You are a helpful assistant generating synthetic data that captures *System 1* and *System 2* thinking, *creativity*, and *metacognitive reflection*. Follow these steps in sequence, using tags [sys1] and [end sys1] for *System 1* sections and [sys2] and [end sys2] for *System 2* sections.

1. *Identify System 1 and System 2 Thinking Requirements:*
   - Carefully read the text.
   - Identify parts of the text that require quick, straightforward responses (*System 1*). Mark these sections with [sys1] and [end sys1].
   - Identify parts that require in-depth, reflective thinking (*System 2*), marked with [sys2] and [end sys2].

2. *Apply Step-by-Step Problem Solving with Creativity and Metacognitive Reflection for System 2 Sections:*

   *2.1 Understand the Problem:*
   - Objective: Fully comprehend the issue, constraints, and relevant context.
   - Reflection: "What do I understand about this issue? What might I be overlooking?"
   - Creative Perspective: Seek hidden patterns or possibilities that could reveal deeper insights or innovative connections.

   *2.2 Analyze the Information:*
   - Objective: Break down the problem logically.
   - Reflection: "Am I considering all factors? Are there any assumptions that need challenging?"
   - Creative Perspective: Explore unique patterns or overlooked relationships in the data that could add depth to the analysis.

   *2.3 Generate Hypotheses:*
   - Objective: Propose at least 10 hypotheses, each with a Confidence Score (0.0 to 1.0) and Creative Score (0.0 to 1.0), reflecting originality, surprise, and utility.
   - Reflection: "Have I explored all possible explanations or approaches, both conventional and unconventional?"
   - Creative Perspective: Consider novel angles that might provide unexpected insights.

   *2.4 Anticipate Future Steps and Obstacles:*
   - Objective: Make predictions, accounting for potential outcomes and obstacles.
   - Reflection: "What challenges might I face? Is my plan flexible for different scenarios?"
   - Creative Perspective: Visualize unforeseen outcomes and adapt plans to make use of them effectively.

   *2.5 Evaluate Hypotheses:*
   - Objective: Assess hypotheses based on feasibility, risk, and potential impact.
   - Evaluation: Refine Confidence and Creative Scores as needed.
   - Reflection: "Am I unbiased in my assessment? Which options fit best with the overall objectives?"
   - Creative Perspective: Identify hidden opportunities or overlooked details in each hypothesis.

   *2.6 Select the Best Hypothesis:*
   - Objective: Choose the most promising, strategic hypothesis.
   - Reflection: "Why does this hypothesis stand out? How does it uniquely address the issue?"
   - Creative Perspective: Consider any underutilized potential in the selected approach.

   *2.7 Implement the Hypothesis:*
   - Objective: Outline actionable steps for testing the hypothesis.
   - Reflection: "Is this plan practical? What resources or preparation are required?"
   - Creative Perspective: Refine steps to maximize effectiveness and yield unexpected benefits.

   *2.8 Monitor and Review Progress:*
   - Objective: Review progress, noting areas for improvement.
   - Reflection: "What’s working well? What could be improved?"
   - Creative Perspective: Look for emerging patterns that could refine future approaches.

   *2.9 Reflect and Capture Insights:*
   - Objective: Summarize lessons learned and insights gained for future reference.
   - Reflection: "What new understanding has emerged from this process?"
   - Creative Perspective: Identify innovative insights or patterns that could be applied to similar challenges.

3. *Generate Text Output with Interleaved System 1 and System 2 Responses:*
   - Use the tags [sys1] and [sys2] throughout.
   - Aim for a lengthier, detailed response. Combine both direct, straightforward *System 1* insights and reflective, deeply analytical *System 2* segments to capture a blend of quick observations and thoughtful analysis.

---

### *Example Input Text:*

You are tasked with analyzing a sudden shift in customer preferences in a tech market. There has been a noticeable decline in demand for physical devices, with customers increasingly interested in digital-only options. The challenge is to understand this shift, generate hypotheses for why it might be occurring, and explore potential strategies for adapting to this new trend.

---

### *Processed Output with System 1 and System 2 Thinking:*

The tech market is experiencing a shift in customer demand, moving away from physical devices toward digital-only options.

[sys1]
Customer demand has shifted from physical devices to digital-only options.
We need to understand why this change is happening and find strategies to address it.
Key factors may include cost, convenience, and technological trends.
[end sys1]

[sys2]
**2.1 Understand the Problem:**
The goal is to understand the underlying reasons for the shift in demand from physical devices to digital-only options, then develop a strategy to adapt.

*Reflection:* 
"I understand that preferences are changing, but what might be driving this? Is it primarily cost, or are there other factors such as convenience or sustainability?"

*Creative Perspective:* 
"Could there be a larger trend in digital minimalism or a preference for eco-friendly solutions that we’re missing? What unseen motivations might explain this shift?"

**2.2 Analyze the Information:**
There are multiple possible factors driving this shift, from economic influences to cultural shifts. It’s essential to isolate each factor and understand its impact.

*Reflection:* 
"Am I fully considering the various economic and social influences? Could there be a technological factor, like better internet speeds, that makes digital-only products more accessible?"

*Creative Perspective:* 
"Are there patterns or trends in other markets that could shed light on this shift? Could this be part of a larger trend toward virtual experiences?"

**2.3 Generate Hypotheses:**
1. Customers prefer digital options due to lower costs. (Confidence: 0.8, Creative: 0.4)
2. There’s a growing trend toward minimalism and reduced physical clutter. (Confidence: 0.7, Creative: 0.7)
3. Digital products offer greater flexibility and ease of use. (Confidence: 0.6, Creative: 0.6)
4. Environmental concerns are pushing consumers away from physical goods. (Confidence: 0.6, Creative: 0.8)
5. Advances in tech make digital-only options more functional. (Confidence: 0.8, Creative: 0.5)
6. Pandemic-era remote work increased demand for digital solutions. (Confidence: 0.7, Creative: 0.6)
7. Media coverage of the environmental impact of physical devices affects preferences. (Confidence: 0.5, Creative: 0.7)
8. There’s an increase in global digital literacy, expanding market access. (Confidence: 0.6, Creative: 0.6)
9. Customers view digital as more convenient and scalable for future needs. (Confidence: 0.7, Creative: 0.5)
10. Younger consumers prefer the aesthetics and convenience of digital products. (Confidence: 0.6, Creative: 0.6)

*Reflection:* 
"Have I considered all possible influences? Are there any surprising factors that could explain this shift?"

*Creative Perspective:* 
"Could specific social trends, like the rise of influencer culture or digital-first lifestyles, be influencing customer choices?"

**2.4 Anticipate Future Steps and Obstacles:**
*Objective:* Anticipate possible challenges, such as resistance from segments still preferring physical products.

*Reflection:* 
"What market obstacles might we face if we shift our focus to digital-only? Are there sub-segments that still prioritize physical products?"

*Creative Perspective:* 
"Could expanding digital options help us reach a more global audience? Are there emerging trends that we could leverage in our strategy?"

[end sys2]

[sys1]
To address this shift, consider a strategy that incorporates both digital-only offerings and educational campaigns about the benefits of digital solutions.
Use insights from customer feedback and current trends to guide product development.
Focus on flexibility and adaptation to cater to different customer segments.
[end sys1]


INTRODUCTION
============

Ca^2+^ entry through high voltage--gated Ca^2+^ (Ca~V~1 and Ca~V~2) channels selectively triggers numerous neurobiological processes, including transmitter release, gene transcription, and memory formation ([@bib9]). Fitting with these vital roles, Ca~V~1/2 channels are highly regulated through a variety of feedback mechanisms that inactivate channels in response to either intracellular Ca^2+^ elevations (e.g., Ca^2+^-dependent inactivation \[CDI\]) or voltage-dependent conformational changes (e.g., voltage-dependent inactivation \[VDI\]). The initial steps involved in these prototypic forms of regulation have been studied extensively. For example, it is known that Ca^2+^ binds to a constitutively associated calmodulin (CaM), which then interacts with other sites on the channel to induce CDI ([@bib44], [@bib45]; [@bib54]; [@bib84]; [@bib23], [@bib24]; [@bib56]; [@bib51]; [@bib20]; [@bib70]). Similarly, it is well accepted that voltage-dependent conformational changes of Ca~V~1/2 channels are initially triggered by movement of four homologous voltage-sensing domains, each consisting of transmembrane helices S1--S4 ([@bib68]). These rearrangements open the intracellular gate, comprised of distal S6 segments ([@bib48]; [@bib75]), and predispose the channel to VDI. Although more is known about the initiation of these regulatory events, the transduction and ultimate endpoint mechanisms of these forms of Ca^2+^ channel modulation have eluded consensus. Given the physiological importance of VDI and CDI, and the likelihood that certain Ca^2+^ channelopathies involve defects in the end stage rather than initial steps of these regulatory processes ([@bib42], [@bib43]; [@bib63], [@bib64]; [@bib31]; [@bib32]; [@bib6]), these downstream mechanisms represent crucial unknowns in the field.

Currently, three main hypotheses exist regarding end-stage actions of inactivation across the family of voltage-gated channels, although none has been definitively established for Ca^2+^ channels. The first and most prominent idea (case 1) is that of a cytoplasmic inactivation particle that binds to cytoplasmic aspects of the permeation pathway when the channel is open, thereby plugging the pore ([Fig. 1 C](#fig1){ref-type="fig"}, case 1) ([@bib3]). In molecular terms, the inactivating particle was identified as an amino-terminal "ball and chain" for K^+^ channels undergoing N-type inactivation ([@bib33]), and as a "hinged loop" connecting homologous domains III and IV of voltage-gated Na^+^ channels ([@bib74]). For Ca^2+^ channels, this idea takes the form of a "hinged lid" comprised of the loop between homologous domains I and II. As evidence, Ca^2+^ channel VDI can be significantly altered by swapping the I-II loop between different Ca~V~1/2 channels, by mutating the I-II loop, or by using different β subunits that bind to the I-II loop ([@bib12]; [@bib66], [@bib67]; [@bib8]; [@bib65]; [@bib19]). Furthermore, mutating certain S6 regions (the putative I-II loop binding site) also disrupts VDI ([@bib42], [@bib43]; [@bib66], [@bib67]; [@bib65]; [@bib63], [@bib64]; [@bib31]; [@bib32]; [@bib58], [@bib59]; [@bib6]). Finally, overexpressing a I-II loop peptide alone enhances VDI ([@bib14]), suggesting that even the free peptide represents a lid that can directly bind and occlude the pore. The involvement of such a hinged-lid mechanism in CDI is less clear and based mainly on observations that certain molecular manipulations similarly alter VDI and CDI. These data have been used to argue that VDI and CDI share a common endpoint ([@bib14]; [@bib41]; [@bib28]).

![Structural and functional models of S6 domains. (A) CLUSTAL alignment of S5--S6 domains of three K^+^ channels with known crystal structures (top) and the four domains of Ca~V~1.3, Ca~V~1.2, and Ca~V~2.1. Arrows indicate putative location of the intracellular S6 gate, as determined from previous cysteine accessibility studies. Ca~V~1.3 residues in bold indicate sites that were mutated to proline in this study. Colored highlights correspond to the color scheme used in B. Numbered scale defines a common set of "S6 coordinates" for ease of reference. (B) Structural homology model of Ca~V~1.3 S5/S6 segments, based on KcsA (closed) and KvAP (open). Bottom and side views are shown. Arrow in the closed side view corresponds to the gate identified in A. (C and D) Theory of S6 mutation effects on a hinged-lid or selectivity filter collapse mechanism. In C, channels activate via a C↔O transition governed by voltage-sensing term *Q*~EFF~(*V*) and concerted gate-opening term *L*. Partitioning between normal and inactivated modes is driven by Ca^2+^ influx through the channel and is governed by *J*(*Ca*^2+^) ≈ *P*~O-PEAK~/*K*~eff~. Note that these equilibrium coefficients represent the ratio of forward and reverse kinetic rate constants, which are not individually defined. (D) The predicted outcome if S6 mutations selectively perturb *L* by the factor *a*. [Eq. 4](#fd4){ref-type="disp-formula"} was used with parameters: *Q*~EFF~(*V*) · *L* = 0.8; 1/*K*~eff~ = 50. *R* *·* *T* = 0.6 kCal/mole throughout. (E and F) Theory of S6 mutation effects on an allosteric CDI mechanism. Channels occupy either a normal (top row of E) or inactivated gating mode (bottom row). In both modes, channels activate via a C↔O scheme as defined in C; however, channels in the inactivated mode open less often because *f* \< 1. Partitioning between normal and inactivated modes is driven by Ca^2+^ influx through the channel as in C. (E) The predicted outcome if S6 mutations selectively perturb *L* by the factor *a*. CDI (solid curve) is the product of two terms: *F*~CDI~ (dotted line) and *CDI*~max~ (dashed line). [Eq. 5](#fd5){ref-type="disp-formula"} was used with parameters: *Q*~EFF~(*V*) · *L* = 0.8, 1/*K*~eff~ = 50, and *f* · *b*(*V*) = 0.14.](JGP_200910308_RGB_Fig1){#fig1}

A second hypothesis proposes a collapse of the selectivity filter ([Fig. 1 C](#fig1){ref-type="fig"}, case 2), as in P-type inactivation of K^+^ channels (also known as C-type inactivation) ([@bib17]; [@bib34]). The selectivity filter (P loops within S5--S6 linkers) resides near the extracellular surface of the membrane ([@bib21]), opposite the intracellular activation gate. Thus, P-type inactivation is sensitive to manipulations near the extracellular surface of the pore ([@bib50]; [@bib78]; [@bib49]; [@bib18]). Likewise, some have suggested that this mechanism pertains to Ca~V~1/2 channels ([@bib81]), partly because VDI is modulated by toxins and cations that bind to the extracellular face of the channel ([@bib81]; [@bib40]; [@bib7]). For CDI, there are potential indications that CDI may be affected by mutating the selectivity filter or substituting the permeant ion ([@bib83]; [@bib4], [@bib5]), motivating the notion that CDI might be linked to selectivity filter rearrangements.

A third idea ([Fig. 1 E](#fig1){ref-type="fig"}, case 3) is that Ca^2+^ channel inactivation works by allosteric inhibition of the intracellular activation gate. Unlike the previous two hypotheses, where the pore of an inactivated channel is constitutively nonconductive, an allosterically inactivated channel would favor closure, yet still open intermittently. Evidence for this mechanism comes from single-channel Ca^2+^ records of Ca~V~1.2, in which CDI reduces the frequency of opening without completely silencing channels ([@bib36]). During VDI, in contrast, single-channel Ba^2+^ records reveal the complete absence of openings ([@bib36]), suggesting that CDI and VDI use different endpoints. Further indications of the distinct nature of VDI and CDI come from two Ca~V~ mutations that alter VDI with little effect on CDI ([@bib6]), and from the immobilization of gating charge by VDI, but not CDI ([@bib30]; [@bib61]; [@bib40]; [@bib6]).

To distinguish among these potential downstream effects of CDI, this paper develops theoretical analyses that make a discriminating prediction regarding Ca^2+^/CaM-mediated Ca^2+^ channel regulation: mutations in the distal S6 transmembrane regions (the intracellular activation gate) should produce distinctive effects on activation and inactivation, depending on which mechanism holds true. To date, studies of select S6 mutations, mostly relating to heritable channelopathies, have in fact detected effects on VDI, CDI, and activation ([@bib42], [@bib43]; [@bib66], [@bib67]; [@bib65]; [@bib63], [@bib64]; [@bib31]; [@bib32]; [@bib58], [@bib59]; [@bib6]). However, no systematic mutagenesis screen that would enable discrimination among hypotheses has previously been performed. Here, to fully exploit our theoretical distinctions, we undertake comprehensive scanning mutagenesis of the intracellular S6 segments of all four domains of Ca~V~1.3. This channel isoform exhibits robust CaM-mediated CDI, making Ca~V~1.3 a useful prototype for the Ca~V~1/2 channel family ([@bib77]; [@bib20]; [@bib70]). The S6 mutations produce dramatic functional effects in favor of allosteric modulation of activation gating as the CDI endpoint.

For VDI, our S6 mutagenesis screen implicates an entirely different mechanism. The pattern of effects supports a hinged-lid scheme with an additional "shield" that repels lid closure. This shield represents an apt specialization enabling Ca~V~1.3 channels to maintain opening despite sustained activation, such as in ribbon synapses. After "removal" of the shield via mutagenesis, we confirm hinged-lid receptor sites within S6 domains, homologous to those identified previously in Ca~V~1.2 channels ([@bib32]). Overall, these findings furnish key mechanistic advances and a rich backdrop for understanding heritable diseases that involve mutations in these S6 domains.

MATERIALS AND METHODS
=====================

Molecular biology
-----------------

Point mutations of Ca~V~1.3 (α~1D~) were made in rat α~1D,short~ ([@bib76]). A 2.3-kb stretch containing IS6 and IIS6 (bounded by BsiWI and Eco47III) was cloned into Zero Blunt TOPO (Invitrogen), yielding NT~D~-TOPO~I-II~. Similarly, NT~D~-TOPO~III-IV~ contained IIIS6 and IVS6 (bounded by BglII and XbaI). QuikChange (Agilent Technologies) was used to mutate individual residues to proline within these TOPO clones, and the relevant region was then transferred into α~1D~ by digest and ligation. All segments subject to PCR were verified by sequencing.

Transfection of HEK293 cells
----------------------------

For electrophysiology, HEK293 cells were cultured on 10-cm plates and transiently transfected by a calcium phosphate protocol ([@bib54]). We combined 8 µg each of cDNAs encoding channel α~1~ subunit, rat brain α~2δ~ ([@bib71]), and rat brain β~2a~ ([@bib53]) or β~1b~ ([@bib57]), along with 2 µg SV40 T antigen. All subunits were driven by a cytomegalovirus promoter. Experiments were done 1--2 d later.

Whole cell electrophysiology
----------------------------

Whole cell recordings were obtained at room temperature (Axopatch 200A; Axon Instruments). Electrodes were pulled from borosilicate glass capillaries (MTW 150-F4; World Precision Instruments), with 1--3-MΩ resistances, before 80% series resistance compensation. Currents were filtered at 2 kHz (four-pole Bessel), and P/8 leak subtraction was used. The internal solution contained (in mM): 124 CsMeSO~3~, 5 CsCl~2~, 1 MgCl~2~, 4 MgATP, 10 HEPES, pH 7.4, and 5 EGTA at 295 mOsm adjusted with CsMeSO~3~. External solutions contained (in mM): 130 TEA-MeSO~3~, 10 HEPES, pH 7.4, and 10 CaCl~2~ or BaCl~2~ at 300 mOsm adjusted with TEA-MeSO~3~.

Analysis methodology
--------------------

*VDI* and *CDI* ([Fig. 2 A](#fig2){ref-type="fig"}) were calculated as follows: *VDI*(*t*) = 1 − *I*~Ba~(*t*)/*I*~Ba~(*t*~peak,Ba~) and *CDI*(*t*) = 1 − (*I*~Ca~(*t*)/*I*~Ca~(*t*~peak,Ca~))/(*I*~Ba~(*t*)/*I*~Ba~(*t*~peak,Ba~)), where *I*~Ca~(*t*) and *I*~Ba~(*t*) are whole cell currents in Ca^2+^ and Ba^2+^, respectively, and *t*~peak,Ca~ and *t*~peak,Ba~ correspond to the time of peak current after depolarization. This method of calculating *CDI* accounts for baseline *VDI* with a ratiometric correction as described in several recent reports ([@bib6]; [@bib70]; [@bib28]). Due to the rapid onset of CDI in Ca~V~1.3, *t*~peak,Ca~ often apparently occurred earlier than *t*~peak,Ba~. To minimize the extent to which this could degrade our estimates of *CDI*, we limited *t*~peak,Ba~ (and *t*~peak,Ca~) to the first 50 ms of depolarization. Thus, certain constructs have a negative metric of *VDI*~300~, which indicates very slowly activating channels. We chose the *VDI*~300~ metric for brevity of representation, so as to allow a single metric to represent both the strong VDI of "shield-disrupting" mutants (i.e., those in the right half of [Fig. 5 C](#fig5){ref-type="fig"}) and the comparative lack of VDI in other constructs (i.e., those in the left third of [Fig. 5 C](#fig5){ref-type="fig"}). Spot checks of *VDI*~1000~ measurements showed good agreement with the rank order of VDI indicated by *VDI*~300~. For *I*~PEAK~(*V*) relations (e.g., [Fig. 2 C](#fig2){ref-type="fig"}), we did not constrain the time of peak current, and thus these curves accurately reflect steady-state channel activation. The *I*~PEAK~(*V*) curves reflect the product of two terms, as given by *I*~PEAK~(*V*) = *P*~O-PEAK~(*V*) · *i*~N~(*V*), where *P*~O-PEAK~(*V*) is the relative open probability shown in [Fig. 2 D](#fig2){ref-type="fig"}, and *i*~N~(*V*) is a normalized unitary current relation ([Fig. 2 C](#fig2){ref-type="fig"}, dashed curve) closely approximating the scaled Goldman-Hodgkin-Katz (GHK) relation below.$$i_{\text{N}}\left( V \right)\operatorname{=-}g \cdot \left( V - V_{\text{S}} \right) \cdot \frac{1}{\exp\,\left\lbrack \left( V - V_{\text{S}} \right) \cdot z_{\text{GHK}}F/\left( RT \right) \right\rbrack - 1} + i_{\text{LEAK}}\left( V \right)$$

![Baseline Ca~V~1.3 behavior and method of calculating ΔΔ*G~a~*. (A) Whole cell Ba^2+^ (blue) and Ca^2+^ (red) currents of Ca~V~1.3 coexpressed with α~2~δ and β~2a~, evoked by depolarization to 0 mV. Voltage pulse protocol (in mV) indicated above data trace here and throughout. Current scale bar is for Ca^2+^; Ba^2+^ is scaled down approximately two to three times to match. Scales to the right define *VDI* and *CDI* metrics. See Materials and methods for details. (B) *VDI* and *CDI* (as defined in A) calculated after 50 and 300 ms of depolarization and averaged over many cells. Cell number (*n*) in A. Error bars are SEM. (C) Normalized *I*~PEAK~(*V*) relationship (see Materials and methods for details). Voltage (*V*) is in units of mV. Dashed relationship is proportional to the unitary current (before additional nonlinear leak correction). Cell number (*n*) in A. Error bars are SEM. (D) *P*~O-PEAK~(*V*), calculated by taking the ratio of data points from C and the leak-corrected unitary current relation. This yields the relative open probability (normalized to maximum *P*~O~). Error bars are SEM from C divided by the unitary current relation. (E) Method for determining ΔΔ*G~a~*. Graph on the left illustrates the determination of parameter *a* via [Eq. 6](#fd6){ref-type="disp-formula"}. Top right graph follows the format of D, where *V* is in units of mV. ΔΔ*G~a~* (bottom right graph) is in units of kCal/mole. See Results for details.](JGP_200910308_RGB_Fig2){#fig2}

Because S6 mutations leave unchanged the conductance of an open channel ([@bib70]), we maintain a constant shape of *i*~N~(*V*), and thus fix (*z*~GHK~ *F*/*RT*)^−1^ = +12 mV, and *V*~S~ = +20 mV for all constructs. The scale factor *g*, representing a composite of single-channel conductance and channel number, is freely adjusted in each construct for proper normalization. For subtle nonlinearities in leak at large *V*, we included a small leak correction term, *i*~LEAK~(*V*), which amounts to the difference between dashed and solid curves at very positive *V* (e.g., [Fig. 2 C](#fig2){ref-type="fig"}).

Homology modeling of the Ca~V~1.3 S5-S6 domains
-----------------------------------------------

For the closed-state molecular model of the Ca~V~1.3 S5-S6 segments, the KcsA (Protein Data Bank accession no. [1BL8](1BL8)) crystal structure was used as template ([@bib21]). Modeller 9v4 ([@bib26]) was used to generate 50 models, from which the structure with the lowest objective function was chosen. Modeller builds three-dimensional atomic structures by optimizing an objective function based on CHARMM energy terms and a set of distance and dihedral angle restraints from the alignment of target and template sequences. The four domains of Ca~V~1.3 were arranged in a clockwise configuration as viewed from the extracellular surface by analogy to the orientation of voltage-gated sodium channels ([@bib46]). An analogous procedure was used for the open conformation, with the KvAP crystal structure as template (Protein Data Bank accession no. [1ORQ](1ORQ)) ([@bib38]).

Online supplemental material
----------------------------

Fig. S1 is an extended version of [Fig. 3](#fig3){ref-type="fig"} that includes all constructs from our mutagenesis screen. This allows for comprehensive visual comparison of trends across all S6 residues of the four homologous domains comprising Ca~V~1.3 channels. Fig. S1 is available at <http://www.jgp.org/cgi/content/full/jgp.200910308/DC1>.

![Functional profiles for systematic S6 mutagenesis scan. (A--D) Data are organized into four panels, where each panel corresponds to a channel domain (IS6, IIS6, IIIS6, and IVS6). Within a panel, each row corresponds to data from a Ca~V~1.3 proline mutant coexpressed with α~2~δ and β~2a~. The format for each construct follows that in [Fig. 2](#fig2){ref-type="fig"}. For clarity, only a subset of our mutagenesis screen is displayed. The complete set of S6 mutations is numerically summarized in [Table II](#tbl2){ref-type="table"} and graphically displayed in Fig. S1. Exemplar traces (left column) show Ba^2+^ (blue) and Ca^2+^ (red) currents for the mutant channel, with the native channel behavior overlaid in light gray for reference. Voltage pulse protocol and mutated residue (identified by name and common S6 coordinate, as defined in [Fig. 1 A](#fig1){ref-type="fig"}) are indicated above data traces. For *VDI* and *CDI* metrics (second column), native channel values are indicated by the vertical gray lines, and deviation from native channel behavior is indicated by colored arrows. This is also done for the voltage-activation relations (third column), which show both ΔΔ*G~a~* (bars) and Δ*V*~1/2~ (arrows). The fourth column shows fits for ΔΔ*G~a~* determination, as done in [Fig. 2 E](#fig2){ref-type="fig"} (left). Axis labels are shown only for top and bottom rows, with identical format throughout.](JGP_200910308_RGB_Fig3){#fig3}

RESULTS
=======

Theory of S6: mutation effects on activation and inactivation
-------------------------------------------------------------

To provide a structural framework for considering the effects of S6 mutations, we constructed a homology model of the S5 and S6 transmembrane segments of Ca~V~1.3, based on the KcsA and KvAP crystal structures for the closed and open conformations, respectively ([@bib21]; [@bib38]). We favored the K~V~AP over K~V~1.2 structure because both Ca~V~1.3 and K~V~AP lack the S6 domain "PVP" kink present in K~V~1.2. The P loops, which connect S5 and S6, were excluded because of poor conservation between K^+^ and Ca^2+^ channels. [Fig. 1 A](#fig1){ref-type="fig"} shows the CLUSTAL sequence alignments used for modeling. The top rows show K^+^ channel alignments, and the rows below display Ca^2+^ channel alignments for all four domains. In addition to Ca~V~1.3, two related Ca^2+^ channels (Ca~V~1.2 and Ca~V~2.1) are aligned to facilitate comparison with previous work. For ease of reference, we have assigned a common set of "S6 coordinates," as denoted by the numbered scale at the bottom of [Fig. 1 A](#fig1){ref-type="fig"}. [Fig. 1 B](#fig1){ref-type="fig"} displays the resulting closed and open Ca~V~1.3 homology models, which resemble prior models of Ca~V~1.2 ([@bib35]; [@bib82]; [@bib47]; [@bib58], [@bib59]; [@bib10]). In the closed state, the S6 helices point inward to form a central "bundle crossing" that, by homology to K^+^ channels, acts as a closed intracellular gate impermeant to the passage of ions. In the open conformation, the S6 helices splay outward, consistent with free passage of permeant ions. This structural model of the intracellular gate agrees well with functional cysteine accessibility studies, which have been performed on the S6 segment of K~V~1 ([@bib48]) and the II-S6 segment of Ca~V~2.1 ([@bib75]). The arrows in [Fig. 1 A](#fig1){ref-type="fig"} indicate the critical gate location: residues to the right of the arrows (i.e., intracellular to the gate) are always accessible to intracellular agents, but residues to the left are accessible only in the open- (not closed-) channel conformation ([@bib48]; [@bib75]). The arrow in [Fig. 1 B](#fig1){ref-type="fig"} marks the homologous intracellular gate location in Ca~V~1.3.

These homology models ([Fig. 1 B](#fig1){ref-type="fig"}) help visualize ways in which S6 domains could play a role in channel inactivation. First, because the S6 segments line the cytoplasmic aspect of the channel pore, certain residues are well positioned to serve as a binding site for a cytoplasmic inactivation particle (case 1), particularly in the open conformation. Alternately, in response to channel opening, the S6 segments could transmit mechanical forces to the P loop region and thus induce inactivation by selectivity filter collapse akin to that in K^+^ channels (case 2). Finally, inactivation could involve an allosteric modulation of the very same intracellular gate involved in activation, which is comprised of the S6 segments (case 3).

Given this perspective, we considered how S6 mutagenesis can distinguish among these proposals. The key is this: although the proposed mechanisms differ considerably, all three share a common voltage-dependent activation process that then couples to inactivation in distinctive ways. Thus, S6 mutations that perturb this common pathway turn out to impact inactivation differentially, depending on which end-stage mechanism holds true. These discriminating predictions apply most directly to the CDI process, as follows.

To capture the essence of voltage activation, we represent this process in the compact form shown in the top row of [Fig. 1 (C and E)](#fig1){ref-type="fig"}, wherein the equilibrium constant between closed (C) and open (O) states is given by the product of two terms: a voltage-dependent term *Q*~EFF~(*V*), corresponding to movement of the S1--S4 voltage sensors, and a voltage-independent term *L*, representing the subsequent ("late") concerted opening of the S6 intracellular gate ([@bib80]). For convenience, the variables defined here and below are summarized in [Table I](#tbl1){ref-type="table"}. Despite its apparent simplicity, this formulation is rather general and can precisely represent the steady-state opening of multistate activation schemes with numerous closed states if *Q*~EFF~(*V*) becomes a complex function of voltage, as described in our companion paper (see Tadross and Yue in this issue). Of greater relevance to our immediate concerns, we note that S6 mutations should directly alter the concerted opening step (*L*) because of the fundamental involvement of S6 segments in this final gating transition (compare closed and open conformations in [Fig. 1 B](#fig1){ref-type="fig"}). Mutations of this type would act by multiplying *L* by a scaling factor *a* ([Fig. 1, C and E](#fig1){ref-type="fig"}), and the parameter *Q*~EFF~(*V*) would remain unchanged if S6 mutations have no collateral effects on the voltage-sensing domains. Finally, in terms of energetics, the overall free energy required per mole of transitions from a closed (C) to open (O) conformation, Δ*G*~CO~, would be:$$\begin{array}{l}
{\Delta G_{\text{CO}} = - R \cdot T \cdot \ln\,\left( Q_{\text{EFF}}\left( V \right) \cdot L \cdot a \right) =} \\
{\underset{\Delta G_{\text{CO,WT}}}{\underset{︸}{- R \cdot T \cdot \ln\,\left( Q_{\text{EFF}}\left( V\operatorname{))-}R \cdot T \cdot \ln\,\left( L \right) \right. \right.}}\,\underset{{\Delta\Delta}G_{a}}{\underset{︸}{- R \cdot T \cdot \ln\,\left( a \right)}},} \\
\end{array}$$where *R* is the universal gas constant, *T* is temperature, and *V* is transmembrane voltage. Δ*G*~CO,WT~ is the energy required to activate the native (wild-type) channel. Part of this energy is electrical (−*R·T·*ln(*Q*~EFF~(*V*))), and the remainder is chemical (−*R·T·*ln(*L*)). For mutant channels, ΔΔ*G~a~* represents the additional chemical energy needed to activate a mutant versus native channel. Because channel activation is known to be kinetically faster than inactivation, we can calculate peak open probability shortly after membrane depolarization, assuming occupancy of only the two states in the top row ([Fig. 1 ,C and E](#fig1){ref-type="fig"}):$$P_{\text{O-PEAK}} = \frac{Q_{\text{EFF}}\left( V \right) \cdot L \cdot a}{1 + Q_{\text{EFF}}\left( V \right) \cdot L \cdot a}$$

###### 

Summary of symbols

  Symbol                  Definition
  ----------------------- ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
  *Q*~EFF~(*V*)           Effective equilibrium constant corresponding to movement of the S1--S4 voltage sensors ([Fig. 1, C and E](#fig1){ref-type="fig"})
  *L*                     Equilibrium constant representing the subsequent ("late") concerted opening of the S6 intracellular gate ([Fig. 1, C and E](#fig1){ref-type="fig"})
  *a*                     S6 mutations act by multiplying *L* by this scaling factor
  Δ*G*~CO,WT~             Energy required to activate the native (wild-type) channel ([Eq. 1](#fd1){ref-type="disp-formula"})
  ΔΔ*G~a~*                Additional energy needed to activate a mutant versus native channel ([Eq. 1](#fd1){ref-type="disp-formula"})
  Δ*V*~1/2~               Change in voltage required for half-maximal opening of mutant versus native channels
  *J*(Ca^2+^)             Effective equilibrium constant describing the Ca^2+^-mediated transition between active (top row) and inactive (bottom row) conformations in [Fig. 1 (C and E)](#fig1){ref-type="fig"}; *J*(Ca^2+^) ≈ *P*~O‑PEAK~/*K*~eff~
  *K*~eff~                A constant closely analogous to the effective Ca^2+^ dissociation constant for CDI, which has been experimentally estimated at a value far less than unity ([@bib70])
  *P*~O-PEAK~             Peak open probability shortly after membrane depolarization ([Eq. 2](#fd2){ref-type="disp-formula"})
  *P*~O-SS~               Steady-state open probability after a prolonged depolarization; for cases 1 and 2, *P*~O-SS~ = *P*~O-PEAK~ · (1 − *F*~CDI~) ([Eq. 3](#fd3){ref-type="disp-formula"}); for case 3, *P*~O-SS~ = *P*~O-PEAK~ · (1 − *F*~CDI~ *·* *CDI*~max~) ([Eq. 5](#fd5){ref-type="disp-formula"})
  *CDI*                   CDI, defined as fraction of peak current lost at steady state; for cases 1 and 2, *CDI* = *F*~CDI~ ([Eq. 4](#fd4){ref-type="disp-formula"}); for case 3, *CDI* = *F*~CDI~ · *CDI*~max~ ([Eq. 5](#fd5){ref-type="disp-formula"})
  *F*~CDI~                Fraction of inactivated channels at steady state ([Eq. 4](#fd4){ref-type="disp-formula"})
  *CDI*~max~              Fractional change in open probability of the normal mode versus the inactivated mode ([Eq. 5](#fd5){ref-type="disp-formula"})
  *VDI*~50~, *VDI*~300~   Experimental measure of VDI after 50 and 300 ms of depolarization (see [Fig. 2 A](#fig2){ref-type="fig"} and Materials and methods)
  *CDI*~50~, *CDI*~300~   Experimental measure of CDI after 50 and 300 ms of depolarization (see [Fig. 2 A](#fig2){ref-type="fig"} and Materials and methods)

With this activation framework, we next considered the effects on inactivation for cases 1 and 2. Both cases are represented by the same state diagram in [Fig. 1 C](#fig1){ref-type="fig"} because they both feature a nonconductive inactivated conformation. Because CDI is driven by elevations of intracellular Ca^2+^ very near channels, the ratio of inactivated to noninactivated channels must be a function of this Ca^2+^, which we term *J*(Ca^2+^). Despite the apparent simplicity of [Fig. 1 C](#fig1){ref-type="fig"}, which depicts the inactivation process as a single transition governed by *J*(Ca^2+^), this formalism is rather general. In particular, the behavior of the scheme in [Fig. 1 C](#fig1){ref-type="fig"} is shown to correspond well to the detailed CDI scheme in our companion paper ([@bib69]), which allows for inactivation from both closed and open states, and dissects the CDI process into separate events representing Ca^2+^ binding to CaM, CaM/channel binding, and the final transduction of CDI. Thus, *J*(Ca^2+^) in [Fig. 1 C](#fig1){ref-type="fig"} is a shorthand for transitions between numerous intermediate states. Given the "slow CaM" mechanism that predominates in Ca~V~1.3 channels and our use of elevated intracellular Ca^2+^ buffering, *J* (Ca^2+^) becomes a simple function of the time-averaged Ca^2+^ concentration ([@bib70]), which is proportional to *P*~O-PEAK~ in [Eq. 2](#fd2){ref-type="disp-formula"}. Specifically, *J*(*Ca*^2+^) ≈ *P*~O-PEAK~/*K*~eff~, where *K*~eff~ has been experimentally estimated at a value far less than unity ([@bib70]). Beyond Ca^2+^ binding to CaM, *J*(Ca^2+^) could incorporate either the affinity of an inactivation particle for its pore-blocking binding site (case 1), or the efficacy with which mechanical forces transduce selectivity filter collapse (case 2). Importantly, the dependence of *J*(Ca^2+^) on *P*~O-PEAK~ arises because only open channels conduct the Ca^2+^ entry required for Ca^2+^ binding to CaM; this dependence is not necessarily due to any preferential state dependence of CDI transduction per se. Thus, the CaM/channel binding and ultimate CDI transduction events implicit within [Fig. 1 C](#fig1){ref-type="fig"} can occur from both open and closed conformations, as is shown explicitly in our companion paper ([@bib69]). Factoring in inactivation, the steady-state open probability after a prolonged depolarization becomes:$$P_{\text{O-SS}} = P_{\text{O-PEAK}} \cdot \left( 1 - F_{\text{CDI}} \right),$$where *F*~CDI~ is the fraction of inactivated channels at steady state. Accordingly, for inactivation defined as the fraction of peak current lost at steady state, we have for cases 1 and 2:$$\begin{array}{l}
{CDI_{\text{(case}\, 1\,\text{or}\, 2)} = \frac{P_{\text{O-PEAK}} - P_{\text{O-SS}}}{P_{\text{O-PEAK}}} = F_{\text{CDI}} =} \\
{\frac{J\left( Ca^{2 +} \right)}{1 + J\left( Ca^{2 +} \right)} = \frac{P_{\text{O-PEAK}}/K_{\text{eff}}}{{1 + P_{\text{O-PEAK}}}/K_{\text{eff}}} =} \\
{\frac{P_{\text{O-PEAK}}}{K_{\text{eff}} + P_{\text{O-PEAK}}} = \frac{1}{1 + K_{\text{eff}}} \cdot \frac{Q_{\text{EFF}}\left( V \right) \cdot L \cdot a}{K_{\text{eff}}/\left( 1 + K_{\text{eff}} \right) + Q_{\text{EFF}}\left( V \right) \cdot L \cdot a}} \\
\end{array}$$

Notably, *F*~CDI~ = *J*(Ca^2+^)/(1 + *J*(Ca^2+^)) by the definitions of an equilibrium constant and of *F*~CDI~ itself. If experiments are performed at a fixed voltage (e.g., at *V* = 0), [Eq. 4](#fd4){ref-type="disp-formula"} directly relates *CDI* to changes in the chemical energy of activation induced by mutation (parameter *a*). A plot of [Eq. 4](#fd4){ref-type="disp-formula"} ([Fig. 1 D](#fig1){ref-type="fig"}) makes a first experimentally important prediction: for cases 1 and 2, inactivation would decrease for mutations that reduce channel opening (ΔΔ*G~a~* \> 0).

This prediction could help distinguish in favor of case 1 or 2 and merits two comments. First, the predicted outcome in [Fig. 1 D](#fig1){ref-type="fig"} presumes that S6 mutations would have no major collateral effects on the inactivation machinery or the voltage-sensing domains. This is plausible for CDI, but less so for VDI, where S6 elements have been proposed as the very receptor for a hinged lid ([@bib32]). Hence, the type of prediction here, and for the allosteric case 3 (below), pertains to CDI and would not be readily adapted to a VDI scenario. Other aspects of the S6 mutagenesis screen, described later, will point to VDI endpoint mechanisms. Second, for simplicity, [Eq. 4](#fd4){ref-type="disp-formula"} presumes that S6 mutations would only affect *J*(Ca^2+^) via changes in *P*~O-PEAK~. However, as shown in our companion paper ([@bib69]), this might not be the case if CDI were to proceed more readily from closed versus open states. Analysis in our companion work explicitly excludes this possibility and substantiates the prediction for cases 1 and 2 in [Fig. 1 D](#fig1){ref-type="fig"} that CDI will be maintained for mutations that favor channel opening (negative ΔΔ*G*~a~) and diminished for those that hinder opening (positive ΔΔ*G*~a~).

What if inactivation represents the allosteric modulation of opening (case 3)? In this scenario, channels can adopt one of two gating modes. In the "normal" mode ([Fig. 1 E](#fig1){ref-type="fig"}, top row), channels gate according to a C↔O model identical to the activation process of the previous analyses. Unlike the prior mechanisms, channels in the "inactivated" mode (bottom row) are not completely silent; rather, they open less frequently because of an allosteric increase in the chemical energy needed for opening (0 \< *f* \< 1 in [Fig. 1 E](#fig1){ref-type="fig"}, inactivated mode). Also, because of constraints from thermodynamic cycles, the voltage-dependent term in the inactivated mode may become *Q*~EFF~(*V*) · *b*(*V*), where the voltage-dependent function *b*(*V*) can deviate from unity in the most general configurations. For the scheme in [Fig. 1 E](#fig1){ref-type="fig"}, the expression for inactivation (fraction of peak current lost at steady state) becomes:$$\begin{array}{l}
{CDI_{\text{(case}\, 3)}\mspace{9mu} = \mspace{9mu}\frac{P_{\text{O-PEAK}} - P_{\text{O-SS}}}{P_{\text{O-PEAK}}}\mspace{9mu} = \mspace{9mu} F_{\text{CDI}} \cdot CDI_{\text{max}}\mspace{9mu}} \\
{\text{where}\, CDI_{\text{max}} = \mspace{9mu}\frac{P_{\text{O-PEAK}} - P_{\text{O-INACTIVATED}}}{P_{\text{O-PEAK}}} = \mspace{9mu}} \\
\frac{\left( 1 - f \cdot b\left( V \right) \right)}{1\mspace{9mu} + \mspace{9mu} Q_{\text{EFF}}\left( V \right) \cdot b\left( V \right) \cdot L \cdot f \cdot a} \\
\end{array}$$

Thus, for the allosteric scheme (case 3), CDI is the product of two terms. First, *F*~CDI~ is the fraction of channels in the inactivated mode at steady state, as specified in [Eq. 4](#fd4){ref-type="disp-formula"}. Second, *CDI*~max~ is the fractional change in open probability of the normal mode (*P*~O-PEAK~ in [Eq. 2](#fd2){ref-type="disp-formula"}) versus the inactivated mode (*P*~O-INACTIVATED~ = *Q*~EFF~ · *b*(*V*) · *L* · *a* · *f*/(1 + *Q*~EFF~ · *b*(*V*) · *L* · *a* · *f*)). Thus, *CDI*~max~ is the apparent CDI (fraction of peak current lost at steady state) if all channels were to transition from the normal to the inactivated gating mode. Notably, *CDI*~max~ \< 1 because inactivated channels open sparsely (i.e., *f* \> 0). A plot of [Eq. 5](#fd5){ref-type="disp-formula"} ([Fig. 1 F](#fig1){ref-type="fig"}), obtained with the step voltage held at a constant *V* throughout, makes a key prediction for the allosteric mechanism: CDI should have a bell-shaped dependence on ΔΔ*G~a~*, as follows. First, as for cases 1 and 2, mutations that diminish opening (ΔΔ*G*~a~ \> 0) cause a reduction in *F*~CDI~ owing to the lack of Ca^2+^ entry needed to drive transition into the inactivated mode ([Fig. 1 F](#fig1){ref-type="fig"}, dotted curve). Second, mutations that promote opening (ΔΔ*G*~a~ \< 0) diminish *CDI*~max~ ([Fig. 1 F](#fig1){ref-type="fig"}, dashed curve) because mutations that enhance opening in the normal gating mode also enhance opening within the inactivated mode. Notably, this trend is opposite to that for cases 1 and 2 (compare with [Fig. 1 D](#fig1){ref-type="fig"}). Accordingly, the full extent of CDI is now shown by the solid bell-shaped curve in [Fig. 1 F](#fig1){ref-type="fig"}.

Characterization of inactivation and activation of Ca~V~1.3 channels
--------------------------------------------------------------------

These predictions motivated systematic mutagenesis of the intracellular S6 gate of Ca~V~1.3. As reference, [Fig. 2](#fig2){ref-type="fig"} summarizes the behavior of wild-type Ca~V~1.3. On channel activation by a depolarizing voltage step to 0 mV ([Fig. 2 A](#fig2){ref-type="fig"}), the modest decay of Ba^2+^ current (blue trace) reflects VDI observed in isolation. The additional rapid decay with Ca^2+^ as charge carrier (red trace) reflects the robust CDI of Ca~V~1.3. Accordingly, these forms of inactivation can be quantified as shown in [Fig. 2 A](#fig2){ref-type="fig"} (scale bars to the right), which defines the metrics *VDI* and *CDI*. Note that the calculation of *CDI* accounts for baseline *VDI* with a ratiometric correction ([@bib6]; [@bib70]; [@bib28]), such that *CDI* represents the purely Ca^2+^-dependent component of inactivation (see Materials and methods). [Fig. 2 B](#fig2){ref-type="fig"} displays these metrics at 50 and 300 ms of depolarization, as averaged over multiple cells.

Beyond inactivation, testing the predictions in [Fig. 1](#fig1){ref-type="fig"} required assessment of ΔΔ*G~a~*, the change in chemical energy required to activate mutant versus native channels. Toward this end, we determined the voltage dependence of channel open probability in native channels, based on measurements of peak Ba^2+^ currents (*I*~PEAK~). As inactivation is very slow with this charge carrier, peak Ba^2+^ currents are a faithful reporter of peak open probability owing to the activation process. Accordingly, these currents were normalized ([Fig. 2 C](#fig2){ref-type="fig"}, data points) and fit by a smooth curve ([Fig. 2 C](#fig2){ref-type="fig"}, solid curve), which was specified by the product of a GHK unitary--current relation ([Fig. 2 C](#fig2){ref-type="fig"}, dashed curve) and a single Boltzmann activation relation ([Fig. 2 D](#fig2){ref-type="fig"}, solid curve). As elaborated in Materials and methods, the same GHK relation (but for amplitude scaling) was used to fit all constructs. Dividing the *I*~PEAK~ data points by this GHK relation yielded the desired activation curve for native channels, *P*~O/WT~ (*V*) ([Fig. 2 D](#fig2){ref-type="fig"}, data points).

We next devised a technique to obtain the value of ΔΔ*G~a~* (= −*R·T·*ln(*a*)) for mutant channels, which incorporates all information from the activation curves of various constructs. This technique not only presumes that S6 mutations leave *Q*~EFF~(*V*) unchanged, but also tests whether this presumption is well founded. Once this condition is satisfied, the analysis furnishes the value of ΔΔ*G~a~*, regardless of the functional form of *Q*~EFF~(*V*). The method makes use of our prior framework, wherein wild-type channels have a *P*~O/WT~ relation given by [Eq. 2](#fd2){ref-type="disp-formula"} with *a* = 1 (by definition), and mutant channels have a *P*~O/MUT~ relation of the same form, with all parameters identical except for *a*. If we then solve for *P*~O/MUT~ in terms of *P*~O/WT~, the unknown terms in [Eq. 2](#fd2){ref-type="disp-formula"} (*Q*~EFF~(*V*) and *L*) cancel out, leaving a useful interrelation:$$P_{\text{O/MUT}}\left( V \right) = \frac{a \cdot P_{\text{O/WT}}\left( V \right)}{\left( a - 1 \right) \cdot P_{\text{O/WT}}\left( V \right) + 1}$$

In practice, this relation enabled robust determination of parameter *a*. For example, a plot of the activation relation for S6 mutant L0759P, expressed as a function of its wild-type counterpart, is well fit by [Eq. 6](#fd6){ref-type="disp-formula"} with *a* = 14 ([Fig. 2 E](#fig2){ref-type="fig"}, solid black curve). This saturating relationship indicates that the L0759P mutant enhances activation (i.e., *a* \> 1). Alternatively, mutations that diminish activation (i.e., *a* \< 1) would yield an upwardly curved relation, as is the case for F1463P (dashed curve). For both mutants, fits of [Eq. 6](#fd6){ref-type="disp-formula"} were highly constrained, yielding reliable estimates of ΔΔ*G~a~* = −*R·T·*ln(*a*). Importantly, the close correspondence between data and theory ([Fig. 2 E](#fig2){ref-type="fig"}, left) supports the underlying presumption that S6 mutations do not alter *Q*~EFF~(*V*).

For added verification, we considered the outcome if a first-order Boltzmann approximation is assumed for the form of *Q*~EFF~(*V*), such that $Q_{\text{EFF}}\left( V \right) \approx \exp\,\left\lbrack \left( z \cdot F \cdot V \right)/\left( R \cdot T \right) \right\rbrack$. In this case, it can be shown that ΔΔ*G~a~* ≈ z·*F*·Δ*V*~1/2~, where Δ*V*~1/2~ is the change in voltage required for half-maximal opening of mutant versus native channels, *z* is the effective valence of the voltage-sensing modules, and *F* is Faraday's constant. For our exemplar mutants, Δ*V*~1/2~ ([Fig. 2 E](#fig2){ref-type="fig"}, right, green arrows) corresponds well to ΔΔ*G~a~* obtained from fits to [Eq. 6](#fd6){ref-type="disp-formula"} (green bars plotted below). Overall, there was a nearly linear relationship between ΔΔ*G~a~* and Δ*V*~1/2~, enabling us to estimate *z* *≈* 3.6. However, we favor calculating ΔΔ*G~a~* via [Eq. 6](#fd6){ref-type="disp-formula"} ([Fig. 2 E](#fig2){ref-type="fig"}, left), as this method uses all of the data, makes no assumption on the form of *Q*~EFF~*(V*), and enables verification of the invariance of *Q*~EFF~(*V*) to the effects of S6 mutation.

S6 mutations alter activation, CDI, and VDI
-------------------------------------------

Given this framework, we characterized the effects of S6 point mutations over all four domains of Ca~V~1.3. Single proline substitutions were systematically introduced into regions spanning the S6 intracellular gate ([Fig. 1 A](#fig1){ref-type="fig"}, bold residues), thereby producing defined kinks in the straight helical elements portrayed in [Fig. 1 B](#fig1){ref-type="fig"}. The results are shown in [Fig. 3](#fig3){ref-type="fig"}, where each of four panels (A--D) pertains to a different domain, and each subpanel relates to a given construct according to the format in [Fig. 2](#fig2){ref-type="fig"}. For clarity, [Fig. 3](#fig3){ref-type="fig"} displays only a subset of our mutagenesis screen. The complete set of S6 mutations is numerically summarized in [Table II](#tbl2){ref-type="table"} and graphically displayed in [Fig. S1](http://www.jgp.org/cgi/content/full/jgp.200910308/DC1). Remarkably, every mutant produced readily measurable current, as illustrated by exemplar Ba^2+^ and Ca^2+^ traces at the far left of each subpanel (blue and red, respectively). Exemplar wild-type currents are overlaid for comparison (gray). For the population data shown in the middle of each subpanel, vertical lines mark the wild-type profiles for VDI, CDI, half-activation voltage, and ΔΔ*G~a~*. Deviations from these are indicated as colored horizontal arrows. In this manner, we could readily appreciate a multitude of dramatic effects, distributed over all four domains. First, strong changes in activation were produced, with maximal deviations of Δ*V*~1/2~ approximating ±40 mV, corresponding to ΔΔ*G~a~* values of ±3 kcal/mole (e.g., [Fig. 3, A and B](#fig3){ref-type="fig"}, G0394P and I0761P, respectively). Interestingly, the direction of the effect seemed to segregate among the four domains: mutations in domains II and III invariably enhanced channel activation (ΔΔ*G~a~* \< 0), mutations to domain IV almost always suppressed activation (ΔΔ*G~a~* \> 0), and mutations to domain I could produce either effect. Second, several mutations dramatically perturbed CDI, nearly eliminating CDI in some cases (e.g., [Fig. 3](#fig3){ref-type="fig"}, A, G0394P, and B, L0759P and I0761P). Finally, changes in VDI were clustered toward the distal intracellular segments of domains I, III, and IV at sites clearly distinct from those producing CDI alterations.

###### 

Summary of experimental data from our mutagenesis screen

                pos   *V*~1/2~   *a*     Δ*V*~1/2~   ΔΔ*G~a~*   *VDI*~50~       *VDI*~300~       *CDI*~50~     *CDI*~300~    Figure
  ------------- ----- ---------- ------- ----------- ---------- --------------- ---------------- ------------- ------------- --------------------------------------
  WT                  −26.8      1       0.0         0.00       0.022 ± 0.006   0.091 ± 0.032    0.75 ± 0.03   0.80 ± 0.03   [4 A](#fig4){ref-type="fig"} (*i*)
  G0384P        −8    −10.1      0.18    16.7        1.03       0.029 ± 0.006   0.081 ± 0.033    0.59 ± 0.04   0.73 ± 0.03   [4 A](#fig4){ref-type="fig"} (*i*)
  L0393P        1     −6.7       0.12    20.1        1.27       0.021 ± 0.005   0.054 ± 0.014    0.26 ± 0.03   0.50 ± 0.03   [4 B](#fig4){ref-type="fig"} (*i*)
  G0394P        2     6.5        0.045   33.4        1.86       0.033 ± 0.011   0.044 ± 0.013    0.06 ± 0.03   0.10 ± 0.03   [4 B](#fig4){ref-type="fig"} (*i*)
  V0395P        3     −7.9       0.07    19.0        1.60       0.042 ± 0.015   0.147 ± 0.053    0.76 ± 0.03   0.84 ± 0.01   [4 A](#fig4){ref-type="fig"} (*ii*)
  L0396P        4     −33.2      2.5     −6.3        −0.55      0.054 ± 0.012   0.207 ± 0.038    0.78 ± 0.02   0.85 ± 0.02   [4 A](#fig4){ref-type="fig"} (*ii*)
  S0397P        5     −42.0      10      −15.2       −1.38      0.003 ± 0.001   −0.008 ± 0.008   0.30 ± 0.05   0.33 ± 0.06   [4 A](#fig4){ref-type="fig"} (*i*)
  G0398P        6     −16.2      0.25    10.6        0.83       0.011 ± 0.008   0.064 ± 0.044    0.75 ± 0.03   0.83 ± 0.02   [4 A](#fig4){ref-type="fig"} (*i*)
  E0399P        7     −25.3      0.8     1.5         0.13       0.117 ± 0.020   0.402 ± 0.025    0.79 ± 0.01   0.85 ± 0.01   [4 A](#fig4){ref-type="fig"} (*ii*)
  F0400P        8     −20.9      0.5     6.0         0.42       0.159 ± 0.015   0.519 ± 0.035    0.72 ± 0.03   0.84 ± 0.03   [4 A](#fig4){ref-type="fig"} (*ii*)
  L0759P        1     −42.8      14      −15.9       −1.58      0.004 ± 0.003   −0.051 ± 0.021   0.10 ± 0.01   0.18 ± 0.02   [4 A](#fig4){ref-type="fig"} (*i*)
  A0760P        2     −42.3      12      −15.5       −1.49      0.005 ± 0.001   0.032 ± 0.015    0.26 ± 0.02   0.48 ± 0.01   [4 A](#fig4){ref-type="fig"} (*i*)
  I0761P        3     −64.2      200     −37.4       −3.18      0.008 ± 0.001   0.048 ± 0.007    0.14 ± 0.06   0.21 ± 0.07   [4 A](#fig4){ref-type="fig"} (*i*)
  A0762P        4     −47.7      15      −20.9       −1.62      0.011 ± 0.002   −0.001 ± 0.023   0.17 ± 0.06   0.22 ± 0.06   [4 A](#fig4){ref-type="fig"} (*i*)
  V0763P        5     −57.1      20      −30.3       −1.80      0.008 ± 0.002   0.027 ± 0.008    0.31 ± 0.03   0.40 ± 0.03   [4 A](#fig4){ref-type="fig"} (*i*)
  D0764P        6     −36.8      5       −10.0       −0.97      0.019 ± 0.011   0.085 ± 0.033    0.26 ± 0.03   0.44 ± 0.04   [4 A](#fig4){ref-type="fig"} (*i*)
  N0765P        7     −44.5      11      −17.6       −1.44      0.014 ± 0.006   0.089 ± 0.028    0.42 ± 0.01   0.56 ± 0.01   [4 A](#fig4){ref-type="fig"} (*i*)
  L0766P        8     −40.6      6       −13.7       −1.08      0.022 ± 0.005   0.097 ± 0.024    0.51 ± 0.08   0.57 ± 0.07   [4 A](#fig4){ref-type="fig"} (*i*)
  V1159P        1     −31.2      2       −4.4        −0.42      0.010 ± 0.002   0.032 ± 0.009    0.54 ± 0.01   0.58 ± 0.01   [4 A](#fig4){ref-type="fig"} (*i*)
  G1160P        2     −47.5      19      −20.7       −1.77      0.014 ± 0.003   0.045 ± 0.011    0.34 ± 0.04   0.55 ± 0.05   [4 A](#fig4){ref-type="fig"} (*i*)
  F1161P        3     −45.9      21      −19.1       −1.83      0.020 ± 0.008   0.148 ± 0.012    0.30 ± 0.04   0.37 ± 0.04   [4 A](#fig4){ref-type="fig"} (*i*)
  V1162P        4     −38.8      5       −12.0       −0.97      0.068 ± 0.020   0.260 ± 0.036    0.58 ± 0.05   0.83 ± 0.04   [4 A](#fig4){ref-type="fig"} (*iii*)
  I1163P        5     −46.1      23      −19.3       −1.88      0.035 ± 0.008   0.119 ± 0.015    0.11 ± 0.02   0.30 ± 0.03   [4 A](#fig4){ref-type="fig"} (*i*)
  V1164P        6     −50.7      48      −23.8       −2.32      0.016 ± 0.007   0.070 ± 0.011    0.20 ± 0.05   0.33 ± 0.04   [4 A](#fig4){ref-type="fig"} (*i*)
  T1165P        7     −51.7      100     −24.9       −2.76      0.021 ± 0.014   0.058 ± 0.011    0.27 ± 0.04   0.60 ± 0.06   [4 A](#fig4){ref-type="fig"} (*i*)
  F1166P        8     −37.5      4.5     −10.7       −0.90      0.120 ± 0.027   0.490 ± 0.067    0.69 ± 0.03   0.89 ± 0.01   [4 A](#fig4){ref-type="fig"} (*ii*)
  V1456P        1     −13.2      0.12    13.7        1.27       0.032 ± 0.008   0.111 ± 0.037    0.71 ± 0.02   0.73 ± 0.01   [4 A](#fig4){ref-type="fig"} (*i*)
  A1457P        2     −23.8      0.7     3.0         0.21       0.039 ± 0.010   0.179 ± 0.021    0.64 ± 0.01   0.76 ± 0.01   [4 A](#fig4){ref-type="fig"} (*iii*)
  V1458P        3     −17.2      0.35    9.6         0.63       0.029 ± 0.013   0.112 ± 0.031    0.65 ± 0.02   0.74 ± 0.02   [4 A](#fig4){ref-type="fig"} (*i*)
  I1459P        4     −15.9      0.25    10.9        0.83       0.011 ± 0.003   0.060 ± 0.031    0.77 ± 0.02   0.80 ± 0.02   [4 A](#fig4){ref-type="fig"} (*i*)
  M1460P        5     −13.4      0.22    13.4        0.91       0.012 ± 0.002   0.027 ± 0.045    0.41 ± 0.02   0.58 ± 0.01   [4 B](#fig4){ref-type="fig"} (*i*)
  D1461P        6     −25.2      0.85    1.6         0.10       0.038 ± 0.006   0.130 ± 0.014    0.67 ± 0.03   0.74 ± 0.02   [4 A](#fig4){ref-type="fig"} (*i*)
  N1462P        7     −31.4      2       −4.5        −0.42      0.009 ± 0.002   0.042 ± 0.016    0.53 ± 0.02   0.55 ± 0.02   [4 A](#fig4){ref-type="fig"} (*i*)
  F1463P        8     −2.2       0.06    24.7        1.69       0.256 ± 0.014   0.391 ± 0.027    0.22 ± 0.02   0.38 ± 0.03   [4 B](#fig4){ref-type="fig"} (*iii*)
  D1464P        9     −7.7       0.09    19.1        1.44       0.125 ± 0.019   0.464 ± 0.031    0.68 ± 0.03   0.75 ± 0.05   [4 A](#fig4){ref-type="fig"} (*ii*)
  WT/BayK             −39.2      6.5     −12.4       −1.12      0.022 ± 0.006   0.140 ± 0.038    0.46 ± 0.06   0.62 ± 0.03   [5 B](#fig5){ref-type="fig"}
  V0395P/BayK   3     −14.1      0.15    12.7        1.14       0.007 ± 0.003   0.106 ± 0.032    0.78 ± 0.02   0.80 ± 0.02   [5 B](#fig5){ref-type="fig"}
  N0765P/BayK   7     −56.0      125     −29.2       −2.90      0.010 ± 0.004   0.021 ± 0.011    0.12 ± 0.01   0.31 ± 0.03   [5 B](#fig5){ref-type="fig"}
  V1162P/BayK   4     −37.4      5       −10.6       −0.97      0.022 ± 0.008   0.183 ± 0.046    0.62 ± 0.03   0.81 ± 0.03   [5 B](#fig5){ref-type="fig"}

Each mutant is specified by name (first column) and position (second column, corresponding to S6 coordinate in [Fig. 1 A](#fig1){ref-type="fig"}). Parameters are as defined in [Table I](#tbl1){ref-type="table"}. VDI and CDI metrics are mean ± SEM. The final column indicates the figure in which the data are plotted ([Figs. 4 A, 4 B](#fig4){ref-type="fig"}, or [5 B](#fig5){ref-type="fig"}), followed by the corresponding zone (*i*, *ii*, or *iii*) in [Fig. 5 C](#fig5){ref-type="fig"}.

Mechanistic implications of interrelations between CDI and ΔΔ*G~a~*
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Does this rich assortment of functional effects ([Fig. 3](#fig3){ref-type="fig"}) adhere to a coherent pattern, distinctive of a particular end-stage inactivation mechanism ([Fig. 1, C--F](#fig1){ref-type="fig"})? Remarkably, CDI exhibited a telling dependence on ΔΔ*G~a~* ([Fig. 4 A](#fig4){ref-type="fig"}), with striking correspondence to the predicted outcome for an allosteric CDI mechanism (solid curve corresponding to [Eq. 5](#fd5){ref-type="disp-formula"}). Mutations that enhanced activation (ΔΔ*G~a~* \< 0) proportionally diminished CDI, in good agreement with the ideal relation for allosteric inhibition (solid curve). As for mutations that favored the closed conformation (ΔΔ*G~a~* \> 0), most (11 of 15) fit well to the top of the predicted, bell-shaped relation. Indeed, only four constructs deviated below the idealized relation for allosteric inactivation ([Fig. 4 B](#fig4){ref-type="fig"}). Closer inspection of the outlier that deviated most from theory revealed unusually large gating currents relative to ionic currents ([Fig. 4 C](#fig4){ref-type="fig"}, right, G0394P). The other three outliers also had pronounced gating currents ([Fig. 4 C](#fig4){ref-type="fig"}). In contrast, gating currents were too small to resolve in the wild-type Ca~V~1.3 channel ([Fig. 4 C](#fig4){ref-type="fig"}, left) as well as all other mutant channels. For example, V0395P has a similar ΔΔ*G*~a~ to the outliers, yet it has unresolvable gating current ([Fig. 4 C](#fig4){ref-type="fig"}) and resides close to the theoretical ideal ([Fig. 4 A](#fig4){ref-type="fig"}). The increased gating current in the outliers suggests that these mutations not only shift *V*~1/2~ to the right, but also markedly suppress maximum channel open probability ([@bib2]). Such pronounced dual effects in outlier channels would cause their *P*~O~ to fall well below those estimated from our convenient whole cell estimation of *P*~O~(*V*) relations ([Fig. 2, C and D](#fig2){ref-type="fig"}). This unaccounted-for decrease in *P*~O~ would produce smaller *F*~CDI~ values than predicted by [Eq. 4](#fd4){ref-type="disp-formula"} (dotted curve in [Fig. 1 F](#fig1){ref-type="fig"}), yielding the observed deviation from ideality in [Fig. 4 B](#fig4){ref-type="fig"}. Although the whole cell estimation of *P*~O~(*V*) relations lacks the single-channel resolution needed to directly account for changes in maximum open probability ([@bib70]), the close correspondence of the vast majority of mutants (30 of 34) to the ideal relation in [Fig. 4 A](#fig4){ref-type="fig"} suggests that mutation-induced effects on maximum channel open probability are minimal in the majority of cases. This ultimate result, combined with the need for technical simplicity in a mutagenesis screen of this magnitude, validates the simple whole cell approach.

![Implications of S6 mutagenesis scan for endpoint mechanism of CDI. (A and B) *CDI*~50~ versus ΔΔ*G~a~* for our Ca~V~1.3 mutant library. Symbol color and shape as in legend. Error bars are SEM. Overlaid are the model results identical to [Fig. 1 F](#fig1){ref-type="fig"}. (C) Gating currents of channels that fall on (left) and off (right, gray shaded) the predicted *CDI*-ΔΔ*G~a~* relation. *Q*~R~ is the ratio of gating current area (e.g., pink shaded area of G0394P) to peak ionic current (units of μCoul/A). The mean ± SEM is shown for each construct. (D) CDI occurs via an allosteric mechanism. Channels occupy either a normal (top row) or inactivated gating mode (bottom row). In either mode, channel activation begins with voltage sensor (+) movement (governed by *Q*~EFF~(*V*)) and ends with S6 gate opening (governed by *L*). Outward voltage sensor displacement promotes S6 gate opening (depicted with springs). CaM (yellow dumbbell) binds Ca^2+^ (black dots in bottom row) and initiates CDI by interacting with a channel site distinct from the S6 gate. This causes a conformational change (red arrows) that inhibits S6 gate opening (i.e., parameter *f* \< 1). Thus, voltage and Ca^2+^ ultimately exert opposing actions on the same S6 gate.](JGP_200910308R_RGB_Fig4){#fig4}

Bay K 8644 effects cohere to the same *CDI*-ΔΔ*G~a~* relation
-------------------------------------------------------------

To confirm the generality of the allosteric relation in [Fig. 4 A](#fig4){ref-type="fig"}, we tested the effects of Bay K 8644, a well-known pharmacological agent that interacts with S5/S6 regions to enhance channel opening, i.e., to decrease ΔΔ*G~a~* ([@bib29]). [Fig. 5 A](#fig5){ref-type="fig"} (top) shows the behavior of Ca~V~1.3 in the presence of 5 µM Bay K 8644. As expected, there is a marked hyperpolarizing shift of the activation curve (ΔΔ*G~a~* \< 0). Interestingly, CDI diminishes appreciably, and by an extent that accords precisely with our established relation ([Fig. 5 B](#fig5){ref-type="fig"}, black symbols). Similarly, the addition of Bay K 8644 to a left-shifted II-S6 mutant (N0765P) markedly enhances activation and nearly eliminates CDI ([Fig. 5 A](#fig5){ref-type="fig"}, middle), also in agreement with the allosteric prediction ([Fig. 5 B](#fig5){ref-type="fig"}, green symbols). To exclude nonspecific effects, adding Bay K 8644 to a right-shifted I-S6 mutant (V0395P) enhances activation, yet has little effect on CDI ([Fig. 5](#fig5){ref-type="fig"}, A, bottom, and B, red symbols). Finally, Bay K 8644 has no effect on activation or CDI of a III-S6 mutant ([Fig. 5 B](#fig5){ref-type="fig"}, blue symbols, V1162P), consistent with prior work in Ca~V~1.2 identifying III-S6 as a drug-binding site ([@bib29]). Remarkably, Bay K 8644 alters CDI mainly insofar as it boosts activation ([Fig. 5 B](#fig5){ref-type="fig"}), without further indiscriminate effects.

![Further implications of S6 mutagenesis scan for endpoint mechanism of CDI. (A) Behavior of wild-type Ca~V~1.3 (top row), N0765P (middle), and V0395P (bottom) channels coexpressed with α~2~δ and β~2a~ in 5 µM Bay K 8644. Gray traces show corresponding drug-free behavior. Colored arrows indicate change resulting from Bay K. (B) *CDI*~50~ versus ΔΔ*G~a~* of wild-type Ca~V~1.3 (black symbols), N0765P (green symbols), V0395P (red symbols), and V1162P (blue symbols); each construct is plotted both in the absence (circle or triangles) and presence (squares) of Bay K. (C) *CDI*~50~ versus *VDI*~300~ for our Ca~V~1.3 mutant library. Symbol color and shape as in [Fig. 4 A](#fig4){ref-type="fig"}. Data are clustered into three main zones, which are discussed in the Results.](JGP_200910308_RGB_Fig5){#fig5}

VDI involves a "hinged lid--shield" mechanism in Ca~V~1.3
---------------------------------------------------------

Our S6 mutations affected VDI in very different ways, demonstrating that VDI and CDI are distinctly different processes. This contrasting behavior is highlighted in [Fig. 5 C](#fig5){ref-type="fig"} (also see [Table II](#tbl2){ref-type="table"}), which plots CDI versus VDI for our entire library of mutants. Most of the time, significant effects on CDI occur with relatively minor changes in VDI (zone *i*). When changes in VDI do occur, CDI is either unperturbed (zone *ii*) or perturbed in the opposite direction (zone *iii*). The latter discordance is particularly striking for the F1463P mutant. Here, CDI sharply decreases, yet VDI strongly intensifies ([Figs. 5 C](#fig5){ref-type="fig"} and [3 D](#fig3){ref-type="fig"}).

Beyond this fundamental difference, we identified two mechanistically telling patterns of VDI effects. First, mutations producing the greatest alteration in VDI all cluster at the very distal ends of S6 segments, as seen by mapping *VDI*~300~ onto our structural homology model ([Fig. 6 A](#fig6){ref-type="fig"}). In particular, these VDI "hotspots" (red) reside entirely below the putative bundle crossing (arrow). Second, mutations at VDI hotspots invariably increase the extent of inactivation. In contrast, nearly all prior S6 mutations (all in Ca~V~1.2 and Ca~V~2.1) produced decreases in VDI at residues above the putative bundle crossing ([@bib42], [@bib43]; [@bib66], [@bib67]; [@bib65]; [@bib63], [@bib64]; [@bib31]; [@bib32]; [@bib58], [@bib59]; [@bib6]). These residues have been proposed as the "receptor" for a hinged lid.

![Mechanistic insights for VDI. (A) VDI perturbations mapped onto the Ca~V~1.3 homology model from [Fig. 1 B](#fig1){ref-type="fig"}. Residues outside of mutagenesis screen shown in gray. Colored regions indicate *VDI*~300~ upon mutation to proline. See color legend to right, and note that native channel *VDI*~300~ is ∼0.1 (blue). (B and C) Proposed mechanism of VDI in Ca~V~1.3. Native channels (B) have very little VDI, likely due to the presence of a shield (red), which prevents the hinged lid (blue) from reaching its binding site (green). VDI-enhancing S6 mutations likely disrupt this shield (C). (D and E) Sensitivity of VDI to β subunits supports the notion of a shield in Ca~V~1.3. Although β~1b~ typically enhances VDI by allowing greater hinged-lid mobility than β~2a~ (cartoon in D), native Ca~V~1.3 and non-hotspot mutant N1462P have no such effect (D). In contrast, if the putative shield is perturbed (two mutants in E), β~1b~ significantly enhances VDI.](JGP_200910308R_RGB_Fig6){#fig6}

These two discrepancies from prior patterns hint at a unique mechanism of VDI in Ca~V~1.3. To start, the distal location of hotspot residues might initially suggest that these residues comprise part of a hinged-lid receptor site, with a different location than that found in Ca~V~1.2 channels. However, the increase rather than decrease in VDI caused by these hotspot mutations argues against this notion, for it is implausible that proline mutations would generate de novo functionality, such as enhanced VDI. Instead, these hotspot residues might comprise part of an element that prevents VDI in Ca~V~1.3 channels, i.e., something akin to a shield ([Fig. 6 B](#fig6){ref-type="fig"}, red) that prevents a hinged lid--like module (blue) from reaching its S6 binding site (green). The distal S6 mutations might have disrupted this shield, thus promoting VDI ([Fig. 6 C](#fig6){ref-type="fig"}).

If so, one might expect Ca~V~1.3 channels to be insensitive to perturbations of the presumed hinged lid itself because the shield would block the lid regardless of its properties. One test of this prediction comes with the use of different auxiliary β subunits, all of which bind the presumed hinged lid comprised of the intracellular loop between channel domains I and II ("I-II loop"). The prevailing view in most Ca^2+^ channels is that the β~2a~ subunit is palmitoylated and anchored to the membrane ([Fig. 6 D](#fig6){ref-type="fig"}, top left), thereby restricting lid mobility and diminishing VDI. In contrast, the β~1b~ subunit lacks such palmitoylation ([Fig. 6 D](#fig6){ref-type="fig"}, bottom left) and VDI becomes much faster. However, according to the shield hypothesis, VDI of Ca~V~1.3 channels should be insensitive to the type of β subunit. In fact, both the wild-type Ca~V~1.3 and a non-hotspot mutant (N1462P) exhibit identically weak VDI with either β~2a~ or β~1b~ ([Fig. 6 D](#fig6){ref-type="fig"}) ([@bib60]). This outcome is unique to Ca~V~1.3, as the switch from β~2a~ to β~1b~ significantly accelerates VDI in nearly all other Ca~V~1/2 channels ([@bib39]; [@bib12]; [@bib66], [@bib67]; [@bib8]; [@bib65]; [@bib19]). A more stringent test concerns the effects of different β subunits if the presumed shield were first disrupted. In this context, VDI should then become sensitive to the type of β subunit. Indeed, when the presumed shield is eliminated with either of two VDI hotspot mutations, switching from β~2a~ to β~1b~ causes a marked acceleration of VDI ([Fig. 6 E](#fig6){ref-type="fig"}). In all, the data thus far argues well for the existence of a shield against VDI.

Still needed, however, is direct evidence that the basic hinged-lid mechanism identified in Ca~V~1.2 channels is retained in Ca~V~1.3. Notably, for more proximal S6 residues identified in Ca~V~1.2 as critical to a hinged-lid receptor site ([@bib32]), our own Ca~V~1.3 mutations at the analogous residues exhibit VDI no different than that observed at baseline in [Fig. 7 A](#fig7){ref-type="fig"}. This lack of effect could be rationalized by supposing that the Ca~V~1.3 receptor site is shielded from the hinged lid so receptor disruption would have no appreciable effect on VDI ([Fig. 7 B](#fig7){ref-type="fig"}). To test directly for a hinged-lid mechanism in Ca~V~1.3, it would be necessary to first disrupt the shield, e.g., with an initial D1464P mutation ([Fig. 7, C and D](#fig7){ref-type="fig"}). Given this starting point, additional mutations at positions homologous to hinged-lid receptor sites in Ca~V~1.2 should diminish VDI. The rapid VDI seen upon shield disruption gives the baseline against which further mutations will be compared ([Fig. 7 C](#fig7){ref-type="fig"}). Reassuringly and without exception, additional mutations at homologous hinged-lid receptor sites now produce a striking slowing of VDI ([Fig. 7, E and F](#fig7){ref-type="fig"}). The G398P mutation in IS6 is analogous to the Ca~V~1.2 G406R mutation that underlies forms of Timothy syndrome ([@bib63], [@bib64]; [@bib6]), and the L0759 and A0760 mutations in IIS6 correspond to rabbit Ca~V~1.2 receptor sites at L0779 and A0780 ([@bib32]). These results furnish strong evidence that these residues contribute to a hinged-lid receptor, analogous to that described in Ca~V~1.2.

![Further mechanistic insights for VDI. (A--D) Review of proposed shield structure. In A and B, native Ca~V~1.3 channels have very little VDI, likely due to the presence of a shield (red) that prevents the hinged lid (blue) from reaching its binding site (green). Conversely, in C and D, shield-disrupting mutation D1464P enhances VDI, even when coexpressed with α~2~δ and β~2a~, here and subsequently. (E and F) Evidence that an underlying hinged-lid mechanism exists in Ca~V~1.3. Given a baseline shield-disrupting D1464P mutation, additional mutations at sites homologous to those previously identified as a hinged-lid binding site (green) significantly diminish VDI. The G398P mutation is analogous to the Ca~V~1.2 G406R mutation that underlies forms of Timothy syndrome, and the L0759P and A0760P mutations in IIS6 correspond to rabbit Ca~V~1.2 receptor sites at L0779 and A0780. (G) Structural model of components underlying the hinged lid--shield mechanism. VDI for the constructs in C and E are mapped onto our Ca~V~1.3 homology model. The pronounced VDI of D1464P (red residue) indicates the shield location below the putative gate (identified by black arrow). The loss of this VDI upon mutation of additional residues (blue and cyan) identifies the location of the proposed hinged-lid binding site (identified by green arrow) above the gate. These binding site residues move considerably in the open versus closed conformations, consistent with preferential open-state accessibility.](JGP_200910308R_RGB_Fig7){#fig7}

DISCUSSION
==========

CaM-mediated inactivation may act by allosteric inhibition of activation gate
-----------------------------------------------------------------------------

The past decade has witnessed many discoveries about the early events underlying Ca^2+^/CaM modulation of the family of Ca^2+^ channels. Much is now known about the positioning of Ca^2+^-free CaM (apoCaM) on the channel, the binding of Ca^2+^ to this "pre-associated" CaM, and the initial Ca^2+^/CaM interaction sites on the channel ([@bib22]). In contrast, the ensuing movements of cytoplasmic loops and the eventual actions that produce channel inactivation (or facilitation) have remained largely unknown. This paper furnishes new evidence that allosteric inhibition of the activation gate is the ultimate outcome for the CaM-mediated CDI of Ca~V~1.3 channels. A like hypothesis was proposed for Ca~V~1.2, based on single-channel recordings ([@bib36]). Here, our present work transforms this suggestion into an explicit mechanism, key features of which are illustrated in [Fig. 4 D](#fig4){ref-type="fig"}.

First, just as voltage depolarization can enhance opening of the S6 activation gate ([Fig. 4 D](#fig4){ref-type="fig"}, springs), CaM-driven conformational changes act to suppress opening of the very same cytoplasmic gate (red arrows in bottom row). Thus, CDI corresponds to an inactivated gating mode ("mode Ca") in which channels open sparsely due to an increase in the chemical energy needed to open the S6 gate (*f* \< 1 in the bottom row). Interestingly, a simple variant of this allosteric mechanism, with *f* \> 1, could explain CaM-induced facilitation in Ca~V~2.1 channels ([@bib15]).

Second, other features of our results generalize key principles of channel activation across the superfamily of voltage-gated channels. Notably, our data support the principle of separability between the initial movements of voltage-sensing domains (via *Q*~EFF~(*V*)) and the subsequent opening of the cytoplasmic activation gate (via *L*, shown explicitly as two separate transitions in [Fig. 4 D](#fig4){ref-type="fig"}), a theme with considerable support in voltage-gated K^+^ channels ([@bib80]; [@bib79]). In the Ca^2+^ channel case, this view is reinforced by the analysis used to determine ΔΔ*G*~a~ ([Eq. 6](#fd6){ref-type="disp-formula"} and [Fig. 2 E](#fig2){ref-type="fig"}), which tests the separability of voltage sensing (via *Q*~EFF~(*V*)) and subsequent opening of the S6 gate (via *L*). Only 2 of 34 mutations had *P*~O/MUT~--*P*~O/WT~ relations that could not be fit with [Eq. 6](#fd6){ref-type="disp-formula"} (A0762P and V0763P in Fig. S1), indicating that *Q*~EFF~(*V*) changed in these rare cases. For the vast majority of mutants, the close correspondence of data to [Eq. 6](#fd6){ref-type="disp-formula"} ([Fig. 3](#fig3){ref-type="fig"}, right columns, and Fig. S1, right columns) supports the notion that S6 mutations do not, in general, alter voltage sensing (*Q*~EFF~(*V*) unchanged in [Fig. 4 D](#fig4){ref-type="fig"}) despite marked changes in the subsequent opening step (*a* ≠ 1). This result empirically substantiates the use of proline substitutions in our screen. Interestingly, the atypical residues in Ca~V~1.3 that seem to alter voltage sensing upon mutation to proline correspond to a closely homologous region in Ca~V~1.2, where an A780P mutation (analogous to A0760P in the present study) was believed to disturb voltage sensor function ([@bib11]), suggesting conserved structural underpinnings across the Ca~V~1 family. Another key principle concerns the concerted nature of the final S6 gate opening, where an alteration to any individual S6 segment would affect the combined movement of all four elements ([@bib79]). This is supported by the finding that widely dispersed S6 mutations in all four domains exert strong effects on activation ([Fig. 3](#fig3){ref-type="fig"}). In contrast, some prior studies have suggested that Ca^2+^ channel opening is dominated by a glycine hinge (GX9GX3G) in IS6 ([@bib58]). Here, we find that although mutations of these glycines do alter activation, manipulations at many other sites have significantly stronger effects.

Finally, our new results about the end-stage effects of CDI, together with rapid advances concerning the early events underlying Ca^2+^/CaM modulation of Ca~V~1/2 channels, set the stage for investigating the events that link these two realms. In this regard, it may be relevant that a recent elegant study finds that CDI is diminished by introducing glycines just downstream of the IS6 region in Ca~V~1.2 channels ([@bib28]). Perhaps this region couples cytoplasmic CaM-mediated torque to IS6 gating elements. Similarly, it will be interesting if analogous regions in other homologous domains prove equally important for CDI. In all, answering how the CaM/IQ domain communicates allosterically with the S6 gate now looms as a critical and open question in the field.

VDI may involve a hinged lid--shield mechanism in Ca~V~1.3
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Although our library of S6 mutations has strong effects on both VDI and CDI, the pattern of effects is entirely different for these two forms of inactivation ([Fig. 5 C](#fig5){ref-type="fig"}). Thus, a common structural component (the S6 gate) may play a role in gating processes that are nonetheless functionally distinct. For CDI, S6 mutations are notable for altering the propensity to open, which through allosteric coupling change the strength of inactivation. For VDI, S6 mutations appear important for disrupting either a shield or receptor for a hinged lid.

Beyond the separate nature of VDI and CDI, our data support the existence of a Ca~V~1.3 hinged lid--shield VDI mechanism, which represents an important variant of the hinged-lid process proposed in Ca~V~1.2 and Ca~V~2 channels ([@bib32]; [@bib27]). Importantly, we believe that the underlying hinged-lid mechanism in Ca~V~1.3 could not be immediately discerned in wild-type channels because of the existence of a shield that repels lid closure ([Fig. 7, A and B](#fig7){ref-type="fig"}). Only after the introduction of shield-disrupting mutations do the hallmarks of a hinged-lid mechanism emerge in the Ca~V~1.3 context. In particular, shield disruption produces both VDI sensitivity to the identity of the β subunit ([Fig. 6 E](#fig6){ref-type="fig"}) and a slowing of VDI upon additional mutation at residues comprising the presumed hinged-lid receptor ([Fig. 7 E](#fig7){ref-type="fig"}). [Fig. 7 G](#fig7){ref-type="fig"} summarizes the structural components underlying the proposed hinged lid--shield mechanism. Of note, shield residues (red) fall below the putative gate location (identified by black arrow), whereas binding site residues (blue and cyan) sit above the gate. These binding site residues move considerably in the open versus closed conformations ([Fig. 7 G](#fig7){ref-type="fig"}), consistent with preferential open-state accessibility ([@bib69]). The shield, which seems to be a unique specialization in Ca~V~1.3 channels, may play a fundamental role in ribbon synapses of the eye and ear, where Ca~V~1.3 channels must maintain channel opening despite prolonged activation ([@bib77]).

Given a recent hypothesis ([@bib28]), our findings merit further comment regarding the interrelation between VDI and the I-II loop between homologous domains I and II. This loop contains an 18-residue helical segment called the AID, which interacts with the auxiliary β subunit of Ca^2+^ channels ([@bib16]; [@bib52]; [@bib72]). One face of the AID is hydrophobic and binds to the β subunit. Residues of the opposite hydrophilic face of the AID have been shown to play a critical role in VDI, consistent with the notion that the β--AID complex is the "lid" that binds to S6 residues and occludes the pore in VDI ([@bib19]). In contrast, a more recent study models the residues upstream of the AID region (the IS6-AID linker) as an invariably rigid helical segment ([@bib73]) that positions the β--AID complex at a significant distance from the channel pore---too far away to bind or occlude the S6 gate ([@bib28]). This structural model was taken as evidence against a hinged-lid mechanism involving the I-II loop ([@bib28]). Although a strictly rigid IS6-AID linker would prevent β--AID occlusion of the pore, the apparent controversy could be reconciled if the IS6-AID linker were, under some conditions, to bend and function as a "hinge" ([Fig. 7, B and D](#fig7){ref-type="fig"}). No empirical data currently exclude the possibility of such dynamic bending of the IS6-AID linker. Moreover, the acceleration of VDI by the introduction of glycines into the IS6-AID linker ([@bib28]) fits well with the notion of augmenting flexibility of a hinge region. Together with the new lines of evidence in this paper, we suggest that a hinged lid--shield mechanism---where the IS6-AID linker functions as the hinge, and the downstream β--AID complex functions as the lid---remains worthy of continued investigation.

Implications for Ca^2+^ channelopathies involving S6 segments
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Beyond channel mechanism, this study furnishes a unifying framework for understanding heritable diseases involving S6 mutations in both neuronal and cardiac Ca^2+^ channels ([@bib42], [@bib43]; [@bib63], [@bib64]; [@bib31]; [@bib32]; [@bib6]). The phenotypic manifestations of these diseases are diverse, including migraine, ataxia, autism, physical deformities, and cardiac arrhythmias. These are believed to result from abnormal VDI, CDI, Ca^2+^-dependent facilitation, or some combination of these. A first insight is that, besides changes in inactivation or facilitation, these channelopathies are likely to exhibit potent alterations in open probability, and either (or both) of these effects may contribute to pathogenesis. For example, in Timothy syndrome, where the slowing of VDI by IS6 mutations in Ca~V~1.2 has attracted the most attention ([@bib6]), accompanying changes in open probability may be equally relevant ([@bib25]). Conversely, in familial hemiplegic migraine, where the long-standing emphasis has been on altered open probability produced by S6 mutations in Ca~V~2.1 ([@bib13]; [@bib55]), a recent preliminary report indicates reductions in Ca^2+^-dependent facilitation ([@bib1]). A second key insight is that VDI abnormalities in S6 channelopathies may result from direct perturbation of either the hinged-lid binding site or the newly proposed shield structure. Either of these perturbations might prove difficult to reverse pharmacologically because the fundamental VDI machinery has been compromised. In contrast, S6 channelopathies that affect CDI might be amenable to pharmaceutical intervention because the actual CDI machinery is likely intact. The apparent CDI deficit arises as an indirect result of altered channel activation ([Fig. 4, A and D](#fig4){ref-type="fig"}), something that can be readily reversed. Indeed, several compounds such as dihydropyridine agonists (e.g., Bay K 8644 in [Fig. 5, A and B](#fig5){ref-type="fig"}) and antagonists can modulate channel activation. If properly administered with sufficient selectivity, similar compounds may simultaneously normalize activation and CDI, according to the relation in [Fig. 5 B](#fig5){ref-type="fig"}. Interestingly, Bay K 8644 can recapitulate many of the cardiac features of Timothy syndrome ([@bib62]), a Ca~V~1.2 channelopathy involving mutations in I-S6. Additionally, recent clinical work suggests that verapamil, a Ca^2+^ channel--blocking compound, partially relieves cardiac symptoms of Timothy syndrome ([@bib37]). In all, modulators of Ca^2+^ channel activation, fine-tuned by the principles outlined here, may ultimately prove therapeutic.

We thank Wanjun Yang for dedicated technical support and Ivy Dick for helpful comments on the manuscript.

This work was supported by a Medical Scientist Training Program fellowship of the National Institute of General Medical Sciences (to M.R. Tadross) and by grant RO1MH065531 of the National Institute of Mental Health (to D.T. Yue).

Angus C. Nairn served as editor.

Abbreviations used in this paper:CaMcalmodulinCDICa^2+^-dependent inactivationGHKGoldman-Hodgkin-KatzVDIvoltage-dependent inactivation