect to the displacement distance of the protein’s center of mass

Figure 7. Secondary structural evolution of the adsorbed lysozyme on the Trans50% AzoSAM surface. Secondary structures were identified by using the method of structural identification (STRIDE).57

and became attached in less than 5 ns. In Figure 7, we show the secondary structural evolution of the adsorbed lysozyme for a period of 300 ns. Only small changes in the secondary structures were observed, in contrast to the dramatic structural loss when lysozyme adsorbed on the rigid crystalline polyethylene surface.26 This indicates that surface softness can contribute to the protein structural stability. This observation is consistent with previous experiments17,18,20 that showed that under the irradiation of blue light the photodeformable Azo-SAMs surface can effectively suppress the thermal motions of immobilized protein and greatly reduce the desorption rate without denaturing protein’s structure. The identification of an adsorbed protein precursor state on the substrate surface would be critical to biosensor surface design or bioseparation and theoretical modeling.58 In our simulation, we also calculated the lysozyme surface diffusivity (+ lat ) by monitoring the mean square displacement of the protein’s center of the mass (COM) on the X−Y plane as follows + lat = lim

Δt →∞

⟨[r(t + Δt ) − r(t )]2 ⟩ 4Δt

(15)

where r denotes the protein’s COM position vectors and t is time. The computed lysozyme surface diffusivity on the high-density trans-Azo-SAM is 2.42 × 10−9 cm2/s. This value is much lower than that in the bulk solution (5.84 × 10−6 cm2/s)59 and on a surface of graphene (1.8 × 10−5 cm2/s)29 and crystallized ethylene (0.029 × 10−6−4.1 × 10−6 cm2/s).26 3.3.2. Lysozyme Desorption Free Energy. It is worth noting that the protein desorption free energy (ΔA) is also a measure of the strength of protein−surface interactions during adsorption. In this work, the desorption free energy of lysozyme from transAzo-SAM was calculated using two complementary methods: (i) the nonequilibrium theorems based on the Jarzynski equality and (ii) the equilibrium approach of umbrella sampling combined with WHAM analysis. Starting from the final equilibrium configuration obtained after an adsorption simulation of 300 ns (shown in Figure 8(a)) for lysozyme on the Trans50% Azo-SAM surface, the lysozyme molecule was pulled away from the original adsorption position along the surface normal (Z axis) with external forces by subjecting the lysozyme to a biased harmonic potential. Because of overwhelming computational loads, only a limited number (36 here) of pulling experiments were performed in our nonequilibrium simulations. Figure 8(b) compares the ΔA profiles

F (z ) = −

∂A(z) ∂z

(16)

where ΔA(z) is from Figure 8(b). F(z) represents the overall effect of the interactions of the surface and the surrounding solution environment on the protein molecule. As Figure 9 shows, F(z) is large and repulsive at small values of Zcom when the lysozyme molecule is pressed against the surface (a). As Zcom increases, F(z) rapidly becomes attractive (see b−d). The rapid changes are likely attributable to surface hydration.29 However, understanding the quantitative relationship between protein adsorption and the hydration/dehydration of amorphous SAM surface by using general atomistic MD simulations is still an open question for us. Other alternative methods such as molecular 13549

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Figure 8. Lysozyme desorption: (a) snapshot of the protein equilibrium adsorption position after 300 ns, which serves as a starting configuration at Z ≈ 3.65 nm measured from the bottom of the solid substrate; (b) desorption free energy, ΔA, as a function of the displacement of the protein center of the mass, Zcom, estimated with average external pulling work (MW), the Jarzynski equality (JE), fluctuation−dissipation (FD), and umbrella sampling (US); (c) the averaged protein−surface interactions energy (Lennard-Jones (LJ), electrostatics (Elect), and the total (Total)) as a function of the displacement distance, Zcom.

Figure 9. Mean force (F) as a function of the displacement distance (Zcom) and the corresponding snapshots.

theory28 and the hybrid molecular mechanics/Poisson− Boltzmann surface area (MM/PBSA)29 combined with MD simulation could yield a detailed thermodynamic explanation. At large Zcom, F(z) approaches zero as expected. The fluctuations in F(z) from (b) to (g) can be attributed to lysozyme rotation, resulting in different residues/groups interacting with the surface.

4. CONCLUSIONS With a view to further applications of azobenzene SAM surfaces, particularly for biomaterials or biotechnology involving proteins, we performed atomistic MD simulations to investigate the surface morphology and water interfacial diffusivity. Moreover, we examined protein adsorption and desorption behaviors 13550

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by using MD simulation in combination with free-energy computation. Our results revealed that the ordering of terminal benzene rings of azo groups and the backbone packing are highly correlated with the chain surface coverage. More ordered and larger local packing structures regulated by the benzene rings’ π−π stacking are observed at higher packing density, especially for the trans-isomer state. Such packing significantly limits water penetration; however, lateral water diffusion in the narrow penetration layer is not significantly impeded, implying that the top Azo-SAM surface is relatively soft and mobile. At the lower surface, the chain density on the SAM surface becomes thinner and chains segregate on the silica substrate surface and form cavities, permitting much greater water penetration as well as higher water mobility. Our results also demonstrate that on the trans-Azo-SAM of high surface coverage, lysozyme displays stable secondary structure and low diffusivity, very likely because of the surface softness. Our free-energy computation estimates that lysozyme has a moderate desorption free energy (∼60kT) on the high-surface-density trans-Azo-SAM surface. Lysozyme desorption free energy computations using several different estimators based on Jarzynski’s equality were compared with umbrella sampling results. For the systems studied here, the conventional equilibrium umbrella sampling method performed better than did the nonequilibrium Jarzynski equality-based estimators.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS T.W. is grateful for support from the Extreme Science and Engineering Discovery Environment program from the National Science Foundation (XSEDE/NSF), the Oak Ridge National Laboratory (OLCF)/Director Discretion Project, the Argonne Leadership Computing Facility, and the Research Enhanced Grant (REG) fund from Lamar University.

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REFERENCES

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