Sandipan Chowdhury

Estimating the voltage-dependent free energy change of ion channels using the median voltage for activation

Voltage-gated ion channels are crucial for electrical activity and chemical signaling in a variety of cell types. Structure-activity studies involving electrophysiological characterization of mutants are widely used and allow us to quickly realize the energetic effects of a mutation by measuring macroscopic currents and fitting the observed voltage dependence of conductance to a Boltzmann equation. However, such an approach is somewhat limiting, principally because of the inherent assumption that the channel activation is a two-state process. In this analysis, we show that the area delineated by the gating charge displacement curve and its ordinate axis is related to the free energy of activation of a voltage-gated ion channel. We derive a parameter, the median voltage of charge transfer (Vm), which is proportional to this area, and prove that the chemical component of free energy change of a system can be obtained from the knowledge of Vm and the maximum number of charges transferred. Our method is not constrained by the number or connectivity of intermediate states and is applicable to instances in which the observed responses show a multiphasic behavior. We consider various models of ion channel gating with voltage-dependent steps, latent charge movement, inactivation, etc. and discuss the applicability of this approach in each case. Notably, our method estimates a net free energy change of approximately −14 kcal/mol associated with the full-scale activation of the Shaker potassium channel, in contrast to −2 to −3 kcal/mol estimated from a single Boltzmann fit. Our estimate of the net free energy change in the system is consistent with those derived from detailed kinetic models (Zagotta et al. 1994. J. Gen. Physiol. doi:10.1085/jgp.103.2.321). The median voltage method can reliably quantify the magnitude of free energy change associated with activation of a voltage-dependent system from macroscopic equilibrium measurements. This will be particularly useful in scanning mutagenesis experiments.

A Molecular Framework for Temperature-Dependent Gating of Ion Channels

Perception of heat or cold in higher organisms is mediated by specialized ion channels whose gating is exquisitely sensitive to temperature. The physicochemical underpinnings of this temperature-sensitive gating have proven difficult to parse. Here, we took a bottom-up protein design approach and rationally engineered ion channels to activate in response to thermal stimuli. By varying amino acid polarities at sites undergoing state-dependent changes in solvation, we were able to systematically confer temperature sensitivity to a canonical voltage-gated ion channel. Our results imply that the specific heat capacity change during channel gating is a major determinant of thermosensitive gating. We also show that reduction of gating charges amplifies temperature sensitivity of designer channels, which accounts for low-voltage sensitivity in all known temperature-gated ion channels. These emerging principles suggest a plausible molecular mechanism for temperature-dependent gating that reconcile how ion channels with an overall conserved transmembrane architecture may exhibit a wide range of temperature-sensing phenotypes. :

Molecular determinants of coupling between the domain III voltage sensor and pore of a sodium channel

In a voltage-dependent sodium channel, the activation of voltage sensors upon depolarization leads to the opening of the pore gates. To elucidate the principles underlying this conformational coupling, we investigated a putative gating interface in domain III of the sodium channel using voltage-clamp fluorimetry and tryptophan-scanning mutagenesis. Most mutations have similar energetic effects on voltage-sensor activation and pore opening. However, several mutations stabilized the activated voltage sensor while concurrently destabilizing the open pore. When mapped onto a homology model of the sodium channel, most localized to hinge regions of the gating interface. Our analysis shows that these residues are involved in energetic coupling of the voltage sensor to the pore when both are in resting and when both are in activated conformations, supporting the notion that electromechanical coupling in a voltage-dependent ion channel involves the movement of rigid segments connected by elastic hinges.

Molecular mechanism of allosteric modification of voltage-dependent sodium channels by local anesthetics.

The hallmark of many intracellular pore blockers such as tetra-alkylammonium compounds and local anesthetics is their ability to allosterically modify the movement of the voltage sensors in voltage-dependent ion channels. For instance, the voltage sensor of domain III is specifically stabilized in the activated state when sodium currents are blocked by local anesthetics. The molecular mechanism underlying this long-range interaction between the blocker-binding site in the pore and voltage sensors remains poorly understood. Here, using scanning mutagenesis in combination with voltage clamp fluorimetry, we systematically evaluate the role of the internal gating interface of domain III of the sodium channel. We find that several mutations in the S4–S5 linker and S5 and S6 helices dramatically reduce the stabilizing effect of lidocaine on the activation of domain III voltage sensor without significantly altering use-dependent block at saturating drug concentrations. In the wild-type skeletal muscle sodium channel, local anesthetic block is accompanied by a 21% reduction in the total gating charge. In contrast, point mutations in this critical intracellular region reduce this charge modification by local anesthetics. Our analysis of a simple model suggests that these mutations in the gating interface are likely to disrupt the various coupling interactions between the voltage sensor and the pore of the sodium channel. These findings provide a molecular framework for understanding the mechanisms underlying allosteric interactions between a drug-binding site and voltage sensors.

Thermodynamics of electromechanical coupling in voltage-gated ion channels

Membrane proteins are uniquely placed at the interface of the internal and external milieu of cells, and many of them unsurprisingly function as signal transducers involved in pathways critical for normal physiological activity. A majority of these membrane proteins have a modular architecture with

Free-energy relationships in ion channels activated by voltage and ligand

Many ion channels are modulated by multiple stimuli, which allow them to integrate a variety of cellular signals and precisely respond to physiological needs. Understanding how these different signaling pathways interact has been a challenge in part because of the complexity of underlying models. In this study, we analyzed the energetic relationships in polymodal ion channels using linkage principles. We first show that in proteins dually modulated by voltage and ligand, the net free-energy change can be obtained by measuring the charge-voltage (Q-V) relationship in zero ligand condition and the ligand binding curve at highly depolarizing membrane voltages. Next, we show that the voltage-dependent changes in ligand occupancy of the protein can be directly obtained by measuring the Q-V curves at multiple ligand concentrations. When a single reference ligand binding curve is available, this relationship allows us to reconstruct ligand binding curves at different voltages. More significantly, we establish that the shift of the Q-V curve between zero and saturating ligand concentration is a direct estimate of the interaction energy between the ligand- and voltage-dependent pathway. These free-energy relationships were tested by numerical simulations of a detailed gating model of the BK channel. Furthermore, as a proof of principle, we estimate the interaction energy between the ligand binding and voltage-dependent pathways for HCN2 channels whose ligand binding curves at various voltages are available. These emerging principles will be useful for high-throughput mutagenesis studies aimed at identifying interaction pathways between various regulatory domains in a polymodal ion channel.

Deconstructing thermodynamic parameters of a coupled system from site-specific observables

Cooperative interactions mediate information transfer between structural domains of a protein molecule and are major determinants of protein function and modulation. The prevalent theories to understand the thermodynamic origins of cooperativity have been developed to reproduce the complex behavior of a global thermodynamic observable such as ligand binding or enzyme activity. However, in most cases the measurement of a single global observable cannot uniquely define all the terms that fully describe the energetics of the system. Here we establish a theoretical groundwork for analyzing protein thermodynamics using site-specific information. Our treatment involves extracting a site-specific parameter (defined as χ value) associated with a structural unit. We demonstrate that, under limiting conditions, the χ value is related to the direct interaction terms associated with the structural unit under observation and its intrinsic activation energy. We also introduce a site-specific interaction energy term (χdiff) that is a function of the direct interaction energy of that site with every other site in the system. When combined with site-directed mutagenesis and other molecular level perturbations, analyses of χ values of site-specific observables may provide valuable insights into protein thermodynamics and structure.

Interfacial gating triad is crucial for electromechanical transduction in voltage-activated potassium channels

Gating interaction analysis reveals a cluster of three conserved amino acids that couple structural transitions in the potassium channel voltage sensor to those in the pore.

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.

Free-Energy Relationships in Ion Channels Dually Activated by Voltage and Ligand

Many ion channels are modulated by multiple stimuli which allow them to integrate a variety of cellular signals and precisely respond to physiological needs. Understanding how these different signaling pathways interact has been a challenge in part due to the complexity of underlying models. In this study, we analyzed the energetic relationships in polymodal ion channels using linkage principles. We first show that in proteins dually modulated by voltage and ligand, the net free-energy change can be obtained in a model-independent manner, by measuring the charge-voltage (QV) and the ligand binding curves, using the median transformation (Wyman, J., J. Am. Chem. Soc., 1964; Chowdhury, S., and Chanda, B., J. Gen. Phys., 2012). Next, we show that the voltage-dependent changes in ligand occupancy of the protein can be directly obtained by measuring the QV curves at multiple ligand concentrations, which also allow us to reconstruct ligand binding curves at different voltages. More significantly, we establish that the shift of the QV curve between zero and saturating ligand concentration is a direct estimate of the interaction energy between the ligand and voltage-dependent pathway. These free-energy relationships were tested by numerical simulations of a detailed gating model of the BK channel. Furthermore, as a proof of principle, we estimate the interaction energy between the ligand binding and voltage-dependent pathways for HCN2 channels whose ligand binding curves at various voltages are available. These emerging principles will be useful for high-throughput mutagenesis studies aimed at identifying interaction pathways between various regulatory domains in polymodal ion channels.