NMR determined Rotational correlation time: Difference between revisions
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Brownian rotation diffusion of a particle in solution has a characteristic time constant called rotational correlation time (τ<sub>c</sub>). It is the time it takes the particle to rotate by one radian and it depends on the particle size. For globular proteins a spherical approximation can be used and the rotational correlation time is given by Stoke's law | [[Image:T1wiki fig5.png|right|400px]] Brownian rotation diffusion of a particle in solution has a characteristic time constant called rotational correlation time (τ<sub>c</sub>). It is the time it takes the particle to rotate by one radian and it depends on the particle size. For globular proteins a spherical approximation can be used and the rotational correlation time is given by Stoke's law | ||
:<math>\tau_c=\frac{4\pi\eta r^3}{3kT}</math>, | :<math>\tau_c=\frac{4\pi\eta r^3}{3kT}</math>, | ||
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where <math>\rho</math> is the average density for proteins (1.37 g/cm3), <math>N_a</math> is the Avogadro's number and <math>r_w</math> is the hydration radius (1.6 to 3.2 A)<ref>Cavanagh J., Fairbrother W.J., Palmer, A.G, Rance M., Skelton N.J. (2007) Protein NMR Spectroscopy: Principles and Practice, p21, Elsevier</ref>. As a general rule of thumb, the τ<sub>c</sub> of a monomeric protein in solution in nanoseconds is approximately 0.6 times its molecular weight in kDa. | where <math>\rho</math> is the average density for proteins (1.37 g/cm3), <math>N_a</math> is the Avogadro's number and <math>r_w</math> is the hydration radius (1.6 to 3.2 A)<ref>Cavanagh J., Fairbrother W.J., Palmer, A.G, Rance M., Skelton N.J. (2007) Protein NMR Spectroscopy: Principles and Practice, p21, Elsevier</ref>. As a general rule of thumb, the τ<sub>c</sub> of a monomeric protein in solution in nanoseconds is approximately 0.6 times its molecular weight in kDa. | ||
For rigid protein molecules, in the limit of slow molecular motion (τ<sub>c</sub> >> 0.5 ns) and high magnetic field (500 MHz or greater), a closed-form solution for τ<sub>c</sub> as a function of the ratio of the longitudinal (T<sub>1</sub>) and transverse (T<sub>2</sub>) <sup>15</sup>N relaxation times exists: | For rigid protein molecules, in the limit of slow molecular motion (τ<sub>c</sub> >> 0.5 ns) and high magnetic field (500 MHz or greater), a closed-form solution for τ<sub>c</sub> as a function of the ratio of the longitudinal (T<sub>1</sub>) and transverse (T<sub>2</sub>) <sup>15</sup>N relaxation times exists: | ||
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:<math>\tau_c\approx\frac{1}{4\pi\nu_N}\sqrt{6\frac{T_1}{T_2}-7}</math>, | :<math>\tau_c\approx\frac{1}{4\pi\nu_N}\sqrt{6\frac{T_1}{T_2}-7}</math>, | ||
where ν<sub>N</sub> is the <sup>15</sup>N resonance frequency (in Hz). This equation is derived from Eq. 8 in <ref>Kay, L.E., Torchia, D.A. and Bax, A. (1989) Backbone dynamics of proteins as studied by <sup>15</sup>N inverse detected heteronuclear NMR spectroscopy: Application to staphylococcal nuclease. ''Biochemistry'', '''28''', 8972-8979.</ref> by considering only J(0) and J(ωN) spectral density terms and neglecting higher frequency terms. | where ν<sub>N</sub> is the <sup>15</sup>N resonance frequency (in Hz). This equation is derived from Eq. 8 in ref.<ref>Kay, L.E., Torchia, D.A. and Bax, A. (1989) Backbone dynamics of proteins as studied by <sup>15</sup>N inverse detected heteronuclear NMR spectroscopy: Application to staphylococcal nuclease. ''Biochemistry'', '''28''', 8972-8979.</ref> by considering only J(0) and J(ωN) spectral density terms and neglecting higher frequency terms. | ||
Revision as of 17:57, 4 January 2010
Brownian rotation diffusion of a particle in solution has a characteristic time constant called rotational correlation time (τc). It is the time it takes the particle to rotate by one radian and it depends on the particle size. For globular proteins a spherical approximation can be used and the rotational correlation time is given by Stoke's law
- <math>\tau_c=\frac{4\pi\eta r^3}{3kT}</math>,
where <math>\eta</math> is the viscosity of the solvent, <math>r</math> is the effective hydrodynamic radius of the protein molecule, <math>k</math> is the Boltzmann constant and <math>T</math> is the temperature. The hydrodynamic radius can be estimated from the molecular weight of the protein (M) as
- <math>r\approx\sqrt[3]{\frac{3M}{4\pi\rho N_a}}+r_w</math>,
where <math>\rho</math> is the average density for proteins (1.37 g/cm3), <math>N_a</math> is the Avogadro's number and <math>r_w</math> is the hydration radius (1.6 to 3.2 A)[1]. As a general rule of thumb, the τc of a monomeric protein in solution in nanoseconds is approximately 0.6 times its molecular weight in kDa.
For rigid protein molecules, in the limit of slow molecular motion (τc >> 0.5 ns) and high magnetic field (500 MHz or greater), a closed-form solution for τc as a function of the ratio of the longitudinal (T1) and transverse (T2) 15N relaxation times exists:
- <math>\tau_c\approx\frac{1}{4\pi\nu_N}\sqrt{6\frac{T_1}{T_2}-7}</math>,
where νN is the 15N resonance frequency (in Hz). This equation is derived from Eq. 8 in ref.[2] by considering only J(0) and J(ωN) spectral density terms and neglecting higher frequency terms.
Average 15N T1 and T2 relaxation times for a given protein can be measured using 1D 15N-edited relaxation experiments [3]. To minimize contributions from unfolded segments each 1D spectum is integrated over the downfield backbone amide 1H region (typically 10.5 to 8.5 ppm) and the results are used to fit an exponential decay as a function of delay time. One then computes the correlation time using Eq. 3, and compares it to a standard curve of τc vs. protein molecular weight (MW) obtained at the same temperature on a series of known monomeric proteins of varying size. The T1/T2 method is suitable for proteins with molecular weight of up to MW ≈ 25 kDa. Accurate measurement of the diminishing 15N T2 becomes difficult for larger proteins and cross-correlated relaxation rates are measured instead.
Protocols for Bruker and Varian NMR Instruments
References
- ↑ Cavanagh J., Fairbrother W.J., Palmer, A.G, Rance M., Skelton N.J. (2007) Protein NMR Spectroscopy: Principles and Practice, p21, Elsevier
- ↑ Kay, L.E., Torchia, D.A. and Bax, A. (1989) Backbone dynamics of proteins as studied by 15N inverse detected heteronuclear NMR spectroscopy: Application to staphylococcal nuclease. Biochemistry, 28, 8972-8979.
- ↑ Farrow, N.A., Muhandiram, R., Singer, A.U., Pascal, S.M., Kay, C.M., Gish, G., Shoelson, S.E., Pawson, T., Forman-Kay, J.D. and Kay, L.E. (1994) Backbone dynamics of a free and phosphopeptide-complexed Src homology 2 domain studied by 15N NMR relaxation. Biochemistry, 33, 5984-6003.