2558 Nucleic Acids Research, 2007, Vol. 35, No. 8 The complete analysis of all possible 15NH4þ ion site exchange steps by simultaneous equations proved impos- sible to solve uniquely with the available experimental data because the number of competing exchange processes exceeds the number of experimental observables. Therefore, our analysis of ion movement has concentrated on individual processes, which aﬀorded resolved cross- peaks in NzExHSQC spectra. Each 15NHþ ion at any of the three binding sites 4 within G-quadruplex can, in principle, move to either of two binding sites (which includes movement to bulk solution for cations initially at O1 and O2). An 15NH4þ ion that moves from one binding site to the other can move back to its original binding site, to the next binding site or into the bulk solution, and so forth. The longer the mixing time, the more exchange scenarios (i.e. double, triple) that must be taken into consideration. In order to simplify our analysis, we have quantitatively analyzed only NzExHSQC spectra with mixing times up to 600 ms. The basic model in which 15NHþ ions are allowed to 4 move from binding site 1 through the intermediate G-quartet plane to binding site 2 was introduced, Equation (1), binding site 1 k ! binding site 2 1 where k represents exchange rate constant. According to Equation (1), the volume of cross-peak corresponding to movement of 15NH4þ ions to binding site 2 increases as a function of mixing time ( m). Exchange cross-peaks also decrease in intensity due to spin relaxation (T1). These two factors contribute to cross-peak volume and can be expressed by Equation (2). 2 Vcrossð mÞ ¼ e T1 1 m 1 e k m Iterative least-square ﬁtting of experimental O1I and O2I cross-peak volumes by optimizing k and T1 parameters in Equation (2) showed good agreement between experi- mental data and the simple model for exchange peak intensity (Figure 4). Exchange rate constants and T1 relaxation times are reported in Table 1. The largest individual discrepancy between the experimental data point and the ﬁtted curve was 0.01 normalized volume units with low RMSD. The curve ﬁtting of the data shown in Figure 4 conﬁrmed that cross-peak volumes depend upon speciﬁc site-to-site exchange rates and T1 values for each site. At 283 K, 15NH4þ ion movements from O1- and O2-binding sites into the inner binding site are relatively slow, with the low exchange rate constants of 0.05 and 0.07 s 1, respectively (Table 1). Both rates increase with increasing temperature. Exchange rate constants corresponding to the O1I and O2I processes are comparable in the temperature range from 283 to 303 K (Table 1). At 313 K, however, the exchange rate constant becomes greater for O1I (0.66 s 1) than for O2I process (0.50 s 1), which is clearly evident from examination of the experimentally observed cross-peak volumes in Figure 4B. T1 relaxation also plays a determining role for individual O1I and O2I cross-peak volumes at a given temperature (Table 1). Interestingly, T1 relaxation times are shorter for O2I in comparison to O1I cross-peak. As expected, Figure 4. Relative volumes of cross-peaks as a function of mixing time ( m) at 283 K (A) and 313 K (B). Red open circles and black ﬁlled squares represent experimental data points for O1I and O2I cross-peaks, respectively. Curves represent the best ﬁts of the experimental data to Equation (2). Table 1. Exchange rate constants (k) and longitudinal relaxation times (T1) for the movement of 15NH4þ ions from the two outer into the inner binding sites T (K) 283 293 303 313 O1I process k (s 1) 0.05 ( 0.01) 0.16 ( 0.01) 0.36 ( 0.04) 0.66 ( 0.05) T1 (s) 0.77 ( 0.26) 0.80 ( 0.11) 0.60 ( 0.09) 0.46 ( 0.04) RMSD 0.00240 0.00187 0.00502 0.00573 O2I process k (s 1) 0.07 ( 0.01) 0.14 ( 0.02) 0.37 ( 0.05) 0.50 ( 0.06) T1 (s) 0.57 ( 0.09) 0.57 ( 0.08) 0.38 ( 0.05) 0.30 ( 0.03) RMSD 0.00304 0.00191 0.00413 0.00395 Values were obtained through iterative ﬁtting of the experimental data to Equation (2). Quality of the individual ﬁts is expressed as RMSD. Errors of individual k and T1 values are given in brackets.