T1 relaxation time is reduced when the temperature is increased from 293 to 313 K. At 283 K, T1 values are somewhat lower than expected because there is no clear inﬂection in the experimental data points, which makes the ﬁtting procedure less sensitive to T1 values and thus its calculated value less accurate (Table 1). A similar analysis was not possible for the reverse processes (i.e. IO1 and IO2) due to nearly identical chemical shifts of both cross-peaks in the 1H dimension of the NzExHSQC spectrum. The intensity of the IOx cross-peak therefore corresponds to the weighted sum of the two contributions. The volume integral of the IOx cross-peak is approximately equal to twice the sum of volumes of O1I and O2I cross-peaks at a given mixing time. According to Equation (2), the IOx cross-peak is characterized by two individual exchange rate constants and two longitudinal relaxation times for the IO1 and IO2 processes. These four variables could not be calculated by ﬁtting the IOx experimental data set. The use of k and T1 values derived from O1I and O2I cross-peaks (Table 1) could not reproduce the experimentally observed volumes for IOx cross-peak using Equation (2). The amount of 15NH4þ ions that move from binding site I to the outer binding sites is under steady-state conditions the same as the amount of ions moving back. However, individual cross-peaks that correspond to speciﬁc ion movement within the G-quadruplex are characterized with individual rate constants and T1 relaxation times that cannot be simply transferred from one to the other. The decrease of volume of a given cross-peak as a function of mixing time is a complex function of T1 relaxation at the initial and ﬁnal binding sites as well as many other phenomena (e.g. proton exchange). Movement of 15NH4þ ions into bulk solution The intensity of cross-peaks corresponding to 15NH4þ ion movement from G-quadruplex into bulk is reduced due to proton exchange with bulk solvent. At neutral pH, exchange of protons is suﬃciently fast that cross-peaks involving bulk ions (B) are broadened to baseline. The same applies for cross-peaks corresponding to the move- ment of 15NH4þ ions into bulk solution from within the G-quadruplex. We were therefore able to follow the movement of 15NH4þ ions into and from bulk solution only for samples with pH 6. The cross-peaks O1B and Figure 5. Relative volumes of O1B (red open circles) and O2B (black ﬁlled squares) cross-peaks as a function of mixing time ( m) at 293 K. Curves represent the best ﬁt of the experimental data to Equation (2). Nucleic Acids Research, 2007, Vol. 35, No. 8 2559 O2B showed distinct behavior as a function of mixing time (Figure 5). Movement of 15NH4þ ions from the binding site O2 into bulk solution is characterized by the exchange rate constant of 0.75 s 1 at 293 K (Table 2). Observed changes in cross-peak volumes as a function of mixing time are ﬁtted well by Equation (2) (Figure 5). The largest individual discrepancy between the experimental data points and the ﬁtted curve was 0.03 normalized volume units, with low RMSD (Table 2). Movement of 15NH4þ ions from binding site O1 to bulk solution is almost ﬁve times slower. The data obtained for both of these exchange processes are also inﬂuenced by relaxation. Curve ﬁtting revealed that T1 relaxation time is more than twice as long for O1B in comparison to the O2B process (Table 2). Quantitative analysis of autocorrelation peaks The movement of 15NH4þ ions from certain binding site results in exponential decrease of volume for the corres- ponding autocorrelation peak with increasing mixing time. Simultaneously autocorrelation peak is reduced by various types of relaxation. Attempts to ﬁt our experi- mental data revealed that exponential function with a single rate constant does not adequately describe the observed decrease in autocorrelation peak volume (Vauto) as a function of mixing time ( m). However, good agreement with experimental data points was achieved using a biexponential function [Equation (3)], 3 Vautoð mÞ ¼ fe d1 m þ ð1 f Þe d2 m where f is the fraction of autocorrelation peak decay through the faster relaxation mechanism, d1 and d2 are the rate constants of the fast and slow relaxation mechanisms, respectively. The use of Equation (3), where parameters f, d1 and d2 were freely optimized resulted in satisfactory agreement between the experimental data and calculated parameters (Figure 6). Reproducible optimized parameter sets were obtained from a wide range of starting parameters. The results of iterative ﬁtting procedure are given in Table 3. The two rate constants d1 and d2 diﬀer considerably for a given binding site and temperature (Table 3). The rate constant d1 is higher and cannot be correlated to the rate(s) of 15NH4þ ion movement. Furthermore, the mechanism of decrease of volume of autocorrelation peak, which is not well understood, involves many terms including cross-correlated relaxation. The slow relaxation mechanism characterized by rate constant d2 accounts for Table 2. Exchange rate constants (k) and longitudinal relaxation times (T1) for the movement of 15NH4þ ions from the outer binding sites into bulk solution at 293 K T (K) O1B process 293 k (s 1) T1 (s) 0.16 2.63 ( 0.03) ( 2.44) RMSD 0.00478 O2B process k (s 1) T1 (s) 0.75 1.19 ( 0.08) ( 0.27) See footnote to Table 1. RMSD 0.00953