Deuterium MAS NMR and Local Molecular Dynamic Model to Study

Article pubs.acs.org/JPCC

Deuterium MAS NMR and Local Molecular Dynamic Model to Study Adsorption−Desorption Kinetics of a Dipeptide at the Inner Surfaces of SBA-15 Sundaresan Jayanthi,† Shifi Kababya,‡ Asher Schmidt,*,‡ and Shimon Vega§ †

Department of Physics, Indian Institute of Space Science and Technology, Valiamala, Thiruvananthapuram 695 547, Kerala, India Schulich Faculty of Chemistry and Russell Berrie Nanotechnology Institute, TechnionIsrael Institute of Technology, Haifa 32000, Israel § Department of Chemical Physics, Weizmann Institute of Science, Rehovot 7610001, Israel ‡

S Supporting Information *

ABSTRACT: This work presents a deuterium magic angle spinning (MAS) NMR study of the adsorption−desorption dynamics of glycine-(2,2)-d2-alanine dipeptide adsorbed at the inner surfaces of mesoporous SBA-15 silica under different hydration levels and temperatures. The experimental and theoretical challenges posed by the strong quadrupolar interaction of the rigid CD2 group, 3-fold bigger than that of the rotating methyl CD3, were addressed. Deuterium MAS NMR spectra modulated by exchange were analyzed using theoretically calculated exchange spectra based on the two-site Bloch−McConnel exchange equation represented in Floquet space. To solve this equation, which is composed of a high dimensional Floquet exchange matrix, our former computational approach was modified to reduce the overall computation time by orders of magnitude so as to yield more accurate exchange parameters from the spectral analysis. The adsorption−desorption kinetics of minutely hydrated silica surfaces is understood to originate from the diffusion of water molecules into and out of adsorbate binding sites, thereby gating the dynamic behavior of the adsorbate via increase or reduction of the size of the surrounding water cluster. Molecular dynamic (MD) simulations were employed to model the dynamic behavior of the adsorbate at the two states. Deviations between the MD and experimental observations are attributed to the simplified surface modeling, thereby highlighting the importance of experimental MAS NMR data to improve future modeling of realistic functional surfaces.

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INTRODUCTION Study of binding of biomolecules onto inorganic surfaces bridges materials and biomedical research because of its diverse applications.1,2 These molecular interfaces play an important role in understanding self-assembly, catalysis, biomineralization, drug delivery, and many other nano- and biotechnological applications.3−7 Study of the interactions of dissolved molecules with the surface of porous materials is yet another approach to retrieve information about molecular transport, binding, chemical reactivity, etc.8−12 Materials possessing regular arrays of uniform pore openings can provide a homogeneous confined space and were therefore employed to understand adsorption more quantitatively and at the molecular level. Mesoporous silica materials fall into this category of systems with large surface areas (>800 m2/g), uniform array of cylindrical pores (narrow distribution of 2−50 nm tunable diameters), and tunable surface density of hydroxyls.12−14 These properties aid diffusion of guest molecules into the pores and their subsequent surface adsorption.15 Moreover, the ease of chemically modifying the surface hydroxyls enabled anchoring a variety of functional groups or linkers to serve diverse purposes. © 2016 American Chemical Society

Understanding the binding and dynamics of adsorbed or anchored molecules, the role of water and temperature, is essential for tuning the properties of such functional surfaces. One of the earliest introduced mesoporous silica materials, MCM-4113 and SBA-15,14 were thoroughly studied through various surface characterization techniques including NMR.16−20 The siloxanes or silanols may exist either as isolated, germinal or vicinal −OH groups and their surface distribution determines the degree of hydrophobicity, the acidity, and the specific adsorption of guest molecules.20−25 In studying such systems, it is important to characterize surface binding specificity as reflected by the binding site structure, interactions and mobility of molecular adsorbates at the surface sites. Introducing solvent to the pores changes the binding of adsorbates and eventually leads to desorption/dissolution depending on the intermolecular interactions−adsorbate− Received: November 23, 2015 Revised: January 8, 2016 Published: January 8, 2016 2797

DOI: 10.1021/acs.jpcc.5b11429 J. Phys. Chem. C 2016, 120, 2797−2806

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The Journal of Physical Chemistry C surface vs solute−solvent, and solvent−surface. Likewise is the case for the pending end of grafted molecules.26−29 Solid state NMR spectroscopy is an excellent technique to distinguish between different chemical moieties, to determine intermolecular distances (geometries) and to monitor the dynamics of small molecules on the surface over a wide range of time scales.28,30,31 2H, 29Si, 13C, 15N, and 1H solid state MAS NMR were employed to investigate the dynamics of water dissolved amino acids and small peptides impregnated in SBA15 and MCM-41.31−35 Especially 2H NMR is a powerful local dynamics probe due to the strong dependence of the 2H quadrupolar frequency on molecular orientation. In these studies, stable isotope enrichment of for example 2H, 15N and 13 C at specific sites enhanced the NMR sensitivity. To infer the binding properties of the surface sites and adsorption− desorption kinetics, studies were carried out at controlled hydration levels at selected temperatures.36 When these surfaces are dry (on average less than 2 H2O molecules/ nm2), 1H MAS NMR was employed to identify the single, geminal and vicinal −OH groups, as well as ordered water molecules that are bound together by hydrogen bonding networks to surface silanol site. At such low hydration welldefined 1H spectral peaks were observed indicating that no hydrogen exchange (water/hydroxyls) occurs at these dry surfaces. When the hydrogen level was increased a distribution of water-cluster sizes appeared that developed into pools of water characterized by bulk-like water peaks. Complex dynamic properties were also observed for guest molecules, such as amino acids and small peptides, isobutyric acid and benzene, introduced into the pores of mesoporous materials.32−35,37,38 In these systems dynamic 2H MAS NMR spectra revealed the existence of two types of adsorbate populations: surface immobilized molecules, and molecules undergoing exchange between surface bound and free states; here free corresponds to molecules that are dissolved by solvent (water) molecules and exert rapid isotropic motion. Deconvolution and lineshape analysis of the 2H MAS spectra yielded the exchange rates between the bound and free states and their respective populations. The motion-modulated spectra were analyzed by introducing a two-site exchange model based on the Bloch-McConnel exchange equation represented in Floquet space that was solved numerically.39−41 1H and 2H MAS spectra, recorded at temperatures ranging from 200−320 K and at different hydration levels, established that the onset of dissolution and exchange are mediated by very small water clusters, which are present when the average hydrogen surface density, p (H atoms/nm2), is below 15.32−34 In a more recent study, linker molecules were grafted onto the amorphous silica surface of SBA-1542 and the 2H MAS spectra of a deuterated methyl group (CD3) at their pendent end served to monitor their restricted dynamics. A two-site exchange model served to analyze the spectra and to extract the parameters defining the motion-averaged quadrupolar tensors. To interpret these values in terms of a motional model, molecular dynamics (MD) calculations were conducted. The dynamics of the grafted molecule was evaluated stepwise and the orientation of the CD3 moiety was calculated at each time step. Averaging over all orientations allowed to obtain a timeaverage 1H quadrupolar coupling tensor which was consistent with the values derived from the lineshape analysis. This NMRMD approach was extended to study a linker grafted onto MCM-41, where two deuterated CD2 groups served to monitor its restricted dynamics.43

Herein, this novel approach combining MD simulations with deuterium lineshape analysis, is further pursued to molecules that are not grafted and can therefore part of the time exert nonrestricted (isotropic) dynamics. Surface adsorption is of vast interest also in studying conformational changes of adsorbed proteins that involves large competing energy scales and conformational statistics.44,45 The kinetics and thermodynamics of protein adsorption has been studied by many groups, introducing different theoretical models and experimental techniques.45−48 A general aspect that emerged from these studies concerns the time scales involved in describing the local conformational changes which range from milliseconds to hours.47 Clearly, the computational approach of studying protein dynamics with such a broad time scale poses an impossible task with current methodologies and hardware. This has been alleviated to some extent by predicting theoretically kinetic pathways when the local thermodynamic environment is optimal for that process. The computational time scale is then reduced as this approach removes the necessity of introducing different pathways that may occur through the adsorption process. This simplification also enables to predict very slow dynamic processes, thereby bridging the gap between atomistic time scales to the macroscopic ones. Similar modifications and advancements have been incorporated in the molecular dynamic studies to monitor surface induced protein adsorption and conformational changes.44,45 In this study we address the physical phenomenon of apparent surface adsorption−desorption processes occurring at the milliseconds time scale. The adsorbate-dynamics on SBA-15 is revisited with a dipeptide adsorbate, glycine(2,2)-d2-alanine (gly(d2)-ala), whose rigid −CD2− deuterium quadrupolar interaction is of the order νQ ∼ 240 kHz, η ∼ 0.43 Similarity of this adsorbate and the SBA-15 inner surface to those in earlier studies32−34 justifies invoking the two-site exchange model to interpret the dynamic 2H spectra. With the advent of various molecular modeling techniques and associated software, we succeeded to model most of the fast dynamic processes in our system at a molecular level.26,49−53 Their integration with the experimental data enabled us to extend our understanding how surface modifications affect binding. The outline of the paper is as follows. First the experimental 1 H and 2H MAS NMR data are presented. The spectral components that represent exchange are deconvoluted from the total 2H MAS spectra and the relative exchanging populations are determined. In parallel, a modified Floquet Theory approach is developed to enable the analysis of the two-site dynamic 2H spectra. The computational challenges encountered while considering larger quadrupolar interactions are discussed and the subsequent modifications to the computer program addressing these challenges are explained. This Floquet theory approach is then used to derive the dynamic rate constants. Following, molecular dynamic simulations demonstrate the surface immobilized adsorbate versus waterinduced mobilization of the bound adsorbate. An approach to envision adsorbate at a hydrated surface site that overcomes limitations due to the extensive computational time and associated computer memory requirements is employed. Finally, the two-state adsorption−desorption evidenced by the MAS NMR is interpreted in terms of an exchange process that is gated by the diffusion of water molecules to and from a surface adsorbate site. 2798


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The Journal of Physical Chemistry C

Figure 1. 2H MAS NMR spectrum of SBA-15/gly(d2)-ala at four temperatures and three hydration states. The four conditions (hydration, temperature) where dynamics affects the static MAS lineshapes are encircled with a dashed line.

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ization60 employed 2 ms contact time with rf levels centered at 50 kHz (ramped 1H at ±15%).

EXPERIMENTAL SECTION

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Materials. SBA-15 was synthesized in an acidic environment as reported by Vradman et al.54 All starting materials for the dipeptide, Gly-2,2-d2-Ala, synthesis were of analytical grade and used without further purification. Fmoc-Gly-OH-2,2-d2 was purchased from Isotec, Inc. The dipeptide was synthesized manually using the standard solid-phase Fmoc strategy55 on a 2-chlorotrityl chloride resin (100−200 mesh, 1.5 mmol/g, Novabiochem) and was characterized by mass spectrometry and amino acid analysis.60 mg of SBA-15 was calcined for 2 h at 200 °C to remove residual water, followed by addition of 1.5 mL of a 0.44 M aqueous solution of gly(d2)-ala. The suspension was stirred for 4 h at room temperature. The mixture was filtered and the remaining powder was allowed to dry in air at room temperature for 48 h. This dried powder of gly(d2)-ala loaded SBA-15, denoted SBA-15/gly(d2)-ala, was weighed and packed into a 4 mm NMR zirconia rotor for further studies. In order to increase or decrease sample hydration, the rotor cap was removed and the rotor was left open for few hours in the lab or on a vacuum line. When the cap is closed the water content remained fixed as was evident by the 1H MAS NMR spectrum (not shown). All NMR experiments were measured on a three-channel Bruker Avance III 500 MHz spectrometer equipped with a triple resonance 4 mm MAS Probe and a BCU-X sample temperature controller. 1H and 2H MAS experiments employed 2.5 and 4 μs 90° excitation pulses, 10,000 ± 5 and 6,666 ± 5 Hz spinning frequency, 1.0 and 0.3s recycle delays, respectively. 2 H experiments used TPPM56 1H decoupling with 60 kHz rf power. 2D 1H{13C} HETCOR57 of SBA-15/gly(d2)-ala was acquired with PMLG558 homonuclear decoupling during t1 evolution, and SPINAL59 decoupling during t2; cross-polar-

RESULTS AND DISCUSSION Solid State MAS NMR Measurements. Single pulse 500 MHz 1H MAS NMR spectra of loaded SBA-15/gly(d2)-ala were recorded at four temperatures of 253, 273, 293, and 315 K and at three different hydration levels−low, intermediate and high (Figure S1, Supporting Information). The room temperature spectra for the intermediate and high hydration levels were used to estimate the average hydrogen surface density, p, at ∼8, ∼ 11, and ∼13 1H atoms/nm2, respectively; this estimate is based on earlier quantitative 1H MAS study32−34 of variably hydrated SBA-15 surfaces (Figure 9 in ref 34). The 1H{13C} 2D-HETCOR spectrum (Figure S2, Supporting Information) of SBA-15/gly(d2)-ala exhibits crosspeaks that identify the intramolecular carbon−hydrogen correlations within the adsorbed dipeptide. Following, 2H MAS NMR spectra were recorded (Figure 1) across the different temperatures and hydration levels in order to characterize the dynamics of gly(d2)-ala at the inner pore surfaces of SBA-15. At the lowest hydration state (p ∼ 8 H atoms/nm2) full quadrupolar spinning sideband pattern was measured for gly(d2)-ala throughout the 253−313 K temperature range. This pattern closely superimposes with a simulated MAS pattern of νQ ∼ 240kHz, and η ∼ 0 (Figure S3, Supporting Information). The close similarity between the spectra attests that the excitation profile effectively covers the full frequency width of the quadrupolar interaction. In the absence of any evidence of dynamics at this low hydration level, it is concluded that all gly(d2)-ala molecules are surface immobilized and represent the surface-bound state. Deviations from the static spectral characteristics (Figure 1) are seen for the highest temperature (315 K) of the intermediate hydration 2799


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The Journal of Physical Chemistry C level (p ∼ 11) and for the three highest temperatures of the high hydration level (p ∼ 13). Examination of these four spectra shows they are composed of two distinct components. The first is of a narrow linewidth spinning sideband pattern (δν < 0.3 kHz) of surface-immobilized gly(d2)-ala molecules, identical with the “frozen” adsorbate molecules at the low hydration level, denoted Sb as in earlier studies.32−34 The second component, 1 − Sb, exhibits a superposition of a static spinning sideband pattern and an isotropic peak both with increased linewidth (δν ∼ 1.3 kHz). A representative deconvolution of the two components is shown in Figure S4 (Supporting Information). The broadening of the spectral features represents slow exchange of the gly(d2)-ala molecules between two states: immobilized and freely reorienting. Slow refers here to rates that are an order of magnitude slower than the CD2 quadrupole interaction anisotropy (νQ ∼ 240 kHz) which therefore lead only to line broadening. We note that this interpretation is consistent with earlier studies where the CD3 group served to probe dynamics. In these studies similar exchange processes induced spectral changes that due to CD3’s 3-fold smaller νQ value than that of CD2 were classified intermediate-to-fast regime. At the intermediate hydration level and for T = 313 K (Figure 1) a bound-to-free two-state exchange process sets forth for the (1 − Sb) fraction of the molecules; the exchange becomes more pronounced at the high hydration level for 273 K, and is further enhanced with increased temperature (295 and 313 K). In the bound state the molecule is surface anchored, while in the free state the molecule undergoes “fast” isotropic motion. In this free state, fast implies dipeptide reorientation with correlation time τC ≪ 1/νQ, such that the anisotropic quadrupolar interaction is averaged to zero. This motion is envisioned as an isotropic reorientation in a small cluster of water molecules which are localized at the binding site of the deuterated dipeptide. This molecule may therefore be regarded in the two states as surface immobilized-bound, or as a solute-like-free. Both hydration and temperature change the relative populations and exchange rates between the two states as is evident in Figure 1.32−34 The similarity of the spectra of the high hydration at 273 K and intermediate hydration at 315 K further demonstrate the interchangeable role of increased temperature and hydration. Following, we limit the analysis and discussion only to the exchanging population, namely the (1 - Sb) fraction. Hence, within this fraction, the parameters defining the exchange model are the relative populations of the molecules in the bound and free states, Pb and Pf = (1 − Pb), and the desorption and absorption rate constants kbf and kf b, respectively. Thermodynamic equilibrium is assumed which translates to kf bPf = kbf Pb and Pf + Pb = 1. These parameters will be extracted from the 2H MAS spectra aided by Floquet theory analysis as will be shown below. We further emphasize the fact that the full spinning sideband pattern which is noted for the bound state implies a slow exchange limit. In earlier studies, where intermediate and fast exchange rate regimes were explored,33,34 the unequivocal implication of the 2H MAS NMR data was that the molecule must return to its original surface; this is assumed a prevailing property also throughout the current study. Guided by the above realization of a two-state, bound-to-free, exchange model to obtain the exchange parameters (Pf, Pb, kfb, kbf), the spectra must first be decomposed to their two distinct components: a static spectrum with narrow spinning sideband

pattern and a dynamic spectrum with broadened peaks composing a spinning sideband pattern and an isotropic peak (Figure S4, Supporting Information). The narrow static MAS spectral component that represents the immobilized fraction is not considered further in the manuscript. For the broadened (second) component only a select set of high S/N spinning sidebands are deconvoluted and used to reconstruct (DMFIT)61 the whole MAS pattern (Figure 2). Subsequently, these are subjected to the Floquet lineshape analysis (below) to extract the populations and exchange rate constants.

Figure 2. (a) Deconvoluted experimental 2H MAS spectra of gly(d2)ala in a sample of SBA-15 at different hydration levels (p ∼ 13 and ∼ 11) and temperatures. Shown are deconvolutions of the broad-line components−isotropic and spinning sideband pattern, to which symmetrization was applied. DMFIT was applied to the deconvoluted spinning pattern of the spectra in part a to reconstruct the complete powder spinning sideband pattern. Subsequently, the Floquet analysis was used to search kbf values and relative bound vs free populations, Pb and 1 − Pb, that best fit the spectra. The best fits are shown in part b together with the Pb and kbf values.

Floquet Lineshape Analysis of the Two-State Exchange. The sample spinning modulates the 2H quadrupolar interaction frequency and makes it periodically time dependent. This results in characteristic symmetric 2H MAS spectra consisting of centerband flanked by spinning sidebands. The time dependent spin-1 MAS Hamiltonian in the rotating frame can be expressed as 1 HQ (t ) = ωQ (t )(3Iz 2 − I(I + 1)) (1) 3 with the orientation and time dependent quadrupolar frequency62 2

ωQ (t ) = ωQ

∑ n =−2

2800

Gn(α , β , γ ; η)ein2πνrt

(2)


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The Journal of Physical Chemistry C where Gn’s are the geometric coefficients which depend on the initial Euler angles (α, β, γ) that relate the principal axis system (PAS) of the quadrupolar tensor to the spinning axis, η is the asymmetry parameter and νr is the sample rotation frequency. The orientational dependence of the quadrupolar Hamiltonian makes the 2H MAS spectra highly sensitive to molecular dynamics.31 The temporal evolution of deuterons that undergo exchange, namely the resulting free induction decay, can be obtained by solving the Bloch−McConnel equation in the Floquet63 manifold; its Fourier transform generates the simulated spectrum as explained below. In this approach, mutual interactions between the spins are neglected. The Bloch−McConnel equations for the rotating frame magnetizations of the two-site exchange process of I = 1 nuclei in molecules under sample spinning can be represented in terms of the two complex transverse magnetizations m(+)(t) and m(−)(t) of the single quantum transitions, {|+1⟩ − |0⟩} and {|0⟩ − |−1⟩} respectively, of the free (f) and bound (b) states (sites): ⎡ (±) ⎤ ⎡ m(±)(t ) ⎤ d ⎢ m f (t ) ⎥ ⎥ ±⎢ f = −i Γ ⎢ ⎥ (±) dt ⎢ m (±)(t )⎥ ⎣ b ⎦ ⎣ mb (t )⎦

where we used the infinite dimensional ladder, identity, and number Floquet operators64 ⟨i± , ν|Fni|i± , ν + n⟩ = 1, and ⟨i± , ν|N i|i± , ν⟩ = ν ,

⎡ (±) ⎤ ⎡ m(±)(t ) ⎤ d ⎢ m̅ f (t ) ⎥ ⎥ ±⎢ ̅ f i = − Γ F⎢ ⎥ (±) dt ⎢ m (±)(t )⎥ ⎣ ̅b ⎦ ⎣ m̅ b (t )⎦

⟨i±|U (±)(t )|j± ⟩ =

∑

in

(5)

⎛0 ⎞ ⎛Nf 0 ⎞ 0 ⎜⎜ ⎟ ⎜ ⎟⎟ + ω r⎜ 0 ±ωQb GnbFnb ⎟⎠ ⎝ 0 N b⎠ n =−2,2; n ≠ 0 ⎝ ⎛−k F f k I fb ⎞ fb ⎜ fb 0 ⎟ + i⎜ bf b⎟ −kbf F0 ⎠ ⎝ kbf I

(11)

{m(f +)(t ) + mb(+)(t )} = {U (ff+)(t ) + Ubf(+)(t )}m(f +) (+) + {Ubb (t ) + U (fb+)(t )}mb(+)

(6)

Using eq 5 and introducing the Floquet states |i±, n > results

Γ ±F =

(10)

where the real parts are independent of ωbQ as a result of the fact that the quadrupolar Hamiltonian in eq 1 is diagonal and Gb0 = 0. The imaginary parts can have two values, the possible rate 39 (±) constants ρ(±) 1 and ρ2 , thus k = 1,2. The free induction decay of the spin-1 is composed of the (+) (−) (−) two {m(+) f (t) + mb (t)} and {mf (t) + mb (t)} magnetizations that result in two MAS NMR spectra that are correlated by a reflection with respect to the center frequency of the spectra. The reason for this symmetry is the fact that the ± signs in eq 7 result in diagonalization transformation correlated by D−F = (D+F)−1. It is therefore sufficient to simulate the temporal evolution of only

mi(,±n )(t )einωr t

n =−∞ , ∞

(±)

⟨i± , n|e−i Γ F t |j± , 0⟩einωr t

λk(,±n) = nωr − iρk±

All bound molecules have the same quadrupolar coefficient for the bound state ωbQ, and ωfQ = 0 for the free state. The values of the Gbn coefficients are determined by the PAS orientation of the quadrupole tensor of the 2H spin in each molecule with respect to the rotor fixed frame. Because of the periodicity of the Hamiltonian we can transfer eq 5 to its infinite dimensional Floquet representation by expanding the magnetizations as mi(±)(t ) =

∑

The diagonalization of the Floquet matrices Γ(±) for each F orientation of the bound molecule results in diagonalization (±) −1 (±) (±) matrices D(±) F and ΛF = DF ΓF DF where the diagonal ΛF ’s (±) (±) have complex elements λk,n = ⟨k±, n|ΛF |k±, n⟩. The general forms of these elements are

(4)

Gnieinωr t

n =−2,2; n ≠ 0

(9)

n =−Nmax , Nmax

The rate constants kbf and kfb are the elements of the exchange matrix describing the dynamic process and are the same for both single quantum transitions. In addition, we assume that the time dependent precession frequencies of the nuclei of the two transitions in the rotating frame at both sites are solely determined by the quadrupolar interactions and we can write that for i = f, b:

∑

(8)

To solve this equation we choose at t = 0 that the m(±) i (0)’s are the initial magnetizations immediately after a single 90° radio frequency pulse which are proportional to the initial populations, Pi. Solving these equations requires diagonalization of a truncated form of the Floquet matrices Γ(±) with a 2Nmax × F 2Nmax dimension, where Nmax is an integer at least of the order (±) of ωQ/ωr. After calculating the truncated e−iΓF t, the matrix elements of the single quantum transitions propagators U(±)(t) (±) = e−iΓ t can be obtained via:

with

ωi(+)(t ) = −ωi(−)(t ) = ωQi

for ν = −∞ , ∞

The equation for the infinite-dimensional vectors m̅ (±) i (t), composed of all m(±) i,n (t), gets the form

(3)

⎛ ω±(t ) ⎛−k fb k fb ⎞ 0 ⎞ f ⎟ + i⎜ ⎟ Γ ± = ⎜⎜ ⎜k ⎟ ⎟ ωb±(t )⎠ ⎝ bf −kbf ⎠ ⎝ 0

⟨i± , ν|I ij|j± , ν⟩ = 1,

(12)

Using the general form of λk,n± , the evolution operator U+(t) can now be expressed as Uij(+)(t ) =

∑

∑ {{∑ ⟨i+ , n|DF(+)|k+ , 0⟩einω t } r

k+

e

−ρk+ t

n

{∑ ⟨k+ , 0|DF(+) − 1|j+ , n′⟩}} n′

(7)

(13)

and results in the generalized expressions 2801


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The Journal of Physical Chemistry C U (ff+)(t ) + Ubf(+)(t ) =

(+) 1 t

+ Sn(+,2; f )einωr − ρ2

(+) 1 t

+ Sn(+,2; b)einωr − ρ2

∑ Sn(+,1;f )einω − ρ r

(+)

cells of alpha quartz was created followed by a vacuum slab that is formed after cleaving along the (1 0 0) plane. All freestanding bonds of the silicon atoms were neutralized with hydroxyl groups and the surface oxygens with hydrogens such that the net charge on the surface is zero.52,69−72 The presence of net charge on the template and its subsequent effect on dynamic calculation has not been considered in this study. Our molecular dynamics modeling comprises of three computational stages: (i) simulating the binding of the dipeptide to the dehydrated silica surface (Figure 3a); (ii) simulating the hydration of the surface-bound dipeptide (Figure 3b); (iii) simulating the hydration-induced dynamics of the surfacebound dipeptide (Figure 3c−e).

t

n (+) Ubb (t )

+

U (fb+)(t )

=

∑ Sn(+,1;b)einω − ρ r

(+)

t

n

(14)

where S(+;i) n,1/2 are straightforwardly derived from eq 12. For each orientation of the molecule in site-b in the powder and a set of dynamic parameters {Pb, kfb} the four elements of U(+)(t) were calculated using home-written MATLAB programs. The diagonalization of the Γ(+) matrices and the F evaluation of U(+)(t) using eq 10 are time-consuming because of the large size Nmax of the Floquet matrices Γ(+) F . Generation of a single dynamic MAS NMR powder spectrum would typically take a few hours in a 4−8 CPU cluster. To shorten the computation time we modified the straightforward calculation of the elements of U(+)(t) by relying on eq 11. A necessary requirement for doing so is that the eigenvalues of Γ(+) F and their corresponding eigenvectors are (+) ordered in a way according to λ(+) 1,n = nωr − iρ1 for increasing n (+) = nω − iρ again for increasing n = = −Nmax, Nmax and λ(+) 1,n r 2 −Nmax, Nmax. Sorting the eigenvalues and eigenvectors in this values way numerically enabled the determination of the ρ(+) i (+)−1 |j+, n′⟩ and of the elements ⟨i+, n|D(+) F |k+, 0⟩ and ⟨k+, 0|DF with i, j = f, b. Insertion into eq 13 resulted then in U(+) ij and thereby using eq 14 the free induction signal S(+)(t) of the |+1⟩ − |0⟩ transition is calculated. In order to add the signal of the | 0⟩ − |−1⟩ transition and to obtain the frequency MAS NMR spectrum for each crystallite, the Fourier transform of the real part of S(+)(t) was calculated. This modified computational approach reduced the computation time significantly to less than 10 CPU minutes to provide the final spectrum for the entire powder for given exchange rates {kbf, kfb} and initial population ratio Pb/(1 − Pb). Spectra simulated with different exchange rate constants and populations were used to fit the experimental spectra in order to determine the exchange rate. In parts a and b of Figure 2, the broad deconvoluted experimental spectra for three temperatures for p ∼ 13 are shown together with their best fitted simulated spectra. These simulated spectra are obtained using the two-site exchange model (between free and bound states) and solving eq 13 for a set of rate constants {kbf, kfb}. The good agreement between the experimental and simulated spectra in Figure 2 show that the Pb value changes from 0.45 to 0.75 as the temperature decreases from 315 to 273 K. Although changes of the rate constants kbf are small in this small temperature range, these changes suffice to shift the equilibrium populations. Drying the sample by changing p from ∼13 to ∼11 changed Pb from 0.45 to 0.62 (Figure 2, lower frame). From this analysis we can conclude that the two-site model indeed provides the major features of the dynamic MAS spectra and that in the temperature range investigated, the bound site population (Pb) increases for decreasing temperature and hydration level. Molecular Dynamic Models of the Adsorbate at the Two-States. In the present study, using MD tools we attempt to visualize the surface binding and dynamics of gly(d2)-ala under no hydration and high hydration conditions. Toward this, we have utilized the MD model commonly used for interpreting contact angle measurements of wetted surface.65−67 All MD calculations were done using the Accelerys materials studio package.68 Initially a supercell of 8 × 8 × 8 unit

Figure 3. (a) Bottom: bound conformation of the dipeptide in the absence of water molecules at the site. Top: A cluster of 150 water molecules with density of 1 g/cm3 after subjected to FORCITE dynamic run (Figure S4, Supporting Information) introduced to the hydrated silica slab with the gly-ala molecule bound to the surface (refer to text). Si−O network with dynamic constraints imposed are shown in green. (b) FORCITE dynamic run of part a after 1 ns illustrates a localized hydrated surface site and solvated surface-bound dipeptide. (c, d) Close-up of representative trajectory points at 0.5 and 1.2 ns of the solvated surface-bound dipeptide along with the water cluster. (e) Spatial variation of one of the two C−D vectors from individual trajectory files derived from a 3 ns FORCITE dynamic calculation represented on a unit sphere is shown. Data points behind the sphere are shown in gray.

i. Bound Dehydrated Configuration. Initially a glycinealanine molecule was created in the Materials Studio (MS) visualizer and its energy was minimized using DISCOVER. Care has been taken to keep the molecule in its zwitter ionic form. The energy minimized molecule is then put at a distance of ∼3.0 Å above the surface of the vacuum slab and the system as a whole was subjected to minimization. This is accomplished in the MD calculation by allowing the molecule and the surface hydroxyls to move freely while keeping the coordinates of the silicon−oxygen network fixed. The FORCITE dynamic simulation package was employed for further calculations by time evolving the minimized system in integration steps of 1 fs at 295 K. An NVT dynamic ensemble is selected with the Anderson thermostat. Each 1000th configuration was appended to a trajectory file. After an initial equilibration run of ∼1 ns the final configuration is chosen and subjected to a similar run for another 1 ns with identical parameters as before. A close observation of the 1001 trajectory files shows short-distance contacts of the dipeptide with surface silanols that is stable for an extended duration of ∼300 ps. This dipeptide configuration 2802


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amorphous silica surfaces, combined with the current MD simulations, call for a novel interpretation of how to view the molecular details that underlie the actual exchange process. The agreeable realization is that while both states can be classified as bound, they are distinguished within the accessible 2H MAS NMR time scale by having two different mobility characteristics - frozen and isotropically reorienting adsorbate. In these studies, the sparse (about one adsorbate per 5 nm2) adsorbates, single amino acids or di- or tetrapeptides, were shown to undergo an isotropic motion when on the average as few as 4− 7 water molecules per nm2 are present at the surface. Furthermore, the analysis of the NMR results has indicated that the adsorbates are localized, i.e., nondiffusing on the NMR time scale; moreover, it was concluded that exchanging adsorbates “freeze” at their original binding conformations.32−34 Given the above, a plausible description of the exchange process would be that it is the result of the diffusion of water molecules between surface sites. When water molecules diffuse to a surface site occupied by a dipeptide and increase the size of its surrounding water cluster, binding loosens and the “frozen” molecule can undergo rapid isotropic reorientation at its surface site. When the excessive waters leave the site, the reorientational motion stops and the molecule snaps to its dehydrated binding conformation. With this scenario, the exchange rates derived above therefore reflect the water diffusion rates that gate the motional properties of the surface-bound molecules.

is taken as a representative bound state configuration (Figure 3a, bottom) in the absence of surrounding water molecules. ii. Hydration of the Surface-Bound Dipeptide. To mimic the binding process on a highly hydrated surface we introduced a cluster of water molecules capable of hydrating the surfacebound gly-ala and its binding site. Initially 150 water molecules were built into a periodic cube with 1 g/cm3 density using the Amorphous Cell@ Calculation subroutine present in the MS package. Subsequently the cubic lattice was removed to cancel the periodic condition and the cube was separated from the bulk. A 700 ps NVT dynamic run resulted in a water droplet of ∼16 Å diameter (Figure 3a, top and Figure S5, Supporting Information). The 700th trajectory file of the dynamic run was taken and placed ∼3 Å away from the bound conformation of the gly-ala molecule as described in part i. The system as a whole is again subjected to minimization procedure. The minimized model is subjected to a dynamic run of ∼3 ns by keeping all other parameters identical as before. The water drop, as a whole, approaches the surface, wets the binding site, and solvates the bound dipeptide. A representative snapshot of the resulting wetting−solvating process after 1 ns of the dynamic run is shown in Figure 3b. iii. Surface Dynamics of the Dipeptide at the Hydrated Surface Site. Monitoring the conformation of the bound dipeptide under these hydration conditions throughout the MD run shows that the dipeptide, while surface bound, undergoes rapid conformational changes. Detailed views of the dipeptide are shown for two time steps in Figure 3c,d. Tracking the orientations of a selected set of dipeptide bonds during this 3.2 ns dynamic run confirms they all undergo rapid large amplitude reorientation consistent with the high local hydration level; specifically, the orientations assumed by the C−D bond are shown in Figure 3e. Such large amplitude motion with subnanosecond time scale would lead to substantial fast limit averaging of the 2H quadrupolar interaction of the dipeptide. The fact that the simulations do not yield fully isotropic motional averaging as seen in the experimental data even with much fewer water molecules must therefore reflect the fact that the modeled surfaces exhibit far stronger binding strengths to the dipeptide. One major contribution to this increased affinity is the higher silanol density, ∼6 silanols/nm2 of the simulated surface compared to 3−4 silanols/nm2 of the MCM-41 and SBA-15 surfaces.70,73 This state of the molecule in which solvating waters weaken surface binding and facilitate rapid large amplitude motion of the dipeptide at its binding site is analogous to the free state observed experimentally. With this view at hand, both immobile and mobile states represent surface-bound states of the dipeptide. In the first, in the absence of water molecules at the binding site, the dominant dipeptide-surface interactions “freeze” the dipeptide conformation and is therefore denoted the bound state. In the second case, the water cluster at the binding site is sufficiently large to weaken binding and to induce rapid reorientation of the dipeptide at the surface binding site denoted f ree state. Experimentally the free state reflects a molecule that reorients rapidly and isotropically at its binding site, yet with fewer water molecules than the MD. Regardless of the deviation that arises from the increased binding affinity, the MD modeling demonstrates analogous states to the experimentally observed states. Molecular Mechanism: Water-Gated Exchange Model. The accumulated, past and current, experimental 2H MAS NMR observations of two-state exchange on minutely hydrated

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DISCUSSION Molecular dynamics simulations yielded a description of the adsorbate gly(d2)-ala bound to silica surfaces exhibiting two different characteristic adsorbate dynamics depending on the hydration level of the site; in a binding site that is not hydrated the adsorbate is immobilized with a “frozen” conformation, while in an excessively hydrated site the adsorbate is in isotropic-like motional state undergoing large amplitude and rapid (subnanosecond) conformational changes. During the simulations of the latter a motion that is fully isotropic was only approached at hydration levels that are much higher than those necessary for observing these isotropic motions experimentally; clusters of 150 water molecules at the binding site in the simulation yet experimentally measured average density of only ∼6 water molecules per nm2. This deviation indicates that surface-to-adsorbate affinity in the simulations is higher than the actual. Among the factors that may rationalize this deviation are the higher simulated silanol density compared with that of the real surface,70,73 the uniformity of silanol distribution in the simulated surface versus local nonaverage arrangements,25 geometric factors of the surface structure like roughness and steps present in SBA-15,20,21 and the lack of any surface charges in the simulation. The experimental results and computational insights obtained for this class of silica surfaces with very low hydration levels call for a new perception of the two-state exchange mechanism. A dynamic model was proposed in which the motion of the bound dipeptides is regulated by the size of the water clusters at their binding sites, and the immobile-to-mobile exchange is gated by diffusion of water molecules to and from such sites. Diffusion of water molecules to a binding site with a small water cluster will increase its size and can result in a solvation of the adsorbate; upon water diffusion away from this water cluster, its size decreases and the adsorbate returns to its bound state. This description of the exchange process unifies 2803


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earlier studies which showed that the adsorbate, after exerting water-induced isotropic reorientation, “snaps” back to its original immobilized position. In this view, as the water molecules leave the binding site, the original binding potential is reinstated and guides the adsorbate to assume its initial (no water) bound conformation. Given this dynamics model, the Floquet theory derived twosite exchange rates of the dipeptides do reflect the diffusion rates of the water molecules between their binding sites. The earlier and present data also suggest that there exists a “threshold” cluster size for onset of isotropic motion, and that this threshold increases with the adsorbate size, for example, going from single amino acids toward di- and tetrapeptides.65 In addition, the exchange rates as well as the relative free versus bound populations are shown to rise for increasing temperatures and/or hydration levels, hence exposing the interchangeable role of these two factors. The high sensitivity of the surface properties to surface structural details further emphasizes the importance of the vast information embedded in MAS NMR spectroscopy to enhance future modeling of more realistic surfaces, and to enable more reliable extraction of surface reactivity and functionality characteristics.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.5b11429. Additional NMR measurements that enabled determination of hydration level (Figure S1), confirmed identity of the adsorbate (Figure S2), the full 2H excitation bandwidth for the −CD2− group under MAS conditions (Figure S3), and models derived from MD simulations (Figures S4 and S5) (PDF)

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AUTHOR INFORMATION

Corresponding Author

*(A.S.) E-mail: [email protected]. Telephone: +972-48292583. Fax: +972-4-829-5703. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Dr. Veronica Frydman, Weizmann Institute of Science, for the synthesis of the dipeptide and Dr. Ira Ben Shir from the Technion for stimulating discussions. This research was supported by German−Israel Foundation Grant 76-2009.

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REFERENCES

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Deuterium MAS NMR and Local Molecular Dynamic Model to Study

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