# Fluorescence Quenching And Ligand Binding Biology Essay

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In recent years fluorescence quenching has become a popular tool to investigate various aspects of ligand binding. Unfortunately, various pitfalls are often overlooked in a large number of papers, published in many different journals. In this criticism we discuss a number of possible mistakes and show how they may affect the data and their analysis. Moreover, we point to problems in the understanding of the fundamentals of fluorescence quenching, and show direct contradictions within many of these papers. This paper hopefully contributes to a re-appraisal of the published literature and to a more appropriate use of fluorescence quenching to study ligand binding.

Keywords: Fluorescence quenching; ligand binding; Fluorescence spectroscopy.

## 1. Introduction

Recent years have seen an enormous popularity of using fluorescence quenching methodology to study ligand binding to a variety of (usually biological) molecules. In many cases these papers follow a common blueprint:

A ligand is proposed to bind to a fluorescent (macro)molecule, the latter usually a protein;

Addition of that ligand is shown to quench the emission of the fluorophore;

Using the Stern-Volmer equation it is shown that the bimolecular quenching rate constant is too large for a collisional quenching mechanism. This suggests ligand binding as the cause for quenching;

Binding constant (and often stoichiometry) are then determined;

Many papers also determine the distance between fluorophore and quencher using Förster Resonance Energy Transfer (FRET) as the proposed quenching mechanism.

Unfortunately, the apparent simplicity of the methodology has led to the introduction of a number of errors in the data interpretation.

Recently, we independently criticised in short communications the methodology used in many articles using fluorescence quenching to study ligand binding [1,2]. However, the incorrect use of this experimental approach is so widespread that we believe it is necessary to reiterate our criticism in a more expanded form in this journal. In this paper we have tried to explain, as simply as possible, the most important fluorescence- and ligand binding-related complications in this methodology. For illustrative purposes we have included mathematical modeling of theoretical data to illustrate the impact of some of the pitfalls.

The criticism is general, but we have at times inserted some specific references from this journal for illustrative purposes. Moreover, we will focus mainly on ligand binding to proteins, with the fluorophore generally being tryptophan, as this situation applies to the vast majority of the articles using this methodology. However, many elements of the criticism apply to any fluorophore-ligand binding analysed using fluorescence quenching. Henceforeward we will refer to the articles we criticise as The Articles or Articles.

## 2. The methodology and its pitfalls

2.1. Why does the fluorescence change?

Addition of a compound to a solution containing a fluorescent macromolecule may change its emission through different mechanisms. The first important question to answer is "why does this addition change the fluorescence?" There are several possible answers:

The inner-filter effect

Collisional quenching

Binding-related changes in fluorescence

Ground-state complex formation between the ligand and the fluorophore(s) in the macromolecule

Excited-state quenching in the complex (e.g. energy transfer)

Binding-induced structural changes of the protein around the fluorophore(s)

Of course, only changes in fluorescence associated to binding (point 3) can be used to follow association phenomena, and therefore effects 1 and 2 must be demonstrated to be negligible or appropriately corrected for before any data analysis is even attempted.

2.2. The inner-filter effect

The inner-filter effect refers to the absorbance (or optical dispersion) of light at the excitation or emission wavelength by the compounds present in the solution. Usually, the optics of commercial fluorimeters focuses the exciting light and collects the emission from the center of the cuvette. Therefore, when absorption at the excitation wavelength is significant, less light reaches the center of the sample and thus the fluorescence of the fluorophore is reduced, while absorption at the emission wavelength reduces the emitted light that reaches the detector. This is a problem whenever the ligand used in a titration absorbs at the excitation and/or emission wavelengths. Also any dilution of the fluorophore upon ligand titration needs to be corrected. Due to the non-linear nature of the inner-filter effect this may require special attention.

If the geometry of the instrument is such that the collected intensity comes exactly from the center of the cuvette, the inner filter effect can be estimated from Equation 1:

(Eq. 1)

where Fobs is the measured fluorescence, Fcorr the correct fluorescence intensity that would be measured in the absence of inner-filter effects, dex and dem the cuvette pathlength in the excitation and emission direction (in cm), respectively, and Aex and Aem the measured change in absorbance value at the excitation and emission wavelength, respectively, caused by ligand addition (in a 1 cm pathlength) [3].

It is important to realise that Equation 1 assumes that the fluorescence comes exactly from the middle of the cuvette. This may be the case for some spectrometers, but certainly not all. Thus, rather than correcting the inner-filter effect, it may be more appropriate to minimize it by simple practical considerations, such as reducing cuvette thickness, or selecting excitation and emission wavelengths that minimize ligand absorption. However, this may not always be practically possible, and in those cases the correction method may be used, but with the caveat that this does not necessarily fully correct the impact of the inner-filter effect. Alternatively, more sophisticated correction approaches have been proposed [4].

But what increase is significant enough to warrant attention? From Equation 1 it is easy to show that a change in absorbance equal to 0.03 already corresponds to a 3% reduction in fluorescence intensity. To more clearly show the potential impact of the inner-filter effect, we performed mathematical modeling on a simple fluorophore in a solution with increasing absorbance upon addition of a non-binding compound. Figure 1 shows the effect of titration with different compounds, which, at the maximal added concentration, have an absorbance ranging from 0.1 to 4. Even with the lowest increase to 0.1 at the highest added concentration, we can see a drop of approximately 10% in observed fluorescence. That is, the inner-filter effect has a measurable impact even at very low absorbances. One may even construct Stern-Volmer plots (see further below) that appear meaningful solely from inner-filter induced quenching. Many of The Articles show increases in absorbance at excitation and/or emission wavelength that are much larger than 0.1 at the highest concentrations added, sometimes easily reaching an increase of 1 [5]. Thus, the inner-filter effect must be considered a confounding factor in the observed quenching in many Articles. It is important to note that an inner-filter effect can be caused also by non-absorbing ligands in case they induce significant light scattering, as in the case of protein-membrane interaction studies, in which titration is performed with a suspension of liposomes [6,7]. In this case correction by use of Equation 1 is problematic, and control experiments are more appropriate [8].

2.3 Collisional quenching

When the inner-filter effect is not an issue or can be removed using the methods described above, any observed reduction in fluorescence (quenching) is likely related to either binding between fluorophore and ligand, or collisional quenching. For the sake of the argument, let us from here onward assume that the inner-filter effect has been corrected, and a change in fluorescence is still observed.

In most Articles the next step in the analysis usually is to determine whether the observed quenching may be due to collisional quenching. To that purpose the Stern-Volmer equation is used (derivation in [3]):

(Eq. 2)

where F0 is the starting fluorescence, F the measured fluorescence (corrected for the inner-filter effect) upon addition of a known amount of quencher, [Q], KSV, the Stern-Volmer quenching constant, kq the bimolecular quenching rate constant, and ï´ the fluorescence lifetime of the fluorophore. In practice, kq cannot be larger than 1 to 2âˆ™1010 M-1 s-1 for a collisional quenching process [3].

Using a typical fluorescence lifetime of the main fluorophore in proteins (tryptophan) of ca. 1 to 10 ns, it is easily shown in The Articles that the bimolecular quenching rate constant is often much too large (well above 1âˆ™1010 M-1 s-1) to be consistent with collisional quenching. This leaves a direct binding interaction as the most likely cause of quenching. One way to discriminate collisional from binding-related quenching is to vary the temperature. For collisional quenching, it is expected (and observed) that an increase in temperature increases collisions and thus the quenching efficiency. By contrast, binding usually decreases with increasing temperature (with the exception of entropy-driven complexes), and thus less quenching is observed at higher temperatures. An additional possibility is to perform a control experiment in which the ligand is added not to the protein, but simply to the fluorophore (e.g tryptophan). Usually, in this latter case no specific association is to be expected, and therefore any observed change in fluorescence can be attributed to inner-filter effects, or to collisional quenching. If, on the other hand, no emission intensity variation is observed in the control experiment, any fluorescence quenching measured with the real sample can be safely attributed to binding-induced phenomena.

2.4 Binding-related changes in fluorescence - dynamic versus static quenching

The binding of a compound to a fluorophore may alter the fluorescence of that fluorophore in different ways. That is, binding may cause an increase or decrease in fluorescence or no change at all. We will not discuss this last case here, since it cannot be used to follow association phenomena. However, as long as the fluorescence signal changes, it can be exploited to characterize binding, as further discussed in the following sections.

Even though the specific molecular processes causing this variation are not important for data analysis, we first need to take on a semantic issue. In almost all Articles the authors claim that the rejection of collisional quenching means that the quenching mechanism must be static. This is an apparently common misunderstanding of the definitions of static and dynamic quenching. Dynamic quenching refers to any non-radiative process in which the quencher interacts with the excited state of the fluorophore [9]. This includes collisional quenching, but also Förster Resonance Energy Transfer (FRET), enhanced intersystem crossing, photoinduced electron transfer, etc. Dynamic quenching results in a change of both the steady-state fluorescence intensity and the fluorescence lifetime.

By contrast, static quenching refers to any mechanism that inhibits the formation of the excited state of the fluorophore [9], and thus completely quenches its original fluorescence. As a result, any measured fluorescence is due just to those fluorophores which are not interacting with the quencher, and therefore their decay lifetime is unaffected, while the total steady-state fluorescence is obviously reduced, since the quenched fluorophores are nonfluorescent. In many cases these so-called ground-state complexes can lead to changes in the absorbance spectrum of the fluorophore, as has also been suggested in some of The Articles [10,11].

According to these definitions, static and dynamic quenching can be distinguished by measuring fluorescence lifetimes. Only if these change, dynamic quenching is present. In any case, it is important to stress that binding-induced quenching can be static (in case of a direct complexation between the ligand and the fluorescing protein residue, forming a nonfluorescent adduct), dynamic (for instance in the case of FRET between fluorophore and ligand), or a combination of both. However, the precise mechanism causing a binding-induced change in fluorescence does not have to be clarified in order to exploit this signal to follow the association process.

2.5. Binding-related quenching -FRET analysis

Many of the Articles, in order to provide a structural insight about the protein-ligand complex, analyze the quenching data in terms of FRET, thus providing an estimate of the distance between fluorophore and ligand in the complex. For FRET to occur, the absorbance spectrum of the acceptor (generally the ligand) should overlap with the fluorescence spectrum of the donor (the fluorophore, usually tryptophan in the protein). The extent of overlap between the two, along with a number of other parameters, can be used to calculate the so-called Förster distance, R0. The latter is the distance between donor and acceptor that results in a 50% reduction in fluorescence (assuming a random orientation of donor and acceptor). The actual reduction in fluorescence (corrected for any inner-filter effect) can then be used to calculate the distance, r, between fluorophore and acceptor (see equation 3) [3].

(Eq. 3)

For this analysis to hold, two conditions must be met, but these have often been disregarded in the Articles:

FRET must be the only quenching mechanism.

This is difficult to ascertain, since ligand-binding can always induce a conformational change in the protein. It is well known that the local microenvironment around the tryptophan has a major influence on its quantum yield [12]. This means that any structural changes may lead to variation in the fluorophore's environment, which in turn may alter the fluorescence (both an increase and decrease is possible). Additionally, ground-state quenching might be present too. Ground-state complexes are often considered "dark", i.e the original fluorescence is fully quenched. However, it is also possible that a new fluorescent system, with a different quantum yield, is formed, although this appears to be uncommon.

Despite the potential presence of structural changes and/or ground-state complex formation as a quenching mechanism, essentially all Articles solely discuss the quenching in the context of FRET. Nonetheless, some Articles do suggest the formation of a ground-state complex [10,11] and/or structural changes of the protein as determined by fluorescence maximum shifts, synchronous fluorescence, CD, and/or FTIR measurements [13,14]. Thus, in various cases the implicit, but unproven and unlikely, assumption is made that neither the ground-state complex nor the structural changes affect the observed quenching.

The quenching efficiency should be determined under conditions of complete saturation. Otherwise, unquenched molecules will contribute to the overall emission intensity, making the FRET analysis meaningless.

This situation is likely never achieved in most Articles. In those cases where experimental conditions are reported, it appears that equal concentrations of protein and ligand are used to determine the reduction in fluorescence [15,16]. Moreover, these concentrations are often around or below the dissociation constant. There are significant methodological problems with the reported dissociation constant in The Articles, as will be discussed below, but for the sake of the discussion let us assume they are correct. In that case, and under the conditions discussed above, one can easily calculate that only a minor portion of the protein and ligand are actually in a complex, which then invalidates the FRET determination. In practice, when using a 1:1 ratio of protein to ligand the concentrations of protein and ligand need to be well above the value of the dissociation constant (at least a factor 10) to assure full ligation. More appropriate is to use a low protein concentration combined with a ligand concentration well above the dissociation constant.

2.6. Determining the binding constant - Equations and pitfalls

There are a number of different equations used to analyse the quenching data in The Articles, but unfortunately the various pitfalls of those equations are often overlooked or poorly taken into account. For example, Wei et al [17] have compiled a list of the equations that are commonly used, but due to their failure to recognise the various pitfalls, their conclusion on the suitability of the various equations is questionable.

We will start here with looking at the simplest of situations for ligand binding, namely the formation of a 1:1 complex. Later we will discuss the more complex case of multiple binding sites. The most generally valid equation to analyse fluorescence changes upon formation of a 1:1 complex is given by equation 4 (derivation in Supplementary Information - section 1 (SI-1)) [1] :

(Eq. 4)

Where F is the measured fluorescence, F0 the starting fluorescence, Fc the fluorescence of the fully complexed protein, Kd the dissociation constant, P0 the concentration of protein, and Qa the concentration of added quencher [18]

There are two reasons for the complexity of equation 4. First, the added quencher concentration cannot necessarily be approximated as the free quencher concentration. This results in having to solve a quadratic equation, and thus the rather extensive right hand term. Second, the complexed protein may well be fluorescent (Fc ï‚¹ 0). Note that equation 4 allows the fluorescence of the complex to be both smaller and larger than that of the uncomplexed protein. No prior assumption is required in this regard.

Now suppose a situation where Qfree ï‚» Qa. This situation is achieved if the added quencher concentration is much larger than the protein concentration, at least a factor 10 higher, but preferably even more. In that case equation 4 is significantly simplified and can be written as shown in equation 5 (see SI-2):

(Eq. 5)

Also shown in SI-2 is how this equation can be further rewritten to yield an even simpler equation (equation 6):

(Eq. 6)

The attentive reader will note that this equation simplifies further to the Stern-Volmer equation (equation 2, with KSV = Ka) if the complex has no residual fluorescence (Fc = 0). The Stern-Volmer equation allows a simple linear regression, while equation 4 requires a non-linear fitting procedure. However, with modern software packages this should not be any problem, and should even be the preferred approach, due to its statistical advantages [19].

Unfortunately, essentially all Articles have skipped over the two pitfalls mentioned earlier (Qa versus Qfree and the formation of a fluorescent complex), without showing that these issues are not relevant for their experimental set-up. As a result, they generally do not use any of the equations 4-6 shown above, but start out with the Stern-Volmer equation or analogous equations. Before discussing the problems with the other equations used in most Articles, we will first show how residual complex fluorescence and failing to correct for Qa vs Qfree affects the data analysis when using the Stern-Volmer equation.

In Figure 2 we show graphically how failing to correct for residual fluorescence may affect the data analysis, in this case with a minor residual fluorescence of 10%. Linear regression is not suitable for the full curve shown in the insert to Figure 2, but this would not be visible if data were collected only up to some ligand concentration. For instance, if in our example we take just the data with [Q]free ï‚£ 0.042, a linear regression yields a correlation coefficient of 0.99, but leads to a serious underestimation of the association constant Ka (63 M-1, versus an actual value of 100 M-1). That is, neglecting to take into account even this minor residual fluorescence of 10% changes the calculated binding constant by 37% for this particular example.

In Figure 3 we show a situation where there is significant difference between Qa and Qfree. Such an extreme difference will occur especially when the protein concentration is much higher than the dissociation constant, Kd, while the ligand concentration is similar to the protein concentration. Also with protein concentrations around the dissociation constant significant differences may occur if the ligand concentration is not in high excess with respect to the protein. In the example in Figure 3 the protein concentration is ten times higher than Kd, while Qa ranges from 0 to 2 times the protein concentration. Figure 3 clearly illustrates that any determination of the association constant in the presence of such large deviations will result in major errors. However, even in this case if we just consider quencher concentrations below 0.4 M, a regression line with r2 of 0.99 is obtained, but the fit yields a slope (Ka) that is a mere 12% of the true value.

2.7. Determining the binding constant - beyond the Stern-Volmer equation

Some Articles follow the analysis using the Stern-Volmer equation by some other equations they believe are (more) suited for "static binding". For example, some introduce equation 7 [20,21,22], which is sometimes referred to as the "Lineweaver Burk" equation:

(Eq. 7)

Although some Articles argue that equation 7 should be used because the quenching is found to be static rather than dynamic, the equation can be transformed back into the Stern-Volmer equation by simple algebraic manipulation. However, using equation 7 to determine binding constants would likely introduce larger errors than the Stern-Volmer equation, as it gives largest weight to the lowest quencher concentrations, which are particularly affected by the difference between Qa and Qfree. Moreover, at low concentrations the quenching is also more limited, introducing further potential for errors. This is a well-known problem with all linearised equations (see also [19]) that use reciprocal values of the data as input, and will be illustrated further below.

Others have used the Modified Stern-Volmer equation (equation 8) [23,5], without realising it can be transformed into equation 6, and thus again involves the unnecessary use of a reciprocal fitting procedure.

(Eq. 8)

Where fa, for a binding-related process, is the fractional difference between the emission of uncomplexed and complexed fluorophore, i.e (F0-Fc)/F0.

The problem of using the reciprocal equation 8 is illustrated in Figure 4, which shows the Modified Stern-Volmer plots for the same data as in Figure 3, where there is a major difference between Qa and Qfree. A linear curve fit of F0/(F0-F) versus 1/Qa gives a very good correlation coefficient (r2=0.9976), but a binding constant that is a factor 28 lower than the true value, and an fa of 2.6 versus a real value of 1. Note also the excellent linearity for the full concentration range, unlike that in Figure 3 (insert), giving a false impression of the methodology being very suitable.

Note also that some Articles contain Modified Stern-Volmer plots that cross the y-axis below 1 [24,25], while in one case fractions larger than 1 are reported in a table without further comments [23]. This is physically not possible and further illustrates the uncritical use of the Modified Stern-Volmer equation.

2.8. Determining binding constant and stoichiometry - the Double Log Stern-Volmer equation

The presence of more than one binding site significantly complicates the situation:

The binding sites may have different affinities for the ligand;

The binding affinity of each site may change when other sites are occupied (i.e, cooperativity between the sites);

Binding in each site may lead to a different change in the emission signal.

Of course, each of these points is reflected in the equation that has to be used when analyzing the data, and which has been discussed extensively in the literature [26]. However, without taking into account these complexities and ignoring this "older" literature, almost all Articles introduce a double log equation to determine both the binding constant and the number of binding sites, n (equation 9).

(Eq. 9)

The first thing to be stressed is that this double log Stern-Volmer equation suffers from the same pitfalls as the Stern-Volmer equation: the formation of a non-fluorescent complex is assumed, and Qa is generally set equal to Qfree [2] . Deviations from these assumptions will lead to erroneous values even for a simple 1:1 binding. Moreover, somewhat similar to the Modified Stern-Volmer equation, the double log plotting linearises even highly non-linear data, often resulting in a false impression of a very good correlation.

Most importantly, however, equation 9 is essentially a linearization of the Hill equation [30], as shown in its derivation in SI-3. This equation implies "infinite" cooperativity: the occupation of one binding site favours ligand association in the others, so much that essentially only two species are significantly populated: the protein with all binding sites free and the protein with all binding sites occupied. This is of course a very unrealistic assumption. It is well known that Equation 9 can be used to fit the data even if the hypothesis of "infinite" cooperativity is not satisfied, but in this case n is just a phenomenological parameter (the Hill coefficient), which is lower than the real number of binding sites [30,31].

To illustrate that equation 9 does not yield information on the binding stoichiometry we have used reported data on binding of the fluorescent probe ANS bound to BSA [32]. In their paper, Togashi & Ryder showed by using the appropriate approaches, such as the Job plot (see below), that BSA has at least 5 binding sites for ANS.

We extracted their binding-induced fluorescence quenching data from Figure 4b of their paper and used them as input for equation 9 (Fig. 5). Note that the input parameters here are the total ANS concentration, and that we did not correct for residual fluorescence either. A linear fit of the data yields n = 1.14; that is, the calculated "stoichiometry" deviates significantly from the real value of 5. In fact, the calculated "stoichiometry", in reality the Hill coefficient, suggests that the binding sites are mostly non-cooperative.

So, what to do to determine binding stoichiometry and binding constants for each binding site? There is unfortunately no simple and short answer to this question. Some useful equations are provided by Eftink [26], but prior knowledge on binding stoichiometry significantly simplifies the analysis. One potential method to determine binding stoichiometry is the continuous variation method (or Job plot) [32,33,34]. However, there are a number of complexities in using this method, most importantly the requirement of using protein and ligand concentrations well above the value of the dissociation constants, as well as the requirement that each binding site significantly alters the parameter being studied. For the particular method of fluorescence quenching discussed in this paper this means that binding of a ligand to a binding site must (significantly) quench the fluorescence. This is not necessarily the case, and it is thus easy to draw erroneous conclusions.

Other methods, such as the Halfman-Nishida [35], Bujalowski-Lohman [36], and Schwarz [37] approaches, allow "model-free" data analysis that is independent on the specific binding model, and are likely to be more appropriate to study complex binding equilibria. However, discussing these different approaches falls outside the scope of the present paper, and the reader is referred to the original publications.

## 3. Conclusion

In this Commentary we have discussed the use of a popular fluorescence quenching method to study ligand binding. Based on the data, data analysis, and argumentation in those Articles, we unfortunately have to conclude that many are based on insufficient understanding of the methodology. Pitfalls are often unknown or not corrected for, there are implicit contradictions in the articles, and various fundamental aspects of both fluorescence spectroscopy and ligand binding appear to be insufficiently appreciated. It is our contention that many of these Articles will require a re-evaluation and correction.

We hope this (renewed) criticism aids authors, reviewers and readers alike in identifying potential flaws in ligand binding analysis using fluorescence quenching. Fortunately, many of the likely flawed papers are easily recognisable. The most important red flags are:

1. There is no correction for the potential inner-filter effect;

2. Calculation of binding constants involves the use of simplified linearised equations, without any discussion of and correction for potential pitfalls such as Qa vs Qfree and residual complex fluorescence;

3. A linearised Hill equation is used to determine binding constant and stoichiometry;

4. FRET calculations are performed without proof this is the sole quenching mechanism.