Protein Diffusion and Long-Term Adsorption States at Charged Solid

Oct 12, 2012 - In Table 1, we list the transition time scales for various activation energy at 300 K, ..... Movies showing protein desorption and diff...
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Protein Diffusion and Long-Term Adsorption States at Charged Solid Surfaces Karina Kubiak-Ossowska†,‡ and Paul A. Mulheran*,† †

Department of Chemical and Process Engineering, University of Strathclyde, James Weir Building, 75 Montrose Street, Glasgow G1 1XJ, United Kingdom ‡ Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, ul. Grudziadzka 5/7, 87-100 Torun, Poland S Supporting Information *

ABSTRACT: The diffusion pathways of lysozyme adsorbed to a model charged ionic surface are studied using fully atomistic steered molecular dynamics simulation. The simulations start from existing protein adsorption trajectories, where it has been found that one particular residue, Arg128 at the N,C-terminal face, plays a crucial role in anchoring the lysozyme to the surface [Langmuir 2010, 26, 15954−15965]. We first investigate the desorption pathway for the protein by pulling the Arg128 side chain away from the surface in the normal direction, and its subsequent readsorption, before studying diffusion pathways by pulling the Arg128 side chain parallel to the surface. We find that the orientation of this side chain plays a decisive role in the diffusion process. Initially, it is oriented normal to the surface, aligning in the electrostatic field of the surface during the adsorption process, but after resorption it lies parallel to the surface, being unable to return to its original orientation due to geometric constraints arising from structured water layers at the surface. Diffusion from this alternative adsorption state has a lower energy barrier of ∼0.9 eV, associated with breaking hydrogen bonds along the pathway, in reasonable agreement with the barrier inferred from previous experimental observation of lysozyme surface clustering. These results show the importance of studying protein diffusion alongside adsorption to gain full insight into the formation of protein clusters and films, essential steps in the future development of functionalized surfaces.

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INTRODUCTION How do adsorbed proteins diffuse at an ionic surface? Atomic force microscopy experiments reveal that adsorbed protein is clustered together as a result of its surface diffusion.1−3 Indeed, in a recent study one of us showed that such images can be interpreted using Monte Carlo simulation of the clustering process.4 Careful statistical analysis showed that in the case of hen egg-white lysozyme (HEWL) adsorbed onto mica the protein clusters themselves are mobile on the surface, with diffusivity varying inversely to cluster size.5 Furthermore, the spacing of the clusters is consistent with the low monomer diffusion rate of ∼10−15 cm2/s, so that cluster size can be controlled by protein deposition rate. However, detailed molecular-level understanding into how the protein diffusion takes place is lacking, and it is the purpose of this paper to provide this for the first time. While we focus on the specifics of adsorbed lysozyme diffusing across a model charged ionic surface, these insights significantly advance our understanding of protein film growth and help guide future work in the field of surface functionalization. Numerous detailed questions about particular mechanisms are extremely difficult to answer using only experimental studies; some processes are too fast to monitor in experiment, while other effects are simply too subtle to © 2012 American Chemical Society

detect. Therefore, the importance of theoretical investigations of various systems, including biomolecules, has been increasing dramatically. Provided the models reliably reproduce observable aspects, they can be used to develop insight into how and why the molecular level processes occur. Elucidation of each particular problem gives some information to be used to generalize our understanding of nature. Therefore, case studies on model systems, like the HEWL adsorption on an ionic surface investigated here, have great potential to widen our understanding of generic properties of adsorption, desorption, and diffusion of hard proteins on charged, hydrophilic surfaces. Protein interactions with surfaces are essential for the application of many medical and technological materials,6 and significant efforts have been made to elucidate protein adsorption on various surfaces. Both experimental7−12 and theoretical studies13−20 agree that the adsorption mechanism, list of crucial residues, driving force, and the range of conformational changes depend on the surface type. Despite the fact that protein interactions with nanoparticle surfaces are in general still poorly understood,21 it seems to be already clear Received: August 16, 2012 Revised: October 9, 2012 Published: October 12, 2012 15577

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that in the case of proteins and peptides adsorbing on silica-like surfaces that electrostatic attraction is a major driving force, with positively charged residues helping to anchor the proteins to the negatively charged surfaces.22 Recently, a few studies have attempted to elucidate protein diffusion mechanisms: Knight et al.23 reported results of singlemolecule fluorescence microscopy and coarse-grained MD simulations of membrane-bounded protein diffusion; Tsourkas and Raychaudhuri24 investigated diffusion of receptors and ligands bound to two opposing cell surfaces using Monte Carlo simulation; and Wang et al.25 studied small fluorescent molecule diffusion on hard, soft, and liquid surfaces using a fluorescence correlation spectroscopy method. In a recent series of papers, the present authors have studied the adsorption of HEWL at a model charged ionic surface that mimics mica using fully atomistic molecular dynamics (MD) simulation.14,26−29 The purpose of our model surface is to template structured water layers above the surface and to provide an electrostatic field, capturing key features of charged ionic surfaces. We found that the lysozyme adopts a preferred orientation above the surface, dictated by is dipole moment and the electrostatic field of the surface. Adsorption therefore takes place primarily at the N,C-terminal face, leaving the lysozyme’s active cleft exposed to solution allowing the possibility of it retaining its antibacterial functionality. Crucially, this predicted orientation agrees well with experimental evidence.30−33 Furthermore, we find that the protein is anchored to the surface by a few crucial residues, the most important of which is Arg128. The side chain of Arg128 is oriented normal to the surface as the protein approaches, again due to the electrostatic field, allowing it to penetrate the two surface water layers that form above the ionic surface. This adsorption state is shown in Figure 1 and referred to as state A in this paper. We were able to demonstrate that Arg128 plays a key role; when mutated to Gly128, so that its side chain is replaced by hydrogen, the adsorbed protein is seen to diffuse even on the 90 ns time scale of a traditional MD simulation.28 In contrast, the adsorbed native lysozyme does not diffuse on this time scale. We have also studied protein clustering, simulating multiple proteins adsorbing simultaneously at the surface.29 Again Arg128 plays an important role, since it is able to bind to other protein as well as to the surface. This competition between protein−surface and protein−protein interaction suggests that perhaps the Arg128 side-chain orientation is not as definite as the single adsorption simulations suggest. In fact, below we will find that this orientation perpendicular to the surface is rather special to the initial adsorption event and that in fact the long-term orientation, following surface diffusion, allows the side chain to lie parallel to the surface. Before proceeding further, it will be useful to remind ourselves of how Arrhenius rates vary with activation energy. While properly capturing the number of degrees of freedom in soft matter systems can be subtle, it is nevertheless instructive to consider the following. In Table 1, we list the transition time scales for various activation energy at 300 K, assuming a frequency prefactor of 1012−1013 s−1 commonly used for molecular processes. Processes associated with breaking hydrogen bonds, requiring ∼0.2 eV, happen on the nanosecond time scale and so are readily observed in traditional MD simulations. The experimental value of 10−15 cm2/s for the surface diffusion of lysozyme4,5 can be used to anticipate the size of the energy barrier the adsorbed protein must overcome. Given the protein size of ∼3 nm, we see that the protein must

Figure 1. Typical surface adsorbed state of lysozyme at the end of an adsorption simulation, denoted state A in this work. In state A the Arg128 side chain is almost perpendicular to the surface (the angle between the side chain and the surface φ ∼ 10°; see text for a definition of this angle) and penetrates the inner water layer. The protein surface is indicated as a ghost surface colored by name (C = cyan, H = white, N = blue, O = red, S = yellow), secondary structure is shown as a cartoon, and the main residues anchoring the protein on the surface are annotated and indicated by licorice. Two surface water layers are shown by CPK, and the bulk water is not shown for clarity. The protein termini are also annotated.

Table 1. Activation Energy and Associated Arrhenius Rates at 300 K, Assuming Frequency Prefactor 1012−1013 s−1 activation energy (eV)

Arrhenius rate

activation energy (eV)

Arrhenius rate

0.2 0.4 0.6 0.8

nanoseconds (10−9 s) microseconds (10−6 s) milliseconds (10−3 s) seconds (100 s)

1.0 1.2 1.4 1.6

hours (103 s) years (107 s) millenia (1010 s) million years (1013 s)

move this distance on a time scale of seconds, inferring an activation energy of ∼0.8 eV if the diffusive hops are 3 nm. In fact, below we will find a lower step size of 3 Å used in the protein’s diffusive hops, implying a time scale of 10−2 s and a slightly lower activation energy of 0.7 eV. Nevertheless, such a slow process is clearly unlikely to be directly observed in traditional 90 ns MD simulations of adsorbed lysozyme, and we need an alternative approach to uncover the molecular details of how the protein diffuses at the surface. To the best of our knowledge, protein diffusion mechanisms on a solid surface have not been studied so far using fully atomistic simulation. Nevertheless, a steered molecular dynamics (SMD) method which uses the external force(s) to speed up the process(es) have already proven its utility to study a wide range of problems.34−38 In particular, Koppen and Langel39 have simulated the adhesion forces of peptides on titania surfaces, interpreting the force−distance curves from SMD in terms of the energy barriers. We adopt this approach in this work, since SMD is readily available and easily interpreted and yet is sufficiently versatile to uncover the diffusion pathways and energy barriers we seek. 15578

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surface. However, with lower rates we find that the protein retains its shape, desorbing from the surface in its folded form with structural changes confined to the N,C-terminal face used in surface adsorption as further explained below. The same conclusion is reached when pulling the protein across the surface to investigate diffusion pathways as we also do below. Since we wish to understand the protein desorption and diffusion pathways accessible in the absence of an applied external force, we focus on these lower energy processes where the protein largely keeps is folded conformation intact. As a consequence of our preliminary investigations, we select a constant pulling velocity of 0.005 Å/ps to perform the detailed studies discussed below. This allows us to probe desorption and diffusion events using 10 ns simulations (or longer), since in this time the pulled species move about 5 nm, a distance greater than the size of the protein itself. In the majority of our simulations, we choose to pull the Cζ atom of Arg128 since this residue has been shown to be crucial in the adsorption and anchoring of the lysozyme to the charged ionic surface.14,26−29 We have performed a further three trajectories (see below) with other choices of pulled residues to verify the conclusions we draw from our majority choice of pulling the Cζ atom of Arg128. Desorption. In total, we have simulated 14 desorption trajectories with the constant pulling velocity, starting from two independent adsorbed states. These are state A shown in Figure 1 and state A1 in Figure 2, which is an alternative strongly

MATERIALS AND METHODS 40

All our simulations were performed using the NAMD 2.6 package with the Charmm27 force field and analyzed using VMD.41 The initial protein structure used for desorption and diffusion simulations were obtained from our previous 90 ns adsorption trajectories14,26−29 which used the lysozyme structure 1iee.pdb42 as input to the model. The adsorption simulations were prepared with one HEWL molecule located in close proximity to the model surface. The protein was neutralized by adding NaCl salt with ionic strength 0.02 M, and the system was solvated in a water box that extended at least 20 Å from any protein atom and 1 Å from any surface atom. The net charge of the system was equal to the surface charge. The surface was initially located about 8 Å away from the closest protein side chain (Arg128) and about 12 Å away from the protein backbone (Arg128). The total system contained ∼51 000 atoms. 90 ns MD adsorption trajectories in the NVT ensemble at 300 K, preceded by a minimization and equilibration period, were simulated. We used a time step of 2 fs, the SHAKE algorithm, and periodic boundary conditions (box size: 89 Å × 95 Å × 71 Å). Further details of the adsorption simulation protocol are given in refs 14 and 26−29. The surface (size 86.4 Å × 92.8 Å) was built from a square array of silicon and oxygen atoms located 1.6 Å away from each other, with charges +1.11 e and −0.66 e, respectively. Such partial charges produced a surface charge density σ = −0.217 e/Å2, which is almost equal to the nominal surface charge density of natural mica at pH = 7. For the Si atom, ε = −0.585 kcal/mol and 1/2Rmin was 2.15 Å, while for oxygen atoms these parameters were −0.152 kcal/mol and 1.77 Å. A single charged SiO2 surface was used and atom positions were fixed during all stages of the various MD simulations. In the desorption and diffusion SMD simulations discussed in this paper we have applied an external force both with constant-force pulling, and more frequently, with constant-velocity pulling to a previously adsorbed protein on the model surface. Other variables such as temperature, model surface parameters, the amount and type of counterions, the size of the water box, time step, etc., were not changed. The only difference between regular MD and SMD simulation was the presence of the external force. In various runs, the pulling force ranged from 100 pN (1.44 kcal/(mol Å)) to 800 pN (11.54 kcal/(mol Å)), while the pulling velocity ranged from 0.000364 to 5 Å/ps. We found that the best choice was constant-velocity pulling at 0.005 Å/ps (see the Results and Discussion section). Following the detailed description of the SMD approach in refs 34 and 37 in our simulations a dummy atom attached to a protein atom by a virtual spring is pulled. In simulations where the dummy atom is pulled at a constant velocity, the force in the spring is measured and used to calculate the energy released by transitions. Other simulation parameters were the same in all runs: the integration step was 2 fs, the harmonic constraint force constant was 4 kcal/(mol Å2) (equivalent to 278 pN/Å), and the cutoff distance for both van der Waals and Coulomb interactions was 12 Å. For ionizable residues, the most probable charge states at pH 7 were chosen. Our simulation protocol has been already validated, and it has been shown that the computationally more expensive smooth particle mesh Ewald (SPME) summation43 does not reveal different behavior.27 To get information about protein desorption, readsorption, and diffusion mechanisms a protocol of pulling, releasing, and pulling again in various directions was applied. In total, we have analyzed 71 trajectories with the length varying from 2 to 100 ns.

Figure 2. An alternative surface adsorbed state of lysozyme at the end of an adsorption simulation, denoted state A1 in this work. Here the Arg128 side chain is perpendicular to the surface (the angle between the side chain and the surface φ ∼ 10°) and penetrates the inner water layer as in state A, but in addition Arg125 interacts with the inner water layer. The coloring scheme is the same as in Figure 1.

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adsorbed state found in our adsorption simulations where Arg125 also interacts with the inner water layer alongside Arg128. The desorption mechanism observed is consistent for all these trajectories, and here we discuss in detail one exemplar which we denote trajectory T1. This trajectory started from the adsorbed lysozyme structure state A (see Figure 1) found at the end of a 90 ns adsorption simulation conducted at 300 K with ionic strength 0.02 M.14 Note that the lysozyme maintains its structure upon adsorption, using its N,C-terminal face to interact with the surface. The

RESULTS AND DISCUSSION Steered Molecular Dynamics Pulling Rate. We start our series of simulations with an investigation into the impact that various pulling rates, with either constant force or constant velocity, has on desorption processes. The simulations start with the lysozyme adsorbed in its most common conformation (state A) shown in Figure 1, which has been discussed in detail elsewhere.14,27 If the pulling force or speed is too high, the protein tends to unfold while remaining adsorbed to the 15579

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Figure 3. Alternative states of lysozyme interacting with the surface. In state A′, Arg128 lies parallel to the surface just above the inner water layer (φ ∼ 90°); in state B it lies just above the second water layer with φ ∼ 45°; and in state C Arg128 no longer interacts with the surface water layers (φ ∼ 135°). In state D the lysozyme is desorbed from the surface and the Arg128 side chain, φ ∼ 180°. The coloring scheme is the same as in Figure 1.

0.499 ns the side chain reoriented with respect to the surface and the angle φ ∼ 45°. This adsorbed conformation is shown in Figure 3, and for clarity in the following discussion we denote it as state B. At 0.86 ns the Arg128 side chain moved away from the outer water layer although some interactions with those water molecules are visible until 1.11 ns. After this time, Arg128 completely lost contact with the outer water layer, and we denote this adsorbed state C (see Figure 3). Because of pulling away from the surface the side chain−surface angle φ ∼ 135°. The closest spatial neighbor of Arg128 involved in the surface adsorption is Arg14, and this residue desorbed after 4.478 ns. Arg5 then desorbed in two steps, first from the inner water layer and then from the outer one, this process completing by 5 ns. After this only Lys1 anchored the protein to the surface. Subsequently, the protein rotated and moved away from the surface, with the N-terminus detaching from the protein and maintaining the Lys1−surface interaction until 7.377 ns, whereupon Lys1 finally broke away from the surface. The protein long axis and the dipole moment were left parallel to the surface, whereas they were initially oriented toward the surface at an angle 45°, with a minimum protein−surface separation of 11 Å. This desorbed state D is also shown in Figure 3. In this state the Arg128 side chain−surface angle φ ∼ 180°. During the remaining time of the trajectory the protein followed the external force and moved away from the surface. The energy barriers for the key steps in the desorption process can be assessed by plotting the force acting on the CζArg128 atom versus time, alongside the displacement of this atom along the direction of the force. As Figure 4 indicates, the

main residues anchoring the protein on the surface are (in order of importance): Arg128, Arg5, Lys1, Arg14, and Arg125.14 Of these, Arg128 interacts directly with the surface, meaning that it penetrates through both surface water layers. Arg5 partially penetrates the inner water layer but does not interact directly with the surface, Lys1 and Arg14 penetrate the outer water layer only, while Arg125 is above the outer water layer. The latter reflects the commonly observed ability of all these residues to change their location with respect to the water layers independently of the others. Note that the side chain of the most important residue, Arg128, is perpendicular rather than parallel to the surface. To define the angle between Arg128 side chain and the surface quantitatively, we introduce the vector between the Cζ and Nε atoms which lies approximately in the plane created by the NH1−NH2−Nε atoms. Now the angle of interest, which we label φ, can be defined as the angle between this vector and the surface normal. In the initial structure φ ∼10°. As stated above, we denote this conformation of the adsorbed lysozyme with the perpendicular Arg128 side chain as state A. During the 10 ns trajectory T1, the Cζ-Arg128 atom is pulled in the direction normal to the surface with a constant velocity of 0.005 Å/ps; see Supporting Information T1.avi for a movie of this trajectory. Arg128 desorbed in two steps in trajectory T1. First, it moved out of the inner water layer at 0.464 ns to then interact only with the outer water layer. Because of the higher mobility of water molecules within this layer, the Arg128 side-chain conformation and orientation with respect to the surface is more readily changed than within the inner water layer; at 15580

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We have repeated this analysis of the A → B transition for all 14 trajectories; we have obtained an average value of 0.4 ± 0.1 eV in the case of the state A initial structure and 0.5 ± 0.2 eV using state A1. Nevertheless, we have to remember that this is the energy related to desorption of only one (albeit crucial) anchor which directly interacted with the surface. Counting the anchors adsorbed to the inner and outer water layer and using 0.4 and 0.3 eV barrier energies, respectively, we estimate the activation energy for lysozyme desorption to be ∼1.6 eV. At such a high value of the protein desorption energy, the Arrhenius rate is measured in millions of years (Table 1). This explains why in our previous adsorption simulations of the native protein which adsorbed using its main adsorption site, the N,C-terminal face,14,26−29 we have never observed spontaneous desorption. Readsorption. We have performed seven normal MD simulations starting from various time moments during the desorption simulations to check the protein behavior when the external force is removed. If the protein is far away from the surface (state D in Figure 3), it rotates to expose the N,Cterminal face to the surface and then adsorbs to state A as reported previously.14,26−29 If the protein is close to the surface, or still adsorbed but with only Arg128 desorbed (states C and B in Figure 3, respectively), the picture is a little different. Because of the strong attraction to surface, there is not enough time and space for the Arg128 side chain to reorientate toward the surface, and the protein adsorbs with this side chain lying parallel to the surface (the angle between the side chain and the surface normal φ ∼ 90°), beneath the outer water layer and interacting strongly with the inner layer. We denote this adsorbed conformation state A′ in Figure 3. In order to see whether the adsorbed lysozyme could be forced back into state A, we performed another steered trajectory T2. In T2 we start from the state C (see Figure 3) with Arg128 desorbed and apply a force to Cζ-Arg128 normal to the surface but directed toward it rather than away. The force−time and displacement−time curves for T2 are displayed in Figure 5. After about 0.5 ns, the end of the Arg128 side chain started to penetrate the outer water layer to interact with the inner (as in state B), and at about 0.95 ns the side chain jumped to become parallel to the inner water layer so that the protein has moved to state A′ (see Figure 3). From eq 1, the released spring energy is ∼0.4 eV, the same barrier to the forced motion of the side chain through the outer layer that we found in the desorption simulations. Thereafter, the side chain did not move again in T2, and deeper penetration of the inner water layer was not observed. In other words, this steered trajectory also finds the adsorbed state A′ rather than A. In all our simulations with the native protein, we never observed spontaneous lateral diffusion across the surface, whether the protein is fully or partially desorbed. The protein attraction to the surface dominated the trajectories, and whenever an externally applied force was released, the protein started its adsorption process immediately. Multiatom Pulling. To provide a check on our conclusions from the single atom pulling simulations, we simulated three multiatom pulling trajectories. In these, we pull all residues (Arg128, Arg14, Arg5, and Lys1) that act as surface anchors for the protein away from the surface in the normal direction. These trajectories did not reveal any substantially new features for the desorption mechanisms, and we focus on only one representative case (denoted T3) here.

Figure 4. Force (A) and displacement (B) of Arg128 as a function of time during the desorption trajectory T1. For clarity, only the first 2 ns (out of 10 ns) is shown. Transitions between states A and B, and between states B and C, are labeled.

first and the biggest barrier appears at 0.46 ns when the lysozyme jumps from state A to state B (see Figures 1 and 3) with Arg128 changing orientation. A distinct subsequent barrier is apparent for the move B → C, when Arg128 moves away from the second surface water layer. The energy barriers for the positional changes can be calculated from the stored energy released by the spring in the move, specifically ⎛ dF ⎞⎟⎜⎛ dF ⎞⎟ dE = ⎜F0 + ⎝ 2 ⎠⎝ K ⎠

(1)

where F0 is the force at the end of the transition, dF is the change in force, and K is the spring constant. Recalling that K = 278 pN/Å, we find ∼0.4 eV (equivalent to 650 pN·Å = 0.65 × 10−19 J) for the transition A → B, ∼0.3 eV for B → C, and ∼0.9 eV for C → D. Our various adsorption and desorption trajectories indicate that the 0.2 eV barrier can be spontaneously and reversibly crossed in the 10 ns simulations, while the 0.4 eV barrier cannot. This is to be expected from the time scales given in Table 1 for such barrier crossings. For example, Arg125 spontaneously adsorbs to the outer water layer and desorbs again in our simulations. Moreover, we have observed similar behavior for other anchor residues adsorbed only to the outer water layer (e.g., Arg14) but have never seen a residue adsorbed to the inner water layer spontaneously desorb. This reinforces the key role played by the anchoring residues which interact with the inner water layer. 15581

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mass on the surface. We can now discount the first possibility, since we have seen that its activation energy of ∼1.6 eV is too high to allow diffusion on the one second time scale found experimentally. Therefore, we investigate pathway (2) by pulling the adsorbed lysozyme across the surface instead of away from it. The trajectory T4 started from the same adsorption state as trajectory T1, but this time the Cζ-Arg128 atom was pulled in the lateral direction with the constant velocity parallel to the surface. Within first 1.9 ns of the trajectory Arg128 desorbs from the inner water layer and orients above the outer water layer with the Arg128 side chain−surface angle φ ∼ 45°, as in state B of Figure 3. Simultaneously, Arg125 adsorbs to the outer water layer, just as it can do in the absence of the external applied pulling force. After this, the protein starts to translate on the surface in the direction of the pulling, and the anchor residues interacting with the surface waters jump from one water binding position to another. Note that during those jumps Arg128 side chain penetrates the outer water layer and the angle between the side chain and the surface normal usually is ∼45° (as in state B), although jumps between φ ∼ 90° are sometimes observed. This is visualized in the movie T4.avi provided in the Supporting Information and in the force and displacement plots shown in Figure 6. The overall lysozyme conformation remains largely unchanged during this motion. The energy released by the movement of the pulled CζArg128 atom as it jumps from one position to another along Figure 5. Force (A) and displacement (B) of Arg128 as a function of time during the readsorption trajectory T2. Transitions between states C and B, and between states B and A′, are labeled.

The first residue which desorbed in T3 was Arg14 which was adsorbed only to the outer water layer. Then Arg128 and Arg5 desorbed from the inner and later from the outer water layer, and finally Lys1 desorbed as well. The protein desorption has been completed within 2.2 ns in T3, and no significant conformational changes have been observed in the lysozyme apart from the expected alterations at the N,C-terminal face. The energy required for the whole protein desorption calculated from the force and displacement plots (not shown) was ∼2.3 eV. This value is higher than the estimate ∼1.6 eV above from the pulled-Arg128 desorption energy, because it includes energy clearly used for protein backbone reorganization. Since Arg128 lies almost at the end of the protein chain, it can change its conformation relatively easily, requiring only a small amount of energy to do so. The same is true for Lys1. However, Arg5 and Arg14 are much more rigid because they are a part of α-helix A (residues 5−16). Therefore, the direct pulling of these residues induces some local conformational changes, consuming some of the external energy. It is worth noting that when the pulling force is removed and a normal MD is started from the desorbed structure, the protein again rapidly readsorbs as described above. Diffusion Mechanism from State A. Two alternative diffusion pathways might be envisaged: (1) The protein desorbs and loses all contact with surface, as in state D of Figure 3, to later readsorb at a different lateral position. (2) The protein remains adsorbed to the surface, but its anchoring side chains desorb from the inner water layer and move above it, as in state B of Figure 3, thereby changing the protein’s center of

Figure 6. Force (A) and displacement (B) of Arg128 as a function of time during the lateral-pulling trajectory T4. Jumps in the position of the pulled residue across the surface are numbered, along with the associated jump in the force. 15582

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as we found in our trajectory T5 (see Supporting Information). Note that changing the angle between Arg128 side chain and the surface normal from 90° to 45° (as in state B) is allowed. From Figure 7, and using eq 1, the energy barrier to this

the surface is again obtainable from the plots in Figure 6. The initial desorption of Arg128 from the inner water layer to the outer is again seen to require ∼0.4 eV. The subsequent jumps numbered on the plots are all of a similar size. However, as examination of the trajectory T4 shows, the movement of Arg128 is synchronous with that of the other anchoring residues Lys1, Arg5, and Arg14. This means that the energy released by these movements is being used to overcome the diffusion barriers of all these residues, not just Arg128. From the energy released in the 10 jumps recorded in Figure 6, using eq 1, we estimate these diffusion barriers to be ∼0.8 eV. Including the initial energy barrier for the release of Arg128 from the first water layer, we find the total activation energy for diffusion from state A ∼1.2 eV. We have repeated this type of lateral pulling trajectory 12 times and have consistently reached the same conclusions. Therefore, we believe that this pulling trajectory reveals the key steps required for the lysozyme diffusion across the surface from state A, namely (a) the key anchoring residue Arg128 must desorb from the first water layer and (b) the remaining anchors move cooperatively above the inner water layer. The activation energy required for these movements is lower than that required for the total desorption of the lysozyme (∼1.6 eV). However, it is again worth noting that when the pulling force is removed and normal MD trajectory resumed, the lysozyme quickly readsorbs to state A′ as described above. Desorption and Diffusion from State A′. In the simulations described above, we have repeatedly observed that when Arg128 is released from the pulling force, it will return to state A′ if it is already close to the surface, with the side chain unable to fully penetrated the first water layer due to geometric constraints (see Figure 3; here φ ∼ 90° rather than 10° in state A). This is in contrast to the adsorption from bulk, where the preferred adsorption state is A or A1 with Arg128 presenting normal to the surface and penetrating both water layers (Figure 1, φ ∼ 10°). Therefore, it is of interest to investigate how readily the protein can move from state A′ in comparison to state A. We have performed steered MD simulations starting from state A′, first pulling Arg128 away from the surface in the normal direction to study desorption and then across the surface to probe diffusion pathways and barriers. In the desorption simulations, the chain of events is rather similar to those above from state A, as might be expected. The first significant movement of the Arg128 side chain is from its position parallel to the surface to one where it interacts primarily with the outer water layer. We can characterize this as state B in Figure 3, although the side chain is more curved in this case. This transition has an energy barrier ∼0.3 eV. The next transition is B → C, also with an energy barrier ∼0.3 eV. Therefore, the total barrier for the lifting of Arg128 from its adsorption site to above the outer water layers is comparable to the ∼0.7 eV observed for the desorption pathway from state A. We conclude that the energies of adsorption in states A and A′ are therefore comparable. In the diffusion pathways, the behavior from state A′ does show a significant difference to that from state A. Above we found that a necessary first step for diffusion was the lifting of Arg128 side chain from A to B, from where the protein can diffuse as a whole without significant changes to its structure. In contrast, starting from state A′ we find that there is no requirement for this first step to state B. Instead, the protein is able to diffuse as a whole while retaining it is A′ conformation

Figure 7. Force (A) and displacement (B) of Arg128 as a function of time during the lateral-pulling trajectory T5. Jumps in the position of the pulled residue across the surface are numbered, along with the associated jump in the force.

motion is measured to be ∼0.9 eV. Thus, we find that the protein is more able to diffuse in the A′ state than starting from A (where the diffusion barrier ∼1.2 eV). We also note that the diffusion barrier is larger than that for the transition A′ → C (∼0.7 eV), and indeed we see this movement occurring toward the end of the trajectory T5, after ∼7.8 ns.

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CONCLUSIONS From the above results, we can construct the following pathway and associated energy barriers (summarized in Figure 8) for the

Figure 8. Schematic representation of energetic barriers for desorption (left picture) and diffusion from various states (middle and right pictures). 15583

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Here the Arg128 side chain lies parallel to the surface (φ ∼ 90°) and interacts with the inner water layer rather than the initial adsorption state A where the side chain penetrates the water layers perpendicular to the surface (φ ∼ 10°). We did not find state A′ in our initial adsorption simulations because it is only accessed from A via transition to state B which occurs on a time scale beyond that of typical 90 ns simulations. This work shows that to understand the longer time scale surface states, diffusion mechanisms must be taken into account. This lesson would seem to apply to the adsorption of all hard proteins onto ionic surfaces and complements our previous discussions of how these can be anchored by positively charged residues Arg or Lys with long side chains which can interact with the structure surface water layers.

surface diffusion of lysozyme adsorbed at a charged ionic surface. Lysozyme adsorbed from bulk is characterized by state A in Figure 1 (or alternatively state A1 in Figure 2), where it is anchored to the surface by the Arg128 side chain which presents itself normal to the surface (φ ∼ 10°) penetrating both surface water layers. In order for the protein to diffuse, this anchoring side chain must be raised to state B. From here the protein may diffuse across the surface in state B, giving a total energy barrier ∼1.2 eV for diffusion from state A. In order to desorb the protein from state A, several other interactions with the outer water layer need to be broken, resulting in an adsorption energy of ∼1.6 eV. Note that these barriers are primarily associated with the breaking of hydrogen bonds rather than long-range movement against the electrostatic field due to the charged surface. However, we have seen that this is not the complete picture as far as surface diffusion in concerned. From state B, the Arg128 side chain can easily relax to a lower energy adsorption position. Because of geometric constraints in the close proximity to the surface, this position is unlikely to be the original state A. Instead, the side chain more readily moves to state A′ where it lies parallel to the inner water layer. The desorption trajectories above imply that state A′ is (more or less) as strongly bound to the surface as state A, so interestingly its existence does not imply more weakly bound protein. Nor does it imply a different orientation of the protein, which remains determined by its dipole moment and its interaction with the negatively charged surface. We have found that the lysozyme diffusion in this state is more straightforward and does not require the initial lifting of the side chain. Instead, the protein can move while remaining in state A′, with a lower energy barrier of ∼0.9 eV. This implies surface diffusion on the second time scale (Table 1), in reasonable agreement with experiment as discussed above in the Introduction.4,5 These results also imply that the long-time adsorption state is A′ rather than the initial adsorbed state A, since the A → A′ transition via state B has only to overcome a barrier of ∼0.4 eV and so occurs on the microsecond time scale (Table 1). How confident can we be in the pathways, the adsorption conformations, and their energetic ordering? While we use one particular potential set (Charmm27) with simple estimates of interactions with our charged planar surface, we note the rather generic nature of our interpretations in terms of hydrogen bond breaking to allow the transitions and the geometric constraints of the structured water layers at the surface. We expect these features to be prominent in all atomistic models of protein− ionic surface interactions in an aqueous environment, and therefore we expect the conclusions we have reached to withstand further scrutiny in future work. Of course, realistic models of crystalline surfaces, such as used by Patwardhan et al. for silica,44 may allow for varying densities of charged surface species as well as for hydroxyl groups. The presence of the latter can change the behavior of the water and protein side chains at the surface, effects beyond the scope of the work presented here. Nevertheless, we note that the previous work on peptide adsorption at charged surfaces39,44 show similar importance of the charged residues at ionic surfaces and adsorption energetics that are consistent with our results for the adsorbing residues at the N,C surface of lysozyme. In summary, our simulations show that while the lysozyme is anchored to the surface by Arg128, the long-term stable conformation of the adsorbed protein is likely to be state A′.

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ASSOCIATED CONTENT

S Supporting Information *

Movies showing protein desorption and diffusion. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]; Tel +44 (0)141 548 2385. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Results were obtained using the Faculty of Engineering High Performance Computer at the University of Strathclyde.

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REFERENCES

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