Site-Selective Dynamics of Azidolysozyme
SSite-Selective Dynamics of Azidolysozyme
Seyedeh Maryam Salehi and Markus Meuwly ∗ Department of Chemistry, University of Basel, Klingelbergstrasse 80 , CH-4056 Basel,Switzerland.
E-mail: [email protected] a r X i v : . [ phy s i c s . b i o - ph ] F e b bstract The spectroscopic response of and structural dynamics around all azido-modifiedalanine residues (AlaN ) in Lysozyme is characterized. It is found that AlaN is apositionally sensitive probe for the local dynamics, covering a frequency range of ∼ − for the center frequency of the line shape. This is consistent with findings fromselective replacements of amino acids in PDZ2 which reported a frequency span of ∼
10 cm − for replacements of Val, Ala, or Glu by azidohomoalanine (AHA). For thefrequency fluctuation correlation functions (FFCFs) the long-time decay constants τ range from ∼ ∼
10 ps which compares with experimentally measured correlationtimes of 3 ps. Attaching azide to alanine residues can yield dynamics that decays tozero on the few ps time scale (i.e. static component ∆ ∼ − ) or to a remaining,static contribution of ∼ . − (corresponding to 2.5 cm − ), depending on the localenvironment on the 10 ps time scale. The magnitude of the static component corre-lates qualitatively with the degree of hydration of the spectroscopic probe. Althoughattaching azide to alanine residues is found to be structurally minimally invasive withrespect to the overall protein structure, analysis of the local hydrophobicity indicatesthat the hydration around the modification site differs for modified and unmodifiedalanine residues, respectively. Introduction
Understanding the structural and functional dynamics of proteins in the condensed phaseis a prerequisite for characterizing cellular processes at a molecular level. As an example,knowledge of the mechanisms and physical principles underlying protein-ligand recognitionfacilitates rational drug design for treatment of diseases.
One possibility to directly andquantitatively probe the structure and dynamics of proteins and protein-ligand complexes isvibrational, in particular 2-dimensional infrared (2D-IR) spectroscopy. ∼ − and frequencies above ∼ − , suitable vibrational labels should absorb in thewindow between ∼ ∼ − . A range of such probes has been proposed andconsidered in the past, including cyanophenylalanine, nitrile-derivatized amino acids, thesulfhydryl band of cysteines, deuterated carbons, non-natural labels consisting of metal-tricarbonyl modified with a -(CH ) n - linker, nitrile labels, cyano and SCN groups, orcyanamide. Another promising and sensitive label that was recently used is azidohomoala-nine (AHA) for which it has been demonstrated that it can be used to characterize therecognition site between the PDZ2 domain and its binding partner to provide site-specificinsight into the underlying mechanisms of how signaling proteins function. The noncanonical amino acid AHA absorbs around ∼ − with a comparatively largeextinction coefficient of up to 400 M − cm − . From a preparative perspective attachment ofN − to alanine (to give AlaN ) and AHA and incorporation at almost any position of a proteinthrough known expression techniques has been demonstrated. Furthermore, attachment ofan N − probe is a spatially small modification and the chemical perturbations induced areexpected to be small. This makes AlaN and AHA worthwhile modifications to probe localprotein dynamics.Optical spectroscopy, and especially two-dimensional infrared (2D-IR) spectroscopy, quanti-tatively provides information about the structure and dynamics of the solvent environmentsurrounding a probe molecule. Such techniques can also be used to measure the subpicosec-ond to picosecond dynamics in condensed-phase systems. With that, the coupling betweeninter- and intramolecular degrees of freedom such as the hydrogen bonding network in solu-tion, or structural features of biological macromolecules can be investigated by monitoringthe fluctuation of fundamental vibrational frequencies of a probe molecule or ligand attachedto a complex or a biological macromolecule. The possibility to use infrared spectroscopy for3haracterizing protein-ligand complexes has already been proposed for the nitrile containinginhibitor IDD743 complexed with WT and mutant human aldose reductase and explicitlydemonstrated for cyano-benzene in the active site of WT and mutant lysozyme. The AHA label was previously used in 2D-IR spectroscopy studies of ligand binding to thePDZ2 domain. The spectral changes observed for various modified pepdidic binders wereconsistent with the known X-ray structure of the wild-type peptide bound to the protein.This suggests that AHA is suitable as a specific IR reporter and to highlight subtle changesof the electrostatic environment on the protein surface. In the present work, attaching N − to all alanine residues in Lysozyme in succession is used to characterize the local dynamicsaround such modification site.Recent investigations have demonstrated that the vibrational dynamics of N − in the gasphase and in solution can be captured quantitatively. Based on high-level electronic struc-ture calculations at the multi-reference configuration interaction (MRCI) level of theoryand representing the 3-dimensional potential energy surface (PES) as a reproducing kernelHilbert space (RKHS), the infrared spectroscopy in the gas and condensed phase wascorrectly described. Also, the frequency correlation function exhibited time scales consistentwith experiment which suggests that the coupling between solvent and solute was correctlydescribed.The present work explores the local dynamics of all alanine residues in lysozyme as a typicalmodel system by attaching N − as a spectroscopic reporter. First, the computational methodsare summarized. Then, the structural dynamics and spectroscopy for all 14 AlaN labels isdiscussed and the local dynamics and hydration are explored. Finally, conclusions are drawn.4 ethods Molecular Dynamics Simulations
For the Molecular Dynamics (MD) simulations of WT and modified Lysozyme in solution,CHARMM together with the CHARMM force field was used. A suitably modified ver-sion of CHARMM was employed for the simulations with the 3-dimensional RKHS PESs(see below). The initial lysozyme structure was the X-ray structure (3FE0 ). Simulationsof Lysozyme in TIP3P water were carried out in a cubic box of size (62 . ˚A . Figure 1shows the structure of the system for the present work in which N − is attached individuallyto each of the 14 Ala residues, replacing one hydrogen atom of the terminal CH group. Thisyields Azidoalanine-modified Lysozyme. Compared with protein structures in which AHAis introduced, the two modifications differ by one CH -group. The systems were minimized, heated for 25 ps and equilibrated for 100 ps in the
N V T ensemble. Production runs, 2 ns in length, were carried out in the
N V T ensemble, with co-ordinates saved every 5 fs for subsequent analysis. All nonbonded interactions were treatedwith a 14 ˚A cutoff switched at 10 ˚A, and bonds involving hydrogen atoms are constrainedusing SHAKE. Figure 1: Structure of Lysozyme with positions of Alanine residues indicated. The Alanineresidues are at positions 9, 26, 32, 42, 47, 73, 76, 83, 90, 92, 94, 96, 108, 111. Ala residuesare displayed as CPK spheres and the rest of the protein structure is shown as NewRibbons.As an example, AlaN is shown at residue 47. Energy Function for the Spectroscopic Probe
For representing the 3-dimensional energy function of the N − label two strategies were pur-sued. First, the existing 3-dimensional PES for N − , computed at the MRCI+Q level oftheory in the gas phase, was used to describe the stretching and bending distortions of thelabel attached to the CH group of alanine.Because the N − moiety and the rest of the Ala residue are not fully electronically decou-pled, a second approach was pursued. For this, the structure of AHA was optimized at theMP2/aug-cc-pVTZ level of theory. Next, the structure of AHA was frozen except for thecoordinates involving the spectroscopic label. Then, a new 3-dimensional PES was computedat the pair natural orbital based coupled cluster level (PNO-LCCSD(T)-F12) together6ith the aug-cc-pVTZ basis set using the MOLPRO suite of codes. As for the gas phasePES, the ab initio energies were calculated in Jacobi coordinates ( R, r, θ ), see Figure 2B,where r is the distance between the nitrogen atoms N1 and N2, R is the distance betweentheir center of mass and the atom N3, and θ is the angle between ~r and ~R . The angulargrid ( θ ) used here contains 5 Gauss-Legendre quadrature points between 156 ◦ and 180 ◦ . Theradial grids include 16 points along r ranging from 0.90 to 1.51 ˚A and 16 points along R between 1.45 and 2.12 ˚A. The PNO-LCCSD(T)-F12 level of theory was chosen as it combinesaccuracy with feasibility for the present problem because recomputing the MRCI PES forAHA is computationally intractable.For both PESs the parameters for the C-N3 stretch, the C-C-N3 and the C-N3-N2 bend arethose from Swissparam. All remaining parameters for the alanine residues were those of theCHARMM force field and were not readjusted after attaching N − to guarantee compatibilitywith the CHARMM22 force field.To carry out MD simulations for labelled Lysozyme, a continuous and differentiable repre-sentation of the ab initio energies is required. For this, a reproducing kernel Hilbert space-based representation is used. A RKHS representation provides approximate values fora function f ( x ) at positions x , away from the grid points x i . For this, the linear problem f ( x i ) = P j α j k ( x i , x j ) for the 1-dimensional kernels is solved which yields the coefficients α j . There are many possible choices for the kernel functions k ( · , · ) but inverse powers of thedistance have been found to perform well for intermolecular interactions. For multidi-mensional problems, tensor products of 1-dimensional kernels can be used.
For the present work, the 3-dimensional kernel K is K ( X, X ) = k ( n,m ) ( R, R ) k ( n,m ) ( r, r ) k (2) ( z, z ) . (1)7here X stands for all dimensions involved, r , and R are as defined above (see also Figure2), and z = 1 − cos( θ )2 maps the angle θ onto the interval [0 , k ( n,m ) ) with smoothness n = 2 and asymptotic decay m = 6 k (2 , ( x, x ) = 114 1 x > − x < x > , (2)are used for r and R whereby x > and x < are the larger and smaller values of x and x ,respectively. For the angular degree of freedom, a Taylor spline kernel k (2) ( z, z ) = 1 + z < z > + 2 z < z > − z < (3)is used.Charges were calculated for the optimized structure of AlaN at the MP2/aug-cc-pVTZ levelof theory from an NBO analysis using Gaussian and scaled to maintain overall neutrality.This yields a charge of − . e for the nitrogen atom N1 attached to CH group, 0 . e for the central N2 and − . e for the terminal nitrogen N3. Frequency Fluctuation Correlation Function and Lineshape
From each production simulation, 4 × snapshots are taken as a time-ordered series for com-puting the frequency fluctuation correlation function (FFCF) h δω (0) δω ( t ) i and line shapes.Here, δω ( t ) = ω ( t ) − h ω ( t ) i and h ω ( t ) i is the ensemble average of the transition frequency.The FFCF was determined from instantaneous harmonic vibrational frequencies based on anormal mode analysis. Normal modes were determined for each snapshot after minimizingthe structure of the N label and keeping the surrounding solvent frozen. Thus, frequencytrajectories ω i ( t ) for label i were obtained for the asymmetric stretch vibration of N attached8o Ala. From the FFCF the line shape function g ( t ) = Z t Z τ h δω ( τ ) δω (0) i dτ dτ . (4)is determined within the cumulant approximation. To compute g ( t ), the FFCF is numericallyintegrated using the trapezoidal rule and the 1D-IR spectra is then calculated as I ( ω ) = 2 < Z ∞ e i ( ω −h ω i ) t e − g ( t ) e − t T e − D OR t dt, (5)where h ω i is the average transition frequency obtained from the distribution, T (0 . ± . D OR = 1 / T R with T R = 1 . ± . From the FFCF, the decay time can be determined by fitting the FFCF to a general expres-sion h δω ( t ) δω (0) i = a cos( γt ) e − t/τ + n X i =2 a i e − t/τ i + ∆ (6)where a i , τ i , γ and ∆ are fitting parameters. The decay times τ i of the frequency fluctuationcorrelation function reflect the characteristic time-scales of the solvent fluctuations to whichthe solute degrees of freedom are coupled. In all cases the FFCFs were fitted to an expressioncontaining two decay times (i.e. n max = 2) using an automated curve fitting tool from theSciPy library. esults The Potential Energy Surface for the N − Label
Two PESs for the energetics of the N − are considered in the present work. One is basedon earlier MRCI+Q calculations with the aug-cc-pVTZ basis set for N − in the gas phase which was used without change for the simulation of the AlaN unit. The second one wasthe LCCSD(T) PES for AHA which included coupling between the N − probe and the aminoacid framework. The RKHS representations of the two PESs are reported in Figures 2A andB and the scans within CHARMM are shown in panels C and D.The RKHS representation of the PES for AHA was constructed from 1280 ab initio LCCSD(T)-F12 energies. An additional 230 ab initio energies are calculated at off-grid geometries toassess the quality of the RKHS representation. Figure S1 shows the correlation between thereference energies and the RKHS with a correlation coefficient of R = 0 . ab initio calculated energies whereasFigures 2C and D are from scanning the r and R coordinates for AHA in the gas phasein CHARMM. Comparing the PNO-LCCSD(T)-F12 PES (Figure 2A) with that at theMRCI+Q level of theory (Figure 2B) shows that the minima for the two are slightly dis-placed ( r = 1 .
19 ˚A vs. r = 1 .
24 ˚A and R = 1 .
77 ˚A vs. R = 1 .
76 ˚A). Furthermore, theLCCSD(T) PES is steeper along both, the r and R coordinates, which pushes the respectivevibrations up compared with the MRCI+Q PES, see Figure S2. Differences between the twoPESs are due to both, the methods (MRCI+Q vs. PNO-LCCSD(T)-F12) and the modelsystem (N − vs. AHA) considered. Comparing the isolated, gas-phase PESs (panels A andB) with those for AlaN (panels C and D) indicates that the PESs are close but not identicaldue to coupling between the spectroscopic probe and the alanine residue.10igure 2: Contour diagrams of the RKHS representations for AHA (panel A, PNO-LCCSD(T)-F12) and N − (panel B, MRCI+Q/aug-cc-pVQZ) PESs based on ab initio pointscalculated in Jacobi coordinates ( R, r, θ ) for θ = 180 ◦ , see inset in panel B. Panels C andD report the corresponding CHARMM energies for AHA. All energies are in kcal/mol andrelative to the zero of energy which is the minimum energy structure.In the following, all MD simulations were carried out with the PNO-LCCSD(T)-F12 PES asit yields harmonic frequencies for AlaN around 2110 cm − cm − (see Table 1) which is con-sistent with those experimentally observed for the replacement of AHA in PDZ2 domainat 2114 cm − and for AlaN3 in H O at 2116 cm − , respectively. Moreover, the influence ofthe covalent bonding to the Alanine residue is included in the construction of the potentialenergy surface. Additional refinements of the PES would, in principle, be possible through11orphing but were not deemed necessary for the present work which is mainly concernedwith the differential dynamics, i.e. the relative positional sensitivity, and spectroscopy forthe same label at different positions along the polypeptide chain. Structural Dynamics
For the structural dynamics first the root mean squared deviation (RMSD) of unmodifiedand modified Lysozyme in solution compared with the starting X-ray structure as the refer-ence is analyzed. For this, the RMSD of all C α atoms was considered. Figure 3 shows theRMSD for all C α atoms (blue) and those for the 14 Alanine residues (red) specifically fromthe 2 ns simulation of the modified protein at position Ala47. For the WT protein simi-lar RMSD values are reported in Figure S3. The RMSD values fluctuate below or around1 ˚A which is indicative of a stable simulation. This suggests that attaching a N − labelto Ala has an insignificant effect on the structural dynamics of Lysozyme, consistent withearlier findings for the PDZ domain for which also a minimally invasive effect was reported. Time (ps) R M S D ( Å ) C α (all residues)C α (all Ala residues) Figure 3: The structural RMSD for the C α atoms from all residues (blue) and for the 14 Alaresidues (red) specifically for Ala76N . 12 ibrational Spectra and Frequency Correlation Functions First, the power spectra and frequency trajectories for the asymmetric stretch of the azidelabel attached to all 14 alanine residues are presented. The power spectra as determinedfrom the Fourier transform of the N2-N3 distance correlation function are shown in Figure4A for all AlaN from 2 ns production runs. The peak maxima ω max cover a range of ∼ − (between 2160 and 2180 cm − ) and the full widths at half maximum (fwhm) of thespectra are around 20 cm − . Hence, although the same energy function was used for allmodified AlaN moieties, their power spectra differ depending on the position of the modi-fied Ala residue along the polypeptide chain. Frequency (cm -1 ) I n t e n s i t y ( a . u . ) Figure 4: Power spectrum based on the N2–N3 separation for all modified AlaN residues.The position of the frequency maxima differ for most of the AlaN labels and cover a rangebetween 2160 and 2180 cm − .The power spectra reported in Figure 4 are also representative of the infrared spectrumas shown in Figure S4. The top panel of Figure S4 reports the power spectrum and peakpositions of all three modes for Ala47N with the asymmetric stretch centered around 2170cm − , the symmetric stretch at 1333 cm − and the bending mode at 610 cm − . The bot-tom panel of Figure S4 demonstrates that the infrared spectrum (IR) determined from the13ipole autocorrelation function supports the peak positions found from the power spectrumto within 2 cm − .Next, the frequency trajectories ω i ( t ) for each of the spectroscopic probes i from 4 × snapshots were determined from instantaneous normal mode calculations. From the fre-quency time series the frequency fluctuation correlation functions (FFCFs) are obtained.They contain valuable information about the environmental dynamics around each site i ,i.e. the azide probes of the various Ala residues considered.The FFCFs, shown in Figure 5, are fitted to Eq. 6 with a parametrization motivated by theoverall shape of the FFCF. This functional form has also been used in previous work.
It is an extension of the typical multiexponential decay, which is traditionally employed to capture an anticorrelation at short times ( t < .010.110.010.110.010.110.010.11 FF C F ( p s - ) Time (ps)
Figure 5: FFCFs from correlating the instantaneous harmonic frequencies for all 14 AlaN in Lysozyme. The labels in each panel refer to the alanine residue which carries the azidelabel. Black traces are the raw data and red dashed lines the fits to Eq. 6. The y − axis islogarithmic.The shape of the FFCFs can differ appreciably. Some of them display a pronounced min-imum at short correlation times ( t ∼ . and has been related to the strength of the interactionbetween the infrared probe and its environment. Several of the FFCFs show one (Ala9,Ala32, Ala42, Ala76, Ala94, Ala96, Ala108, Ala111) or even two (Ala92) recurrences at shortcorrelation times. For the remaining Alanine residues this feature is less pronounced (Ala47,Ala73, Ala83, Ala90) or entirely absent (Ala26). Similarly, some of the FFCFs exhibit clearstatic components ∆ ’ . − (Ala26, Ala73, Ala96) whereas the remaining ones decay15o zero on the ∼
10 ps time scale. With respect to the correlation times, the fast correlationis generally τ ∼ . τ = 1 . τ < is a positionally sensitive probe to providequantitative information about the local dynamics of a protein. Table 1: Parameters obtained from fitting the FFCF to Eq. 6 for INM frequen-cies for all different AlaN residues in lysozyme. Average frequency h ω i of theasymmetric stretch in cm − , the amplitudes a to a in ps − , the decay times τ to τ in ps, the parameter γ in ps − , the offset ∆ in ps − , and the conformationallyaveraged local hydrophobicity (LH). Res h ω i a γ τ a τ ∆ LH Numerical integration of g ( t ) and using Eq. 6 yields the 1-dimensional IR spectra for eachlabel based on instantaneous normal modes, see Figure 6. Similar to the power spectra,the center frequencies cover a range of ∼
15 cm − , with center frequencies of 2104 cm − for Ala9N and 2116 cm − for Ala96N , and the fwhm ranges from 13 to 21 cm − . Also,the ω max for Ala9N (blue solid line in Figures 4 and 6) is lowest in frequency and thosefor Ala96N (dashed red) and Ala73N (solid green) are highest from the power spectra andthe INM lineshapes, respectively. The blue shift of the power spectra compared with those16rom INM for the symmetric and asymmetric stretch modes was already found for N − insolution. The magnitude of this shift is larger in the present case probably due to couplingbetween the spectroscopy probe and the amino acid it is attached to.
Frequency (cm -1 ) I n t e n s i t y ( a . u . ) Figure 6: 1D IR spectra for all 14 AlaN residues in Lysozyme. For the IR lineshape theraw FFCF from the INM analysis was numerically integrated to give g ( t ) from which the 1Dlineshape is obtained.An alternative to instantaneous normal modes is to obtain instantaneous frequencies fromsolving the 1- or 3-dimensional nuclear Schr¨odinger equation. For this, the corresponding 1-or 3-d PES is scanned for a given snapshot with frozen environment and representedas a RKHS. This is a computationally much more demanding approach, in particular in3 spatial dimensions. Here, the 1-dimensional PES along the asymmetric stretch motionwas mapped out for 4 × snapshots and the nuclear Schr¨odinger equation was solved.Then, the FFCF was again determined and fit to Eq. 6, see Figure S5. From this, the1-dimensional IR lineshape was determined, see solid lines in Figure S6. This was donefor Ala90N and Ala94N . As was found for the 1-d lineshapes from INM, the frequencymaximum for Ala90N is shifted to the blue relative to Ala94N but the shift is smaller (1cm − vs. 3 cm − ). 17ecently, the “INM”, “scan” and “map” approaches have been compared for insulin monomerand dimer. It was found that the “INM” and “scan” approaches yield comparable 1-d in-frared spectra for the amide-I bands and conclusions drawn from the spectra concerningmonomeric and dimeric insulin are consistent. Nevertheless, the two approaches can differin the absolute frequencies as is also found in the present case.Typically, spectroscopic work has used AHA as an infrared label instead of azidoalanineas used here. To quantify the difference between AlaN and AHA, residue Ala47 has alsobeen replaced by AHA through inserting an additional CH group before the N − label. Theparametrization of the CH group is identical to that already used for alanine. Then, a 2ns simulation for AHA in water was carried out and the IR spectrum was determined froman INM analysis, see Figure S7. It is found that the position of the frequency maximum forthe asymmetric stretch of the azide label differs by less than 1 cm − from that with AlaN which confirms that for IR spectroscopy, the two systems are very similar. Solvent Structure and Dynamics
Next, the solvent structuring around the modification sites is characterized. This also pro-vides the information for an attempt to relate the spectral signatures (position of the fre-quency maximum, characteristics of the FFCFs) for the azide labels at different positionsalong the polypeptide chain with structural features and environmental properties. For this,the solvent structure around each of the 14 AlaN probes was analyzed. First, the radial dis-tribution functions g ( r ) were computed along all production simulations for the 14 modifiedproteins, see Figure 7. The distance analyzed was the separation between the water-oxygenatom (O W ) and the middle nitrogen (N2) of the N probe in AlaN . The corresponding18unning coordination number N ( r ) is N ( r ) = 4 π Z r r g ( r ) ρdr where ρ is the pure water density (Figure 7B). As is shown in Figure 7, the g ( r ) and N ( r )differ for the 14 modification sites.For some of the residues (Ala26, Ala42, Ala47, Ala73, Ala76, Ala108, Ala111; Set1) the g ( r )exhibits a pronounced first maximum at 3 . ≤ r max1 ≤ N ( r ) of water molecules within a distance r supports this, seeFigure 7B. Up to a distance of 5 ˚A, which is typically the extent of the first hydration shell,residues in Set1 contain 10 or more water molecules whereas those belonging to Set2 havenot more than 1 water molecule in their vicinity. g ( r ) A r (N2−O) (Å)
2 3 4 5 6 7 8 9 0.01 0.1 1 10 100 N ( r ) B r (N2−O) (Å) Figure 7: The radial distribution function g ( r ) (panel A) and the number of water oxygenatoms N ( r ) (panel B) between O of water and N2 of AlaN for all alanine residues from the2 ns production simulations. The color code for the lines is given in panel B.A structural illustration for this observation is given in Figure 8 which reports all watermolecules within 7 ˚A of Ala47N (belonging to Set1) and Ala96N (belonging to Set2). Con-19istent with Figure 7 only 3 water molecules are within the cutoff radius of atom N2 ofAla96N whereas the hydration shell of Ala47N is extensive. A B Figure 8: Solvent distribution based on the water-oxygen atoms within 7 ˚A of any atom ofresidues Ala96N (panel A) and Ala47N (panel B). The small and large hydration spheresare consistent with the g ( r ) and N ( r ) reported in Figure 7.Another measure to quantify the solvent exposure of amino acids is to determine the timedependent quantity, δλ ( r )phob ( t ), which is referred to as the local hydrophobicity (LH) of residue r at time t . This measure is based on analyzing the occupation and orientational statisticsof surface water molecules at the protein/water interface, given by the three dimensionalvector ~κ = ( a, cos θ OH1 , cos θ OH2 ). Here, a is the distance of the water oxygen atom to thenearest atom of residue r , and θ OH1 and θ OH2 are the angles between the water OH1 andOH2 bonds and the interface normal. More specifically, the local hydrophobicity (LH) is δλ ( r )phob ( t ) = λ ( r )phob ( t ) − h λ phob i , where λ ( r )phob ( t ) = − P N a ( r ) a =1 N w ( t ; a ) N a ( r ) X a =1 N w ( t ; a ) X i =1 ln (cid:20) P ( ~κ ( i ) ( t ) | phob) P ( ~κ ( i ) ( t ) | bulk) (cid:21) (7)and h λ phob i is the ensemble average sampled from the ideal hydrophobic reference system(see below). The summation over N a ( r ) involves all atoms in residue r and the summationover N w ( t ; a ) includes all water molecules within a cut-off of 6˚A of atom a at time t . The20ector ~κ ( i ) ( t ) describes the orientation (see above) of the i th water molecule in the sampledpopulation.The distribution P ( ~κ ( i ) ( t ) | phob) is determined for a reference hydrophobic reference system(’phob’), whereas P ( ~κ ( i ) ( t ) | bulk) is determined from the actual simulations (’bulk’). As thequantity LH includes both, the distance a of the water molecules from the interface and theorientation of a specific water molecule ( θ OH1 , θ
OH2 ), LH can be considered as a generalizationof the radial distribution function g ( r ). The local hydrophobicity is a measure of the statisti-cal similarity of the sampled configurations to that of an ideal hydrophobic reference system.When sampled configurations P ( ~κ ( i ) ( t ) | bulk) are dissimilar to the hydrophobic reference sys-tem, this indicates that the site r considered is less hydrophobic, i.e. rather hydrophilic andvice versa. In other words, δλ ( r )phob ( t ) ≈ δλ ( r )phob ( t ) significantly larger than zero, the environment is hydrophilic. In pre-vious work, sustained values of δλ ( r )phob > . -1 0 1 2 3 0 1000 2000 3000 4000 5000 δ λ ( r ) phob ( t ) Time (ps)
Figure 9: Local hydrophobicity as a function of time for all alanine residues from the simula-tion of WT Lysozyme. The LH coefficient was determined from Eq. 7. Values of δλ phob ≈ whereas values around 2 pointtowards a hydrophilic site. 21igure S8 gives an overview of the average LH per residue and the fluctuations around theaverage for WT Lysozyme. The Alanine residues (in red) are found to include both, low andhigh values for LH, representative of more hydrophobic and hydrophilic environments, re-spectively. The change in LH as a function of simulation time (over 2 ns) for WT (blue) andN − labelled (red) Lysozyme for Ala76 is reported in Figure S9. Without spectroscopic labelthe Ala-residue is rather hydrophilic on average whereas with the label attached it is morehydrophobic (less hydrophilic). On the other hand, the LH can have a rather pronouncedtime-dependence, see Figure 9 (solid orange line for Ala76) from the 5 ns simulation of WTLysozyme. Thus, attaching the N − label to Ala may modulate recruitment or displacementof solvent molecules. Discussion and Conclusion
The present findings confirm that azide attached to alanine residues in Lysozyme is a struc-turally minimally invasive, specific infrared label to quantitatively probe the local dynamicsaround the modification site. This has already been reported for the PDZ2 domain. Similarto the situation in insulin monomer and dimer, for which the amide-I vibration was found to cover a range of ∼
20 cm − , attaching azide to give AlaN spans a comparable frequencyrange but in a region of the infrared spectrum (around 2100 cm − ) that is typically “empty”.Together with their minimal impact on the overall protein structure (see Figure 3), and thestill favourable extinction coefficient, such modifications bear great potential to resolve thestructural dynamics of proteins and protein-ligand complexes at a molecular level. Studiesthat provide structural and spectroscopic information at the same time are of great interestfor characterizing potential ligand-binding sites and for functional studies of protein allostery.22 ∆ ( p s - 2 ) F r e qu e n cy ( c m - ) A N(r
F i r s t H y d r a t i o n S h e l l )
26 42 4773 76 108111 B Figure 10: Correlation between the maximum of the 1-d lineshape from INM and he staticoffset ∆ of the FFCF (panel A) and the maximum of the 1-d lineshape from INM and thenumber of water molecules in the first hydration shell (panel B) for the residues that hasbeen considered to be rather “water exposed” (Set1). Residues of Set1 are shown as bluesquares and those of Set2 as green circles. The solid line is an empirical linear fit and suggeststhat, typically, for more blue shifted frequency maxima the static component increases whilethe number of water molecules in the first hydration shell decreases, i.e. with increasinghydration, ω max shifts typically to the red for alanine residues in Set1.It is of interest to delineate whether correlations can be found between structural and spec-troscopic characteristics analyzed in the present work. As the dynamics is coupled andinvolves a potentially complicated superposition of different structural substates, no “sim-ple” or “obvious” correlations are expected. Rather and at best, discovering trends can beexpected from such an analysis. One example is shown in Figure 10B which reports the rela-tionship between the number of water molecules in the first hydration shell (see also Figure7) and the position of the frequency maximum ω max from the 1-d lineshape determined fromthe instantaneous normal mode analysis. Typically, with increasing hydration, the positionof ω max shifts to the red. Similarly, the magnitude of the static offset ∆ of the FFCF isrelated to ω max in that larger values of ∆ are associated with a blue shift of the position ofthe frequency maximum, see Figure 10A.Spectroscopic probes to characterize the local environment of a protein provide valuable23nformation about local hydration. This is of particular relevance given the findings thatindividual water molecules can play decisive roles in protein function. For example, in HIV-Iprotease a single catalytic water molecule was located in the active site of the proteinor for insulin individual water molecules were found to attack the dimerization inter-face to reduce the thermodynamic stability of the dimer by a factor of two. Similarly, watermolecules have been reported to play essential roles in protein folding, and for function. Thus, probing and characterizing the local solvent environment of particular regions of a pro-tein can provide important insights into functional aspects of proteins.The utility of infrared spectroscopy to study the strength of protein-ligand complexes hasbeen proposed and explicitly demonstrated from molecular dynamics simulations for cyano-substituted benzene in lysozyme. Using AHA as a probe, it was reported that unboundand ligand-bound PDZ2 differ in that the frequency correlation function for the two systemsdecay to different levels at longer correlation times. Similarly, infrared spectroscopy is alsoa sensitive probe - both, in terms of spectroscopy and dynamics - to characterize protein-protein interactions. Together with experimental studies, such efforts pave the way forfunctional, in vivo studies of protein-ligand and protein-protein association. In conclusion, the present work provides a comprehensive analysis of the spectroscopy anddynamics of azide-labelled alanine in Lysozyme. The results demonstrate that AlaN is apositionally sensitive probe for the local dynamics, covering a frequency range of ∼
15 cm − .This is consistent with findings from selective replacements of amino acids in PDZ2 whichreported a frequency span of ∼
10 cm − for replacements of Val, Ala, or Glu by AHA. Furthermore, the long-time decay constants τ range from ∼ ∼
10 ps which compareswith experimentally measured correlation times of 3 ps. Attaching azide to alanine residuescan yield dynamics that decays to zero on the few ps time scale (i.e. ∆ ∼ − ) or toa remaining inhomogeneous contribution of ∼ . − (corresponding to 2.5 cm − ). One24xciting prospect of this is to determine how the spectroscopy and dynamics of the modifi-cation site changes upon ligand binding to the active site for Lysozyme or other proteins. Acknowledgments
The authors gratefully acknowledge financial support from the Swiss National Science Foun-dation through grant 200021-117810 and to the NCCR-MUST. The authors thank Prof. P.Hamm and Dr. D. Koner for discussions on the experiments and some of the electronicstructure calculations.
Data Availability Statement
The data that support the findings of this study are available from the corresponding authorupon reasonable request. 25 eferences (1) Plitzko, J. M.; Schuler, B.; Selenko, P. Structural Biology outside the box - inside thecell.
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E-mail: [email protected] E PNO-LCCSD(T)-F12 (kcal/mol) E RKH S ( kca l/ m o l ) Figure S1: Correlation between ab initio and RKHS interpolation for 230 randomly selectedgeometries. The R = 0 . a r X i v : . [ phy s i c s . b i o - ph ] F e b
200 1400 1600 1800 2000 2200 2400
Frequency (cm -1 ) I n t e n s i t y ( a . u . ) MRCI+QLCCSD(T)-F12
Figure S2: Power spectrum based on the N1-N2 separation for AHA in the gas phase andfrom MRCI+Q and LCCSD(T)-F12 surface.
Time (ps) R M S D ( Å ) C α (all residues)C α (all Ala residues) Figure S3: The structural RMSD for the C α atoms from all residues (blue) and for the 14Ala residues (red) for WT Lysozyme. S2
100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300
Frequency (cm -1 ) I n t e n s i t y ( a . u . )
400 500 600 700 800400 500 600 700 800PSIR
Figure S4: Power (PS, top panel) and IR (bottom panel) spectrum for Ala47N . The powerspectrum is based on N2-N3 bond displacement. The inset shows the bending mode ofthe Azide group. IR spectrum is calculated the Fourier transform of the molecular dipolemoment autocorrelation function. S3 FF C F ( p s - ) INM 90SCAN 90
Time (ps)
Figure S5: The FFCF for Ala90 based on INM (red) and scan (blue) frequencies. The dashedlines show the corresponding fit to Eq. ?? with 3 time scales and the fitting parameters areas follows: INM: a = 0 . γ = 21 . τ = 0 .
18 ps, a = 1 . τ = 0 .
05 ps, a = 0 . τ = 2 .
70 ps, ∆ = 0 .
25 and scan: a = 0 . γ = 17 . τ = 0 .
11 ps, a = 0 . τ = 0 . a = 0 . τ = 1 .
62 ps, ∆ = 0 .
07. The comparison shows that the two different waysto determine the instantaneous frequency ( ω ( t ) and ν ( t ), respectively) does not affect theoverall appearance of the FFCF except for the magnitude of the asymptotic value ∆ .S4 Frequency (cm -1 ) I n t e n s i t y ( a . u . ) Figure S6: 1D IR spectra for Ala90N and Ala94N of lysozyme obtained from frequencycalculations using “scan” (solid lines) and INM (dashed lines). Both analyses agree in thatthe frequency maximum for Ala90N is to the blue of that for Ala94N but the magnitudeof the shift differs for the two approaches. Frequency (cm -1 ) I n t e n s i t y ( a . u . ) AlaN3AHA
Figure S7: Comparison between the 1D-IR spectra of AlaN and AHA at position Ala47in Lysozyme. For AHA, an additional CH group is inserted before the N − label. Thelineshapes for azidoalanine and azidohomoalanine are very similar. The position of thefrequency maximum for the asymmetric stretch of the azide label differs by less than 1cm − . S5