# Protein Correlation Time Calculators

## At desired temperature, given correlation time at old temperature:

### (Also use to convert between H_{2}O and D_{2}O solvents)

## At desired temperature, given molecular weight:

### Notes:

Calculating the correlation time at a new temperature, given a known correlation time at an old temperature, is accurate and relatively straightforward (tau is inversely proportional to the temperature, in kelvins, and directly proportional to the viscosity of water, which depends on temperature). The viscosity (for H_{2}O or D_{2}O) is calculated from temperature as in Cho et al.

Calculating the correlation time from the molecular weight is much more error-prone and should only be treated as a very rough estimate, because the correlation time depends so much on the shape of the protein. The calculation based on Stokes' Law is done as on p. 21 of Cavanagh et al., using a hydration layer of 3.2 angstroms. This is only truly valid for a perfect sphere. The "empirical formula" is based on a best fit of data from the NESG website, using the formula tau = 0.0005998 x MW + 0.1674, using units of Da and ns. This is probably much more useful, at least in the range of the provided data (MW between 7.2 and 21.9 kDa). This (lower) calculator only calculates correlations times for H_{2}O solutions, though values for D_{2}O solutions can be calculated by plugging the values into the upper calculator.

### References:

Cavanagh, Fairbrother, Palmer, Rance, Skelton. Protein NMR Spectroscopy: Principles and Practice, 2nd ed.

Cho, Urquidi, Singh, Robinson. Thermal Offset Viscosities of Liquid H_{2}O, D_{2}O, and T_{2}O. J. Phys. Chem. B, 103, 1991-4, 1999.

NESG. NMR determined rotational correlation time. www.nmr2.buffalo.edu/nesg.wiki/NMR_determined_Rotational_correlation_time. Accessed 11 Feb. 2013