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Effect of Interprotein Polarization on Protein–Protein Binding Energy Chang G. Ji[a] and John Z. H. Zhang*[a,b] Molecular dynamics simulation in explicit water for the binding of the benchmark barnase-barstar complex was carried out to investigate the effect polarization of interprotein hydrogen bonds on its binding free energy. Our study is based on the AMBER force field but with polarized atomic charges derived from fragment quantum mechanical calculation for the protein complex. The quantum-derived atomic charges include the effect of polarization of interprotein hydrogen bonds, which was absent in the
standard force fields that were used in previous theoretical calculations of barnase-barstar binding energy. This study shows that this polarization effect impacts both the static (electronic) and dynamic interprotein electrostatic interactions and significantly lowers the free energy of the barnase-barstar C 2012 Wiley Periodicals, Inc. complex. V
Introduction
binding if vdW molecular surface or artificially higher dielectric constant (e ¼ 20) for protein is used in PB calculation.[22,23] Thus, the result is heavily dependent on the dielectric constant of protein used in PB calculation, but the question of whether electrostatic interaction is favorable or unfavorable to protein– protein binding is still inconclusive. A major limitation in previous theoretical studies for protein–protein binding is the lack of protein-specific polarization, in addition to the limitation of using just a single reference structure for energy calculation. When proteins bind together, subsequent electronic as well as geometric relaxations are produced to minimize the energy of the complex. Thus, to provide a more reliable and definite conclusion about the role of electrostatic interaction in protein–protein binding, explicit consideration of protein polarization and dynamic motion are needed in theoretical studies. In this work, we used a quantum fragment method[24] to carry out quantum calculation for the protein complex and derived polarized protein-specific atomic charges (force field) to study electrostatic interaction for the benchmark barnase-barstar complex. This work aims to overcome some deficiencies in earlier theoretical studies in several respects. First, the polarization of interprotein hydrogen bonds is explicitly included in the force field (atomic charges) derived from quantum calculation of the protein complex, and thus
Protein–protein interaction is vital to biomolecular recognition and many other important biological processes.[1–3] Examples include signal transduction, control of gene expression, inhibition of enzymes, and apoptosis. Thus studying protein–protein interaction based on physics-based atomic level interaction helps elucidate the microscopic mechanism that underlies important biological processes.[4–7] Extensive experimental and theoretical studies found overwhelming evidence that electrostatic interaction plays important roles in structures and dynamics of protein systems.[2,4,8–15] Therefore accurate description of electrostatic interaction in protein–protein binding is extremely important to our fundamental understanding of biomolecular recognition. Early experiments revealed that electrostatic interaction plays an essential role in the binding process of barnase-barstar,[8] a benchmark system for studying protein–protein recognition. These systematic experiments by Schrieber and Fersht[8] demonstrated that electrostatics played an important role in stabilizing the barnase-barstar complex. Examination of the crystal structure of barnase/barstar complex[16] also showed that most of the interprotein interactions between barnase and barstar are dominated by hydrophilic interactions such as salt-bridge and hydrogen bonds. However, these experimental findings were not supported by theoretical studies as far as free energy of binding is concerned. For example, theoretical calculations predicted that interprotein electrostatic interactions contribute little to the stability of barnase-barstar complex due to large desolvation penalty from burying polar groups during the binding process.[17–19] Further systematic studies for hundreds of protein–protein interaction systems using the molecular mechanics/Poisson Boltzmann (PB) approach also found that electrostatic interaction contributed unfavorably to the free energy of binding in more than 90% of the protein–protein systems theoretically studied.[20,21] However, a recent work by Dong et al. showed that the overall electrostatic contribution may be favorable in barnase/barstar 1416
Journal of Computational Chemistry 2012, 33, 1416–1420
DOI: 10.1002/jcc.22969
[a] C. G. Ji, J. Z. H. Zhang State Key Laboratory of Precision Spectroscopy, Department of Physics, Institute of Theoretical and Computational Science, East China Normal University, Shanghai 200062, China E-mail: [email protected] [b] J. Z. H. Zhang Department of Chemistry, New York University, New York, New York 10003 Contract/grant sponsor: National Natural Science Foundation of China; Contract/grant numbers: 21003048, 10974054, 20933002; contract/grant sponsor: Shanghai PuJiang Program; contract/grant number: 09PJ1404000; contract/grant sponsor: The Fundamental Research Funds for the Central Universities. C 2012 Wiley Periodicals, Inc. V
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the use of artificial dielectric constant for protein is eliminated. Second, 80 ns molecular dynamics (MDs) simulation is carried out to capture the effect of geometric relaxation by statistically sampling electrostatic and solvation energies over many configurations, rather than just a single structure as was done in most of the previous theoretical studies. As a result, this study is expected to provide a more reliable answer to address the question of electrostatic contribution to barnase-barstar binding. Of particular interest is the polarization effect of interprotein hydrogen bonds, which is found to play significant roles in stabilizing dynamic structure of the protein complex.[24–31]
Theoretical Approach The crystal structure of barnase-barstar complex determined by Buckle et al.[16] is used as the starting structure from which quantum fragment calculation is performed to derive polarized protein-specific charge (PPC).[24] Hydrogen atoms are added according to residues’ standard protonation states. All Histidine side chains are protonated at atom NE. PPC has been developed to provide partial atomic charges of proteins for better description of protein dynamics near native structures.[24,26–28] In this approach, fully quantum mechanical calculation of electronic structure of protein in solution is achieved with the molecular fragmentation with conjugated caps scheme,[32] in which the protein is partitioned into amino acid-based fragments and the PB equation for protein in solvent is numerically solved.[24] PPC is then derived by fitting the atomic charges of protein fragments to their electrostatic potentials calculated for a given protein structure in solution. Thus, effective atomic charges of PPC correctly represent the polarized electronic state of the particular protein at a given structure (often native structure). Detailed description of how the PPC is derived can be found elsewhere.[24] In this simulation study, Amber software is used as our computational tool.[33] The protein complex is solvated in an octahedron-like box and the system is neutralized by adding counter ions. After heating and equilibration, the production MD simulation was performed at 300 K (NPT). Two MD trajectories were generated for further analysis: (1) MD simulation with the standard Amber99SB force field; (2) MD simulation with atomic charges replaced by PPC[24] while keeping other parameters of Amber99SB intact. All the analyses were performed on configurations derived from 80 ns MD simulation. This study is focused on electrostatic component of binding free energy through combined molecular mechanics with PBbased continuum model. The electrostatic binding free energy can be divided into two parts as given below:
DGele ¼ DE ele þ DGele dslov ele ele ele DGele dslov ¼ Gslov ðcomplexÞ Gslov ðligandÞ Gslov ðreceptorÞ ele ele ele Eligand Ereceptor DE ele ¼ Ecomplex
The first part DEele represents interprotein electrostatic interaction energy whereas the second part is the electrostatic desol-
vation energy calculated using the PBSA module[34] of AMBER with the default amber-vdW radii. The solvent probe radius used to define the molecular surface is 1.4 A˚. Intermediate structures of the protein complex were saved every 10 ps in 80 ns trajectories. The final result was averaged over the 80 ns interval.
Result and Discussion Total electrostatic contribution In this study, the PPC derived from quantum calculation contains the polarization effect of the protein complex near the crystal structure and thus dielectric constant for protein is set to unity. As a result, the ambiguity associated with the empirical choice of dielectric constant for protein is eliminated. To explicitly investigate the polarization effect on protein–protein binding, we performed both calculations based, respectively, on PPC as well as standard AMBER force fields. Our result shows that electrostatic interaction is a positive contributor to barnase/barstar binding when polarization effect is included. The calculated electrostatic binding free energy is 7.1 kcal/mol in MD simulation based on PPC. In contrast, the same quantity from MD simulation using standard Amber force field is 23.6 kcal/mol. Obviously, our result based on the standard Amber force field is consistent with previous theoretical calculations, showing negative electrostatic contribution to protein–protein binding. Because the PPC and AMBER calculations performed in this work are almost identical except for the atomic charges, the large difference in electrostatic free energy must come from electrostatic polarization. The polarization of protein can have both static and dynamics effects. The static effect or electronic relaxation is responsible for enhanced electrostatic interprotein interaction energy for a given complex configuration. The dynamic effect is largely related to dynamical stability of hydrogen bonds or salt bridges whose importance have been recognized very recently.[25,31] Both effects have to be included in simulation study to fully address the main question of this article.
Effect of structural relaxation To obtain thermodynamically averaged electrostatic binding energy, statistical average of the energies over simulation time was performed. As shown in Figure 1, sufficient statistical sampling over simulation time is imperative to obtain thermodynamically meaningful result. In earlier theoretical studies,[19,22,23] only a single structure (mostly crystal structure) of the protein complex was used to compute electrostatic interaction energy and solvation energy. The result in Figure 1 shows that the computed energy exhibits significant fluctuations along the simulation time. Thus, conclusion made from calculations based on a single fixed structure is too arbitrary. This clearly shows the need to statistically sample the energy of the protein complex to correctly evaluate the binding free energy. The result in Figure 1 shows that the electrostatic Journal of Computational Chemistry 2012, 33, 1416–1420
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lack of protein polarization. As will be discussed in the following, the standard Amber force field does not correctly describe the dynamics of interprotein hydrogen bonds, which are abundant in barnase-barstar complex.
Dynamical effect of polarization
Figure 1. Electrostatic binding energy of barnase-barstar complex as a function of MD simulation time. Each point was obtained by averaging over 100 snapshots. (Green: PPC, Red: Amber).
energy computed under PPC is systematically lower than that obtained under standard Amber force field. Static effect of polarization The electrostatic free energy of protein–protein binding is obtained by averaging the individual configuration-specific electrostatic energies over the simulation time. The polarization of interprotein hydrogen bonds impacts the free energy in two respects, static and dynamic. The static effect refers to extra electrostatic interaction energy resulting from electronic polarization of hydrogen bonds at given configurations of the protein complex. The dynamic effect refers to the extra electrostatic interaction energy resulting from dynamically stabilized configurations of protein–protein complex due to electronic polarization of interprotein hydrogen bonds. To investigate the static effect of protein polarization (electronic relaxation), we first utilized complex protein structures generated from MD trajectories under PPC but using standard Amber charges to evaluate the electrostatic energies. This gives a total electrostatic binding energy of 11.2 kcal/mol, compared to 7.1 kcal/mol when PPC is used to evaluate the energy. This mixed charge calculation shows that the static electrostatic energy is not evaluated correctly when standard Amber force field is used. The difference of about 18 kcal/mol is due to electronic polarization energy for given configurations of the protein complex. This energy is mainly due to the electronic polarization of interprotein hydrogen bonds in barnase-barstar complex as will be discussed in more detail later. The standard Amber force field failed to capture this polarization energy. In another swap, we utilized complex protein configurations generated from MD trajectories under standard Amber force field but using PPC to evaluate electrostatic energies. This type of mixed calculation gives a total electrostatic binding energy of 13.8 kcal/mol. Although in this mixed calculation scheme, the static polarization energy is correctly captured under PPC, but configurations of the protein complex generated under standard Amber force field is inaccurate due to the 1418
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As shown in the previous subsection, protein structures sampled from MD simulation under standard Amber force field gives binding energy too positive even when PPC is used to evaluate energies of these structures. Thus dynamic structures generated from such MD simulation are problematic due to the lack of protein-specific polarization. Our previous studies established that polarization enhances the stability of intraprotein hydrogen bonds and the lack of such effect can have material effect on dynamical structures of protein. Thus, it is not difficult to imagine that dynamic stability of interprotein hydrogen bonds in barnase-barstar complex will also be seriously affected by the lack of polarization. For this purpose, we explicitly compared the dynamical stability of hydrogen bonds in MD simulations under, respectively, PPC and standard Amber force field. In the latter, hydrogen bonds are not polarized. In this work, standard empirical rules for hydrogen bond definition are used for analysis: (1) distance between H and A ˚ ; (2) angle of A0 -A-D (donor) is (acceptor) is shorter than 2.5 A larger than 90 . Figure 2 plots the occupancy of interprotein hydrogen bonds calculated from two separate trajectories under two force fields mentioned above. Among many interprotein hydrogen bonds, their thermodynamic stabilities or life times vary from very short to very long. However, comparison between the two sets of results in Figure 2 shows that the occupancy of hydrogen bonds under PPC is clearly higher than those generated under standard AMBER force field. Higher occupancy means that H-bonds are more stable or energetically stronger. In another view, the number of H-bonds, using standard definition of bond length and bond angle, was plotted as a function of simulation time in Figure 3. The result shows that there are 17.9 H-bonds on average over the
Figure 2. Interprotein hydrogen bond occupancy in barnase-barstar complex from two separate MD trajectories (Green: PPC; Red: Amber).
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Figure 3. Number of hydrogen bond as a function of simulation time. Each point was averaged over 100 snapshots. (Red: Amber, Green: PPC).
simulation period under PPC while there is only 14.7 H-bonds under standard Amber force field. To further demonstrate this feature, Figure 4 displays a standard hydrogen bond formed between GLU60 of barnase and LEU34 of barstar. To analyze the strength of this hydrogen bond, we plot in Figure 5 the bond length as a function of simulation time under both force fields. It is shown in Figure 5, this hydrogen bond in Amber trajectory is weaker than that in PPC trajectory, due to lack of polarization in the former. Figure 5 also shows that the hydrogen bond was broken half of the time during MD simulation under standard Amber force field. Our analysis indicates that the hydrogen bond breaks due to competition from water molecules. As a result, this hydrogen bond contributes much less to the stability of complex than a stable hydrogen bond does, as was recently found in the case of avidin-biotin binding.[31] The reduced dynamical stability of hydrogen bonds results in lower hydrogen bond occupancy under standard Amber force field as shown in Figure 2. The reduced number of effective hydrogen bonds (by about three) resulting from decreased stability of hydrogen bonds due to the lack of polarization is a dynamical effect and is responsible for loss of about half of the calculated electrostatic binding energy of barnase-barstar complex.
Figure 4. Interprotein hydrogen bond between GLU60 of barnase and LEU34 of barstar.
Figure 5. Length of the interprotein hydrogen bond between GLU60 of barnase and LEU34 of barstar as a function of simulation time.(Upper: Amber, Lower: PPC).
It was recognized that hydrogen bond plays a critical role in maintaining protein’s specific three-dimensional structure since Linus Pauling.[35] Thus, simulation results based on traditional nonpolarizable force fields could give incorrect dynamical results. Previous study on PPAR-gamma demonstrated that polarization of hydrogen bond is critical in maintaining the stability of protein’s domain.[26] By comparing with NMR experiments, Ji and coworkers found that systematic deviation from experiment of order parameters[30] and scalar coupling constant[27] across hydrogen bonds computed from MD simulation under standard force field is due to the lack of polarization effect of hydrogen bonds. Tong et al. further demonstrated that polarization of hydrogen bond is responsible for significant electrostatic contribution to avidin-biotin binding,[31] a conclusion contradictory to earlier studies by Kollman and coworkers who found no electrostatic contribution to aviding-biotin binding based on the standard Amber force field. This study is highly consistent with our previous work on the effect of polarization on stability of hydrogen bonds.
Summary This study demonstrated that electrostatic polarization of interprotein hydrogen bonds plays important roles in protein–protein recognition process. Correct inclusion of polarization is critical in uncovering interaction mechanism of protein–protein binding. Computational studies based on the standard (nonpolarizable) force fields failed to capture the protein-specific polarization effect and therefore underestimated the importance of electrostatic contribution to protein–protein binding. By performing MD simulation under polarized force field derived from quantum fragment calculation of protein, we uncovered important polarization effect in protein–protein binding. The current polarization effect originates from the polarization of hydrogen bonds, which impacts both static and dynamic interprotein electrostatic interaction energy. The static polarization is represented in the form of stronger interprotein electrostatic interaction due to electronic polarization of hydrogen bonds at a given Journal of Computational Chemistry 2012, 33, 1416–1420
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configuration. The dynamic polarization arises from increased dynamical stability of polarized interprotein hydrogen bonds which results in more stabilized protein complex. Both static and dynamic polarization contributes significantly to the increased interprotein electrostatic interaction energy and their combined effect provides an overall positive contribution to barnase-barstar binding. Thus, protein polarization is the key to the positive electrostatic contribution to protein–protein binding, which is consistent with experimental findings. A note is in order here. In this study, the native structure of the protein complex is used as the reference structure to compute PPC. Ideally, one may wish to use two sets of charges, one for the complex structure and the other for two monomers. However, due to the limitation of the force field representation, such mixed use of charges will cause energy discontinuity due to different reference energies corresponding to different set of charges,[28,36] which is a well known fact. Based on our previous studies on a number of protein systems, the approximation resulting from using a common set of charge for the complex structure should be minimal for the current system.
Acknowledgments The authors thank the Computational Center of ECNU for providing computational time. Keywords: protein–protein interactions molecular dynamics simulation electrostatic interaction polarization binding energy hydrogen bond How to cite this article: C. G. Ji, J. Z. H. Zhang, J. Comput. Chem. 2012, 33, 1416–1420. DOI: 10.1002/jcc.22969
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[7] F. Pazos, M. Helmer-Citterich, G. Ausiello, A. Valencia, J. Mol. Biol. 1997, 271, 511. [8] G. Schreiber, A. R. Fersht, J. Mol. Biol. 1995, 248, 478. [9] G. Schreiber, A. R. Fersht, Nat. Struct. Biol. 1996, 3, 427. [10] I. Muegge, T. Schweins, A. Warshel, Proteins 1998, 30, 407. [11] A. H. Elcock, D. Sept, J. A. McCammon, J. Phys. Chem. B 2001, 105, 1504. [12] P. Uetz, L. Giot, G. Cagney, T. A. Mansfield, R. S. Judson, J. R. Knight, D. Lockshon, V. Narayan, M. Srinivasan, P. Pochart, A. Qureshi-Emili, Y. Li, B. Godwin, D. Conover, T. Kalbfleisch, G. Vijayadamodar, M. J. Yang, M. Johnston, S. Fields, J. M. Rothberg, Nature 2000, 403, 623. [13] C. Von Mering, R. Krause, B. Snel, M. Cornell, S. G. Oliver, S. Fields, P. Bork, Nature 2002, 417, 399. [14] I. Massova, P. A. Kollman, J. Am. Chem. Soc. 1999, 121, 8133. [15] L.-P. Lee, B. Tidor, Nat. Struct. Mol. Biol. 2001, 8, 73. [16] A. M. Buckle, G. Schreiber, A. R. Fersht, Biochemistry 1994, 33, 8878. [17] F. B. Sheinerman, B. Honig, J. Mol. Biol. 2002, 318, 161. [18] F. B. Sheinerman, R. Norel, B. Honig, Curr. Opin. Struct. Biol. 2000, 10, 153. [19] Z. S. Hendsch, C. V. Sindelar, B. Tidor, J. Phys. Chem. B 1998, 102, 4404. [20] P. J. Kundrotas, E. Alexov, Biophys. J. 2006, 91, 1724. [21] K. Brock, K. Talley, K. Coley, P. Kundrotas, E. Alexovy, Biophys. J. 2007, 93, 3340. [22] F. Dong, M. Vijayakumar, H. X. Zhou, Biophys. J. 2003, 85, 49. [23] F. Dong, H. X. Zhou, Proteins 2006, 65, 87. [24] C. G. Ji, Y. Mei, J. Z. H. Zhang, Biophys. J. 2008, 95, 1080. [25] L. L. Duan, Y. Mei, Q. G. Zhang, J. Z. H. Zhang, J. Chem. Phys. 2009, 130, 115102. [26] C. G. Ji, J. Z. H. Zhang, J. Am. Chem. Soc. 2008, 130, 17129. [27] C. G. Ji, J. Z. H. Zhang, J. Phys. Chem. B 2009, 113, 13898. [28] C. G. Ji, J. Z. H. Zhang, J. Phys. Chem. B 2009, 113, 16059. [29] Y. P. Lu, Y. Mei, J. Z. H. Zhang, D. W. Zhang, J. Chem. Phys. 2010, 132, 131101. [30] Y. Tong, C. G. Ji, Y. Mei, J. Z. H. Zhang, J. Am. Chem. Soc. 2009, 131, 8636. [31] Y. Tong, Y. Mei, Y. L. Li, C. G. Ji, J. Z. H. Zhang, J. Am. Chem. Soc. 2010, 132, 5137. [32] D. W. Zhang, J. Z. H. Zhang, J. Chem. Phys. 2003, 119, 3599. [33] D. A. Case, T. E. Cheatham, T. Darden, H. Gohlke, R. Luo, K. M. Merz, A. Onufriev, C. Simmerling, B. Wang, R. J. Woods, J. Comput. Chem. 2005, 26, 1668. [34] R. Luo, L. David, M. K. Gilson, J. Comput. Chem. 2002, 23, 1244. [35] L. Pauling, M. Delbruck, Science 1940, 92, 77. [36] M. J. Hsieh, R. Luo, Proteins 2004, 56, 475.
Received: 17 January 2012 Revised: . Accepted: 2 March 2012 Published online on 12 April 2012
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Effect of Interprotein Polarization on Protein–Protein Binding Energy Chang G. Ji[a] and John Z. H. Zhang*[a,b] Molecular dynamics simulation in explicit water for the binding of the benchmark barnase-barstar complex was carried out to investigate the effect polarization of interprotein hydrogen bonds on its binding free energy. Our study is based on the AMBER force field but with polarized atomic charges derived from fragment quantum mechanical calculation for the protein complex. The quantum-derived atomic charges include the effect of polarization of interprotein hydrogen bonds, which was absent in the
standard force fields that were used in previous theoretical calculations of barnase-barstar binding energy. This study shows that this polarization effect impacts both the static (electronic) and dynamic interprotein electrostatic interactions and significantly lowers the free energy of the barnase-barstar C 2012 Wiley Periodicals, Inc. complex. V
Introduction
binding if vdW molecular surface or artificially higher dielectric constant (e ¼ 20) for protein is used in PB calculation.[22,23] Thus, the result is heavily dependent on the dielectric constant of protein used in PB calculation, but the question of whether electrostatic interaction is favorable or unfavorable to protein– protein binding is still inconclusive. A major limitation in previous theoretical studies for protein–protein binding is the lack of protein-specific polarization, in addition to the limitation of using just a single reference structure for energy calculation. When proteins bind together, subsequent electronic as well as geometric relaxations are produced to minimize the energy of the complex. Thus, to provide a more reliable and definite conclusion about the role of electrostatic interaction in protein–protein binding, explicit consideration of protein polarization and dynamic motion are needed in theoretical studies. In this work, we used a quantum fragment method[24] to carry out quantum calculation for the protein complex and derived polarized protein-specific atomic charges (force field) to study electrostatic interaction for the benchmark barnase-barstar complex. This work aims to overcome some deficiencies in earlier theoretical studies in several respects. First, the polarization of interprotein hydrogen bonds is explicitly included in the force field (atomic charges) derived from quantum calculation of the protein complex, and thus
Protein–protein interaction is vital to biomolecular recognition and many other important biological processes.[1–3] Examples include signal transduction, control of gene expression, inhibition of enzymes, and apoptosis. Thus studying protein–protein interaction based on physics-based atomic level interaction helps elucidate the microscopic mechanism that underlies important biological processes.[4–7] Extensive experimental and theoretical studies found overwhelming evidence that electrostatic interaction plays important roles in structures and dynamics of protein systems.[2,4,8–15] Therefore accurate description of electrostatic interaction in protein–protein binding is extremely important to our fundamental understanding of biomolecular recognition. Early experiments revealed that electrostatic interaction plays an essential role in the binding process of barnase-barstar,[8] a benchmark system for studying protein–protein recognition. These systematic experiments by Schrieber and Fersht[8] demonstrated that electrostatics played an important role in stabilizing the barnase-barstar complex. Examination of the crystal structure of barnase/barstar complex[16] also showed that most of the interprotein interactions between barnase and barstar are dominated by hydrophilic interactions such as salt-bridge and hydrogen bonds. However, these experimental findings were not supported by theoretical studies as far as free energy of binding is concerned. For example, theoretical calculations predicted that interprotein electrostatic interactions contribute little to the stability of barnase-barstar complex due to large desolvation penalty from burying polar groups during the binding process.[17–19] Further systematic studies for hundreds of protein–protein interaction systems using the molecular mechanics/Poisson Boltzmann (PB) approach also found that electrostatic interaction contributed unfavorably to the free energy of binding in more than 90% of the protein–protein systems theoretically studied.[20,21] However, a recent work by Dong et al. showed that the overall electrostatic contribution may be favorable in barnase/barstar 1416
Journal of Computational Chemistry 2012, 33, 1416–1420
DOI: 10.1002/jcc.22969
[a] C. G. Ji, J. Z. H. Zhang State Key Laboratory of Precision Spectroscopy, Department of Physics, Institute of Theoretical and Computational Science, East China Normal University, Shanghai 200062, China E-mail: [email protected] [b] J. Z. H. Zhang Department of Chemistry, New York University, New York, New York 10003 Contract/grant sponsor: National Natural Science Foundation of China; Contract/grant numbers: 21003048, 10974054, 20933002; contract/grant sponsor: Shanghai PuJiang Program; contract/grant number: 09PJ1404000; contract/grant sponsor: The Fundamental Research Funds for the Central Universities. C 2012 Wiley Periodicals, Inc. V
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the use of artificial dielectric constant for protein is eliminated. Second, 80 ns molecular dynamics (MDs) simulation is carried out to capture the effect of geometric relaxation by statistically sampling electrostatic and solvation energies over many configurations, rather than just a single structure as was done in most of the previous theoretical studies. As a result, this study is expected to provide a more reliable answer to address the question of electrostatic contribution to barnase-barstar binding. Of particular interest is the polarization effect of interprotein hydrogen bonds, which is found to play significant roles in stabilizing dynamic structure of the protein complex.[24–31]
Theoretical Approach The crystal structure of barnase-barstar complex determined by Buckle et al.[16] is used as the starting structure from which quantum fragment calculation is performed to derive polarized protein-specific charge (PPC).[24] Hydrogen atoms are added according to residues’ standard protonation states. All Histidine side chains are protonated at atom NE. PPC has been developed to provide partial atomic charges of proteins for better description of protein dynamics near native structures.[24,26–28] In this approach, fully quantum mechanical calculation of electronic structure of protein in solution is achieved with the molecular fragmentation with conjugated caps scheme,[32] in which the protein is partitioned into amino acid-based fragments and the PB equation for protein in solvent is numerically solved.[24] PPC is then derived by fitting the atomic charges of protein fragments to their electrostatic potentials calculated for a given protein structure in solution. Thus, effective atomic charges of PPC correctly represent the polarized electronic state of the particular protein at a given structure (often native structure). Detailed description of how the PPC is derived can be found elsewhere.[24] In this simulation study, Amber software is used as our computational tool.[33] The protein complex is solvated in an octahedron-like box and the system is neutralized by adding counter ions. After heating and equilibration, the production MD simulation was performed at 300 K (NPT). Two MD trajectories were generated for further analysis: (1) MD simulation with the standard Amber99SB force field; (2) MD simulation with atomic charges replaced by PPC[24] while keeping other parameters of Amber99SB intact. All the analyses were performed on configurations derived from 80 ns MD simulation. This study is focused on electrostatic component of binding free energy through combined molecular mechanics with PBbased continuum model. The electrostatic binding free energy can be divided into two parts as given below:
DGele ¼ DE ele þ DGele dslov ele ele ele DGele dslov ¼ Gslov ðcomplexÞ Gslov ðligandÞ Gslov ðreceptorÞ ele ele ele Eligand Ereceptor DE ele ¼ Ecomplex
The first part DEele represents interprotein electrostatic interaction energy whereas the second part is the electrostatic desol-
vation energy calculated using the PBSA module[34] of AMBER with the default amber-vdW radii. The solvent probe radius used to define the molecular surface is 1.4 A˚. Intermediate structures of the protein complex were saved every 10 ps in 80 ns trajectories. The final result was averaged over the 80 ns interval.
Result and Discussion Total electrostatic contribution In this study, the PPC derived from quantum calculation contains the polarization effect of the protein complex near the crystal structure and thus dielectric constant for protein is set to unity. As a result, the ambiguity associated with the empirical choice of dielectric constant for protein is eliminated. To explicitly investigate the polarization effect on protein–protein binding, we performed both calculations based, respectively, on PPC as well as standard AMBER force fields. Our result shows that electrostatic interaction is a positive contributor to barnase/barstar binding when polarization effect is included. The calculated electrostatic binding free energy is 7.1 kcal/mol in MD simulation based on PPC. In contrast, the same quantity from MD simulation using standard Amber force field is 23.6 kcal/mol. Obviously, our result based on the standard Amber force field is consistent with previous theoretical calculations, showing negative electrostatic contribution to protein–protein binding. Because the PPC and AMBER calculations performed in this work are almost identical except for the atomic charges, the large difference in electrostatic free energy must come from electrostatic polarization. The polarization of protein can have both static and dynamics effects. The static effect or electronic relaxation is responsible for enhanced electrostatic interprotein interaction energy for a given complex configuration. The dynamic effect is largely related to dynamical stability of hydrogen bonds or salt bridges whose importance have been recognized very recently.[25,31] Both effects have to be included in simulation study to fully address the main question of this article.
Effect of structural relaxation To obtain thermodynamically averaged electrostatic binding energy, statistical average of the energies over simulation time was performed. As shown in Figure 1, sufficient statistical sampling over simulation time is imperative to obtain thermodynamically meaningful result. In earlier theoretical studies,[19,22,23] only a single structure (mostly crystal structure) of the protein complex was used to compute electrostatic interaction energy and solvation energy. The result in Figure 1 shows that the computed energy exhibits significant fluctuations along the simulation time. Thus, conclusion made from calculations based on a single fixed structure is too arbitrary. This clearly shows the need to statistically sample the energy of the protein complex to correctly evaluate the binding free energy. The result in Figure 1 shows that the electrostatic Journal of Computational Chemistry 2012, 33, 1416–1420
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lack of protein polarization. As will be discussed in the following, the standard Amber force field does not correctly describe the dynamics of interprotein hydrogen bonds, which are abundant in barnase-barstar complex.
Dynamical effect of polarization
Figure 1. Electrostatic binding energy of barnase-barstar complex as a function of MD simulation time. Each point was obtained by averaging over 100 snapshots. (Green: PPC, Red: Amber).
energy computed under PPC is systematically lower than that obtained under standard Amber force field. Static effect of polarization The electrostatic free energy of protein–protein binding is obtained by averaging the individual configuration-specific electrostatic energies over the simulation time. The polarization of interprotein hydrogen bonds impacts the free energy in two respects, static and dynamic. The static effect refers to extra electrostatic interaction energy resulting from electronic polarization of hydrogen bonds at given configurations of the protein complex. The dynamic effect refers to the extra electrostatic interaction energy resulting from dynamically stabilized configurations of protein–protein complex due to electronic polarization of interprotein hydrogen bonds. To investigate the static effect of protein polarization (electronic relaxation), we first utilized complex protein structures generated from MD trajectories under PPC but using standard Amber charges to evaluate the electrostatic energies. This gives a total electrostatic binding energy of 11.2 kcal/mol, compared to 7.1 kcal/mol when PPC is used to evaluate the energy. This mixed charge calculation shows that the static electrostatic energy is not evaluated correctly when standard Amber force field is used. The difference of about 18 kcal/mol is due to electronic polarization energy for given configurations of the protein complex. This energy is mainly due to the electronic polarization of interprotein hydrogen bonds in barnase-barstar complex as will be discussed in more detail later. The standard Amber force field failed to capture this polarization energy. In another swap, we utilized complex protein configurations generated from MD trajectories under standard Amber force field but using PPC to evaluate electrostatic energies. This type of mixed calculation gives a total electrostatic binding energy of 13.8 kcal/mol. Although in this mixed calculation scheme, the static polarization energy is correctly captured under PPC, but configurations of the protein complex generated under standard Amber force field is inaccurate due to the 1418
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As shown in the previous subsection, protein structures sampled from MD simulation under standard Amber force field gives binding energy too positive even when PPC is used to evaluate energies of these structures. Thus dynamic structures generated from such MD simulation are problematic due to the lack of protein-specific polarization. Our previous studies established that polarization enhances the stability of intraprotein hydrogen bonds and the lack of such effect can have material effect on dynamical structures of protein. Thus, it is not difficult to imagine that dynamic stability of interprotein hydrogen bonds in barnase-barstar complex will also be seriously affected by the lack of polarization. For this purpose, we explicitly compared the dynamical stability of hydrogen bonds in MD simulations under, respectively, PPC and standard Amber force field. In the latter, hydrogen bonds are not polarized. In this work, standard empirical rules for hydrogen bond definition are used for analysis: (1) distance between H and A ˚ ; (2) angle of A0 -A-D (donor) is (acceptor) is shorter than 2.5 A larger than 90 . Figure 2 plots the occupancy of interprotein hydrogen bonds calculated from two separate trajectories under two force fields mentioned above. Among many interprotein hydrogen bonds, their thermodynamic stabilities or life times vary from very short to very long. However, comparison between the two sets of results in Figure 2 shows that the occupancy of hydrogen bonds under PPC is clearly higher than those generated under standard AMBER force field. Higher occupancy means that H-bonds are more stable or energetically stronger. In another view, the number of H-bonds, using standard definition of bond length and bond angle, was plotted as a function of simulation time in Figure 3. The result shows that there are 17.9 H-bonds on average over the
Figure 2. Interprotein hydrogen bond occupancy in barnase-barstar complex from two separate MD trajectories (Green: PPC; Red: Amber).
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Figure 3. Number of hydrogen bond as a function of simulation time. Each point was averaged over 100 snapshots. (Red: Amber, Green: PPC).
simulation period under PPC while there is only 14.7 H-bonds under standard Amber force field. To further demonstrate this feature, Figure 4 displays a standard hydrogen bond formed between GLU60 of barnase and LEU34 of barstar. To analyze the strength of this hydrogen bond, we plot in Figure 5 the bond length as a function of simulation time under both force fields. It is shown in Figure 5, this hydrogen bond in Amber trajectory is weaker than that in PPC trajectory, due to lack of polarization in the former. Figure 5 also shows that the hydrogen bond was broken half of the time during MD simulation under standard Amber force field. Our analysis indicates that the hydrogen bond breaks due to competition from water molecules. As a result, this hydrogen bond contributes much less to the stability of complex than a stable hydrogen bond does, as was recently found in the case of avidin-biotin binding.[31] The reduced dynamical stability of hydrogen bonds results in lower hydrogen bond occupancy under standard Amber force field as shown in Figure 2. The reduced number of effective hydrogen bonds (by about three) resulting from decreased stability of hydrogen bonds due to the lack of polarization is a dynamical effect and is responsible for loss of about half of the calculated electrostatic binding energy of barnase-barstar complex.
Figure 4. Interprotein hydrogen bond between GLU60 of barnase and LEU34 of barstar.
Figure 5. Length of the interprotein hydrogen bond between GLU60 of barnase and LEU34 of barstar as a function of simulation time.(Upper: Amber, Lower: PPC).
It was recognized that hydrogen bond plays a critical role in maintaining protein’s specific three-dimensional structure since Linus Pauling.[35] Thus, simulation results based on traditional nonpolarizable force fields could give incorrect dynamical results. Previous study on PPAR-gamma demonstrated that polarization of hydrogen bond is critical in maintaining the stability of protein’s domain.[26] By comparing with NMR experiments, Ji and coworkers found that systematic deviation from experiment of order parameters[30] and scalar coupling constant[27] across hydrogen bonds computed from MD simulation under standard force field is due to the lack of polarization effect of hydrogen bonds. Tong et al. further demonstrated that polarization of hydrogen bond is responsible for significant electrostatic contribution to avidin-biotin binding,[31] a conclusion contradictory to earlier studies by Kollman and coworkers who found no electrostatic contribution to aviding-biotin binding based on the standard Amber force field. This study is highly consistent with our previous work on the effect of polarization on stability of hydrogen bonds.
Summary This study demonstrated that electrostatic polarization of interprotein hydrogen bonds plays important roles in protein–protein recognition process. Correct inclusion of polarization is critical in uncovering interaction mechanism of protein–protein binding. Computational studies based on the standard (nonpolarizable) force fields failed to capture the protein-specific polarization effect and therefore underestimated the importance of electrostatic contribution to protein–protein binding. By performing MD simulation under polarized force field derived from quantum fragment calculation of protein, we uncovered important polarization effect in protein–protein binding. The current polarization effect originates from the polarization of hydrogen bonds, which impacts both static and dynamic interprotein electrostatic interaction energy. The static polarization is represented in the form of stronger interprotein electrostatic interaction due to electronic polarization of hydrogen bonds at a given Journal of Computational Chemistry 2012, 33, 1416–1420
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configuration. The dynamic polarization arises from increased dynamical stability of polarized interprotein hydrogen bonds which results in more stabilized protein complex. Both static and dynamic polarization contributes significantly to the increased interprotein electrostatic interaction energy and their combined effect provides an overall positive contribution to barnase-barstar binding. Thus, protein polarization is the key to the positive electrostatic contribution to protein–protein binding, which is consistent with experimental findings. A note is in order here. In this study, the native structure of the protein complex is used as the reference structure to compute PPC. Ideally, one may wish to use two sets of charges, one for the complex structure and the other for two monomers. However, due to the limitation of the force field representation, such mixed use of charges will cause energy discontinuity due to different reference energies corresponding to different set of charges,[28,36] which is a well known fact. Based on our previous studies on a number of protein systems, the approximation resulting from using a common set of charge for the complex structure should be minimal for the current system.
Acknowledgments The authors thank the Computational Center of ECNU for providing computational time. Keywords: protein–protein interactions molecular dynamics simulation electrostatic interaction polarization binding energy hydrogen bond How to cite this article: C. G. Ji, J. Z. H. Zhang, J. Comput. Chem. 2012, 33, 1416–1420. DOI: 10.1002/jcc.22969
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Received: 17 January 2012 Revised: . Accepted: 2 March 2012 Published online on 12 April 2012
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