**Refer to J. Biomol NMR (2011) 51: 123-129.**

- Measure two sets of longitudinal exchange experiments in interleaved manor, one with and one without resolving exchange cross peaks (frequency-labeling, swap_flg= ’n’, and swap_flg= ‘y’), e.g. mixing time may be: 0.01, 0.05, 0.1, 0.15, 0.2, 0.3, 0.4, 0.5, 0.6, 0.8 sec; (mixing time = ncyc*5 ms)
- Analyze only direct correlation peaks in both series of experiments, use the same nmrpipe script to process all spectra; use the first time point’s spectra peaks’
**volume**(not intensity) as 1 to normalize the rest time points’ corresponding peaks, and get four curves for every residue you are interested in (AA, A, BB, B four states); - Use (e.g. OriginPro) and the following equations to do simultaneously four curves nonlinear fitting to get the values of dynamics parameters (ms-us conformational exchange: k
_{AB}, k_{BA}, R_{1}^{A}, and R_{1}^{B}); (a11= k_{AB}+R_{1}^{A}; a22= k_{BA}+R_{1}^{B}; a12= -k_{BA}; a21= -k_{AB})

t1=0.5*(-(a11+a22)+sqrt((a11-a22)^2+4*a12*a21));

t2=0.5*(-(a11+a22)-sqrt((a11-a22)^2+4*a12*a21));

y1=((a22+t1)*exp(t1*x)-(a22+t2)*exp(t2*x))/(t1-t2);

y2=((a22-a21+t1)*exp(t1*x)-(a22-a21+t2)*exp(t2*x))/(t1-t2);

y3=((a11+t1)*exp(t1*x)-(a11+t2)*exp(t2*x))/(t1-t2);

y4=((a11-a12+t1)*exp(t1*x)-(a11-a12+t2)*exp(t2*x))/(t1-t2);

(open OriginPro and open one new workbook1, input data in column x, y (or y2,y3,…); and select them all together, and go to “analysis” → “fitting” → “nonlinear curve fitting” → “ Open dialog”; from “Category” select “user defined”; from “function” select “new”; choosing “express” can define like “y=a+b*x” ,… one equation; and choosing “equation” can define like “y1=a+b*x^2; and y2=c+d*sqrt(x);… multiple equations”,… click “parameter” tab to give initial values,… and click “fit” to start iteration1, and click twice fitting twice,… click fitting to get converging result,… and get those fitting coefficients’ values: a, b, c, d…)

Hongwei edited on 12/27/2021