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Calcium-Binding Protein Protocols Calcium-Binding Protein Protocols

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<strong>Calcium</strong>-43 NMR 219<br />

are different and field dependent (9). For systems where the 43 Ca 2+ ion undergoes<br />

exchange between a large excess of free, solvated ions, and protein bound<br />

ions the apparent relaxation rates will be mono-exponential even though ω 0τ c<br />

>1.5 for the protein bound ions. Halle and Wennerström (10) have derived<br />

approximate analytical expressions for the relaxation rates in the near extreme<br />

narrowing regime for spin I = 5/2 and I = 7/2 nuclei. The longitudinal and<br />

transverse relaxation rates of the major relaxation components are to firstorder<br />

given by Eqs. 2 and 3.<br />

R1 = 3π2 /10*χ2 *(2I + 3)/[I2 (2I – 1)]*[0.2*J1 + 0.8*J2] (2)<br />

R2 = 3π2 /10*χ2 *(2I + 3)/[I2 (2I – 1)]*[0.3*J0 + 0.5*J1 + 0.2*J2] (3)<br />

where the spectral densities are given by<br />

J q = τ c/[1 + (q*ω 0*τ c) 2 ]<br />

These equations are analogous to those derived by Bull (11) for spin I = 3/2 and<br />

ω 0τ c

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