# Förster Resonance Energy Transfer (FRET) Correlates of Altered Subunit Stoichiometry in Cys-Loop Receptors, Exemplified by Nicotinic α4β2

^{1}

^{2}

^{*}

## Abstract

**:**

_{3}(β2)

_{2}vs. (α4)

_{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.

## 1. Introduction

_{2}(β2)

_{3}and (α4)

_{3}(β2)

_{2}stoichiometries differ in their sensitivity to agonists [1,2] and to antagonists [2], their rectification properties [3], their Ca

^{2+}permeability [4], their sensitivity to upregulation by chronic nicotine and other drugs [5,6], and possibly their subcellular localization. Some of these characteristics may provide signatures for determining the stoichiometry of nAChRs when they appear on the plasma membrane. However, several nAChRs and other Cys-loop receptors localize to the endoplasmic reticulum (ER) [6–8], where stoichiometry measurements with biochemical methods are either tedious [5] or impossible. Therefore it is necessary to have additional robust measurements of changes in intracellular receptor stoichiometry.

_{2}(β2)

_{3}receptor pentamers within the ER [6,9], enhances the ER exit of nAChRs, and therefore upregulates plasma membrane receptors [6]. Such selective intracellular pharmacological chaperoning of acetylcholine receptor number and stoichiometry explains several aspects of nAChR upregulation by nicotine and other nicotinic ligands [6,9–15]. In addition to the obvious connection with nicotine addiction, pharmacological chaperoning may provide the mechanistic basis for the inverse correlation between a person’s history of smoking and his/her susceptibility to Parkinson’s disease [12]. These points increase our interest in intracellular measurements of alterations in α4β2 nAChR stoichiometry.

_{3}(β2)

_{2}vs. (α4)

_{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 [20–23]. The theory is of interest because the measurements have yielded estimates about changes in stoichiometry that are consistent with known structural information and with chaperoning by nicotine, as well as a novel effect of chaperoning by cytisine.

## 2. Results and Discussion

#### 2.1. Simulations

_{3}(β2-EGFP)

_{2}vs. (α4-mCherry)

_{2}(β2-EGFP)

_{3}stoichiometry. We define the average FRET values as Ē

_{3,2}and Ē

_{2,3}respectively, so that the desired ratio is Ē

_{3,2}/ Ē

_{2,3}. We then extend these calculations to NFRET and calculate the analogous ratios, NFRET

_{3,2}/NFRET

_{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 [18,21], as described below (see Figure 1).

_{2}(β2)

_{3}implies (α4-mCherry)

_{2}(β2-EGFP)

_{3}.

_{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. Figure 1A also shows the usual assumption, that two interfaces exist in which the β subunit is immediately counterclockwise to the α subunit. These appropriately polarized interfaces, which we term β2 < α4, are important for function because they form high-affinity agonist/antagonist binding sites; however the presence of a ligand site does not affect the FRET properties (the analogous terminology applied to GABA

_{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. Figure 1A thus emphasizes that the donor and acceptor fluorophores can also differ with respect to their radial distance. The donors can also reside in a different plane from the acceptors; this point is not shown. The distances between donor and acceptor fluorophores, angle between the donor emission and acceptor absorption dipoles, and spectral overlap integrals, lead to four possible microscopic FRET probabilities p

_{j}for each donor. These are calculated as described below. Figure 1B depicts the energy transfer pathways when a donor is flanked by adjacent acceptors; and Figure 1C shows the pathways when two acceptors are both non-adjacent to a donor. Depending on the order and stoichiometry of the subunits, only specific subsets of these pathways exist for each donor. Figure 1D tabulates the “n-factors” for the nAChR stoichiometries under consideration. The subunit order is clockwise, seen from the extracellular surface. The two or three β2-EGFP subunits are numbered, as in A. The first column corresponds to A, top panel; the second, to A, bottom panel. Each cell in the table reports n

_{i,j}values that equal 1 (all others = 0), corresponding to possible energy transfer pathways. The n

_{i,j}values control the appearance of terms in Equations 2 through 6.

_{DA,i}

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

_{D}

^{−1}is the unperturbed rate constant. The equations select among the available energy transfer pathways as follows: each p

_{j}is multiplied by a parameter that we term an “n-factor” n

_{i,j}. The index i describes one of the two (i = 1, 2) or three (i = 1, 2, 3) individual donor fluorophores in the pentamer, and j = −2, −1, +1, +2 describe acceptors located at adjacent (±1), non-adjacent (±2) positions, where negative numbers indicate anticlockwise transfer as described in Figure 1B,C. The “n-factor” n

_{i,j}is unity if donor i has an acceptor at relative position j, and zero if not. For example, if there is an α4-mCherry acceptor immediately clockwise to β2-EGFP donor #2, then n

_{2, +1}= 1; and the associated p

_{+1}therefore exists in the term describing β2-EGFP donor #2 in Equations 2, 3, 9, and 10 below. Figure 1D is a table of all “n-factors” that equal unity.

_{P}of fluorophores participating in the energy transfer within assembled pentamers. The parameter is less than unity because donor and/or acceptor fluorophores fold incompletely, mature incompletely, become proteolyzed, undergo partial bleaching, or otherwise fail to participate in FRET [24]. The parameter f

_{P}is included in Equations 2 and 3 below. The possibility of unpaired, free donors residing outside of pentamers is considered later.

_{j}

_{,0}is the Förster distance for each j-valued donor-acceptor pair, and R

_{j}is the distance between each j-valued donor-acceptor pair (length of the arrow in Figure 1). The Förster distance is determined by the spectral overlap between EGFP and mCherry (this is constant among all j-valued pairs) and by the dipole angle between donor and acceptor; the latter parameter determines the orientation factor κ

^{2}, which potentially varies among the j values. For the specific assumption that κ

^{2}= 2/3, the Förster radius R

_{0}for the EGFP-Cherry pair is 51.4 Å [25]. However, we do not explicitly assume that the fluorophores move so quickly that they sample many orientations; indeed, this assumption is unacceptable for fluorescent proteins embedded within a loop. The parameter Δ, described below, embodies the possibility that κ

^{2}differs among donor-acceptor pairs within a pentamer.

_{3, 2}/E

_{2, 3}. The (α4)

_{2}(β2)

_{3}nAChR stoichiometry of Figure 1A, top panel, has 3 donor molecules:

_{3,2}/ Ē

_{2,3}.

_{1,}

_{ave}between fluorophores on adjacent subunits. We then calculate the quantities of interest for a range of R

_{1,}

_{ave}values. The sensitivity of FRET measurements is limited to distances within a factor of two of R

_{0}. The lower limit of our simulations, 25 Å, represents both ~ R

_{0}/2 and the closest possible distance between adjacent fluorophores of the GFP family. The upper limit corresponds to ~2R

_{0}= 100 Å. As discussed below (Figure 2), the Ē

_{3,2}/ Ē

_{2,3}and NFRET

_{3,2}/NFRET

_{2,3}ratios both approach the theoretical limit of 1.5 at ~80 Å, obviating exploration of greater R

_{1,}

_{ave}values.

_{3,2}/Ē

_{2,3}values vary for G between 1.3 and 1.62.

_{j}values, and/or of κ

^{2}values, between the donor and two possible flanking acceptors that are both adjacent to the donor (as in Figure 1B). For simplicity, we allow the same parameter to represent the asymmetry for the two possible acceptors that are non-adjacent to the donor (as in Figure 1C).

_{+1}differs from p

_{+1}/p

_{−1}~3 p

_{−1}by 4-fold). Figure 1B shows an extreme case in which the difference between R

_{−1}and R

_{+1}produces p

_{+1}/p

_{−1}slightly greater than the 4-fold range. Monte Carlo calculations on a regular pentagon (Figure 10C of Reference [21]) show that κ

^{2}between two adjacent subunits lies mostly within a range of ±10%; the κ

^{2}values between non-adjacent subunits are somewhat larger, but again lie mostly within a range of ±10%. The corresponding range is p

_{+1}/p

_{−1}~3.

_{3,2}/ Ē

_{2,3}versus G and Δ; this curve is repeated at 5 Å intervals of R

_{1,}

_{ave}. Our experiments have used sensitized emission measurements, in which FRET is assessed by acceptor fluorescence [6,18,27]. The average total fluorescence from a given pentamer is the average of the energy transferred via resonance, times the quantum yield of the acceptor fluorophores Q

_{Ai}:

_{Ai}factor cancels out, and the equations for sensitized emission FRET are the right-hand sides of Equations 5 and 6. We also define f

_{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 f

_{P}. Assuming that f

_{D}

^{′}does not depend on stoichiometry, this factor does not contribute to the FRET ratio calculations for sensitized emission.

#### 2.1.1. Calculations of NFRET

_{A}is the fluorescence from all acceptor molecules, both those that receive energy from donors and those that do not [24]. To the extent that I

_{A}is measured accurately by direct excitation at the excitation wavelength for the acceptor, I

_{A}does not depend explicitly on the stoichiometry and therefore cancels out when one takes the ratio NFRET

_{3,2}/NFRET

_{2,3}. In Supplementary Material, we analyze possible deviations from this assumption.

_{D}is the donor fluorescence. This fluorescence is reduced because some EGFP molecules undergo FRET within pentamers; but EGFP molecules outside pentamers have much less or zero FRET. Therefore we write,

_{D}decreases to zero if both Ē =1 and f

_{D}

^{′}=1. Our simulations use f

_{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 E for E < ~0.75, but NFRET becomes infinite as E approaches unity [28]. This poorly behaved range is not approached in our simulations, for three reasons. First, f

_{P}remains <1. Thus, in our previous studies, the maximal FRET efficiency was 48% [17,18,29]. Second, R

_{1,}

_{ave}remains ≥ R

_{0}/2. Third, the process of computing NFRET

_{3,2}/NFRET

_{2,3}cancels out additional poorly behaved characteristics of NFRET. As a result, Figure 2 reveals that NFRET

_{3,2}/NFRET

_{2,3}varies in much the same way as Ē

_{3,2}/ Ē

_{2,3}over a wide range of simulated parameters, as long as f

_{P}< ~0.8 (NFRET

_{3,2}/NFRET

_{2,3}does become poorly behaved for f

_{P}> ~0.9). Our techniques do not require that NFRET remains strictly proportional to FRET over the simulations, or that NFRET

_{3,2}/ NFRET

_{2,3}= Ē

_{3,2}/ Ē

_{2,3}, but simply that NFRET

_{3,2}/NFRET

_{2,3}lies in a useful range for all plausible values of nAChR structure.

#### 2.1.2. Summary of the Predictions

_{3,2}Ē

_{2,3}< and that 1 < NFRET

_{3,2}/NFRET

_{2,3}< 1.5 for all reasonable structures of α4β2 nAChRs. The limit of 1.0 at small values of R

_{1,}

_{ave}occurs because the energy transfer approaches equal efficiency for all donors, regardless of the number of acceptors. The limit of 1.5 at large R

_{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 R

_{0}, the adjacent subunits dominate the energy transfer (p

_{±}

_{1,}p

_{±2}). The quantitative predictions are rather more sensitive to variations in the asymmetry factor Δ than in the geometry factor G (Figure 2).

#### 2.2. Agreement with Biased Transfection Experiments

_{DA}normalized to the square root of the donor × acceptor intensity and is readily comparable between different samples [33]. The simulations (Figure 2) show that NFRET ratios provide measures that are similar to Ē

_{3,2}/ Ē

_{2,3}ratios. We have therefore used pixel-by-pixel sensitized emission NFRET as the most appropriate parameter to monitor changes in subunit stoichiometry [6,18,19,27].

_{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 Ē

_{3,2}Ē

_{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. Figure 2A indicates that the data would be satisfied by R

_{1,ave}values between 35 and 50 Å, depending on the assumptions for G and Δ. Our analyses assume the α4, β2 subunit order in which there are two β2<α4 interfaces (Figure 1A). The data would also be consistent with a single-interface model (see Supplementary Material).

#### 2.2.1. Further Analysis Based on Distinct Populations

_{3,2}and NFRET

_{2,3}, are greater and less than NFRET

_{high}and NFRET

_{low}, respectively, we would expect the NFRET distributions to include peaks or shoulders at these extreme values, outside the range defined by the averages for the biased cDNA ratios. However the distributions reveal no such extreme components. These arguments provide confidence that the NFRET

_{high}and NFRET

_{low}components correspond to the (α4)

_{3}(β2)

_{2}and (α4)

_{2}(β2)

_{3}stoichiometries.

_{low}and Int

_{high}, of the NFRET

_{low}and NFRET

_{high}component in each case. We then calculate the weighted contribution of the Int

_{high}component:

_{high}= 0.56). For cells expressing 0.67 and 0.33 mole fraction of β2-EGFP cDNA, W

_{high}was 0.16 and >0.98 respectively (Figure 2). While there is no straightforward way to provide error estimates for W

_{high}, note that we require a coefficient of determination value of 0.995 to accept the number of components (one or two) in the fitted distributions [6,27]. The idea that a pure (α4)

_{3}(β2)

_{2}population forms more readily than a pure (α4)

_{2}(β2)

_{3}population agrees with recent data from stably transfected cell lines [34]. Thus we conclude that W

_{high}increases monotonically, but perhaps not linearly, with the fraction of (α4)

_{3}(β2)

_{2}stoichiometry. Therefore changes in W

_{high}denote changes in the fraction of α4β2 nAChRs with the two stoichiometries.

#### 2.2.2. Variations in Stoichiometry among Pixels and among Cells

_{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 [32].

_{D}

^{′}or in e, a parameter related to variations in $\sqrt{{I}_{A}}$ (Supplementary Figure S2).

#### 2.3. Pharmacological Chaperoning Stabilizes Alternative α4β2 Stoichiometries

_{2}(β2)

_{3}stoichiometry. On the other hand, cytisine increased $\overline{NFRET}$ [27]. This finding, novel at the time, has since been confirmed by single-molecule measurements of nAChRs on the plasma membrane, using zero-mode waveguides [27]. Clearly, cytisine stabilizes the (α4)

_{3}(β2)

_{2}stoichiometry.

_{2}(β2)

_{3}and (α4)

_{3}(β2)

_{2}nAChRs, respectively. The ratio $\overline{NFRE{T}_{high}}/\overline{NFRE{T}_{low}}$ is usually similar to the values obtained with biased transfections [27]. The values of W

_{high}= Int

_{high}/(Int

_{low}+ Int

_{high}) for the untreated cells were similar to those of Figure 3: for nicotine, less than the untreated cells; and for cytisine, more than the untreated cells. That nicotine and cytisine respectively decrease and increase W

_{high}, compared with untreated cells, was observed in each of five independent transfections like that of Figure 4. The values of W

_{high}produced by the pharmacological chaperones are less extreme than those for biased transfections, again indicating that pharmacological chaperoning by nicotine and cytisine partially shifts the population toward either stoichiometry.

#### 2.4. One vs. Two β2 < α4 Subunit Interfaces

_{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 Figure 1A). Supplementary Materials provides simulations for the single-interface model, but again for only two populations.

#### 2.5. Requirements for the Procedure

^{−2}, because we have utilized similar cells and microscopes for single-molecule fluorescence [38–40]. Much lower densities would provide insufficient signals. Much higher densities could produce “stochastic” FRET.

_{3,2}, Ē

_{2,3}directly, as in Figure 2C. We have accomplished this via transient transfections with biased cDNA ratios. In the absence of this preferred route, one can extract the appropriate NFRET values from Gaussian fits to NFRET distributions. As shown in Figures 3 and 4, the Gaussian fits produce a $\overline{NFRE{T}_{high}}/\overline{NFRE{T}_{low}}$ value corresponding well to directly determined $\overline{NFRET}$.

## 3. Conclusions

_{high}. The values for net FRET, Ē

_{3,2}/ Ē

_{2,3}, follow the same trends (Supplementary Information). Summarizing these conclusions: the biased subunit transfections favor the two stoichiometries in the expected directions; pharmacological chaperoning by nicotine favors the (α4)

_{2}(β2)

_{3}stoichiometry; and cytisine favors the (α4)

_{3}(β2)

_{2}stoichiometry [2,41].

#### 3.1. Investigations that Might Use the Procedures

_{1,ave}. This is fortunate, because the intracellular domains of Cys-loop receptors have not been characterized structurally, despite the excellent progress on structures for the extracellular binding regions and transmembrane domains [43–45]. We emphasize that distance measurements are not the focus of this study; rather, we describe useful experimentally determined FRET-related measurements that reveal changes in stoichiometry.

_{1,ave}values would yield useful data? Because the fluorescent proteins are cylinders with diameter of 25 Å and length 40 Å [46], they could physically approach as close as R

_{1,ave}~25 Å, which is the lower limit of our simulations (Figure 2A) but predicts Ē

_{3,2}/ Ē

_{2,3}and NFRET

_{3,2}/NFRET

_{2,3}values markedly lower than we measure. At the other extreme, R

_{1,ave}might be ~40 Å greater than the intersubunit distance of the residues at the point of insertion; but R

_{1,ave}> ~70 Å would probably give FRET values below the measurable range.

#### 3.2. Other Cys-Loop Receptors

## Supplementary Materials

ijms-13-10022-s001.pdf## Acknowledgments

## Abbreviations

EGFP | enhanced green fluorescent protein |

ER | endoplasmic reticulum |

FRET | Förster resonance energy transfer |

nAChR | neuronal nicotinic acetylcholine receptors |

mCherry | monomeric cherry fluorescent protein |

NFRET | normalized Förster resonance energy transfer |

## References

- Zwart, R.; Vijverberg, H.P. Four pharmacologically distinct subtypes of α4β2 nicotinic acetylcholine receptor expressed in Xenopus laevis oocytes. Mol. Pharmacol
**1998**, 54, 1124–1131. [Google Scholar] - Moroni, M.; Zwart, R.; Sher, E.; Cassels, B.K.; Bermudez, I. α4β2 nicotinic receptors with high and low acetylcholine sensitivity: Pharmacology, stoichiometry, and sensitivity to long-term exposure to nicotine. Mol. Pharmacol
**2006**, 70, 755–768. [Google Scholar] - Xiu, X.; Puskar, N.L.; Shanata, J.A.; Lester, H.A.; Dougherty, D.A. Nicotine binding to brain receptors requires a strong cation-π interaction. Nature
**2009**, 458, 534–537. [Google Scholar] - Tapia, L.; Kuryatov, A.; Lindstrom, J. Ca
^{2+}permeability of the (α4)_{3}(β2)_{2}stoichiometry greatly exceeds that of (α4)_{2}(β2)_{3}human acetylcholine receptors. Mol. Pharmacol**2007**, 71, 769–776. [Google Scholar] - Nelson, M.E.; Kuryatov, A.; Choi, C.H.; Zhou, Y.; Lindstrom, J. Alternate stoichiometries of α4β2 nicotinic acetylcholine receptors. Mol. Pharmacol
**2003**, 63, 332–341. [Google Scholar] - Srinivasan, R.; Pantoja, R.; Moss, F.J.; Mackey, E.D.W.; Son, C.; Miwa, J.; Lester, H.A. Nicotine upregulates α4β2 nicotinic receptors and ER exit sites via stoichiometry-dependent chaperoning. J. Gen. Physiol
**2011**, 137, 59–79. [Google Scholar] - Commons, K.G. α4 containing nicotinic receptors are positioned to mediate postsynaptic effects on 5-HT neurons in the rat dorsal raphe nucleus. Neuroscience
**2008**, 153, 851–859. [Google Scholar] - Shapiro, M.S.; Hille, B. Substance P and somatostatin inhibit calcium channels in rat sympathetic neurons via different G protein pathways. Neuron
**1993**, 10, 11–20. [Google Scholar] - Sallette, J.; Pons, S.; Devillers-Thiery, A.; Soudant, M.; de Carvalho, L.P.; Changeux, J.P.; Corringer, P.J. Nicotine upregulates its own receptors through enhanced intracellular maturation. Neuron
**2005**, 46, 595–607. [Google Scholar] - Kuryatov, A.; Luo, J.; Cooper, J.; Lindstrom, J. Nicotine acts as a pharmacological chaperone to up-regulate human α4β2 acetylcholine receptors. Mol. Pharmacol
**2005**, 68, 1839–1851. [Google Scholar] - Lester, H.A.; Xiao, C.; Srinivasan, R.; Son, C.; Miwa, J.; Pantoja, R.; Dougherty, D.A.; Banghart, M.R.; Goate, A.M.; Wang, J.C. Nicotine is a selective pharmacological chaperone of acetylcholine receptor number and stoichiometry. Implications for drug discovery. AAPS J
**2009**, 11, 167–177. [Google Scholar] - Miwa, J.M.; Freedman, R.; Lester, H.A. Neural systems governed by nicotinic acetylcholine receptors: Emerging hypotheses. Neuron
**2011**, 70, 20–33. [Google Scholar] - Gopalakrishnan, M.; Molinari, E.J.; Sullivan, J.P. Regulation of human α4β2 neuronal nicotinic acetylcholine receptors by cholinergic channel ligands and second messenger pathways. Mol. Pharmacol
**1997**, 52, 524–534. [Google Scholar] - Whiteaker, P.; Sharples, C.G.; Wonnacott, S. Agonist-induced up-regulation of α4β2 nicotinic acetylcholine receptors in M10 cells: Pharmacological and spatial definition. Mol. Pharmacol
**1998**, 53, 950–962. [Google Scholar] - Kishi, M.; Steinbach, J.H. Role of the agonist binding site in up-regulation of neuronal nicotinic α4β2 receptors. Mol. Pharmacol
**2006**, 70, 2037–2044. [Google Scholar] - Nashmi, R.; Dickinson, M.E.; McKinney, S.; Jareb, M.; Labarca, C.; Fraser, S.E.; Lester, H.A. Assembly of α4β2 nicotinic acetylcholine receptors assessed with functional fluorescently labeled subunits: Effects of localization, trafficking, and nicotine-induced upregulation in clonal mammalian cells and in cultured midbrain neurons. J. Neurosci
**2003**, 23, 11554–11567. [Google Scholar] - Drenan, R.M.; Nashmi, R.; Imoukhuede, P.I.; Just, H.; McKinney, S.; Lester, H.A. Subcellular trafficking, pentameric assembly and subunit stoichiometry of neuronal nicotinic ACh receptors containing Fluorescently-Labeled α6 and β3 subunits. Mol. Pharmacol
**2008**, 73, 27–41. [Google Scholar] - Son, C.D.; Moss, F.J.; Cohen, B.N.; Lester, H.A. Nicotine normalizes intracellular subunit stoichiometry of nicotinic receptors carrying mutations linked to autosomal dominant nocturnal frontal lobe epilepsy. Mol. Pharmacol
**2009**, 75, 1137–1148. [Google Scholar] - Moss, F.J.; Imoukhuede, P.I.; Scott, K.; Hu, J.; Jankowsky, J.L.; Quick, M.W.; Lester, H.A. GABA transporter function, oligomerization state, and anchoring: Correlates with subcellularly resolved FRET. J. Gen. Physiol
**2009**, 134, 489–521. [Google Scholar] - Corry, B.; Jayatilaka, D.; Rigby, P. A flexible approach to the calculation of resonance energy transfer efficiency between multiple donors and acceptors in complex geometries. Biophys. J
**2005**, 89, 3822–3836. [Google Scholar] - Corry, B.; Jayatilaka, D.; Martinac, B.; Rigby, P. Determination of the orientational distribution and orientation factor for transfer between membrane-bound fluorophores using a confocal microscope. Biophys. J
**2006**, 91, 1032–1045. [Google Scholar] - Raicu, V. Efficiency of resonance energy transfer in homo-oligomeric complexes of proteins. J. Biol. Phys
**2007**, 33, 109–127. [Google Scholar] - Deplazes, E.; Jayatilaka, D.; Corry, B. ExiFRET: Flexible tool for understanding FRET in complex geometries. J. Biomed. Opt
**2012**, 17, 011005. [Google Scholar] - Wlodarczyk, J.; Woehler, A.; Kobe, F.; Ponimaskin, E.; Zeug, A.; Neher, E. Analysis of FRET signals in the presence of free donors and acceptors. Biophys. J
**2008**, 94, 986–1000. [Google Scholar] - Akrap, N.; Seidel, T.; Barisas, B.G. Forster distances for fluorescence resonant energy transfer between mCherry and other visible fluorescent proteins. Anal. Biochem
**2010**, 402, 105–106. [Google Scholar] - Wolber, P.K.; Hudson, B.S. An analytic solution to the Forster energy transfer problem in two dimensions. Biophys. J
**1979**, 28, 197–210. [Google Scholar] - Srinivasan, R.; Richards, C.I.; Xiao, C.; Rhee, D.; Pantoja, R.; Dougherty, D.A.; Miwa, J.M.; Lester, H.A. Pharmacological chaperoning of nicotinic acetylcholine receptors reduces the ER stress response. Mol. Pharmacol
**2012**, 81, 759–769. [Google Scholar] - Hoppe, A.; Christensen, K.; Swanson, J.A. Fluorescence resonance energy transfer-based stoichiometry in living cells. Biophys. J
**2002**, 83, 3652–3664. [Google Scholar] - Nashmi, R.; Xiao, C.; Deshpande, P.; McKinney, S.; Grady, S.R.; Whiteaker, P.; Huang, Q.; McClure-Begley, T.; Lindstrom, J.M.; Labarca, C.; et al. Chronic nicotine cell specifically upregulates functional α4* nicotinic receptors: Basis for both tolerance in midbrain and enhanced long-term potentiation in perforant path. J. Neurosci
**2007**, 27, 8202–8218. [Google Scholar] - Raicu, V.; Stoneman, M.; Fung, R.; Melnichuk, M.; Jansma, D.; Pisterzi, L.; Rath, S.; Fox, M.; Wells, J.; Saldin, D. Determination of supramolecular structure and spatial distribution of protein complexes in living cells. Nat. Photonics
**2009**, 3, 107–113. [Google Scholar] - Singh, D.R.; Raicu, V. Comparison between whole distribution- and average-based approaches to the determination of fluorescence resonance energy transfer efficiency in ensembles of proteins in living cells. Biophys. J
**2010**, 98, 2127–2135. [Google Scholar] - Tadross, M.R.; Park, S.A.; Veeramani, B.; Yue, D.T. Robust approaches to quantitative ratiometric FRET imaging of CFP/YFP fluorophores under confocal microscopy. J. Microsc
**2009**, 233, 192–204. [Google Scholar] - Xia, Z.; Liu, Y. Reliable and global measurement of fluorescence resonance energy transfer using fluorescence microscopes. Biophys. J
**2001**, 81, 2395–2402. [Google Scholar] - Kuryatov, A.; Onksen, J.; Lindstrom, J. Roles of accessory subunits in α4β2α5 nicotinic receptors. Mol. Pharmacol
**2008**, 74, 132–143. [Google Scholar] - Zhou, Y.; Nelson, M.E.; Kuryatov, A.; Choi, C.; Cooper, J.; Lindstrom, J. Human α4β2 acetylcholine receptors formed from linked subunits. J. Neurosci
**2003**, 23, 9004–9015. [Google Scholar] - Khakh, B.S.; Fisher, J.A.; Nashmi, R.; Bowser, D.N.; Lester, H.A. An angstrom scale interaction between plasma membrane ATP-gated P2×2 and α4β2 nicotinic channels measured with FRET and TIRF microscopy. J. Neurosci
**2005**, 25, 6911–6920. [Google Scholar] - Richards, C.I.; Srinivasan, R.; Xiao, C.; Mackey, E.D.W.; Miwa, J.M.; Lester, H.A. Trafficking of α4* nicotinic receptors revealed by superecliptic phluorin: Effects of a β4 ALS-associated mutation and chronic exposure to nicotine. J. Biol. Chem
**2011**, 286, 31241–31249. [Google Scholar] - Chiu, C.S.; Kartalov, E.; Unger, M.; Quake, S.; Lester, H.A. Single-molecule measurements calibrate green fluorescent protein surface densities on transparent beads for use with ‘knock-in’ animals and other expression systems. J. Neurosci. Methods
**2001**, 105, 55–63. [Google Scholar] - Chiu, C.S.; Jensen, K.; Sokolova, I.; Wang, D.; Li, M.; Deshpande, P.; Davidson, N.; Mody, I.; Quick, M.W.; Quake, S.R.; et al. Number, density, and surface/cytoplasmic distribution of GABA transporters at presynaptic structures of knock-in mice carrying GABA transporter subtype 1-green fluorescent protein fusions. J. Neurosci
**2002**, 22, 10251–10266. [Google Scholar] - Pantoja, R.; Rodriguez, E.A.; Dibas, M.I.; Dougherty, D.A.; Lester, H.A. Single-molecule imaging of a fluorescent unnatural amino Acid incorporated into nicotinic receptors. Biophys. J
**2009**, 96, 226–237. [Google Scholar] - Richards, C.I.; Luong, K.; Srinivasan, R.; Turner, S.W.; Dougherty, D.A.; Korlach, J.; Lester, H.A. Live-cell imaging of single receptor composition using zero-mode waveguides nanostructures. Nano Lett
**2012**, 12, 3690–3694. [Google Scholar] - Fabian, A.I.; Rente, T.; Szollosi, J.; Matyus, L.; Jenei, A. Strength in numbers: Effects of acceptor abundance on FRET efficiency. Chemphyschem
**2010**, 11, 3713–3721. [Google Scholar] - Brejc, K.; van Dijk, W.J.; Klaassen, R.V.; Schuurmans, M.; van der Oost, J.; Smit, A.B.; Sixma, T.K. Crystal structure of an ACh-binding protein reveals the ligand-binding domain of nicotinic receptors. Nature
**2001**, 411, 269–276. [Google Scholar] - Unwin, N. Refined structure of the nicotinic acetylcholine receptor at 4A resolution. J. Mol. Biol
**2005**, 346, 967–989. [Google Scholar] - Hibbs, R.E.; Gouaux, E. Principles of activation and permeation in an anion-selective Cys-loop receptor. Nature
**2011**, 474, 54–60. [Google Scholar] - Ormo, M.; Cubitt, A.B.; Kallio, K.; Gross, L.A.; Tsien, R.Y.; Remington, S.J. Crystal structure of the Aequorea victoria green fluorescent protein. Science
**1996**, 273, 1392–1395. [Google Scholar]

**Figure 1.**Diagrams depicting FRET analysis of nAChR stoichiometry. (

**A**) Two examples of stoichiometry, thought to correspond to the major α4β2 nAChRs in brain [12]. Both stoichiometries contain two β2 < α4 interfaces. The < character implies a correctly polarized high-affinity ligand binding interface, contrasting with the arrows in (

**B**) and (

**C**) which denote energy transfer. The nAChR is viewed from the extracellular surface. In the top panel the stoichiometry is (α4)

_{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; (

**B**) Nomenclature for energy transfer to acceptors that are adjacent to the donor. The first subscript denotes the identity of the β2-EGFP donor subunit. The second subscript is ±1 for adjacent and non-adjacent energy transfer, respectively; the positive sign denotes clockwise transfer. β2-EGFP donor #1 is shown with two immediately flanking α4-mCherry acceptors. Because these two pathways exist, the “n-factors” n

_{1, −1}= n

_{1, +1}= 1. The arrows show the fluorophore separations R

_{±1}, R

_{±2}and the corresponding energy transfer probabilities, p

_{±1}, p

_{±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; (

**C**) Nomenclature for energy transfer to acceptors that are non-adjacent to the donor. β2-EGFP donor #1 is shown with two α4-mCherry acceptors that are non-adjacent to the donor (but incidentally adjacent to each other). Because these two pathways exist, the “n-factors” n

_{1, −2}= n

_{1, +2}= 1. Other details as in (

**B**); (

**D**) Table showing the “n-factors” for the nAChR stoichiometries under consideration. See text.

**Figure 2.**Simulations. (

**A**) The y-axis is the simulated Ē

_{3,2}/ Ē

_{2,3}, the ratio of classical FRET efficiency for the two stoichiometries. The vertical arrows give parameters associated with the regular pentagonal receptor. The theoretical curves are computed for various values of the average distance between fluorophores on adjacent subunits R

_{1,ave}. X-axes are (

**left**) the geometry factor G, and (

**right**) the asymmetry factor Δ. The assumed f

_{P}= 0.5; (

**B**) Same parameters as in (

**A**); the plotted values are NFRET

_{3,2}/NFRET

_{2,3}, the ratio of NFRET efficiency for the two stoichiometries; (

**C**) (

**D**) Values of NFRET

_{3,2}/NFRET

_{2,3}vs. asymmetry factor Δ for assumed f

_{P}= 0.2 (

**C**) or 0.8 (

**D**).

**Figure 3.**Data from NFRET measurements with biased transfection ratios. (

**A**) NFRET images for representative cells transfected with 0.5 mole fraction plasmid ratios of β2-EGFP and α4-mCherry. The lookup table runs from 0 to 0.2 fractional NFRET. Scale bars, 5 μm; (

**B**) NFRET data for transfection with 0.67, 0.5, and 0.33 mole fraction plasmid ratios of β2-EGFP. For each graph, the heavy line is the measured histogram; this is generally obscured by the blue curve which sums the Gaussians fitted to the high and low NFRET components (dashed lines). The computed fractional area of high NFRET pixels (W

_{high}) is shown in each case; (

**C**) Average NFRET and W

_{high}vs. mole fraction of β2-EGFP cDNA transfected, from the data in (

**B**). The left y-axis gives mean NFRET. The standard errors of the mean are much smaller than the size of symbols, because each sample had > 10

^{6}pixels. The right y-axis is W

_{high}; (

**D**) Plots of the CV of the NFRET pixel distribution (y-axis) vs. the expression level (x-axis). Each point corresponds to a cell. Expression level is quantified as NFRET normalization, the mean of $\left(\sqrt{{I}_{eGFP}}\sqrt{{I}_{mcherry}}\right)$ for each cell. The fitted curves have the form, $y=b(a+\sqrt{x})$.

**Figure 4.**Data from NFRET measurements with pharmacological chaperones. Further analysis of a published experiment [27]. (

**A**) NFRET images for representative cells transfected with 0.5 mole fraction plasmid ratios of β2-EGFP and α4-mCherry. Incubation for 48 h in 0.1 μM nicotine (left), no added drug (center), and 0.1 μM cytisine (right). The lookup table runs from 0 to 0.2 fractional NFRET. Scale bars, 10 μm; (

**B**) Average NFRET and W

_{high}for each incubation, from data like those of Figure 1B. The left y-axis gives mean NFRET. The standard errors of the mean are much smaller than the size of symbols, because each sample had >10

^{6}pixels. The right y-axis is W

_{high}.

© 2012 by the authors; licensee Molecular Diversity Preservation International, Basel, Switzerland. This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

## Share and Cite

**MDPI and ACS Style**

Srinivasan, R.; Richards, C.I.; Dilworth, C.; Moss, F.J.; Dougherty, D.A.; Lester, H.A.
Förster Resonance Energy Transfer (FRET) Correlates of Altered Subunit Stoichiometry in Cys-Loop Receptors, Exemplified by Nicotinic α4β2. *Int. J. Mol. Sci.* **2012**, *13*, 10022-10040.
https://doi.org/10.3390/ijms130810022

**AMA Style**

Srinivasan R, Richards CI, Dilworth C, Moss FJ, Dougherty DA, Lester HA.
Förster Resonance Energy Transfer (FRET) Correlates of Altered Subunit Stoichiometry in Cys-Loop Receptors, Exemplified by Nicotinic α4β2. *International Journal of Molecular Sciences*. 2012; 13(8):10022-10040.
https://doi.org/10.3390/ijms130810022

**Chicago/Turabian Style**

Srinivasan, Rahul, Christopher I. Richards, Crystal Dilworth, Fraser J. Moss, Dennis A. Dougherty, and Henry A. Lester.
2012. "Förster Resonance Energy Transfer (FRET) Correlates of Altered Subunit Stoichiometry in Cys-Loop Receptors, Exemplified by Nicotinic α4β2" *International Journal of Molecular Sciences* 13, no. 8: 10022-10040.
https://doi.org/10.3390/ijms130810022