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Probability fluxes and transition paths in a Markovian model describing complex subunit cooperativity in HCN2 channels.

Benndorf K, Kusch J, Schulz E - PLoS Comput. Biol. (2012)

Bottom Line: The time-dependent probability fluxes quantify the contributions of all 13 transitions of the model to channel activation.The binding of the first, third and fourth ligand evoked robust channel opening whereas the binding of the second ligand obstructed channel opening similar to the empty channel.These results provide quantitative insight into the complex interaction of the four structurally equal subunits, leading to non-equality in their function.

View Article: PubMed Central - PubMed

Affiliation: Friedrich-Schiller-Universität Jena, Universitätsklinikum Jena, Institut für Physiologie II, Jena, Germany. Klaus.Benndorf@mti.uni-jena.de

ABSTRACT
Hyperpolarization-activated cyclic nucleotide-modulated (HCN) channels are voltage-gated tetrameric cation channels that generate electrical rhythmicity in neurons and cardiomyocytes. Activation can be enhanced by the binding of adenosine-3',5'-cyclic monophosphate (cAMP) to an intracellular cyclic nucleotide binding domain. Based on previously determined rate constants for a complex Markovian model describing the gating of homotetrameric HCN2 channels, we analyzed probability fluxes within this model, including unidirectional probability fluxes and the probability flux along transition paths. The time-dependent probability fluxes quantify the contributions of all 13 transitions of the model to channel activation. The binding of the first, third and fourth ligand evoked robust channel opening whereas the binding of the second ligand obstructed channel opening similar to the empty channel. Analysis of the net probability fluxes in terms of the transition path theory revealed pronounced hysteresis for channel activation and deactivation. These results provide quantitative insight into the complex interaction of the four structurally equal subunits, leading to non-equality in their function.

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Unidirectional probability flux densities in the closed-open isomerizations.The time courses of the unidirectional probability flux densities, fU,CxOx and fU,OxCx (x = 0…4) for the closed-open isomerizations are plotted together with the respective net probability flux densities, fCxOx, when applying 7.5 µM fcAMP (left) and removing it (right). The arrows indicate the time point of concentration change. For explanation see text.
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pcbi-1002721-g006: Unidirectional probability flux densities in the closed-open isomerizations.The time courses of the unidirectional probability flux densities, fU,CxOx and fU,OxCx (x = 0…4) for the closed-open isomerizations are plotted together with the respective net probability flux densities, fCxOx, when applying 7.5 µM fcAMP (left) and removing it (right). The arrows indicate the time point of concentration change. For explanation see text.

Mentions: For the principal conformational change of the closed-open isomerization we considered the time courses of the unidirectional probability flux densities, fU,CxOx>0 and fU,OxCx<0 (x = 0…4), at the saturating fcAMP concentration of 7.5 µM fcAMP and related them to the net probability flux density, fCxOx (Fig. 6; c.f. Fig. 2C), according to(6)For the time after application of fcAMP, these time courses show that the transitions C0↔O0 and C2↔O2 are functionally irrelevant. In contrast, the net probability flux densities in the transitions C1↔O1 and C3↔O3 are robust and the unidirectional probability flux densities exceed the respective net probability flux density substantially. An extreme surplus of the unidirectional probability flux densities with respect to the net probability flux density is inherent in the transition C4↔O4, suggesting pronounced conformational flexibility when the channel is fully liganded. It is also notable that the empty activated channel (Fig. 6, top left) is much less flexible in this sense compared to the fully liganded channel (Fig. 6, bottom left).


Probability fluxes and transition paths in a Markovian model describing complex subunit cooperativity in HCN2 channels.

Benndorf K, Kusch J, Schulz E - PLoS Comput. Biol. (2012)

Unidirectional probability flux densities in the closed-open isomerizations.The time courses of the unidirectional probability flux densities, fU,CxOx and fU,OxCx (x = 0…4) for the closed-open isomerizations are plotted together with the respective net probability flux densities, fCxOx, when applying 7.5 µM fcAMP (left) and removing it (right). The arrows indicate the time point of concentration change. For explanation see text.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3475657&req=5

pcbi-1002721-g006: Unidirectional probability flux densities in the closed-open isomerizations.The time courses of the unidirectional probability flux densities, fU,CxOx and fU,OxCx (x = 0…4) for the closed-open isomerizations are plotted together with the respective net probability flux densities, fCxOx, when applying 7.5 µM fcAMP (left) and removing it (right). The arrows indicate the time point of concentration change. For explanation see text.
Mentions: For the principal conformational change of the closed-open isomerization we considered the time courses of the unidirectional probability flux densities, fU,CxOx>0 and fU,OxCx<0 (x = 0…4), at the saturating fcAMP concentration of 7.5 µM fcAMP and related them to the net probability flux density, fCxOx (Fig. 6; c.f. Fig. 2C), according to(6)For the time after application of fcAMP, these time courses show that the transitions C0↔O0 and C2↔O2 are functionally irrelevant. In contrast, the net probability flux densities in the transitions C1↔O1 and C3↔O3 are robust and the unidirectional probability flux densities exceed the respective net probability flux density substantially. An extreme surplus of the unidirectional probability flux densities with respect to the net probability flux density is inherent in the transition C4↔O4, suggesting pronounced conformational flexibility when the channel is fully liganded. It is also notable that the empty activated channel (Fig. 6, top left) is much less flexible in this sense compared to the fully liganded channel (Fig. 6, bottom left).

Bottom Line: The time-dependent probability fluxes quantify the contributions of all 13 transitions of the model to channel activation.The binding of the first, third and fourth ligand evoked robust channel opening whereas the binding of the second ligand obstructed channel opening similar to the empty channel.These results provide quantitative insight into the complex interaction of the four structurally equal subunits, leading to non-equality in their function.

View Article: PubMed Central - PubMed

Affiliation: Friedrich-Schiller-Universität Jena, Universitätsklinikum Jena, Institut für Physiologie II, Jena, Germany. Klaus.Benndorf@mti.uni-jena.de

ABSTRACT
Hyperpolarization-activated cyclic nucleotide-modulated (HCN) channels are voltage-gated tetrameric cation channels that generate electrical rhythmicity in neurons and cardiomyocytes. Activation can be enhanced by the binding of adenosine-3',5'-cyclic monophosphate (cAMP) to an intracellular cyclic nucleotide binding domain. Based on previously determined rate constants for a complex Markovian model describing the gating of homotetrameric HCN2 channels, we analyzed probability fluxes within this model, including unidirectional probability fluxes and the probability flux along transition paths. The time-dependent probability fluxes quantify the contributions of all 13 transitions of the model to channel activation. The binding of the first, third and fourth ligand evoked robust channel opening whereas the binding of the second ligand obstructed channel opening similar to the empty channel. Analysis of the net probability fluxes in terms of the transition path theory revealed pronounced hysteresis for channel activation and deactivation. These results provide quantitative insight into the complex interaction of the four structurally equal subunits, leading to non-equality in their function.

Show MeSH