D80 state and the dynamics of the SF and the ions

The dynamics of the region behind the pore were further investigated in order to demonstrate the direct influence on the permeation path. Simulation on E71A demonstrated that the rearrangements of the aspartic acid D80 can be delivered to the TVGYG sequence. A targeted simulation was developed to demonstrate that this is also valid for the WT. In the latter case, the state of D80 was shown as being influenced by arginines R64, which are capable of promote relatively wide transitions. The simulation was performed on a protein conformation in which the probability of these events occurring was enhanced by the maximisation of D80--R64 interactions. This conformation was obtained based on the FES shown in Fig. 4.9. An equili- brated conformation (\sim 6ns) was relaxed for20ps, restraining every L81 residue in the flipped conformation (harmonic potential with a spring constant of24kcal/mol degree2 _{and centred on 185}\circ _{). An additional restraint on\chi 1 dihedral angles of R64}

●●●●●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ●● ●●●●_● ● ● ●_● ● ●●●●●●●●●●●●●●●●●●●●●●● ●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●●● ●●●●●●●●●●●● 0 5 10 15 20 2.5 5.0 7.5 10.0 d71 PMF Configuration ● _{L81 non−flip, 10101} L81 non−flip, 00101 L81 flip, 10101 L81 flip, 00101

Figure 4.12: Estimate of the free-energy as a function of the distance d71 (FES),

the distance between side chains of D80 (defined by the C\gamma atom) and E71 (defined

by the H-bond donor oxygen belonging to the carboxyl group). Different FESs

are computed with respect of different conformations of the K+ _{ions in the SF,}

10101+0 and 00101+0, and conformations of the residue L81, flipped and non- flipped. Energy in kcal/mol, distances in \r A.

residues was applied to speed up the process (spring constant20 kcal/mol degree2 centred on - 160\circ ), even if a few tests showed that this was not strictly necessary. Further25 ps of relaxation were performed without any restraint. The R64 guani- dino groups moved towards D80, approaching the closest minimum ``b'' in the FES (Fig.4.13b). The total length of the productive sampling was \sim 45 ns.

From the beginning SF showed an increased variability with respect to the calculations originating from the X-ray structure. The R64 influence promoted long breaks of linkages between E71-D80-W67 (\sim 17 ns) for subunit C and brief disrup- tions in all the remaining subunits. The long break involved a large number of small rearrangements but can be summarised as: the initial break promoted by R64 caused an outward movement of D80 toward the extracellular side (Fig. 4.13b) which was accompanied by the stretching of the TVGYG sequence and the flipping of V76.

Scatter plot in Fig.4.13b shows for subunit C the evolution of the system in the conformational space in the first 22.5 ns, the period of time in which most of the relevant transition occurred. Three order parameters were considered: i) d73CA, the position of D80 side chain (see sec.2.4.1); ii) psi76, thepsidihedral angle of residue

V76 (see sec. 2.4.1); and iii) the length of the TVGYG (SF length in the figure) measured as the distance of the C atoms of the residue T75 and G79. The time is

SF length psi76 d73CA B A 17 16 15 14 13 13 12.5 12 11.5 11 10.5 100 0 -100 0 1.9 3.8 5.7 7.5 9.4 11.2 13.1 15 16.9 18.8 20.6 22.5 Time (ns) X-rays structure R64 R89 E71 D80 W67 L81 b) a) V76 R64 R89 D80 B A SF length d73CA psi76

b) Initial conformation and order parameters:

L81 flipped

A B

C D

Figure 4.13: Dynamics of the filter and the nearby residues during a simulation started from a conformation in which the R64-D80 interactions were maximised (b). The L81 residues in the flipped state are the reason for the maximised R64-D80

interactions. The simulation was preceded by20ps of relaxation in which the state

of every L81 residue was restrained in the flipped conformation (harmonic potential

with a spring constant of24kcal/mol degree2_{and centred on185}\circ _{) as well as the}

\chi 1dihedral angles of R64 residues (spring constant20kcal/mol degree2_{centred on}

- 160\circ ). Further25ps of relaxation were performed without any restraint. Panel

(a) shows, for comparison, the configuration of the network of residues behind in

the X-ray structure used to build the system (pdb code 1K4C157_{). c) Evolution}

of the SF region for the subunit C in the first 22.5 ns of simulation represented

in a convenient conformational space in which the three dimension are: i) the

position of D80 side chain with respect of the C\alpha atom of residue 73 used as a

stable reference (d73CA, \r A); ii) the length of the TVGYG sequence defined as the

distance between the C\alpha atoms of the residue T75 and G79 (SF length, \r A); iii) the

\psi dihedral angle of residue V76 (psi76, degrees). The extra dimension is the time, represented as a colour gradient. Additionally, two representative snapshots for the two main states of the system within this conformational space are reported. The figures demonstrate that the interactions with R64 can promote the breaking of the E71-D80-W67 linkages (black dotted lines) and the outward movement of D80 side chain, which is further stabilised by R89 (magenta dotted lines). This movement, in turn, induces a stretching of the TVGYG sequence which causes structural rearrangements in the filter. These rearrangements primarily involve the V76, which was found practically always in the flipped state for bigger values of d73CA.

represented by a colour gradient. The figure shows very brief initial transitions of V76 (psi76 from\sim - 50\circ to \sim 145\circ ) which demonstrate the inherent variability of the V76/G77 peptide group and the causes of which are difficult to determine. After 5 ns the interactions between D80 and R64 side chains promoted the breaking of E71-D80-W67 linkages and a clear drift in the position of D80 (d73CA from\sim 13.5

to \sim 15.5. This new state led to a stretching of TVGYG sequence which involved

few small rearrangements which can be seen comparing the two relevant snapshots (A and B) from the simulation reported in Fig.4.13b. Among these rearrangements, the flipping of V76 was the most noticeable, which was stabilised by the new state of D80 (Fig.4.13b) until the E71-D80-W67 linkages were re-established. The snapshot ``B'' reported in Fig. 4.13b demonstrated that the new state after the breaking of the linkages was stabilised by H-bonds between D80 and both the arginines R64 and R89. This suggests a certain degree of cooperation between the two arginines in determining the state of the D80 side chain.

The rearrangements of D80 and surrounding residues strongly influenced the dynamics of the elements within the pore. Fig.4.14shows statistical analyses on K+

ions bound to the SF (K1 and K2) in that part of the simulation when the E71--D80 H-bond was broken: scatter plots, distributions and correlations (Pearson's coeffi- cients) for the z coordinates centred with respect to the COM of the SF (defined as previously described). A comparison is shown with the same analyses performed on part of a simulation characterised by an identical configuration of K+ _{ions 01010+1}

and commencing with the X-ray conformation. The complex dynamics of the re- gion behind the pore, delivered through D80, caused rearrangements of TVGYG sequences which were able to disrupt the strong correlation between the K+ _{ions, a}

feature of the conductive state,134_{with the Pearson's coefficients dropping from0.74}

to 0.06. This resulted in an increased variability of the ions leading to wider distri- butions and unexpected reverse transitions of the innermost ion K2 01010\rightleftarrows 01001.

The re-establishment of the E71-D80-W67 linkages previously mentioned resumed the features of the conductive and was soon followed by outward transitions of the K+ _{ions 01010+1 - \rightarrow 01011+0 - \rightarrow 10101+0.}