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We provide a theory for employing Förster resonance energy transfer (FRET) measurements to determine altered heteropentameric ion channel stoichiometries in intracellular compartments of living cells. We simulate FRET within nicotinic receptors (nAChRs) whose α4 and β2 subunits contain acceptor and donor fluorescent protein moieties, respectively, within the cytoplasmic loops. We predict FRET and normalized FRET (NFRET) for the two predominant stoichiometries, (α4)_{3}(β2)_{2} _{2}(β2)_{3}. Studying the ratio between FRET or NFRET for the two stoichiometries, minimizes distortions due to various photophysical uncertainties. Within a range of assumptions concerning the distance between fluorophores, deviations from plane pentameric geometry, and other asymmetries, the predicted FRET and NFRET for (α4)_{3}(β2)_{2} exceeds that of (α4)_{2}(β2)_{3}. The simulations account for published data on transfected Neuro2a cells in which α4β2 stoichiometries were manipulated by varying fluorescent subunit cDNA ratios: NFRET decreased monotonically from (α4)_{3}(β2)_{2} stoichiometry to mostly (α4)_{2}(β2)_{3}. The simulations also account for previous macroscopic and single-channel observations that pharmacological chaperoning by nicotine and cytisine increase the (α4)_{2}(β2)_{3} and (α4)_{3}(β2)_{2} populations, respectively. We also analyze sources of variability. NFRET-based monitoring of changes in subunit stoichiometry can contribute usefully to studies on Cys-loop receptors.

A superfamily of ligand-gated ion channels comprises homo- and heteropentameric combinations of subunits. The superfamily includes neuronal nicotinic acetylcholine receptors (nAChRs) comprised of α (α2 to α10) and β (β2 to β4) subunits. Possible changes in the stoichiometry of these subunits within the α4β2 pentamer have generated interest, because the (α4)_{2}(β2)_{3} and (α4)_{3}(β2)_{2} stoichiometries differ in their sensitivity to agonists [^{2+} permeability [

Chronic nicotine increases the assembly of (α4)_{2}(β2)_{3} receptor pentamers within the ER [

We and others have utilized fluorescent protein (FP)-tagged α4 and β2 nAChR subunits and fluorescence microscopy in transfected cells to study altered α4β2 stoichiometry [_{3}(β2)_{2} _{2}(β2)_{3}. We show that the new method does not require additional strong assumptions about symmetry, or about distances between fluorophores. The method may be considered a special case within the tradition of analyzing pentameric proteins by FRET [

We calculate the relative FRET efficiency _{3}(β2-EGFP)_{2} _{2}(β2-EGFP)_{3} stoichiometry. We define the average FRET values as _{3,2} and _{2,3} respectively, so that the desired ratio is _{3,2} / _{2,3}. We then extend these calculations to NFRET and calculate the analogous ratios, _{3,2}/_{2,3}. The assumptions provide a special case of previous theories about pentameric proteins, but are less restrictive than previous analyses of pentameric ion channels [

(a) All β2-EGFP subunits have identical structure, and all α4-mCherry subunits have identical structure. For simplicity, we generally omit the description of the fluorophore when discussing stoichiometry; thus in most cases (α4)_{2}(β2)_{3} implies (α4-mCherry)_{2}(β2-EGFP)_{3}.

(b) FRET interactions are fully determined by relative positions of subunits within the pentamer. The EGFP donor fluorophores need not be located at the same radial distance as the mCherry acceptors. The donor fluorophores also need not have the same dipole moment angle with the radius, nor lie in the same plane, as the acceptors. Indeed, the intracellular domain of the wild-type α4 subunit has roughly twice as many amino acids as that of the wild-type β2 subunit, rendering it likely that the α4-linked fluorophores have a different disposition from β2-linked fluorophores.

(c) Donor subunits can be either adjacent or non-adjacent to acceptor subunits. _{2}(β2)_{3} and (α4)_{3}(β2)_{2} stoichiometry in the upper and lower panels respectively, and also shows the nomenclature for distinguishing among the three or two donor fluorophores, so that calculations can proceed for each donor. _{A} or GluCl receptors would be α<β, because for such receptors, the principal interface for binding lies on the β subunit). The fluorophores are shown as green (EGFP donor) and red (mCherry acceptor) bars, to emphasize the importance of the fluorophores’ dipoles. The locations and orientations of the dipoles are arbitrary. The wild-type α4 M3–M4 intracellular loop has a sequence roughly twice as long the wild-type β2 subunit; this loop is depicted schematically, and the EGFP donor fluorophore projects from the loop. _{j}_{i,j}_{i,j}

For _{DA,i}^{−1} for decay from the excited state increases linearly with the contribution from each potential donor-acceptor interaction:

where τ_{D}^{−1} is the unperturbed rate constant. The equations select among the available energy transfer pathways as follows: each _{j}_{i,j}_{i,j}_{2, +1} = 1; and the associated _{+1} therefore exists in the term describing β2-EGFP donor #2 in

Measured spectral FRET values always return products of the Förster efficiency E multiplied by the fraction _{P}_{P}

In _{j}_{,0} is the Förster distance for each _{j}^{2}, which potentially varies among the ^{2} = 2/3, the Förster radius _{0} for the EGFP-Cherry pair is 51.4 Å [^{2} differs among donor-acceptor pairs within a pentamer.

We now compute the desired ratio, _{3, 2}/_{2, 3}. The (α4)_{2}(β2)_{3} nAChR stoichiometry of

In the (α4)_{3}(β2)_{2} configuration of

We now apply the equation,

We average over the two donors or the three donors, as appropriate (all conventional optical methods perform such averaging, because the resolution is much poorer than the subunit spacing). Thus,

and

These relations allow us to calculate _{3,2} / _{2,3}.

(d) An unknown value is the distance between fluorophores on adjacent subunits, because there are no structural data for the cytoplasmic M3–M4 loops. We define an average distance _{1,}_{ave}_{1,}_{ave}_{0}_{0}_{0}_{3,2} / _{2,3} and _{3,2}/_{2,3} ratios both approach the theoretical limit of 1.5 at ~80 Å, obviating exploration of greater _{1,}_{ave}

In order to perform specific calculations in the absence of structural data about the M3–M4 loops, we further define a regular pentagon-shaped receptor, as well as variations around this standard, as follows.

(e) If the five fluorophores are located at the vertices of a pentagon, we may write,

We define a “geometry factor”, _{3,2}/_{2,3} values vary for

(f) We define an “asymmetry factor”, Δ, that can arise from unequal _{j}^{2} values, between the donor and two possible flanking acceptors that are both adjacent to the donor (as in

The special case of Δ = 0 defines a regular pentameric, pentagonal receptor: (i) the five fluorophores are located at 72° intervals with respect to the nAChR axis of pseudo symmetry, presumably the channel pore; and (ii) their dipole moments make a common angle with the radius. In the simulations, we allow the range Δ = 0 to 0.6 (the latter value indicates that _{+1} differs from _{+1}/_{−1} ~3 _{−1} by 4-fold). _{−1} and _{+1} produces _{+1}/_{−1} slightly greater than the 4-fold range. Monte Carlo calculations on a regular pentagon (Figure 10C of Reference [^{2} between two adjacent subunits lies mostly within a range of ±10%; the ^{2} values between non-adjacent subunits are somewhat larger, but again lie mostly within a range of ±10%. The corresponding range is _{+1}/_{−1} ~3.

These relations lead to _{3,2} / _{2,3} _{1,}_{ave}_{Ai}

Thus, the _{Ai}_{D}^{′}, the fraction of donors that actually reside in fully assembled pentamers (including fully assembled, but immature, non-glycosylated or post-translationally modified pentamers). The remaining donors would reside in FRET-incapable soluble proteins or in partially FRET-capable, partially assembled receptors. The prime notation reminds us that FRET capability is additionally represented, within assembled pentamers, by _{P}_{D}^{′} does not depend on stoichiometry, this factor does not contribute to the FRET ratio calculations for sensitized emission.

Most of our experiments use NFRET, a variant in which the sensitized emission is normalized as follows:

In _{A}_{A}_{A}_{3,2}/_{2,3}. In

In _{D}

where _{D}_{D}^{′} =1. Our simulations use _{D}^{′} =1, because this is the most “pessimistic” assumption from the viewpoint that NFRET is a reasonable monitor of FRET. With these assumptions, NFRET is approximately proportional to FRET efficiency _{P}_{1,}_{ave}_{0}_{3,2}/_{2,3} cancels out additional poorly behaved characteristics of _{3,2}/_{2,3} varies in much the same way as _{3,2} / _{2,3} over a wide range of simulated parameters, as long as _{P}_{3,2}/_{2,3} does become poorly behaved for _{P}_{3,2} / _{2,3} = _{3,2} / _{2,3}_{3,2}/_{2,3} lies in a useful range for all plausible values of nAChR structure.

Measurements of net FRET are treated in

We emphasize the major predictions that 1 / 1.5 < _{3,2} _{2,3} < and that 1 < _{3,2}/_{2,3} < 1.5 for all reasonable structures of α4β2 nAChRs. The limit of 1.0 at small values of _{1,}_{ave}_{1}, arises from the fact that the average β2-EGFP donor has 1.5 times as many adjacent α4-mCherry acceptors in the (α4)_{3}(β2)_{2} stoichiometry as in the (α4)_{2}(β2)_{3} stoichiometry; and at distances much greater than _{0}_{±}_{1,} _{±2}

We have utilized nAChR α4-mCherry (acceptor) and β2-EGFP (donor) subunits. These fluorophores have, in our hands, optimal characteristics for pixel-by-pixel sensitized emission in living cells. These proteins are expressed in Neuro-2a cells, a favorable system in which membrane protein expression remains linear with respect to several factors under the experimenter’s control [_{DA}_{3,2} / _{2,3} ratios. We have therefore used pixel-by-pixel sensitized emission NFRET as the most appropriate parameter to monitor changes in subunit stoichiometry [

_{2}(β2)_{3} and (α4)_{3}(β2)_{2} nAChRs, respectively (this assumption will be explored further in the next section). These data yield / 1.27 _{3,2} _{2,3} =. Thus, the data confirm that the NFRET approach can differentiate between the (α4)_{2}(β2)_{3} and (α4)_{3}(β2)_{2} receptor stoichiometries. _{1,ave}

We wish to detect changes in the fractions of receptors with each stoichiometry, utilizing the full power of analyzing each pixel. The most appropriate way to analyze NFRET distributions uses Gaussian components [

Trends similar to _{3,2} and _{2,3}, are greater and less than _{high}_{low}_{high}_{low}_{3}(β2)_{2} and (α4)_{2}(β2)_{3} stoichiometries.

We calculate the integrals, _{low}_{high}_{low}_{high}_{high}

Cells transfected with a mole fraction of 0.5 β2-EGFP cDNA subunits and 0.5 α4-mCherry showed a nearly equal proportion of high and low NFRET distributions (_{high}_{high}_{high}_{3}(β2)_{2} population forms more readily than a pure (α4)_{2}(β2)_{3} population agrees with recent data from stably transfected cell lines [_{high}_{3}(β2)_{2} stoichiometry. Therefore changes in _{high}

The formal Gaussian fits in our experimental data (_{3}(β2)_{2} or (α4)_{2}(β2)_{3} population, or (b) individual pixels contain a mixture of (α4)_{3}(β2)_{2} or (α4)_{2}(β2)_{3}. The subcellular mechanisms that partially segregate these populations are not yet clear. At present our ability to distinguish among these is limited by variability in FRET measurements arising in part from optical distortions [

NFRET serves well to compare data among cells with varying expression levels. Nonetheless, a cell with a higher expression level is expected to provide a less noisy overall estimate of FRET. Suppose that the number of nAChR molecules undergoing FRET in a given pixel is a uniformly distributed random variable whose mean varies among cells. (A cell is also a collection of compartments that may have their own means; NFRET in intracellular compartments has been reported separately [

Thus, the biased expression levels generate a component of CV that does not decrease with expression levels. This extra variation has an unknown source. We note that biased transfections are expected to produce an excess of unpaired donor or acceptor fluorophores, depending on the subunit ratio. Therefore part of the excess variation may arise from pixel to pixel variations in _{D}^{′} or in

We have also studied pharmacological manipulations thought to produce changes in the subunit stoichiometry [_{2}(β2)_{3} stoichiometry. On the other hand, cytisine increased
_{3}(β2)_{2} stoichiometry.

From these pharmacological experiments, we have analyzed the pixel-by-pixel data [_{2}(β2)_{3} and (α4)_{3}(β2)_{2} nAChRs, respectively. The ratio
_{high}_{high}_{low}_{high}_{high}_{high}

The data do not allow for a choice between subunit orders that involve one _{3}, GABA_{A}, glycine, and GluCl channels) may display different subunit orders. All theory and analysis in the paper assumes that only two populations are present (those pictured in

We outline the optimal pre-requisites for the procedures. First, one requires some assurance that the fluorophores do not markedly distort function. For the present fluorescent constructs, several studies provide this assurance [

One requires a modest density of receptors. We estimate that the nAChRs in our studies are present at a density of 3–100 μm^{−2}, because we have utilized similar cells and microscopes for single-molecule fluorescence [

One would prefer a system to determine the NFRET values of nearly pure stoichiometries. This allows one to define the NFRET values corresponding to _{3,2}_{2,3} directly, as in

These experiments analyze FRET-based measurements of changed nAChR stoichiometry in live cells with good spatial resolution. We emphasize the detection of altered stoichiometry rather than absolute values. Nonetheless, it is rather satisfactory that the experimental values of
_{high}_{3,2} / _{2,3}_{2}(β2)_{3} stoichiometry; and cytisine favors the (α4)_{3}(β2)_{2} stoichiometry [

The present simulations and experiments incorporate donors or acceptors within all receptor subunits. This tactic provides the largest possible fluorescence signals [

The experiments produce valid results independently of knowledge about _{1,ave}

Which range of _{1,ave}_{1,ave}_{3,2} / _{2,3} and _{3,2}/_{2,3} values markedly lower than we measure. At the other extreme, _{1,ave}_{1,ave}

The Introduction summarizes the various pharmacological and electrophysiological characteristics that depend on the subunit stoichiometry. It is also possible to employ the pixel-based resolution in order to distinguish between nAChR stoichiometry in distinct organelles, providing a cell biological basis for the partially distinct pixel distributions. For instance, we concluded that the GABA transporter GAT1 exists in different multimerization states in perinuclear

We expect most Cys-loop receptors to be characterized by a geometry factor nearer to 1.62 and by an asymmetry factor nearer to zero, compared with the α4β2 receptors, for the reason that intracellular M3–M4 loop lengths of other Cys-loop receptors occupy a more uniform distribution. Thus the analysis presented here may be generally applied.

We thank Kimberly Scott for discussions. Supported by grants from the U.S. National Institutes of Health (NS-11756, NS-34407, AG-033954), Targacept Inc., Louis and Janet Fletcher, the Michael J. Fox Foundation, the California Tobacco-Related Disease Research Program postdoctoral fellowship (18FT-0066 to R.S.), a Beckman Institute Fellowship (C.I.R) and an NIH Kirschstein National Research Service Award (DA030877 to C.I.R).

enhanced green fluorescent protein

endoplasmic reticulum

Förster resonance energy transfer

neuronal nicotinic acetylcholine receptors

monomeric cherry fluorescent protein

normalized Förster resonance energy transfer

^{2+}permeability of the (α4)

_{3}(β2)

_{2}stoichiometry greatly exceeds that of (α4)

_{2}(β2)

_{3}human acetylcholine receptors

Diagrams depicting FRET analysis of nAChR stoichiometry. (_{2}(β2)_{3}, and in the bottom panel (α4)_{3}(β2)_{2}. The donor molecules are labeled 1 through 3, as in the equations in the text; (_{1, −1} = _{1, +1} = 1. The arrows show the fluorophore separations _{±1}, _{±2} and the corresponding energy transfer probabilities, _{±1}, _{±2} Clockwise energy transfer is shown as a black arrow; anticlockwise, as gray. The remaining two subunits are shown in gray; they may be either donors or acceptors; (_{1, −2} = _{1, +2} = 1. Other details as in (

Simulations. (_{3,2} / _{2,3}_{1,ave}_{P}_{3,2}/_{2,3}, the ratio of NFRET efficiency for the two stoichiometries; (_{3,2}/_{2,3} _{P}

Data from NFRET measurements with biased transfection ratios. (_{high}_{high}^{6} pixels. The right _{high}

Data from NFRET measurements with pharmacological chaperones. Further analysis of a published experiment [_{high}^{6} pixels. The right _{high}