Thermal Denaturation of Polyalanine Peptide in Water by Molecular

J. Phys. Chem. B 2007, 111, 605-617

605

Thermal Denaturation of Polyalanine Peptide in Water by Molecular Dynamics Simulations and Theoretical Prediction of Infrared Spectra: Helix-Coil Transition Kinetics Seongeun Yang* and Minhaeng Cho* Department of Chemistry and Center for Multidimensional Spectroscopy, Korea UniVersity, Seoul 136-701, Korea ReceiVed: July 31, 2006; In Final Form: NoVember 6, 2006

Perspectives in the helix-coil transition kinetics of secondary structures are examined by temperature-jump molecular dynamics (T-jump MD) simulations and theoretically calculated infrared (IR) spectra. Homopolymeric polyalanine, Ac-(A)21-NHMe (A21), is unfolded in water by T-jumps from 273 to 300 K ∼ 450 K using AMBER ff99 and ff03 force fields. MD simulation results provide in silico evidence that 310-helix and type I β-turn motifs are highly probable in both ff99 and ff03 results. Temperature-dependent difference IR spectra of A21 do not possess an isosbestic point in both results, and isotope-labeled difference IR spectra in ff03 results predict characteristic profiles observed in experiments. Unfolding rates obtained from simulated timeresoled IR spectra are in good agreement with those estimated by helical contents, but they are still an order of magnitude smaller than experimental values. We demonstrate that the conventional criteria such as singleexponential fit of transient amide I absorbance, sigmoidal fit of temperature-dependent amide I absorbance, and Arrhenius plot of relaxation rates cannot guarantee the validity of assuming a two-state mechanism. We suggest a way of determining Tm by the temperature dependence of center frequency and full width at halfmaximum of amide I band. Overall, both ff99 and ff03 force fields give consistent results in reproducing key aspects concerned experimentally, but are not predominantly satisfactory in quantitative aspects.

Introduction Secondary structure formation has been recognized as the fastest event in protein folding, and the idea has been corroborated with rapid progresses in time-resolved spectroscopic techniques.1-6 Vibrational spectroscopies combined with laserinduced temperature jump (T-jump) method,7,8 among others, prove themselves to be powerful in tracking the fast events occurring in submicroseconds. Since the first de novo alaninebased peptides were introduced to have a high helicity, as much as over ∼80% in water,9,10 synthetic peptides based on more or less the same design have been vigorously studied using these techniques. Williams et al.11 reported the first example of fast folding kinetics of the FS peptide,12,13 of which the folding time deduced from the unfolding kinetics is merely 16 ns, and confirmed that secondary motifs of proteins, R-helix in this case, should form prior to tertiary contacts. They fitted the temperature-dependent equilibrium Fourier transform infrared (FTIR) optical densities at 1632 cm-1, the amide I′ frequency at around 8.3 °C, to a functional form derived by assuming a two-state transition, and obtained a melting temperature (Tm) of 61 °C and an unfolding enthalpy of -0.6 ((0.1) kcal‚mol-1/residue. With a T-jump of 18 °C, the transient optical densities at several frequencies due to helical and unfolded ensembles were all fitted to double exponentials with the same sets of time constants, of which the longer one of 160 ( 60 ns was assigned to the helix relaxation time. Although they analyzed their results based on a two-state model, they suggested that the absence of a sharp isosbestic point in the difference FTIR spectra and the rather small unfolding enthalpy indicate the lack of a two-state equilibrium. In another laser-induced T-jump experiment using a fluorescent N-terminal probe, Thompson et al.14 obtained ∼8* Address correspondence to either author. E-mail [email protected] (MC); [email protected] (SY).

fold smaller unfolding time constant of ∼20 ns than ∼160 ns of Williams et al. They attributed the faster kinetics to the relaxation of the N-terminal segment while assigning the long time unfolding kinetics by Williams et al. to the relaxation of the entire helix using the kinetic-zipper model based on the single-sequence approximation. Meanwhile, the weak temperature dependence of the relaxation rates and a shallow minimum at the midpoint were interpreted to mean that the helix-coil conversion is a diffusive process. The peptide unfolding rates are usually measured by monitoring the time-dependent relaxation of the amide I(I′) absorption in FTIR combined with the laser-induced T-jump method. Many kinetic measurements for Ala-based peptides, having N-terminal modifications to the original FS peptide, could be fitted to an exponential function and were modeled by the two-state mechanism.14-17 On the contrary, Huang et al.18-20 reported a multiexponential and even a nonexponential kinetics for the helix-coil transitions of Ala-rich peptides, also derived from the FS-peptide but having a helix-stabilizing N-terminal cap and D-Arg at the C-terminal. Combining isotope-labeling technique21,22 with the time-resolved FTIR, their results show, evidently, that the helix nucleation process is fast enough to occur within a few hundred nanoseconds, as reported in earlier experiments. They suspected the presence of on-path or offpath intermediates for the processes fitted with multiexponentials, while they attributed the non-exponential kinetics and temperature dependence of the relaxation rates to the diffusive conformational search23,24 on the energy landscape. In a recent time-resolved IR experiment of a photoswitchable Ala-based peptide by Bredenbeck et al.,25 the amide I′ transient profile at 322 K shows single-exponential kinetics comparable to time constants obtained from previous T-jump experiments, while the folding kinetics becomes slower and nonexponential at 281

10.1021/jp0649091 CCC: $37.00 © 2007 American Chemical Society Published on Web 01/03/2007

606 J. Phys. Chem. B, Vol. 111, No. 3, 2007 K, suggesting further studies about the causes of nonexponentiality at low temperatures. The 310-helix motif, defined by hydrogen-bonds between i-th CdO and (i + 3)-th N-H, has long been suggested to be significant and distinguishable in helical peptides by Millhauser et al. using circular dichroism (CD), one-dimensional (1D) FTIR, electron spin resonance (ESR), and nuclear magnetic resonance (NMR) techniques.26-29 But studies by Keiderling and coworkers,30-35 based mainly on 1D FTIR and vibrational circular dichroism (VCD) spectra of isotope-edited peptides, suggest that the peptides are R-helical, and the previous assignment by Millhauser et al. is erroneous. Even though pure 310-helix can be distinguished from R-helix with VCD spectra,32,33 the presence of 310 in equilibrium with R-helix cannot be identified separately in their results. Additionally, in a report using HNCO NMR spectra,36 π-helix, characterized by hydrogen-bonds between i-th and (i ( 5)-th peptide groups, as well as 310-helix were not observable. Recently, however, a two-dimensional (2D) IR study of a Val-based octapeptide37 reported how to discriminate 310-helix from R-helix and expected further applications of the technique. In spite of the forementioned continuing efforts, there seems to be no general consensus until now among different experimental setups about the existence and the identity of helical motifs other than R-helix in the helix-coil transition of small peptides. Thus, the inconsistency observed in their kinetics is inevitable. The correlation between structure, dynamics, and spectra of peptides and proteins sets the need for experiments to accompany theoretical analyses, and a few theoretical schemes to calculate 1D and 2D IR and VCD spectra38-44 have been addressed to obtain simulated spectra. So far, however, there seems to be no report bridging kinetic information obtained from experimental spectra with the corresponding one from simulations. We have developed our own computational methods to predict amide I 1D and 2D IR and VCD spectra of protein secondary structures,45-50 by combining a theoretical framework, quantum chemical calculations, and molecular dynamics (MD) simulations. The helix-coil transition thermodynamics and kinetics51 of the Ala-based peptides have been extensively studied by MD simulations,52-64 but those studies lack insights into the kinetics perspective directly comparable to spectroscopic observables. In the present study, we perform T-jump MD simulations of a capped helical polyalanine peptide, Ac-(A)21NHMe (hereafter, denoted as A21), chosen as a template to further study the FS-like peptides, at several temperatures using AMBER force fields ff9965 and ff0366 and first discuss the unfolding kinetics by calculating the temperature-dependent and time-resolved 1D IR spectra. We cast doubts on the validity of conventional criteria to determine the helix-coil transition mechanism and suggest a new set of spectroscopic signatures to determine Tm of a peptide. All computational results in the present study are compared with those of previous experimental and MD simulation studies to obtain compromising explanations on the arguments persistent in establishing the helix-coil transition mechanism of small polypeptides. Materials and Methods MD Simulations. The A21 peptide, initially having ideal backbone dihedral angles of R-helix, (φ ) -57°,ψ ) -47°), is immersed in a TIP3P67 water box. The solvent water molecules are energy minimized with the solute constrained, then vice versa, and finally the whole system is minimized without constraints, for 1000 steps each using conjugate gradient method. The peptide solution is heated gradually from 0 to 273 K for

Yang and Cho 30 ps under the constant volume and temperature (NVT) condition and equilibrated at 273 K and 1 atm under the constant pressure and temperature (NPT) condition for 5.7 ns, of which the later 5 ns data is used in trajectory analyses. The simulation time step is 1 fs for heating and 2 fs for subsequent runs. The trajectory is saved every 1 ps in all simulations. At least 10 coordinate sets, in which the peptide is highly helical, are arbitrarily chosen from the equilibrium trajectory at 273 K to be used as initial conformations in T-jump simulations to higher temperatures, 285 and 300 K to 450 K at 30 K increments. At all temperatures, 10 different unfolding trajectories are generated for 5 ns, respectively, except for as many as up to 50 trajectories at 450 K. All bonds involving hydrogen atoms are constrained using the SHAKE68 algorithm. The nonbonding interactions are calculated by using the particle mesh Ewald (PME)69 method and are updated every 20 ps with the cutoff of 8 Å. Temperature and pressure are scaled using the weak-coupling algorithm,70 with the coupling time of 1 ps for both. The simulation times for production runs are 500 ns using ff99 and 600 ns using ff03, respectively. The procedure above is applied equally for all simulations at all temperatures using both ff9965 and ff0366 force fields. The simulation box size is determined by preliminary calculations at the highest temperature of 450 K, i.e., the edge length of a cubic box is the sum of the longest end-to-end distance (the distance between CR atoms of terminal alanines) and at least twice the nonbonding cutoff distance. The number of water molecules contained in the cubic box is 4544 and 6038 for ff99 and ff03 simulations, respectively. Due to the well-known shortcomings of the older AMBER force fields up to ff99 that the energy balance is overweighed to prefer helical than extended structures, there have been continuing efforts to correct the sampling bias by nullifying the 1-4 through-bond interactions,57,59,71 by modifying only the torsional parameters,72 or even further modifying the nonbonding interaction parameters.73 Performances of those modified force fields have been improved to the direction that the unfolded ensemble of small peptides is to be sampled heavily in extended regions, especially in polyproline II (PII) structure. The AMBER ff03 force field, in which atomic charges were reevaluated at a higher quantum mechanical level than the one used in previous force fields and in the condensed phase using implicit solvent model with an effective dielectric constant of ) 4, is the most recent one born out of these efforts. As comparative studies for the performances of other force fields in predicting conformational preferences of small peptides are already available,74,75 we chose the most recent forces fields AMBER ff99 and ff03 to study whether the two results give consistent answers to our questions on the use of conventional criteria in determining the helixcoil transition mechanism, even if they seem to be different quantitatively each other. Amide I IR Spectra. Due to its high degree of localization on the backbone carbonyl groups in polypeptides and proteins, the amide I band has been exploited as a popular probe to distinguish different secondary structural motifs or to figure out solvation effects on the spectra. For polypeptides or proteins of which the ab initio vibrational analyses are expensive, a Hessian matrix is usually constructed using the transition dipole coupling (TDC) model,38 to get normal amide I modes. In previous studies38,39 using the TDC model to simulate amide I IR spectra, the off-diagonal frequencies, i.e., the coupling constants, are calculated based on the TDC mechanism. It is well-known, however, that the TDC model suffers from its low validity for evaluating the coupling constants between the nearest

Helix-Coil Transition Kinetics of Secondary Structures

J. Phys. Chem. B, Vol. 111, No. 3, 2007 607

peptide groups.76,77 Meanwhile, the diagonal frequencies of a Hessian matrix are set equally to the value of average amide I frequency of proteins observed in experiments, which is no longer a reasonable approximation for cases having a high conformational inhomogeneity due to neighboring peptide groups and solvent molecules. To take the inhomogeneity of amide I frequencies into account, we decompose the contributions to each local amide I frequency into three terms.45,46 The m-th local amide I frequency of a polypeptide, ν˜ m(t), is modulated by the interpeptide and the peptide-solvent interactions, resulting in the shift from the value of an isolated model unit peptide, ν˜ o,

ν˜ m(t) ) ν˜ o + δν˜ peptide (t) + δν˜ water m m (t)

(1)

where Ujk is the eigenvector elements of k-th instantaneous normal mode (INM) obtained from the Hessian matrix diagonalization, µk is the k-th local amide I dipole moment and qk is the k-th local amide I coordinate. The right-hand side of eq 2 can be further approximated as

〈 ( )| ( ) 〉 ∑j | ∂Q N

∂µ

〈 ( )| ∑j | ∂Q N

4

δν˜ peptide (t) ) m

peptide l j φj(m) (t) ∑ j)1

4

)

l ∑ j)1

j

(t)

The lj values for C, O, N, and H atoms in the amide group are lC ) 1.60 × 10-3, lO ) -5.54 × 10-3, lN ) 4.79 × 10-3, and lH ) -8.60 × 10-4 e, respectively.78 The electrostatic potential exerted on the atom j of m-th peptide by neighboring peptide peptide groups or by surrounding water molecules, φj(m) (t) or water φj(m) (t), is calculated using atomic partial charges, which were previously determined to be cC ) 0.419, cO ) -0.871, cN ) 0.793, and cH ) -0.341,79 and atomic coordinates obtained from MD simulations. The atomic charges of oxygen and hydrogen atoms of TIP3P water are -0.834 and 0.417 e, respectively. The diagonal elements of a Hessian matrix in the amide I subspace comprise these local amide I frequencies. Meanwhile, the off-diagonal elements due to the vibrational coupling of a pair of local amide I modes are evaluated using the TDC model for all possible pairs, except for the (j, j ( 1)-th elements which are substituted with a high level ab initio calculation results of a glycine dipeptide analogue.78 The Hessian matrix is then diagonalized to get amide I normal modes, instantaneous due to their transient character. The procedure is repeated for every set of coordinates saved during MD simulations and takes systematically the inhomogeneous broadening effect into the IR spectra. The amide I IR absorption spectrum is obtained by Fourier transforming the corresponding dipole autocorrelation function,80 which can be written in the limit of harmonic oscillator approximation as

〈 ( )

∑j | ∂Qj 0|2 Qj(t)Qj(0) N

〈µ(t)‚µ(0)〉 =

∂µ

〉

(2)

where µ(t) is the time-dependent dipole moment of the amide I vibrations and N is the number of normal modes or the number of peptide units in a polypeptide. The transition dipole of the j-th amide I normal coordinate (Qj) is given by a linear combination of the local amide I mode transition dipoles:

∂µ ∂Qj

N

)

∂µk

∑k U jk ∂q

(3) k

∂µ

2

(4)

〉

δ(ω - ωj)

j 0

〈∑|( ) | N

I(ω) ∝ water j φj(m)

cosωjt

(5)

where the Dirac delta function is again replaced by a Lorentzian function as

and

δν˜ water m (t)

Mjωj2

j 0

where kB is the Boltzmann constant, T is temperature, Mj is the mass of j-th oscillator, and ωj is the j-th normal-mode frequency which corresponds to the eigenvalue of j-th INM. The IR absorption spectrum is then given by

I(ω) ∝

where

k BT

2

∂µ

∂Qj

0

2

γj (ω - ωj)2 + γ2j

〉

(6)

to take the vibrational dephasing into account. The dephasing constant γj, as a measure of the homogeneous broadening, was optimized to get the maximum agreement with experiments in our previous studies45 and the value of 8 cm-1 is used for every normal mode in all calculations. Results and Discussion Conformational Analyses of MD Trajectories. Equilibrium simulations of A21 at 273 K using AMBER ff99 and ff03 force fields yield quite different results for CR root-mean-square deviation (rmsd), radius of gyration (RG), end-to-end distance (DA1-A21), helical content defined by the Lifson-Roig model,81 etc., as shown in Figure 1. Initial helix structure of A21 deforms significantly early in time, extends to a coil after about 1.5 ns in ff99 results. On the contrary, A21 remains highly helical throughout 5 ns in ff03 results. The average helicities for 5 ns are 30% (23% for the later 3.5 ns) and 87% for ff99 and ff03 runs, respectively, in Figure 1d. Alanine has been known to be a helix-stabilizing amino acid having a high helical propensity (1.6 e w e 1.9) on the one hand.82 But it also has been argued for alanine to have a lower helical propensity (1.03 e w e 1.15) on the other.83,84 The high helicity as large as over 80% observed in FS-like peptides has been suspected to be due to the charged amino acids such as lysine, arginine, or glutamate inserted regularly as solubilizers.85 In the case where the core polyalanine segment as long as 19 residues is effectively separated from charged solubilizers at each end of the peptide by neutral spacers, the fractional helicity obtained from circular dichroism (CD) spectra was merely 50%.84 The helicity of A21 calculated by the ff99 force field at 273 K is closer to the latter case. Other than the R-helical motif, the dominant secondary motifs seen at high temperatures in the present MD simulations are 310-helix and type I β-turn, which have hydrogen-bondings between i-th and (i ( 3)-th peptide units in common. If ( 30° deviations from the ideal backbone torsion angles are permitted for φ/ψ of helical motifs including π-helix, which is ignorable in the present simulations, all the helical motifs are not discernible explicitly, and a segment on A21 can be defined as more than two secondary structures simultaneously as shown in Figure 2. At 300 K, shown in the upper panel of Figure 2,

608 J. Phys. Chem. B, Vol. 111, No. 3, 2007

Yang and Cho

Figure 1. Comparison of equilibrium simulation results at 273K using ff99 and ff03 force fields averaged over 10 trajectories: (a) CR root-meansquare deviation which is estimated with respect to the initial R-helical structure (b) radius of gyration, (c) end-to-end distance between CR atoms of A1 and A21, (d) helical content defined by the Lifson-Roig model where three consecutive helical Ala residues is counted as one.

the R-helical structure of A21 transforms to 310-helix or type I β-turn as time elapses in the ff99 runs (patches on the first row), while the peptide remains highly helical throughout simulations and the type I β-turn motif prevails only near the C-terminal half in the ff03 runs (patches on the second row). At an elevated temperature of 360 K, shown in the bottom panel of Figure 2, the similar features are observed except for the fact that the overall helical content is significantly lower than the value at 300 K. It is almost equally likely for each residue to form the type I β-turn structure nearly at all times at 360 K for ff99 simulations, but residues in the C-terminal end have higher tendency to have the turn motif in ff03 simulations. At both temperatures, the R- and 310-helical structures are bifurcated for most residues only in the ff03 results. If we progress from a lower T-jump to a higher T-jump simulation results using the ff03 force field, it can be seen that the bifurcated R- and 310helical structures transform to the type I β-turn until reaching 360 K, and subsequently, they are disrupted to coil-like structures at higher temperatures up to 450 K (data not shown). On average, less than 40% of type I β-turn character survives even at 450 K in both ff99 and ff03 simulations and the average probability of A21 to have well-defined secondary structures at 450 K is larger in the ff03 results. Even at the highest T-jump simulations at 450 K, however, the extended secondary structures such as β-sheets and PII are not noticeable in both ff99 and ff03 results, unexpectedly. As already discussed in previous simulation studies,86 310-helix, β-turns,87 and π-helix have been thought to be highly probable intermediates during the helixcoil transitions. Except for π-helix, our simulation results show the high propensity of 310 at low temperatures and the intermittent β-turns persistent at all temperatures. This indicates that the thermally denatured A21 is not thoroughly a random coil but resembles a coiled coil with a hydrophobic core formed by type I β-turns.

Helical contents defined by the Lifson-Roig model at temperatures from 273 K to 450 K at 30 K interval using the ff99 and ff03 simulation results are shown in Figure 3a and b. The maximum possible helicity of A21 should be 19. To have a quantitative picture of the total conformational distribution, the random coil contents are also plotted in Figure 3c and d. The random coil content is counted as the number of residues whose backbone dihedral angles are in regions which are not represented by any of the known helical and extended structures. Comparing the helical and the random coil contents together, there are about 30% residues having non-R-helical and noncoil structures even at 450 K. For the purpose of comparing effects by different definitions of helicity, we calculated the helical contents by applying H-bonding restraints of R-helix in addition to the Lifson-Roig definition. The helicity relaxation pattern with time is very similar in two definitions at all temperatures for both ff99 and ff03 helicities, but the average helicities by the latter definition is a little bit lower. The helicity and coil contents converge within 5 ns in most cases, except at lower temperatures in ff03 results, where the potential lack of adequate equilibration seems to be present. The helicity relaxation time constant, τ, is obtained from a single-exponential fit of each curve in Figure 3a and b and is plotted against temperature in Figure 4a. Due to large-amplitude fluctuations of the helicity, the smaller time constant in double exponential fit is smaller than its own standard deviation. Only the bigger time constant, which is similar to the one obtained from a single-exponential fit within error range, is worth credit. Seemingly, therefore, there is no big difference even if we use single-exponential fits. The ff99 time constants are well fitted to a single exponential and the extrapolated value at 273 K is 1.25 ns. If the ff03 time constants are also fitted to an exponential except for the value at 300 K, the extrapolated time constants are 20.5 ns at 273 K and 9.22 ns at 300 K, which is



Figure 2. Distribution of secondary motifs over peptide sequence and their evolution with time: results at 300 K (a) and at 360 K (b). The first and the second rows in each panel represents the ff99 and ff03 results, respectively, while each column is for R-helix, 310-helix, and type I β-turn distribution from left to right. Data obtained from 10 trajectories are averaged over 10 ps. The percentage of each motif is depicted as six different colors: 100% is red and with decreasing order by 20% interval, orange (less than 100%, greater than 80%), yellow, green, cyan, and blue.

still over an order of magnitude smaller than the experimental relaxation time of the FS-peptide.11 The logarithm of relaxation rates, the inverse time constants, are plotted against temperature in Figure 4b. Except for the value at 300 K in ff03 results, they can be fitted to a straight line for both ff99 and ff03 relaxation rates and this means the helix-coil transition could “superficially” be interpreted as a two-state process, even with the presence of other motifs than the R-helix. The apparent activation energies in the Arrhenius plots are 6.3 and 6.7 kcal/ mol in the ff99 and ff03 results, respectively. These are about half the value estimated experimentally.11 Temperature Dependence of Amide I IR Spectra. The simulated amide I IR absorption spectra at temperatures 273 K through 450 K and the difference IR spectra with the reference at 273 K are presented in Figure 5. The common features shown

in both ff99 and ff03 IR spectra are that the amide I frequency at the maximum absorbance shifts to higher frequency region with increasing temperature and that there are only two peaks in the difference spectra. These are qualitatively in excellent agreement with those observed in laser-induced T-jump experiments,18-20 especially for the ff99 spectra, although the temperature variation range is unrealistically wide in simulations. Definitely, there is no isosbestic point in both difference spectra and this is consistent with the interpretation correlating the nonexistence of an isosbestic point with the presence of intermediates.11 In spite of the large gap in average helicities at 273 K, the ff99 and ff03 IR spectra at 273 K have no big difference in the band shape or in the amide I center frequency. This indicates that the amide I bands by the helical and the coil segments are summed to give coincidentally the similar IR


Yang and Cho

Figure 3. Temperature-dependence of Lifson-Roig helicities and coil contents averaged over 10 trajectories: (a) ff99 helicity, (b) ff03 helicity, (c) ff99 coil content, and (d) ff03 coil content at 273 K (black), 300 K (red), 330 K (orange), 360 K (green), 390 K (cyan), 420 K (blue), and 450 K (magenta).

Figure 4. (a) Single-exponential fit results of the Lifson-Roig helicities using a functional form of y(t) ) y0 + A exp(-t/τ), where y is helicity. The vertical bars are standard deviations and the solid line is an exponential fit of the relaxation times. (b) Logarithm of the relaxation rates, the inverse time constant, vs temperature. The apparent activation energies (slopes of solid lines) of helix-coil transition are 6.3 (ff99) and 6.7 (ff03) kcal/mol, respectively. The ff99 results are colored in black and the ff03 results are in red.

spectra only due to the helical conformations. Noticeable differences between ff99 and ff03 IR spectra can be seen above 300 K. It is interesting to note that one can figure out a crude temperature range where the melting transition occurs by the big decrease in the amide I intensity in Figure 5. It should also be noted that the spectral behavior after the melting transition is quite different in the ff99 and ff03 spectra. The amide I frequency shift with increasing temperature in the ff99 spectra is due to the transformation of random coil distribution itself. By contrast, the ff03 difference spectra above 390 K indicate that the conformational distribution does not change so much. There is almost no frequency shift in the negative peaks in the ff99 difference spectra, but the shift in the positive peaks is 9 cm-1. This tendency is consistent with experimental spectra.11

Meanwhile, both the negative and the positive peaks shift to higher frequencies considerably in the ff03 difference spectra. The center frequencies and the full width at half-maximum (fwhm) of amide I IR absorption spectra are plotted in Figure 6. If the scattered data are fitted to straight lines (not shown in the Figure), the rates of variation of the amide I center frequency and fwhm are 0.83 cm-1/10 °C and 0.6 cm-1/10 °C, respectively, in the ff99 results. These values are in excellent agreement of those reported in previous experimental studies,27 although the absolute values of amide I center frequency and fwhm are rather large in the simulated spectra. The corresponding values in the ff03 results are 0.68 cm-1/10 °C and 1.55 cm-1/10 °C, respectively, and are far from being satisfactory. Taking a closer look at the amide I frequency plots, a transition



Figure 5. Amide I IR absorption and the difference IR spectra at temperatures 273 K (black), 300 K (red), 330 K (orange), 360 K (green), 390 K (cyan), 420 K (blue), and 450 K (magenta). (a) and (b) are calculated using the ff99 MD trajectories, while (c) and (d) using the ff03 MD trajectories. The arrowhead dictates the direction of increasing temperature.

Figure 6. Temperature and force field dependence of the center frequency and the full width at half-maximum (fwhm) of amide I band; (a) two linear fits of the amide I center frequency, (b) a linear (ff99) and a sigmoidal fit of the fwhm. The ff99 results are colored in black and the ff03 results are in red.

can be observed approximately at 300 K (ff99) and at 390 K (ff03). This becomes evident by fitting the data with two separate straight lines which have correlation coefficients close to 1. fwhm of the ff99 amide I bands shows similar behavior with the amide I frequency itself and it varies significantly near 300 K. The ff99 fwhm is tightly fitted using two sigmoids separated at 360 K, but the data between 300 and 450 K can be seen as linearly increasing with temperature. By contrast, fwhm of the ff03 amide I bands is well fitted to a sigmoid and the transition appears to occur at a wide range of 330∼390 K and the biggest leap is seen at 360∼390 K. The deviation from the linearity shown in both the amide I center frequency and in fwhm is correlated with the helix-coil transition. According to the fluctuation-dissipation theorem in the classical limit, the mean square frequency fluctuation of amide I mode, 〈δω2〉 ) 〈[2π(ν˜ I(t) - 〈ν˜ I〉)]2〉, is linearly proportional to temperature.88 The seemingly sigmoidal transitions shown in Figure 6b, therefore, can be divided into two (for the ff99 fwhm) or three linear

sectors. In the ff99 spectral estimates, the first linear interval is missing, if we assume that the ff99 fwhm can be also overlapped on a sigmoid. The transition interval is bounded by the last linear interval at 300 K. In the ff03 fwhm plot, three separate linear sectors can be assigned, < ∼330 K, 330∼390 K, and >390 K. The slope of fwhm with respect to temperature is steepest but not abrupt in the transition interval for both results. Detailed understandings on the sigmoidal behavior of fwhm will be found in future studies. We suggest here that spectroscopic signatures such as the center frequency and fwhm of the amide I band can give us approximate but consistent measures about where the helix-coil transition takes place. It should be mentioned that Tm determined by 50% helicity is evidently lower than 273 K and is different from the value obtained from simulated spectra, in ff99 results. The conventional way of determining Tm in T-jump FTIR spectra is to fit the temperature-dependent amide I frequency to an ideal curve drawn by assuming a two-state transition.89


Figure 7. Temperature-dependent normalized absorbance of the amide I center frequency (scatters): (a) a linear fit of intensity at 1666 cm-1 calculated using the ff99 MD trajectories, (b) a sigmoidal fit of intensity at 1667 cm-1 calculated using the ff03 MD trajectories, and (c) the van’t Hoff plot of the ff03 results in (b). The unfolding enthalpy obtained from the linear fit in (c) is ∆Hu ) -5.6 ( 0.16 kcal/mol.

The helix nucleation (σ) and propagation (s) parameters90 are determined from this fit at the 50% helicity (θ). If we choose the amide I center frequency at 273 K as a probe to be plotted vs temperature, the amide I intensity in the ff99 spectra fits tightly to a straight line, while that in the ff03 spectra can be fitted to a sigmoid. The results are shown in Figure 7. Unexpectedly, the ff99 amide I intensity plot does not give any useful tips to determine Tm in Figure 7a. The ff03 absorbance at 1667 cm-1 (scatters) in Figure 7b can be overlapped partially on ideal two-state sigmoidal curves, which are calculated using σ ) 0.005 and 0.01, and any curves drawn with σ values between two are the best fits. The propagation parameter is 1. Then, the transition mid-temperature at θ ) 0.5 is found to be Tm ) 343 K, which is much lower than the one determined in Figure 6, i.e., 360∼390 K. The discord in Tm is worth attention. With σ ) 0.005, the amide I intensity fits well until 360 K, but

Yang and Cho subsequently it deviates from the sigmoid. It now becomes evident that even if there are more than two kinds of helical structures, discernible by the H-bonding character, we can misunderstand the unfolding as a two-state process. The issue that the sigmoidal transition does not guarantee the validity of a two-state model was also pointed out in a recent thermodynamic study.91 The negative slope of the linear fit in Figure 7c is the unfolding enthalpy assuming a two-state transition,89 ∆Hu ) -5.6 ( 0.16 kcal/mol, which corresponds to per residue unfolding enthalpy of -0.27 kcal/mol‚residue-1 and is a half the ∆Hu of FS peptide reported in Williams et al.’s.11 To have a spectral resolution on a-few-residue basis, the isotope-labeled IR and difference IR spectra of A21 are simulated using the ff99 and ff03 force fields and are shown in Figure 8. The difference spectra are obtained by subtracting the IR spectrum at 273 K from the one at higher temperatures. The peptide is divided into three segments comprising seven consecutive alanine residues. To obtain clear resolution, the shift as much as ∼65 cm-1, corresponding to the 13Cd18O labeling, is used in spectral simulations. Although the detailed couplings between labeled and unlabeled peptide groups should be rigorously treated in principle, the diagonal frequencies of labeled peptides are simply subtracted by 65 cm-1 in prediagonalized Hessian matrix in our method. This is based on the following observation: we obtained the coupling constants between the labeled and the unlabeled neighboring peptide units of alanine dipeptide on a φ/ψ map using a high level ab initio method (unpublished results), and found no significant differences compared to those between unlabeled peptide groups obtained in previous studies.48,78 According to the experimental results by Huang et al.,19,20 in which 3∼4 adjacent Ala residues were 13C labeled, the ratio of relative intensities of negative peaks in the difference spectra is distinct depending on the position of the labeling. Irrespective of the amount of the shift, the gross spectral profile shown in the ff03 spectra resembles the characteristics shown in the experimental results,19,20 while the ff99 spectra do not capture the essential features. In the ff03 difference spectra, the negative peaks at 1600∼1610 cm-1 are due to the decreasing helicity of the labeled segment and the positive peaks at 1620∼1645 cm-1, which cannot be resolved in 13C labeled experimental spectra,19,20 are due to the increasing coil content of the labeled segment. Likewise, the second negative peaks at 1660∼1680 cm-1 and the positive peaks at 1685∼1705 cm-1 are attributed to the decreasing helical and the increasing coil contents of the unlabeled segments. The normalized absorbance at some probe frequencies are plotted in Figure 9 to get an insight into the relaxation rate of each labeled segment. The unlabeled absorbance is probed at 1666 cm-1 (ff99) and at 1667 cm-1 (ff03), while the labeled ones are probed at 1610 cm-1 in all cases. In the ff99 results shown in Figure 9a, the unlabeled peptide and two species labeled on the N-terminal and on the middle of the peptide relax with almost the same rate. But the C-terminal labeled peptide shows very slow and isolated dynamic behavior from those three cases. Meanwhile, the ff03 results in Figure 9b apparently seem to be quite satisfactory in reproducing the experimental behaviors,11,14,20 except for the N-terminal labeled peptide. This deviation may be due to the use of different model peptides or to insufficient samplings. For the latter origin, we tested the dependence of IR spectra on the number of MD trajectories sampled. Since the transient fluctuations in the amide I IR frequency at 450 K is the most severe, we compared the IR spectra at 450 K simulated using 10 and 50 trajectories (30 trajectories for the ff99 simulated spectra). Consequently, it



Figure 8. 13Cd18O isotope-labeled IR absorption and difference IR spectra (reference at 273 K) estimated using ff99 and ff03 MD simulation results at temperatures 273 K (black), 300 K (red), 330K (orange), 360 K (green), 390 K (cyan), 420 K (blue), and 450 K (magenta). The N-terminal labeled segment is denoted as [A1-A7], the middle segment as [A8-A14], and the C-terminal segment as [A15-A21]. The arrowhead dictates the direction of increasing temperature.

turned out there is no big difference between them with respect to the amide I center frequency and fwhm (data not shown). Time-Resolved Amide I IR Spectra. One of the most interesting aspects in laser-induced T-jump experiments is the time resolution of the absorbance at specific probe frequencies. The helix-coil transition kinetics is then measured by fitting the transient IR intensity to exponential functions. To get a firm basis in interpreting the computational results, we also simulated the time-dependent amide I IR spectra at temperatures from 300 to 450 K, shown in Figure 10. The lower probe frequencies correspond to the amide I center frequencies at 273 K and the higher ones are the frequencies representative of random coils. In the ff99 spectra shown in Figure 10, the absorbance at 1666 cm-1 decreases monotonically with increasing temperature while

the absorbance at 1686 cm-1 increases until 360 K, after which it is indifferent to temperature. The ff99 time-resolved spectra beyond 360 K have a very weak time-dependence. In the ff03 spectra shown in Figure 10, the absorbance at 1667 cm1- and at 1692 cm-1 does not reach a similar level even at 450 K, contrary to the results shown in the ff99 spectra. Moreover, the transient intensity at 1692 cm-1 is very weakly time-dependent at all temperatures, except for the first 1 ns to relax to a new equilibrium. Due to the intensity fluctuations, which are not reduced significantly even if we use up to 50 trajectories to simulate the spectra (at 450 K, data not shown), the absorbance probed at 1686 cm-1 (ff99) and 1692 cm-1 cannot be fitted to exponential functions, and we cannot prove whether the two fits at a lower and at a higher probe frequencies give the same relaxation time constants, as reported in experiments.11


Yang and Cho

Figure 9. Normalized absorbance of the unlabeled amide I band probed at 1666 cm-1 (ff99) and 1667 cm-1 (ff03) and of the isotope labeled amide I bands probed at 1610 cm-1; (a) ff99, and (b) ff03 results. The absorbance (scatters) is normalized with respect to the value at 273 K and is fitted to an exponential (solid line) in all cases.

Figure 10. Time-resolved IR absorbance plotted at two probe frequencies and its temperature dependence. The ff99 IR intensity is probed at 1666 cm-1 (black) and 1686 cm-1 (red), while the ff03 IR intensity at 1667 cm-1 (black) and 1692 cm-1 (red). The time resolution is 10 ps in all spectra which are also averaged over 10 MD trajectories.

The relaxation time constants are obtained by fitting the simulated time-resolved spectra at 1666 cm-1 (ff99) and at 1667

cm-1 (ff03) to a single-exponential function, which is used instead of multiexponential functions due to the same problem



Figure 11. Exponential fit results of the time-resolved IR absorbance in Figure 11; (a) relaxation time constants (scatters) and their exponential fits (solid line), (b) temperature dependence of the relaxation rates. The apparent activation energies from the linear fits are 6.0 (ff99) and 8.7 kcal/mol (ff03), respectively. The ff99 results are colored in black and the ff03 results are in red.

as in fitting peptide helicities. The relaxation times are plotted against temperature in Figure 11a. The ff99 time constants are well fitted to an exponential as done in Figure 4a, but the ff03 time constants are ill-defined below 330 K as in Figure 4b. The relaxation times of 488 ps (ff99) and 21.7 ns (ff03) at 300 K are comparable within error range to those obtained using helicity, 603 ps (ff99) and 9.22 ns (ff03) at the same temperature. The relaxation rates are plotted in Figure 11b and the scattered data can be fitted to a straight line. The apparent activation energies of the transition estimated from the simulated spectra are 6.0 (ff99) and 8.7 kcal/mol (ff03), which are also comparable with those computed in Figure 4, but smaller than experimentally reported values.11 Consequently, the scattered plots in Figure 4 and Figure 11 are in good agreement with each other and the essential properties of the helix-coil transition of A21 peptide are predicted consistently using two different ways, measuring helicity directly or simulating amide I IR spectra. But the numerical estimates predicted by computational approaches are still far from experimental measurements in their accuracy. Conclusions We studied the helix-coil transition kinetics of A21 peptide by carrying out T-jump MD simulations and calculating theoretical IR spectra. We investigated how the results depend on the molecular mechanical force fields and the T-jump magnitude. Conclusively, both ff99 and ff03 force fields give consistent results in reproducing key aspects concerned experimentally, but are not predominantly satisfactory in quantitative aspects. The average helicity at 273 K is estimated to be 30% by ff99, which is closer to 50% or lower helicity reported previously,57,84 while it is calculated to be 87% by ff03, which is closer to the helicity of heteropolymeric Ala-based peptides such as FS peptide. At all temperatures studied in the present study, residues in the central segment of A21 have both R-helical and (or) 310-helical characters. It should be noted that the distinction between two helical motifs becomes ambiguous in solution if we adopt rather generous criteria in backbone torsion angles and H-bonding parameters. In spite of that, on average in ff03 simulations, R-helical motif prevails at lower temperatures. At higher temperatures, intriguingly, coil-like disordered structures presumably having a hydrophobic core formed by several type I β-turns is highly likely in both ff99 and ff03 simulations, questioning the validity of the single sequence approximation assumed in the kinetic zipper theory.14 The average helical content of A21 decreases dramatically with

increasing temperature in ff99 simulations, but it does rather slowly in ff03 simulations. The helix melting is predicted to occur at Tm < 273 K (ff99) or at Tm ∼ 380 K (ff03), where the helical and the coil contents are equal. The difference IR spectra of unlabeled A21 have no isosbestic point in both cases simulated by ff99 and ff03 MD trajectories. The center frequency and fwhm of amide I band presents interesting behaviors that they seem to experience a transition in the vicinity of where the melting occurs by the criteria of helical contents, in ff03 results. We suggest here that amide I center frequency and fwhm estimated over a wide temperature range can be used as signatures to estimate the approximate transition temperature. Inspecting the temperature dependence of IR absorbance at some probe frequencies, believed to represent the changes of helical and random coil contents, it becomes evident that the structural distribution at 450 K is not totally in disorder in both simulations using ff99 and ff03. The temperature-dependent amide I absorbance is linear in ff99 results while it is sigmoidal to give Tm ) 343 K at θ ) 0.5 in ff03 results, which is rather closer to the experimental Tm ) 334 K.11 The nucleation parameter σ ) 0.01∼0.005 gives good overlaps between the ideal sigmoids and the simulated intensity only until 360 K, after which the absorbance deviates from any sigmoidal fits. The van’t Hoff enthalpy of unfolding is calculated to be -5.6 ( 0.16 kcal/mol, which is half the value predicted for the FS peptide.11 The isotope-labeled IR and difference IR spectra simulated by ff03 MD trajectories show excellent performance comparable to experimental spectra.20 The simulated spectra by ff99 MD trajectories, however, are not so satisfactory. The simulated time-dependent absorbance at amide I center frequency gives relaxation times which are comparable with those estimated by the helical content. The relaxation rates can be fitted to a straight line and the apparent activation energies in the Arrhenius plots are 6.0∼6.3 kcal/mol (ff99) and 6.7∼8.7 kcal/mol (ff03), which are again about half the value predicted experimentally for an Ala-based peptide.18 According to the results in the present study, the nature of helix-coil transition of A21 peptide cannot be explained by the conventional two-state model. The MD simulation results suggests definitely the presence of intermediates such as 310helix, but we demonstrate theoretically that 1D amide I IR spectra cannot resolve 310-helix separately from R-helix when they coexist, as well-known experimentally in 1D IR and VCD spectroscopies30-35 having a time resolution insufficient to track fast dynamics. We find that the number of exponentials used

616 J. Phys. Chem. B, Vol. 111, No. 3, 2007 in fitting the helical content or the transient amide I absorbance, sigmoidal fits of the temperature-dependent amide I absorbance, and the Arrhenius plot of relaxation rates cannot be good and sufficient criteria to guarantee the validity of assuming the twostate mechanism. It is interesting that the simulated IR spectra are comparable to experimental spectra, without the presence of considerable PII structures in the thermally unfolded A21 peptide. Further studies are in progress to scrutinize whether simulated VCD and 2D IR spectra can tell us about the detailed picture of the thermally denatured state of a peptide, the presence of intermediates during unfolding, and H-bonding dynamics critical to understand the helix-coil transitions, the term no longer sounding contemporary to describe the folding or unfolding transitions of polypeptides and proteins. Acknowledgment. This work was supported by the Creative Research Initiatives Program of KOSEF (MOST, Korea). References and Notes (1) Callender, R. H.; Dyer, R. B.; Gilmanshin, R.; Woodruff, W. H. Annu. ReV. Phys. Chem. 1998, 49, 173-202. (2) Gruebele, M. Annu. ReV. Phys. Chem. 1999, 50, 485-516. (3) Eaton, W. A.; Munõz, V.; Hagen, S. J.; Jas, G. S.; Lapidus, L. J.; Henry, E. R.; Hofrichter, J. Annu. ReV. Biophys. Biomol. Struct. 2000, 29, 327-359. (4) Havel, H. A., Ed. Spectroscopic Methods for Determining Protein Structure in Solution; VCH Publishers: Inc.; New York; 1996. (5) Chen, E.; Goldbeck, R. A.; Kliger, D. S. Annu. ReV. Biophys. Biomol. Struct. 1997, 26, 327-355. (6) Zanni, M. T.; Hochstrasser, R. A. Curr. Opin. Struct. Biol. 2001, 11, 516-522. (7) Gruebele, M.; Sabelko, J.; Ballew, R.; Ervin, J. Acc. Chem. Res. 1998, 31, 699-707. (8) Dyer, B.; Gai, F.; Woodruff, W. H.; Gilmanshin, R.; Callender, R. H. Acc. Chem. Res. 1998, 31, 709-716. (9) Marqusee, S.; Baldwin, R. L. Proc. Natl. Acad. Sci. U.S.A. 1987, 84, 8898-8902. (10) Marqusee, S.; Robbins, V. H.; Baldwin, R. L. Proc. Natl. Acad. Sci. U.S.A. 1989, 86, 5286-5290. (11) Williams, S.; Causgrove, T. P.; Gilmanshin, R.; Fang, K. S.; Callender, R. H.; Woodruff, W. H.; Dyer, R. B. Biochemistry 1996, 35, 691-697. (12) Lockhart, D. J.; Kim, P. S. Science 1992, 257, 947-951. (13) Lockhart, D. J.; Kim, P. S. Science 1993, 260, 198-202. (14) Thompson, P. A.; Eaton, W. A.; Hofrichter, J. Biochemistry 1997, 36, 9200-9210. (15) Thompson, P. A.; Munõz, V.; Jas, G. S.; Henry, E. R.; Eaton, W. A.; Hofrichter, J. J. Phys. Chem. B 2000, 104, 378-389. (16) Lednev, I. K.; Karnoup, A. S.; Sparrow, M. C.; Asher, S. A. J. Am. Chem. Soc. 1999, 121, 8074-8086. (17) Lednev, I. K.; Karnoup, A. S.; Sparrow, M. C.; Asher, S. A. J. Am. Chem. Soc. 2001, 123, 2388-2392. (18) Huang, C.-Y.; Klemke, J. W.; Getahun, Z.; DeGrado, W. F.; Gai, F. J. Am. Chem. Soc. 2001, 123, 9235-9238. (19) Huang, C.-Y.; Getahun, Z.; Wang, T.; DeGrado, W. F.; Gai, F. J. Am. Chem. Soc. 2001, 123, 12111-12112. (20) Huang, C.-Y.; Getahun, Z.; Zhu, Y.; Klemke, J. W.; DeGrado, W. F.; Gai, F. Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 2788-2793. (21) Decatur, S. M.; Antonic, J. J. Am. Chem. Soc. 1999, 121, 1191411915. (22) Decatur, S. M. Acc. Chem. Res. 2006, 39, 169-175. (23) Dill, K. A.; Chan, H. S. Nat. Struct. Biol. 1997, 4, 10-19. (24) Onuchic, J. N.; Luthey-Schulten, Z.; Wolynes, P. G. Annu. ReV. Phys. Chem. 1997, 48, 545-600. (25) Bredenbeck, J.; Helbing, J.; Kumita, J. R.; Woolley, G. A.; Hamm, P. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 2379-2384. (26) Miick, S. M.; Martinez, G. V.; Fiori, W. R.; Todd, A. P.; Millhauser, G. L. Nature 1992, 359, 653-655. (27) Martinez, G.; Millhauser, G. L. J. Struct. Biol. 1995, 114, 23-27. (28) Millhauser, G. L. Biochemistry 1995, 34, 3873-3877. (29) Bolin, K. A.; Millhauser, G. L. Acc. Chem. Res. 1999, 32, 10271033. (30) Yoder, G.; Pancoska, P.; Keiderling, T. A. Biochemistry 1997, 36, 15123-15133. (31) Silva, R. A. G. D.; Kubelka, J.; Bour, P.; Decatur, S. M.; Keiderling, T. A. Proc. Natl. Acad. Sci. U.S.A. 2000, 97, 8318-8323.

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