Network centred on D80

The analyses performed in the present chapter provide a complex picture of the strong coupling between the structural dynamics of the pore region and permeation. A strong interconnection exists between small rearrangements in the region behind the SF and the dynamics of the permeating ions. The main elements involved in these

Figure 4.14: Correlations and scatter plots of two permeating ions (K1 and K2) for identical ion occupancy 01010+1. Two trajectories are compared: the first (left) obtained starting from the X-ray structure, with R64 relatively far away from D80; the second (right) was a portion of a trajectories when E71-D80 and D80-W67 H- bonds were broken as a consequence of D80-R64 interactions (WT-R64D80). The figures shows that the dynamics of the residues in the region behind the selectivity

filter strongly influence the permeating K+ _{ions: the strong correlated motion is}

lost (Pearson correlation coefficient drops from 0.75 to 0.055) and the two ions move over wider ranges, as a consequence of the distortions of the filter which lead the binding sites to be spatially more weakly defined.

rearrangements have been recognised and the existence of a network centred on the aspartic acid D80 is suggested as being able to determine the state of the permeation path. In the following chapters, this network is suggested as being responsible for the fine regulation of the K+ _{current at the SF, which includes the inactivation of}

the channel.

Fig.4.15shows the network drawn following simple rules: i) blue dashed lines represent non-bonded electrostatic interactions that can eventually lead to strong H- bonds; ii) black lines represent connections through the backbone of the protein; iii) green dotted lines represent all the remaining non-bonded interactions, such as the steric interactions or repulsions between positive or partially-positive charged groups. The sizes of the nodes are weighted according to the number of edges connecting each node.

D80

E71

W67

SF

R89

L81

R64

Figure 4.15: Network of residue that regulates the conductivity in KcsA. The

figure was produced using gephi.14

The picture shows the central role of the residue D80, the main hub, which clearly arose from the calculations. Together with the surrounding H-bond donors, E71, W67, R64, R89, it creates the first level of the network (red and blue in figure). L81 belongs to a second level, comprised of the residues that play a relevant but secondary role. L81 shows a connectivity similar to the elements of the first level, but it is linked with D80 through the protein backbone. Its conformation in the WT mainly regulates the interactions between R64 and D80, while its direct influence on D80 is likely to be weaker than the elements of the first level. It is likely that additional elements belong to the second level which have not been discussed in this work. A third level can also be recognised in those residues, such as Y82, that are able to affect the behaviour of the first level without any direct contact with its element. The number of elements in the third level is also expected to be larger than

that shown in Fig. 4.15, and its existence, and the influence of its elements on the first and second levels could explain the behaviour of a number of different mutants with respect to conductivity and inactivation.

4.10 Conclusions

Different patterns of macroscopic currents in K+ _{ion channels originate from the}

complicated behaviours which are governed by small structural rearrangements of the pore region once the inner gate is opened.28,29,66_{The pore region exhibits a com-}

plex variability which is mostly obscure and requires detailed mechanistic studies at a microscopic level in order to be understood. At the present time experimental techniques are unable to investigate these microscopic dynamics and theoretical ap- proaches, such as MD, greatly help in their understanding.

In this work, comparisons of the behaviours of the KcsA WT and the mutants E71A, Y82A and R64A were performed by means of MD simulations, free-energy calculations (well-tempered metaD13_{) and statistical analyses. They provide a de-}

tailed description of the main elements involved in the rearrangements directly linked with the state of the filter, their different roles and the way they interact and col- laborate in influencing the permeation path. A complex picture is delivered that demonstrates that the hydrogen-bond network between the triad E71-D80-W67 pro- posed by Cordero-morales et al.36,37 _{is indeed a small part of a wider highly-coupled}

network of residues centred on the aspartic acid D80. The latter plays the main role in delivering to the selectivity filter structure the conformational changes that occur in the surrounding region, acting as a ``filter handle''. Modification in the state of D80 was found directly linked with the state of the SF and responsible for relevant structural rearrangements both in the mutant E71A and, most significantly, in the WT. The state of D80, in turn, was found strongly linked with the dynamics of the surrounding H-bond donors E71, W67, R64, R89. In particular the two arginines has been shown as being able to perturb the conductive conformation, promoting outward motions of the D80. In the WT R64 demonstrated to have the stronger influence, although a certain degree of cooperation between the two has been seen. Additionally the ability of R64 to interact with D80 and to influence the structure of the SF was found dependent on the conformation of the leucine in position 81 (L81). The L81 side chain behaves as a ``gate'' for R64 to approach D80.

These residues, proposed as being the principal molecular determinants for structural rearrangements of the permeation path, form a highly-correlated network. The main hub is D80 which form the main level of the network together with the

surrounding H-bond donors E71, W67, R64, R89. This result assumes a more gen- eral importance taking into account the fact that the aspartic acid D80 belongs to the signature sequence TXXTXGYGD, which is highly conserved among K+ _ion

channels and is usually surrounded by different H-bond donors.26,31,37,85 _{This sug-}

gests that the existence of similar complex networks may be a general feature of K+ _{ion channels. L81 is suggested as belonging to a second level of the network}

constituted by the residues that have a secondary role which is relevant but only indirectly determines the state of the D80 side chain.

Moreover, the residue in position 82 was proved by free-energy calculations to be capable of influencing L81, and consequently R64 variability. In the following chapter this variability of R64 will be shown to be fundamental in order to explain the increased probability of inactivation reported in the literature for Y82A, which is strongly reduced when R64 is removed in R64A.

Additionally, the role of V76 flipping was investigated. In the published literature it was referred to as being capable to generate non-conductive states of the channel. In our simulations V76 was found to be adopting flipped states very easily in all the proteins, including the non-inactivating mutant E71A. Starting from V76 flipped states of the proteins E71A and WT, permeation was seen occurring in both accompanied by reverse transitions of V76. Although conformation of V76 influences the energetic involved in the permeation, as demonstrated in previous works20_{, this}

result suggests that additional conformational readjustments are necessary in order to hinder K+_{permeation and generate long-lasting non-conductive states. Otherwise}