It should be noted that the applied
It should be noted that the applied steered unfolding of the i-motif and G-quadruplex satisfies the conditions of Jarzynski inequality for computations of the free energy change.  However, in order to reproduce the free energy with an adequate quality a number of nonequilibrium unfolding transitions, started from the canonical distribution, should be performed and the free energy can then be determined as the exponential average.  However, this methods is useful when a single run takes not much time and many independent runs can be performed in a reasonable timescale. In our case a single unfolding transition takes a lot of time and therefore we cannot determine an exact free energy profile accompanied the unfolding transitions. Instead, we limit our considerations to comparative analysis of single runs which represent the work done during the enforced unfolding in nonequilibrium conditions. Thus, in that way we can compare the relative stabilities of the considered systems as functions of the parameters of choice.
Results and discussion The iG structure, as shown in the inset in Fig. 1, consists of 45 MHY1485 pairs. In the middle of the initially existing Watson-Crick duplex the G-quadruplex and i-motif were formed in the guanine and cytosine rich strands, respectively. This structure is, as mentioned, either highly or significantly stable depending on the pH.  The unfolding of these noncanonical forms within the nanosecond timescale can thus be done only by applying biased simulations. Fig. 2 shows the snapshots of the iG structures after the enforced unfolding and relaxation of both the G-quadruplex and the i-motif at the neutral and acidic pH. Analysis of Fig. 2 leads to a few qualitative conclusions, namely, it is easy to notice that the i-motif parts of the iG are well preserved after the destruction of the G-quadruplexes only at acidic pH. Definitely, the enforced unfolding of the G-quadruplex does not affect the structure of the i-motif when the third hydrogen bond exists within the C+–C pairs. At the neutral pH the symmetry of the i-motif is rather loosely kept and we can state that stability of the i-motif without the complementary G-quadruplex is rather weak. The weakening of the i-motif structure can be due to the strain being associated with the enforced unfolding of the G-quadruplex but the main reason of such a behavior is the lack of the protonated cytosines and the third hydrogen bond at the neutral pH.  On the other hand the G-quadruplex structure is preserved after destruction of the i-motif either at acidic or at the neutral pH. Moreover, the sodium ions, entrapped in the guanine quartets, stay for the whole simulation time at their places and no exchange of these ions with the bulk occurs. It is interesting to note that after the relaxation without biasing forces the i-motif parts tend to form hairpin structures. These structures are alternative to i-motif forms of the cytosine rich strand with similar stability, as found in our previous work.  A more quantitative conclusions concerning the unfolding processes can be drawn from Fig. 3 which shows how the distances between atoms forming hydrogen bonds evolve in time. This figure shows only the cases of the G-quadruplexes unfolding at both pH conditions. However, no matter that the associated i-motif parts of the iG systems are not affected by the biasing potential, these parts of the iG are affected by the processes of the G-quadruplexes unfolding. Obviously, the most visible changes of the distances occur within the G-quadruplexes as they are directly affected by the biasing potential. Another interesting observation concerns the sequence of the hydrogen bonds breaking. In the case of the neutral pH (parts (A) and (B)) the deterioration of the G-quadruplex starts from the innermost quartet (see Fig. 1) though 2 or 4 hydrogen bonds are still preserved until the end of the calculations. It should be noted that the biasing force acts until 20th nanosecond of the calculation, the last 20 ns are without any bias and we can see a rapid drop of the distances and quite a fast stabilization around the new values. Of course a spontaneous refolding to G-quadruplex is highly unlikely within the available simulation time of the unbiased calculations. Thus, these new values can be treated as representative of transient but long lasting forms of the unfolded G-quadruplex. At acidic pH the unfolding of G-quadruplex proceeds in a different way though the pH cannot directly alter the G-quadruplex state. It can be seen that the unfolding starts from the opposite side, i.e. from the outermost guanine quartet. However, after 5 ns all quartets become partially broken though a few hydrogen bonds still exists until the end of the run. As seen in Fig. 2 in both cases of pH the sodium ions escaped from the cages formed by the G-qudruplexes and the final structures do not resemble G-quadruplexes at all.