A Microscopic Capacitor Model of Voltage Coupling in Membrane Proteins: Gating Charge Fluctuations in Ci-VSD

A novel theoretical framework reveals more than one voltage-sensing pathway in the lateral membrane of outer hair cells

Outer hair cell (OHC) electromotility amplifies acoustic vibrations throughout the frequency range of hearing. Electromotility requires that the lateral membrane protein prestin undergo a conformational change upon changes in the membrane potential to produce an associated displacement charge. The magnitude of the charge displaced and the mid-reaction potential (when one half of the charge is displaced) reflects whether the cells will produce sufficient gain at the resting membrane potential to boost sound in vivo. Voltage clamp measurements performed under near-identical conditions ex vivo show the charge density and mid-reaction potential are not always the same, confounding interpretation of the results. We compare the displacement charge measurements in OHCs from rodents with a theory shown to exhibit good agreement with in silico simulations of voltage-sensing reactions in membranes. This model equates the charge density to the potential difference between two pseudo-equilibrium states of the sensors when they are in a stable conformation and not contributing to the displacement current. The model predicts this potential difference to be one half of its value midway into the reaction, when one equilibrium conformation transforms to the other pseudo-state. In agreement with the model, we find the measured mid-reaction potential to increase as the charge density decreases to exhibit a negative slope of ∼1/2. This relationship suggests that the prestin sensors exhibit more than one stable hyperpolarized state and that voltage sensing occurs by more than one pathway. We determine the electric parameters for prestin sensors and use the analytical expressions of the theory to estimate the energy barriers for the two voltage-dependent pathways. This analysis explains the experimental results, supports the theoretical approach, and suggests that voltage sensing occurs by more than one pathway to enable amplification throughout the frequency range of hearing.

Gating Charge Calculations by Computational Electrophysiology Simulations

Electrical cell signaling requires adjustment of ion channel, receptor, or transporter function in response to changes in membrane potential. For the majority of such membrane proteins, the molecular details of voltage sensing remain insufficiently understood. Here, we present a molecular dynamics simulation-based method to determine the underlying charge movement across the membrane-the gating charge-by measuring electrical capacitor properties of membrane-embedded proteins. We illustrate the approach by calculating the charge transfer upon membrane insertion of the HIV gp41 fusion peptide, and validate the method on two prototypical voltage-dependent proteins, the Kv1.2 K⁺ channel and the voltage sensor of the Ciona intestinalis voltage-sensitive phosphatase, against experimental data. We then use the gating charge analysis to study how the T1 domain modifies voltage sensing in Kv1.2 channels and to investigate the voltage dependence of the initial binding of two Na⁺ ions in Na⁺-coupled glutamate transporters. Our simulation approach quantifies various mechanisms of voltage sensing, enables direct comparison with experiments, and supports mechanistic interpretation of voltage sensitivity by fractional amino acid contributions.

Theory of single-molecule controlled rotation experiments, predictions, tests, and comparison with stalling experiments in F1-ATPase

A recently proposed chemomechanical group transfer theory of rotary biomolecular motors is applied to treat single-molecule controlled rotation experiments. In these experiments, single-molecule fluorescence is used to measure the binding and release rate constants of nucleotides by monitoring the occupancy of binding sites. It is shown how missed events of nucleotide binding and release in these experiments can be corrected using theory, with F₁-ATP synthase as an example. The missed events are significant when the reverse rate is very fast. Using the theory the actual rate constants in the controlled rotation experiments and the corrections are predicted from independent data, including other single-molecule rotation and ensemble biochemical experiments. The effective torsional elastic constant is found to depend on the binding/releasing nucleotide, and it is smaller for ADP than for ATP. There is a good agreement, with no adjustable parameters, between the theoretical and experimental results of controlled rotation experiments and stalling experiments, for the range of angles where the data overlap. This agreement is perhaps all the more surprising because it occurs even though the binding and release of fluorescent nucleotides is monitored at single-site occupancy concentrations, whereas the stalling and free rotation experiments have multiple-site occupancy.

Analyzing the electrogenicity of cytochrome c oxidase

Measurements of voltage changes in response to charge separation within membrane proteins can offer fundamental information on spectroscopically "invisible" steps. For example, results from studies of voltage changes associated with electron and proton transfer in cytochrome c oxidase could, in principle, be used to discriminate between different theoretical models describing the molecular mechanism of proton pumping. Earlier analyses of data from these measurements have been based on macroscopic considerations that may not allow for exploring the actual molecular mechanisms. Here, we have used a coarse-grained model describing the relation between observed voltage changes and specific charge-transfer reactions, which includes an explicit description of the membrane, the electrolytes, and the electrodes. The results from these calculations offer mechanistic insights at the molecular level. Our main conclusion is that previously assumed mechanistic evidence that was based on electrogenic measurements is not unique. However, the ability of our calculations to obtain reliable voltage changes means that we have a tool that can be used to describe a wide range of electrogenic charge transfers in channels and transporters, by combining voltage measurements with other experiments and simulations to analyze new mechanistic proposals.

Estimation of Potentials of Mean Force from Nonequilibrium Pulling Simulations Using Both Minh-Adib Estimator and Weighted Histogram Analysis Method

Nonequilibrium pulling simulations have been a useful approach for investigating a variety of physical and biological problems. The major target in the simulations is to reconstruct reliable potentials of mean force (PMFs) or unperturbed free-energy profiles for quantitatively addressing both equilibrium mechanistic properties and contributions from nonequilibrium processes. While several current nonequilibrium methods were shown to be accurate in computing free-energy profiles in systems with relatively simple dynamics, they have proved to be unsuitable in more complicated systems. To extend the applicability of nonequilibrium sampling, we demonstrate a novel method that combines Minh-Adib's bidirectional estimator with nonlinear WHAM equations to reconstruct and assess PMFs from relatively fast pulling trajectories. We test the method in a one-dimensional model system and in a system of an antibiotic gramicidin-A (gA) channel, which is considered a significant challenge for nonequilibrium sampling. We identify key parameters for efficiently performing pulling simulations to improve and ensure the convergence and accuracy of estimated PMFs. We show that a few pulling trajectories of a relatively fast pulling speed v = 10 Å/ns can return a fair estimate of the PMF of a single potassium ion in gA.