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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 subsaturating fcAMP.The illustration is analogous to Fig. 4. The two main net probability fluxes at each concentration are shown. Pathway net probability fluxes associated with activation (C0→Ox, O0→Ox) and deactivation (Cx→O0, Ox→O0) are shown in red and blue color, respectively. (A) 0.75 µM fcAMP, C0↔O4. (B) 0.75 µM fcAMP, net probability flux along C0↔O2 in addition to that included in C0↔O4. (C) 0.075 µM fcAMP, C0↔O2. (D) 0.075 µM fcAMP, net probability flux along C0↔O1 in addition to that included in C0↔O2.
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pcbi-1002721-g005: Transition pathways in the C4L-O4L model at subsaturating fcAMP.The illustration is analogous to Fig. 4. The two main net probability fluxes at each concentration are shown. Pathway net probability fluxes associated with activation (C0→Ox, O0→Ox) and deactivation (Cx→O0, Ox→O0) are shown in red and blue color, respectively. (A) 0.75 µM fcAMP, C0↔O4. (B) 0.75 µM fcAMP, net probability flux along C0↔O2 in addition to that included in C0↔O4. (C) 0.075 µM fcAMP, C0↔O2. (D) 0.075 µM fcAMP, net probability flux along C0↔O1 in addition to that included in C0↔O2.

Mentions: To demonstrate the function of our model at subsaturating fcAMP concentrations we considered the fluxes to the two main collectors at 0.75 µM fcAMP (O2 and O4; Fig. 5A,B) and 0.075 µM fcAMP (O1 and O2; Fig. 5C,D) and the respective reverse fluxes when removing fcAMP. Notably, these selected fluxes are only the dominating fluxes. The results show that at the intermediate concentration of 0.75 µM fcAMP activation proceeds along C1→O1 predominantly to O4 (Fig. 5A) and to a minor extent to O2 (Fig. 5B). In addition there is a remarkably big net probability flux in the open channel along O0→O2 and in the reverse direction along O2→O0 which is absent along O0→O4 and O4→O0, respectively. This indicates that O2 is a metastable state. Moreover, this result corresponds to the high energy barrier for the transition O2→O3[22]. At 0.075 µM fcAMP the predominant activation proceeds along C1→O1 to O2 but not anymore to O4. O1 is only passed in the activation pathway. However, it is of importance as a collector for the probability flux in the open channel (Fig. 5D).


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 subsaturating fcAMP.The illustration is analogous to Fig. 4. The two main net probability fluxes at each concentration are shown. Pathway net probability fluxes associated with activation (C0→Ox, O0→Ox) and deactivation (Cx→O0, Ox→O0) are shown in red and blue color, respectively. (A) 0.75 µM fcAMP, C0↔O4. (B) 0.75 µM fcAMP, net probability flux along C0↔O2 in addition to that included in C0↔O4. (C) 0.075 µM fcAMP, C0↔O2. (D) 0.075 µM fcAMP, net probability flux along C0↔O1 in addition to that included in C0↔O2.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1002721-g005: Transition pathways in the C4L-O4L model at subsaturating fcAMP.The illustration is analogous to Fig. 4. The two main net probability fluxes at each concentration are shown. Pathway net probability fluxes associated with activation (C0→Ox, O0→Ox) and deactivation (Cx→O0, Ox→O0) are shown in red and blue color, respectively. (A) 0.75 µM fcAMP, C0↔O4. (B) 0.75 µM fcAMP, net probability flux along C0↔O2 in addition to that included in C0↔O4. (C) 0.075 µM fcAMP, C0↔O2. (D) 0.075 µM fcAMP, net probability flux along C0↔O1 in addition to that included in C0↔O2.
Mentions: To demonstrate the function of our model at subsaturating fcAMP concentrations we considered the fluxes to the two main collectors at 0.75 µM fcAMP (O2 and O4; Fig. 5A,B) and 0.075 µM fcAMP (O1 and O2; Fig. 5C,D) and the respective reverse fluxes when removing fcAMP. Notably, these selected fluxes are only the dominating fluxes. The results show that at the intermediate concentration of 0.75 µM fcAMP activation proceeds along C1→O1 predominantly to O4 (Fig. 5A) and to a minor extent to O2 (Fig. 5B). In addition there is a remarkably big net probability flux in the open channel along O0→O2 and in the reverse direction along O2→O0 which is absent along O0→O4 and O4→O0, respectively. This indicates that O2 is a metastable state. Moreover, this result corresponds to the high energy barrier for the transition O2→O3[22]. At 0.075 µM fcAMP the predominant activation proceeds along C1→O1 to O2 but not anymore to O4. O1 is only passed in the activation pathway. However, it is of importance as a collector for the probability flux in the open channel (Fig. 5D).

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