Intrinsic Alterations in the Partial Molar Volume on the Protein

Feb 20, 2009 - This is consistent with the phenomenological question of the protein volume paradox. Furthermore, using the surficial Kirkwood−Buff a...
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J. Phys. Chem. B 2009, 113, 3543–3547

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Intrinsic Alterations in the Partial Molar Volume on the Protein Denaturation: Surficial Kirkwood-Buff Approach Isseki Yu,† Masayoshi Takayanagi, and Masataka Nagaoka* Graduate School of Information Science, Nagoya UniVersity, Furo-cho, Chikusa-ku, Nagoya 464-8601, Japan ReceiVed: September 27, 2008; ReVised Manuscript ReceiVed: December 28, 2008

The partial molar volume (PMV) of the protein chymotrypsin inhibitor 2 (CI2) was calculated by all-atom MD simulation. Denatured CI2 showed almost the same average PMV value as that of native CI2. This is consistent with the phenomenological question of the protein Volume paradox. Furthermore, using the surficial Kirkwood-Buff approach, spatial distributions of PMV were analyzed as a function of the distance from the CI2 surface. The profiles of the new R-dependent PMV indicate that, in denatured CI2, the reduction in the solvent electrostatic interaction volume is canceled out mainly by an increment in thermal volume in the vicinity of its surface. In addition, the PMV of the denatured CI2 was found to increase in the region in which the number density of water atoms is minimum. These results provide a direct and detailed picture of the mechanism of the protein volume paradox suggested by Chalikian et al. 1. Introduction Many experimental efforts have been directed toward analyzing partial molar volume (PMV), which is the contribution that the protein makes to the overall volume of the solution.1-3 Recent rapid advances in computational power also enable the theoretical investigation of the PMV of proteins from the atomic level.4 In the current understanding, a question referred to as the protein Volume paradox5 remains with regard to the PMV alteration accompanying protein denaturation. Due to the gain of solvent-accessible surface area (SASA), the denatured protein accumulates many more water molecules than the native protein does. In addition, the denatured structure of a protein is considered to lose the void volume created in the interior of its native structure. Therefore, a significant negative volume change would be expected to accompany protein denaturation. However, only small negative, or even positive, volume changes are observed with the denaturation of proteins.1-3 We used the Kirkwood-Buff (KB) theory combined with all-atom MD simulation to calculate the PMV of chymotrypsin inhibitor 2 (CI2) in its native and denatured structure in pure water. Furthermore, using our own surficial KB approach,6 we analyzed the spatial distribution of PMV as a function of the distance from the protein surface to obtain detailed information about the protein volume paradox. Intrinsic alterations in the PMV were examined by comparing the PMV profiles between the native and the denatured structures of CI2. This article is organized as follows: first, in the following section, Computational Methods, the computational methods and the model systems are explained. Precise numerical results are provided and discussed in the Results and Discussion section. Finally, the present study is summarized in the Concluding Remarks section. * Corresponding author. E-mail: [email protected]. URL: http://www.ncube.human.nagoya-u.ac.jp/. Tel./Fax: +81-52-789-5623. † Current affiliation: Department of Chemistry and Biological Science, College of Science and Engineering, Aoyama Gakuin University, 5-10-1 Fuchinobe, Sagamihara, Kanagawa 229-8558, Japan.

2. Computational Methods 2.1. Surficial Kirkwood-Buff Integral. The Kirkwood-Buff (KB) integral of solvent component s around a certain atom site k is defined as follows:

Gks )

∫ [gks(r) - 1] dr

(1)

where gks(r) is the pair correlation function between the atom site k and the atoms in s when they are separated by r. The integral should be taken in whole 3-dimentional space around k. Conventionally, R dependence of Gks is defined as

Gks(R) )

r)R [gks(r) - 1]4πr2 dr ∫r)0

(2)

with the use of gks(r) as the radial distribution function (RDF) between the atom site k and the atoms in the solvent component s,7,8 which is related to gks(r) as

∫V gks(r) dr ) ∫0∞ gks(r) · 4πr2 dr

(3)

When the atom site k is one of the constituent atoms of a solute molecule R, the KB integral of s for R, GRs, is obtained by Gks(R) with a sufficiently large integration range including the whole inhomogeneous solvent phase around the solute molecule R4 as

GRs ) lim Gks(R) R f∞

(4)

However, the conventional R-dependent KB integral, Gks(R),7,8 is awkward in discussing the solvent spatial distributions around different conformations of the focused solute R, because such RDF-derived profiles depend sensitively on the location of the k.

10.1021/jp808575k CCC: $40.75  2009 American Chemical Society Published on Web 02/20/2009

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Figure 1. Schematic representations of the integration range in (a) conventional (R-dependent) KB integral Gks(R) around one of the (centers of) S (R) for the solute constituent atoms k (black point) of the solute molecule R (wormlike shape depicted in gray), and in (b) surficial KB integral GRs molecule R. The boundary of integration range υR(r,t) is defined as the surface whose minimum distance to any atom site k of the solute molecule R is r and is represented as the dashed curve. The volume and the surface area of υR(r,t) are denoted by UR(r,t) and SR(r,t), respectively.

To overcome this problem, we introduced another type of S (R), the surficial KB integral6 as R-dependent KB integral, GRs follows, S GRs (R)

)

)

P P S VRs (R) ) 〈VRs (R, t)〉T ) 〈-GRs (R, t)〉T

S 〈GRs (R, t)〉

r)R ∫r)0

〈{ (

) }

〉

1 ∂NRs(r, t) ∂UR(r, t) - 1 SR(r, t) dr / Fs(∞) ∂r ∂r T NRs(R, t) ) (5) - UR(R, t) Fs(∞) T

〈

〉

where 〈 · · · 〉T denotes the time-average, defined as 1/T ∫0T ( · · · ) dt. UR(r,t) and SR(r,t) are the volume and the surface area of hypothetical spatial region υR(r,t) around the solute molecule R. The boundary of υR(r,t) is defined as the surface whose minimum distance to any atom site k of the solute molecule R is r. Schematic representations of υR(r,t), UR(r,t), and SR(r,t) are shown in Figure 1b. Here, the distance r from (or between) certain atom(s) is that from (or between) the center of the atom(s). NRs(r,t) is the instantaneous integrated coordination number of atoms in solvent component s within υR(r,t)6. Fs(∞) is the atomic number density of s in the bulk phase. S (R) and conventional Gks(R) show exactly the same Both GRs constant value when their integrations reach the bulk solvent phase as follows:

lim GSRs(R) ) lim Gks(R)

R f∞

R f∞

(6)

S (R) enables a clearer understanding of the However, GRs profile of solvent distribution and the related thermodynamic quantities, as functions of the distance from the surface of solute molecule R. 2.2. R-Dependent Partial Molar Volume. PMV of the P , is expressed solute molecule R in the solvent component s, VRs 4 by using GRs as follows:

VPRs ) kBTχT0 - GRs χT0

S Using the surficial KB integral, GRs (R), the R-dependent PMV P (R), can be expressed as follows: of solute molecule R, VRs

(7)

where is the isothermal compressibility of the pure solvent. The first term, kBTχT0, corresponds to the ideal volume contribution and comes from the translational degree of freedom of the solute molecule R. The value of the ideal term is only about 1.0 cm3 mol-1, and therefore usually can be ignored when considering large solutes.5

(8)

Taking R to infinite distance, the PMV of the solute molecule R is expressed as follows: P P P VRs ) 〈VRs (t)〉T ) lim 〈VRs (R, t)〉T R f∞

(9)

The differential of VRP(R) at distance r is defined as P P P δVRs (r) ) VRs (r + ∆r/2) - VRs (r - ∆r/2)

(10)

2.3. Molecular Dynamics Simulations. Molecular dynamics (MD) calculations were all performed using the AMBER8 program.9 The force field parameter set, parm99,10 was used for all the molecules in the present systems. MD simulation of the denaturation of CI2 was performed as follows. First, the X-ray structure of CI2 was set in a periodic boundary box filled with 14823 TIP3P water molecules.11 After the starting structures were minimized molecular mechanically for 2000 cycles to reduce any bad contact pairs, the system was initially equilibrated for the first 600 ps at 300 K, 1 atm under the NPT condition. After the equilibration, the box size was fixed (77.4 × 76.8 × 77.4 Å3). Then, further simulation of 2 ns was performed at 300 K under the NVT condition. To obtain the denatured structure of CI2, the temperature was elevated to 800 K during the next 1 ns NVT simulation. Finally, additional 2 ns NVT simulation was performed again at 300 K. Trajectories were numerically integrated by Verlet method with a time step of 2.0 fs. The electrostatic interactions were treated by the particle-mesh Ewald (PME) method.12 All the bonds involving hydrogen atoms were constrained by the SHAKE method.13 For equilibration, both temperature and pressure were regulated using the Berendsen algorithm.14 3. Results and Discussion 3.1. Denaturation Pathway of CI2. Figure 2 shows the time dependency of the rmsd of backbone R carbon atoms, CRs, in CI2 during the entire duration of MD simulation, with typical snapshots of native and denatured CI2. During the hightemperature simulation, CI2 showed the following structural changes. Initially, the N terminus and the active-site loop became

Partial Molar Volume of Chymotrypsin Inhibitor 2

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Figure 2. Time history of the rmsd of backbone CRs in CI2. Snapshots of the native CI2 (red tube and green transparent space filling) at t ) 2.0 ns and that of the denatured CI2 at t ) 5.0 ns are depicted in the insets with unit periodic boundary boxes filled with water molecules (ice blue). High-temperature (T ) 800 K) MD simulation was done with time duration of 2.0-3.0 ns (red line).

very mobile. Then, the bottom of the core opened and was exposed to the solvent. Finally, with the corruption of the active site loop, CI2 moved to the denatured state. This denaturation pathway was similar to that of a previous simulation of CI2 unfolding.15 In addition, the maximum rmsd value from the starting structure in the present MD simulation ()18 Å) also corresponds with that in the previous work.15 3.2. Invariance of Partial Molar Volume of CI2. Currently, time durations 1.0-2.0 ns and 4.0-5.0 ns are referred to as natiVe period and denatured period, respectively, and are utilized for comparison analysis of PMV. Conformations of CI2 in each period are collectively denoted as “N” (native) and “D” (denatured), respectively. The solvent in this study, i.e., water, P (t) and is denoted as “w”. PMV of CI2 in both periods, VNw P VDw(t), defined at infinite distance from the solute (eq 9), are substituted at R ) 10.0 Å and are presented in Figure 3. For both periods, 100 snapshots of the system, with time intervals of 10 ps, were extracted for the calculation. P P and the standard deviation of VNw (t) Time-average value VNw 3 -1 was 5771.85 ( 219.82 cm mol , which could be reasonably compared to that of the similar size of proteins in previous experimental and theoretical works.3,4 Despite the large structural deviation from the native structure, denatured CI2 exhibited a P , and a slightly larger standard similar time average value VDw P (t) (i.e., 5845.45 ( 241.12 cm3mol-1) (Figure deviation of VDw 2b). These facts indicate that the protein volume paradox is reproduced in our MD simulation of CI2. 3.3. Intrinsic Alteration in the Partial Molar Volume of CI2. To elucidate the detailed mechanism of the protein volume paradox, we examined the alterations in the constituent volume components of the PMV. Previously, Chalikian et al. decomP as follows:3,5 posed the VRs P VRs ) VRsM + VTRs + VIRs + kBTχT0

(11)

M where VRs is the geometric volume, equal to the sum of the van der Waals volumes of the constituent atoms of the solute molecule R (VRW) plus the total volume of the voids resulting V ) (Figure 4): from the imperfect packing (VRs

M V VRs ) VRW + VRs

(12)

T , is the thermal volume that The second term in eq 11, VRs comes from thermally induced mutual molecular vibrations of I , is the interaction the solute and the solvent.3 The next term, VRs volume that represents the decrease in the solvent volume associated with the interaction between the solvent (water) molecules and the charged or polar atomic groups of the solute.3 Previously, these volume components were estimated by geometric calculation, and by subtracting the other volume components from the total (experimental or theoretical) PMV T I and VRs values.4,5 However, the microscopic definitions for VRs are still arbitrary. Meanwhile, considering the physical and chemical origins of these volume components, there should be a difference in the spatial region that each volume component dominantly occupies. In other words, the magnitude of each volume component can be understood by analyzing the depenP on the distance r from the solute surface. This is dence of VRs our motivation in applying the surficial KB approach on the analysis of PMV. P P (r) and δVDw (r) are shown in Figure 5. The value of ∆r δVNw in eq 10 was set to 0.05 Å, and UR(r,t) in eq 5 was calculated with resolution of 0.008 Å3. Compared with the native CI2, the PMV in the denatured CI2 is clearly seen to increase from r ≈ 1.0 to 2.4 Å. Considering that the average thickness of the empty layer on the solute van der Waals surface (generated by the thermal fluctuation of solute and solvent) is estimated to be about P P (r) and δVNw (r) in this 0.5 Å,16,17 the difference between δVDw region can be attributed to the increase in the thermal volume T in eq 11) by the denaturation of the solute. (VRs In addition to the contribution of the thermal volume, we V in eq 12). As we considered the influence of void volume (VRs mentioned in the Introduction, it has been thought that protein in its denatured structure would lose the void volume created in the interior of its native structure. However, in the case of CI2, the native structure has a highly packed conformation, and there are no large structural voids in its interior. Therefore, when CI2 is denatured the total volume from such internal voids would not significantly decrease. On the other hand, the total volume of the voids existing everywhere on the outer surface of CI2 increases according to the SASA increase. Hence, the increase in total void volume can also be considered one of the factors P (r) in this region. In the near future, we will increasing δVDw V V and VDw for many CI2 calculate the difference between VNw snapshots, and also analyze their r dependencies. P (r) In Figure 5, denatured CI2 significantly decreases δVDw from r ) 2.5 to 3.5 Å. According to our analysis, the position P P (r) and δVNw (r) (r ) 2.8 Å) of the negative peak in both δVDw exactly corresponds to that of the largest peak in the number density profile of the water atoms around CI2 in both periods (data not shown here). This indicates that the significant decrease P (r) in this region originates in the increase in hydration, of δVDw which results mainly from the SASA increase. In other words, the result shows that a significant reduction in the interaction I in eq 11) occurs at r ) 2.8 Å in the denatured volume (VRs P (r) CI2. On the other hand, we found a slight increase in δVDw around r ) 4.5 Å. The position corresponds to that where the number density profile of the water atoms around CI2 is at the minimum in both periods. It would be interesting to know if these alterations in the PMV profile vary depending on exposure to, for example, hydrophilic or hydrophobic groups. As we mentioned above, P (r) from r ≈ 1.0 to 2.4 Å is mainly due to the increase in δVDw T V ) or void volume (VRs ). the increase in the thermal volume (VRs Because both volume components are unrelated to the chemical properties of the solute surface, not only exposure of the

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P P Figure 3. Time histories of (a) VNw (t) in the native period (1.0-2.0 ns) and (b) VDw (t) in the denatured period (4.0-5.0 ns).

TABLE 1: Estimated Values of the Volume Components Presented in Eqs 11 and 12 (in cm3 mol-1)

M M Figure 4. Schematic representation of the geometric volume VRs . VRs is the volume of the region that the surface of the solvent prove (blue) cannot access and is equal to the sum of the van der Waals volumes of the constituent atoms VRW (gray) plus the total volume of the voids V result from the imperfect packing VRs (green).

P Figure 5. Profile of δVNw (r) in the native period (light blue) P superimposed on the profile of δVDw (r) in the denatured period (red mesh) (in cm3 mol-1). 95% confidence intervals (CI)s of average values are depicted at several points. To obtain their numerical values, ∆r (in eq 10) was set to 0.05 Å.

nonpolar (hydrophobic) groups but also that of the polar (hydrophilic) groups should contribute to the increment of PMV in this region. In the case of CI2, the fraction of the nonpolar solvent accessible surface area (SASA) with respect to the total SASA of denatured CI2 is not significantly different from that with native CI2,18 implying that denaturation of CI2 increases relatively large hydrophilic SASA. For these reasons, it would difficult to conclude that the increase in PMV is due only to the exposure of the hydrophobic groups. On the other hand, the decrease in the PMV of denatured CI2 from r ) 2.5 to 3.5 Å comes from exposure of the hydrophilic groups resulting from the denaturation.

R

P VRs

VRW

V VRs

T VRs

I VRs

CI2n CI2d

5771.85 5845.45

4017.74 4017.74

1339.25 1339.25

1348.24 1809.32

-933.38 -1320.86

Finally, we estimated the values of the volumetric contributions presented in eqs 11 and 12 (Table 1). We defined the integrated value of PMV from r ) 2.45 Å to the bulk as the I . The value of r corresponds to the interaction volume VRs distance by which the atomic number density of water molecules W V and VRs are calculated by exceeds that of the bulk value. VRs W ) 0.75 using their relationships to molecular weight M, VRs V (1200 + 1.04 M) and VRs ) 0.25 (1200 + 1.04 M) (in Å3)5. T was obtained by subtracting all the Finally, the value VRs components from the whole PMV. 4. Concluding Remarks The surficial KB approach is a simple but useful method that connects the microscopic solvent structure to the macroscopic thermodynamic properties of large biomacromolecules.6 Because the surficial KB integral uses the distance from the solute surface as the integration variable, it enables unified analysis of a large number of protein snapshots even though they have significantly different conformations. Therefore, the surficial KB approach shows high compatibility with MD simulation of biomolecules in an explicit solvent environment. In the present study, we identified the dynamic behavior of PMV directly from an all-atom MD simulation of the denaturation of protein CI2. The denatured CI2 showed slightly larger fluctuation of PMV than, and had almost the same average PMV value as, the native CI2. This is consistent with the phenomenological question of the protein volume paradox.5 Furthermore, with the aid of the surficial KB approach, we obtained the spatial distributions of PMV to investigate the volume components that caused the PMV of denatured CI2 to increase or decrease. The differential profiles of the new P P (r) and δVDw (r), indicated that in R-dependent PMV, δVNw denatured CI2 the reduction in the solvent interaction volume I is canceled out mainly by the increment in the thermal VRs volume VRsT in the vicinity of the protein surface. In addition, P (r) increases in the region in which the we found that δVDw number density of water atoms is minimum (i.e., r ≈ 4.5 Å). This is a new factor in the increase in PMV of denatured proteins. These results provide a direct and detailed picture of the mechanism of the protein volume paradox suggested by Chalikian et al.5 Acknowledgment. This work was supported partly by Grants-in-Aid for Scientific Research and for Young Scientists (B) (1975004) from the Ministry of Education, Culture, Sport,

Partial Molar Volume of Chymotrypsin Inhibitor 2 Science and Technology in Japan. It was also supported by a Grant-in-Aid for the 21st Century COE program “Frontiers in Computational Science” at Nagoya University, and for the Core Research for Evolutional Science and Technology (CREST) “High Performance Computing for Multiscale and Multiphysics Phenomena” from the Japan Science and Technology Agency. References and Notes (1) Kauzmann, W. Nature 1978, 325, 763–764. (2) Chalikian, T. V.; Gindikin, V. S.; Breslauer, K. J. J. Mol. Biol. 1995, 250, 291–306. (3) Chalikian, T. V.; Totrov, M.; Abagyan, R.; Breslauer, K. J. J. Mol. Biol. 1996, 260, 588–603. (4) Imai, T.; Kovalenko, A.; Hirata, F. J. Phys. Chem. B 2005, 109, 6658–6665. (5) Chalikian, T. V.; Breslauer, K. J. Biopolymers 1996, 39, 619–626. (6) Yu, I.; Jindo, Y.; Nagaoka, M. J. Phys. Chem. B 2007, 111, 10231– 10238. (7) Kirkwood, J. G.; Buff, F. P. J. Chem. Phys. 1951, 19, 774–777. (8) Ben-Naim, A. Statistical Thermodynamics for Chemist and Biochemist; Plenum Press: New York, 1992.

J. Phys. Chem. B, Vol. 113, No. 11, 2009 3547 (9) Case, D. A.; Pearlman, D. A.; Caldwell, J. W.; Cheatham III, T. E.; Wang, J.; Ross, W. S.; Simmerling, C. L.; Darden, T. A.; Merz, K. M.; Stanton, R. V.; Cheng, A. L.; Vincent, J. J.; Crowley, M.; Tsui, V.; Gohlke, H.; Radmer, R. J.; Duan, Y.; Pitera, J.; Massova, I.; Seibel, G. L.; Singh, U. C.; Weiner, P. K.; Kollman, P. A. AMBER8; University of California: San Francisco, 2004. (10) Wang, J.; Cieplak, P.; Kollman, P. A. J. Comput. Chem. 2000, 21, 1049–1074. (11) Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L. J. Chem. Phys. 1983, 79, 926–935. (12) Darden, T.; York, D.; Pedersen, L. J. Chem. Phys. 1993, 98, 10089– 10092. (13) Ryckaert, J. P.; Ciccotti, G.; Berendsen, H. J. C. J. Comput. Phys. 1977, 23, 327–341. (14) Berendsen, H. J. C.; Postma, J. P. M.; van Gusteren, W. F.; Dinola, A.; Haak, J. R. J. Chem. Phys. 1984, 81, 3684–3690. (15) Day, R.; Bennion, B. J.; Ham, S.; Daggett, V. J. Mol. Biol. 2002, 322, 189–203. (16) Hirata, F.; Arakawa, K. Bull. Chem. Soc. Jpn. 1973, 46, 3367– 3369. (17) Kharakoz, D. P. J. Solution Chem. 1992, 21, 569–595. (18) Kurt, N.; Cavagnero, S. J. Am. Chem. Soc. 2005, 127, 15690–15691.

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