Examining cooperative gating phenomena in voltage-dependent potassium channels: taking the energetic approach

Estimating the Cholesterol Affinity of Integral Membrane Proteins from Experimental Data

The cholesterol affinities of many integral plasma membrane proteins have been estimated by molecular computation. However, these values lack experimental confirmation. We therefore developed a simple mathematical model to extract sterol affinity constants and stoichiometries from published isotherms for the dependence of the activity of such proteins on the membrane cholesterol concentration. The binding curves for these proteins are sigmoidal, with strongly lagged thresholds attributable to competition for the cholesterol by bilayer phospholipids. The model provided isotherms that matched the experimental data using published values for the sterol association constants and stoichiometries of the phospholipids. Three oligomeric transporters were found to bind cholesterol without cooperativity, with dimensionless association constants of 35 for Kir3.4* and 100 for both Kir2 and a GAT transporter. (The corresponding ΔG° values were -8.8, -11.4, and -11.4 kJ/mol, respectively). These association constants are significantly lower than those for the phospholipids, which range from ∼100 to 6000. The BK channel, the nicotinic acetylcholine receptor, and the M192I mutant of Kir3.4* appear to bind multiple cholesterol molecules cooperatively (n = 2 or 4), with subunit affinities of 563, 950, and 700, respectively. The model predicts that the three less avid transporters are approximately half-saturated in their native plasma membranes; hence, they are sensitive to variations in cholesterol in vivo. The more avid proteins would be nearly saturated in vivo. The method can be applied to any integral protein or other ligands in any bilayer for which there are reasonable estimates of the sterol affinities and stoichiometries of the phospholipids.

Allosteric signaling in C-linker and cyclic nucleotide-binding domain of HCN2 channels

Opening of hyperpolarization-activated cyclic nucleotide-modulated (HCN) channels is controlled by membrane hyperpolarization and binding of cyclic nucleotides to the tetrameric cyclic nucleotide-binding domain (CNBD), attached to the C-linker (CL) disk. Confocal patch-clamp fluorometry revealed pronounced cooperativity of ligand binding among protomers. However, by which pathways allosteric signal transmission occurs remained elusive. Here, we investigate how changes in the structural dynamics of the CL-CNBD of mouse HCN2 upon cAMP binding relate to inter- and intrasubunit signal transmission. Applying a rigidity-theory-based approach, we identify two intersubunit and one intrasubunit pathways that differ in allosteric coupling strength between cAMP-binding sites or toward the CL. These predictions agree with results from electrophysiological and patch-clamp fluorometry experiments. Our results map out distinct routes within the CL-CNBD that modulate different cAMP-binding responses in HCN2 channels. They signify that functionally relevant submodules may exist within and across structurally discernable subunits in HCN channels.

Intra- and Intersubunit Dynamic Binding in Kv4.2 Channel Closed-State Inactivation

We studied the kinetics and structural determinants of closed-state inactivation (CSI) in Kv4.2 channels, considering a multistep process and the possibility that both intra- and intersubunit dynamic binding (i.e., loss and restoration of physical contact) may occur between the S4-S5 linker, including the initial S5 segment (S4S5), and the S6 gate. We expressed Kv4.2 channels in Xenopus oocytes and measured the onset of low-voltage inactivation under two-electrode voltage clamp. Indicative of a transitory state, the onset kinetics were best described by a double-exponential function. To examine the involvement of individual S4S5 and S6 amino acid residues in dynamic binding, we studied S4S5 and S6 single alanine mutants and corresponding double mutants. Both transitory and steady-state inactivation were modified by these mutations, and we quantified the mutational effects based on apparent affinities for the respective inactivated states. Double-mutant cycle analyses revealed strong functional coupling of the S6 residues V404 and I412 to all tested S4S5 residues. To examine whether dynamic S4S5/S6 binding occurs within individual α-subunits or between neighboring α-subunits, we performed a double-mutant cycle analysis with Kv4.2 tandem-dimer constructs. The constructs carried either an S4S5/S6 double mutation in the first α-subunit and no mutation in the second (concatenated) α-subunit or an S4S5 point mutation in the first α-subunit and an S6 point mutation in the second α-subunit. Our results support the notion that CSI in Kv4.2 channels is a multistep process that involves dynamic binding both within individual α-subunits and between neighboring α-subunits.

Intersubunit Concerted Cooperative and cis-Type Mechanisms Modulate Allosteric Gating in Two-Pore-Domain Potassium Channel TREK-2

In response to diverse stimuli, two-pore-domain potassium channel TREK-2 regulates cellular excitability, and hence plays a key role in mediating neuropathic pain, mood disorders and ischemia through. Although more and more input modalities are found to achieve their modulations via acting on the channel, the potential role of subunit interaction in these modulations remains to be explored. In the current study, the deletion (lack of proximal C-terminus, ΔpCt) or point mutation (G312A) was introduced into TREK-2 subunits to limit K⁺ conductance and used to report subunit stoichiometry. The constructs were then combined with wild type (WT) subunit to produce concatenated dimers with defined composition, and the gating kinetics of these channels to 2-Aminoethoxydiphenyl borate (2-APB) and extracellular pH (pH_o) were characterized. Our results show that combination of WT and ΔpCt/G312A subunits reserves similar gating properties to that of WT dimmers, suggesting that the WT subunit exerts dominant and positive effects on the mutated one, and thus the two subunits controls channel gating via a concerted cooperative manner. Further introduction of ΔpCt into the latter subunit of heterodimeric channel G312A-WT or G312A-G312A attenuated their sensitivity to 2-APB and pH_o alkalization, implicating that these signals were transduced by a cis-type mechanism. Together, our findings elucidate the mechanisms for how the two subunits control the pore gating of TREK-2, in which both intersubunit concerted cooperative and cis-type manners modulate the allosteric regulations induced by 2-APB and pH_o alkalization.

Determinants of ligand selectivity in a cyclic nucleotide-regulated potassium channel

Preference for cGMP binding to a cyclic nucleotide–binding domain can achieved by compensating for ligand dehydration or through retention of solvation waters in the bound state.

Cyclic nucleotide–binding (CNB) domains regulate the activity of channels, kinases, exchange factors, and transcription factors. These proteins are highly variable in their ligand selectivity; some are highly selective for either cAMP or cGMP, whereas others are not. Several molecular determinants of ligand selectivity in CNB domains have been defined, but these do not provide a complete view of the selectivity mechanism. We performed a thorough analysis of the ligand-binding properties of mutants of the CNB domain from the MlotiK1 potassium channel. In particular, we defined which residues specifically favor cGMP or cAMP. Inversion of ligand selectivity, from favoring cAMP to favoring cGMP, was only achieved through a combination of three mutations in the ligand-binding pocket. We determined the x-ray structure of the triple mutant bound to cGMP and performed molecular dynamics simulations and a biochemical analysis of the effect of the mutations. We concluded that the increase in cGMP affinity and selectivity does not result simply from direct interactions between the nucleotide base and the amino acids introduced in the ligand-binding pocket residues. Rather, tighter cGMP binding over cAMP results from the polar chemical character of the mutations, from greater accessibility of water molecules to the ligand in the bound state, and from an increase in the structural flexibility of the mutated binding pocket.

A self-consistent approach for determining pairwise interactions that underlie channel activation

Net free-energy measurements can be combined with mutant cycle analysis to determine interaction energies between specific amino acid pairs during channel activation.

Signaling proteins such as ion channels largely exist in two functional forms, corresponding to the active and resting states, connected by multiple intermediates. Multiparametric kinetic models based on sophisticated electrophysiological experiments have been devised to identify molecular interactions of these conformational transitions. However, this approach is arduous and is not suitable for large-scale perturbation analysis of interaction pathways. Recently, we described a model-free method to obtain the net free energy of activation in voltage- and ligand-activated ion channels. Here we extend this approach to estimate pairwise interaction energies of side chains that contribute to gating transitions. Our approach, which we call generalized interaction-energy analysis (GIA), combines median voltage estimates obtained from charge-voltage curves with mutant cycle analysis to ascertain the strengths of pairwise interactions. We show that, for a system with an arbitrary gating scheme, the nonadditive contributions of amino acid pairs to the net free energy of activation can be computed in a self-consistent manner. Numerical analyses of sequential and allosteric models of channel activation also show that this approach can measure energetic nonadditivities even when perturbations affect multiple transitions. To demonstrate the experimental application of this method, we reevaluated the interaction energies of six previously described long-range interactors in the Shaker potassium channel. Our approach offers the ability to generate detailed interaction energy maps in voltage- and ligand-activated ion channels and can be extended to any force-driven system as long as associated “displacement” can be measured.

State-dependent network connectivity determines gating in a K+ channel

X-ray crystallography has provided tremendous insight into the different structural states of membrane proteins and, in particular, of ion channels. However, the molecular forces that determine the thermodynamic stability of a particular state are poorly understood. Here we analyze the different X-ray structures of an inwardly rectifying potassium channel (Kir1.1) in relation to functional data we obtained for over 190 mutants in Kir1.1. This mutagenic perturbation analysis uncovered an extensive, state-dependent network of physically interacting residues that stabilizes the pre-open and open states of the channel, but fragments upon channel closure. We demonstrate that this gating network is an important structural determinant of the thermodynamic stability of these different gating states and determines the impact of individual mutations on channel function. These results have important implications for our understanding of not only K⁺ channel gating but also the more general nature of conformational transitions that occur in other allosteric proteins.

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Functional validation of different crystallographic states of Kir channels

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Presence of a state-dependent gating network revealed by large-scale mutagenesis

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Biased effect of mutations on Kir channel gating due to open-state destabilization

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Long-range allosteric coupling mediated by a physically connected residue network

Inter-subunit interactions across the upper voltage sensing-pore domain interface contribute to the concerted pore opening transition of Kv channels

The tight electro-mechanical coupling between the voltage-sensing and pore domains of Kv channels lies at the heart of their fundamental roles in electrical signaling. Structural data have identified two voltage sensor pore inter-domain interaction surfaces, thus providing a framework to explain the molecular basis for the tight coupling of these domains. While the contribution of the intra-subunit lower domain interface to the electro-mechanical coupling that underlies channel opening is relatively well understood, the contribution of the inter-subunit upper interface to channel gating is not yet clear. Relying on energy perturbation and thermodynamic coupling analyses of tandem-dimeric Shaker Kv channels, we show that mutation of upper interface residues from both sides of the voltage sensor-pore domain interface stabilizes the closed channel state. These mutations, however, do not affect slow inactivation gating. We, moreover, find that upper interface residues form a network of state-dependent interactions that stabilize the open channel state. Finally, we note that the observed residue interaction network does not change during slow inactivation gating. The upper voltage sensing-pore interaction surface thus only undergoes conformational rearrangements during channel activation gating. We suggest that inter-subunit interactions across the upper domain interface mediate allosteric communication between channel subunits that contributes to the concerted nature of the late pore opening transition of Kv channels.

KCNQ1 channels do not undergo concerted but sequential gating transitions in both the absence and the presence of KCNE1 protein

The co-assembly of KCNQ1 with KCNE1 produces I(KS), a K(+) current, crucial for the repolarization of the cardiac action potential. Mutations in these channel subunits lead to life-threatening cardiac arrhythmias. However, very little is known about the gating mechanisms underlying KCNQ1 channel activation. Shaker channels have provided a powerful tool to establish the basic gating mechanisms of voltage-dependent K(+) channels, implying prior independent movement of all four voltage sensor domains (VSDs) followed by channel opening via a last concerted cooperative transition. To determine the nature of KCNQ1 channel gating, we performed a thermodynamic mutant cycle analysis by constructing a concatenated tetrameric KCNQ1 channel and by introducing separately a gain and a loss of function mutation, R231W and R243W, respectively, into the S4 helix of the VSD of one, two, three, and four subunits. The R231W mutation destabilizes channel closure and produces constitutively open channels, whereas the R243W mutation disrupts channel opening solely in the presence of KCNE1 by right-shifting the voltage dependence of activation. The linearity of the relationship between the shift in the voltage dependence of activation and the number of mutated subunits points to an independence of VSD movements, with each subunit incrementally contributing to channel gating. Contrary to Shaker channels, our work indicates that KCNQ1 channels do not experience a late cooperative concerted opening transition. Our data suggest that KCNQ1 channels in both the absence and the presence of KCNE1 undergo sequential gating transitions leading to channel opening even before all VSDs have moved.

Thermodynamic coupling between activation and inactivation gating in potassium channels revealed by free energy molecular dynamics simulations

The amount of ionic current flowing through K⁺ channels is determined by the interplay between two separate time-dependent processes: activation and inactivation gating. Activation is concerned with the stimulus-dependent opening of the main intracellular gate, whereas inactivation is a spontaneous conformational transition of the selectivity filter toward a nonconductive state occurring on a variety of timescales. A recent analysis of multiple x-ray structures of open and partially open KcsA channels revealed the mechanism by which movements of the inner activation gate, formed by the inner helices from the four subunits of the pore domain, bias the conformational changes at the selectivity filter toward a nonconductive inactivated state. This analysis highlighted the important role of Phe103, a residue located along the inner helix, near the hinge position associated with the opening of the intracellular gate. In the present study, we use free energy perturbation molecular dynamics simulations (FEP/MD) to quantitatively elucidate the thermodynamic basis for the coupling between the intracellular gate and the selectivity filter. The results of the FEP/MD calculations are in good agreement with experiments, and further analysis of the repulsive, van der Waals dispersive, and electrostatic free energy contributions reveals that the energetic basis underlying the absence of inactivation in the F103A mutation in KcsA is the absence of the unfavorable steric interaction occurring with the large Ile100 side chain in a neighboring subunit when the intracellular gate is open and the selectivity filter is in a conductive conformation. Macroscopic current analysis shows that the I100A mutant indeed relieves inactivation in KcsA, but to a lesser extent than the F103A mutant.

Probing the transition state of the allosteric pathway of the Shaker Kv channel pore by linear free-energy relations

Long-range coupling between distant functional elements of proteins may rely on allosteric communication trajectories lying along the protein structure, as described in the case of the Shaker voltage-activated potassium (Kv) channel model allosteric system. Communication between the distant Kv channel activation and slow inactivation pore gates was suggested to be mediated by a network of local pairwise and higher-order interactions among the functionally unique residues that constitute the allosteric trajectory. The mechanism by which conformational changes propagate along the Kv channel allosteric trajectory to achieve pore opening, however, remains unclear. Such conformational changes may propagate in either a concerted or a sequential manner during the reaction coordinate of channel opening. Residue-level structural information on the transition state of channel gating is required to discriminate between these possibilities. Here, we combine patch-clamp electrophysiology recordings of Kv channel gating and analysis using linear free-energy relations, focusing on a select set of residues spanning the allosteric trajectory of the Kv channel pore. We show that all allosteric trajectory residues tested exhibit an open-like conformation in the transition state of channel opening, implying that coupling interactions occur along the trajectory break in a concerted manner upon moving from the closed to the open state. Energetic coupling between the Kv channel gates thus occurs in a concerted fashion in both the spatial and the temporal dimensions, strengthening the notion that such trajectories correspond to pathways of mechanical deformation along which conformational changes propagate.