In the following sections, we evaluate first the model parameters and the robustness of the method by comparing several structures of the model channel KcsA. We then perform calculations with the pore modules of a library of structures ranging from simple structures with two transmembrane domains (Fig. 1, bi,ii) to complex potassium channels (Fig. 1, biii,iv) (Table 1) and discuss functional implications of our findings. Finally, we investigate highly mechanically coupled and uncoupled regions in ion channels.
The anisotropic network of KcsA can be reduced to four amino acid positions
As a test case, we started the analysis with the pore module of KcsA, the best studied \(\hbox {K}^+\) channel pore. The mechanical connections in this structure can be represented by the aforementioned ANMs. The edges in such a network represent physical interactions in a protein, which, in turn, are reduced to harmonic interactions between all residues closer than a critical cut-off distance. Previous studies had shown that analyses of these network models are able to generate global maps for the mechanical connections in these proteins (Shen et al. 2002; Shrivastava and Bahar 2006; Hoffgaard et al. 2015). All this should provide information on interactions between functional domains, which are essential for the function of these channel pores.
In the first application, we ask the question whether it is possible to reduce the network models to an even smaller size without compromising their main functional features. For this purpose, we minimize the AIC value (which is equivalent to maximization of \(f^\mathrm {sc}\)) according to Eq. (12) for models of decreased size. The AIC value quantifies the trade-off between the number of fitting parameters and accuracy of the fitting results. Since KcsA is a homotetramer with 4l amino acids (l per monomer), we were choosing the model residues with a fourfold symmetry (see Sect. 2.5).
The analysis shows that the lowest AIC value is obtained with a value of \(|{\mathcal{M}}| = 16\), i.e., 4 residues for each monomer. A representative plot which shows a minimum of the AIC value for 16 residues in the KcsA tetramer is shown in Fig. 3a. In Fig. 3b, we exemplify the stability of those “cluster assignments”. For this, we consider AIC minimization with a different number of model residues \(|{\mathcal{M}}| \in \{8,12,16,20,24\}\) (which correspond due to the fourfold symmetry to 2, 3, 4, 5, 6 clusters, respectively). Our results show that the identified residues for \(|{\mathcal{M}}| = 12\) are a subset of the identified residues for \(|{\mathcal{M}}| = 16\), which are again a subset of the identified residues for \(|{\mathcal{M}}| = 20\). These findings imply a stability of the AIC minimization for a varying number of model residues. Supplement Table 2 shows the same calculation performed on the other channels with a Kir-type architecture. As for KcsA, a total number of \(|{\mathcal{M}}| = 16\) model residues have the lowest AIC value in all channels.
The critical residues in the KcsA structure in Fig. 3a,b were calculated with the constraint that they must be separated by more than 4 amino acids. This criterion was introduced to lower the importance of mechanical connections, which are determined by covalent bonds in the protein backbone; the \(\alpha \)-helices determining the TMDs are characterized by consecutive \(i+4\) interactions along the backbone. To test the impact of this constraint on the general results of the calculation, the same procedure was repeated with the KcsA channel in Fig. 3c using a minimum separation along the backbone of \(|i-j| > s\) with \(s \in \{0, 1, 2 , 3\}\). The results show that a value of \(s \le 2\) generates clusters of residues in the inner transmembrane domain, which include the cluster of critical residues discovered with a value of \(s=4\) (Fig. 3d). An increase in the s values to 3 lowers the impact of direct amino acid interactions and uncovers essentially the same 4 residues that were identified in the analysis of Fig. 4a. From these control calculations, we conclude that the constraint of \(s \ge 4\) guarantees the discovery of critical residues in the entire protein.
Location of critical amino acids in pore module is insensitive to presence or absence of cytosolic C-terminus
Figure 4a shows the location of the critical four residues in the pore module of the KcsA channel (1BL8). The respective amino acids are 76 in the filter, 71 in the pore helix, and 105 and 110 in the inner transmembrane domain (Table 1). Before evaluating functional implications of the critical residues, we first address the question whether the results are depending on the length of the sequence. Notably, most of the pores, which are evaluated here, are truncated structures from more complex channels (see Table 1).
To test the influence of the length of the structure on the critical residues, we performed the same analysis as in Fig. 4 with two KcsA structures, which include the entire C-termini (Fig. 5). This analysis highlights the same residues in the filter domain and similar residues in the inner transmembrane domain as in the reference structure (Fig. 4). The results of this analysis confirm the robustness of the approach. They furthermore suggest that the residues 71 and 76 in the filter domain have a unique importance for function. The residues in the transmembrane domain seem less precisely defined and are presumably more a representation of small critical regions than individual amino acids. The data further imply that the detection of the critical residues is not an artifact of the truncation of the structure.
In the analyses so far, we have only considered four residues with the best score value. The aforementioned data, however, imply that the precise position of the four critical residues can be variable. To judge the significance of these four individual residues, we plotted a normalized histogram of the four residues within the 10 and 100 best AIC score values in Fig. 4a. The data show that the aforementioned four residues occur with a different frequency. While V76 emerges in all cases as a single residue, the other three residues are the peak values of small regional maxima. This indicates that V76 has a unique importance for the function of the KcsA channel. The other residues seem to represent small hot spots, which are important for the function of the KcsA channel. In the pore helix, also the residue V70 seems to be important for function, together with E71. In the inner TM domain, we identify a small cluster of residues around amino acid (AA) M96 and V95 and two clusters around L105 and L110.
The predictions are robust and most critical residues are discovered in different KcsA Structures
In a further step, we analyzed the robustness of the predictions with different KcsA structures. Calculations as in Fig. 4a were repeated with structures obtained under different experimental conditions, e.g., in the absence and presence of a blocker or from KcsA mutants (Table 1). Another difference was that the proteins were crystallized either without or with a antigen-binding fragment (FAB) (Fig. 6). A comparison of the results should imply whether a monoclonal FAB fragment, which supports crystallization by mechanically stabilizing the protein, has any influence on the mechanical connectivity in the channel. The results in Fig. 6/Table 1 show that the critical residues in the filter, which were identified in Fig. 4a, are discovered with high propensity in all KcsA structures. The results of this analysis underscore that these residues seem to be most critical for the functional mechanics of the channel. This appears to be independent of a block of the pore for example by Ba\(^{2+}\) (pdb 2ITD) or quaternary ammonium compounds (pdb 1JVM, 2W0F). Also the presence or absence of the FAB fragments has no appreciable impact on the mechanical connectivity of the KcsA pore.
Scrutiny of the remaining residues reveals that they are all located, independent from the crystallization conditions, in the inner transmembrane domain. Their precise localization is more variable than those in the filter domain. This result can already be anticipated from the data in Fig. 4a, which suggests the importance of small clusters of residues rather than of individual amino acids. Independent on whether the structures were obtained with or without FAB fragments, the analysis highlights the crucial importance of residues 105 or 110 and their direct vicinity. The two exceptions are found in the pdbs 3F5W and 2NLJ. In the former structure, the critical residues in the transmembrane domain occur further upstream. In the latter structure, the residues around 105 and 110 are found with a lower propensity, while the maximum is shifted to residue M96, a residue, which shows up with a lower frequency in all other KcsA structures. This finding is very interesting, because the channel structure of pdb 2NLJ was obtained from a KcsA mutant in which the critical M96 was mutated into an V (Lockless et al. 2007). In this channel, the filter remains in a collapsed configuration even in high \(\hbox {K}^+\) concentrations. It is tempting to speculate that our analysis is picking up this change in the mechanics of the KcsA channel, which is imposed by a mutation of this critical residue.
The same critical amino acid positions, which are identified in KcsA, are also relevant in other \(\hbox {K}^+\) channel pores
In a next step, we performed the same analysis to a set of other channel pore modules (from KirBac3.1, NaK, MthK, Kcv) which all have the same architecture as KcsA (Fig. 1b, c). An interesting test case is Kcv, because this miniature channel comprises not more than the pore module of all other \(\hbox {K}^+\) channels. Even though there is no experimental structure available for this channel, we still considered it for the analysis, because homology models exhibit spontaneous ion translocation in MD simulations (Tayefeh et al. 2009; Andersson et al. 2018). The remaining pores are from Kir-type channels, which have in addition more or less long cytosolic domains (Fig. 1). When we used the same analysis, which was performed on KcsA, on these channels, the obtained 10 highest scores show very similar results (Fig. 7; left panel).
With the exception of the Kcv channel, we found in all cases a singular peak for the residue, which is equivalent to V76 in KcsA in all other channels. Also the equivalent of E71 in KcsA was detected in all other channels with a high frequency. The results of this analysis underscore the unique importance of a residue in the selectivity filter of all channel pores, which is equivalent to the V76 position in KcsA. Also important are residues in the pore helix, which are equivalent to V70 and E71 in KcsA. The situation is more variable in the inner TM domain. All channels contain in this domain clusters with important residues. However, they appear with different frequencies and at different positions relative to the selectivity filter. For example, while the KirBac channel has a small cluster of residues with a low frequency approx. 15 amino acids (AA) downstream of the GYG motive, the critical AA in KcsA are ca. 30 AA away of this domain.
The results so far underpin that the pore modules of \(\hbox {K}^+\) channels, which arrange as tetramer with 2 transmembrane domains, have a common functional architecture with four critical amino acid positions, two in the selectivity filter and two at the end of the inner transmembrane domain. The position of these critical residues is not identical in different channels but in the same region of the channel. The channels, which were used for this analysis, exhibit different degrees of selectivity for \(\hbox {K}^+\) over Na\(^+\) (e.g., KcsA versus NaK) and are gated by different mechanisms (e.g., KcsA versus MthK). The finding that they all share the same critical residues suggests that these positions in the protein are responsible for general functional features but not for selectivity or gating.
The critical amino acid positions are relevant for function
A scrutiny of the rich literature on structure/function correlates in the KcsA channel confirms the importance for the four crucial amino acids, which emerged from our analysis. All four amino acids turned out in a number of experimental and computational studies as key amino acids for function. The E71 residue in the pore helix has been described as a crucial part of a complex hydrogen-bond network between the pore helix and the selectivity filter. It involves the side chains of E71, D80, and W67, a water molecule, and the backbone atoms of G77 and Y78. Mutations of residues in this network affect the central functions of the channel, namely ion selectivity (Cheng et al. 2011) and gating (Cordero-Morales et al. 2011). Additionally, also the tetramer stability is affected (Choi and Heginbotham 2004). A well-studied mutation in this context is E71A, which suppresses an inactivation process similar to C-type inactivation in KcsA.
The amino acid Val76 in the selectivity filter is mentioned in a number of papers as an important amino acid for proper folding of the KcsA channel (Splitt et al. 2000; Raja and Vales 2009). But also channel function is sensitive to changes in this position. A mutant of KcsA, which imitates the filter sequence of Kir channels (V76I), shows a lower unitary conductance and reduced open probability (Raja and Vales 2009). This stresses an impact of this site on both key functions of channels, namely, conductance and gating. Mechanistic insight for the function of V76 in the KcsA channel comes from the analysis of NMR spectra of the full-length KcsA channel in the activated and inactivated state (Imai et al. 2010). From these data, it occurs as if V76 undergoes a large chemical shift when the channel switches between the resting state, the activation state, and the inactivation state. This has been interpreted as evidence for the importance of this amino acid in filter gating. It has been speculated that this gating is due to a formation of hydrogen bonds between V76 and water and a consequent removal of \(\hbox {K}^+\) from the filter (Imai et al. 2010).
The amino acid L110 and its immediate neighbors in the inner TMD of KcsA have been identified in computational (Shen et al. 2002; Shrivastava and Bahar 2006) and experimental studies (Liu et al. 2001; Sompornpisut et al. 2001) as a crucial amino acid in channel function. It is part of a pivot region for inter-subunit interactions formed by a stretch of AAs from Thr107 to Leu110. In this domain, in particular, L110 makes in the truncated KcsA structure an inter-unit contact between the inner TMDs in KcsA (Minor et al. 1999). Computational data including normal-mode analysis suggest that this region is undergoing a low-energy deformation in the context of the operation of the inner gate. This gating motion is discussed in the context with a kink that occurs at Thr 107 in KcsA and which is conserved in KirBac as Gly134 (Shrivastava and Bahar 2006).
Also, the AA L105 is mentioned in the context of KcsA function albeit less frequently than the three other AA. One piece of evidence for its importance in KcsA function is derived from the aforementioned NMR analysis, which reports the chemical shift between the resting state, and the active and inactive states of this channel (Imai et al. 2010). In the NMR spectra, it occurs that the chemical shift of V76 with its impact on filter gating is correlated with that of L105 and V95. Interesting to note is that the plots in Figs. 4a and 7a show an additional peak at residues around V95 (see also Supplement Fig. 9), suggesting that this region is part of a functional hot spot for KcsA gating (Shen et al. 2002; Imai et al. 2010). This may suggest a concerted action of residues in the inner TM and the selectivity filter in channel gating. Other evidence for a role of residue L105 and its vicinity in KcsA function comes from a genetic selection of KcsA mutants with a gain of function. All these mutations were clustering in the helix bundle crossing of the inner TMD including mutations in L105 (Paynter et al. 2008). The functional impact of this amino acid may once again depend on the fact that the inner TMD is involved in subunit–subunit interactions in which Ala29 on the first outer TMD is interacting with L105 and V106 in the inner TMD (Williamson et al. 2002).
A comparison of the critical residues between the different channels (Fig. 7, Supplement Fig. 9) shows that they are, with the exception of the Val in the selectivity filter, not formed by conserved amino acids. This suggests that the proteins have retained throughout evolution a common architecture rather than individual amino acids. A combination of the present results and experimental data from the respective channel pores advocates two architectural principles, which characterize these proteins. One structural feature seems to be a stabilization of the filter domain by an interaction of the pore helix with the selectivity filter. Experimental evidence for these interactions is available for all the channels (Miloshevsky et al. 2008; Shen and Guo 2009; Rauh et al. 2018). The second conserved building principle seems to be a flexibility of the lower part of the inner transmembrane domain. The critical cluster(s) of residues in this domain in all channels (apart from Kcv) are close to a Gly residue (Fig. 7, Supplement Fig. 9). This AA and its neighboring residues have been identified in many channels as a key hinge for promoting flexibility in the lower part of this domain (Jiang et al. 2002b; Rosenhouse-Dantsker and Logothetis 2006; Grottesi et al. 2005; Alam and Jiang 2009a). Interesting to note is that the same functional principle is maintained in Kcv. Only in this channel, the transition from a rigid upper part to a flexible lower part of the transmembrane domains is achieved by a \(\pi \)-stacking between a His in the inner and a partner amino acid in the outer transmembrane domain (Gebhardt et al. 2011). The cluster of critical residues in TM2, which emerge from the present analysis, includes the aforementioned His83 in Kcv (Fig. 7).
The critical amino acid positions are also relevant in the pore modules from complex channels
Next, we analyzed the equivalent pore modules from more complex channels (Fig. 1). The latter include the pores of KvATP, Eag1, HCN1, and hERG from which the pore module was cut out in silico. Additionally, also the pore module from the bacterial Kv channel KvLm-PM (Table 1) was included. This is an interesting case, because this pore was experimentally separated from the voltage sensor domain before crystallization (Santos et al. 2012). The same pore module is functional in the context of the whole protein but also as an isolated pore.
The analysis was further supplemented by a representative of a K2P channel and two TRPV channels. These channels were included into the analysis, because the pore of K2P channels corresponds structurally to the alpha subunits of two joined pores from the aforementioned \(\hbox {K}^+\) channels (Fig. 1biv,c). The pores of TRPV channels are interesting for the present analysis, because their global architecture is similar to that of the canonical \(\hbox {K}^+\) channels. However, in spite of this similarity, TRPV channels exhibit very different ion selectivity and gating features from canonical \(\hbox {K}^+\) channels (Huynh et al. 2016).
The results of the analyses show that the critical amino acids, which correspond to 71 and 76 in KcsA are also detected with a high scoring value in all the pore modules of \(\hbox {K}^+\) channels with a 6 TMD type architecture (Fig. 1bii). Like in KcsA and the other Kir-type channels, all the pores from Kv channels also exhibit small clusters of important amino acids exclusively in the inner transmembrane domain. This finding is consistent with the general view that this domain has a central importance in the gating of \(\hbox {K}^+\) channels (Magidovich and Yifach 2004). The precise localization of the critical residues, however, seems more variable among the different channels than those in the filter domain. One reason for this variability could be the difference in the length of the loop, which connects the filter with the downstream transmembrane domain. To account for this variability, we aligned the data to the start of the transmembrane domain of each of the Kv channels. The plot in Fig. 7 shows that the clusters of critical amino acids in the transmembrane domain occur after this correction in similar positions. This underscores a conserved mechanical connectivity in these channels independent on whether they are ligand or voltage gated. An interesting observation is that the critical residues in the respective transmembrane domain are not identical among very similar channels like Eag1, hERG, and HCN1. This discrepancy may originate from the fact that the structure of hERG was solved in the open state, while those of the two others are from a closed channel (Wang and MacKinnon 2017). Comparison of the respective structures shows that large deviations between an open and closed channel occur in particular in the inner transmembrane domain. The location of the critical residues in the inner transmembrane domain may capture this difference in structure.
The data furthermore imply that the pore module maintains its basic mechanical connectivity independent on whether it is isolated in Kir-type channels or connected to a voltage-sensing domain in Kv channels. This finding is in good agreement with experimental data on the KvLm channel, in which the pore is functional in the entire protein as well as in an isolated form (Santos et al. 2012).
The data further suggest that differences in ion selectivity are not affected by this mechanical properties of the pore; there is no apparent difference between all the \(\hbox {K}^+\) selective channels and channels like NaK and HCN1, which also exhibit a conductance for Na\(^+\) (Lee et al. 2005; Alam and Jiang 2009b). Furthermore, the conserved mechanical connectivity in the pore module seems not to be responsible for the difference in voltage sensitivity; there is no obvious difference between the outward rectifying Eag1 (Whicher and MacKinnon 2016) and the inward rectifying HCN1 channel (Lee et al. 2005).
In recent studies, we used anisotropic network models of HCN1 to understand the mechanical connections, which are involved in the modulation of gating of this channel by cAMP binding in the cytosolic termini (Gross et al. 2018; Porro et al. 2019). In the context of the present results, we asked the question whether the critical residues, which are highlighted in the reduced model (Fig. 7), maintain their importance in the full protein. To answer this question, we performed an analysis on the full channel structure and identified the same residues as in the isolated pore (Table 1). This again suggests the existence of crucial interactions between the filter and the inner transmembrane domain. Their relative importance seems to be maintained even in the full channel. Furthermore, these findings highlight the stability of our method and its ability to detect important residues even in large channels.
The pores of KP2 and TRPV channels differ from \(\hbox {K}^+\) channels with tetramer architecture
The results from all the canonical \(\hbox {K}^+\) channel pores differ from those obtained with the KP2 channel and the TRPVs. The two critical positions in the filter corresponding to 71 and 76 in KcsA are also highlighted in the K2P channel but with a low propensity. The remaining results bear little similarity between the K2P channel and the other \(\hbox {K}^+\) channels. This may reflect the fact that K2P channels are unlike the other \(\hbox {K}^+\) channels not fourfold symmetric tetramers. Also, unlike the other \(\hbox {K}^+\) channels, mammalian K2P channels like the present K2P4.1 contain a large extracellular domain, the cap structure, which extends from the first pore loop (Lolicato et al. 2014). All these structural differences seem to generate a different mechanical connectivity in the pore of these channels.
Scrutiny of the data from the TRPV channels shows that they differ, in spite of their overall similarity in structure (Huynh et al. 2016), dramatically from each other (see Fig. 10). Based on this diversity, which may reflect their difference in gating (Huynh et al. 2016), it is impossible to discuss any similarities and differences from \(\hbox {K}^+\) channels.
Detection of mechanical coupling/uncoupling in channel pores
Using the AIC function as a score value, we identified the amino acids, which are most important for the dynamics of a channel protein. In the next step, we intended to uncover the amino acids which exhibit the strongest and weakest mechanical coupling in the five Kir-type channel proteins, respectively. To obtain this information, we substituted in the simulated annealing procedure the AIC function as a score value with Eqs. (13) and (14) as a measure for the coupling strength. In this procedure, the sum of the square root (Eq. (13)) was used as a score to estimate the maximal connectivity and the sum of the square (Eq. (14)) as score for the most independent residues.Footnote 5 Since the analysis in Fig. 3 suggested that 4 residues per monomer are sufficient for describing the basic dynamics in the channels, we limited the analysis of connected and disconnected residues also to 4 per monomer.
Figure 4b shows the estimates of the maximal connectivity in the KcsA channel. The critical residues and the frequency of detection are basically the same as those obtained from the AIC function. The data suggest that the importance of the critical amino acids for the function in the KcsA channel originates from their mutual interaction in the mechanical network of the channel protein. The most prominent interactions are located in the filter/pore helix; connectivity in the inner TM domain is also important but apparently less relevant. The general conclusion from this analysis, which suggests a mechanical coupling between these residues in the KcvA channel, is supported by the aforementioned experimental data. Most of the reports on the importance of the critical residues stress a mutual interaction between them in channel gating (Shrivastava and Bahar 2006; Shen et al. 2002; Imai et al. 2010).
The general implication of the discovered couplings for the function of all channel pores is again supported by a comparison of the results from all channels. For all the five Kir-type pores, the top scores for connectivity are found for the residues in the pore helix and the filter, which correspond to E71 and V76 in KcsA (Fig. 8left panel). Other critical residues occur in the inner transmembrane domain but at different distances from the selectivity filter. Interesting to note is that, in all channels, an additional more or less pronounced peak of residues occurs just upstream of the pore helix. In KcsA, this peak is located around residues R64,A65.
The analysis of the most disconnected residues in the KcsA channel (Fig. 4c) provides an additional test for consistency of the method. This analysis should only pick up noise in the system from the most flexible parts of the ion channel, namely loops and the termini of the protein. With this procedure, we, indeed, uncovered two residues in clusters around P55 and V84 and two at the end of each transmembrane domain (A23, E118). The inherent high degree of flexibility of the ends of transmembrane domains bears the hazard that the latter positions are an artifact of a truncation of the pores. To test this assumption, we repeated the analysis with the elongated version of the KcsA structure (Fig. 5c,d). In this structure, we found that one of the disconnected residues was again identified at the end of the elongated helix domain. This implies that the ends of the protein structures with the high mobility are maximally disconnected. This is relevant for a protein like the Kcv channel in which the total structure is identical to that analyzed here. In the case of truncated structures like those of KirBac and KcsA, the identification of independent residues in these positions is presumably artifacts and not further considered here.
The remaining amino acids, with a high degree of independency in the KcsA channel (Fig. 4c) and in all other Kir-type channels (Fig. 8), are as expected associated with the flexible loops, which connect the outer transmembrane domain with the pore helix (=turret domain) and with the loop, which connects the selectivity filter with the inner TM domain. We anticipate that this information about less critical regions of a protein is helpful in protein design, e.g., for the question of where to attach an additional domain without disrupting the structure.