pubs.acs.org/Langmuir © 2010 American Chemical Society
Secondary Structure Specific Entropy Change of a Partially Unfolded Protein Molecule Sudipta Kumar Sinha, Sudip Chakraborty, and Sanjoy Bandyopadhyay* Molecular Modeling Laboratory, Department of Chemistry, Indian Institute of Technology, Kharagpur -721302, India Received January 25, 2010 The conformational disorder of a protein in its partially unfolded molten globule (MG) form leads to an overall gain in the configurational entropy of the protein molecule. However, considering the differential degree of unfolding of different secondary structural segments of the protein, the entropy gained by them may be nonuniform. In this work, our attempt has been to explore whether any correlation exists between the degree of unfolding of different segments of a protein and their entropy gains. For that, we have carried out atomistic molecular dynamics simulations of the folded native and a partially unfolded structures of the protein villin headpiece subdomain or HP-36 in aqueous medium. It is found that among the three R-helical segments of the protein, the central R-helix (helix-2) underwent unfolding during the transition with a consequent entropy gain significantly higher than that of the other two helical segments. The calculations further revealed that the differential entropy gain by the segments of a protein can be used as an effective measure to identify the unfolded segments of the protein and hence to explore the folding pathways.
1. Introduction A protein folds to its three-dimensional native conformation following the synthesis and becomes functionally active in a particular environment.1,2 Slight modifications of the environment can lead to unfolding of the protein with a consequent loss of its function.1 Considering its significance, protein folding-unfolding is one of the most important problems in biology which has been an area of great interest at present. The ideal unfolded structure of a protein is the extended polypeptide chain that is devoid of any secondary structure. However, the completely extended chain is unlikely to be present in solution under normal conditions. Because of the rugged nature of the folding free energy surface,3-7 whenever a protein unfolds from its native form, it generally attains a partially unfolded conformation by moving to a nearby state in the configurational space. A noticeable fraction of secondary structures and hydrophobic contacts remain intact in those conformations. An ensemble of such partially unfolded structures can be formed which constitute the so-called molten globule (MG) state.8 The molten globules are essentially the intermediates along the rugged folding-unfolding pathways. For large multidomain proteins, unfolding usually occurs through a sequence of transitions, while for small proteins one often observes sharp transitions to the unfolded state. Theoretical calculations, experiments, and simulations have been extensively used over many years to understand different *To whom correspondence should be addressed. E-mail: sanjoy@ chem.iitkgp.ernet.in. (1) Nelson, D. L.; Cox, M. M. Lehninger Principles of Biochemistry; Worth; New York, 2000. (2) Berg, J. M.; Tymoczko, J. L.; Stryer, L. Biochemistry; Freeman; New York, 2002. (3) Bryngelson, J. D.; Wolynes, P. G. Proc. Natl. Acad. Sci. U.S.A. 1987, 84, 7524. (4) Dill, K. A. Biochemistry 1990, 29, 7133. (5) Dill, K. A.; Fiebig, K. M.; Chan, H. S. Proc. Natl. Acad. Sci. U.S.A. 1993, 90, 1942. (6) Onuchic, J. N.; Wolynes, P. G. Curr. Opin. Struct. Biol. 2004, 14, 70. (7) Honeycutt, J. D.; Thirumalai, D. Proc. Natl. Acad. Sci. U.S.A. 1990, 87, 3526. (8) Ptitsyn, O. B. Curr. Opin. Struct. Biol. 1995, 5, 74.
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aspects of the protein folding problem.3-7,9-32 NMR and ultrafast solvation dynamics experiments have provided valuable information on the structure of the folding intermediates and the dynamics of protein folding.9,11-13 Fluorescence energy transfer (FET) experiments have been used by Winkler and co-workers14,15 to investigate the conformational heterogeneity of unfolded structures of cytochrome c. It is shown that differential scanning calorimetry (DSC) can be used to measure the barrier heights in (9) Dyson, H. J.; Wright, P. E. Chem. Rev. 2004, 104, 3607. (10) Tang, Y.; Rigotti, D. J.; Fairman, R.; Raleigh, D. P. Biochemistry 2004, 43, 3264. (11) Vu, D. M.; Peterson, E. S.; Dyer, R. B. J. Am. Chem. Soc. 2004, 125, 6546. (12) Sen, P.; Mukherjee, S.; Dutta, P.; Halder, A.; Mandal, D.; Banerjee, R.; Roy, S.; Bhattacharyya, K. J. Phys. Chem. B 2003, 107, 14563. (13) Guha, S.; Sahu, K.; Roy, D.; Mondal, S. K.; Roy, S.; Bhattacharyya, K. Biochemistry 2005, 44, 8940. (14) Pletneva, E. V.; Gray, H. B.; Winkler, J. R. J. Mol. Biol. 2005, 345, 855. (15) Pletneva, E. V.; Gray, H. B.; Winkler, J. R. J. Am. Chem. Soc. 2005, 127, 15370. (16) Naganathan, A. N.; Sanchez-Ruiz, J. M.; Mu~noz, V. J. Am. Chem. Soc. 2005, 127, 17970. (17) Chung, H. S.; Ganim, Z.; Jones, K. C.; Tokmakoff, A. Proc. Am. Chem. Soc. 2007, 104, 14237. (18) Brujic, J.; Hermans, R. I. Z.; Garcia-Manyes, S.; Walther, K. A.; Fernandez, J. M. Biophys. J. 2007, 92, 2896. Garcia-Manyes, S.; Brujic, J.; Badilla, C. L.; Fernandez, J. M. Biophys. J. 2007, 93, 2436. (19) Garcia-Manyes, S.; Dougan, L.; Badilla, C. L.; Brujic, J.; Fernandez, J. M. Proc. Am. Chem. Soc. 2009, 106, 10534. (20) Sali, A.; Shakhnovich, E.; Karplus, M. Nature 1994, 369, 248. (21) Duan, Y.; Kollman, P. A. Science 1998, 282, 740. (22) Duan, Y.; Wang, L.; Kollman, P. A. Proc. Natl. Acad. Sci. U.S.A. 1998, 95, 9897. (23) Garcia, A. E.; Onuchic, J. N. Proc. Natl. Acad. Sci. U.S.A. 2003, 100, 13898. (24) Jayachandran, G.; Vishal, V.; Pande, V. S. J. Chem. Phys. 2006, 124, 164902. (25) Rhee, Y. M.; Pande, V. S. J. Phys. Chem. B 2008, 112, 6221. (26) Day, R.; Daggett, V. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 13445. (27) McCully, M. E.; Beck, D. A. C.; Daggett, V. Biochemistry 2008, 47, 7079. (28) Bryngelson, J. D.; Wolynes, P. G. J. Phys. Chem. 1989, 93, 6902. Saven, J. V.; Wolynes, P. G. J. Mol. Biol. 1996, 257, 199. (29) Onuchic, J. N.; Nymeyer, H.; Garcia, A. E.; Chahine, J.; Socci, N. D. Adv. Protein Chem. 2000, 53, 87. (30) Li, M. S.; Klimov, D. K.; Thirumalai, D. Phys. Rev. Lett. 2004, 93, 268107. (31) Srinivas, G.; Bagchi, B. J. Phys. Chem. B 2003, 107, 11768. (32) Mukherjee, A.; Bhimalapuram, P.; Bagchi, B. J. Chem. Phys. 2005, 123, 014901.
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protein folding.16 Recently, Tokmakoff and co-workers17 applied transient two-dimensional infrared (2D-IR) spectroscopy to understand the unfolding dynamics of proteins. Fernandez and coworkers18,19 showed that recently developed force-clamp spectroscopy can be used to experimentally characterize the foldingunfolding trajectories of single protein molecules. Computer simulation studies capable of probing the structure and dynamics at different levels of resolution can play important roles in elucidating the structure of the intermediates as well as the time scale and the mechanisim of protein folding. Many simulation studies on protein folding-unfolding have been reported over past several years.20-27 Various theoretical concepts have also been developed to understand different aspects of the multidimensional free energy surface of the folding funnel.3-7,28-32 For many proteins at ambient conditions, it is found that the free energy of the folded native state is marginally lower than that of the unfolded state, although the enthalpy difference between the two states can be very large. It is clear that the large enthalpy cost is largely compensated by the entropy gain that occurs during unfolding.33 Thus, the estimation of entropy change during folding-unfolding of a protein is of fundamental importance to understand the stability of its conformations and the folding pathways. There are several approaches proposed to estimate the entropies of proteins and other macromolecules from simulation studies. In most of these methods, internal non-Cartesian coordinates are used to avoid handling of slow translational and rotational motions of the molecules. Thus, the calculations based on these methods are restricted to the molecular configurational entropies. Karplus and Kushick34 first proposed a quasiharmonic approach to estimate the configurational entropy of large molecules from trajectories generated by using classical simulations. This method was used for biomolecules in some of the earlier studies.35,36 However, application of this method is limited due to the use of internal coordinates. Schlitter37 later proposed another method of calculation of the absolute configurational entropy of macromolecules based on a quantum mechanical harmonic approximation. The advantage of Schlitter’s method is the direct use of Cartesian coordinates in its formalism (as discussed later). This allows one to avoid transformation to internal coordinates. This method has been used in several studies to calculate configurational entropies of biomolecules. This was extensively tested and validated by measuring the entropy changes associated with the reversible folding of polypeptides from molecular dynamics (MD) simulations by Sch€afer et al.38,39 They estimated the contributions of the backbone and the side-chain atoms toward the total entropy of the polypeptide at different temperatures. They further extended their study to estimate the configuratinal entropy of the molten globule state of the protein R-lactalbumin.40 The correlation between the configurational entropy of the protein side chains and their exposure was explored in detail. Recently, Hsu et al41 applied the Schlitter’s approach to calculate (33) Andricioaei, I.; Karplus, M. J. Chem. Phys. 2001, 115, 6289. (34) Karplus, M.; Kushick, J. N. Macromolecules 1981, 14, 325. (35) Di Nola, A. H.; Berendsen, H. J. C.; Edholm, O. Macromolecules 1984, 17, 2044. (36) Levy, R. M.; Karplus, M.; Kushick, J. N.; Perahia, D. Macromolecules 1984, 17, 1370. (37) Schlitter, J. Chem. Phys. Lett. 1993, 215, 617. (38) Sch€afer, H.; Mark, A. E.; van Gunsteren, W. F. J. Chem. Phys. 2000, 113, 7809. (39) Sch€afer, H.; Daura, X.; Mark, A. E.; van Gunsteren, W. F. Proteins: Struct. Funct. Genet. 2001, 43, 45. (40) Sch€afer, H.; Smith, L. J.; Mark, A. E.; van Gunsteren, W. F. Proteins: Struct. Funct. Genet. 2002, 46, 215. (41) Hsu, S. D.; Peter, C.; van Gunsteren, W. F.; Bonvin, A. M. J. J. Biophys. J. 2005, 88, 15.
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the configurational entropy change that occurs during complexation of a protein and its receptor. The entropy change associated with the binding of a ligand to DNA groove has also been estimated successfully using this approach.42 The results showed that such binding leads to significant loss of configurational entropy of the ligands. By varying the temperature, the correlation between the configurational entropy of a protein and the number of salt bridges at its surface has been established recently.43 In this article, we have estimated the configurational entropy of different segments of a partially unfolded structure of a small globular protein containing 36 amino acid residues, HP-3644 from atomistic MD simulations. By comparing the results with that of the folded native form of the protein, we have attempted to explore the existence of any correlation between the unfolding of different segments of the protein and their corresponding entropy gains. HP-36 is the thermostable helical subdomain present at the C-terminus of the globular villin headpiece protein containing 76 residues.44,45 Villin is a unique protein that can both assemble and disassemble actin structures.46 In the absence of calcium ions, it can act as an actin-bundling protein, while in the presence of calcium it becomes an actin-severing protein. HP-36 contains one of the two binding sites in villin necessary for the bundling activity.46 The residues of HP-36 are numbered from 1 to 36, which correspond to residues 41 to 76 of villin protein.44 The primary sequence of HP-36 is MLSDEDFKAVFGMTRSAFANLPLWKQQNLKKEKGLF. The native structure of HP36 contains three short R-helices which are connected by turns and loops. For convenience,we denote the three R-helices as helix-1 (Asp-4 to Lys-8), helix-2 (Arg-15 to Phe-18), and helix-3 (Leu-23 to Glu-32).47 The binding activity of HP-36 is centered around helix-3 which contains 10 amino acid residues.44 The rest of the article is organized as follows. In the next section (section 2), we give a brief account of the setup of the simulation systems and the methodologies employed. The mathematical formulation of the Schlitter’s method of entropy calculation is highlighted in section 3. The results obtained from our investigations are presented and discussed in section 4. In the last section (section 5), we summarize the important findings from our study.
2. System Setup and Simulation Details Two different simulations denoted as S1 and S2 were carried out. The folded native structure of the protein has been studied at 300 K in simulation S1, while the unfolding of the protein was studied in simulation S2. The initial coordinates of the 36-residue protein HP-36 as obtained from NMR studies44 were taken from the Protein Data Bank (PDB ID: 1VII) for the simulation S1. After capping the two end residues (Met-1 and Phe-36), the protein molecule was immersed in a large cubic box of water with 61 A˚ dimension. After carefully removing the water molecules that were in unfavorable contacts with the protein, the system contained 6842 water molecules. At first, the system was equilibrated at constant temperature (T = 300 K) and pressure (42) Dolenc, J.; Baron, R.; Oostenbrink, C.; Koller, J.; van Gunsteren, W. F. Biophys. J. 2006, 91, 1460. (43) Missimer, J. H.; Steinmetz, M. O.; Baron, R.; Winkler, F. K.; Kammerer, R. A.; Daura, X.; van Gunsteren, W. F. Protein Sci. 2007, 16, 1349. (44) McKnight, C. J.; Matsudaira, P. T.; Kim, P. S. Nat. Struct. Biol. 1997, 4, 180. McKnight, C. J.; Doering, D. S.; Matsudaira, P. T.; Kim, P. S. J. Mol. Biol. 1996, 260, 126. (45) Tang, Y.; Grey, M. J.; McKnight, C. J.; Palmer, A. G., III; Raleigh, D. P. J. Mol. Biol. 2006, 355, 1066. (46) Doering, D. S.; Matsudaira, P. Biochemistry 1996, 35, 12677. Pope, B.; Way, M.; Matsudaira, P. T.; Weeds, A. FEBS Lett. 1994, 338, 58. (47) Bandyopadhyay, S.; Chakraborty, S.; Balasubramanian, S.; Pal, S.; Bagchi, B. J. Phys. Chem. B 2004, 108, 12608.
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consistent with the chosen protein force field was employed for water. We have used the MD code PINY-MD51 to carry out the calculations. The simulations utilized the Nose-Hoover chain thermostat extended system method.52 Application of the reversible multiple time step algorithm, RESPA52,53 allowed us to employ a MD time step of 4 fs. Electrostatic interactions were calculated by using the particle-mesh Ewald (PME) method.54 The PME and RESPA were combined following the method suggested by Marchi and co-workers.55 The minimum image convention56 was employed to calculate the Lennard-Jones interactions and the real-space part of the Ewald sum, using spherical truncations of 7 and 10 A˚, respectively, for the short- and the longrange parts of the force decomposition. Figure 1. (a) Configuration of the protein HP-36 as obtained from the simulation of its native form, S1. The secondary structures contain three R-helices and four coils as indicated. The primary sequence of the protein is also displayed in one-letter code, with the N-terminus residue M(1) on the left and the C-terminus residue F(36) on the right. (b) Configuration of the protein in its partially unfolded form as obtained from simulation S2.
(Pext = 0) (NPT) for about 500 ps with isotropic volume fluctuation. At the end of this equilibration run, the volume of the system attained a steady value with an edge length of 58.92 A˚ of the simulation cell. At this point we fixed the cell volume, and the simulation conditions were changed from NPT to constant volume and temperature (NVT). The NVT run was then continued at 300 K for about 3.5 ns duration. The configuration of the protein in its native form as obtained at the end of simulation S1 was taken to initiate the unfolding simulation, S2. An NPT simulation was first carried out at high temperatures of 500-600 K for approximately 1.4 ns duration. During this time period the protein underwent a transition from the native to a partially unfolded structure with the segment corresponding to the central R-helix (helix-2) transformed into a coil.48 This partially unfolded form is a representative member of the ensemble of structures that collectively form the molten globule (MG) state of the protein. At this point with completion of the unfolding of helix-2, the temperature of the system was lowered to 300 K, and the NPT run was continued for another 300 ps. The simulation conditions were then changed from NPT to NVT ensemble. The trajectory of the partially unfolded structure in NVT ensemble was then generated for about 2.5 ns duration at 300 K. The native and partially unfolded configurations of the protein as obtained from simulations S1 and S2 are displayed in Figure 1. The primary sequence and the secondary structures of the protein are marked for clarity. As reported earlier,48 the unfolded structure obtained from simulation S2 at 300 K was associated with an average root-mean-square deviation (rmsd) of ∼9 A˚ with respect to the folded native form of the protein. The MD trajectories were stored for both the simulations (S1 and S2) with a time resolution of 400 fs. The results reported are calculated over the equilibrated trajectories at 300 K. We have employed the CHARMM22 all-atom force field and potential parameters for proteins49 to describe the interaction between the atoms of the protein, while the TIP3P model50 that is (48) Bandyopadhyay, S.; Chakraborty, S.; Bagchi, B. J. Chem. Phys. 2006, 125, 084912. (49) MacKerell, A. D., Jr.; Bashford, D.; Bellott, M.; Dunbrack, R. L., Jr.; Evanseck, J. D.; Field, M. J.; Fischer, S.; Gao, J.; Guo, H.; Ha, S.; JosephMcCarthy, D.; Kuchnir, L.; Kuczera, K.; Lau, F. T. K.; Mattos, C.; Michnick, S.; Ngo, T.; Nguyen, D. T.; Prodhom, B.; Reiher, W. E., III; Roux, B.; Schlenkrich, M.; Smith, J. C.; Stote, R.; Straub, J.; Watanabe, M.; Wiorkiewicz-Kuczera, J.; Yin, D.; Karplus, M. J. Phys. Chem. B 1998, 102, 3586. (50) Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L. J. Chem. Phys. 1983, 79, 926.
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3. Entropy Calculation In this work, we have estimated the configurational entropy of the protein using the methodology as suggested by Schlitter.37 According to this method, the absolute entropy (Sabs) at a given temperature (T) can be approximated as
Sabs
" # 1 kB Te2 1=2 1=2 < S ¼ kB ln det 1 þ 2 M σM 2 p
ð1Þ
where, kB is Boltzmann’s constant, e is Euler’s number, M is the 3-N dimensional diagonal matrix containing N atomic masses of the solute, σ is the covariance matrix of atom positional fluctuations, and p is Planck’s constant divided by 2π. The elements of the covariance matrix, σij, are given by σ ij ¼ Æðxi - Æxi æÞðxj - Æxj æÞæ
ð2Þ
where, xi are the Cartesian coordinates of the atoms after removal of the translation of the center of mass and rotation around the center of mass of the molecule with respect to the reference configuration. This ensures that the calculated entropy value (S) is the configurational entropy of the molecule. Here, the initial configurations of the analyzed trajectories are considered as the reference structures. Further details of the Schlitter’s method can be found in the literature.33,37,41,42 Since the matrix 1þ
kB Te2 p2
M1=2 σM1=2
is a symmetric positive-definite one, we have evaluated the determinant using a more efficient triangularization procedure, known as the Cholesky decomposition method.33 The covariance matrix elements have been calculated by time averaging over the configurations stored during the simulations. One particular advantage of this method is that it is possible to calculate the configurational entropy for a particular segment of a large molecule like protein. This allows one to compute the contribution arising from a subset of atoms in a residue, which otherwise is difficult to obtain from other methods. (51) Tuckerman, M. E.; Yarne, D. A.; Samuelson, S. O.; Hughs, A. L.; Martyna, G. J. Comput. Phys. Commun. 2000, 128, 333. (52) Martyna, G. J.; Tuckerman, M. E.; Tobias, D. J.; Klein, M. L. Mol. Phys. 1996, 87, 1117. (53) Tuckerman, M. E.; Berne, B. J.; Martyna, G. J. J. Chem. Phys. 1992, 97, 1990. (54) Darden, T.; York, D.; Pedersen, L. J. Chem. Phys. 1993, 98, 10089. (55) Procacci, P.; Darden, T.; Marchi, M. J. Phys. Chem. 1996, 100, 10464. Procacci, P.; Marchi, M.; Martyna, G. J. J. Chem. Phys. 1998, 108, 8799. (56) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Clarendon: Oxford, U.K., 1987.
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Sinha et al. Table 1. Configurational Entropy Per Atom (in J K-1 mol-1) of the Three Helical Segments of the Protein in Its Folded Native Form and in the Partially Unfolded MG Structure at 300 K As Obtained by Considering All the Non-Hydrogen Heavy Atoms as Well as Only the Backbone Atoms (N, C, and Cr)a all heavy atoms segment
native
MG
backbone atoms ΔS
native
MG
ΔS
whole 25.5 28.6 3.1 20.5 25.6 5.1 helix-1 24.3 24.4 0.1 12.9 13.6 0.7 helix-2 18.8 29.7 10.9 11.3 24.7 13.4 helix-3 26.3 27.1 0.8 15.3 16.4 1.1 a The entropy gained (ΔS = SMG - Snative) by the segments are listed for comparison.
Figure 2. Cumulative configurational entropy per atom of the protein in the partially unfolded structure as obtained from simulation S2 at 300 K (dashed line). Corresponding data for the folded native structure as obtained from simulation S1 under identical conditions (solid line) are also displayed. The calculations are carried out by considering (a) all the non-hydrogen heavy atoms of the molecule, and (b) only the backbone atoms (N, C, and CR).
4. Results and Discussion We have calculated the cumulative configurational entropy of the protein molecule in its folded native (Snative) and partially unfolded molten globule (MG) structures (SMG), as shown in Figure 2. The entropies are estimated by including all the nonhydrogen heavy atoms of the protein, as well as by considering only the backbone atoms (N, C, and CR) in the calculation of the covariance matrix, σ. Because of the difference in the number of atoms between the backbone and the residue side chains, the entropy values are normalized by dividing with the number of atoms. The calculations are carried out with the assumption that HP-36 being a small protein molecule, its conformational sampling is complete within the time scale of the present simulation. This is a common practice followed in earlier works.38 All the curves show rapid build-up of entropies before attaining almost steady values. The normalized cumulative average configurational entropy values per atom for the native and the unfolded structures are listed in Table 1. It can be seen that the entropy values are higher for the unfolded structure as against that for the folded native form. Such a gain in entropy by the unfolded structure of the protein is a signature of its more disordered flexible configuration. Further, it is found that the entropy gain due to unfolding (ΔS = SMG - Snative) is 5.1 J K-1 mol-1 when only the backbone atoms are considered as against 3.1 J K-1 mol-1 when all the non-hydrogen atoms are included in the calculations. This suggests that the contribution arising from the disordered backbone structure is more significant toward the configurational entropy of the protein in its unfolded form. We have mentioned before that the structure of helix-1 and helix-3 remained mostly intact during the transition, while helix-2 unfolded into a coil (see Figure 1). To explore such inhomogeneous and preferential unfolding pattern, we have calculated and compared the normalized configurational entropies per atom of the segments corresponding to the three helices in the two structures, as shown in Figure 3. The results obtained are quite interesting. It can be seen that the cumulative build-ups of 9914 DOI: 10.1021/la1012389
Figure 3. Cumulative configurational entropy per atom of the segments corresponding to the three R-helices of the protein in the partially unfolded structure as obtained from simulation S2 at 300 K (drawn with symbol circle). Corresponding data for the helices in the folded native structure as obtained from simulation S1 under identical conditions (drawn without symbol) are also displayed. The calculations are carried out by considering (a) all the non-hydrogen heavy atoms of the segments, and (b) only their backbone atoms (N, C, and CR).
configurational entropies for helices 1 and 3 are almost identical in the folded native and partially unfolded structures of the protein. This is also true when only the backbone atoms are considered. It confirms that compared to the native structure these two helical segments did not undergo any significant conformational disorder during the unfolding process. However, note the entropy build-up of the segment corresponding to helix-2 in the two structures. The unfolding of this helix resulted in significant gain in its configurational entropy as compared to that in the native form of the protein molecule. The effect seems to be more prominent when only the backbone atoms are considered. As already discussed, there is practically no change in the entropy associated with the backbones of helices 1 and 3, whereas unfolding of helix-2 resulted in significant gain in its backbone entropy. Thus, our results indicate that the unfolding of a protein is not only associated with a gain in its configurational entropy, but such gain can be nonuniform among different segments of the molecule depending on the extent of unfolding of those segments. The normalized cumulative average configurational entropies per atom for the three helical segments of the protein in the native and the partially unfolded structures are listed in Table 1. Note the Langmuir 2010, 26(12), 9911–9916
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Article Table 2. Configurational Entropy per Atom (in J K-1 mol-1) of the Four Residues (Arg-15, Ser-16, Ala-17, and Phe-18) of Helix-2 of the Protein in Its Folded Native Form and in the Partially Unfolded MG Structure at 300 K as Obtained by Considering All the Non-hydrogen Heavy Atoms as Well as Only the Backbone Atoms (N, C, and Cr)a all heavy atoms residue
native
MG
backbone atoms ΔS
native
MG
ΔS
Arg-15 17.5 17.7 0.2 1.8 1.9 0.1 Ser-16 9.9 16.5 6.6 1.7 2.0 0.3 Ala-17 5.6 7.9 2.3 1.7 2.0 0.3 Phe-18 10.5 17.7 7.2 1.7 2.1 0.4 a The entropy gained (ΔS = SMG - Snative) by the segments are listed for comparison.
Figure 4. Cumulative configurational entropy per atom of the four residues of the segment corresponding to helix-2 in the partially unfolded structure of the protein as obtained from simulation S2 at 300 K (drawn with symbol circle). Corresponding data for these residues in the folded native structure as obtained from simulation S1 under identical conditions (drawn without symbol) are also displayed. The calculations are carried out by considering (a) all the non-hydrogen heavy atoms of the residues, and (b) only their backbone atoms (N, C, and CR).
large entropy gain (ΔS) by helix-2 in the unfolded structure (more than 10 J K-1 mol-1) as against rather insignificant gains by the other two helical segments (within 1 J K-1 mol-1). Such large entropy gained by helix-2 is reflected in relatively rapid build-up of entropy of the whole protein molecule in its partially unfolded form (see Figure 2). It may be noted that by calculating the entropies of the three helical segments separately, the correlations between the helices are neglected. So far, we have shown that the unfolding of helix-2 is associated with a relatively large gain in its configurational entropy. In an earlier work,48 we found that Phe-18 is the residue where the unfolding transition of helix-2 was first initiated. It would be interesting to explore whether such transition around Phe-18 is correlated with its entropy change. For this, we have estimated the normalized configurational entropies per atom of the four amino acid residues of helix-2 (Arg-15, Ser-16, Ala-17, and Phe-18) in the unfolded structure and compared that with the corresponding data obtained from the native form of the protein. The results are shown in Figure 4. As before, the calculations are carried out by considering all the non-hydrogen heavy atoms of the residues as well as with only their backbone atoms. The estimated entropy values are listed in Table 2. It may be noted that due to neglect of correlations, the sum of the individual entropy values of the four residues are different from that of the segment comprising of these residues, helix-2. It can be seen from Figure 4 that the entropy build-ups for the backbone atoms of these residues are quite homogeneous in nature in each of the two structures of the protein. However, interesting behavior is observed when all the non-hydrogen atoms (backbone and side chain) of these residues are included in the calculation (see Figure 4a). At first, it can be seen that significant differences in entropy build-ups exist among the four residues of helix-2 irrespective of whether the protein molecule is in its folded native form or in the partially unfolded form. Further, it can be seen that there is a rapid entropy gain for Langmuir 2010, 26(12), 9911–9916
almost all the four residues in the unfolded structure. This is particularly noticeable for Ser-16 and Phe-18, with entropy gains (ΔS) of 6.6 J K-1 mol-1 and 7.2 J K-1 mol-1, respectively (see Table 2). Considering the fact that unfolding was first initiated around Phe-18, maximum entropy gained by it in the unfolded structure of the protein is an important finding. This suggests that not only a correlation exists between the unfolding of a secondary structural segment with its configurational entropy, but the nucleation site for the unfolding process attains maximum disorder and hence gains maximum entropy. Therefore, our findings indicate that a simple computation of the configurational entropy can be used as a suitable measure to identify the nucleation site for the folding-unfolding transition of a protein molecule.
5. Conclusions In this work, we have presented atomistic MD simulation studies at room temperature to estimate and compare the configurational entropy of the folded native structure and a partially unfolded molten globule (MG) structure of a small globular protein containing 36 amino acid residues, HP-36 in aqueous medium. An attempt has been made to explore the correlation between the differential unfolding of the three R-helical segments of the protein and the entropy gained by these segments. The calculations revealed several interesting results. At first, it is found that the protein molecule gained entropy on transforming from its folded native form to the partially unfolded structure. Importantly, the entropy build-ups for the segments corresponding to the three helices of the protein in its unfolded form were found to have been influenced in a differential manner due to the structural transition of the molecule. Among the three segments, helices 1 and 3 were found to exhibit almost identical entropy build-up patterns in both folded and partially unfolded structures of the protein. This is consistent with the fact that these two helices retained their native conformations in the unfolded form too. On the other hand, the segment corresponding to helix-2, which was unfolded during the transition, has been found to gain significant configurational entropy compared to the other two helical segments. This clearly suggests that different secondary structural segments of a protein molecule can exhibit differential entropy gains due to an unfolding transition. The extent of such differential behavior is expected to depend on the degree of unfolding of different segments of the protein. The calculations further revealed a nonuniform entropy gain among the residues of helix-2 in the unfolded structure. In particular, the residue Phe-18 around which unfolding of helix-2 was first nucleated, has been found to undergo maximum disorder with a consequent maximum gain in its entropy. Thus, in this work we have been able to establish a correlation between the extent of unfolding of a particular segment of a protein molecule and its gain in configurational entropy. DOI: 10.1021/la1012389
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Article
Such correlation can be used as a tool to identify the nucleation site for the folding/unfolding transition and hence to understand the folding pathways of proteins. It may be noted that the entropy change associated with the water molecules surrounding a protein can also play an important role in guiding the unfolding process. Currently, we are exploring this aspect as well in our laboratory.
9916 DOI: 10.1021/la1012389
Sinha et al.
Acknowledgment. This study was supported by a grant from the Department of Science and Technology (SR/S1/PC-23/2007), Government of India. Part of the work was carried out using the computational facility created under DST-FIST programme (SR/ FST/CSII-011/2005). S.K.S. thanks the Council of Scientific and Industrial Research (CSIR), Government of India for providing a scholarship.
Langmuir 2010, 26(12), 9911–9916
