Conformational Changes of Trialanine in Water ... - ACS Publications

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Conformational Changes of Trialanine in Water Induced by Vibrational Relaxation of the Amide I Mode Adolfo Bastida,*,† José Zúñiga,† Alberto Requena,† Beatriz Miguel,‡ María Emilia Candela,§ and Miguel Angel Soler∥ †

Departamento de Química Física, Universidad de Murcia, 30100 Murcia, Spain Departamento de Ingeniería Química y Ambiental, Universidad Politécnica de Cartagena, 30203 Cartagena, Spain § Departamento de Biología Vegetal, Universidad de Murcia, 30100 Murcia, Spain ∥ Department of Medical and Biological Sciences, University of Udine, 33100 Udine, Italy ‡

S Supporting Information *

ABSTRACT: Most of the protein-based diseases are caused by anomalies in the functionality and stability of these molecules. Experimental and theoretical studies of the conformational dynamics of proteins are becoming in this respect essential to understand the origin of these anomalies. However, a description of the conformational dynamics of proteins based on mechanoenergetic principles still remains elusive because of the intrinsic high flexibility of the peptide chains, the participation of weak noncovalent interactions, and the role of the ubiquitous water solvent. In this work, the conformational dynamics of trialanine dissolved in water (D2O) is investigated through Molecular Dynamics (MD) simulations combined with instantaneous normal modes (INMs) analysis both at equilibrium and after the vibrational excitation of the C-terminal amide I mode. The conformational equilibrium between α and pPII conformers is found to be altered by the intramolecular relaxation of the amide I mode as a consequence of the different relaxation pathways of each conformer which modify the amount of vibrational energy stored in the torsional motions of the tripeptide, so the α → pPII and pPII → α conversion rates are increased differently. The selectivity of the process comes from the shifts of the vibrational frequencies with the conformational changes that modify the resonance conditions driving the intramolecular energy flows.

1. INTRODUCTION Understanding the conformational dynamics of small peptides and proteins is undoubtedly one of the most challenging problems in the field of molecular biology, and it attracts the interest of scientists from diverse areas, ranging from computational to biomedical sciences.1−4 In the past 20 years, the development of sophisticated experimental techniques5−10 and the advances in computing power and increasingly accurate force fields11,12 have fostered the convergence of experiments and atomistic simulations a great deal.3 However, a description of the conformational dynamics of proteins based on general principles still remains elusive because of the intrinsic high flexibility of the peptide chains, the participation of weak noncovalent interactions, and the role of the ubiquitous water solvent. Protein folding,1,6,7,10,13−17 allosterism,18−20 and prion aggregation21,22 are important phenomena in which conformational changes in proteins are triggered by perturbations that modify their biochemical function dramatically. From a mechanical point of view, a conformational change in proteins requires the storage of a certain amount of vibrational energy in some specific torsional degrees of freedom. The flow of vibrational energy through the molecule emerges then as an © 2015 American Chemical Society

important point to be considered for the understanding of the conformational dynamics.1,6,7,10,13−17 The anisotropy of the vibrational energy flows1,23−25 and the connection between energy transport efficiency and structural flexibility13 underline the selectivity of these processes. Meech et al.7 have recently shown that a point mutation in photoactive flavoprotein which inactivates biological functions also alters the relaxation pathways in order to suppress a photoinduced conformational change. Experiments that provide a high degree of time resolution typically alter the conformational state of the polypeptide due to the use of an ultrafast temperature jump of the solvent surrounding the biomolecule5,8,26 or a visible-UV pulse promoting a chromophore to a short-lived excited electronic state.6,7,14 While these experiments are of great help in establishing the time scales of the different processes involved in the conformational dynamics, their interpretation in terms of elementary steps is often problematic due to both the low selectivity of the excitation techniques and the substantial Received: October 6, 2015 Revised: December 18, 2015 Published: December 21, 2015 348

DOI: 10.1021/acs.jpcb.5b09753 J. Phys. Chem. B 2016, 120, 348−357

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The Journal of Physical Chemistry B

excitation of a fundamental is modest compared to electronic excitation using visible or UV pulses or to a T-jump process, the vibrational energy is much more localized in a single vibrational mode, so its effect on the conformational equilibrium cannot be discarded. Third, we show that the alteration of the conformational equilibrium of the molecule is a direct consequence of the fact that the IVR pathways depend on the configuration of the polypeptide; that is, the energy flows are significantly different in the α and pPII conformers of the molecule. We provide a simple explanation of this effect in terms of the shifts of the vibrational frequencies during the conformational changes, which modifies the resonance conditions that drive the energy transfers.

distortion caused by the high amount of energy deposited in the molecule.3 Molecular Dynamics simulations serve then as an invaluable complementary tool for determining the conformational dynamics, In this work, we have carried out Molecular Dynamics (MD) simulations of trialanine in deuterated water both at equilibrium and when considering the vibrational relaxation of the Cterminal amide I mode of the molecule. Trialanine has been used as a model polypeptide in experimental27−35 and theoretical36−39 studies since it shows rich conformational dynamics despite its limited size, so facilitating comparison between atomistic simulations and experimental measurements. The experimental evidence27−35 point out that trialanine is predominantly found in the polyproline II (pPII) conformation (∼80%), but there are some discrepancies about the additional presence of the αR27−29 or β30−35 conformers. The comparison of the conformational populations obtained through Molecular Dynamics (MD) simulations using different force fields35−37 widely used for peptides reveals that they all provide significant populations of two or more conformers but the precise values strongly depend on the particular force field considered. We have used the MD simulations first to propose a simple method to analyze quantitatively the conformational dynamics of unexcited trialanine using a kinetic model in which the existence of molecules that change their conformation through a downhill process40 is explicitly invoked. Second, we provide quantitative evidence that the conformational equilibrium of the tripeptide is altered after absorption of an IR pulse by the amide I mode. This mode closely resembles the carbonyl stretching mode and can be selectively excited by using 13C isotopic substitution to shift the vibrational frequencies of individual CO groups.9,27,41 Since the carbon atom of the carbonyl group participates in the definition of the dihedral (ϕ,ψ) angles which control the conformation of trialanine (see Figure 1), its excitation may have a significant influence on the

2. METHODOLOGY 2.1. Molecular Dynamics Simulations. We have simulated the vibrational dynamics of the trialanine molecule in its zwitterion form (ND3+−CH(CH3)−CO−ND−CH(CH3)−13CO−ND−CH(CH3)−COO−) solvated in D2O water (see Figure 1) to help the comparison with experiments.27−34 The carbon atom of the C-terminal carbonyl group is here 13C isotopically substituted in order to separate the frequencies of the two amide I modes, which are mainly associated with the CO stretchings. This isotopic substitution shifts the vibrational frequency of the C-terminal amide I mode by a calculated value of −43.0 cm−1, which is in quite good agreement with the observed shift of −45.0 cm−1,28 making it possible to excite the C-terminal amide I mode selectively. The MD simulations are carried out using the TINKER package v6.1.43,44 A solute molecule of trialanine surrounded by 851 water molecules are placed specifically in a cubic box with a length chosen to reproduce the experimental density of the liquid at room temperature. The trialanine molecule is described using the CHARMM2245 force field, which correctly localizes amide I modes over the carbonyl groups,42 while the solvent is described using the flexible TIP3P model included in the CHARMM2245 force field. Periodic boundary conditions are imposed in the simulations using the Ewald sum method to treat the long-range interactions, and the equations of motion are integrated employing a time step of 1 fs so that the total energy of the system is conserved with a standard deviation equal to ±23 cm−1 which is accurate enough to account for the vibrational energy flows during the relaxation process. The chronology of the MD simulations performed is as follows. The system is equilibrated first for 2 ns in an NVT ensemble at T = 298 K by coupling to a thermal bath.46 Equilibrium NVT simulations are then run to generate a total of 76 800 initial configurations by exporting data every 20 ps. These configurations are subsequently used to carry out two sets of independent simulations in the NVE ensemble comparatively to avoid any interference of the velocity scaling. In the first set, trajectories continue to be propagated at equilibrium, and in the second set, trajectories account for the nonequilibrium evolution of the system after depositing a vibrational quantum of energy in the C-terminal amide I vibrational mode by displacing the corresponding vibrational normal mode until its energy reaches the proper value. In these simulations, the atomic positions, momenta, forces, and Hessian matrix of the solute are exported every 50 fs and values of the torsional angles ϕ and ψ are exported every 10 fs for proper analysis. The total propagation time reached for all trajectories is 5 ps. In order to evaluate the statistichal reliability of our results we systematically evaluate the standard deviations

Figure 1. Characteristic α and pPII conformations of trialanine.

conformational equilibrium. Previous simulations for the alanine dipeptide conducted by our group42 have shown that these conformational changes occur, and they are tested here in the real trialanine tripeptide, which is the simplest case where the environment of the central α carbon atom is identical to that present in polypeptides and proteins. Although the amount of energy deposited in the molecule through a vibrational 349


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the second derivatives to take into account the influence of the solvent molecules. This is an important point since a substantial mixing between water motions and low-frequency peptide vibrations has been found.56 By analyzing the evolution of the INMs along the MD simulations, it is possible to track the timedependent energies and populations of the vibrational modes and identify the corresponding relaxation paths. The INMs have to be repeatedly assigned at the successive instantaneous configurations, since their definitions depend on the vibrational couplings that evolve over time. This is done by establishing a one-to-one correspondence with the Equilibrium Normal Modes (ENMs), which are used as templates at every instantaneous snapshot. The INMs to ENMs connection is made by maximizing the overlaps between both sets of normal modes using the so-called Min-Cost algorithm,51 where the overlap matrix is expressed in terms of the Cartesian contributions of every atom of the biomolecule to the definitions of the ENMs and INMs. The resulting assignment method, which is referred to as the Effective Atomic Min-Cost (EAMC) method,42 identifies all the INMs of the molecule, including the six modes associated with the translational and rotational motions. Flexible molecules, such as polypeptides, have different conformational minima and, therefore, different sets of ENMs may be used as templates. It is has been shown, however, by using the alanine dipeptide (AlaD) molecule as a test case that the identification of the INMs is practically irrespective of the set of ENMs chosen as a template.42 The overlap is evaluated using the total contribution of every atom to the definition of the modes. In this way the changes of the spacial orientation of each atomic displacement during the simulation does not modify the value of the overlap. We have found that the total contributions of every atom to the definition of the normal modes is almost independent of the conformer used as a template in the assignation procedure. In this work, we use the ENMs of trialanine corresponding to the absolute minimum energy conformation of the isolated molecule, which is located at (ϕ,ψ) = (−107.5°,−62.3°) in the α conformational region. Application of the EAMC method may lead, in addition, to unphysical assignments of the INMs when two or more INMs have significant contributions of ENMs with quite separated frequencies. To avoid this, the EAMC algorithm is restricted to operate in a frequency window of constant width Δω centered at each ENM frequency.42,51−55 In this work we have refined this procedure by letting the Δω width vary with time when the assignment method is invoked, fixing its value as the minimum Δω width which allows the identification of the INMs. Thus, the Δω width adapts to the requirements of the assignment method continuously, at each instantaneous configuration. The average value of Δω resulting from this work to assign the INMs of trialanine was 125 cm−1.

of the magnitudes of interest by dividing the trajectories into four subsets of identical size. If the values of the standard deviations are too high as to question the tendencies observed in the time evolution of the magnitudes, we increase the number of trajectories and repeat the process. That is how 76 800 trajectories were finally run. The conformations of trialanine are defined by the central peptide dihedral angles ϕ (C−N−Cα−C) and ψ (N−Cα−C− N) (Figure 1), and they basically include the helix conformations αR and αL and the two extended conformations pPII and β. The thermal distribution of the conformers is clearly a subject of intense experimental and theoretical investigations.36,37,47−50 As for the present work, we have grouped the two α conformers in the α region and the pPII and β in the common pPII region. Figure 2 shows the Ramachandran representation of the central dihedral angles ϕ and ψ of trialanine at equilibrium. No

Figure 2. Equilibrium Ramachandran (ϕ,ψ) plot of 13C-Triala-d molecule in liquid D2O at room temperature obtained from MD simulations using the CHARMM22/TIP3P force field.

left-hand α conformers are found in our simulations using the CHARMM22 force field, so we only draw the −180° < ϕ < 0° portion of the Ramachandran plot. The conformational distribution is therefore dominated, as observed, by the righthand α and the pPII conformers. The α region is located in the −150° < ψ < 30° interval, and the pPII region covers the rest of the half-plot. Figure 1 of the Supporting Information shows, in addition, the histograms of population of the dihedral angles ϕ and ψ. It is clearly observed that the lower α/pPII borderline corresponds to the local minimum in the probability distribution of the ψ dihedral lying at ψ = −150° and that there is no clear distinction between the pPII and β conformers in the pPII region. We should indicate also that focusing on the two conformational α and pPII regions allows us to reach statistical convergence of the time evolution of the conformer populations using a tractable number of trajectories. The α and pPII conformer populations at equilibrium extracted from the MD simulations are pα,e = 56.9% and ppPII,e = 43.1%. 2.2. INMs Analysis. The time evolution of the vibrational energy in the trialanine molecule is monitored using the Instantaneous Normal Modes (INMs) analysis recently developed by our group,42,51−55 which we summarize here. The INMs give a decoupled harmonic description of the vibrational energy of a biomolecule in solution at any given instantaneous configuration.The INMs are derived from the diagonalization of the Hessian matrix of the solute molecule. We note that the intermolecular potential energy that describes the solute−solvent interactions is included in the evaluation of

3. NUMERICAL RESULTS AND DISCUSSION 3.1. Kinetic Model for Conformational α/pPII Transitions. Let us consider first the thermal interconversion of the α and pPII conformers of trialanine. We use the set of 76 800 trajectories propagated at equilibrium and separately analyze those evolving from initial α and pPII configurations. There are, specifically, 43 684 α trajectories and 33 116 pPII trajectories at t = 0 which reproduce the equilibrium populations pα,e = 56.9% and p pPII,e= 43.1% given above. To study the kinetic of the α → pPII and pPII → α transitions undergone by the trialanine conformers, we follow the time evolution of the percentage of 350


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where asterisks denote preactivated trialanine molecules, kαd /kαi and kpd /kpi are the activation/deactivation rate constants, and kαp and kpα are the conformer conversion rate constants. The percentage fractions fαe (t) and fpe (t) of molecules that keep their initial conformation, assuming that the conformational changes are irreversible, are then to be respectively identified with the sums of percentage fractions [TriAl(α)]t + [TriAl*(α)]t and [TriAl(p)]t + [TriAl*(p)]t resulting from the conformer’s conversion processes

conformers in each set that remain at their initial α or pPII conformation without any conformational conversion in the (0,t) time interval. These are referred to as fαe (t) and fpPII e (t). Figure 3 shows the time evolution of the unconverted fαe (t) and fpPII e (t) fractions of trialanine conformers. From these plots

kdα

k

αp TriAl(α) ⇄ TriAl*(α) ⎯→ ⎯ TriAl*(p)

kiα

kdp

(2)

k

pα TriAl(p) ⇄ TriAl*(p) ⎯→ ⎯ TriAl*(α)

kip

(3) 61

whose kinetics equations can be solved in closed form giving biexponential-type solutions. We have effectively checked, as shown in Figure 3, that the fractions fαe (t) and fpe (t) extracted from the simulations fit the biexponential functions well

Figure 3. (Top) Time evolution of the percentages of the α (blue lines) and pPII (red lines) conformers that keep their initial conformation without change at equilibrium conditions. Black dotted lines are the fits to biexponential decay functions. (Bottom) Time evolution of the percentages of the α (blue lines) and pPII (red lines) conformers that keep their initial conformation without change during the relaxation of the amide I mode, with respect to their values at equilibrium conditions.

kdα

kα p

kip

kiα

k pα

kd

(4)

f ep (t ) = c p,1e−t / τp,1 + c p,2e−t / τp,2

(5)

and we have numerically derived the rate constants kαd , kαi , kpd, kpi , kαp, kpα and the equilibrium fractions [TriAl(α)]eq, [TriAl*(α)]eq, [TriAl(p)]eq, [TriAl*(p)]eq from the fitted parameters cα,i, τα,i, cp,i, and τp,i, taking into account that cα,1 + cα,2 = pα,e and cp, 1 + cp, 2 = pp,e, plus the equilibrium conditions

we can infer in principle that the α↔pPII conformational changes proceed along two time scales. There is an initial faster decay of the conformer populations, which takes about ∼250 fs, followed by a slower decay in the tens of picoseconds time scale. Both curves must tend asymptotically to zero at long times, since all molecules will finally change their conformation, but we cannot observe that limit because the slower decay time is substantially longer than the 5 ps propagation time. We should note, in addition, that the conformers’ drop in the first step is noticeable smaller than in the second. This behavior recalls the existence of the two well-separated time scales recently reported in the folding of polypeptides5,57−59 related with helix nucleations and propagation processes. In the case of trialanine, where helix formation is not possible due to its reduced molecular size, the conformers’ conversion results extracted from the simulations can be interpreted in terms of a molecular time scale and an activation time scale.3,60 The molecular time scale accounts for the fast crossing of the free energy barrier by preactivated molecules that can change their conformation basically through a downhill process, and the slow activation time scale characterizes the collective processes that allow the solute/solvent system to access the top of the free energy barrier. Accordingly, the trialanine molecules that change their conformation through the fast channel are expected to have conformations close to the saddle point located at (ψ,ϕ) = (−150°,−90°), while the trialanine molecules acceding to the activated state through the slow channel should have a more diffuse distribution of dihedral angles. These considerations are certainly supported by the Ramachandran (ϕ,ψ) diagrams shown in Figures 2 and 3 of the Supporting Information corresponding to the respective α to pPII and pPII to α conversions. The kinetics of the conformers’ conversion dynamics at equilibrium can be then modeled as follows: TriAl(α) ⇄ TriAl*(α) XooY TriAl*(p) ⇄p TriAl(p)

f eα (t ) = cα ,1e−t / τα ,1 + cα ,2e−t / τα ,2

kdα[TriAl(α)]eq = kiα[TriAl*(α)]eq

(6)

kdp[TriAl(p)]eq

(7)

=

kip[TriAl*(p)]eq

kα p[TriAl*(α)]eq = k pα[TriAl*(p)]eq

(8)

The fit parameters and the rate constants and equilibrium fractions derived are all summarized in Table 1. Table 1. Fit Parameters, Rate Constants, Lifetimes, and Equilibrium Fractions Corresponding to the Kinetic Scheme Given by eq 1a cα,1 τα,1 cα,2 τα,2 kαd kαi kαp ταd ταi ταp [TriAl(α)]eq [TriAl*(α)]eq a

= = = = = = = = = = = =

49.89% 26.1 ps 6.99% 0.412 ps 0.0426 ps−1 0.238 ps−1 2.185 ps−1 23.5 ps 4.20 ps 0.458 ps 48.24% 8.64%

cp,1 τp,1 cp,2 τp,2 kpd kpi kpα τpd τpi τpα [TriAl(p)]eq [TriAl*(p)]eq

= = = = = = = = = = = =

36.34% 11.0 ps 6.78% 0.389 ps 0.110 ps−1 0.424 ps−1 2.130 ps−1 9.10 ps 2.36 ps 0.469 ps 34.26% 8.86%

Lifetimes are the inverse values of the rate constants (τj = k−1 j ).

The values obtained for the kαp and kpα rate constants which characterize the equilibrium between the two preactivated conformers, 2.185 and 2.130 ps−1 respectively, are certainly quite close to each other, as are the percentages of the preactivated conformers TriAl*(α) and TriAl*(p) at equilibrium, 8.6% and 8.9%. As can be seen, they account for a small but not negligible fraction of the total number of trialanine

(1) 351


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two relaxation times extracted from simulations, 0.19 and 0.85 ps, are somewhat smaller than the experimental value measured by Hamm et al.27 of 1.25 ps, we think they maintain an acceptable agreement, to the extent that no refinement of the standard force field used in the MD simulations was considered. In order to investigate next the IVR relaxation pathways that the vibrational energy deposited in the C-terminal amide I mode follow through the trialanine molecule, we have organized the INMs in groups (see Figure 4 and Table 1 of

molecules. On the other hand, the values of the rate constants kdα, kiα, kpd, and kip governing the equilibria between the conformers and their corresponding preactivated species are indeed different for one conformation and the other, and higher for the pPII conformers (see Table 1). The faster rate at which the conformers cross the free energy barrier does not depend much therefore on the direction of the conformational change, while the slower rate of formation of preactivated conformers exhibits a strong dependence on the conformation of the molecule. This is in agreement with the different energetics of the processes. The crossing of the energy barrier is expected to depend only on the energy excess of the molecule, somewhat irrespectively of the crossing direction. In contrast, the rate of formation of preactivated conformers is to a large extent influenced by the intra- and intermolecular potential interactions between the molecule and the solvent, which may be significantly different for each conformer. In a recent paper Toal et al.35 have obtained average lifetimes of the different conformers of the trialanine molecule using MD simulations in the tens of picoseconds time scale. These results are comparable to the values of the τpd lifetimes (see Table 1) obtained from our kinetic model in spite of the different force fields used in ταd and both studies. The 20 ps time resolution of their results make impossible the detection of the fast component in the decay of the population evidenced in our results. From the values of the rates and the equilibrium populations included in Table 1 we also note that each of the two exponential terms in eqs 4 and 5 is basically associated with one of the these two processes. 3.2. Amide I Mode Relaxation Lifetimes and IVR Pathways. Let us start now with the analysis of the vibrational dynamics of trialanine after initial excitation of the C-terminal amide I mode and how it affects the α/pPII conformational transitions. We have found first, in agreement with our previous studies on deuterated N-methylacetamide (NMAD)51 and the alanine dipeptide (13C-AlaD-d2),42 that the vibrational relaxation of the C-terminal amide I mode of trialanine follows a biexponential decay parametrized by the expression vib vib,eq EamI (t ) − EamI vib vib,eq EamI (0) − EamI

= crel,1e−t / τrel,1 + crel,2e−t / τrel,2

Figure 4. Normalized INM frequency histograms of the trialanine molecule (red), D2O liquid (green), and H2O liquid (blue).

the Supporting Information). The first group contains the low (L) frequency modes with frequencies below 850 cm−1, which is approximately the limit of the librational band of pure water at room temperature. This frequency limit is nearly half the amide I frequency (1643 cm−1), so only the L modes can develop 2:1 Fermi resonance with the initially excited amide I mode. Since most experiments are carried out in heavy water to avoid the overlap between the H2O bending and the amide I bands, we have divided the L group of modes into two subgroups, L1 and L2, separated by the limit of the librational band of D2O water, of about 650 cm−1. The next group corresponds to the middle (M) frequency modes lying between the L group and the two amide I modes, whose frequencies comprise the interval between 850 and 1600 cm−1. We have also divided this group into two subgroups, M1 and M2, separated now by the ∼100 cm−1 gap existing between the frequencies of the 61st and 62nd INMs. Next come the three single out modes corresponding to the COO asymmetric stretch (80th INM), whose frequency is close enough to the Cterm amide I frequency so as to favor a direct transfer of energy between them, and the C-terminal (81st INM) and the Nterminal (82nd INM) amide I modes. The INMs with higher frequencies are finally all collected in a high (H) frequency group of modes. We present here the results only for the IVR relaxation pathways most directly related with the conformational dynamics, and we provide a more detailed description in the Supporting Information. In Figure 5 we show the time evolution of the vibrational energy stored in the different groups of INMs. The L2, M1, and M2 groups of INMs are the main acceptors of the energy released by the C-terminal amide I mode, with each receiving ∼340 cm−1, that is, about 20% of the total energy deposited initially in the amide I mode (see Table 3 of the Supporting Information). The L2 subgroup, in particular, receives all its energy exclusively through the fast relaxation channel because some of the INMs of the subgroup have vibrational frequencies close to half the value of the Cterminal amide I mode (1643 cm−1), thus favoring the transfer of energy mediated by a 2:1 Fermi resonance. However, the

(9)

vib vib, eq where Evib are the time-dependent, amI(t), EamI(0), and EamI initial and equilibrium amide I vibrational energies, respectively, τrel,i are the lifetimes of the two relaxation channels, and crel,i are the corresponding amplitudes, which satisfy crel,1 + crel,2 = 1. The resulting relaxation lifetimes are τrel,1 = 0.19 ps and τrel,2 = 0.85 ps with amplitudes crel,1 = 0.496 and crel,2 = 0.504. Comparing these results with those previously obtained for NMAD51 and 13 C-AlaD-d2,42 we observe that the two channels through which the amide I mode relaxation occurs, one slow (1) and the other fast (2), have roughly identical weights (∼50%) and rates, with both increasing with the size of the molecule. This rate increase is likely due to the rise in the density of the vibrational levels which can receive the excess energy initially stored in the amide I mode. As for experimental evidence, Hamm et al.27 fitted the normalized population decay of the resonantly excited amide I state of trialanine to a single exponential curve, in contrast with experimental studies on NMAD62,63 and AlaD,41 and our MD simulations which support a biexponential decay of the amide I population for the three molecules. Nevertheless, although our

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concentration can be partially maintained during several picoseconds. In Figure 6 we show how the mean square displacements of the dihedral angles ψ and ϕ calculated at 10 fs time intervals

Figure 5. Time evolution of the vibrational energy of several INMs and groups of INMs with respect to their equilibrium values. Black lines correspond to the average values for all trajectories while blue and red lines correspond to selected trajectories in which the trialanine molecule is in α or pPII conformations when the molecule is excited. Figure 6. Time evolution of the mean values of the square displacement of the torsional angles at 10 fs intervals during the relaxation of the amide I mode relative to the values obtained at equilibrium conditions. Black lines correspond to the average values for all trajectories while blue and red lines correspond to selected trajectories in which the trialanine molecule is in α or pPII conformations when the molecule is excited.

INM frequency averaged values over time do not provide information on instantaneous resonances. To account for the frequency fluctuations of the INMs taking place as the system evolves, we have calculated the probability of instantaneous resonances occurring within a given frequency interval (±10 cm−1). The instantaneous frequency resonance analysis (see Table 2 of the Supporting Information) provides that the sum of probabilities of frequency resonances for the 40th INM is 25.9%, which justifies why that mode alone receives practically half of the total energy transferred into the L2 group, with smaller but significant contributions from the 43rd and 44th INMs. Overall, IVR accounts for at least 75% of the energy released by the C-terminal amide I mode of trialanine which is funneled along the molecule essentially through the L1, L2, M1, M2 groups and the individual 80th and 82nd INMs. Considering, in addition, the energy transferred into the H group, the amount of vibrational energy channeled into the trialanine molecule through IVR reaches 85−90% of the amide I energy, in agreement with our previous results for NMAD and AlaD,42,51 and the rest of the energy is directly dissipated into the solvent. The intermolecular energy transfer into the water molecules is reproduced well by a single exponential decay mechanism with a lifetime of 6.0 ps. This time is similar to the experimental meassurement (5.1 ps) by Dlott et al.64 for the relaxation of the amide I mode of the NMAD molecule solved in heavy water, but shorter than those obtained for NMAD51 (9.6 ps) and AlaD42 (8.6 ps) due likely, as discussed above, to the highest congestion of low energy levels in trialanine that facilitates the energy flow toward the librational modes of the solvent.42 3.3. Time Evolution of the Conformer Populations. Let us finally consider the effect that the vibrational relaxation of the C-terminal amide I mode of trialanine has on the populations of the α and pPII conformers of the molecule. We note first that although the amount of energy deposited in the molecule by exciting the C-terminal amide I mode is modest, 1642.8 cm−1, compared to the total vibrational energy of the molecule at room temperature of about 20500 cm −1 (99 · kBT), it means a significant local perturbation of the molecule which is eight times larger than the correspondieng thermal energy per mode (kBT ≈ 207 cm −1). Moreover the intramolecular vibrational redistribution (IVR) processes in small polypeptides show a substantial degree of selectivity since they are driven by resonance conditions between the donor and acceptor(s) vibrational modes,42,51,52,54,65 so the energy

evolve along the relaxation process with respect to their equilibrium values, calculated by averaging over the whole set of trajectories (black lines). Excitation of the C-terminal amide I mode clearly results, as observed, in significative alterations of the two dihedral angles, as expected, since the C atom of the Cterminal CO group participates in both the amide I group and in the definition of the dihedral angles ψ and ϕ. The time evolution of each dihedral angles is, however, different. While the amplitude of the ϕ torsional motion decreases rapidly after the initial excitation and exhibits a small recurrence at 0.6 ps, the value of the displacement of the ψ angle reaches a maximum at 0.5 ps and then decreases as the trialanine molecule dissipates its excess energy. Figure 6 includes also the time evolution of the displacements of the ψ and ϕ dihedral angles of trialanine extracted from the trajectories starting at α (blue lines) and pPII (red lines) conformations when the vibrational excitation occurs. Since ∼90% of the trialanine molecules keep their initial conformation during the 5 ps simulations (although some may change their conformation several times during that time interval) we can consider that an analysis based on this classification provides a reasonable description of the IVR processes in every conformer. We see that the torsional perturbation is clearly stronger for the α conformers, with the dihedral angle ψ undergoing the most pronounced alteration for these conformers. This finding is fundamental for interpreting the conformational change induced by the IVR processes because the dihedral angle ψ is the one determining the exchange between both conformations. In Figure 3 we show the percentage of molecules that keep their initial configuration α and pPII during the relaxation of the amide I mode, with respect to their values at thermal equilibrium (see Figure 3). As observed, the percentages of molecules that keep their initial configurations during the relaxation process are always smaller than those existing at equilibrium, and the conformational changes are more pronounced for the α conformers than for the pPII ones. During the relaxation of the C-terminal amide I mode the α 353


Article

The Journal of Physical Chemistry B conformers store more energy in the ψ torsional motion, which favors, comparatively, its transformation into pPII conformers. A direct consequence of the different modification of the α↔ pPII conformational change rates is that the relative populations of both conformers are altered during the relaxation process, as observed in Figure 7, where we show

borderline, but a real conformational change of the trialanine molecule involving nonpreactivated conformers. It remains then to analyze how the IVR processes set off the conformational changes observed in trialanine upon the amide I mode excitation. Figure 5 also includes the time evolution of the vibrational energy passing through the INM groups for trajectories initiated at either α or pPII conformations. As observed, the L2 subgroup of INMs and the COO stretching mode (80th INM) are those which make the most important difference in this respect. The COO stretch receives in particular nearly three times more energy in the pPII (150 cm−1) than in the α conformers (60 cm−1), probably due to a shortening in the frequency gap between the C-terminal amide I mode (81st INM) and the COO stretching mode (80th INM) for the pPII (24.7 cm−1) with respect to the α conformers (31.7 cm−1), and to an increasing probability of instantaneous resonances occurring between these two INMs (15.9% for pPII conformers versus 10.5% for α conformers). As for the L2 subgroup of INMs, it receives more energy in the α (421 cm−1) than in the pPII conformers (262 cm−1). In this case the values of the α and pPII frequency gaps between the C-terminal amide I mode and the 40th, 43rd, 44th INMs of the L2 subgroup which are most active in the relaxation process are not conclusive. However, instantaneous resonance probabilities are all higher for the α conformers, especially in the case of the 2:1 Fermi resonance with the 40th INM, which is the main acceptor of energy of the L2 subgroup (see Figure 4 of the Supporting Information). In fact, the sum of probabilities of instantaneous frequency resonances (see Table 2 of the Supporting Information) for the 40th INM is almost double for the α conformers (32.0%) than for the pPII ones (17.8%). Excitations of the COO stretch and the L2 subgroup of modes are expected to have a different effect on the torsional motion of trialanine and subsequently on the conformer dynamics of the molecule. The COO group is quite distant from the atoms participating in the ψ and ϕ dihedrals (see Figure 1), while the most active mode of the L2 group, the collective backbone 40th INM, involves, in contrast, many atoms of the molecular chain, including central CαCN atoms associated with torsional angles ψ and ϕ. The excitation of the 40th INM is therefore expected to cause a substantial distortion in the torsional motions of trialanine, as supported by the similarity of the ϕ excitation curve in Figure 6 with the L2 vibrational energy curve in Figure 5. Consequently, the different degree of excitation of the L2 group in the α and pPII conformers, essentially driven by the collective 40th INM, justifies their different conformational dynamics during the relaxation process as previously discussed. Finally, we should note that the intermolecular energy transfer into the solvent is faster for the pPII conformers (τptot = 5.6 ps) than for the α conformers (ταtot = 6.4 ps). The delay observed for the α conformers is probably related to the vibrational energy stored in the torsional motions of the molecule. As seen in Figure 6, the excitation of the dihedral angles in the α conformers is significant for ∼1 ps, that is, approximately for the time difference between the τtot lifetimes of the conformers.

Figure 7. Time evolution of the population of the α (blue line) and pPII (red line) conformer populations during the relaxation of the amide I mode with respect to the their values at equilibrium conditions. Error bars correspond to the standard deviations of the α conformer populations obtained by dividing the trajectories into four subsets of identical size.

the time evolution of the α (blue line) and pPII (red line) conformer populations during the relaxation of the amide I mode with respect to the their values at equilibrium conditions. During the first relaxation picosecond the conformer populations practically maintain their equilibrium values, but then the α conformer population clearly decreases, so the difference of populations between both conformers reaches a maximun value of ∼0.8% at 2.5 ps. Thereafter, the α conformer population starts to recover slowly but never reaches the equilibrium population after the 5 ps simulations, in agreement with the kinetic analysis presented in the section 3.1 indicating that the recovery of the equilibrium populations of the conformers is governed by the slow channel and takes some tens of picoseconds. Figure 8 shows, in addition, the difference

Figure 8. Differences between the Ramachandran plots obtained during the first 5 ps of the vibrational relaxation of the amide I mode and at equilibrium conditions.

between the Ramachandran (ϕ,ψ) plots obtained during the relaxation process and at equilibrium conditions. As seen, the more pronounced changes are located in well-defined zones of the α and pPII regions and far away from each other. This means that the conformational change is not the result of an oscillation of the conformer populations around the α/pPII

4. CONCLUSIONS Equilibrium Molecular Dynamics simulations carried out for trialanine in deuterated water show that the conformational α/ pPII dynamics of the molecule can be accurately modeled using a kinetic scheme in which preactivated molecules change their 354



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conformation through a downhill process. The rate constants that characterize both the crossing of the free energy barrier between both conformers and the equilibrium between nonactivated and preactivated trialanine molecules are obtained by fitting the results of the simulations to the analytic expressions derived from the kinetic scheme. On the other hand, the non-Equilibrium Molecular Dynamics simulations of the vibrational relaxation of trialanine show that the equilibrium between the α and pPII conformers is altered upon excitation of the C-terminal amide I mode, generating an excess of the pPII conformers. Although the maximum deviations of the α and pPII conformer populations are modest, we note that the relaxation lifetime of the amide I mode is substantially shorter than the time the molecule takes to recover its conformational equilibrium, thus opening up the possibility that accumulative effects occur induced by consecutive absorption of IR photons. The conformational change observed during the relaxation of the trialanine molecule can be explained by the different IVR pathways followed by the α and pPII conformers. The amount of energy deposited in the ψ torsional motion is substantially larger for the α conformers, so the α → pPII conversion rate increases more than the rate of the inverse pPII → α process. The dependence of the relaxation pathways on the conformation of the tripeptide is a direct consequence of the vibrational frequency shifts occurring during the conformational dynamics, which change selectively the frequency resonance conditions driving the intramolecular energy flows within the two conformers. Simulations also show that the pPII conformers are more effective in releasing excess vibrational energy into the solvent due to the storage of energy in the torsional motions of the α conformers that delay the cooling of the polypeptide. This mechanism indicates that the effectiveness of the energy exchange between proteins and water molecules may be directly related with the conformational change.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.5b09753. Description of IVR pathways including the parameter values obtained from the fits of the vibrational INM energy curves; Ramachandran plots of the trialanine molecule during the conformational dynamics and a graphical representation of some INMs (PDF)

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Article

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was partially supported by the Spanish Ministerio de Ciencia e Innovación under Project CONSOLIDER CSD200900038 and by the Fundación Sén eca del Centro de Coordinación de la Investigación de la Región de Murcia under Project 19419/PI/14. 355


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