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Original Article |
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ABSTRACT |
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 Top ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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Key Words: HCN channels • pacemaker • hyperpolarization-activated channels • modeling • channel gating
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INTRODUCTION |
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TopABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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, DiFrancesco 1993; Pape 1996). In cells where pacemaker channels are expressed, their properties serve different purposes, normally associated to the ability to generate a depolarization upon activation by previous hyperpolarization or by the second messenger cAMP.
Four isoforms of hyperpolarization-activated, cyclic nucleotide–gated (HCN) channels have been recently cloned in several organisms (Santoro et al. 1997, Santoro et al. 1998; Gauss et al. 1998; Ludwig et al. 1998, Ludwig et al. 1999; Seifert et al. 1999; Vaccari et al. 1999). Expression experiments have demonstrated that HCN channels are the cloned equivalents of native f/h channels (Santoro et al. 1998; Ishii et al. 1999; Ludwig et al. 1999; Seifert et al. 1999; Moroni et al. 2000). HCN sequences are homologous to those of Kv and cyclic nucleotide–gated (CNG) channels (Clapham 1998), and belong to the same superfamily of six transmembrane (TM) domain channels.
The availability of different isoforms of HCN channels allows a detailed analysis of isoform-specific gating and modulatory properties, and a comparison of these properties with those of native channels as a way to corroborate expression data. Further, the existence of HCN isoforms with different gating properties prompts the question whether a comprehensive model can be developed to describe the kinetic features of the HCN family.
In this work we have analyzed detailed properties of voltage gating of three HCN clones (mHCN1, hHCN2, and hHCN4) based on the following considerations. First, it is known that kinetic features of native f-channel activation/deactivation cannot be described satisfactorily by the use of Hodgkin-Huxley (HH) description (DiFrancesco 1984). To account for these features, a complex kinetic model based on the coexistence of a "delaying" and a proper "gating" process and involving five voltage-dependent gating variables of three different types had been previously proposed (DiFrancesco 1984). Second, voltage gating of several ion channels has been recently interpreted on the basis of allosteric models (Marks and Jones 1992; Rìos et al. 1993; McCormack et al. 1994; Horrigan and Aldrich 1999; Horrigan et al. 1999; Jones 1999). Third, the structural homology of HCN channels to 6-TM domain K+ channels favors the hypothesis that HCN channels, too, are tetramers.
Our starting point was based on a recent investigation in cardiac SAN cells, showing that basic kinetic and modulatory properties of native pacemaker f-channels can be explained by a hybrid HH-MWC model (DiFrancesco 1999). In that model, voltage gating was described by a standard HH scheme with two independent subunits, while cAMP-induced activation occurred according to a cyclic allosteric Monod-Wyman-Changeaux (MWC) model (Monod et al. 1965) involving binding of one cAMP molecule per gating subunit.
On the basis of the above considerations, we explored the possibility that, as well as by cAMP, gating of pacemaker channels is modulated allosterically by voltage, too. In this attempt, we extended the hypothesis made in the gating scheme proposed earlier (DiFrancesco 1999) that pacemaker channels are composed of subunits, each independently gated by voltage and cAMP. We made the assumption that, like mSlo channels (Horrigan and Aldrich 1999; Horrigan et al. 1999), HCN channels are homotetramers, with each subunit carrying one independent voltage sensor, and that closed/open channel transitions involve concerted structural modifications of all four subunits and occur allosterically.
We found that by simply selecting an appropriate set of rate constants for each isoform, the allosteric assumption accounts for quantitative features of voltage-dependent gating of different isoforms. The allosteric hypothesis provides an interpretation of the possible mechanisms responsible for the different gating properties of different isoforms, and may represent an unifying model for HCN channel gating.
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MATERIALS AND METHODS |
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TopABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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). Human HCN4 (hHCN4) was provided by Dr. U.B. Kaupp (Forschungszentrum, Jülich, Germany) in the eukaryotic expression vector pcDNA1 (CLONTECH Laboratories, Inc.). For transient functional expression channel-specific cDNA was transfected into modified HEK 293 (Phoenix) cells (Kinsella and Nolan 1996; Moroni et al. 2000). hHCN2 and hHCN4 constructs were cotransfected with a GFP-containing plasmid. In brief, for each 35-mm Petri dish we used 7 µg of channel-specific construct and 3.5 µg of GFP-containing plasmid. In the case of mHCN1/pIRES-EGFP, we used 10 µg of construct, which coexpresses the channel and the GFP protein on a polycystronic mRNA. Phoenix cells were cultured in Dulbecco's modified essential medium supplemented with 10% FCS (GIBCO BRL) and antibiotics (Sigma-Aldrich). In the following text, the species symbol will be dropped for simplicity and the mHCN1, hHCN2, hHCN4 isoforms will be termed HCN1, HCN2, and HCN4, respectively.
Electrophysiology
Experiments were performed on Phoenix cells incubated after transfection at 37°C in 5% CO2 for 1– 5 d. Before electrophysiological measurements, cells were dispersed by trypsinization and plated onto 35-mm plastic Petri dishes at low density, where they were allowed to settle for 3–4 h. Petri dishes were transferred under the stage of an inverted microscope, and single cells were patch-clamped in the whole-cell configuration according to standard methods (Moroni et al. 2000). For the analysis, we visually selected strongly GFP-reactive cells. Cells were perfused at room temperature (24–25°C) with a control Tyrode solution containing (in mM): 140 NaCl, 5.4 KCl, 1.8 CaCl2, 1 MgCl2, 5.5 D-glucose, and 5 HEPES-NaOH, pH 7.4. The solution was delivered via a fast-flow perfusion pipet.
Whole-cell pipets were filled with an intracellular-like solution containing (in mM): 10 NaCl, 130 KCl, 1.0 EGTA, 5 HEPES-KOH, 0.5 MgCl2, 2 ATP (sodium salt), 0.1 GTP (sodium salt), and 5 phosphocreatine, pH 7.2. We added 1 mM BaCl2, 2 mM MnCl2, 100 µM NiCl2, and 20 µM nifedipine to perfusing solutions (in mM: 110 NaCl, 30 KCl, 1.8 CaCl2, 0.5 MgCl2, and 5 HEPES-NaOH, pH 7.4) to reduce interference from overlapping Ca2+ and K+ components in the measurement of HCN currents.
Data Analysis
Activation curves were obtained by standard two-step voltage-clamp protocols previously used (DiFrancesco et al. 1986; Moroni et al. 2000). The protocols consisted of hyperpolarizations applied in 10-mV steps from a fixed holding potential of –35 mV, followed by steps to test voltages where the amplitude of deactivation current tails was measured. The duration of activation steps varied with the test voltage to allow attainment of steady-state.
Curve Fitting
For all HCN isoforms investigated, activation/deactivation traces were fitted by single exponential curves after an initial delay; delay, time-constant, and current amplitude were free to vary in the best-fitting routine.
Numerical Computations
Analytical treatment of the allosteric scheme proposed (see Fig. 2) is given in the . Calculations were performed by integration of the vectorial differential :
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RESULTS |
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TopABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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).
To probe whether HCN channels also have features not complying with HH kinetics, we analyzed the time course of current activation in cells expressing HCN1, HCN2, or HCN4, and checked if it could be described by a fixed power of an exponential. In Fig. 1 A, HCN1, HCN2, and HCN4 current activation traces recorded on hyperpolarization at voltages in the range –75 to –115 mV are shown. Plots of the function F(t) = ln(1– (I(t)/I
)1/n) should result in straight lines with zero y-intercepts and slope = –1/
if the current activates according to the nth power of an exponential. To verify this, we plotted in Fig. 1 B the function F(t) for each current record with n = 1, 2 and 3, and in Fig. 1 C, we plotted the y-intercepts of fits to the linear part of F(t) plots.
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). Both these features are also observed in HCN channels, and are dealt with later (Fig. 4Fig. 5Fig. 6 and Fig. 8). These observations indicate that, as in native f-channels, voltage gating of HCN channels is not compatible with HH models, and require more complex gating schemes involving multiple open and closed states.
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The analytical treatment, and the methods for numerical computations of the kinetics predicted by the model in Fig. 2 are described in . Under the assumptions made, the kinetic behavior of the allosteric model is fully characterized by knowledge of the parameter a and the eight parameters 
o, βo, 
o, 
o, z, zβ, z, and z describing the voltage dependence of rate constants , β, , according to . A further simplification is obtained by setting zβ = –z, z = –z (see ). This reduces the overall free parameters to n = 7.
HCN Channels Activation and Deactivation Kinetics: Selection of First-guess Fitting Parameters
Since the number of free parameters needed to simulate channel kinetics (n = 7) was too large to allow adequate fitting of data, we searched for criteria to restrict parameters values. The parameter "a" represents the multiplying factor of equilibrium constants of closed/open transitions upon movement of one voltage sensor from the reluctant to the willing state.
The model assumes that the transition of a voltage sensor to the willing state increases the open-to-closed channel ratio by a fixed factor, regardless of the channel subunit the voltage sensor belongs to. This implies that the parameter a is a constant in the range 0 < a < 1. Values of "a" close to 1 determine the condition L 
L1 L2 L3 L4, corresponding to practically ineffective voltage sensors; this would tend to abolish delays in activation and deactivation. Small values of "a" (a << 1), on the other hand, determine the condition L >>L1 >> L2 >> L3 >> L4. This would imply that most openings occur when all four voltage sensors are in the willing state (C4
O4), and that activation kinetics could be approximated by the linear scheme CC1C2C3C4O4, with well separated "delaying" (CC4) and "opening" (C4O4) processes. Because of the symmetry of the cyclic allosteric scheme proposed, small values of "a" would also favor closing to occur mainly when all voltage sensors are in the reluctant state (OC).
To test the predictive ability of the model, we tentatively assumed a = 0.2 and ran pilot computations. We found that, indeed, as expected for small values of a, the single exponential time course (after a delay) of computed activation traces approximated that of C4O4 transitions (time constant 4L; see ). We also noticed that plots of the delay displayed a voltage dependence similar to that of the time constant of voltage sensor transitions (K(V); see ), reflecting the fact that, in the model of Fig. 2, the process responsible for delaying channel opening is the displacement of voltage sensors from reluctant to willing states (data not shown).
These preliminary observations provided a method for a rough estimate of some of the required parameters. We fitted experimental traces by single exponentials after an initial delay. Plots of time constant and delay data, thus, measured for HCN1, HCN2, and HCN4 channels are shown in Fig. 3. We best-fitted the time constant data with the equation for 4L(V) (see ; Fig. 3 A); this yielded the functions 4(V) and β4(V), from which first-guess parameters o, βo, and zβ (= –z) could be calculated as reported in the legend to Fig. 3.
Delay data (Fig. 3 B) were also best-fitted with the equation for K(V) (see ); this generated the functions (V) and (V), from which the parameters o, o, and z (= –z) were calculated as reported in Fig. 3 legend. Table lists the fitting parameters that were used as an initial set for predicting the kinetic behavior of the three HCN isoforms investigated.
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Fitting of Activation and Deactivation Time Course for HCN1, HCN2, and HCN4 Channels
To verify if the model was able to more accurately mimic the kinetics of current activation and deactivation of HCN channels in specific cases, we used semi-empirical fitting routines on individual sets of traces as shown in Fig. 4Fig. 5Fig. 6 for HCN1, HCN2, and HCN4 channels, respectively.
For each trace, we initially used Table to assign starting values to selected parameters (y4, z, 4L, and K) and calculated the rate constants , β, , and according to and of . These values (with a = 0.2) allowed calculation of the matrix A and of vector k ( and ), and thus of the current time course. The process was repeated by trial-and-error approximation, until a satisfactory simulation was obtained.
For all isoforms, the model was able to reproduce the detailed kinetic features of activation and deactivation in the whole voltage range investigated. The data points selected with the above procedure for y4, z, 4L, and K deviated from the first-guess values assumed on the basis of the preliminary analysis of Fig. 3 (compare closed circles with broken lines in Fig. 4Fig. 5Fig. 6, panels C–F). They were best-fitted using the equations for y4, z, 4L, and K (see , and ) and the resulting rate parameters are reported in Table . These can be directly compared with those of Table .
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, which clearly does not represent a Boltzmann type of voltage dependence. Nonetheless, to verify if it can describe the steady-state open probability curve of HCN channels, we used it to fit in Fig. 7 the mean activation curves for HCN1, HCN2, and HCN4.
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, indicating that the two procedures led to comparable predictions.
Removal of the Delay in Current Activation by Conditioning Prehyperpolarization
In cardiac Purkinje fibres, activation delay can be removed by conditioning prehyperpolarizations (DiFrancesco 1984). To verify whether HCN channels have the same property, we applied two-step protocols to cells expressing HCN4 channels. As apparent in the example of Fig. 8 A, short prehyperpolarizations to –150 mV accelerated activation at –110 mV and progressively removed the delay until monoexponential time course was achieved with a 22-ms prepulse (see also semilog plots in Fig. 8 B) monoexponential time course was achieved.
To verify the ability of the allosteric model to mimic this behavior, we fitted records at –110 mV and at –150 mV with the procedure used above (Fig. 6), and then ran two-step model computations reproducing experimental protocols (Fig. 8 C). The model accurately predicted a progressive current acceleration and removal of delay with increasing prepulse durations. With sufficiently long prepulses, the computed time course became a single exponential, as apparent from the semilog plot of Fig. 8 D. This is expected if the action of prehyperpolarizing steps is to "prime" the channel opening process by pushing the majority of voltage sensors to their willing state, such that at –110 mV, the current development reflects mostly C4O4 transitions. The computed traces at –110 mV, however, did not perfectly overlap experimental ones particularly after the longest prepulses. This may be due to the fact that, especially with long prepulses, the experimental current at –110 mV underwent an early acceleration compared with a single exponential (also observed in native f-channel; DiFrancesco and Ferroni 1983; DiFrancesco 1984), as evident in the semilog plots of Fig. 8 D (46-ms prepulse record). The model constraints do not allow to reproduce this behavior.
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DISCUSSION |
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TopABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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). Experimental evidence presented here indicates that some features of the voltage-dependent gating of various HCN channel isoforms (mHCN1, hHCN2, and hHCN4) also do not comply with HH kinetics. These features include the following: (1) sigmoidal activation that cannot be approximated by the nth power of an exponential; (2) sigmoidal deactivation; and (3) removal of the activation delay by prehyperpolarizing steps. This indicates that a multistate non-HH kinetic model may be required for HCN channels.
HCN channels belong to the superfamily of Kv and CNG channels. The amino acid sequence comprises six transmembrane (TM) domains with a pore region between S5 and S6 and a positively charged domain S4, which acts as the primary voltage sensor (Vaca et al. 2000; Chen et al. 2000). The structural similarities to 6-TM domain channels favor the hypothesis that HCN channel subunits coassemble as tetramers, and that their voltage-dependent closed/open transitions are governed by the voltage sensitivity of S4 movement.
A gating model taking into account the molecular information available and the structural similarities with Kv and CNG channels should, therefore, regard HCN channels as tetramers whose closed/open transitions are regulated by voltage sensors. Two additional observations help clarify the features of this model: first, previous work on native f-channels has shown that the cAMP-induced modulation can be described by an allosteric model (DiFrancesco 1999); second, allosteric voltage-dependent gating has been proposed for other channels, including Ca2+ channels (Marks and Jones 1992), Shaker K+ channel (McCormack et al. 1994), and large conductance, Ca2+-activated (mSlo) K+ channels (Horrigan and Aldrich 1999; Horrigan et al. 1999).
Allosteric Model of HCN Channels Voltage Gating and Comparison with Previous Models
Based on the above considerations, we asked whether the voltage gating of HCN channels could be described as an allosteric process, which led to a 10-state cyclic reaction scheme (Fig. 2). A major problem that we faced in using the model was to restrict the choice of free model parameters in a way that would allow the selection of parameter values by data fitting, since clearly too many free parameters would imply the need of arbitrary selection of some of the values.
One assumption of the model at one time intuitive and useful to the effect of limiting free parameters, was to consider that the action on closed/open channel ratio of any voltage sensor's displacement is always the same, regardless of the distribution of voltage sensors (i.e., the number of sensors in the willing state versus those in the reluctant state), or to which channel subunit the voltage sensor belongs. This meant that the parameter a could be considered as a constant (in the range 0–1). This assumption, together with the assumption of balanced rate constant changes (i.e., when the equilibrium constant is multiplied by a, then the opening rate constant is divided by 
a, and the closing rate constant is multiplied by a), was very effective in that it reduced the set of 10 originally free "vertical" rate constants in Fig. 2 (, β, 1, β1, 2, β2, 3, β3, 4, and β4) to just three free rate constants (the parameter a and , β or, equivalently, 4 and β4).
On this basis, after a preliminary selection of model parameters (Table ), we used individual curve fitting to estimate rate constants (Fig. 4Fig. 5Fig. 6 and Table ). In all three HCN isoforms investigated, the allosteric scheme of Fig. 2 could reproduce the observed kinetic behavior, including sigmoidal activation and deactivation (Fig. 4Fig. 5Fig. 6) and removal of activation delay by prehyperpolarizations (Fig. 8). Also, the model accounted for the position and shape of the open probability curve for the three isoforms (Fig. 7).
The allosteric scheme examined here is analogous to that proposed by Marks and Jones 1992 for dihydropyridine-sensitive Ca2+ channels, by Rìos et al. 1993 for the Ca2+-release channel of sarcoplasmic reticulum of skeletal muscle, by McCormack et al. 1994 for Shaker K+ channels, and by Aldrich and collaborators for large conductance Ca2+-activated K+ (mSlo) channels (Horrigan and Aldrich 1999; Horrigan et al. 1999). A distinct property of mSlo channels is the presence of a region of shallow slope in the time constant curve at high negative voltages; according to the allosteric hypothesis, this can be interpreted as due to a weak voltage dependence of closed/open transitions, which are slower than voltage sensor transitions and rate-limiting at large negative voltages (Horrigan et al. 1999).
In our model of HCN channels, closed/open transitions are indeed severalfold slower than sensor transitions for all isoforms (see Fig. 10); however, fitting of the time constant curves in Fig. 3 A and curve reconstruction in Fig. 4Fig. 5Fig. 6 indicate that closed/open transitions have a substantial voltage dependence (zβ = –z = 0.94, 1.07, and 0.80 equivalent electronic charges for HCN1, HCN2, and HCN4 isoform, respectively, Table ).
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and zβ reported in Table were not assumed, but resulted from data fitting, and, therefore, cannot be reduced arbitrarily. In other words, the assumption that each voltage sensor contributes equally to favor channel opening, together with the other model assumptions, leads to experimental data fitting indicating the presence of a substantial voltage dependence for closed/open transitions for all isoforms.
Investigating a model where closed/open transitions are weakly voltage-dependent would imply a different set of assumptions, since most of the voltage dependence of kinetics would derive from voltage sensors' state changes. The operating framework of the model would be likely to change significantly. We would need to release the assumptions concerning the constancy of a and/or the balanced rate constant changes, and let most of the 10 vertical rate constants , β, 1, β1, 2, β2, 3, β3, 4, and β4 free to vary. In fact, the situation could be even more complex since releasing the condition a = constant would also affect the horizontal rate constants.
We did not adopt this solution because it would have involved too much arbitrariness in the selection of parameter values. More importantly, we did not have any real indication that closed/open transitions are weakly voltage-dependent or voltage-independent for HCN channels, since we did not have evidence for regions of shallow slope at negative voltages in time constant curves of any of the HCN isoforms investigated (Fig. 3 A). However, the model scheme of Fig. 2 is not incompatible with a situation where closed/open transitions are nearly voltage-independent (i.e., with a low z) and most of the voltage dependence of channel kinetics is attributable to sensor movements. Although we lack experimental evidence, we cannot rule out this possibility entirely, since, due to experimental constraints, the voltage range where recordings could be made was limited (positive to –135 mV; Fig. 3 A).
Implications of Allosteric Design
Recent data have shown that replacement of basic residues in the S4 segment of HCN2 with neutral ones leads to negative shifts of the activation curve voltage dependence (Chen et al. 2000; Vaca et al. 2000). However, the slope of the activation curve did not decrease as expected if it were correlated to the total number of equivalent charges moving through the electric field during activation/deactivation. The allosteric model may provide a simple explanation for these results, as illustrated in the example of Fig. 9 for HCN2.
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) by 1/6, 2/6, 3/6, and 4/6 of the control value (labeled 1–4). As expected, reductions of z led to proportional reductions in the slope of the z(V) curve. However, in Fig. 9 B, the Po(V) relations calculated with the different z(V) curves in Fig. 9 A were shifted to more negative voltages (by up to 46.9 mV with a four-sixths reduction) with only a minor change in slope. Thus, a possible explanation for the lack of modification of the slope of the activation curve in experiments where charged residues are mutated is that the activation process can be separated, as in the allosteric model proposed here, into two distinct steps (i.e., redistribution of voltage sensors and closed/open transitions). A direct consequence is that the slope of the Po curve does not necessarily reflect the slope of gating charge voltage dependence. Since the model provides a molecular interpretation of gating properties of HCN channels, it will be interesting to use it to simulate expectations of experiments in which structural elements of HCN channels are modified (i.e., mutations and/or coexpression of different isoforms).
Model Interpretation of the Different Kinetic Features of HCN Isoforms
The kinetics and cAMP dependence of different HCN isoforms differ quantitatively. For example, HCN1 subunits form channels with fast voltage-dependent gating and reduced cAMP sensitivity, whereas HCN2 and HCN4 channels respond more efficiently to cAMP and have slower kinetics (Santoro et al. 1998; Seifert et al. 1999; Ishii et al. 1999; Ludwig et al. 1999; this work). The allosteric scheme proposed accounts for quantitative differences in gating properties among HCN isoforms within the framework of a common reaction model. To help understand how the different kinetic properties of HCN isoforms can be interpreted according to the allosteric scheme, we superimposed in Fig. 10 plots of the rate parameters obtained for the three isoforms investigated by the fitting procedures in Fig. 4Fig. 5Fig. 6 ([closed circles] HCN1; [open circles] HCN2; [closed triangles] HCN4) along with their best-fitting curves. These plots are representative of both kinetic and steady-state channel properties according to the allosteric model (see superimposition of Po values in Fig. 7).
The comparison led to the following observations: (1) the y4(V) curves of all three isoforms are almost superimposable; (2) the voltage dependence of 4L(V) curves is similar for all isoforms, the main difference being a scaling-up factor when going from HCN1 to HCN2 and HCN4 curves; (3) the z(V) curves of HCN1 and HCN4 are little different, whereas that of HCN2 is some 40 mV more negative; and (4) a similarly large voltage shift is present for the K(V) curve of HCN2 relative to HCN1 and HCN4 curves; the peak K increases when going from HCN1 to HCN2 and to HCN4.
The above observations allow a few tentative speculations on the mechanisms responsible for the kinetics of HCN channels and their differences. First, a scaling-up of time constant curve that leaves unaltered the distribution curve implies in a Boltzmann mechanism that on- and off-rates are divided by the same factor (>1), equivalent to adding a fixed positive energy term to the energy changes associated to on- and off-reactions. The data in Fig. 10 (A and B), thus, would be compatible with the assumption that closed/open transitions of HCN channels involve two mechanisms: (1) a voltage-dependent one, similar for all isoforms and involving movement of an equivalent electric charge of 
1; and (2) a voltage-independent "mechanical" one perhaps associated to intersubunit interactions that are loose in HCN1, tighter in HCN2, and tighter still in HCN4 channels. Assuming simple scaling-up of time constant curves, the 4L curve of HCN1 is 5 and 15 times smaller than those of HCN2 and HCN4, respectively. Compared with HCN1, the extra energies required by HCN2 and HCN4 closed/open transitions, thus, would be RT ln(5) = 0.956 kcal/mol and RT ln(15) = 1.609 kcal/mol (see and ).
Second, according to the data in Fig. 10, faster activation of HCN1 relative to HCN2 and HCN4 is attributable to both faster voltage sensor activation and channel opening, whereas the more negative position of the HCN2 activation curve relative to that of HCN1 or HCN4 (Fig. 7) essentially depends on the voltage dependence of voltage sensors. Third, transition rates of voltage sensors are several times faster than closed/open transition rates, implying that for all isoforms, the activation process involves early sensor movements (from reluctant to willing states) as a preliminary requirement for efficient channel opening. Finally, lack of major changes in the equivalent charge associated to movement of voltage sensors and closed/open transitions suggests common structural rearrangements responsible for voltage-dependent state changes in the isoforms studied.
| Kinetics of Allosteric Model A general set of equations governing the kinetics of the scheme in 2 is
). The system can be reduced by one degree by use of the relation  pi = 1 and expressed in matrix notation as
To apply the general
Using the numbering of states 1–10 as labeled in 2 and the relations A6, the rate constants ki,j can be tabulated as in
We can now explicitly write the elements of
Although integration of
o, βo, o, and o are rate constants at zero voltage, z, zβ, z, and z are the equivalent units of electronic charge moving in the electric field during corresponding state transitions, and r = RT/F = 25.85 mV (T = 300°K). It is assumed that zβ = –z and z = –z. The former assumption is based on the experimental observation that activation and deactivation rate constants of native pacemaker channels have a nearly symmetrical dependence on voltage (Noble et al. 1989; DiFrancesco 1999); the latter considers that the charge moved across the electric field upon transition of a voltage sensor from a reluctant to a willing state is equal and opposite to that moved in the reverse reaction. Numerical description of the kinetics of 2 scheme, thus, depends on knowledge of the six parameters o, βo, o, o, zβ, and z and of the parameter a.
An equivalent description, useful to a more intuitive interpretation of the meaning of parameters, can be obtained by using fractional distribution parameters and time constants. One such set of parameters equivalent to
(note that
An explicit solution of A2 describing the probability of open state can be obtained by the MWC formulation of cyclic allosteric reactions (Monod et al. 1965
Summing over open and closed states and rearranging yields total open ([Ot]) and total closed ([Ct]) concentrations:
The voltage dependence of Po results from the voltage dependence of rate constants according to
 ) an equivalent description can be obtained by referring to C4 O4, rather than CO transitions. In this case, the variables used are (see ):
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ACKNOWLEDGMENTS |
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This work was supported by the MURST (Cofin 1999 to D. DiFrancesco) and by Telethon (Grant no 971 to D. DiFrancesco).
Submitted: 19 December 2000
Revised: 9 April 2001
Accepted: 13 April 2001
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S. Chen, J. Wang, L. Zhou, M. S. George, and S. A. Siegelbaum Voltage Sensor Movement and cAMP Binding Allosterically Regulate an Inherently Voltage-independent Closed-Open Transition in HCN Channels J. Gen. Physiol., January 29, 2007; 129(2): 175 - 188. [Abstract] [Full Text] [PDF]
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 A. Bucchi, A. N. Plotnikov, I. Shlapakova, P. Danilo Jr, Y. Kryukova, J. Qu, Z. Lu, H. Liu, Z. Pan, I. Potapova, et al. Wild-Type and Mutant HCN Channels in a Tandem Biological-Electronic Cardiac Pacemaker Circulation, September 5, 2006; 114(10): 992 - 999. [Abstract] [Full Text] [PDF]
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F. Elinder, R. Mannikko, S. Pandey, and H. P. Larsson Mode shifts in the voltage gating of the mouse and human HCN2 and HCN4 channels J. Physiol., September 1, 2006; 575(2): 417 - 431. [Abstract] [Full Text] [PDF]
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A. Bucchi, A. Tognati, R. Milanesi, M. Baruscotti, and D. DiFrancesco Properties of ivabradine-induced block of HCN1 and HCN4 pacemaker channels J. Physiol., April 15, 2006; 572(2): 335 - 346. [Abstract] [Full Text] [PDF]
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D. DiFrancesco, G. Michels, F. Er, I. Khan, M. Sudkamp, S. Herzig, and U. C. Hoppe Letter Regarding Article by Michels et al, "Single-Channel Properties Support a Potential Contribution of Hyperpolarization-Activated Cyclic Nucleotide-Gated Channels and If to Cardiac Arrhythmias" * Response Circulation, August 2, 2005; 112(5): e72 - e73. [Full Text] [PDF]
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M. L. Chapman and A. M.J. VanDongen K Channel Subconductance Levels Result from Heteromeric Pore Conformations J. Gen. Physiol., July 25, 2005; 126(2): 87 - 103. [Abstract] [Full Text] [PDF]
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R. Mannikko, S. Pandey, H. P. Larsson, and F. Elinder Hysteresis in the Voltage Dependence of HCN Channels: Conversion between Two Modes Affects Pacemaker Properties J. Gen. Physiol., February 28, 2005; 125(3): 305 - 326. [Abstract] [Full Text] [PDF]
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G. Michels, F. Er, I. Khan, M. Sudkamp, S. Herzig, and U. C. Hoppe Single-Channel Properties Support a Potential Contribution of Hyperpolarization-Activated Cyclic Nucleotide-Gated Channels and If to Cardiac Arrhythmias Circulation, February 1, 2005; 111(4): 399 - 404. [Abstract] [Full Text] [PDF]
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J. Qu, Y. Kryukova, I. A. Potapova, S. V. Doronin, M. Larsen, G. Krishnamurthy, I. S. Cohen, and R. B. Robinson MiRP1 Modulates HCN2 Channel Expression and Gating in Cardiac Myocytes J. Biol. Chem., October 15, 2004; 279(42): 43497 - 43502. [Abstract] [Full Text] [PDF]
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B. Gravante, A. Barbuti, R. Milanesi, I. Zappi, C. Viscomi, and D. DiFrancesco Interaction of the Pacemaker Channel HCN1 with Filamin A J. Biol. Chem., October 15, 2004; 279(42): 43847 - 43853. [Abstract] [Full Text] [PDF]
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A. V. Zholos, A. A. Zholos, and T. B. Bolton G-protein-gated TRP-like Cationic Channel Activated by Muscarinic Receptors: Effect of Potential on Single-channel Gating J. Gen. Physiol., April 26, 2004; 123(5): 581 - 598. [Abstract] [Full Text] [PDF]
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T. N. Doan, K. Stephans, A. N. Ramirez, P. A. Glazebrook, M. C. Andresen, and D. L. Kunze Differential Distribution and Function of Hyperpolarization-Activated Channels in Sensory Neurons and Mechanosensitive Fibers J. Neurosci., March 31, 2004; 24(13): 3335 - 3343. [Abstract] [Full Text] [PDF]
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C. Altomare, B. Terragni, C. Brioschi, R. Milanesi, C. Pagliuca, C. Viscomi, A. Moroni, M. Baruscotti, and D. DiFrancesco Heteromeric HCN1-HCN4 channels: a comparison with native pacemaker channels from the rabbit sinoatrial node J. Physiol., June 1, 2003; 549(2): 347 - 359. [Abstract] [Full Text] [PDF]
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V. Macri, C. Proenza, E. Agranovich, D. Angoli, and E. A. Accili Separable Gating Mechanisms in a Mammalian Pacemaker Channel J. Biol. Chem., September 20, 2002; 277(39): 35939 - 35946. [Abstract] [Full Text] [PDF]
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 J. Qu, A. Barbuti, L. Protas, B. Santoro, I. S. Cohen, and R. B. Robinson HCN2 Overexpression in Newborn and Adult Ventricular Myocytes : Distinct Effects on Gating and Excitability Circ. Res., July 6, 2001; 89 (1): e8 - e14. [Abstract] [Full Text] [PDF]
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C. Viscomi, C. Altomare, A. Bucchi, E. Camatini, M. Baruscotti, A. Moroni, and D. DiFrancesco C Terminus-mediated Control of Voltage and cAMP Gating of Hyperpolarization-activated Cyclic Nucleotide-gated Channels J. Biol. Chem., August 3, 2001; 276(32): 29930 - 29934. [Abstract] [Full Text] [PDF]
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