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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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Transition pathways in the C4L-O4L model at saturating fcAMP.The weight of the pathway net probability fluxes, obtained by equation (5), is given by the numbers besides the colored graphs (as fraction of unity) and, for values >0.030, also encoded by the thickness of the arrows. Fluxes from 0.002 to 0.030 are illustrated by equally thick dotted arrows. All other fluxes are only very small (<4.5×10−4) and therefore not represented by arrows. For further explanation see text. (A) Pathway net probability fluxes along the pathways C0 to O4 (red) and O0 to O4 (blue) after switching to 7.5 µM fcAMP. (B) Pathway net probability fluxes along the pathways O4 to C0 (red) and O4 to O0 (blue) after removing fcAMP.
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pcbi-1002721-g004: Transition pathways in the C4L-O4L model at saturating fcAMP.The weight of the pathway net probability fluxes, obtained by equation (5), is given by the numbers besides the colored graphs (as fraction of unity) and, for values >0.030, also encoded by the thickness of the arrows. Fluxes from 0.002 to 0.030 are illustrated by equally thick dotted arrows. All other fluxes are only very small (<4.5×10−4) and therefore not represented by arrows. For further explanation see text. (A) Pathway net probability fluxes along the pathways C0 to O4 (red) and O0 to O4 (blue) after switching to 7.5 µM fcAMP. (B) Pathway net probability fluxes along the pathways O4 to C0 (red) and O4 to O0 (blue) after removing fcAMP.

Mentions: Let us first consider the pathway net probability flux after applying the ligand at 7.5 µM fcAMP (Fig. 4A). The pathway net probability flux from C0, one of the two flux producers, to O4, the main flux collector, results in five defined pathway fluxes, Fp,, which are, according to equation (5), given by the respective minimum values of FCxOx (x = 0…4). The pathway net probability flux from O0, the other flux producer, to O4 has only one available path because the fluxes of all closed-open transitions are directed to the respective open states. Illustration of the weights of the pathway net probability fluxes in the C4L-O4L model after applying the ligand leads to the result that ligand-induced channel opening proceeds mainly from C3 and C4 (with the uncertainty of the exact attribution; Fig. 3, left), and additionally from C1, but not relevantly from C0 and C2. The same type of analysis was then performed for the pathway net probability flux after removing the ligand from O4, the main flux producer, to C0 and O0, the main flux collectors. Closing of the channels proceeds predominantly from O1 and O0, and to a minor extent from O2 and O3, but not relevantly from O4. Together these results show that there is pronounced hysteresis for ligand-induced activation and deactivation. The pathway flux from O4 to O0, the other flux collector, has again only one available path because the fluxes of all closed-open transitions are directed to the respective 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)

Transition pathways in the C4L-O4L model at saturating fcAMP.The weight of the pathway net probability fluxes, obtained by equation (5), is given by the numbers besides the colored graphs (as fraction of unity) and, for values >0.030, also encoded by the thickness of the arrows. Fluxes from 0.002 to 0.030 are illustrated by equally thick dotted arrows. All other fluxes are only very small (<4.5×10−4) and therefore not represented by arrows. For further explanation see text. (A) Pathway net probability fluxes along the pathways C0 to O4 (red) and O0 to O4 (blue) after switching to 7.5 µM fcAMP. (B) Pathway net probability fluxes along the pathways O4 to C0 (red) and O4 to O0 (blue) after removing fcAMP.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1002721-g004: Transition pathways in the C4L-O4L model at saturating fcAMP.The weight of the pathway net probability fluxes, obtained by equation (5), is given by the numbers besides the colored graphs (as fraction of unity) and, for values >0.030, also encoded by the thickness of the arrows. Fluxes from 0.002 to 0.030 are illustrated by equally thick dotted arrows. All other fluxes are only very small (<4.5×10−4) and therefore not represented by arrows. For further explanation see text. (A) Pathway net probability fluxes along the pathways C0 to O4 (red) and O0 to O4 (blue) after switching to 7.5 µM fcAMP. (B) Pathway net probability fluxes along the pathways O4 to C0 (red) and O4 to O0 (blue) after removing fcAMP.
Mentions: Let us first consider the pathway net probability flux after applying the ligand at 7.5 µM fcAMP (Fig. 4A). The pathway net probability flux from C0, one of the two flux producers, to O4, the main flux collector, results in five defined pathway fluxes, Fp,, which are, according to equation (5), given by the respective minimum values of FCxOx (x = 0…4). The pathway net probability flux from O0, the other flux producer, to O4 has only one available path because the fluxes of all closed-open transitions are directed to the respective open states. Illustration of the weights of the pathway net probability fluxes in the C4L-O4L model after applying the ligand leads to the result that ligand-induced channel opening proceeds mainly from C3 and C4 (with the uncertainty of the exact attribution; Fig. 3, left), and additionally from C1, but not relevantly from C0 and C2. The same type of analysis was then performed for the pathway net probability flux after removing the ligand from O4, the main flux producer, to C0 and O0, the main flux collectors. Closing of the channels proceeds predominantly from O1 and O0, and to a minor extent from O2 and O3, but not relevantly from O4. Together these results show that there is pronounced hysteresis for ligand-induced activation and deactivation. The pathway flux from O4 to O0, the other flux collector, has again only one available path because the fluxes of all closed-open transitions are directed to the respective 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