It's Time for Entropic Clocks: The Roles of Random Chain Protein Sequences in Timing Ion Channel Processes Underlying Action Potential Properties.

In recent years, it has become clear that intrinsically disordered protein segments play diverse functional roles in many cellular processes, thus leading to a reassessment of the classical structure-function paradigm. One class of intrinsically disordered protein segments is entropic clocks, corresponding to unstructured random protein chains involved in timing cellular processes. Such clocks were shown to modulate ion channel processes underlying action potential generation, propagation, and transmission. In this review, we survey the role of entropic clocks in timing intra- and inter-molecular binding events of voltage-activated potassium channels involved in gating and clustering processes, respectively, and where both are known to occur according to a similar 'ball and chain' mechanism. We begin by delineating the thermodynamic and timing signatures of a 'ball and chain'-based binding mechanism involving entropic clocks, followed by a detailed analysis of the use of such a mechanism in the prototypical Shaker voltage-activated K+ channel model protein, with particular emphasis on ion channel clustering. We demonstrate how 'chain'-level alternative splicing of the Kv channel gene modulates entropic clock-based 'ball and chain' inactivation and clustering channel functions. As such, the Kv channel model system exemplifies how linkage between alternative splicing and intrinsic disorder enables the functional diversity underlying changes in electrical signaling.

Regulating Shaker Kv channel clustering by hetero-oligomerization.

Scaffold protein-mediated voltage-dependent ion channel clustering at unique membrane sites, such as nodes of Ranvier or the post-synaptic density plays an important role in determining action potential properties and information coding. Yet, the mechanism(s) by which scaffold protein-ion channel interactions lead to channel clustering and how cluster ion channel density is regulated are mostly unknown. This molecular-cellular gap in understanding channel clustering can be bridged in the case of the prototypical Shaker voltage-activated potassium channel (Kv), as the mechanism underlying the interaction of this channel with its PSD-95 scaffold protein partner is known. According to this mechanism, changes in the length of the intrinsically disordered channel C-terminal chain, brought about by alternative splicing to yield the short A and long B chain subunit variants, dictate affinity to PSD-95 and further controls cluster homo-tetrameric Kv channel density. These results raise the hypothesis that heteromeric subunit assembly serves as a means to regulate Kv channel clustering. Since both clustering variants are expressed in similar fly tissues, it is reasonable to assume that hetero-tetrameric channels carrying different numbers of high- (A) and low-affinity (B) subunits could assemble, thereby giving rise to distinct cluster Kv channel densities. Here, we tested this hypothesis using high-resolution microscopy, combined with quantitative clustering analysis. Our results reveal that the A and B clustering variants can indeed assemble to form heteromeric channels and that controlling the number of the high-affinity A subunits within the hetero-oligomer modulates cluster Kv channel density. The implications of these findings for electrical signaling are discussed.

Direct analysis of cooperativity in multisubunit allosteric proteins.

Allosteric regulation of protein function is a fundamental phenomenon of major importance in many cellular processes. Such regulation is often achieved by ligand-induced conformational changes in multimeric proteins that may give rise to cooperativity in protein function. At the heart of allosteric mechanisms offered to account for such phenomenon, involving either concerted or sequential conformational transitions, lie changes in intersubunit interactions along the ligation pathway of the protein. However, structure-function analysis of such homooligomeric proteins by means of mutagenesis, although it provides valuable indirect information regarding (allosteric) mechanisms of action, it does not define the contribution of individual subunits nor interactions thereof to cooperativity in protein function, because any point mutation introduced into homooligomeric proteins will be present in all subunits. Here, we present a general strategy for the direct analysis of cooperativity in multisubunit proteins that combines measurement of the effects on protein function of all possible combinations of mutated subunits with analysis of the hierarchy of intersubunit interactions, assessed by using high-order double-mutant cycle-coupling analysis. We show that the pattern of high-order intersubunit coupling can serve as a discriminative criterion for defining concerted versus sequential conformational transitions underlying protein function. This strategy was applied to the particular case of the voltage-activated potassium channel protein (Kv) to provide compelling evidence for a concerted all-or-none activation gate opening of the Kv channel pore domain. An direct and detailed analysis of the contribution of high-order intersubunit interactions to cooperativity in the function of an allosteric protein has not previously been presented.

Principles underlying energetic coupling along an allosteric communication trajectory of a voltage-activated K+ channel.

The information flow between distal elements of a protein may rely on allosteric communication trajectories lying along the protein's tertiary or quaternary structure. To unravel the underlying features of energy parsing along allosteric pathways in voltage-gated K(+) channels, high-order thermodynamic coupling analysis was performed. We report that such allosteric trajectories are functionally conserved and delineated by well defined boundaries. Moreover, allosteric trajectories assume a hierarchical organization whereby increasingly stronger layers of cooperative residue interactions act to ensure efficient and cooperative long-range coupling between distal channel regions. Such long-range communication is brought about by a coupling of local and global conformational changes, suggesting that the allosteric trajectory also corresponds to a pathway of physical deformation. Supported by theoretical analyses and analogy to studies analyzing the contribution of long-range residue coupling to protein stability, we propose that such experimentally derived trajectory features are a general property of allosterically regulated proteins.

Molecular and cellular correlates in Kv channel clustering: entropy-based regulation of cluster ion channel density.

Scaffold protein-mediated ion channel clustering at unique membrane sites is important for electrical signaling. Yet, the mechanism(s) by which scaffold protein-ion channel interactions lead to channel clustering or how cluster ion channel density is regulated is mostly not known. The voltage-activated potassium channel (Kv) represents an excellent model to address these questions as the mechanism underlying its interaction with the post-synaptic density 95 (PSD-95) scaffold protein is known to be controlled by the length of the extended 'ball and chain' sequence comprising the C-terminal channel region. Here, using sub-diffraction high-resolution imaging microscopy, we show that Kv channel 'chain' length regulates Kv channel density with a 'bell'-shaped dependence, reflecting a balance between thermodynamic considerations controlling 'chain' recruitment by PSD-95 and steric hindrance due to the spatial proximity of multiple channel molecules. Our results thus reveal an entropy-based mode of channel cluster density regulation that mirrors the entropy-based regulation of the Kv channel-PSD-95 interaction. The implications of these findings for electrical signaling are discussed.

Correction: Live cell single molecule tracking and localization microscopy of bioorthogonally labeled plasma membrane proteins.

Correction for 'Live cell single molecule tracking and localization microscopy of bioorthogonally labeled plasma membrane proteins' by Andres I. König et al., Nanoscale, 2020, 12, 3236-3248, DOI: 10.1039/C9NR08594G.

Live cell single molecule tracking and localization microscopy of bioorthogonally labeled plasma membrane proteins.

Tracking the localization and mobility of individual proteins in live cells is key for understanding how they mediate their function. Such information can be obtained from single molecule imaging techniques including as Single Particle Tracking (SPT) and Single Molecule Localization Microscopy (SMLM). Genetic code expansion (GCE) combined with bioorthogonal chemistry offers an elegant approach for direct labeling of proteins with fluorescent dyes, holding great potential for improving protein labeling in single molecule applications. Here we calibrated conditions for performing SPT and live-SMLM of bioorthogonally labeled plasma membrane proteins in live mammalian cells. Using SPT, the diffusion of bioorthogonally labeled EGF receptor and the prototypical Shaker voltage-activated potassium channel (Kv) was measured and characterized. Applying live-SMLM to bioorthogonally labeled Shaker Kv channels enabled visualizing the plasma membrane distribution of the channel over time with ∼30 nm accuracy. Finally, by competitive labeling with two Fl-dyes, SPT and live-SMLM were performed in a single cell and both the density and dynamics of the EGF receptor were measured at single molecule resolution in subregions of the cell. We conclude that GCE and bioorthogonal chemistry is a highly suitable, flexible approach for protein labeling in quantitative single molecule applications that outperforms current protein live-cell labeling approaches.

Bridging the Molecular-Cellular Gap in Understanding Ion Channel Clustering.

The clustering of many voltage-dependent ion channel molecules at unique neuronal membrane sites such as axon initial segments, nodes of Ranvier, or the post-synaptic density, is an active process mediated by the interaction of ion channels with scaffold proteins and is of immense importance for electrical signaling. Growing evidence indicates that the density of ion channels at such membrane sites may affect action potential conduction properties and synaptic transmission. However, despite the emerging importance of ion channel density for electrical signaling, how ion channel-scaffold protein molecular interactions lead to cellular ion channel clustering, and how this process is regulated are largely unknown. In this review, we emphasize that voltage-dependent ion channel density at native clustering sites not only affects the density of ionic current fluxes but may also affect the conduction properties of the channel and/or the physical properties of the membrane at such locations, all changes that are expected to affect action potential conduction properties. Using the concrete example of the prototypical Shaker voltage-activated potassium channel (Kv) protein, we demonstrate how insight into the regulation of cellular ion channel clustering can be obtained when the molecular mechanism of ion channel-scaffold protein interaction is known. Our review emphasizes that such mechanistic knowledge is essential, and when combined with super-resolution imaging microscopy, can serve to bridge the molecular-cellular gap in understanding the regulation of ion channel clustering. Pressing questions, challenges and future directions in addressing ion channel clustering and its regulation are discussed.

Evolutionary and functional insights into the mechanism underlying body-size-related adaptation of mammalian hemoglobin.

Hemoglobin (Hb) represents a model protein to study molecular adaptation in vertebrates. Although both affinity and cooperativity of oxygen binding to Hb affect tissue oxygen delivery, only the former was thought to determine molecular adaptations of Hb. Here, we suggest that Hb affinity and cooperativity reflect evolutionary and physiological adaptions that optimized tissue oxygen delivery. To test this hypothesis, we derived the relationship between the Hill coefficient and the relative affinity and conformational changes parameters of the Monod-Wymann-Changeux allosteric model and graphed the 'biophysical Hill landscape' describing this relation. We found that mammalian Hb cooperativity values all reside on a ridge of maximum cooperativity along this landscape that allows for both gross- and fine-tuning of tissue oxygen unloading to meet the distinct metabolic requirements of mammalian tissues for oxygen. Our findings reveal the mechanism underlying body size-related adaptation of mammalian Hb. The generality and implications of our findings are discussed.

Direct Evidence for a Similar Molecular Mechanism Underlying Shaker Kv Channel Fast Inactivation and Clustering.

The fast inactivation and clustering functions of voltage-dependent potassium channels play fundamental roles in electrical signaling. Recent evidence suggests that both these distinct channel functions rely on intrinsically disordered N- and C-terminal cytoplasmic segments that function as entropic clocks to time channel inactivation or scaffold protein-mediated clustering, both relying on what can be described as a "ball and chain" binding mechanism. Although the mechanisms employed in each case are seemingly analogous, both were put forward based on bulky chain deletions and further exhibit differences in reaction order. These considerations raised the question of whether the molecular mechanisms underlying Kv channel fast inactivation and clustering are indeed analogous. By taking a "chain"-level chimeric channel approach involving long and short spliced inactivation or clustering "chain" variants of the Shaker Kv channel, we demonstrate the ability of native inactivation and clustering "chains" to substitute for each other in a length-dependent manner, as predicted by the "ball and chain" mechanism. Our results thus provide direct evidence arguing that the two completely unrelated Shaker Kv channel processes of fast inactivation and clustering indeed occur according to a similar molecular mechanism.

Allosteric regulation of Bacillus subtilis threonine deaminase, a biosynthetic threonine deaminase with a single regulatory domain.

The enzyme threonine deaminase (TD) is a key regulatory enzyme in the pathway for the biosynthesis of isoleucine. TD is inhibited by its end product, isoleucine, and this effect is countered by valine, the product of a competing biosynthetic pathway. Sequence and structure analyses have revealed that the protomers of many TDs have C-terminal regulatory domains, composed of two ACT-like subdomains, which bind isoleucine and valine, while others have regulatory domains of approximately half the length, composed of only a single ACT-like domain. The regulatory responses of TDs from both long and short sequence varieties appear to have many similarities, but there are significant differences. We describe here the allosteric properties of Bacillus subtilis TD ( bsTD), which belongs to the short variety of TD sequences. We also examine the effects of several mutations in the regulatory domain on the kinetics of the enzyme and its response to effectors. The behavior of bsTD can be analyzed and rationalized using a modified Monod-Wyman-Changeux model. This analysis suggests that isoleucine is a negative effector, and valine is a very weak positive effector, but that at high concentrations valine inhibits activity by competing with threonine for binding to the active site. The behavior of bsTD is contrasted with the allosteric behavior reported for TDs from Escherichia coli and Arabidopsis thaliana, TDs with two subdomains. We suggest a possible evolutionary pathway to the more complex regulatory effects of valine on the activity of TDs of the long sequence variety, e.g., E. coli TD.

Using the MWC model to describe heterotropic interactions in hemoglobin.

Hemoglobin is a classical model allosteric protein. Research on hemoglobin parallels the development of key cooperativity and allostery concepts, such as the 'all-or-none' Hill formalism, the stepwise Adair binding formulation and the concerted Monod-Wymann-Changuex (MWC) allosteric model. While it is clear that the MWC model adequately describes the cooperative binding of oxygen to hemoglobin, rationalizing the effects of H+, CO2 or organophosphate ligands on hemoglobin-oxygen saturation using the same model remains controversial. According to the MWC model, allosteric ligands exert their effect on protein function by modulating the quaternary conformational transition of the protein. However, data fitting analysis of hemoglobin oxygen saturation curves in the presence or absence of inhibitory ligands persistently revealed effects on both relative oxygen affinity (c) and conformational changes (L), elementary MWC parameters. The recent realization that data fitting analysis using the traditional MWC model equation may not provide reliable estimates for L and c thus calls for a re-examination of previous data using alternative fitting strategies. In the current manuscript, we present two simple strategies for obtaining reliable estimates for MWC mechanistic parameters of hemoglobin steady-state saturation curves in cases of both evolutionary and physiological variations. Our results suggest that the simple MWC model provides a reasonable description that can also account for heterotropic interactions in hemoglobin. The results, moreover, offer a general roadmap for successful data fitting analysis using the MWC model.

An evolutionarily conserved network of amino acids mediates gating in voltage-dependent potassium channels.

A novel sequence-analysis technique for detecting correlated amino acid positions in intermediate-size protein families (50-100 sequences) was developed, and applied to study voltage-dependent gating of potassium channels. Most contemporary methods for detecting amino acid correlations within proteins use very large sets of data, typically comprising hundreds or thousands of evolutionarily related sequences, to overcome the relatively low signal-to-noise ratio in the analysis of co-variations between pairs of amino acid positions. Such methods are impractical for voltage-gated potassium (Kv) channels and for many other protein families that have not yet been sequenced to that extent. Here, we used a phylogenetic reconstruction of paralogous Kv channels to follow the evolutionary history of every pair of amino acid positions within this family, thus increasing detection accuracy of correlated amino acids relative to contemporary methods. In addition, we used a bootstrapping procedure to eliminate correlations that were statistically insignificant. These and other measures allowed us to increase the method's sensitivity, and opened the way to reliable identification of correlated positions even in intermediate-size protein families. Principal-component analysis applied to the set of correlated amino acid positions in Kv channels detected a network of inter-correlated residues, a large fraction of which were identified as gating-sensitive upon mutation. Mapping the network of correlated residues onto the 3D structure of the Kv channel from Aeropyrum pernix disclosed correlations between residues in the voltage-sensor paddle and the pore region, including regions that are involved in the gating transition. We discuss these findings with respect to the evolutionary constraints acting on the channel's various domains. The software is available on our website

Entropic clocks in the service of electrical signaling: 'Ball and chain' mechanisms for ion channel inactivation and clustering.

Electrical signaling in the nervous system relies on action potential generation, propagation and transmission. Such processes are dynamic in nature and rely on precisely timed events associated with voltage-dependent ion channel conformational transitions between their primary open, closed and inactivated states and clustering at unique membrane sites. In voltage-dependent potassium (Kv) channels, fast inactivation and clustering processes rely on entropic clock chains as described by 'ball and chain' mechanisms, suggesting important roles for such chains in electrical signaling. Here, we consider evidence supporting the proposed 'ball and chain' mechanisms for Kv channel fast inactivation and clustering associated with intrinsically disordered N- and C-terminal regions of the protein, respectively. Based on this comparison, we delineate the requirements that argue for such a process and establish the thermodynamic signature of a 'ball and chain' mechanism. Finally, we demonstrate how 'chain'-level alternative splicing of the Kv channel gene modulates the entropic clock-based 'ball and chain' inactivation and clustering channel functions underlying changes in electrical signaling. As such, the Kv channel model system exemplifies how linkage between alternative splicing and intrinsic disorder enables functional diversity.

Alternative splicing modulates Kv channel clustering through a molecular ball and chain mechanism.

Ion channel clustering at the post-synaptic density serves a fundamental role in action potential generation and transmission. Here, we show that interaction between the Shaker Kv channel and the PSD-95 scaffold protein underlying channel clustering is modulated by the length of the intrinsically disordered C terminal channel tail. We further show that this tail functions as an entropic clock that times PSD-95 binding. We thus propose a 'ball and chain' mechanism to explain Kv channel binding to scaffold proteins, analogous to the mechanism describing channel fast inactivation. The physiological relevance of this mechanism is demonstrated in that alternative splicing of the Shaker channel gene to produce variants of distinct tail lengths resulted in differential channel cell surface expression levels and clustering metrics that correlate with differences in affinity of the variants for PSD-95. We suggest that modulating channel clustering by specific spatial-temporal spliced variant targeting serves a fundamental role in nervous system development and tuning.

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.

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.

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

Allosteric regulation of protein function is often achieved by changes in protein conformation induced by changes in chemical or electrical potential. In multisubunit proteins, such conformational changes may give rise to cooperativity in ligand binding. Conformational changes between open and closed states are central to the function of voltage-activated potassium (Kv) channel proteins, homotetrameric pore-forming membrane proteins involved in generating and shaping action potentials in excitable cells. Accessible to extremely high signal-to-noise ratio in functional measurements, combined with the availability of high-resolution structural data for different conformations of the protein, the Kv channel represents an excellent allosteric model system to further understand the aspects of synergism and cooperative effects in protein function. In this chapter, we demonstrate how the use of the simple law of mass action combined with thermodynamic mutant cycle energetic coupling analysis of Kv channel gating can be used to provide valuable information regarding (1) how cooperativity in Kv channel pore opening can be assessed; (2) how one can directly discriminate whether conformational transitions during Kv channel pore opening occur in a concerted or sequential manner; and (3) how mechanistically, the coupling between distant activation gate and selectivity filter functional elements of the prototypical Shaker Kv channel protein might be achieved. In addition to providing valuable insight into the function of this important protein, the conclusions reached at using high-order thermodynamic energetic coupling analysis applied to the Kv channel allosteric model system reveal much about the function of allosteric proteins, in general.