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
The C4L-O4L model.(A) The C4L-O4L model is composed of five closed (Cx) and five open states (Ox; x = 0…4). Ligand (L) binding is possible in both the closed and the open channel. The closed-open isomerization can proceed at each degree of liganding. The rate constants and their errors were determined previously [22]. kO3C3 was set equal to kO4C4. Since for these rate constants only a lower border could be estimated, they were set to 3 s−1 herein if not otherwise noted. This results in kC3O3 = kC4O4 = 2.0×102 s.1. (B) Time-dependent probability to stay in a closed state, PC,x; (x = 0…4) for a ligand jump (green bar) from zero to 7.5 µM and back to zero. Pc denotes the sum of all PC,x at each time. (C) Time-dependent probability to stay in an open state, PO,x; (x = 0…4) for a ligand jump (green bar) from zero to 7.5 µM and back to zero. Po, the sum of all PO,x at each time, indicates the measured time course of the total open probability. (D) Scheme of the C4L-O4L model with means of rate constants provided by Table S1.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1002721-g001: The C4L-O4L model.(A) The C4L-O4L model is composed of five closed (Cx) and five open states (Ox; x = 0…4). Ligand (L) binding is possible in both the closed and the open channel. The closed-open isomerization can proceed at each degree of liganding. The rate constants and their errors were determined previously [22]. kO3C3 was set equal to kO4C4. Since for these rate constants only a lower border could be estimated, they were set to 3 s−1 herein if not otherwise noted. This results in kC3O3 = kC4O4 = 2.0×102 s.1. (B) Time-dependent probability to stay in a closed state, PC,x; (x = 0…4) for a ligand jump (green bar) from zero to 7.5 µM and back to zero. Pc denotes the sum of all PC,x at each time. (C) Time-dependent probability to stay in an open state, PO,x; (x = 0…4) for a ligand jump (green bar) from zero to 7.5 µM and back to zero. Po, the sum of all PO,x at each time, indicates the measured time course of the total open probability. (D) Scheme of the C4L-O4L model with means of rate constants provided by Table S1.

Mentions: For CNGA2 and HCN2 channels we recently developed a strategy to simultaneously measure ligand binding and activation gating by combining confocal microscopy with patch-clamp fluorometry [19], thereby employing a fluorescently labeled ligand [20], [21]. In a subsequent study on HCN2 channels, pre-activated by a voltage pulse to −130 mV, we combined this approach with the method of concentration jumps. By globally fitting multiple time courses of ligand binding and channel activation, this approach allowed us to determine the equilibrium and rate constants in a Markovian model with 4 binding steps in both the closed and the open channel and 5 closed-open isomerizations (Fig. 1A) [22]. The analysis revealed pronounced cooperativity with respect to the microscopic binding affinity in the surprising sequence ‘positive – negative – positive’ for the binding of the second, third, and fourth ligand, respectively. Moreover, we considered the population of all closed and open states as function of time when jumping the ligand concentration. As a result, the total open probability is dominated by open states with either zero, two or four ligands bound whereas states with one or three ligands bound are only transiently populated (Fig. 1B and C) [22].


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)

The C4L-O4L model.(A) The C4L-O4L model is composed of five closed (Cx) and five open states (Ox; x = 0…4). Ligand (L) binding is possible in both the closed and the open channel. The closed-open isomerization can proceed at each degree of liganding. The rate constants and their errors were determined previously [22]. kO3C3 was set equal to kO4C4. Since for these rate constants only a lower border could be estimated, they were set to 3 s−1 herein if not otherwise noted. This results in kC3O3 = kC4O4 = 2.0×102 s.1. (B) Time-dependent probability to stay in a closed state, PC,x; (x = 0…4) for a ligand jump (green bar) from zero to 7.5 µM and back to zero. Pc denotes the sum of all PC,x at each time. (C) Time-dependent probability to stay in an open state, PO,x; (x = 0…4) for a ligand jump (green bar) from zero to 7.5 µM and back to zero. Po, the sum of all PO,x at each time, indicates the measured time course of the total open probability. (D) Scheme of the C4L-O4L model with means of rate constants provided by Table S1.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1002721-g001: The C4L-O4L model.(A) The C4L-O4L model is composed of five closed (Cx) and five open states (Ox; x = 0…4). Ligand (L) binding is possible in both the closed and the open channel. The closed-open isomerization can proceed at each degree of liganding. The rate constants and their errors were determined previously [22]. kO3C3 was set equal to kO4C4. Since for these rate constants only a lower border could be estimated, they were set to 3 s−1 herein if not otherwise noted. This results in kC3O3 = kC4O4 = 2.0×102 s.1. (B) Time-dependent probability to stay in a closed state, PC,x; (x = 0…4) for a ligand jump (green bar) from zero to 7.5 µM and back to zero. Pc denotes the sum of all PC,x at each time. (C) Time-dependent probability to stay in an open state, PO,x; (x = 0…4) for a ligand jump (green bar) from zero to 7.5 µM and back to zero. Po, the sum of all PO,x at each time, indicates the measured time course of the total open probability. (D) Scheme of the C4L-O4L model with means of rate constants provided by Table S1.
Mentions: For CNGA2 and HCN2 channels we recently developed a strategy to simultaneously measure ligand binding and activation gating by combining confocal microscopy with patch-clamp fluorometry [19], thereby employing a fluorescently labeled ligand [20], [21]. In a subsequent study on HCN2 channels, pre-activated by a voltage pulse to −130 mV, we combined this approach with the method of concentration jumps. By globally fitting multiple time courses of ligand binding and channel activation, this approach allowed us to determine the equilibrium and rate constants in a Markovian model with 4 binding steps in both the closed and the open channel and 5 closed-open isomerizations (Fig. 1A) [22]. The analysis revealed pronounced cooperativity with respect to the microscopic binding affinity in the surprising sequence ‘positive – negative – positive’ for the binding of the second, third, and fourth ligand, respectively. Moreover, we considered the population of all closed and open states as function of time when jumping the ligand concentration. As a result, the total open probability is dominated by open states with either zero, two or four ligands bound whereas states with one or three ligands bound are only transiently populated (Fig. 1B and C) [22].

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