Ion velocity distributions in gramicidin channels determined with laser Doppler velocimetry.

Laser Doppler scattering from Tl(I) ions moving synchronously through an ensemble of gramicidin channels in a bilayer membrane gives their intrachannel velocity distribution. The observed velocity distributions are unimodal indicating that ion flow through some region or regions of the channels is relatively steady. Average intrachannel velocities range from 3.75 x 10(-2) m/s to 2.38 x 10(-1) m/s for transmembrane potentials between 10 mV and 150 mV, respectively.

Stationary-state distributions in membrane channels. I. Conservative flux systems.

The population distribution of cations at binding sites in membrane channels is determined for stationary states characterized by a net ion flux. For conservative systems, the net flux conserves the total intra-channel cation population for an ensemble of channels. The requisite matrix formalism is developed and illustrated for some homogeneous channels with N single-ion occupancy states with chemical and electrochemical transmembrane gradients. The lowest eigen-value approximation, which is used effectively for systems with no net cation flux, is applied to these stationary-state systems for comparison with the exact solutions. The stationary states are characterized by special thermodynamic functions for entropy, internal energy, and free energy defined by using information theory. The changes in these parameters for the transition from the equilibrium to the stationary state depend on the ratio of the next flux to the transition velocity for nearest-neighbor transitions within the channel. The free energy changes with the square of this ratio while the internal energy changes linearly.

Resolving linear and non-linear interactive kinetic mechanisms for ions in membrane channels.

Thallous ion in gramicidin channels displays the anomalous molefraction effect and other behavior that suggests its permeationmechanism might be more complicated than the mechanisms for sodiumor potassium ion permeation. The permeation is modeled by eithermultistate first order kinetics where the number of states and therate constants are modified to fit the data or an ion displacementmechanism that requires higher order rate terms. Although the twoclasses of mechanism are difficult to distinguish usingcurrent-voltage data, the two classes give different responses toa modulated transmembrane potential with frequency comparable tothe rate constants for intrachannel ion transitions. Themultistate first order kinetics give currents only at themodulation frequency. Information is transmitted in the phase andamplitude of the observed current. The non-linear iondisplacement mechanism produces harmonic frequencies. A detailedspectral analysis then distinguishes the two classes of mechanismand provides a range of frequency and phase data that permitsdetermination of the appropriate rate constants.

Cooperative denaturation kinetics of homogeneous polymers.

The kinetics of denaturation of a homogeneous, helical biopolymer with nearest neighbor interactions are described, using a kinetic Ising model in which the configuration of its neighbors dictates the transition probability for a single residue in the chain. The actual kinetics that are simulated using Monte Carlo techniques are compared with the results of analytical kinetic equations for the fraction of helix, (s), generated using the mean-field approximation. This mean-field rate equation is expanded as a hierarchy of terms that characterize the nature of rate constants for interacting systems. The first term in the expansion is first order in (s) and varies linearly with the interaction energy. Subsequent rate terms involve higher powers of (s) and demonstrate the need for nonlinear equations in systems with larger interaction energies. Both the simulations and the mean-field approximation show an intrinsic induction period for the single-step kinetic process. They also yield an apparent first-order rate constant that changes as the reaction proceeds. However, only the simulated kinetics yield ordered regions of chain and a nonzero, nearest-neighbor correlation function.

Charge dissociation and the rising phase of gating currents.

Gating currents from voltage-sensitive channels are generally attributed to the translocation or redistribution of ionic charge associated with the channel molecule. Such charge moves in the direction of the applied field to produce a decreasing current in the external circuit. An early rising phase for the gating current is observed for a number of channel systems and might be either some special kinetic redistribution of charge or an experimental artifact. A model that produces net charge in the channel through sequential molecular dissociation of a charged channel segment gives a rising phase for the gating current. Translocation of the charged segment produces the decay phase for a biphasic gating current. This kinetic molecular explanation constitutes a physical explanation for the biphasic gating currents that is consistent with present views of channel structure.

The compensation of potential changes produced by trivalent erbium ion in squid giant axon with applied potentials.

The transmembrane potential of voltage-clamped squid giant axon is increased to compensate for a reduction in the rate of potassium channel kinetics when artificial seawater with trivalent erbium ion is substituted for artificial seawater. The additional potential required to produce an equivalent rise time is a measure of the potential shift produced by the erbium ions. When the kinetics of K+ channels are matched in this manner, the maximal K+ currents are larger for the larger transmembrane potential. This observation requires a functional separation of the open K+ channel and the voltage sensor for the gating mechanism of this channel.

Response of delayed (K+) channels to the time-dependent clamping functions in squid giant axon. II. Descending ramps, hyperbolae, and exponentials.

Squid giant axons are voltage-clamped with decaying ramp, hyperbolic, and exponential potential functions to determine an input potential function that generates parametric current density vs. membrane potential (I-V) plots best approximating the I-V curves generated from the steady state delayed (K+) current densities at a series of step clamp potentials. The optimum potential function must produce consistent I-V plots over an extended range of decay periods. A five-millisecond step clamp at the largest depolarizing potential in the experiment insures identical initial conditions for all potential functions. Although all parametric I-V curves are sensitive to K+ accumulation in the periaxonal space, the alteration of the I-V curves due to this accumulation is minimized for the hyperbolic and exponential decay functions. The advantages of these functions for the rapid generation of I-V curves are discussed.

Response of delayed (K+) channels to the time-dependent clamping function in squid giant axon. I. Ascending ramps.

Squid giant axons are voltage-clamped with ascending potential ramps whose slopes range from 0.5 mV/msec to 60 mV/msec and delayed (K+) currents are observed. The parametric current-voltage curves exhibit a delay period of minimal current followed by a rapid increase of current toward a final steady state. Both the initial delay and the slope of the subsequent rising phase increase with increasing ramp slope. When the Hodgkin-Huxley equations are used to generate theoretical current-voltage curves, the sharp difference between the delay and rising phases is muted and the ramp slope must be increased to produce an adequate representation of the data. A muted biphasic response is also observed when the current-voltage curves are generated using modified Hodgkin-Huxley parameters and a correction for K+ accumulation in the periaxonal space. These modified equations provide an accurate fit for step-potential clamp current data. Since the ramp experiments include all relevant clamping potentials, the experiments provide a sensitive test for kinetic models of K+ on flow in the delayed (K+) channels of squid giant axon.