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Biophysical Chemistry, Biomolecules, and Biomaterials; Surfactants and Membranes

A Direct, Quantitative Connection Between Molecular Dynamics Simulations and Vibrational Probe Lineshapes Rosalind J. Xu, Bartosz B#asiak, Minhaeng Cho, Joshua P. Layfield, and Casey H Londergan J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b00969 • Publication Date (Web): 26 Apr 2018 Downloaded from http://pubs.acs.org on April 27, 2018

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The Journal of Physical Chemistry Letters

A Direct, Quantitative Connection Between Molecular Dynamics Simulations and Vibrational Probe Lineshapes Rosalind J. Xu1, Bartosz Blasiak2, Minhaeng Cho3, Joshua P. Layfield4, Casey H. Londergan1* 1

Department of Chemistry, Haverford College, Haverford, PA

2

Department of Physical and Quantum Chemistry, Faculty of Chemistry, Wrocław University of

Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland 3

Center for Molecular Spectroscopy and Dynamics, Institute for Basic Science (IBS), Seoul

02841, Republic of Korea; Department of Chemistry, Korea University, Seoul 02841, Republic of Korea 4

Department of Chemistry, St. Thomas University, Minneapolis, MN

Corresponding Author *[email protected]

ACS Paragon Plus Environment

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ABSTRACT: A quantitative connection between molecular dynamics simulations and vibrational spectroscopy of probe-labeled systems would enable direct translation of experimental data into structural and dynamical information. To constitute this connection, allatom MD simulations were performed for two SCN probe sites (solvent-exposed and buried) in a calmodulin-target peptide complex. Two frequency calculation approaches with substantial nonelectrostatic components, a QM/MM-based technique and a solvatochromic fragment potential (SolEFP) approach, were used to simulate the IR probe lineshapes. While QM/MM results disagreed with experiment, SolEFP results matched experimental frequencies and lineshapes and revealed the physical and dynamic bases for the observed spectroscopic behavior. The main determinant of the CN probe frequency is the exchange repulsion between the probe and its local structural neighbors, and there is a clear dynamic explanation for the relatively broad probe lineshape observed at the “buried” probe site. This methodology should be widely applicable to vibrational probes in many environments.

TOC GRAPHICS

Experiment Simulation

N C S

2140 2150 2160 2170 2180 Wavenumber (cm-1)

KEYWORDS:

thiocyanate,

protein

dynamics,

conformational

distribution,

infrared

spectroscopy


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Molecular functional group vibrations report with very fast intrinsic time resolution on their local structural environments via their vibrational frequencies, observed by infrared (IR) absorption or Raman scattering.1–4While spectral lineshapes from unique probe vibrations contain structural information not available from other techniques, the physical factors that determine a vibrational probe’s frequency are often not quantitatively understood.5 Some vibrations’ (i.e. carbonyl stretching) frequencies can be well-reproduced using a variety of electrostatic (“Stark effect”) approaches,6–10 while others (like nitriles) are much more difficult to understand with frequency methods based solely on electrostatics3,5,11–15 due to substantial quantum-mechanical effects on the vibrational frequency. These quantum mechanical effects were classically attributed to “Lennard-Jones” or “van der Waals” interactions or “charge transfer” and more recently have been treated using higher levels of theory. This lack of physical understanding has led to many semi-quantitative, rather than rigorously physical, recent applications of probe groups in both one- and multidimensional vibrational spectroscopies to the dynamic structures of biomolecules and other condensed-phase systems. Here we compare two comprehensive (electrostatic + all quantum effects) approaches to simulating experimental data from vibrational probe groups, with the conclusion that while a QM/MM-based method does not reproduce frequencies or lineshapes particularly well, an effective fragment potential approach provides excellent agreement with experiment in two very different molecular scenarios and could be used broadly to provide a direct structural and dynamic interpretation of experimental observations. Recent IR experiments revealed dramatic frequency and lineshape changes in the CN stretching band of the covalently bound thiocyanate group placed directly in the interface between two proteins.16,17 The SCN probe group was non-perturbative to binding, so this probe


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group could be an ideal reporter of protein-protein interactions. Recent computational work suggested two different approaches (that include both electrostatic and non-electrostatic factors) to the simulation of vibrational probe group frequencies in biomolecules: a QM/MM-based scheme based on a strategy used for small molecules in solvents18 and applied previously to the SCN probe group in solvated enzymatic active sites,19,20 and a more general solvatochromic effective fragment potential-based approach (“SolEFP”) that separately evaluates each of the physical contributions to the vibrational frequency shift.5,21–23 Neither method has been systematically characterized across a wide range of systems and environments, nor have the simulated results been quantitatively compared to experimental lineshapes3,19 except in cases of small molecules in solvents.18,24 Here we seek a connection between simulation and experiment that includes quantitative interpretation of lineshapes in heterogeneous protein environments. The methodology that creates such a connection could be applied to data from both many vibrational spectroscopy experiments, including Raman and time-resolved nonlinear experiments, and from many different probe functional groups. We chose two SCN probe sites (see Figure 1) in the complex between calmodulin (CaM) and the probe-labeled CaM-binding sequence from skeletal muscle myosin light-chain kinase (“M13”): one where the probe is solvent-excluded (W4C*, where C* indicates substitution of βthiocyanoalanine for the native residue) and another that is solvent-exposed (S23C*), to compare the QM/MM and SolEFP frequency methods for simulating the experimental results from molecular dynamics (MD) trajectories based on the published NMR structure.25


4

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T he met hods secti W4

on S23

and Sup porti ng

Figure 1: NMR structure (PDB:2BBM) of CaM (blue) bound to M13

Info

peptide (yellow) with native residues W4 and S23 labeled in pink.

rmat

ion file present methodological details of our MD simulations, frequency calculations, and lineshape transformations. Our MD approach consisted of two all-atom, explicit-solvent MD simulations in the AMBER99SB force field with the SCN probe explicitly included at each site. After structural convergence of the unlabeled complex and equilibration of the probe-labeled structures, we simulated each structure for 10 ns at 1 fs time intervals. We then used QM/MM and SolEFP calculations to determine the probe CN frequencies throughout the same MD trajectories, and we applied the fluctuating frequency approximation (see Supporting Information) to calculate absorptive IR lineshapes. Parameters for lineshape transformations, determined as detailed in the Supporting Information, were 40 fs sampling intervals and a maximum correlation delay time of 12 ps. Figure 2 compares the distributions of calculated


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frequencies and the simulated lineshapes from the two different frequency methods to the experimental CN stretching bands.

Figure 2: Simulated IR lineshapes (blue) and frequency distribution histograms (green, bin width 1 cm-1) by either SolEFP or QM/MM methodology, overlaid with experimental lineshape (red), for SCN probe sites W4C* and S23C*. The SCN probe group’s response to its environment has been interpreted as a reporter of either the local electric field12,26–30 or of solvent exposure31–35 of the probe group; the experimental data here were initially compared to the probe’s calculated solvent-accessible surface area (SASA). Figure S2 provides histograms of the SASA for the probe at each site, which are very different: the W4C* probe is completely solvent-excluded, and the S23C* probe exhibits a range of SASA values indicating strong exposure to the solvent. So these two sites together provide a challenging test case for MD-based vibrational frequency calculation methodologies, well


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beyond the small molecules in solvents that have typically been the targets of such simulation work. The SASA’s are qualitatively consistent with the experimental probe frequencies, if greater solvent exposure generally means higher average CN frequency.31,33 The QM/MM methodology previously implemented a quantum mechanical region including the C* residue and nearby protein residues and water molecules that significantly affected frequency calculations, determined by a frequency fluctuation minimization method.19,20 In this work, however, we selected the QM region by a distance-based method, since the local environment around both probe sites was relatively dynamic (see Supporting Info). The QM/MM frequencies (second column of Figure 2) are systematically shifted vs the experimental data, and neither the distributions nor the simulated lineshapes provide good matches to the experimental lineshapes. While the average QM/MM-calculated frequency does shift between W4C* and S23C*, the simulated shift between sites is smaller than the experimental shift. The QM/MM method also does not provide a clear physical basis for the observed shift. This method was especially challenged by W4C*, where the probe group’s main interactions are not with solvent molecules (as they were for all previously reported applications of this method19,20,24). While the QM/MM method does not provide quantitative agreement with either mean frequencies or the experimental lineshapes, its results in this system are not completely out of line with its shortcomings in previous reports19,20. The accuracy of the QM/MM frequencies might be improved through further adjustment of the QM region, but such changes would require careful inspection of each case and preclude an algorithmically consistent approach to each site. Another problem with the QM/MM method in Figure 2 is the relatively narrow QM distributions of simulated frequencies that lead to inaccurately narrow predicted lineshapes. The QM/MM approach uses a reparameterized semi-


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empirical PM3 method24 to determine the QM energy and point-charge interactions to determine the MM energy for several different CN bond lengths, providing a one-dimensional anharmonic potential surface displaced along the CN bond direction that determines the CN frequency. Both the PM3 method (which was parameterized to yield results consistent with DFT calculations19 for methyl thiocyanate in water, and might not be able to address a heterogeneous environment that is not always polar and H-bonding) and the assumption of this particular one-dimensional potential energy surface of the SCN nitrogen atom stretched away from carbon, which does not replicate the actual CN stretching vibrational motion, might miss important aspects of the interactions between the probe groups and their local environments. (Any issues with the MD force field should be systematic to both frequency methods.) The SolEFP frequency calculations (first column of Figure 2), on the other hand, provide close agreement with experimental data at both probe sites. The computational cost of SolEFP is almost the same per MD frame as that of the QM/MM method, while the interaction cutoffs for SolEFP are significantly larger than the QM cutoff (see Supporting Info). SolEFP calculates the physical contributions to the frequency shift (vs the gas phase value) separately; the protein residues are replaced by closed-shell molecular fragments, and the resulting frequency shifts are reported in four separate terms (Coulombic, polarization, exchange repulsion, and dispersion). While SolEFP offers a more algorithmically consistent, first-principles approach requiring neither semi-empirical parametrization nor site-specific QM/MM partitioning, the separation of physical factors governing the frequency shift (see Figure 3) is another major advantage that directly reveals what the SCN probe group’s frequencies and lineshapes truly report. The mode frequency shifts by about -6 cm-1 between solvent-exposed S23C* and buried W4C*, but the main factors governing the frequency in each case are the repulsion and dispersion interactions


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with nearby functional groups. Those interactions lead to relatively broad frequency distributions due to structural fluctuations of the probe and its local neighbors.

40.0 Solvatochromic Shift (cm-1)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


W4C* S23C*

30.0 20.0 10.0 0.0 -10.0 -20.0

Coulombic

Polarization

Repulsion Dispersion

Figure 3: Breakdown of SolEFP frequency shift components (Coulombic, polarization, repulsion, dispersion) with sample standard deviations represented as bars. (Distribution histograms are shown in Figure S6.) The distributions of physical factors (averages in Figure 3 and distributions in Figure S6) also help to interpret the experimental lineshapes. The S23C* frequency distribution is much broader, but the experimental and simulated lineshapes for the two sites have similar widths. This is due to differences in the structural dynamics and associated spectral diffusion at each site and resulting motional narrowing (or lack thereof, in the case of W4C*). Figure 4 shows the calculated frequency-frequency correlation functions (FFCFs) for each site. We note that the frequency calculations implemented here would also be applicable to determining response functions for nonlinear IR experiments, which are currently difficult to collect for SCN groups


9


due to the relatively low oscillator strength; but the SolEFP methodology is quite general and should also be applicable to observables from other probe groups in other systems. T

1. he

0.8

FF

0.6

C(t)/C(0)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.4

CF

0.2

for

0.

S23

0.1

0.2

0.3

0.4 C* dec ays muc

Time (ps)

W4C* S23C*

Δ (ps-1) 0.269 0.413

τ (ps) 86.6 2.99

Δ * τ 23.3 1.24

h mor e

Figure 4: Fluctuating frequency correlation functions (FFCFs) from simulated quic frequency trajectories by SolEFP methodology, for probes at W4C* and S23C*. The kly shortest times appear in the inset. Dynamic parameters were calculated following than procedures detailed in the Supporting Information file. for W4C*: the S23C* frequency fluctuates faster because it is determined mainly by changes in the configuration of mobile water molecules around the probe group. The W4C* frequency fluctuates more slowly due to slower motions of the compact protein-peptide bound structure. The simulated FFCFs (which generate accurate lineshapes) are different between sites on all time


10

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scales. S23C*, which is water-exposed, has shorter correlation decays due to the fast water dynamics, in addition to a larger variance due to variability in its local environment: the ∆*τ value of 1.23 for S23C* is in the partially narrowed regime and resembles ∆*τ for methyl thiocyanate in water.36 The ∆*τ value of 23.3 for W4C* is well within the inhomogeneous limit, but the W4C* lineshape is still slightly narrower than the W4C* frequency histogram due to some significant short-time decay components (the origins of which can be seen in Fig. S10). The generally slower local structural dynamics at the buried W4C* explain the CN band’s broad linewidth as compared to, for example, the narrow linewidth of methyl thiocyanate in tetrahydrofuran (THF):33 in a solvent the frequency fluctuations are fast, but inside a protein they are slower and the W4C* lineshape reports more (but not all) of the frequency distribution. The “electric field”37–39 appears in the Coulombic contribution, which displays relatively broad distributions in Figure S6 but not the largest average change in Figure 3 (and actually shifts the mean frequency in the opposite direction as observed experimentally). The relative unimportance of Coulombic contributions to the mean frequency here is consistent with one prior report in a protein5 and earlier work in non-protein systems40–42: SolEFP’s Coulombic term includes the multipole expansion at the heart of most “electrostatic-only” models of vibrational frequency dependence, so the EFP-enabled decomposition clearly identifies the non-electrostatic nature of the CN group’s environmental dependence. Furthermore, the main determinants here of the mean CN frequency are dispersion and repulsion, which shift the average frequency in opposite directions. The main difference between the two sites’ mean frequencies is that the repulsions with water molecules (which can come very close to the probe N atom) are of different magnitude than the repulsions in a hydrophobic cavity. From this point of view, “hydrogen bonding” by the solvent to the CN group provides a proximity between species that drives a


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quantum mechanical repulsion which shortens the CN bond and increases the frequency (as illustrated previously5). However, inhomogeneity in the Coulombic frequency shift is still a major contributor to the observed probe lineshape. Fig. S10 shows a breakdown of the FFCFs into auto- and crosscorrelated physical components, where the major contributor to the inhomogeneous lineshape (and the long-time tail of the FFCF) at W4C* is clearly the Coulombic term, especially at longer correlation times most relevant to the observed linewidth. The Coulombic contribution is dynamically averaged out for S23C* due to the faster fluctuations of the solvent, while inhomogeneity in the repulsion interactions dominates the FFCF decay. Structural fluctuations nearest to the probe lead to changes in dispersion and repulsion shifts, and the more long-range Coulombic term persists because the longer-range structure fluctuates much less on ps time scales. So the SolEFP-based modeling of W4C* does suggest that a significant “vibrational Stark effect” from the persistent longer-range (beyond a few Å) structure may be present in some protein-interior lineshapes. While SolEFP frequency calculations on MD trajectories are quantitatively accurate and physically informative in two cases here, several challenges and limitations remain. SolEFP divides a protein (or other system) into small, closed-shell fragments that might create superimposition errors or interfragment clashes that could be problematic for certain environments or systems. While “charge transfer” between the probe and solvent molecules (a non-electrostatic, quantum-mechanical effect) was historically implicated13 as a factor in nitrile solvatochromism, that particular quantum effect is accounted for in the EFP framework as inductive changes to the probe’s electron density. But the EFP charge transfer term (a separate physical factor than “charge transfer” in the historical solvatochromic literature),43 might also be


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important if the probe comes very close to ions or highly charged protein side chains (which it does not in the current study, where both probes are at least 10 A away from the nearest bound Ca2+ ion). Charge penetration effects are also not considered yet in SolEFP and might be important in systems with very strong long-range polarizations. We also currently adopt the Condon approximation in our lineshape calculations, while it is known that nitriles display weak non-Condon effects.13,44 SolEFP should accurately report frequencies regardless of any non-Condon effects on the relative intensities of those frequencies. The Condon approximation applies here because each of the two sites displays a relatively homogeneous local environment (S23C* is constantly exposed to water molecules, and W4C* is completely shielded from water molecules), and non-Condon effects in nitriles are most associated with H-bonding interactions.13,44 For sites with different spectral subpopulations where some probes are solvent-exposed and some are not (i.e. some of the lineshapes for probes attached to calmodulin17), including non-Condon effects may be necessary (perhaps via consideration of the EFP dipole) to achieve correct relative spectral weighting of the frequency distribution when calculating the absorptive lineshapes. The greatest challenge to widespread application of this simulation methodology is the atomistic accuracy of molecular dynamics simulations. In earlier application of SolEFP to the SCN probe, a systematic error of 10 cm-1 was found in both solvent and proteins.5 However, SolEFP calculations on EFP2-based simulations of methyl thiocyanate in solvents yielded quantitative agreement with experiments.3 The excellent agreement with experiment here is likely enabled by our use of improved thiocyanate parameters, obtained using a more rigorous approach (following the strategy of Lindquist and Corcelli19,24,36) than provided by the generalized AMBER parameters45 used in previous studies5,46. SolEFP frequencies for the SCN


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probe and most other vibrations are very sensitive to interatomic distances due to the steepness of repulsive interaction potentials. So excellent MD parameters are essential, especially when the repulsion term is dominant.5 A general challenge in all MD simulations is statistically accurate sampling. While the relatively rigid CaM/M13 structure exhibited relatively small fluctuations in a 100 ns simulation (Figure S1) and the ensemble vibrational lineshapes were reproduced after 10 ns of frequency calculations, conformational flexibility is an important feature of other systems.47 In such cases, more extensive sampling will be required and a range of initial protein configurations should be considered for probe insertion. A great promise of vibrational spectroscopy is that the conformational ensemble of dynamic systems can appear directly in the spectral lineshape. The sensitivity and accuracy of the SolEFP method introduces a definitive link between vibrational spectroscopy and MD simulations. Probe frequencies for simulated subpopulations could provide a direct evaluation of structural ensembles from spectroscopic data: this prospect is currently under investigation. Beyond structural ensembles, the methodology applied here should be widely applicable to many different probe groups whose frequencies depend on varying aspects of their local environments, from purely electrostatic and longer-range to more quantum-mechanical and locally-defined. COMPUTATIONAL METHODS

A. Molecular Dynamics (MD) Simulations. All MD simulations were performed in the software package GROMACS 5.1.4,48–54 using the AMBER99SB force field.55,56 Bonded and non-bonded parameters for the non-standard SCN probe in the cyanylated cysteine residue were obtained from Layfield and Hammes-Schiffer.57,58 The initial wild type calmodulin + M13 structure reported by Ikura et al. was obtained from PDB code 2BBM.59 The structure was


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solvated in TIP3P water in a periodically replicated dodecahedron cell, with the edges at least 11 Å away from any protein atoms. Eight sodium atoms were added to ensure charge neutrality. The simulation was performed with electrostatic and van der Waals cutoffs of 10 Å, and long-range electrostatic interactions were treated with the particle-mesh Ewald sum method.60 The integration time step was 1 fs. All bonds involving hydrogen were constrained using the LINCS algorithm.61 The system was equilibrated following the extensive procedure of Layfield and Hammes-Schiffer,57 and a 100 ns production run was performed in a NVT ensemble at 300 K. No drastic structural variations were observed during the production run and the structure appeared to stay near the NMR structural coordinates throughout the simulations. The wild type structure at 100.0 ns was used as the starting point for simulations where the native residues at W4 and S23 were replaced by cyanylated cysteine. The residue replacement was performed in Chimera-UCSF.62 For each mutant, the most probable cysteine rotamer was selected, followed by the insertion of CN in place of the thiol H atom, adjustment of bonded parameters, and renaming of the artificial residue. Then the entire simulation system was continued for 20 ns. The first 10 ns was considered as equilibration, and the later 10 ns was sampled at 40 fs intervals for the frequency calculations reported in Figures 2-4. For the determination of the sampling interval, see Part D and Figure S7. For each trajectory, radius of gyration and root mean square deviation were calculated using the GROMACS gyrate and rms utility (Figure S1).63 Solvent accessible surface area of the SCN group’s nitrogen atom during the 10 ns mutant production runs was calculated using the GROMACS sasa utility,64 with 168 dots per sphere (Figure S2). B. Solvatochromic Effective Fragment Potential (SolEFP): SolEFP/EFP2 Biomolecule Fragmentation and Vibrational Frequency Calculations. SolEFP calculations were performed


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using Python packages developed by Blasiak and Cho during previously published work.65–69 The basic theory is that: the solvatochromic frequency shift, relative to the gas-phase frequency, is proportional to the curvature of the probe-solvent interaction potential energy surface (eqn. 1). By the effective fragment potential (EFP2) theory,70 this interaction energy can be decomposed into five components: Coulombic, exchange-repulsion, polarization, dispersion, and chargetransfer (eqn. 2). Consequently, the solvatochromic frequency shift can be decomposed into contributions from the same five components (eqn. 3). In the current work, the charge-transfer term is ignored as the distance between either probe and the nearest calcium ion is over 10 Å. Differently from previous work,67 the polarization is treated as purely additive (i.e., no manybody polarization is considered). The interaction energy expressions by the EFP2 theory were differentiated and simplified, and expressed in terms of ab-initio QM properties of small, closedshell molecules called “fragments”, including multipole moments, vibrational eigenvectors, and localized molecular orbitals. The detailed formalism is explained elsewhere.65–69 Therefore, frequency calculation by SolEFP is based on first-principles and involves no semi-empirical parametrization. Previous work applied SolEFP to large biomolecules;67 the biomolecule fragmentation scheme is illustrated in Figure S3. The Coulombic, polarization, dispersion and repulsion cutoffs used were 23.8, 8.5, 8.5, and 6.9 Å, respectively.

Eqn. 1

Eqn. 2 Eqn. 3 = solvatochromic frequency shift of jth normal mode = vibrational frequency shift operator; U = solute(probe)-solvent interaction potential energy surface = mechanical anharmonicity component;

= electronic anharmonicity component

Plusharmonic Environment Mj,0 = reduced mass of jth normal mode;ACSj,0Paragon = gas phase frequency of jth normal mode

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Index i = all normal modes in the solute (probe) molecule; gijj = cubic anharmonic constant Qj = coordinates of jth normal mode; Q0 = solute(probe) gas phase equilibrium geometry Coul: Coulombic; Rep: exchange-repulsion; Ind: polarization; Disp: dispersion; CT: charge-transfer

C. QM/MM Frequency Calculations. QM/MM calculations were performed using an adapted version of the Fortran package developed by Layfield and Hammes-Schiffer57,58 that implements Corcelli’s basic approach71 in a protein context. The fundamental approach is that: at each trajectory frame, the SCN nitrogen atom is stretched away from the carbon along the existing C-N axis at 0.1 Å increments, and an anharmonic potential energy surface is constituted using single-point energies from a hybrid QM/MM method. The QM region is treated with a semi-empirical PM3 method with parameters for the SCN nitrogen atom re-optimized so that they reproduce the essential properties of the CN bond as benchmarked vs DFT-based (B3LYP) MeSCN-water interactions;57,72 this modified PM3 approach was adapted based on prior work by Lindquist and Corcelli on acetonitrile ADD REF. [Using the PM3 method makes the QM part of the calculation much more cost-efficient; anything more complicated (or rigorous) would make this QM/MM-based approach cost-prohibitive for most systems and definitely so when compared to the cost of SolEFP calculations detailed below.] The MM region is treated as point charges. The anharmonic potential energy surface is then fitted with B-splines and an anharmonic force constant is calculated, which is then converted into a frequency. The choice of the QM region is separate for protein residues and waters is based on distance + probability cutoffs. In choosing QM protein residues, the probability occurrence for each protein residue in 2BBM coming within 3.5 Å from the center of mass of CN was determined over the 10 ns production trajectory for each probe site. If this probability was higher than 10 %, then the residue was included in the QM region throughout the simulation. While it is impossible to


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include a fixed set of waters in the QM regions since waters constantly move away and to the probe, the number of QM waters was fixed in case changes in the size of the QM region introduced artificial fluctuations in the calculated frequencies. The probability occurrence of a number of waters simultaneously coming within 3.5 Å from the center of mass of CN was calculated over the 10 ns production trajectory for each mutant. The number of waters was chosen so that at least 90 % of the cases of contact within 3.5 Å were accounted for. This procedure is illustrated in Table S1 and Table S2. The QM protein residues for mutant W4C* and S23C* are shown in Figure S4. Outside of the QM region, the MM region was treated as point charges, with a boundary cutoff of 20 Å from the probe. D. Vibrational Lineshape Transformation. For each mutant, the vibrational lineshape, I(ω), was calculated following the fluctuation frequency formalism with the classicized linear response function, Jc(t):57,73–75 I(ω) =

∫

∞ 0

(

dt e−iωt J c (t) e

−t/(2T1 )

)

 J c (t) = exp −i 

∫

t 0

 δω(τ)  

Eqn. 4

In which δω(τ) is the frequency fluctuation at time τ from the classical ensemble average. The

e

−t/(2T1 )

term accounts for lifetime broadening; the lifetime, T1, is approximated to be 50 ps

based on experimental measurements of the thiocyanate probe in proteins and a range of solvents.76 We tested scaling on the sampling interval, d, as well as the maximum delay window for integration, to determine the magnitude of each required to yield a correct and consistent lineshape free of sampling artifacts. Scaling on the sampling interval was determined on a short, 500 ps trajectory of W4C*; the observed result was that d = 20-100 fs was sufficient. Details of this interval determination are shown in Figure S7. Therefore, the production trajectories were sampled at 40 fs intervals for frequency calculations and lineshape transformation. The increased


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sampling interval greatly reduced the frequency calculation times, enabling us to account for structural inhomogeneity by sampling longer trajectories. After establishing a reasonable d, the maximum delay time was tested using the 10 ns production trajectories. For both mutants with both frequency calculation methods, a maximum delay time of 12 ps was sufficient for the lineshape to converge. Details of this determination are shown in Figures S8 and S9. Lineshapes calculated with maximum delay = 12 ps, d = 40 fs are displayed in blue in Figure 2 of the main text. We also calculated the variance (∆, ps-1) and frequency-frequency correlation time constant (τ, ps) of the simulated frequency trajectory. The results are displayed in Figure 4. The τ constant is calculated using the following formula: τ =

∫

∞ 0

dt C(t) / C(0) . Though this formula is only

approximate when the FFCF is not strictly exponential, as in the case of W4C*, it nevertheless provides a reasonable estimate of the time constant for the sake of comparison between different FFCFs. Persistent long-time behavior (beyond the simulation time) is thus accounted for in an extended value of τ. Supporting Information. Detailed experimental methods, SASA calculations, methodology associated with sampling and lineshape construction. The Supporting Information (single .pdf file) is available free of charge on the ACS Publications website. Notes. The authors declare no competing financial interests. ACKNOWLEDGMENT This work was funded by NSF Career grant CHE-1150727 and a Henry Dreyfus TeacherScholar Award to CHL. RJX acknowledges a Velay summer fellowship from the


19


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Panaphill/Uphill foundations. Additional support was provided by IBS grant IBS-R023-D1 to MC. REFERENCES (1)

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S.;

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S.

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Figure 1: Mutant sites.

Page 31 of 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30


W4 S23


Absorbance or Probability Absorbance or Probability

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38


0.06

Page 32 of 35

W4C* - SolEFP 0.08

W4C* - QM/MM

0.07

0.05

0.06 0.04

0.05 0.04

0.03

0.03

0.02

0.02 0.01

0.01

0.05 2130

2150

2170

0.07 2130 2190 0.06

S23C* - SolEFP

0.04

2150

2170S23C* -2190 QM/MM

2150

2170

0.05 0.03

0.04

0.02

0.03 0.02

0.01 0.

0.01 2130

2150

2170

Wavenumber

(cm-1)


2190

2130

Wavenumber

2190

(cm-1)

Figure 2: SolEFP vs. QMMM results.

Page 33 of 35

40.0 Solvatochromic Shift (cm-1)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47


W4C* S23C*

30.0 20.0 10.0 0.0 -10.0 -20.0

Coulombic

Polarization

Repulsion Dispersion




Page 34 of 35

Page 35The of 35 Journal of Physical Chemistry Letters

Experiment Simulation

1 2 3 4 5 6 7

N C S

ACS Paragon Plus Environment 2140 2150 2160 2170 2180 Wavenumber (cm-1)

A Direct, Quantitative Connection Between ... - ACS Publications

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