DynaPro NanoStar manual - Department of Physiology and Biophysics

Cumulants Analysiswhere erfc(x) is the complimentary error function, defined as:The autocorrelation function resulting from the truncated Gaussian distributionis given by:Equation (3)Equation (3) is well behaved and monotonically decreasing everywherewith increasing , as it must be since it is simply a combination ofdecaying exponential functions.Traditional cumulants analysis attempts to determine the first and secondcumulants terms, which are equal to the first and second moments of theintensity distribution, which are given as:(Equation 4)and(Equation 5)For a Gaussian distribution truncated at zero, the center and width of theGaussian does not directly yield the first and second moments of the distribution.Using Equations (2), (4), and (5), the first and second momentsof the truncated Gaussian are calculated to be:and(Equation 6)(Equation 7)DYNAMICS User’s Guide (M1400 Rev. K) A-3