Quantitative Calculation of NMR Spin Relaxation and Dipolar Couplings from Molecular Dynamics Ensembles
Scott A. Showalter and Rafael Brüschweiler
Department of Chemistry and Biochemistry, Florida State University and National High Magnetic Field Laboratory (NHMFL), Tallahassee, FL
Introduction
The function of biomolecules is accompanied by a wide range of motional behavior. MD can provide detailed insights into the nature of biomolecular motion by representing the state of a protein as a conformational ensemble that follows the laws of statistical thermodynamics. However, due to the strong dependence of the MD simulation on the applied force field, validation of simulations against experimental data is critically important. Here we present an MD trajectory of the protein ubiquitin computed using the AMBER99SB force field [1] which produces near quantitative agreement with experimental 15N spin relaxation data [2] and residual dipolar couplings (RDCs) measured in multiple alignment media. [3]
MD Trajecories
Figure 1. Backbone fluctuations over the 20 ns trajectories computed with AMBER99 (yellow) and AMBER99SB (red) under NPT conditions with SPC water.
The trajectories were analyzed using the isotropic Reorientational Eigenmode Dynamics (iRED) formalism [4] to yield order parameters which can be compared with Lipari-Szabo order parameters
S2 is easy to compute, but can be misleading as a measure of simulation quality.
Figure 2. Ubiquitin backbone N-H bond order parameter profiles from 600 MHz NMR data (black circles), [5] and iRED analysis of the AMBER99 trajectory (yellow diamonds) and AMBER99SB (red diamonds) trajectories.
Spin Relaxation from MD
It is possible to model internal motion accurately with state of the art force fields by calculating correlation functions Cint(t) in analogy to NMR spin relaxation. Fully quantitative validation of the MD trajectory requires back-calculation of raw spin relaxation data through the correlation function.
Figure 3. Ubiquitin backbone N-H bond correlation functions from the 20 ns MD trajectories. [2] The experimental S2 are indicated by dashed lines. [5]
Figure 4. 600 MHz T1, T2, and NOE data from the 20 ns trajectories. [2] Experimental values are in black. [5]
Torsion Correlations
Figure 5. Internal motion correlations in the β-hairpin of ubiquitin (residues 5-12) are significantly influenced by the choice of force field.
Dipolar Couplings from MD
The sensitivity of RDCs to dynamics slower than global tumbling makes them an ideal validation tool for longer modern MD trajectories. Here we report remarkable agreement between computed [3] and experimental [6,7] RDCs for ubiquitin.
Figure 6. Residual dipolar coupling quality factors (Qcum) of ubiquitin for the 20 and 50 ns AMBER99SB MD simulations (grey and red), and the 20 ns AMBER99 simulation (yellow). [3]
Due to the nature of the RDC, the Qcum of the MD ensemble is not the same as the Qcum of the average structure. The MD ensemble is a realistic model for the statistical thermodynamic ensemble.
Figure 7. Residual dipolar coupling Qcum factors of ubiquitin for the 50 ns MD simulation (red) and NMR structure ensemble refined against RDC data (pdb code 1d3z; grey).
Conclusions
The MD ensemble provides a dynamic picture of the ubiquitin backbone that shows a remarkably high degree of consistency with NMR relaxation and RDCs and at the same time is meaningful from a statistical thermodynamics perspective. the most recent generation of MD force fields has made a formidable stride toward the quantitative structural dynamic description of protein behavior.
Acknowledgments
This work was funded by the NSF Grant 0621482. SAS is the recipient of an NIH post doctoral fellowship.
References
[1] Hornak, V., Abel, R., Okur, A., Strockbine, B., Roitberg, A., & Simmerling, C. (2006), Proteins, 65, 712-725.
[2] Showalter, S.A., & Brüschweiler, R. (2007), J. Chem. Theory Comput., 3, 961-975.
[3] Showalter, S.A., & Brüschweiler, R. (2007), JACS, 129, 4158-4159.
[4] Prompers, J.J., & Brüschweiler, R. (2002), JACS, 124, 4522-4534.
[5] Lienin, S.F., Bremi, T., Brutscher, B, Brüschweiler, R., & Ernst, R.R. (1998), JACS, 120, 9870-9879.
[6] Ottiger, M. & Bax, A., J. (1998), JACS, 120, 12334-12341.
[7] Peti, W., Meiler, J., Brüschweiler, R., & Griesinger, C. (2002) JACS, 124, 5822-5833
Department of Chemistry and Biochemistry,
Dittmer Building, Room 217,
Florida State University, Tallahassee, FL 32306
Phone: (850) 644-1768 / Fax: (850) 644-8281
National High Magnetic Field Laboratory, Room B234, 1800 E. Paul Dirac Drive, Tallahassee, FL 32310
The function of biomolecules is accompanied by a wide range of motional behavior. MD can provide detailed insights into the nature of biomolecular motion by representing the state of a protein as a conformational ensemble that follows the laws of statistical thermodynamics. However, due to the strong dependence of the MD simulation on the applied force field, validation of simulations against experimental data is critically important. Here we present an MD trajectory of the protein ubiquitin computed using the AMBER99SB force field [1] which produces near quantitative agreement with experimental 15N spin relaxation data [2] and residual dipolar couplings (RDCs) measured in multiple alignment media. [3] The trajectories were analyzed using the isotropic Reorientational Eigenmode Dynamics (iRED) formalism [4] to yield order parameters which can be compared with Lipari-Szabo order parameters It is possible to model internal motion accurately with state of the art force fields by calculating correlation functions Cint(t) in analogy to NMR spin relaxation. Fully quantitative validation of the MD trajectory requires back-calculation of raw spin relaxation data through the correlation function.
The sensitivity of RDCs to dynamics slower than global tumbling makes them an ideal validation tool for longer modern MD trajectories. Here we report remarkable agreement between computed [3] and experimental [6,7] RDCs for ubiquitin. The MD ensemble provides a dynamic picture of the ubiquitin backbone that shows a remarkably high degree of consistency with NMR relaxation and RDCs and at the same time is meaningful from a statistical thermodynamics perspective. the most recent generation of MD force fields has made a formidable stride toward the quantitative structural dynamic description of protein behavior.
Quantitative Calculation of NMR Spin Relaxation and Dipolar Couplings from Molecular Dynamics Ensembles
Scott A. Showalter and Rafael Brüschweiler
Department of Chemistry and Biochemistry, Florida State University and National High Magnetic Field Laboratory (NHMFL), Tallahassee, FL
Introduction
MD Trajecories
Figure 1. Backbone fluctuations over the 20 ns trajectories computed with AMBER99 (yellow) and AMBER99SB (red) under NPT conditions with SPC water.
S2 is easy to compute, but can be misleading as a measure of simulation quality.
Figure 2. Ubiquitin backbone N-H bond order parameter profiles from 600 MHz NMR data (black circles), [5] and iRED analysis of the AMBER99 trajectory (yellow diamonds) and AMBER99SB (red diamonds) trajectories.
Spin Relaxation from MD
Figure 3. Ubiquitin backbone N-H bond correlation functions from the 20 ns MD trajectories. [2] The experimental S2 are indicated by dashed lines. [5]
Figure 4. 600 MHz T1, T2, and NOE data from the 20 ns trajectories. [2] Experimental values are in black. [5]
Torsion Correlations
Figure 5. Internal motion correlations in the β-hairpin of ubiquitin (residues 5-12) are significantly influenced by the choice of force field.
Dipolar Couplings from MD
Figure 6. Residual dipolar coupling quality factors (Qcum) of ubiquitin for the 20 and 50 ns AMBER99SB MD simulations (grey and red), and the 20 ns AMBER99 simulation (yellow). [3]
Due to the nature of the RDC, the Qcum of the MD ensemble is not the same as the Qcum of the average structure. The MD ensemble is a realistic model for the statistical thermodynamic ensemble.
Figure 7. Residual dipolar coupling Qcum factors of ubiquitin for the 50 ns MD simulation (red) and NMR structure ensemble refined against RDC data (pdb code 1d3z; grey).
Conclusions
Acknowledgments
This work was funded by the NSF Grant 0621482. SAS is the recipient of an NIH post doctoral fellowship.
References
[1] Hornak, V., Abel, R., Okur, A., Strockbine, B., Roitberg, A., & Simmerling, C. (2006), Proteins, 65, 712-725.
[2] Showalter, S.A., & Brüschweiler, R. (2007), J. Chem. Theory Comput., 3, 961-975.
[3] Showalter, S.A., & Brüschweiler, R. (2007), JACS, 129, 4158-4159.
[4] Prompers, J.J., & Brüschweiler, R. (2002), JACS, 124, 4522-4534.
[5] Lienin, S.F., Bremi, T., Brutscher, B, Brüschweiler, R., & Ernst, R.R. (1998), JACS, 120, 9870-9879.
[6] Ottiger, M. & Bax, A., J. (1998), JACS, 120, 12334-12341.
[7] Peti, W., Meiler, J., Brüschweiler, R., & Griesinger, C. (2002) JACS, 124, 5822-5833
Department of Chemistry and Biochemistry,
Dittmer Building, Room 217,
Florida State University, Tallahassee, FL 32306
Phone: (850) 644-1768 / Fax: (850) 644-8281
National High Magnetic Field Laboratory, Room B234, 1800 E. Paul Dirac Drive, Tallahassee, FL 32310