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Journal of Biomolecular Structure and Dynamics Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/tbsd20
3 Nsec Molecular Dynamics Simulation of the Protein Ubiquitin and Comparison with X-ray Crystal and Solution NMR Structures a
a
Julie A. Braatz , Mark D. Paulsen & Rick L. Ornstein
a
a
Molecular Science Research Center Pacific Northwest Laboratory , Richland , WA , 99352 , USA Published online: 21 May 2012.
To cite this article: Julie A. Braatz , Mark D. Paulsen & Rick L. Ornstein (1992) 3 Nsec Molecular Dynamics Simulation of the Protein Ubiquitin and Comparison with X-ray Crystal and Solution NMR Structures, Journal of Biomolecular Structure and Dynamics, 9:5, 935-949, DOI: 10.1080/07391102.1992.10507968 To link to this article: http://dx.doi.org/10.1080/07391102.1992.10507968
PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or
indirectly in connection with, in relation to or arising out of the use of the Content.
Downloaded by [New York University] at 19:01 09 May 2015
This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions
Journal of Biomolecular Structure & Dynamics, ISSN 0739-1102 Volume 9, Issue Number 5 (1992), "'Adenine Press (1992).
3 N sec Molecular Dynamics Simulation of the Protein Ubiquitin and Comparison with X-ray Crystal and Solution NMR Structures
Downloaded by [New York University] at 19:01 09 May 2015
Julie A. Braatz, Mark D. Paulsen and Rick L. Ornstein* Molecular Science Research Center Pacific Northwest Laboratory t Richland, WA 99352, USA Abstract Mainly due to computational limitations, past protein molecular dynamics simulations have rarely been extended to 300 psec; we are not aware of any published results beyond 350 psec. The present work compares a 3000 psec simulation of the protein ubiquitin with the available x-ray crystallographic and solution NMR structures. Aside from experimental structure availability, ubiquitin was studied because of its relatively small size (76 amino acids) and lack of disulfide bridges. An implicit solvent model was used except for explicit treatment of waters of crystallization. We found that the simulated average structure retains most of the character of the starting x-ray crystal structure. In two highly surface accessible regions, the simulation was not in agreement with the x-ray structure. In addition, there are six backbonebackbone hydrogen bonds that are in conflict between the solution NMR and x-ray crystallographic structures; two are bonds that the NMR does not locate, and four are ones that the two methods disagree upon the donor. Concerning these six backbone-backbone hydrogen bonds, the present simulation agrees with the solution NMR structure in five out-of-the six cases, in that if a hydrogen bond is present in the x-ray structure and not in the NMR structure, the bond breaks within 700 psec. Of the two hydrogen bonds that are found in the NMR structure and not in the x-ray structure, one forms at 1400 psec and the other forms rarely. The present results suggest that relatively long molecular dynamics simulations, that use protein x-ray crystal coordinates for the starting structure and a computationally efficient solvent representation, may be used to gain an understanding of conformational and dynamic differences between the solid-crystal and dilute-solution states.
Introduction The first molecular dynamics simulation of a protein led to a dramatic change in our view of protein dynamics (1). It has now been realized that globular proteins have a wide variety of internal motions; "any attempt to understand the function of proteins requires an investigation ofthe dynamics of the structural fluctuations and
* Author to whom correspondence should be addressed. tPacific Northwest Laboratory is operated for the U.S. Department of Energy by Battelle Memorial Institute under Contract DE-AC06-76RLO 1830.
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their relation to activity and conformational change" (2). Protein motions that can be investigated either theoretically or experimentally range from the rapid local motions of the individual amino acids to slow collective distortions of secondary structure elements or domains. While sidechain rotations at the surface of a protein typically occur in tens to hundreds of psec, torsional rotations ofburied groups and relative motion of different domains often have longer characteristic times by one to several orders of magnitude. For practical reasons, most protein molecular dynamics simulations have been performed for only about 100 psec. Occasionally, a protein simulation has been extended beyond 200 psec, but we are not aware of any published protein simulations extended to 400 psec. For practical reasons, the early protein simulations were done in vacuo. As noted by Levitt & Sharon (3), it is possible to obtain more realistic protein simulations with explicit solvent and a periodic boundary formulism; however, not all treatments that explicitly include solvent necessarily improve the simulation quality. Furthermore, simulations that explicitly treat a reasonably large solvent layer or use periodic boundary conditions are one to two orders of magnitude longer in duration than simulations with an implicit solvent model. By including explicitly only the waters of crystallization, in an otherwise implicit solvent model simulation, we believe that it maybe possible to account for much of the structural role of solvent yet increase the computational cost by about only 10 per cent. Ubiquitin is a small 76 residue protein that derives its name from its occurrence throughout the plant and animal kingdoms. Although not found in prokaryotes, it is presently believed to be the most highly conserved protein in eukaryotes (4); the first 74 amino acids are conserved in insects (5) and humans (6). Ubiquitin has been shown to play a key role in a variety of essential cellular processes including the selective degradation of cellular proteins, maintenance of chromatin structure, regulation of gene expression, the stress response, ribosome biogenesis and possibly receptor function (4). The best characterized function of the ubiquitin system is in the ATP-dependent degradation of proteins. Ubiquitin generally attaches to the epsilon amino group of lysine residues dispersed throughout the target protein, which signals the proteolytic enzyme(s) to bind to the C-terminus ofubiquitin (7). Regulation of proteolysis is critical for controlling levels of key enzymes and regulatory proteins; about 90% of short lived proteins in cells are degraded by ubiquitin-dependent processes (8). The crystal structure of human erythrocytic ubiquitin has been refined at 1.8 A resolution (9). The overall structure ofubiquitin is extremely compact and tightly hydrogen-bonded and does not contain any disulfide bridges. The x-ray structure contains an a-helix with three and one-half turns and a five-stranded ~-sheet, all of which form a hydrophobic core. Furthermore, a solution NMR structure ofubiquitin (10) has been determined and shown to be virtually identical with the x-ray crystal structure. We now report a 3 nsec molecular dynamics simulation forubiquitin. The purpose of this study is to determine if a protein simulation treating only waters of crystallization explicitly can maintain the average properties observed experimentally and explore some of the differences noted between the x-ray crystal and solution
Downloaded by [New York University] at 19:01 09 May 2015
Figure 4: Stereoviews of theCa-atoms of instanteous simulated structures, at 120 psec intervals, are superimposed on the x-ray structure in two different orientations.
Molecular Dynamics of Ubiquitin
937
NMR structures. A preliminary account of this work was given at the 7th Conversation in the Discipline Biomolecular Stereodynamics at S.U.N.Y./Albany (11).
Downloaded by [New York University] at 19:01 09 May 2015
Methods The coordinates of the reported x-ray structure of human erythrocytic ubiquitin at 1.8 Aresolution (9) obtained from the Brookhaven Protein Data Bank (12) served as the initial molecular model for the molecular dynamics calculations. The system simulated was comprised of76 amino acid residues and 58 crystallographic waters. All of the hydrogen atoms were explicitly modeled, bringing the total number of atoms in the system to 1467. The coordinates of the added hydrogens were generated according to idealized bond lengths and valence angles using the MOLEDT software package from Biosym Technologies. The MD simulation was performed using the Discover simulation software package (version 2.41) from Biosym Technologies on a Cray X-MP. The default Discover model was used for the explicit (crystallographic) waters. No cross terms were used in the energy expression, and a simple harmonic potential was chosen for the bond-stretching terms. All calculations were conducted with a ~roup-based nonbonded cutoff of 10.5 Aimposed over a switching distance of 1.5 A and the nonbonded pair list was updated every 20 time steps. A linear distance-dependent dielectric (equal to the interatomic separation) was used. The parameters used in the force field were those of the standard Discover library (13-14), except that the charges of acidic, basic, N-termini and C-termini functional groups were made net neutral. This was done to compensate for the missing dielectric effect of bulk water, since only the crystallographic waters were included. This type of charge screening effect has been successfully used by others (15-17). The x-ray structure with added hydrogens was energy-minimized using the method of steepest descents for 500 steps with the positions of all heavy atoms fixed to remove any artifacts induced by the addition of explicit hydrogens. The structure was further minimized for 500 steps with only the positions of the heavy atoms of the protein fixed to allow the waters of crystallization to relax. Then the structure was minimized for 5000 steps using the steepest descents method followed by 5000 steps using the conjugate gradients method before beginning molecular dynamics. Dynamics was performed using the leap-frog algorithm with a 1 fsec timestep. A constant temperature for the simulation was maintained by weakly coupling to a thermal bath (18). For the dynamics, 0.5 psec was first performed at 50 K This was followed by elevating the temperature to 300 K using an exponential approach to this temperature (time constant of2.0 psec) such that the target temperature was achieved after 10 psec. At 10 psec, the time constant was adjusted to 0.1 psec and dynamics was reinitialized at 300 K The trajectory was continued for a total of 3000 psec. The simulation was restarted at 200, 500, 800, 1000 and 2000 psec with the previous last structure used as the current starting structure and with new random velocities. The data set considered in the present work was comprised of 501 structures saved at 6.0 psec intervals.
938 1000
Braatz et a/.
,..------------------------r 12.1
12.0 800
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0
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11 .5 3000
+-I""""T-r~r-T""r-r-I"""T"""T"".,....,,.......~,.......,--r......-,.....-.-......-,...,-.-......-r""""T-+
0
500
1000
1500
2000
2500
time (psec) Figure 1: The solid line represents the potential energy and the dotted line represents the radius of gyration over the time course of the simulation.
Results and Discussion A. Time Course of the Simulation
In order to assess the stability of the trajectory, several system properties including the potential energy, the radius of gyration, the rms deviation in position away from the x-ray coordinates, and the hydrogen bonding pattern were monitored as a function of the time course of the simulation. The variation in potential energy as a function of time is shown in Figure 1. Initially, the energy was quite lowwhich reflects the fact that the starting structure was thoroughly minimized. After the gradual rise over the first 10 psec, during the warmup phase of the simulation, the energy leveled off by 50 psec and then remained fairly constant for the duration of the simulation. The variation in the radius of gyration is also plotted as a function of time in Figure 1. The radius of gyration of the energy-minimized x-ray structure is 11.86 A., while the mean throughout the simulation is 11.78 A. The average simulated radius of gyration is only 0.6% smaller than the radius of the initial energy-minimized x-ray structure.
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Molecular Dynamics of Ubiquitin 3.0
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o
Journal of Biomolecular Structure and Dynamics Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/tbsd20
3 Nsec Molecular Dynamics Simulation of the Protein Ubiquitin and Comparison with X-ray Crystal and Solution NMR Structures a
a
Julie A. Braatz , Mark D. Paulsen & Rick L. Ornstein
a
a
Molecular Science Research Center Pacific Northwest Laboratory , Richland , WA , 99352 , USA Published online: 21 May 2012.
To cite this article: Julie A. Braatz , Mark D. Paulsen & Rick L. Ornstein (1992) 3 Nsec Molecular Dynamics Simulation of the Protein Ubiquitin and Comparison with X-ray Crystal and Solution NMR Structures, Journal of Biomolecular Structure and Dynamics, 9:5, 935-949, DOI: 10.1080/07391102.1992.10507968 To link to this article: http://dx.doi.org/10.1080/07391102.1992.10507968
PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or
indirectly in connection with, in relation to or arising out of the use of the Content.
Downloaded by [New York University] at 19:01 09 May 2015
This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions
Journal of Biomolecular Structure & Dynamics, ISSN 0739-1102 Volume 9, Issue Number 5 (1992), "'Adenine Press (1992).
3 N sec Molecular Dynamics Simulation of the Protein Ubiquitin and Comparison with X-ray Crystal and Solution NMR Structures
Downloaded by [New York University] at 19:01 09 May 2015
Julie A. Braatz, Mark D. Paulsen and Rick L. Ornstein* Molecular Science Research Center Pacific Northwest Laboratory t Richland, WA 99352, USA Abstract Mainly due to computational limitations, past protein molecular dynamics simulations have rarely been extended to 300 psec; we are not aware of any published results beyond 350 psec. The present work compares a 3000 psec simulation of the protein ubiquitin with the available x-ray crystallographic and solution NMR structures. Aside from experimental structure availability, ubiquitin was studied because of its relatively small size (76 amino acids) and lack of disulfide bridges. An implicit solvent model was used except for explicit treatment of waters of crystallization. We found that the simulated average structure retains most of the character of the starting x-ray crystal structure. In two highly surface accessible regions, the simulation was not in agreement with the x-ray structure. In addition, there are six backbonebackbone hydrogen bonds that are in conflict between the solution NMR and x-ray crystallographic structures; two are bonds that the NMR does not locate, and four are ones that the two methods disagree upon the donor. Concerning these six backbone-backbone hydrogen bonds, the present simulation agrees with the solution NMR structure in five out-of-the six cases, in that if a hydrogen bond is present in the x-ray structure and not in the NMR structure, the bond breaks within 700 psec. Of the two hydrogen bonds that are found in the NMR structure and not in the x-ray structure, one forms at 1400 psec and the other forms rarely. The present results suggest that relatively long molecular dynamics simulations, that use protein x-ray crystal coordinates for the starting structure and a computationally efficient solvent representation, may be used to gain an understanding of conformational and dynamic differences between the solid-crystal and dilute-solution states.
Introduction The first molecular dynamics simulation of a protein led to a dramatic change in our view of protein dynamics (1). It has now been realized that globular proteins have a wide variety of internal motions; "any attempt to understand the function of proteins requires an investigation ofthe dynamics of the structural fluctuations and
* Author to whom correspondence should be addressed. tPacific Northwest Laboratory is operated for the U.S. Department of Energy by Battelle Memorial Institute under Contract DE-AC06-76RLO 1830.
935
936
Braatz eta/.
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their relation to activity and conformational change" (2). Protein motions that can be investigated either theoretically or experimentally range from the rapid local motions of the individual amino acids to slow collective distortions of secondary structure elements or domains. While sidechain rotations at the surface of a protein typically occur in tens to hundreds of psec, torsional rotations ofburied groups and relative motion of different domains often have longer characteristic times by one to several orders of magnitude. For practical reasons, most protein molecular dynamics simulations have been performed for only about 100 psec. Occasionally, a protein simulation has been extended beyond 200 psec, but we are not aware of any published protein simulations extended to 400 psec. For practical reasons, the early protein simulations were done in vacuo. As noted by Levitt & Sharon (3), it is possible to obtain more realistic protein simulations with explicit solvent and a periodic boundary formulism; however, not all treatments that explicitly include solvent necessarily improve the simulation quality. Furthermore, simulations that explicitly treat a reasonably large solvent layer or use periodic boundary conditions are one to two orders of magnitude longer in duration than simulations with an implicit solvent model. By including explicitly only the waters of crystallization, in an otherwise implicit solvent model simulation, we believe that it maybe possible to account for much of the structural role of solvent yet increase the computational cost by about only 10 per cent. Ubiquitin is a small 76 residue protein that derives its name from its occurrence throughout the plant and animal kingdoms. Although not found in prokaryotes, it is presently believed to be the most highly conserved protein in eukaryotes (4); the first 74 amino acids are conserved in insects (5) and humans (6). Ubiquitin has been shown to play a key role in a variety of essential cellular processes including the selective degradation of cellular proteins, maintenance of chromatin structure, regulation of gene expression, the stress response, ribosome biogenesis and possibly receptor function (4). The best characterized function of the ubiquitin system is in the ATP-dependent degradation of proteins. Ubiquitin generally attaches to the epsilon amino group of lysine residues dispersed throughout the target protein, which signals the proteolytic enzyme(s) to bind to the C-terminus ofubiquitin (7). Regulation of proteolysis is critical for controlling levels of key enzymes and regulatory proteins; about 90% of short lived proteins in cells are degraded by ubiquitin-dependent processes (8). The crystal structure of human erythrocytic ubiquitin has been refined at 1.8 A resolution (9). The overall structure ofubiquitin is extremely compact and tightly hydrogen-bonded and does not contain any disulfide bridges. The x-ray structure contains an a-helix with three and one-half turns and a five-stranded ~-sheet, all of which form a hydrophobic core. Furthermore, a solution NMR structure ofubiquitin (10) has been determined and shown to be virtually identical with the x-ray crystal structure. We now report a 3 nsec molecular dynamics simulation forubiquitin. The purpose of this study is to determine if a protein simulation treating only waters of crystallization explicitly can maintain the average properties observed experimentally and explore some of the differences noted between the x-ray crystal and solution
Downloaded by [New York University] at 19:01 09 May 2015
Figure 4: Stereoviews of theCa-atoms of instanteous simulated structures, at 120 psec intervals, are superimposed on the x-ray structure in two different orientations.
Molecular Dynamics of Ubiquitin
937
NMR structures. A preliminary account of this work was given at the 7th Conversation in the Discipline Biomolecular Stereodynamics at S.U.N.Y./Albany (11).
Downloaded by [New York University] at 19:01 09 May 2015
Methods The coordinates of the reported x-ray structure of human erythrocytic ubiquitin at 1.8 Aresolution (9) obtained from the Brookhaven Protein Data Bank (12) served as the initial molecular model for the molecular dynamics calculations. The system simulated was comprised of76 amino acid residues and 58 crystallographic waters. All of the hydrogen atoms were explicitly modeled, bringing the total number of atoms in the system to 1467. The coordinates of the added hydrogens were generated according to idealized bond lengths and valence angles using the MOLEDT software package from Biosym Technologies. The MD simulation was performed using the Discover simulation software package (version 2.41) from Biosym Technologies on a Cray X-MP. The default Discover model was used for the explicit (crystallographic) waters. No cross terms were used in the energy expression, and a simple harmonic potential was chosen for the bond-stretching terms. All calculations were conducted with a ~roup-based nonbonded cutoff of 10.5 Aimposed over a switching distance of 1.5 A and the nonbonded pair list was updated every 20 time steps. A linear distance-dependent dielectric (equal to the interatomic separation) was used. The parameters used in the force field were those of the standard Discover library (13-14), except that the charges of acidic, basic, N-termini and C-termini functional groups were made net neutral. This was done to compensate for the missing dielectric effect of bulk water, since only the crystallographic waters were included. This type of charge screening effect has been successfully used by others (15-17). The x-ray structure with added hydrogens was energy-minimized using the method of steepest descents for 500 steps with the positions of all heavy atoms fixed to remove any artifacts induced by the addition of explicit hydrogens. The structure was further minimized for 500 steps with only the positions of the heavy atoms of the protein fixed to allow the waters of crystallization to relax. Then the structure was minimized for 5000 steps using the steepest descents method followed by 5000 steps using the conjugate gradients method before beginning molecular dynamics. Dynamics was performed using the leap-frog algorithm with a 1 fsec timestep. A constant temperature for the simulation was maintained by weakly coupling to a thermal bath (18). For the dynamics, 0.5 psec was first performed at 50 K This was followed by elevating the temperature to 300 K using an exponential approach to this temperature (time constant of2.0 psec) such that the target temperature was achieved after 10 psec. At 10 psec, the time constant was adjusted to 0.1 psec and dynamics was reinitialized at 300 K The trajectory was continued for a total of 3000 psec. The simulation was restarted at 200, 500, 800, 1000 and 2000 psec with the previous last structure used as the current starting structure and with new random velocities. The data set considered in the present work was comprised of 501 structures saved at 6.0 psec intervals.
938 1000
Braatz et a/.
,..------------------------r 12.1
12.0 800
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0
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200 11.6
0
11 .5 3000
+-I""""T-r~r-T""r-r-I"""T"""T"".,....,,.......~,.......,--r......-,.....-.-......-,...,-.-......-r""""T-+
0
500
1000
1500
2000
2500
time (psec) Figure 1: The solid line represents the potential energy and the dotted line represents the radius of gyration over the time course of the simulation.
Results and Discussion A. Time Course of the Simulation
In order to assess the stability of the trajectory, several system properties including the potential energy, the radius of gyration, the rms deviation in position away from the x-ray coordinates, and the hydrogen bonding pattern were monitored as a function of the time course of the simulation. The variation in potential energy as a function of time is shown in Figure 1. Initially, the energy was quite lowwhich reflects the fact that the starting structure was thoroughly minimized. After the gradual rise over the first 10 psec, during the warmup phase of the simulation, the energy leveled off by 50 psec and then remained fairly constant for the duration of the simulation. The variation in the radius of gyration is also plotted as a function of time in Figure 1. The radius of gyration of the energy-minimized x-ray structure is 11.86 A., while the mean throughout the simulation is 11.78 A. The average simulated radius of gyration is only 0.6% smaller than the radius of the initial energy-minimized x-ray structure.
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