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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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Time courses of net probability flux density in the C4L-O4L model.The time courses for the net probability flux density, fXY, in the C4L-O4L model were computed for the event of applying the ligand fcAMP (7.5 µM; left diagrams) and removing it again (right diagrams). The inset diagrams show the original diagram with an either higher amplitude or time resolution. (A) Net probability flux densities between closed states following ligand application (left) and removal (right) obtained by equation (1). (B) Net probability flux densities between open states following ligand application (left) and removal (right) obtained by equation (2). (C) Net probability flux density of the closed-open isomerizations following ligand application (left) and removal (right) obtained by equation (3).
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pcbi-1002721-g002: Time courses of net probability flux density in the C4L-O4L model.The time courses for the net probability flux density, fXY, in the C4L-O4L model were computed for the event of applying the ligand fcAMP (7.5 µM; left diagrams) and removing it again (right diagrams). The inset diagrams show the original diagram with an either higher amplitude or time resolution. (A) Net probability flux densities between closed states following ligand application (left) and removal (right) obtained by equation (1). (B) Net probability flux densities between open states following ligand application (left) and removal (right) obtained by equation (2). (C) Net probability flux density of the closed-open isomerizations following ligand application (left) and removal (right) obtained by equation (3).

Mentions: First, the net probability flux density is considered when stepping from zero to 7.5 µM fcAMP. For the four binding steps in the closed channel, the net probability flux density is given by(1)L is the ligand concentration. As expected, the net probability flux density moves like a wave from C0 to C4 (Fig. 2A, left): fC0C1 ceases after less than 100 ms and fC1C2 after about 500 ms. fC2C3 and fC3C4 are slower and not finished after 1s yet. The net probability flux density from the closed states to the respective open states contributes to the reduction of the net probability flux density between the closed states.


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)

Time courses of net probability flux density in the C4L-O4L model.The time courses for the net probability flux density, fXY, in the C4L-O4L model were computed for the event of applying the ligand fcAMP (7.5 µM; left diagrams) and removing it again (right diagrams). The inset diagrams show the original diagram with an either higher amplitude or time resolution. (A) Net probability flux densities between closed states following ligand application (left) and removal (right) obtained by equation (1). (B) Net probability flux densities between open states following ligand application (left) and removal (right) obtained by equation (2). (C) Net probability flux density of the closed-open isomerizations following ligand application (left) and removal (right) obtained by equation (3).
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1002721-g002: Time courses of net probability flux density in the C4L-O4L model.The time courses for the net probability flux density, fXY, in the C4L-O4L model were computed for the event of applying the ligand fcAMP (7.5 µM; left diagrams) and removing it again (right diagrams). The inset diagrams show the original diagram with an either higher amplitude or time resolution. (A) Net probability flux densities between closed states following ligand application (left) and removal (right) obtained by equation (1). (B) Net probability flux densities between open states following ligand application (left) and removal (right) obtained by equation (2). (C) Net probability flux density of the closed-open isomerizations following ligand application (left) and removal (right) obtained by equation (3).
Mentions: First, the net probability flux density is considered when stepping from zero to 7.5 µM fcAMP. For the four binding steps in the closed channel, the net probability flux density is given by(1)L is the ligand concentration. As expected, the net probability flux density moves like a wave from C0 to C4 (Fig. 2A, left): fC0C1 ceases after less than 100 ms and fC1C2 after about 500 ms. fC2C3 and fC3C4 are slower and not finished after 1s yet. The net probability flux density from the closed states to the respective open states contributes to the reduction of the net probability flux density between the closed states.

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
Related in: MedlinePlus