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    • After initial optimization of the distances we obtained the

    2021-09-17

    After initial optimization of the distances we obtained the structure iG shown schematically in Fig. 1. This is the telomeric fragment of chromosome with the noncanonical structures of i-motif and G-quadruplex placed symmetrically in the middle of the duplex. Obviously, we consider the situation when the i-motif and G-quadruplex are located in the same position on the duplex. This is the most intuitive arrangement since formation of either G-quadruplex or i-motif leaves the complementary part of the duplex disordered. Then, it can naturally adopt an ordered complementary structure provided that all the necessary conditions are satisfied. In the case of the G-quadruplex it is the presence of Na+ or K+ ions, [34] for instance. I-motif, in turn, needs a reduced pH in order to produce protonated state of the cytosines. However, the reduction of pH cannot be strong since the full protonation of all cytosines leads again to an unstable state [1,6]. All calculations were based on the amber force field for nucleic acids [35] ff99 with the bsc1 modifications [36]. The constructions of the topologies were done using self-designed scripts and the force field was generated using the tleap program from the AmberTools16 package. We consider two cases of pH: neutral and acidic and this means that at the neutral pH all cytosines are in their standard unprotonated forms. The acidic pH means that we consider the cytosines 13, 14, 15, 19, 20 and 21 as additionally protonated. This was done by the tleap program with the included modification files for the creation of protonated cytosines. In the next step the systems were filled in TIP3P water molecules and suitable amounts of Na+ and Cl− ions were added in order to compensate the total charge and mimic physiological ionic strength of solution 0.145 mol L−1. The number of water molecules was ca. 39,000, Na+ ions 196–202 (neutral – acidic), Cl− ions 114 and the total number of atoms in the simulation boxes was ca. 120,000. Three Na+ ions were used as cations stabilizing the G-quadruplex structure and were placed in the centers of Pemetrexed disodium hemipenta hydrate quartets. The choice of Na+ cation, instead of a more physiologically relevant K+, as central ion in the guanine quartets is justified since both cations are able to stabilize G-quadruplex at the considered temperature. [1] The sizes of the simulation boxes were ca. 100 × 100 × 130 Å. The water molecules were kept rigid using the shake algorithm. [37] The calculations were carried out in NPT ensemble using 2 fs integration timestep and 12 Å cutoff distance for interatomic interactions was applied. The pressure and temperature were controlled using the Nose−Hoover barostat [38] with the relaxation times constants 2 ps and 0.2 ps for pressure and temperature, respectively. All calculations were done using lammps molecular dynamics engine. [39] Every studied system was initially subjected to heating from 100 K to 310 K within 1 ns simulation time at a constant volume. Next, the equilibration runs were performed at constant temperature 310 K and pressure 1 atm for 2 ns. The final states from the equilibration runs were used as starting configurations in production runs. The production runs were based on the steered molecular dynamics since the considered systems reveal very slow motions in the unbiased calculations. We performed 50 ns of the unbiased calculations with the iG structure and found no visible unfoldings of either i-motif or G-quadruplex in both cases of i-motif protonation states. Thus, in order to perform the enforced unfolding of either i-motif or the G-quadruplex we defined a collective variable which is the square root of the mean square displacement of atoms (rmsd) involved in formation of hydrogen bonds within the Hoogsteen pairs. These were all nitrogen and oxygen atoms connected by the dashed lines in Fig. 1. The displacement was measured from the reference (ref) state which is the iG structure taken from the last frame of the equilibration runs. It should be underlined that the rmsd was calculated after performing optimal rotation Uthat best superimposes the coordinates x(t)onto a set of reference coordinates x. That superimposition was done using the colvar [40] module linked to the lammps engine. The choice of the rmsd collective variable for enforcing the unfolding transitions is justified because Cruciform does not use a particular transition path and the system follows actually the easiest path which corresponds to a given rmsd value. The applied range of the moving rmsd restraint values was from 0 to 25 Å. Zero rmsd was the starting point corresponding to full overlapping of the coordinates with the reference state, while 25 Å was simply the value for which a total destruction of the analyzed structure has occurred. The rmsd restraint point was moving with the velocity 1.25 Å ns−1 and a single unfolding process corresponded to 20 ns of real time. The force constant responsible for dragging of the actual rmsd to its moving restraint point was 5 eV Å−2 (115 kcal mol−1 Å−2). The number of atoms to which the bias was applied was 48 in the case of G-quadruplex unfolding and 36 in the case of the i-motif unfolding.