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I Am the Alpha and the …Gamma, and the G. Calibration of Intensity‐Based FRET Measurements
Cytometry Part A ( IF 3.7 ) Pub Date : 2020-08-13 , DOI: 10.1002/cyto.a.24206
Ágnes Szabó 1, 2 , Peter Nagy 1
Affiliation  

As a result of heightened interest in elucidating protein–protein interactions, techniques for mapping the protein interactome are frequently used by biologists. In an era when a multitude of molecular biological and superresolved microscopy techniques are available for this purpose, Förster resonance energy transfer (FRET) preserved its status as a fashionable, accurate and relatively easy‐to‐use approach (1). FRET is a nonradiative energy transfer process from an excited fluorophore (donor) to an acceptor by dipole–dipole coupling. Its sensitivity to molecular interactions and conformations stems from the fact that its efficiency steeply decreases with the donor–acceptor separation in the 2–10 nm range. Although it is already valuable as a standalone approach, its usefulness can be further increased by combining with other modalities, like confocal microscopy (2). Its flexibility and versatility are enhanced by the generation of sensors, that is, donor–acceptor fluorescence protein constructs connected by a linker, whose conformation responds to certain properties of the environment. The FRET efficiency of such sensors can be used as a readout parameter for a multitude of biological processes (3, 4). Although a large number of approaches are available for the determination of FRET, intensity‐based (ratiometric) measurements remain the cornerstone in its biological applications since these experiments are the easiest to implement and they usually provide the answer to the questions asked about protein clustering by ordinary biologists (1). The method typically involves the measurement of fluorescence intensities in three channels corresponding to donor fluorescence, directly excited and FRET‐sensitized acceptor emissions. In order to solve the equation set, two different kinds of correction parameters are required:
  1. None of these channels is pure in the sense that they are contaminated by contribution from the other molecular species. In order to correct for these spectral overspills, donor‐only and acceptor‐only samples are measured to obtain the fractional contribution of these fluorophores to the other fluorescence channels (5). Different approaches are available for calculating these overspill parameters. They can be obtained as the mean of individual overspill factors (mean of ratios) calculated for single pixels (in microscopy) or single cells (in flow cytometry), as the ratio of mean intensities or as the slope in different kinds of regression approaches (6, 7). The approach based on calculating the mean of ratios is a biased estimator, while the ratio of the means approach is an asymptotically unbiased estimator of the overspill parameter (6). The overspill factor has been reported to show apparent intensity dependence as a result of poor photon statistics (7). If, for any reason, the overspill parameters exhibit real intensity dependence, a method has been developed to calculate these bleedthrough parameters for different intensity ranges (8).
  2. As a result of FRET, an excited donor disappears and an excited acceptor is generated. The consequent increase in acceptor emission and the decrease in donor fluorescence (quenching) are related to each other. This relationship is expressed by the parameter, variably termed α, G or y, which is required for calibration of intensity‐based FRET measurements (9-11). Basically, this parameter characterizes how efficiently an excited acceptor can be detected in the FRET channel vs. an excited donor in the donor channel. Since it is only determined by the quantum yields and detection efficiencies of the donor and the acceptor, it is constant for a particular fluorophore pair and for a given experimental setup (Fig. 1).
image
Figure 1
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Interpretation of the parameter variably termed G, α or γ. A. In the absence of an acceptor, a certain fraction of the excited donors (designated by D* in the star symbol) emit a photon. The fraction of donors emitting fluorescence is determined by the fluorescence quantum efficiency (or yield) of the donor (QD), assumed to be 0.5 in the figure. The rest of the excited donors return to the ground state by thermal relaxation (concentric, dotted circles). Besides the fluorescence quantum yield, the donor fluorescence intensity is proportional to the number of excited donors (ND*) and the detection efficiency of donor photons in the donor channel (ηD,1). B. All donors are assumed to be complexed with an acceptor. If the FRET efficiency (E) is 50%, half of the excited donors transfer their energy to an acceptor. Consequently, the donor fluorescence quantum yield is reduced by a factor of (1‐E). In the example shown in the figure the donor quantum yield in the presence of the acceptor is urn:x-wiley:15524922:media:cytoa24206:cytoa24206-math-0001. As a result, the donor fluorescence intensity is reduced (quenched) by urn:x-wiley:15524922:media:cytoa24206:cytoa24206-math-0002. Due to FRET, an extra number of acceptors are excited (ground state and excited acceptors are designated by A and A*, respectively). The number of FRET‐excited acceptors is proportional to urn:x-wiley:15524922:media:cytoa24206:cytoa24206-math-0003. A fraction of these acceptors, equal to the fluorescence quantum yield of acceptors (QA, assumed to be 0.5 in the figure), will fluoresce, and the corresponding FRET‐sensitized acceptor emission (ΔIA) is also influenced by the detection efficiency of acceptor photons in the FRET channel (ηA,2): urn:x-wiley:15524922:media:cytoa24206:cytoa24206-math-0004. The factor, variably called G, α or γ, is the ratio of how much intensity is gained on the acceptor side to how much intensity is lost on the donor side. As shown by the bottom equation in the figure, this factor is determined by the ratio of the fluorescence quantum yields of the acceptor and the donor and the ratio of their detection efficiencies.
Although the definition of the calibration factor, introduced in point (ii) above, is simple, its experimental determination is more challenging. While quantum efficiencies can be determined relatively easily, detection efficiencies are much more difficult to measure in practice. Therefore, the experimental determination of this calibration parameter is based on a different principle. Although several methods have been devised for this purpose, all of them are based on the concept, introduced by Trón et al.(9), of comparing the intensities of an equal number of excited acceptors and excited donors. The original approach was developed for measuring FRET between fluorescent antibodies. In such a system, a sample is labeled with only donor‐conjugated antibodies, and another sample is labeled with only acceptor‐conjugated antibodies against the same epitope. These two samples contain an equal number of donor‐tagged and acceptor‐tagged antibodies if a large enough number of cells are averaged. So that the ratio of the intensities of the acceptor‐only sample, measured in the FRET channel (MA), and the donor‐only sample, measured in the donor channel (MD), correspond to an equal number of donors and acceptors, the intensities are to be corrected with the degrees of labeling (DOL) of the donor‐tagged (LD) and acceptor‐tagged antibodies (LA). If the requirement of an equal number of excited donors and acceptors is to be met, the intensity ratio is to be further corrected with the molar absorption coefficients of the donor (εD) and the acceptor (εA) at the donor excitation wavelength:
urn:x-wiley:15524922:media:cytoa24206:cytoa24206-math-0005((1))

Since the DOLs (LD, LA) are determined for the antibody stock solutions, the correctness of the formula hinges upon the assumption that the DOL of the stock is identical to the mean DOL of the cell‐bound antibody fraction. It has recently been explicitly shown that the average DOL of the cell‐bound fraction is often lower than the mean DOL of the stock due to diminished affinity of fluorescently labeled antibody species. Therefore, correction of the intensities with the DOL of the stock leads to a misestimation (12). It has also been pointed out that a slightly modified formula is required for the calculation of parameter α if fluorophore saturation takes place, that is, when most fluorophores are in the excited state (13). This situation is common when using confocal microscopies equipped with high numerical aperture objectives.

Since it is fairly easy to generate a 1:1 donor–acceptor ratio using fluorescent protein‐based FRET constructs, a plethora of approaches have been devised for such systems. In one of these methods, the loss in sensitized acceptor emission, due to partial acceptor photobleaching, is compared to consequent donor dequenching in order to obtain parameter G (14). Several approaches based on a series of donor–acceptor fluorescent protein constructs exhibiting different FRET values have been developed. Although the formalisms are somewhat different, the donor intensity and the sensitized acceptor intensities are compared in all of them. Initially, a regression approach utilizing an arbitrary number (at least two) of donor–acceptor constructs have been published (15) followed by another paper using two such constructs (16). Practically, the same principle is used in single‐molecule FRET measurements, in which the series of different donor–acceptor fluorescent protein constructs is replaced by different conformations of a single construct. The calibration factor, designated by G or α in other FRET approaches, is termed γ in single‐molecule FRET methods, and it is determined by regression (10). In two consecutive publications, an iterative and a closed‐form approach has been developed for determining G (or α, or γ) for a single donor–acceptor fluorescent protein construct (17, 18).

Recently, different measures of central tendency were evaluated for the determination of parameter G using a previously published method based on two donor–acceptor fluorescent protein constructs (16). Although the mean, the median, and the mode provided statistically insignificantly different estimates for G, the precision (reproducibility) of the mode was the best (19). Menaesse et al. (in this issue, page XXX) went one step further in simplifying the determination of G by using a single donor–acceptor fluorescent protein construct with known FRET efficiency. Using the calibrated FRET efficiency of the construct G was determined by regressing the sensitized emission on the quenched donor intensity. Besides describing the calibration method, the authors also compare this new approach to a previous one based on two FRET constructs with unknown energy transfer efficiencies (16, 19). The authors concluded that a single construct with known FRET efficiency provides a more precise estimation with fewer images compared to the previously used method. It was pointed out that the confidence interval of the estimation is broadened if a FRET construct with low FRET efficiency is used. An admitted drawback of the proposed approach is the requirement for a FRET construct with known energy transfer efficiency. Inaccuracy or uncertainty of the FRET efficiency of the calibration construct (e.g. because of the presence of unpaired donors due to incomplete maturation of the acceptor fluorescent protein) could obviously undermine the reliability of the proposed method. Since FRET calibration constructs with known energy transfer efficiency and rapidly maturing fluorescent proteins suitable for FRET are increasingly available, this approach is a viable and simple alternative for the determination of parameter G. Since the real value of FRET measurements compared to other, less quantitative approaches is the predictability and modelability of the readout parameter, the energy transfer efficiency, any improvement increasing the reproducibility and simplicity of the approach will definitely contribute to its successful implementation in biological research.



中文翻译:

I Am the Alpha and the ...Gamma, and the G. 基于强度的 FRET 测量的校准

由于对阐明蛋白质-蛋白质相互作用的兴趣日益浓厚,生物学家经常使用绘制蛋白质相互作用组的技术。在众多分子生物学和超分辨显微镜技术可用于此目的的时代,Förster 共振能量转移 (FRET) 保持了其作为一种时尚、准确且相对易于使用的方法的地位(1)。FRET 是通过偶极-偶极耦合从激发的荧光团(供体)到受体的非辐射能量转移过程。它对分子相互作用和构象的敏感性源于这样一个事实,即随着供体-受体分离在 2-10 nm 范围内,其效率急剧下降。尽管它作为一种独立的方法已经很有价值,但通过与其他方式(如共聚焦显微镜)结合可以进一步提高其实用性(2)。传感器的产生增强了其灵活性和多功能性,即供体 - 受体荧光蛋白结构通过接头连接,其构象对环境的某些特性做出反应。此类传感器的 FRET 效率可用作多种生物过程的读出参数 ( 3, 4)。尽管有大量方法可用于确定 FRET,但基于强度(比率)的测量仍然是其生物学应用的基石,因为这些实验最容易实施,并且它们通常为有关蛋白质聚类的问题提供答案普通生物学家(1)。该方法通常涉及测量对应于供体荧光、直接激发和 FRET 敏化受体发射的三个通道中的荧光强度。为了求解方程组,需要两种不同的校正参数:
  1. 这些通道中没有一个是纯的,因为它们被其他分子种类的贡献所污染。为了校正这些光谱溢出,测量仅供体和仅受体样品以获得这些荧光团对其他荧光通道的部分贡献 ( 5 )。不同的方法可用于计算这些溢出参数。它们可以作为单个像素(显微镜中)或单个细胞(流式细胞术)计算的单个溢出因子的平均值(比率平均值)、平均强度比或不同类型回归方法中的斜率获得(6、7)。基于计算比率均值的方法是有偏估计量,而均值比率方法是溢出参数 ( 6 )的渐近无偏估计量。据报道,由于光子统计数据不佳,溢出因子显示出明显的强度依赖性 ( 7 )。如果由于任何原因,溢出参数表现出真实的强度依赖性,则已开发出一种方法来计算不同强度范围的这些渗漏参数 ( 8 )。
  2. 作为 FRET 的结果,激发的供体消失并产生激发的受体。随后受体发射的增加和供体荧光(猝灭)的减少相互关联。这种关系由参数表示,可变地称为 α、G 或 y,这是校准基于强度的 FRET 测量所必需的 ( 9-11 )。基本上,该参数表征了在 FRET 通道中检测受激受体与供体通道中受激供体的效率。由于它仅由供体和受体的量子产率和检测效率决定,因此对于特定的荧光团对和给定的实验设置,它是恒定的(图 1)。
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图1
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参数的解释变量称为 G、α 或 γ。一个。在没有受体的情况下,一定比例的受激供体(在星号中用 D* 表示)发射光子。发射荧光的供体比例由供体的荧光量子效率(或产率)决定(Q D),图中假定为 0.5。其余的受激供体通过热弛豫(同心圆点圆)返回到基态。除了荧光量子产率外,供体荧光强度与激发供体的数量 ( N D* ) 和供体通道中供体光子的检测效率 (η D,1 )成正比。. 假定所有供体都与受体复合。如果 FRET 效率 ( E ) 为 50%,则一半的受激供体将其能量转移到受体。因此,供体荧光量子产率降低了 (1- E )倍。在图中所示的例子中,受体存在时的供体量子产率为urn:x-wiley:15524922:media:cytoa24206:cytoa24206-math-0001。结果,供体荧光强度降低(淬灭)了urn:x-wiley:15524922:media:cytoa24206:cytoa24206-math-0002。由于 FRET,额外数量的受体被激发(基态和激发受体分别由 A 和 A* 表示)。FRET 激发受体的数量与 成正比urn:x-wiley:15524922:media:cytoa24206:cytoa24206-math-0003。这些受体的一小部分,等于受体的荧光量子产率 ( Q A,图中假定为 0.5),将发出荧光,相应的 FRET 敏化受体发射(Δ I A)也受 FRET 通道中受体光子的检测效率(η A,2)的影响:urn:x-wiley:15524922:media:cytoa24206:cytoa24206-math-0004。该因子,也称为 G、α 或 γ,是受体侧获得的强度与供体侧失去的强度之比。如图中底部方程所示,该因子由受体和供体的荧光量子产率之比及其检测效率之比决定。
虽然上面 (ii) 点中介绍的校准因子的定义很简单,但它的实验确定更具挑战性。虽然可以相对容易地确定量子效率,但在实践中测量检测效率要困难得多。因此,该校准参数的实验确定基于不同的原理。尽管为此目的设计了几种方法,但所有方法都基于 Trón 等人(9),比较相同数量的受激受体和受激供体的强度。最初的方法是为测量荧光抗体之间的 FRET 而开发的。在这样的系统中,一个样品仅用供体偶联的抗体标记,而另一个样品仅用针对相同表位的受体偶联抗体进行标记。如果对足够多的细胞进行平均,这两个样本包含相同数量的供体标记和受体标记抗体。因此,在 FRET 通道中测量的仅受体样品的强度 ( M A ) 和在供体通道中测量的仅供体样品的强度之比( M D),对应于相同数量的供体和受体,强度将通过供体标记 ( L D ) 和受体标记抗体 ( L A )的标记度 (DOL) 进行校正。如果要满足激发供体和受体数量相等的要求,则强度比应进一步用供体激发波长处的供体(ε D)和受体(ε A)的摩尔吸收系数进行校正:
urn:x-wiley:15524922:media:cytoa24206:cytoa24206-math-0005((1))

由于 DOL ( L D , L A ) 是针对抗体原液确定的,公式的正确性取决于库存的 DOL 与细胞结合抗体部分的平均 DOL 相同的假设。最近已经明确表明,由于荧光标记抗体种类的亲和力降低,细胞结合部分的平均 DOL 通常低于库存的平均 DOL。因此,用股票的 DOL 校正强度会导致错误估计 ( 12 )。也有人指出,如果发生荧光团饱和,即当大多数荧光团处于激发态时,计算参数 α 需要稍微修改公式(13 )。这种情况在使用配备高数值孔径物镜的共聚焦显微镜时很常见。

由于使用基于荧光蛋白的 FRET 构建体很容易产生 1:1 的供体 - 受体比例,因此已经为此类系统设计了大量方法。在这些方法之一中,将由于部分受体光漂白导致的敏化受体发射损失与随后的供体去猝灭进行比较,以获得参数G ( 14 )。已经开发了几种基于一系列表现出不同 FRET 值的供体 - 受体荧光蛋白构建体的方法。尽管形式主义有些不同,但都比较了供体强度和敏化受体强度。最初,已经发表了一种利用任意数量(至少两个)供体-受体结构的回归方法(15) 之后是另一篇使用两个这样的结构的论文 ( 16 )。实际上,在单分子 FRET 测量中使用了相同的原理,其中一系列不同的供体 - 受体荧光蛋白构建体被单个构建体的不同构象所取代。校准因子在其他 FRET 方法中由G或 α指定,在单分子 FRET 方法中称为 γ,它由回归确定 ( 10 )。在连续的两份出版物中,已经开发了一种迭代和封闭形式的方法来确定单个供体-受体荧光蛋白构建体的 G(或 α 或 γ) ( 17, 18 )。

最近,使用先前公布的基于两种供体-受体荧光蛋白构建体的方法,对确定参数G 的不同集中趋势测量进行了评估( 16 )。尽管平均值、中位数和众数为G提供了统计上不显着的估计值,但众数的精确度(再现性)是最好的 ( 19 )。梅内斯等人。(本期第 XXX 页)通过使用已知 FRET 效率的单一供体-受体荧光蛋白构建体,进一步简化了G的测定。使用构造G的校准 FRET 效率通过将敏化发射对淬灭的供体强度进行回归来确定。除了描述校准方法外,作者还将这种新方法与之前基于两种能量转移效率未知的 FRET 结构的方法进行了比较 ( 16, 19)。作者得出的结论是,与以前使用的方法相比,具有已知 FRET 效率的单个构造提供了更精确的估计,图像更少。有人指出,如果使用具有低 FRET 效率的 FRET 构造,则估计的置信区间会扩大。所提出的方法的一个公认的缺点是需要具有已知能量转移效率的 FRET 构造。校准构建体的 FRET 效率的不准确或不确定性(例如,由于受体荧光蛋白的不完全成熟导致未配对供体的存在)显然会破坏所提出方法的可靠性。由于具有已知能量转移效率和适用于 FRET 的快速成熟荧光蛋白的 FRET 校准结构越来越多,。由于与其他定量较少的方法相比,FRET 测量的真正价值在于读出参数的可预测性和可建模性、能量转移效率,任何提高该方法可重复性和简单性的改进肯定会有助于其在生物研究中的成功实施。

更新日期:2020-08-13
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