DESCRIPCIÓN DE LAS CONDICIONES EXPERIMENTALES 1 Ubicación Del Campo Experimental

A FES for L81/R64 interplay were estimated as functions of two CVs: i) C64, i.e. the distance of the R64 guanidino group (defined by its C\zeta atom) from the centre of

mass of the filter (atoms N, C\alpha , and C of residues from 74 to 78) and ii) chi81, i.e.

\chi 1 dihedral angle of L81 residue. The former CV was chosen because the arginine side chain forms strong H-bonds with D80 the closer it gets to the filter.

Y82A

In the simulation of Y82A, R64 and L81 performed several transitions. Therefore an estimation of the FES was directly computed from the sampled distributions, as described in Sec. 2.2.1 Sampling was improved by combining the data from all four subunits, which corresponds to \sim 114 ns. The FES thus obtained is not likely to be completely accurate and will be biased toward the initial configuration (the configuration of the X-ray structure of WT used to build the mutant) because of insufficient sampling. In any event, it was considered satisfactory for the scope of this work in order to obtain approximate heights of the barriers and identify the location of the relevant minima. The FES is reported in Fig.4.9.

Figure 4.9: Estimate of the FES for the interplay between R64 and L81 and representative conformations of the protein in: i) Y82A, computed from unbiased simulation, and ii) WT computed via well-tempered MetaD approach. The CVs, showed in the figure, are: i) C64, the distance of the R64 guanidino group (defined

by its C\zeta atom) from the centre of mass of the filter (atoms N, C\alpha , and C of

residues from 74 to 78) and ii) chi81, the\chi 1dihedral angle of L81 residue. Energy

Two main minima are noticeable: the broad minimum ``a'', corresponding to the configurations closest to the initial configuration and the X-ray structure of the conductive state (C64 \sim 21.5 \r A and chi81 \sim 298\circ ); and the smaller minimum ``b'', corresponding to the L81 side chain in the flipped conformation and the R64 guanidino group located close to the SF and D80 (C64 \sim 16 \r A and chi81 \sim 185\circ ). The existence of these two minima confirms the analysis of the trajectories and the role of L81, which acts as a gate capable of obstructing the path for R64 leading towards D80 and the creation of H-bonds.

WT

The estimate of the FES for L81/R64 interplay in the WT from the simulated trajec- tories was poorer than in Y82A, because the slower kinetics of the process resulted in fewer transitions of R64 and L81. This was overcome by using well-tempered metaD to estimate the FES (Sec.2.2.3,\Delta T = 1200K and integration step 2 fs for a total sampling of \sim 122 ns). The initial configuration was obtained from the unbiased simulation WT (>25 ns of relaxation) with K+ ions arranged 10101+0 in the SF and a vacancy in S3. During the sampling transitions of no K+ _{ions were seen in}

the SF.

The computed FES is reported in Fig. 4.9. The main differences are the heights of the barriers, higher in the WT than in Y82A, and this can explain the slower motions of R64 observed in the simulations of the WT.

The position of the minima confirms that the conformation of the L81 side chain determines the stability of the different configurations of R64: non-flipped conformation favours states for R64 that are far from D80 and close to the one found in the X-ray experiments (minimum ``a'', chi81\sim 295\circ ), while flipped conformation promote the R64's approach towards D80 (chi81\sim 185\circ ). Two minima (``b'' and ``c'') are found in this region: the absolute minimum of the FES, which corresponds to R64 H-bound to D80 (minimum ``c'', C64 between16and 17 \r A) and a neighbouring small minimum, which corresponds to the intermediate state towards the creation of the D80--R64 H-bond described in Sec.4.5.2, which was observed in the unbiased simulations (minimum ``b'', C64 between17and18\r A). The presence of this additional minimum with respect to the Y82A's FES probably depends on the lower mobility of sequence L81-X82-P83-V84 in the WT.

The interplay between R64 and L81 mainly follows two low-energy paths

``a \leftrightarrows b'' according to the FES. The first path is highlighted by a magenta dotted

line in the figure and consists of an initial flipping of the L81 side chain (chi81

gradient towards the SF. The second path is highlighted by a black dotted line and involves the initial creation of a relatively unstable D80--R64 H-bond which is finally stabilised by the flipping of the L81 side chain. Both paths require similar energies of between 5 and 7 kcal/mol, even if the second path appears to be more accessible because of the presence of an intermediate state that makes the higher barrier4 - 5 kcal/mol.

Interestingly, the absolute minimum of the FES did not contain the confor- mation obtained by X-ray experiments. Analogous result was also obtained for R89, which is described later. At this point, it is useful to bear in mind that arginines are charged residues which are exposed to the ions from the bulk. Radial distri- bution functions (RDF) for Cl - _{ions from the atom C}

\zeta of R64 and R89 reveal the

strong interactions between the arginines and the negatively charged elements in the outer bulk (Fig.4.10). Variations in the concentration of these elements can possibly modify relative depths of the minima. In our simulations the ion concentration was chosen to reproduce a common experimental set-up for the ionic concentration in the bulk ([K+] = 0.2 M).29,34--36,46,157 It is very difficult to determine the actual ionic strength close to the membrane in the real system, particularly when an electrochem- ical gradient across the membrane is present. Different ionic strengths from those considered in the simulations may eventually lead to the stabilisation of the X-ray configuration for R89 and R64. In any event, the main feature of the cooperative motions between the R64 and L81 residues will be retained.