Limits...
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.

Show MeSH

Related in: MedlinePlus

Total net probability fluxes in the individual transitions of the C4L-O4L model.The total net probability fluxes per transition, FXY (given as fraction of unity), were obtained by integrating (equation (4)) the time courses of the net probability flux densities obtained by equation (1) to (3). The data after stepping to 7.5 µM fcAMP and after its removal are shown on the left and right side, respectively. The dotted bars indicate the effect of fitting with kO3C3 to 30, instead of 3, on FC3C4, FO3O4, FC3O3, and FC4C4. The sum of FC3O3 and FC4C4 is practically unchanged. The other total net probability fluxes were unchanged. (A) Total net probability fluxes for the transitions between neighbored closed states. (B) Total net probability fluxes for the transitions between neighbored open states. (C) Total net probability fluxes for the five closed-open transitions.
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC3475657&req=5

pcbi-1002721-g003: Total net probability fluxes in the individual transitions of the C4L-O4L model.The total net probability fluxes per transition, FXY (given as fraction of unity), were obtained by integrating (equation (4)) the time courses of the net probability flux densities obtained by equation (1) to (3). The data after stepping to 7.5 µM fcAMP and after its removal are shown on the left and right side, respectively. The dotted bars indicate the effect of fitting with kO3C3 to 30, instead of 3, on FC3C4, FO3O4, FC3O3, and FC4C4. The sum of FC3O3 and FC4C4 is practically unchanged. The other total net probability fluxes were unchanged. (A) Total net probability fluxes for the transitions between neighbored closed states. (B) Total net probability fluxes for the transitions between neighbored open states. (C) Total net probability fluxes for the five closed-open transitions.

Mentions: From the net probability flux densities, fXY, one can easily compute the total net probability fluxes, FXY, as the time integral over the time interval from the concentration jump (t = 0 s) to an end time, tend,(4)tend is either 5 s for the fcAMP pulse or 20 s after removal of fcAMP. Adapted to our C4L-O4L model, FXY indicates how much of the total net probability flux moves along a transition X↔Y. The main results are: (1) The total net probability flux is bigger in the binding steps of the open than the closed channel in both the presence of fcAMP and after its removal (Fig. 3A and B). (2) The total net probability flux between the closed states is larger for the binding than for the unbinding process (Fig. 3A). (3) FC0O0 is negligible in the binding-induced relaxation but significantly present in the unbinding-induced relaxation whereas FC4O4 is negligible in the unbinding-induced relaxation but significantly present in the binding-induced relaxation (Fig. 3C). Together, these results suggest different pathways for activation and deactivation.


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)

Total net probability fluxes in the individual transitions of the C4L-O4L model.The total net probability fluxes per transition, FXY (given as fraction of unity), were obtained by integrating (equation (4)) the time courses of the net probability flux densities obtained by equation (1) to (3). The data after stepping to 7.5 µM fcAMP and after its removal are shown on the left and right side, respectively. The dotted bars indicate the effect of fitting with kO3C3 to 30, instead of 3, on FC3C4, FO3O4, FC3O3, and FC4C4. The sum of FC3O3 and FC4C4 is practically unchanged. The other total net probability fluxes were unchanged. (A) Total net probability fluxes for the transitions between neighbored closed states. (B) Total net probability fluxes for the transitions between neighbored open states. (C) Total net probability fluxes for the five closed-open transitions.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1002721-g003: Total net probability fluxes in the individual transitions of the C4L-O4L model.The total net probability fluxes per transition, FXY (given as fraction of unity), were obtained by integrating (equation (4)) the time courses of the net probability flux densities obtained by equation (1) to (3). The data after stepping to 7.5 µM fcAMP and after its removal are shown on the left and right side, respectively. The dotted bars indicate the effect of fitting with kO3C3 to 30, instead of 3, on FC3C4, FO3O4, FC3O3, and FC4C4. The sum of FC3O3 and FC4C4 is practically unchanged. The other total net probability fluxes were unchanged. (A) Total net probability fluxes for the transitions between neighbored closed states. (B) Total net probability fluxes for the transitions between neighbored open states. (C) Total net probability fluxes for the five closed-open transitions.
Mentions: From the net probability flux densities, fXY, one can easily compute the total net probability fluxes, FXY, as the time integral over the time interval from the concentration jump (t = 0 s) to an end time, tend,(4)tend is either 5 s for the fcAMP pulse or 20 s after removal of fcAMP. Adapted to our C4L-O4L model, FXY indicates how much of the total net probability flux moves along a transition X↔Y. The main results are: (1) The total net probability flux is bigger in the binding steps of the open than the closed channel in both the presence of fcAMP and after its removal (Fig. 3A and B). (2) The total net probability flux between the closed states is larger for the binding than for the unbinding process (Fig. 3A). (3) FC0O0 is negligible in the binding-induced relaxation but significantly present in the unbinding-induced relaxation whereas FC4O4 is negligible in the unbinding-induced relaxation but significantly present in the binding-induced relaxation (Fig. 3C). Together, these results suggest different pathways for activation and deactivation.

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