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Quantitative modeling of currents from a voltage gated ion channel undergoing fast inactivation.

Camacho CJ - PLoS ONE (2008)

Bottom Line: If the membrane potential is hyperpolarized, essential dynamics further suggests that the T1 domain returns to a configuration where the peptide is un-stretched and the S1-T1 linker is extended.Coupling this novel hyperpolarized substate to the closed, open and blocked pore states is enough to quantitatively estimate the number of open channels as a function of time and membrane potential.A straightforward prediction of the model is that a slow ramping of the potential leads to very small currents.

View Article: PubMed Central - PubMed

Affiliation: Department of Computational Biology, University of Pittsburgh, Pittsburgh, Pennsylvania, USA. ccamacho@pitt.edu

ABSTRACT
Ion channels play a central role in setting gradients of ion concentration and electrostatic potentials, which in turn regulate sensory systems and other functions. Based on the structure of the open configuration of the Kv1.2 channel and the suggestion that the two ends of the N-terminal inactivating peptide form a bivalent complex that simultaneously blocks the channel pore and binds to the cytoplasmic T1 domain, we propose a six state kinetic model that for the first time reproduces the kinetics of recovery of the Drosophila Shaker over the full range of time scales and hyperpolarization potentials, including tail currents. The model is motivated by a normal mode analysis of the inactivated channel that suggests that a displacement consistent with models of the closed state propagates to the T1 domain via the S1-T1 linker. This motion stretches the bound (inactivating) peptide, hastening the unblocking of the pore. This pulling force is incorporated into the rates of the open to blocked states, capturing the fast recovery phase of the current for repolarization events shorter than 1 ms. If the membrane potential is hyperpolarized, essential dynamics further suggests that the T1 domain returns to a configuration where the peptide is un-stretched and the S1-T1 linker is extended. Coupling this novel hyperpolarized substate to the closed, open and blocked pore states is enough to quantitatively estimate the number of open channels as a function of time and membrane potential. A straightforward prediction of the model is that a slow ramping of the potential leads to very small currents.

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(A) Kinetic model of inactivation and recovery of K+ channel.Three pore states: C→closed, O→open, and B→blocked by the inactivating peptide, and two channel substates: R→repolarization (membrane potential less than resting potential), and H→hyperpolarization. The kinetics of recovery is fully determined by three voltage dependent free parameters: a voltage-dependent force of energy Esp applied to the N-terminal peptide, and the on and off rates k±2 between the R and H substates. (B) Rates obtained from the literature [8]. (C) The free energy landscapes of the peptide blocking the pore in the depolarized state (green) and during repolarization (black). During repolarization, the peptide is assumed to stretch, exerting a force that contributes to the release of the ball from the pore. The dimensions of the ball and the transition state of the mostly hydrophobic ball-pore complex are estimated to be about XL = 13 Å and Xo = 3 Å (∼water layer), respectively (see Methods).
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pone-0003342-g001: (A) Kinetic model of inactivation and recovery of K+ channel.Three pore states: C→closed, O→open, and B→blocked by the inactivating peptide, and two channel substates: R→repolarization (membrane potential less than resting potential), and H→hyperpolarization. The kinetics of recovery is fully determined by three voltage dependent free parameters: a voltage-dependent force of energy Esp applied to the N-terminal peptide, and the on and off rates k±2 between the R and H substates. (B) Rates obtained from the literature [8]. (C) The free energy landscapes of the peptide blocking the pore in the depolarized state (green) and during repolarization (black). During repolarization, the peptide is assumed to stretch, exerting a force that contributes to the release of the ball from the pore. The dimensions of the ball and the transition state of the mostly hydrophobic ball-pore complex are estimated to be about XL = 13 Å and Xo = 3 Å (∼water layer), respectively (see Methods).

Mentions: In this paper, we model the kinetics of recovery of a Shaker channel that undergoes N-type inactivation. The model is based on three channel pore states (i.e., open, closed and blocked) and two substates (repolarization and hyperpolarization). The kinetic scheme, shown in Fig. 1A, is perhaps the simplest model yet proposed to account for recovery currents under different conditions. Motivated by a normal mode analysis of the Kv1.2 structure, the model assumes that during repolarization a voltage dependent elastic force pulls the inactivating peptide from the pore, whereas for hyperpolarization potentials there is no pulling force. The analysis suggests that structural transitions are triggered by voltage gating. In particular, a rotation of the S1 helix observed in models of the closed state [15], [16] acts as a “lever” that pushes the S1-T1 linker and T1 domain, generating a relative displacement of the TM and T1 domains that pulls the bivalent complex of the inactivating peptide away from the pore. If the S1-lever rotates too much, the channel can transition back into a state where the peptide is no longer stretched but the S1-T1 linker extends into a new conformation. In combination with Murrell-Lagnado and Aldrich kinetic parameters [8] of N-type inactivation and deactivation (Fig. 1B), the quantitative model resulting from fitting three voltage-dependent free parameters (Esp, k2 and k−2) reproduces key experimental observations. For instance, recovery from inactivation [14] is modeled over the full range of hyperpolarization potentials and time scales, including the fast and slow recovery phases for hyperpolarization potentials; and, the time course of tail currents [14], [17]. A striking prediction of our kinetic model is that a slow enough ramping of the membrane potential significantly hinders the ion current [12].


Quantitative modeling of currents from a voltage gated ion channel undergoing fast inactivation.

Camacho CJ - PLoS ONE (2008)

(A) Kinetic model of inactivation and recovery of K+ channel.Three pore states: C→closed, O→open, and B→blocked by the inactivating peptide, and two channel substates: R→repolarization (membrane potential less than resting potential), and H→hyperpolarization. The kinetics of recovery is fully determined by three voltage dependent free parameters: a voltage-dependent force of energy Esp applied to the N-terminal peptide, and the on and off rates k±2 between the R and H substates. (B) Rates obtained from the literature [8]. (C) The free energy landscapes of the peptide blocking the pore in the depolarized state (green) and during repolarization (black). During repolarization, the peptide is assumed to stretch, exerting a force that contributes to the release of the ball from the pore. The dimensions of the ball and the transition state of the mostly hydrophobic ball-pore complex are estimated to be about XL = 13 Å and Xo = 3 Å (∼water layer), respectively (see Methods).
© Copyright Policy
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC2551740&req=5

pone-0003342-g001: (A) Kinetic model of inactivation and recovery of K+ channel.Three pore states: C→closed, O→open, and B→blocked by the inactivating peptide, and two channel substates: R→repolarization (membrane potential less than resting potential), and H→hyperpolarization. The kinetics of recovery is fully determined by three voltage dependent free parameters: a voltage-dependent force of energy Esp applied to the N-terminal peptide, and the on and off rates k±2 between the R and H substates. (B) Rates obtained from the literature [8]. (C) The free energy landscapes of the peptide blocking the pore in the depolarized state (green) and during repolarization (black). During repolarization, the peptide is assumed to stretch, exerting a force that contributes to the release of the ball from the pore. The dimensions of the ball and the transition state of the mostly hydrophobic ball-pore complex are estimated to be about XL = 13 Å and Xo = 3 Å (∼water layer), respectively (see Methods).
Mentions: In this paper, we model the kinetics of recovery of a Shaker channel that undergoes N-type inactivation. The model is based on three channel pore states (i.e., open, closed and blocked) and two substates (repolarization and hyperpolarization). The kinetic scheme, shown in Fig. 1A, is perhaps the simplest model yet proposed to account for recovery currents under different conditions. Motivated by a normal mode analysis of the Kv1.2 structure, the model assumes that during repolarization a voltage dependent elastic force pulls the inactivating peptide from the pore, whereas for hyperpolarization potentials there is no pulling force. The analysis suggests that structural transitions are triggered by voltage gating. In particular, a rotation of the S1 helix observed in models of the closed state [15], [16] acts as a “lever” that pushes the S1-T1 linker and T1 domain, generating a relative displacement of the TM and T1 domains that pulls the bivalent complex of the inactivating peptide away from the pore. If the S1-lever rotates too much, the channel can transition back into a state where the peptide is no longer stretched but the S1-T1 linker extends into a new conformation. In combination with Murrell-Lagnado and Aldrich kinetic parameters [8] of N-type inactivation and deactivation (Fig. 1B), the quantitative model resulting from fitting three voltage-dependent free parameters (Esp, k2 and k−2) reproduces key experimental observations. For instance, recovery from inactivation [14] is modeled over the full range of hyperpolarization potentials and time scales, including the fast and slow recovery phases for hyperpolarization potentials; and, the time course of tail currents [14], [17]. A striking prediction of our kinetic model is that a slow enough ramping of the membrane potential significantly hinders the ion current [12].

Bottom Line: If the membrane potential is hyperpolarized, essential dynamics further suggests that the T1 domain returns to a configuration where the peptide is un-stretched and the S1-T1 linker is extended.Coupling this novel hyperpolarized substate to the closed, open and blocked pore states is enough to quantitatively estimate the number of open channels as a function of time and membrane potential.A straightforward prediction of the model is that a slow ramping of the potential leads to very small currents.

View Article: PubMed Central - PubMed

Affiliation: Department of Computational Biology, University of Pittsburgh, Pittsburgh, Pennsylvania, USA. ccamacho@pitt.edu

ABSTRACT
Ion channels play a central role in setting gradients of ion concentration and electrostatic potentials, which in turn regulate sensory systems and other functions. Based on the structure of the open configuration of the Kv1.2 channel and the suggestion that the two ends of the N-terminal inactivating peptide form a bivalent complex that simultaneously blocks the channel pore and binds to the cytoplasmic T1 domain, we propose a six state kinetic model that for the first time reproduces the kinetics of recovery of the Drosophila Shaker over the full range of time scales and hyperpolarization potentials, including tail currents. The model is motivated by a normal mode analysis of the inactivated channel that suggests that a displacement consistent with models of the closed state propagates to the T1 domain via the S1-T1 linker. This motion stretches the bound (inactivating) peptide, hastening the unblocking of the pore. This pulling force is incorporated into the rates of the open to blocked states, capturing the fast recovery phase of the current for repolarization events shorter than 1 ms. If the membrane potential is hyperpolarized, essential dynamics further suggests that the T1 domain returns to a configuration where the peptide is un-stretched and the S1-T1 linker is extended. Coupling this novel hyperpolarized substate to the closed, open and blocked pore states is enough to quantitatively estimate the number of open channels as a function of time and membrane potential. A straightforward prediction of the model is that a slow ramping of the potential leads to very small currents.

Show MeSH
Related in: MedlinePlus