Introduction

Calcium entry through voltage-gated calcium channels (CaV) initiates and controls a large variety of cellular functions such as generation and propagation of electrical impulses, sensory processes, muscle contraction, secretion of hormones and neurotransmitters, cell differentiation and gene expression [1]. Mammalian Ca2+ channel α1 subunits are encoded by at least ten genes [7]. Depending on the potential where voltage-gated Ca2+ channels first open during a depolarisation (so-called threshold potential), they can be subdivided in high-voltage-activated (CaV1–CaV2) or low-voltage-activated (CaV3) Ca2+ channels. Different thresholds of activation were also reported for different isoforms of high-voltage-activated Ca2+ channels [7].

We have recently shown that a point mutation (I/T) in segment IIS6 of CaV1.2 that is associated with a channelopathy transforms the high-voltage-activated CaV1.2 channel into a low-voltage-activated channel [16, 19]. Additional gating-sensitive residues were identified in other S6 segments of CaV1.2 [22, 28].

The molecular mechanisms underlying channelopathy mutations in CaV1.2 are currently unknown. CaV1.2 are heterooligomeric protein complexes composed of an α1 subunit and auxiliary β and α2–δ subunits (see [7] for review). Their pore-forming/voltage-sensing α1 subunit is composed of four homologous domains formed by six transmembrane segments (S1–S6) each [6].

Compared to Kv, the pore of CaV1.2 is asymmetric. The ‘helix-bending’ PXP motif of Kv1.2 is absent and the conserved glycine (corresponding to position 220 in KvAP and 83 in MthK, see [21]) is only present in segments IS6 and IIS6 (see review by Hering et al. [17]). We have shown that substituting proline for this glycine in IIS6 of CaV1.2 has minor effects on gating of CaV1.2 [19].

There is evidence, however, that CaV α1 subunits share a common architecture with voltage-gated potassium channels. A cysteine scan of the pore-lining S6 segments of CaV2.1 by Zhen et al. [36] revealed that opening and closing of the channel changes the accessibility of cysteines in a pattern consistent with a gate localised on the intracellular side. This view is supported by pharmacological studies. On one hand, the inner channel mouth of CaV1.2 has to open to enable access of the charged (quaternary) phenylalkylamine devapamil (qDev) from the cytosolic side [3]. Interestingly, qDev has unrestricted (voltage independent) access to its binding pocket in the vestibule, suggesting a ‘widely open’ inner channel mouth in the open state that is in line with Poisson distribution of voltage in the open conformation of a potassium channel [21]. On the other hand, pore-forming S6 segments are apparently able to close the channel vestibule thereby restricting dissociation of organic CaV1.2 inhibitors such as qDev [3].

Scanning the pore-forming S6 segments with mutations to alanine [4], a bulky tryptophan, a ‘helix kinking’ proline, a small flexible glycine, a small polar threonine or aspartate or a small cysteine which can form disulphide bonds enabled the identification of gating-sensitive positions in the pore of various voltage-gated ion channels (e.g. [14, 19, 22, 27, 33, 35, 36]).

In the present study, we ask the question how physicochemical properties of amino acids in gating-sensitive positions of CaV1.2 S6 segments affect the threshold of channel activation (i.e. the open-closed equilibrium).

In continuation of our previous work, we focus on the ‘bundle-crossing region’ of segments IS6, IIS6 and IIIS6 where the channel is likely closed by tight sealing. G1193 was identified as a novel strong gating determinant in segment IIIS6. Systematic substitution of this residue with amino acids with different properties affected pore stability. A common kinetic phenotype was a leftward shift of the activation curve that is accompanied by decelerated channel deactivation (see also [3, 35]).

Pivotal physicochemical properties of mutated gating determinants in segments IS6, IIS6 and IIIS6 were identified by correlating magnitudes of the shifts of the activation curves with descriptors of the amino acids. By means of this ‘mutation correlation analysis’, we discovered significant links between activation gating and physicochemical properties in positions L434 (IS6), I781 (IIS6) and G1193 (IIIS6).

Materials and methods

Mutagenesis

The CaV1.2 α1-subunit coding sequence (GenBank™ X15539) in-frame 3′ to the coding region of a modified green fluorescent protein was kindly donated by Dr. M. Grabner et al. [12]. Substitutions in segment IS6 and IIIS6 of the CaV1.2 α1-subunit were introduced using the QuikChange® Lightning Site-Directed Mutagenesis Kit (Stratagene) with mutagenic primers according to the manufacturer’s instructions. Mutations were introduced in segment IIIS6 in position 1193 (G1193T/V/N/M/A/Q/W/P) and positions F1191T, V1192T, F1194T, V1195T and I1196T and in IS6 in position 434 (L434A/G/T/V/N/S/W/M).

We systematically introduced residues of different sizes, polarity/hydrophobicity, and aromaticity. All constructs were checked by restriction site mapping and sequencing.

Cell culture and transient transfection

Human embryonic kidney tsA-201 cells were grown at 5% CO2 and 37°C to 80% confluence in Dulbecco’s modified Eagle’s/F-12 medium supplemented with 10% (v/v) foetal calf serum and 100 U/ml penicillin/streptomycin. Cells were split with trypsin/EDTA and plated on 35 mm Petri dishes (Falcon) at 30–50% confluence ~16 h before transfection. Subsequently, tsA-201 cells were co-transfected with cDNAs encoding wild-type or mutant CaV1.2 α1-subunits with auxiliary β2a [26] as well as α2–δ1 subunits [10]. The transfection of tsA-201 cells was performed using the FUGENE6 Transfection Reagent (Roche) following standard protocols. tsA-201 cells were used until passage number 15. No variation in channel gating related to different cell passage numbers was observed.

Ionic current recordings and data acquisition

Barium currents (I Ba) through voltage-gated Ca2+ channels were recorded at 22–25°C using the patch-clamp technique [15] by means of an Axopatch 200A patch-clamp amplifier (Axon Instruments, Foster City, CA, USA) 36–48 h after transfection. The extracellular bath solution contained (in millimolars) BaCl2 5, MgCl2 1, HEPES 10, and choline-Cl 140, titrated to pH 7.4 with methanesulphonic acid. Patch pipettes with resistances of 1 to 4 MΩ were made from borosilicate glass (Clark Electromedical Instruments, UK) and filled with pipette solution containing (in millimolars) CsCl 145, MgCl2 3, HEPES 10, and EGTA 10, titrated to pH 7.25 with CsOH. All data were digitised using a DIGIDATA 1200 interface (Axon Instruments, Foster City, CA, USA), smoothed by means of a four-pole Bessel filter and saved to disc. One hundred-millisecond current traces were sampled at 10 kHz and filtered at 5 kHz; tail currents were sampled at 50 kHz and filtered at 10 kHz. Holding potential of −100 mV was applied to exclude effects of inactivation on measured parameters. Peak current at more positive holding potentials (−90 mV) was routinely measured to confirm complete recovery from inactivation. Leak currents were subtracted digitally using average values of scaled leakage currents elicited by a 10-mV hyperpolarizing pulse or electronically by means of an Axopatch 200 amplifier (Axon Instruments, Foster City, CA, USA). Capacity currents were not subtracted. When the pipettes were filled with pipette solution, their input resistance ranged between 1 and 4 MΩ. The mean cell capacity was 33 ± 5 pF (n = 12). The mean series resistance was 4.7 ± 1.9 MΩ. It was compensated (60–85% compensation) by the following procedure: The depth of the positive feedback was gradually increased until oscillations (small overcompensation) appear. Even in large cells, the time constant of the capacity current (τ capacity) did not exceed ≈0.25 ms. The early current phase was excluded from data processing (at least 3 × τ capacity ≈ 0.75 ms). The pClamp software package (Version 7.0 Axon Instruments, Inc.) was used for data acquisition and preliminary analysis. Microcal Origin 7.0 was used for analysis and curve fitting.

Current–voltage (I–V) relationships for individual cells were normalized to the maximal current. Normalized I–V curves were averaged and the mean I–V curve was fitted to the modified Boltzmann equation:

$$ I = \frac{{{G_{\max }}\; \cdot \;\left( {V - {V_{\rm{rev}}}} \right)}}{{1 + \exp \frac{{{V_{0.5}} - V}}{{{k_{\rm{act}}}}}}} $$

where I is the peak current, V is the membrane potential, V rev is the reversal potential, G max is the maximal membrane conductance, V 0.5 is the voltage for half-maximal activation and k act is the slope factor.

The values of V 0.5 and k act were used for calculation of the steady-state activation:

$$ {m_\infty } = \frac{1}{{1 + \exp \frac{{{V_{0.5}} - V}}{{{k_{\rm{act}}}}}}} $$

Data points for activation were calculated dividing the averaged peak currents at given potential by G max × (V − V rev).

The time course of current activation was fitted to a mono-exponential function:\( I(t) = A\; \times \;\exp \left( {\frac{t}{\tau }} \right) + C, \)where I(t) is the current at time t, A is the amplitude coefficient, τ is the time constant and C is the steady-state current. Data are given as mean ± SE.

Calculation of amino acid descriptors

Physicochemical descriptors were calculated for amino acids substituted in positions L434 (IS6), I781 (IIS6) and G1193 (IIIS6) using the Molecular Operating Environment (MOE; version 2008.10, Chemical Computing Group, Inc., Montreal, QC, Canada). This software package calculates more than 300 descriptors. Examples include polarity measures, size and shape indices, flexibility, accessible surface area and others. Seventeen out of 327 possible descriptors were selected to analyse their potential role in channel gating (see Supplementary Tables 1 and 2 for list of descriptors and calculated values).

A turn propensity scale describing the relative turn preferences of the different amino acids in formation of transmembrane helical hairpins was taken from Monné et al. [25] (see also [34]). The hydrophobicity scales were taken from Kyte and Doolittle [23], Hessa et al. [18], White and Wimley [32], Guy [13], Eisenberg et al. [9] and Hopp and Woods [20]. Rigidity and flexibility indices accounting for a series of descriptors, i.e. number of bonds, number of rings, number of rings per atoms in molecule, number of rotatable bonds, number of rotatable bonds per atoms in molecule, number of rigid bonds (i.e. aromatic or double bonds), number of rigid bonds per atoms in molecule, longest flexible chain, ditto per atoms in molecule, number of rigid fragments, ditto per atoms in molecule, number of partial flexible chains and ditto per atoms in molecule, were taken from Gottfries and Eriksson [11].

Correlating amino acid properties with ΔV act

The capability of a given descriptor to predict the shift of the activation curve was established by ranking the correlation coefficients and its significance (t test). This approach enabled the identification of a ‘leading descriptor’, i.e. the one with the largest correlation coefficient (r) and the highest significance. Linear regressions were calculated using the ORIGIN subroutine which also yielded correlation coefficients and their statistical significance.

Subsequently, we correlated weighted linear combinations of all 17 descriptors with ΔV act. Combined descriptors were calculated as \( \Delta D = a\Delta {D_1} + b\Delta {D_2} \) where ΔDs represent the difference between descriptor values for mutant and wild-type CaV1.2. Weighting factors (a and b) were used to estimate the contribution of each descriptor to correlation (see Table 3). For mutations in positions I781 (IIS6) and G1193 (IIIS6), this approach enabled us to establish a second descriptor of relevance by ranking the combined correlations with respect to the lowest root mean square error and the highest r (see Table 2).

Correlating amino acid properties with ΔG

ΔG in the mutant channels relative to WT channel was calculated according to the equation:

$$ \Delta G = RT\left( {\frac{{{V_{0.5,{\rm{mut}}}}}}{{{k_{\rm{mut}}}}} - \frac{{{V_{0.5,{\rm{WT}}}}}}{{{k_{\rm{WT}}}}}} \right) $$

with V 0.5 representing the voltage of half activation and k the slope of the curve at V 0.5 (see Table 1). The shifts of the steady-state activation curves (ΔV act) of the CaV1.2 mutants compared to wild-type channels and the calculated changes in free energy ΔG were plotted against the descriptor values and analysed as described above for ΔV act (see Supplemental data).

Table 1 Pore mutations affect voltage-dependent gating of CaV1.2
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Results

G1193 is a gating-sensitive residue in IIIS6

We have recently shown that gradual changes in hydrophobicity in the bundle-crossing region of transmembrane segment IIS6 gradually shift the activation curve of CaV1.2 [17]. To investigate whether hydrophobic interactions play a similar role in the equivalent section of segment IIIS6, we substituted the small and polar threonine for each of several hydrophobic residues (F1191–I1196) of the CaV1.2 α1-subunit (Fig. 1a). Barium (Ba2+) currents were subsequently measured with the patch-clamp technique after co-expression of the auxiliary β2a and α2–δ1 subunits in tsA-201 cells. All six threonine mutants (F1191T–I1196T) conducted ionic currents. The largest shift in channel activation (ΔV act = −31.2 ± 1.3 mV) and the correspondingly slowest kinetics of current activation and deactivation were observed for mutation G1193T, suggesting a potentially important role of this glycine in CaV1.2 gating (Table 1; G1193 is ten residues downstream from the putative glycine hinge position). A family of inward Ba2+ currents and the corresponding activation curve of mutant G1193T are shown in Fig. 1. The activation time constant of G1193T ranged between 14.5 ms (−60 mV) and 1.8 ms (10 mV; Fig. 1d) and the deactivation time constant between 1.8 ms (−100 mV) and 14.2 ms (−60 mV).

Fig. 1
figure 1

Gating changes induced by threonine mutations in segment IIIS6 of CaV1.2. a Alignment of pore-lining S6 segments of CaV1.2. Mutated residues are shaded grey. Previously identified gating determinants are underlined. GxxxG motif is shown in bold. b Averaged activation curves of wild-type (n = 8) and mutants V1192T (n = 7), G1193T (n = 7) and I1196T (n = 9). c Representative families of I Ba through wild-type and G1193T mutant channels during depolarising test pulses from −100 mV. Zero current levels are indicated as dotted lines. d Mean time constants of channel activation of WT (n = 8) and mutants V1192T (n = 7), G1193T (n = 7) and I1196T (n = 9) are plotted against test potential. e Representative tail currents of WT and G1193T channels. Currents were activated during a 20-ms conditioning depolarisation to −10 mV for wild-type and −40 mV for G1193T. Deactivation was recorded during subsequent repolarisations with 10-mV increments starting from −100 mV. f Mean time constants of channel deactivation of wild-type (n = 7) and mutants V1192T (n = 6), G1193T (n = 6) and I1196T (n = 7) are plotted against test potential. Time constants were estimated by fitting current activation and deactivation to a mono-exponential function

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Smaller kinetic changes were observed for mutations V1195T (ΔV act = −10.3 ± 1.1 mV), I1196T (ΔV act = −8.0 ± 1.1 mV) and F1191T (ΔV act = −7.1 ± 1.3 mV). Other threonine substitutions had negligible effects (Table 1; see Fig. 1d, f for corresponding changes in current activation and deactivation kinetics of representative mutants V1192T, G1193T and I1196T compared to wild-type CaV1.2).

Mutating G1193 to residues with different properties

To gain insight into the structural requirements for stabilisation of the closed state of the channel at this position, we then replaced G1193 with a series of residues of different hydrophobicity, size and polarity. The resulting changes in voltage dependence of CaV1.2 are illustrated in Fig. 2a. Replacement of G1193 by threonine, asparagine, glutamine, valine, methionine, proline and alanine shifts channel activation ranging from ΔV act of –27.9 ± 1.3 mV for G1193N to 6.5 ± 1.3 mV for G1193A (Fig. 2a; Table 1). Interestingly, the mutation G1193A shifted the activation curve towards more depolarised voltages (ΔV act = 6.5 ± 1.3 mV). Replacement of G1193 by tryptophan results in a non-functional channel. The larger shifts in channel activation in the hyperpolarising direction were accompanied by slower kinetics of current activation and deactivation (Fig. 2b, c). We observed no significant effects on the reversal potential (data not shown) suggesting that the studied deep pore mutations did not affect selectivity.

Fig. 2
figure 2

Gating changes induced by mutations of G1193 in segment IIIS6 of CaV1.2. a Averaged activation curves of the WT (n = 8) and mutants G1193T (n = 7), G1193A (n = 6), G1193N (n = 5) and G1193V (n = 8). b, c Mean time constants of channel activation (b) and deactivation (c) for WT and mutants G1193T, G1193A, G1193N and G1193V are plotted against test potential (n = 5–8). Time constants were estimated by fitting current activation and deactivation to a mono-exponential function

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Mutation correlation analysis in position G1193

In order to get insights into possible links between channel activation and physicochemical properties of amino acids, regression analysis was performed for selected descriptors (see “Materials and methods” section and Supplementary Table 1), including size, hydrophobicity, flexibility and rigidity indices, propensity to van der Waals interactions and others.

Descriptor values were calculated with MOE or taken from the literature (see “Materials and methods”) and plotted against the corresponding shifts of the activation curves or calculated changes in free energy (ΔG). The correlations were ranked by correlation coefficient and significance. The best correlation with ΔV act in position G1193, with the highest statistical significance (t test, p < 0.009), was obtained with the accessible surface area of all polar atoms (ASA_P; Fig. 3). Table 2 shows the correlation coefficients (r) for the linear regression plots of physicochemical descriptors against the measured ΔV act. In contrast to our findings in segment IIS6 [17], ΔV act did not correlate with hydrophobicity (Table 2). We subsequently searched for optimal two-descriptor correlations by combining all 17 descriptors in pairs (see “Materials and methods”). The most significant correlation was observed for the combination of ASA_P (leading descriptor) and the number of rotatable bonds (Fig. 3). Potentially modulating effects of other physicochemical properties are summarised in Table 3.

Fig. 3
figure 3

The accessible surface area of all polar atoms in position G1193 (IIIS6) predicts the shift of the activation curve. a Correlation between the shifts of the activation curves (ΔV act) and the changes in accessible surface area of all polar atoms (ΔASA_P). b Correlation between ΔV act and the best linear combination of two descriptors ASA_P and b_rotN (the number of rotatable bonds, see Table 3 for ranking). c, d No correlation between ΔV act and Δb_rotN and ΔV act and Δt-Rig (an amino acid side-chain rigidity index). See complete list of descriptors in Supplementary Table 1

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Table 2 Identification of leading descriptors predicting ΔV act
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Table 3 Combined descriptor analysis
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Correlation analysis in gating-sensitive position L434 (IS6)

A similar methodological approach was used to estimate the predictive value of amino acid properties for mutations in position L434. This amino acid was previously identified as a gating-sensitive residue in segment IS6 [22]. Mutating L434 to eight amino acids with different properties (compare with mutations in segment IIIS6) resulted in different shifts of the activation curve (Fig. 4).

Fig. 4
figure 4

Gating changes induced by mutations of L434 in segment IS6 of CaV1.2. a Averaged activation curves of the WT (n = 8) and mutants L434A (n = 5), L434N (n = 6) and L434V (n = 5). b, c Mean time constants of channel activation (b) and deactivation (c) for WT and mutants L434A, L434N and L434V are plotted against test potential (n = 5–8). Time constants were estimated by fitting current activation and deactivation to a mono-exponential function

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The best prediction of ΔV act was observed for the number of rotatable bonds (b_RotN, see Table 2). A rotatable bond is defined as any single non-ring bond to a non-terminal heavy atom within the amino acid molecule. The regression line for b_RotN is illustrated in Fig. 5 (r = 0.86, p < 0.006). No improvement was observed for any combined descriptor correlation (Table 3).

Fig. 5
figure 5

Side-chain flexibility in position L434 (IS6) predicts the shifts of the activation curve. a Correlation between ΔV act and Δb_rotN (number of rotatable bonds). b Correlation with the amino acid flexibility index Δt-Flx (see Supplementary Table 1)

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Modulation of hydrophobic interactions in I781 (IIS6) by other amino acid properties

In a previous study, we found a highly significant correlation between changes in hydrophobicity (ΔH) and ΔV act for mutations in position I781 of segment IIS6 [17]. This correlation suggested that either the closed channel state is stabilised by hydrophobic interactions with neighbouring residue or a stabilisation of the open state by exposure of more polar residues in this position to water, or both. Here we confirmed the leading role of hydrophobicity in this position by accounting for all 17 descriptors in this position (r = 0.86 and p < 0.005; see Table 3). Improved correlations were obtained for several descriptor combinations (e.g. hydrophobicity and the number of O and N atoms, with r = 0.97 and p < 0.0001; see Table 3 for improved correlations for other amino acid properties).

Discussion

We have previously reported that the shift of the activation curve induced by point mutations in segment IIS6 correlates with changes in hydrophobicity in a cluster of residues in segment IIS6 (779–784: LAIA) and particularly in position I781 (see [17] for review). Mutations of I781 in the α1 subunit of CaV1.2 to residues of different hydrophobicity, size and polarity all shifted channel activation in the hyperpolarising direction with I781P causing the most severe (−37 mV shift) effect [19]. Mutations in position I781 decelerated activation and deactivation, and the shifts to more hyperpolarized voltages usually correlate with slower activation kinetics. Similar shifts of the activation curve and even more dramatic slowing of the activation and deactivation kinetics were observed in NaChBac when a conserved glycine 219 (corresponding to a putative hinge glycine in S6 of most K+ channels) was mutated to a helix breaking proline [35]. Furthermore, when a locus of conserved hydrophobic residues in pore/gate-forming segment IVS6 of CaV2.3 (1718–1722: VAVIM) was systematically replaced by flexible glycines, slow deactivation of mutants A1719G and V1720G was accompanied by a −20-mV shift of the activation curve [27]. Thus, leftward shifts of the activation curve and slowing down of current activation in CaV are induced by mutations to amino acids with different physicochemical properties. Interestingly, the leftward shifts in the steady-state activation curves and the deceleration of the activation and deactivation resemble very much the action of L-type Ca2+ channel agonists such as BayK 8644 (see also [19]). Here we investigate whether these properties (descriptors) predict the measured shifts of the activation curve.

G1193 is a gating-related residue in segment IIIS6

Mutating the hydrophobic residues of the ‘bundle-crossing’ region of segment IIIS6 (Fig. 1a) to the small and polar threonine revealed a gating-sensitive residue at position G1193. Mutations of G1193 caused the largest changes in gating of CaV1.2 as measured by activation curves and current deactivation kinetics (Figs. 1b–f and 2).

Changes in the accessible surface area of all polar atoms in position G1193 (IIIS6) predict the shifts of the activation curve

Crystal structures of KcsA, KvAP and MthK potassium channels revealed that a flexible glycine at analogous positions 99, 220 and 83 provides a hinge point for helix bending of Kv during channel opening [21, 24, 35]. Mutation of the analogous glycine in NaChBac (G219P) to proline, which forces an α-helix into a bent conformation, substantially slowed deactivation and shifted the activation curve [36]. The functional role of S6 glycines and the positions for helix bending during channel activation of CaV remain unclear. No correlations either with side-chain rigidity or with helix turn propensity were observed for mutations of G1193 (Fig. 3d; Table 2; localised ten residues downstream from the putative glycine hinge position). We then examined the effect of side-chain size because we suspected that if the structure around G1193 were tightly packed, the small size of glycine might be functionally important. No significant correlation with the mass of the substituted residues was found (p > 0.05; Table 3). However, a significant correlation between ΔV act and the accessible surface area of all polar atoms was observed (ASA_P; Fig. 3a, b). Since ASA_P would indicate more favourable energy for solvation in water [8, 29, 31] than packing in the interior of a protein, this relationship suggests that the open gate conformation either exposes this position to more water than the closed conformation or allows the side chain to avoid unfavourable interactions with other residues, or both.

Number of rotatable bonds and a side-chain amino acid flexibility index predict the shift of the activation curve by mutations in position L434 (IS6)

A strong correlation (r = 0.86, p < 0.006) between the number of rotatable bonds and ΔV act was observed for mutations of L434 in segment IS6 (Figs. 4 and 5). These data suggest that a certain degree of side-chain flexibility of residues in this position of the ‘bundle-crossing region’ is necessary for normal channel gating. A flexibility index introduced by Gottfries and Eriksson [11] for amino acids confirms the role of side-chain flexibility in this position. Interestingly, the gating-sensitive L434 occupies the central position of a GxxxG motif (Fig. 1a) which is known to allow backbone–backbone helix interactions in a hydrophobic environment [5]. The GxxxG motif participates in helix packing typically in a way where glycines allow close contacts between helices crossing at angles atypical of ‘knobs-into-holes’ packing. Other larger residues in these positions would probably tend to clash with atoms of the adjacent helix. L434 is located in the middle of this pattern (i.e. on the opposite face) and thus would not be involved in the helix–helix interactions that involve the glycines. We speculate that L434 is involved in interactions with other helices (e.g. if the glycines are involved with S6–S6 interactions than L434 could interact with S5 or L45 linker).

Co-correlations provide additional insight into modulatory properties of amino acid residues

In positions L434 (IS6), I781 (IIS6) and G1193 (IIIS6), we identified different leading descriptors providing the highest correlations with a single amino acid descriptor. A side-chain flexibility index, hydrophobicity and the accessible surface area of polar atoms predicted the shifts of the activation curves induced by mutations in the corresponding positions (Figs. 3, 5 and 6). We performed a co-correlation analysis where ΔV act was correlated with any of the 136 weighted linear combination of two descriptors (see Supplementary Table 1 for complete list of descriptors combined for co-correlations). The predictive capability of side-chain flexibility in position L434 (i.e. number of rotatable bonds or the related amino acid descriptor Δt-Flx) was not improved by any of the 136 co-correlations tested.

Fig. 6
figure 6

Hydrophobicity in position I781 (IIS6) predicts the shifts of the activation curve. a Correlation between ΔV act and changes in hydrophobicity. b The best prediction of ΔV act by a linear combination of two descriptors was obtained for ΔHydrophobicity and ∆lip_acc (number of O and N atoms; hydrogen bond acceptors). c Second best co-correlation was observed for ΔHydrophobicity and ∆b_rotN (see also Table 3). d No correlation between ΔV act and ∆lip_acc (see Supplementary Table 1)

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Analysing all linear combinations between two descriptors for mutations in position I781 and G1193 revealed some very strongly linear predictions of ΔV act. The leading descriptor was found to be always one out of the best correlating descriptor pairs. The fractional weighting of the leading descriptors in the best-ranking combinations ranged from 60% to 83% (see Table 3, examples are illustrated in Figs. 3b and 6b, d). The second descriptors alone had no predictive capability (Figs. 3c and 6d). The best prediction of ΔV act for mutations in position I781 was obtained for a combination of ΔHydrophobicity and the number of hydrogen bound acceptors (N and O atoms) with second best ranking of the combination ΔHydrophobicity and a side-chain flexibility index. These data suggest that hydrogen bonding and side-chain flexibility in this position affect the closed-open equilibrium. The same analysis for mutations in position G1193 revealed better correlations for the combination of the accessible surface area of all polar atoms with one of the side-chain flexibility.

The improved predictive capability of combined descriptors suggests that the dominating interaction (leading descriptor) in selected positions can be modulated by additional interactions (see Table 3 for other potentially modulating interactions in position I781, e.g. side-chain flexibility, van der Waals interactions and others).

Link between ΔV act and changes in free energy (ΔG)

Replacing pore residues by amino acids with different physicochemical properties affects the free energy of CaV1.2 gating. Estimation of changes in free energies and cycle mutant analyses in voltage-gated ion channels enabled important insights into the energetics of channel opening (e.g. [30, 33]; see [22] for a study on CaV1.2). Accordingly, we have calculated the changes of free energy during the activation of wild-type and all IS6, IIS6 and IIIS6 CaV1.2 mutants. ΔV act and ΔG correlate strongly (Supplementary Figure 1). Nevertheless, ΔG deduced from a Boltzmann distribution reflects not only the energy of pore opening but also the energy of voltage sensor transition. In general, it can be assumed that mutations in the pore region do not disturb the voltage sensor transition and that ΔG of S6 mutations reflects the changes in the pore. However, some mutations apparently affect the transition of the voltage-sensing machinery from the resting to the activated state (e.g. I780P (IIS6) in [2]). Changes in the slope factor reflect changes in δ × Z, where Z is the charge and δ is a fraction of membrane potential that the voltage sensors cross during their movement. Obviously the mutations in the pore are unable to change the charge Z. They may, however, modify the fraction of the effective membrane potential by releasing or restricting voltage sensor movements. Minor changes in the slope factor (see Table 1) have effects on the calculated ΔG and may affect correlations. For the studied S6 mutations, ΔG and ΔV act appeared to be equivalent measures of the pore energetics. This may, however, not always be the case and care has to be taken with pore mutations that significantly change the slope factor (e.g. I1196T; Table 1) or significantly change the kinetics of channel opening and closure (A780P [2]).

Conclusions and outlook

Mutations in the bundle-crossing region of pore-forming S6 segments frequently shift the activation curves along the voltage axis and affect the kinetics of channel gating. Making use of mutation correlation analysis, we identified descriptors of side chains at specific positions that predict these changes in channel activation gating. In segment IS6 (L434), ΔV act correlated with the number of rotatable bonds reflecting side-chain flexibility. In position G1193 in segment IIIS6, ΔV act depended on the accessible surface area of all polar atoms, and in position I781, ΔV act correlated with hydrophobicity. Leading descriptors were identified by single and combined correlation analysis (i.e. correlations between ΔV act and all possible pairs of amino acid descriptors were analysed). Correlation analysis emerges thus as a useful tool to unravel the importance of particular amino acid properties in pore-lining S6 segments. Different leading descriptors in different S6 segments indicate individual contributions of four homologous but not identical domains in CaV1.2 gating.