14.2.1 Electromagnetic Radiation and Molecular Energy Levels

Fluorescence spectroscopy, like other forms of molecular spectroscopy, is based on the interaction of EM radiation with matter. EM radiation can be described both as a wave and as a stream of discrete particles called photons. A transverse EM wave consists of an oscillating electric ( ) and magnetic ( ) field, each in phase and oriented perpendicular to one another (Figure 14.1a). The sinusoidal wave can be described by

14.1

where c is the speed of light in a vacuum (3.00 × 10⁸ m/s), λ is the wavelength (typically in nm), which defines the distance between successive peaks (alternatively reported as wavenumber, , in cm⁻¹), and ν is the frequency (in s⁻¹ or Hz), which describes the number of wavefronts passing a fixed point in space per second. When considered as distinct particles, each photon of EM radiation contains a precise amount of energy termed a quantum. From Planck's law, this energy is

14.2

where h is the Planck constant (6.626 × 10⁻³⁴ J s). The energy stored in EM radiation is therefore proportional to frequency (and wavenumber) and inversely proportional to wavelength. Fluorescence spectroscopy generally utilises EM radiation ranging from the UV through the visible regions of the EM spectrum (λ from ∼250 to 700 nm, Figure 14.1b).

The phenomenon of fluorescence is based on transitions between quantised energy levels of fluorescent molecules (Figure 14.2a). Electronic energy levels (S _n ) correspond to the potential energy of different electronic configurations, vibrational energy levels (V _n ) pertain to oscillatory motions between bonds and rotational energy levels (R _n ) correspond to molecular angular momentum. As shown in Figure 14.2a, electronic states can be depicted as plots of potential energy as a function of internuclear distance, following the formalism of the anharmonic Morse oscillator. Although such depictions strictly pertain to diatomic molecules, they can be used to schematically describe energy transitions of polyatomic molecules such as fluorophores as well. Each electronic state contains vibrational and rotational energy levels. As shown graphically, differences in energy between electronic states are large (on the order of 10⁻¹⁹ J), those between vibrational levels are smaller (about 10⁻²⁰ J) and those between rotational states are even smaller (about 10⁻²³ J). The fluorescence process is usually represented by a Perrin–Jablonski diagram (Figure 14.2b), which gives a simpler rendering of molecular energy levels. In such diagrams, electronic and vibrational levels are depicted horizontally (rotational levels are generally omitted), electronic transitions (light absorption or emission) are depicted as vertical transitions due to their near‐instantaneous nature and slower relaxation processes are depicted as squiggly lines. We will refer to such Perrin–Jablonski diagrams throughout this chapter.

When describing electronic transitions, one must also account for the spin state of the molecule (Figure 14.2b, inset). Electrons have two possible spin orientations (s _i = +1/2 or −1/2, represented by ‘up’ and ‘down’ arrows). Based on the Pauli Exclusion Principle, each orbital can contain two electrons with opposite spins, as depicted for valence electrons in the equilibrium (ground state). This results in a total spin (S = Σs _i ) of zero or a spin multiplicity (M = 2S + 1) of 1, resulting in a ground singlet state (S ₀). Following excitation, an electron usually preserves its spin, resulting in an excited singlet state (S ₁). If the electron undergoes spin conversion (e.g. from s _i = −1/2 to +1/2) following excitation, the total spin of the molecule will be 1 and the multiplicity will be 3, resulting in a triplet state (T ₁). As discussed below, the conversion between S and T states has important implications for fluorescence spectroscopy.

Taken together, the molecular energy level diagrams of Figure 14.2 can be used to describe the photophysical processes of fluorescence, summarised as four steps: (1) the fluorophore absorbs a photon and becomes promoted from the ground (fundamental) electronic state (S ₀) to a vibrational energy level of an excited electronic state (S _n>0); (2) the fluorphore relaxes to the lowest vibrational energy level of the first excited singlet state (S ₁); (3) the fluorophore decays to a vibrational energy level of the ground electronic state, which may be associated with the emission of a fluorescent photon; and (4) the fluorophore relaxes back to a lower vibrational energy level of the ground state. The following section covers steps 1 to 4 in detail.

14.2.2 The Fluorescence Sequence

14.2.2.1 Step 1: Light Absorption

Any molecule that absorbs light is termed a chromophore. Under typical thermal conditions, a molecule at equilibrium will exist in its electronic ground state (S ₀) in different rotational states of the lowest accessible vibrational level(s). Absorption of a photon (hν _A ) by a ground state molecule occurs by the interaction of the electric field vector of the EM radiation with outermost (valence) electrons of specific molecular orbitals in the molecule, which promotes it to an excited electronic state. This entails the excitation of an electron from a ground state bonding or non‐bonding orbital to a vacant orbital of higher energy (e.g. an anti‐bonding orbital).

For absorption to occur, the energy of the photon (E _photon) must be equal to the energy difference between the ground state and an accessible excited state (ΔE _transition). For instance, based on Eq. 14.2, absorbance of a photon from spectrally pure violet light with wavelength λ = 420 nm would promote a transition from the ground state to an excited state with an energy difference of 4.73 × 10⁻¹⁹ J (∼280 kJ/mol), an energy consistent with electronic quantum transitions. For a given wavelength (and solvent), the efficiency with which a chromophore will absorb light is given by the Beer–Lambert law

14.3

where A(λ) is the absorbance, defined from the ratio of incident (I ₀) to transmitted (I) light; ε(λ) is the molar absorption coefficient (in M⁻¹ cm⁻¹), which quantifies the probability of a chromophore absorbing light of a given wavelength under specified conditions; c is concentration (in M); and l is the light pathlength for measurement (in cm). Given the number of possible energetic transitions due to vibrational and rotational states among the electronic energy levels, molecules can absorb light over a range of wavelengths. This can give rise to absorbance spectra that are broadened, asymmetric and/or contain some fine structure.

Absorption of a photon (hν_A), a ‘vertical’ transition, occurs extraordinarily quickly, on a femtosecond (10⁻¹⁵ s) timescale. Attendant with the transition from the ground to an excited state is a redistribution of the cloud of electrons within the molecule that gives rise to an excited state dipole moment. However, as dictated by the Franck–Condon Principle, the molecule reaches the excited state before significant changes can occur in its own nuclear coordinates or in the orientations of surrounding solvent molecules. Hence, immediately upon absorption, the molecule is in the Franck–Condon excited state, having an altered electronic structure out of equilibrium with its surroundings.

14.2.2.3 Step 3: De‐excitation of the Excited State and Fluorescent Photon Emission

The excited molecule resides in the lowest excited singlet state S ₁ on the order of nanoseconds (10⁻⁹ s), making this state the longest lived of all steps in the fluorescence process. The decay of the fluorophore back to one of the many vibrational levels of S ₀ with the concurrent emission of a fluorescent photon is the origin of fluorescence. However, returning to the ground state can also proceed by a number of alternative non‐radiative routes in which a photon is not emitted (Figure 14.3a). Each de‐excitation pathway has an associated rate constant (k), which describes the rate at which the excited state is depopulated by that particular process. We consider the following de‐excitation modes:

1. (i) Fluorescence (k _f): Relaxation from S ₁ to S ₀ with the emission of a photon (hν) is the formal definition of fluorescence. It should be noted that although the fluorophore resides in the equilibrium excited state for an extended time, the emission of a fluorescent photon itself occurs rapidly, on the same timescale as photon absorption, ∼10⁻¹⁵ s (emission is also a ‘vertical’ transition).
2. (ii) Internal conversion (k _IC): The excited fluorophore can return to the ground state by internal conversion, as described above. However, the efficiency with which this process occurs between electronic states is inversely related to the energy gap between the states. For most fluorophores, the energy difference between S ₂ and S ₁ is much smaller than the difference between S ₁ and S ₀; therefore, the rate at which internal conversion mediates the decay among higher electronic energy levels is generally much higher than the rate at which it depopulates the equilibrium excited state of S ₁.
3. (iii) Intermolecular processes (k _IM): The excited state can be depopulated by chemical reactions or interactions with nearby molecules. We will later cover two of these processes, fluorescence quenching (Section 14.3.4) and resonance energy transfer (Section 14.3.5).
4. (iv) Intersystem crossing (k _ISC) and phosphorescence (k _p): The transition between electronic states of different multiplicities involves the spin reversal of the excited electron (see Section 14.2.1), resulting in intersystem crossing between the S and T states. Although this spin transition is in principle forbidden by the rules of quantum mechanics, it can be promoted by a process termed spin–orbit coupling (coupling between spin and orbital magnetic moments). Further, intersystem crossing is most probable between vibrational energy levels of the S and T states that are equal in energy (isoenergetic), or nearly so. Following intersystem crossing, a molecule can relax to the lowest vibrational level of T ₁, followed by the decay to S ₀ (which, again, requires electron spin reversal). Return to the singlet ground state can occur via intersystem crossing or with the emission of a photon, which in the case of the T ₁ to S ₀ conversion is termed phosphorescence. Given the forbidden nature of these conversions, the k _p rate constant is usually low.

The process by which these many events can depopulate an excited state can be modelled within the framework of classical kinetics for branched pathways. To model the depopulation of singlet excited state S ₁, we will consider the rate of fluorescence emission (k _f) along with a rate constant that includes all non‐radiative pathways, k _nr = k _IC + k _IM + k _ISC. The process of de‐excitation can be visualised as shown in Figure 14.3b. Imagine a population of fluorophore F subjected to an infinitely short (δ function) pulse of light. Some fraction of F will absorb the light and reach the excited state (*F) so that the initial concentration of excited fluorophores is [*F ₀]. The rate law for the disappearance of *F can be modelled as an exponential decay:

14.4

Integration of this differential equation gives the time evolution of the concentration of molecules in the excited state:

14.5

As an alternative measure of the amount of time a fluorophore remains in the excited state, we can define the lifetime (τ) of the excited state as the reciprocal of the rate constants:

14.6

We can therefore recast Eq. 14.5 as

14.7

From these definitions, we see that τ is the time required for the excited state to decay to 1/e of its original value (when t = τ, [*F] = [*F ₀]/e).

It is important to emphasise here that de‐excitation is a stochastic process by which the S ₁ state is spontaneously depopulated by a number of parallel pathways, both radiative and non‐radiative. Fluorescence emission therefore ‘competes’ with other processes in a manner dependent on the relative rate constants of each pathway. Therefore, the amount of fluorescence that is measured in the time decay obtained in the experiment of Figure 14.3b would be proportional to our calculated value of [*F], but depend on the rates of other non‐radiative de‐excitation paths. Most fluorophores have lifetime values ranging from tens of picoseconds to tens of nanoseconds. In the absence of all non‐radiative pathways, we define the radiative (or natural) lifetime as

14.8

The fluorescence quantum yield (Φ) is the ratio of the number of photons emitted to the number of photons absorbed (i.e. the fraction of photons that return to S ₀ from S ₁ by emission of a fluorescent photon):

14.9

Values of Φ can in principle range from 0 (a non‐fluorescent chromophore) to a limiting value of 1 (a ‘perfectly efficient’ fluorophore).

14.2.3 Information Content of Fluorescence Excitation/Emission Spectra

In relation to the previous section, two fundamental types of information can be gleaned from spectral analysis of fluorophores. First, the wavelengths associated with absorbance/excitation and with emission (λ _ex and λ _em, respectively) are related to the energies of the S ₀ S _n and the S ₁ S ₀ transitions, respectively. From Figure 14.2 it is clear that the wavelengths of absorption will be lower (higher in energy) than those of emission (lower in energy). Second, the intensity of the emitted light will be a direct outcome of the probability of the fluorophore absorbing light of a particular wavelength (reflected in ε(λ)) and the relative efficiencies of radiative versus non‐radiative paths for de‐excitation (reflected in Φ). Fluorescence spectroscopy often involves measurements of emission intensity over a range of wavelengths of exciting and/or emitting light. Such measurements yield spectra that can provide a great deal of information about the fluorophore and its environment or can render spectral characteristics of an unknown sample (i.e. its fluorescence ‘fingerprint’).

Consider the spectra of a hypothetical fluorophore shown in Figure 14.4a, which includes an absorption/excitation spectrum (dashed line) and an emission spectrum (solid line) corresponding to transitions between ground (S ₀) and excited (S ₁) electronic states. An absorbance spectrum, measured in a spectrophotometer, shows the degree to which light at different wavelengths is absorbed by the chromophore (Eq. 14.3). In this example, one might measure light absorbance from ∼ λ = 295 to 450 nm. Four distinct transitions (upward arrows) are delineated as discrete absorption bands relating to the excitation of the molecule from the ground state (V ₀ of S ₀) to the different vibrational energy levels of the excited state (V ₀ to V ₃ of S ₁). These transitions coincide with photon energies that match the ΔE _transition between ground and excited states (Eq. 14.2). The density of rotational energy levels (not shown) within each vibrational energy level expands the number of energetically accessible transitions; hence, absorption spectra in reality appear as broadened distributions rather than discrete peaks. Moreover, the height of each peak is based on the relative efficiency of absorption, dictated by the value of ε(λ) at each particular wavelength.

By comparison with an absorbance spectrum, which measures the amount of light absorbed, an excitation spectrum measures the amount of fluorescence that results from light absorption. Such spectra are measured in a fluorometer by exposing the sample to light with a range of excitation wavelengths (λ _ex) and reading the resulting total fluorescence intensity at a single wavelength (λ _em, generally the wavelength at maximal emission). In the example of Figure 14.4a, one might therefore excite the fluorophore over a range of wavelengths (say, λ _ex = 290–440 nm) and read the fluorescence emission at ∼λ _em = 460 nm. The important point to note here is that for a given fluorophore, an excitation spectrum will generally have the same shape as its absorbance spectrum. To understand why this is so, consider the Perrin–Jablonski diagram (Figure 14.2b). Following excitation, the fluorophore will relax to the lowest vibrational energy level of S ₁ prior to the emission of a fluorescent photon, regardless of the energy level to which it was initially excited (Kasha's rule). This is an outcome of the rapid rate of vibrational relaxation and internal conversion (picosecond timescale) relative to fluorescence emission (nanosecond timescale). Hence, in most cases, the fluorescence emission wavelength is independent of the wavelength of exciting light and the excitation spectrum can be considered an indirect readout of the absorption spectrum.

Now consider an emission spectrum, which is measured in a fluorometer by exposing the sample to light at a single λ _ex and reading the resulting fluorescence intensity over a range of λ _em values. Because fluorescence emission almost always occurs from the lowest vibrational level of S ₁, the emission spectrum is largely independent of λ _ex. Moreover, because the fluorophore can relax to any vibrational level of S ₀, and vibrational level spacing is largely similar between S ₀ and S ₁, excitation and emission spectra often appear as inverse images (the mirror‐image rule). Finally, the difference in wavelengths between excitation and emission spectra is known as the Stokes shift, quantified as the difference in the wavelength of maximum excitation (λ _{ex max}) and that of maximum emission (λ _{em max}). Consider the excitation and emission spectra for an actual fluorophore, Di‐4‐ANEPPS, whose Stokes shift is quite large (∼200 nm) (Figure 14.4b). Note that for actual fluorophores in solution at room temperature, vibrational structure is lost and spectra are broadened.

14.2.4 Solvent Effects

The polarity of solvent molecules (related to the solvent dielectric) in the vicinity of a fluorophore can significantly impact its spectral properties [16] (Figure 14.5a). In the ground state, polar solvating molecules around a polar fluorophore orient optimally with the molecular dipole moment (Figure 14.5a, left). Upon excitation, fluorophores generally have an altered electronic distribution that increases the dipole moment and changes its orientation. In the Frank–Condon excited state, electronic redistribution occurs before solvent molecules have a chance to reorient and the solvent–fluorophore interaction is high energy and unstable. However, following vibronic relaxation through the energy levels of S ₁, the polar solvent molecules can reorient for a more stabilising interaction that further lowers the energy of the equilibrium excited state. Both the permanent and induced dipoles of the solvent play a role in this process. This solvent relaxation has the effect of reducing the energy difference between S ₁ and S ₀, thereby causing an increase in emission wavelengths (also called a red shift). By contrast, when such a fluorophore is in a non‐polar solvent, there is no solvent relaxation in the excited state and the energy gap between S ₁ and S ₀ is relatively higher, thereby causing a blue shift in emission (Figure 14.5a, right). Such solvent effects depend on the polarity of both the solvent and fluorophore molecules. Moreover, other features of the solvent can be important, such as specific interactions like the ability of solvent molecules to form hydrogen bonds with the fluorophore. As a result, the emission spectra of polarity‐sensitive fluorophores are often blue‐shifted and of higher intensity in a non‐polar environment and red‐shifted and of lower intensity in a polar environment (Figure 14.5b).

14.3.1 Instrumentation

The instrument used to perform analytical fluorescence spectroscopy is a spectrofluorometer. At its essence, the function of this instrument is twofold: (i) to generate the wavelength(s) of light (λ _ex) that excite the fluorescent analyte of interest and (ii) to measure the intensity of the resulting fluorescent light at the appropriate wavelength(s) (λ _em). The basic design of a research‐grade spectrofluorometer is shown in Figure 14.6. The light source produces light for sample excitation. For steady‐state measurements, the most common light source is the high pressure xenon arc lamp, which produces reasonably continuous spectral power distribution from 250 to 700 nm. Other potential sources include lasers, light‐emitting diodes (LEDs) and laser diodes. Pulsed LEDs and laser diodes are commonly used for making time‐domain lifetime measurements. Monochromators disperse the broadband source light into different wavelengths, typically with diffraction gratings. User‐controlled settings for the excitation and emission monochromators define the wavelengths of incident light (λ _ex) and detected emission (λ _em). Light emerging from the monochromators has a Gaussian intensity distribution centred at λ _ex or λ _em and a spectral bandwidth (full width at half maximum) dictated by monochromator slits. Variable slit widths dictate light resolution and intensity passing through each monochromator (the smaller the slit, the higher the spectral resolution at the expense of lower intensity of passed light). Detectors convert emitted light into an electrical signal that is proportional to light intensity and interpreted by the system electronics. Most fluorometers use photomultiplier tubes, which greatly amplify the detected signal in a manner that can be controlled as the detector gain. Polarisers convert incident unpolarised light, which has electric vectors in equal distributions normal to the direction of light propagation, into polarised light with the electric vector amplitude greater at a particular angle. Fluorometers typically have linear birefringent polarisers (commonly Glan–Thompson polarisers) that can be selectively inserted in the excitation and emission light paths for anisotropy measurements. Finally, a reference detector measures emission from a reference fluorophore (a quantum counter) from a fraction of the excitation light to correct emission from the sample based on wavelength‐dependent intensity of the exciting light.

14.3.2 Fluorophores

There are thousands of probes that can be used for different fluorescence‐based approaches. Fluorophores are typically organic molecules consisting of planar or rigid ring structures with extended π systems: chemical features that allow for light absorption and radiative emission. They can be broadly classified as intrinsic, or naturally occurring probes, and extrinsic, or synthetic probes that are added to a sample of biomolecules. Fluorophores are characterised by their spectral properties (ε (λ), λ _{ex max}, λ _{em max}, Φ, Stokes shift, lifetime, etc.) as well as other practical attributes such as photostability (ability to withstand continuous illumination without irreversible degradation). These features are all considered when selecting probes for fluorescence experiments. Comprehensive lists of commercially available fluorophores are available online, such on the Molecular Probes website (www.thermofisher.com/us/en/home/brands/molecular‐probes), and several sites with interactive graphical viewers for fluorophore spectral data are also available (e.g. www.nightsea.com/sfa‐sharing/fluorescence‐spectra‐viewers). A few example fluorophores are described below.

Intrinsic fluorophores of proteins include tryptophan, tyrosine and phenylalanine side chains, which contain optically active aromatic rings (Figure 14.7a). These side chains absorb light in the UV range; however, Trp and Tyr have larger ε(λ) and Φ values, which accounts in part for the predominance of the Trp indole group (and, to a lesser extent, the Tyr phenol group) in the intrinsic fluorescence of natural proteins. Trp is a particularly useful probe because its fluorescence is highly sensitive to local polarity and can thus be used to monitor exposure to aqueous versus non‐polar microenvironments that occur, for example, during protein unfolding. Other naturally occurring fluorophores include pyridine (NADH) and flavin (FAD⁺) nucleotides as well as other aromatic enzyme cofactors. Fluorescent proteins including green fluorescent protein (GFP), yellow fluorescent protein (YFP) and cyan fluorescent protein (CFP) constitute a class of autofluorescent proteins that spontaneously form a fluorophore in their folded state and have been engineered to cover a broad spectral range [17].

Extrinsic fluorophores encompass a broad range of chemical structures [18,19]. Such probes are designed for optimal absorbance, quantum yield and spectral range. Many extrinsic fluorophores can be classified based on the parent structures from which they are derived (Figure 14.7b). Fluoresceins and rhodamines, examples of xanthene‐based fluorophores, have high extinction coefficients and small Stokes shifts, whereas fluorophores such as dansyl have large Stokes shifts (Figure 14.7c). In general, probes with larger π systems have absorbance and emission spectra at longer wavelengths. Many probes also have emission properties that are sensitive to the environment, which can be utilised for experimental purposes. For instance, the emission of fluorescein is sensitive to pH, whereas dansyl is highly sensitive to solvent polarity. Some families of fluorophores such as Alexa dyes, two of which are shown in Figure 14.7d, are designed to absorb and emit across a wide spectral range. For labelling biomolecules, derivatives of extrinsic probes are available that react with naturally occurring functional groups. For example, maleimide and iodoacetamide moieties react with sulphhydryl groups on cysteine side chains, whereas sulfonyl chlorides and N‐hydroxysuccinimide ester moieties react with primary amines, as illustrated in the structures for dansyl chloride and Alexa dyes (Figure 14.7c and d).

14.3.3 Measuring Fluorescence Spectra

Emission scans are one of the most common types of measurements in fluorescence spectroscopy. Some of the fundamental considerations in making such measurements can be illustrated by emission scans of dilute solutions of tryptophan in aqueous buffer (Figure 14.8). For these spectral measurements, two types of scans were taken: one for buffer only (‘blank’) and one with tryptophan in buffer (‘sample’). Inspection of the blank traces (Figure 14.8, left) shows why it is critical to account for a signal that arises even in the absence of the sample being analysed. This background signal comes from two types of light scattering phenomena. First, Rayleigh scattering arises from the scattering of incident light on the solvent molecules without a change in wavelength. Hence, it is observed at emission wavelengths that are close to the selected λ _ex (depending on selected slit widths). Second, Raman scattering results from the inelastic scattering of incoming light by the solvent. For a given solvent, the Raman peak appears at a constant energy from the exciting light and will therefore shift depending on the λ_ex used. For water, the Raman peak is located at a wavenumber about 3600 cm⁻¹ lower than that of the incident light; hence, when λ_ex = 295 nm, the Raman peak is at . Uncorrected emission scans with tryptophan present (Figure 14.8, centre) show a signal from both background scatter and from the fluorophore. To obtain the fluorescence originating only from the sample of interest, one simply subtracts the signal intensity of the blank from that of the uncorrected sample at each wavelength to obtain the blank‐corrected spectra (Figure 14.8, right). Here we see a broad emission peak with a λ_{em max} around 360 nm, typical of tryptophan in a polar solvent (compare with Figure 14.7a). Instrument settings are also important in the signal obtained from blanks and samples. For instance, when the emission slit widths are increased from 4 to 8 nm, Rayleigh scattering intensity increases significantly (Figure 14.8, compare a and b).

These relatively simple measurements highlight the importance of accounting for background signal, particularly when analysing a fluorophore in a complex background that may include large light‐scattering particles and/or other endogenously fluorescent molecules whose signal is comparable to the fluorophore being analysed. Ideally, the blank will include everything that the sample has except for the fluorophore of interest. Moreover, blanks and samples must be measured with identical instrument settings (detector gain, slit widths, integration times, etc.) for accurate background subtraction.

14.3.4 Fluorescence Quenching

To this point, we have considered a number of intrinsic pathways that can depopulate the excited state of a fluorophore. We now turn to fluorescence quenching, an intermolecular process that alters fluorescence by interaction between the fluorophore and neighbouring solutes (ions or molecules). Here we consider two specific types of fluorescence quenching that entail direct contact between the fluorophore and quenching agents. Dynamic quenching involves diffusive collisions between a quencher and the fluorophore during its excited state lifetime (Figure 14.9a, left). This process effectively opens an additional de‐excitation pathway that competes with emission, thereby decreasing both steady‐state emission and the fluorescence lifetime. Static quenching involves the binding of a quencher to a fluorophore in the ground state, which renders it non‐fluorescent (Figure 14.9a, right). This process therefore reduces emission intensity because fewer fluorophores can become excited, but it has no effect on lifetime because the de‐excitation process for non‐complexed fluorophores is not affected. Both dynamic and static quenching experiments can provide information regarding the accessibility of a fluorescent probe to quenching agents within a system because both phenomena require direct contact between fluorophore and quencher. We will now consider mathematical descriptions of each of these quenching processes in turn.

In dynamic quenching, quencher Q collides with *F at a rate defined by the bimolecular rate constant k _q (in units of M⁻¹ s⁻¹). We can therefore consider k _q [Q] as a pseudo‐first order rate constant that describes a path for excited state depopulation in parallel with other non‐radiative pathways. In this case, the rate of disappearance of *F following a short light pulse (Eq. 14.4) can be rewritten as

14.10

and the fluorescence lifetime is

14.11

Let us define F ₀, Φ₀ and τ ₀ as the fluorescence intensity, quantum yield and lifetime in the absence of quencher ([Q] = 0) and F, Φ and τ as the same parameters in the presence of quencher. We can then set up the following ratiometric relationships:

14.12

Given that in the absence of Q, τ ₀ = 1/(k _r  + k _nr ), rearrangement of the fourth term in the above equation gives

14.13

For a single fluorophore and quencher under a given condition, k _q and τ ₀ will be constants. We can therefore define the following Stern–Volmer equation:

14.14

in which K _SV = k _q τ ₀ is the Stern–Volmer constant. Because F ₀/F = τ ₀/τ, this equation can also be written as

14.15

These relationships show that increasing [Q], and therefore the number of possible encounters between Q and *F, will result in a linear decrease in fluorescence intensity (and lifetime), resulting in an increase in F ₀/F (and τ ₀/τ). Dynamic quenching data are typically presented as Stern–Volmer plots, in which F ₀/F (or τ ₀/τ) are shown as a function of [Q] at different concentrations, wherein the y‐intercept is 1 and the slope is equal to K _SV (Figure 14.9b).

A wide variety of substances can act as collisional quenchers of different fluorophores. They can be free in solution (e.g. ions such as atomic halogen anions, transition metals or molecular oxygen) or covalently bound to larger molecules (e.g. paramagnetic moieties bound to lipid acyl chains or specific amino acid side chains in proteins). Moreover, the quenching mechanism will depend on the nature of the quencher and fluorophore. Dynamic quenching can occur by photophysical processes such as the formation of charge‐transfer complexes. Among the most common quenching agents are heavy atoms (e.g. iodide and bromide), which promote spin–orbit coupling with *F, resulting in intersystem crossing to the excited triplet state and non‐radiative de‐excitation due to the low efficiency of phosphorescent photon emission. For a given fluorophore and quencher, the k _q value reflects the frequency with which collisions occur, dependent not only on the accessibility of the Q to *F but also on factors such as the radii and diffusion coefficients of the two as well as quenching efficiency upon contact. Typical values of k _q are on the order of 10¹⁰ M⁻¹ s⁻¹. Rapid collisional rates are required because in dynamic quenching, Q must make contact with *F during its excited state lifetime. For highly efficient quenching, k _q can approach rates near the limits of diffusion.

In most cases of static quenching, F in the ground state forms a non‐fluorescent complex with a quencher Q. This ‘dark complex’, F•Q, absorbs light, typically with altered absorption properties, but immediately returns to the ground state without emission of a fluorescent photon. Consider the equilibrium relationship of the 1 : 1 complex F + Q ⇆ F•Q with association constant K _S:

14.16

Based on mass conservation, the total amount of fluorophore [F]^tot is equal to the sum of free and complexed fluorophore; therefore, [F]^tot = [F] + [F•Q]. Substituting this relationship into Eq. 14.16 and rearranging, we obtain

14.17

Noting that the relative fluorescence intensities in the absence and presence of Q will be proportional to [F]^tot/[F], we obtain

14.18

Thus Eq. 14.18 takes the same form as the Stern–Volmer relation for dynamic quenching (Eq. 14.14); namely, there is a linear relationship between the proportional fluorescence decrease and [Q]. However, in this case the quenching constant is the complex association constant K _S. Moreover, because F•Q is non‐fluorescent, the fraction of fluorophores in this complex are removed from observation but the emission properties of free F, including lifetime, remain unaffected. Thus, static quenching effectively just reduces the total number of fluorophores that are able to emit fluorescence within the system. As a result, with increasing [Q] there will be a reduction in emission intensity (F ₀/F) but τ ₀/τ remains constant, as shown in the corresponding Stern–Volmer plot (Figure 14.9c). Hence, measurements of an excited state lifetime provide the most fundamental diagnostic feature to distinguish dynamic from static quenching.

14.3.4.1 Fluorescence Quenching Sample Experiment: Iodide Quenching of Tryptophan Fluorescence

One application of fluorescence quenching is to address the solvent accessibility of particular sites in macromolecules. Consider two proteins, each with a single environment‐sensitive probe in either a polar environment (protein A) or a non‐polar environment (protein B). We wish to directly test the hypothesis that the probe of protein A is solvent‐accessible and the probe of protein B is not solvent‐exposed, but likely to be buried in the non‐polar core of the protein (Figure 14.10a). Many probes are quenched by water‐soluble quenching agents such as acrylamide and halogens including iodide ions (I⁻). We can therefore perform dynamic quenching experiments in which solutions of the two proteins are titrated with I⁻ and the resulting changes in steady‐state emission and lifetime are analysed by Stern–Volmer plots.

14.3.5 Förster Resonance Energy Transfer (FRET)

Förster Resonance Energy Transfer (FRET) is a process by which a fluorophore in the excited singlet state, termed the donor (D), transfers its excitation energy to a nearby fluorophore or chromophore, termed the acceptor (A), in a manner that does not require direct contact between the two molecules (Figure 14.11a). The transfer of energy occurs non‐radiatively; that is, D does not emit a fluorescent photon as it relaxes to the ground state and A does not absorb a photon as it becomes excited. Rather, D and A behave like coupled oscillators with D transferring its excited state energy to A via long‐range dipole–dipole interactions. During such resonant transitions, the energy available from D must match the energies to excite A to the various vibronic levels of its S ₁ state. Hence, if we consider the excitation (or absorption) and emission spectra of D and A, it is clear that the emission spectrum of D must partially overlap with the excitation (absorption) spectrum of A (Figure 14.11b). If A is a non‐fluorescent chromophore, then it acts as a long‐distance quencher of fluorescence from D. If A is a fluorophore, then it can subsequently emit a fluorescent photon as it relaxes to the ground state.

Because FRET can occur over long distances (∼10–100 Å, comparable to the sizes of macromolecules), it provides a powerful tool for analysing the proximity of specific sites within or between molecules. With the right experimental conditions, it can serve as a ‘spectroscopic ruler’ to estimate distances between D and A. Each D–A pair has a characteristic distance over which FRET will occur, determined by the parameter R ₀, the Förster distance, described below. Steady‐state experiments can measure FRET by a decrease in D emission or, alternatively, as an increase in A emission, provided that A is fluorescent. Time‐resolved measurements can measure FRET as decreases in the D lifetime in the presence of A. As shown mathematically below, the efficiency of FRET depends primarily on the distance between D and A, the extent of spectral overlap between D emission and A absorption and the relative orientations of D and A.

FRET creates a path for the de‐excitation from the S ₁ state of D in parallel with radiative and other non‐radiative paths. The rate constant of energy transfer from D to A, k _ET, is defined as

14.19

where k _D and τ _D are the emission rate constant and lifetime of D, respectively, in the absence of A; R ₀ is the Förster distance and r is the distance between D and A. This equation shows that the rate of energy transfer is inversely proportional to the sixth power of r (i.e. k _ET ∝ r ⁻⁶), underscoring the dominant role that the D–A distance has in energy transfer. It also shows that when r = R ₀, the rate of energy transfer is equal to the intrinsic decay rate of D (i.e. k _ET = k _D = 1/τ _D). Hence, R ₀ defines the D–A distance at which FRET is 50% efficient. R ₀, which ranges between 10 and 60 Å for typical D–A pairs, is calculated by the following equation:

14.20

Equation 14.20 indicates that R ₀ depends on the spectral characteristics of D and A as well as the environment through which energy transfer is occurring, as follows. First, the term J is the spectral overlap between D emission and A absorbance (Figure 14.11b). J is defined as

14.21

where F _D(λ) represents the emission spectrum of D normalised so that and ε _A(λ) is the wavelength‐specific molar absorption coefficient of A. When ε _A(λ) is in units of M⁻¹ cm⁻¹ and λ is in units of nm, the overlap integral J is in terms of M⁻¹ cm⁻¹ nm⁴. Second, Φ_D is the quantum yield of D in the absence of A. Third, n is the average refractive index of the medium between D and A, typically taken to be 1.4 for biomolecules. Finally, the κ ² term is an orientation factor that describes the spatial relationship between the emission dipole of D and the absorption dipole of A, where κ ² can assume values between 0 (transition moments perpendicular) and 4 (transition moments collinear). However, when D and A are free to rotate at a rate faster than the lifetime of the excited state, one can assume isotropic dynamic averaging such that κ ² = 2/3.

The efficiency of energy transfer, E, can be calculated as the fraction of photons absorbed by D that are resonantly transferred to A:

14.22

Combining Eqs. 14.19 and 14.22, we can recast E in terms of r and R ₀ to obtain

14.23

Due to its inverse sixth power dependence on distance, E varies dynamically when r is between 0.5R ₀ and 2R ₀ (Figure 14.11c). Accurate distance measurements can only be made within this distance window because when r < 0.5R ₀, energy transfer is essentially 100% efficient, and when r > 2R ₀, essentially no energy transfer will occur. Rearrangement of Eq. 14.23 gives

14.24

which allows the calculation of r based on measured E and R ₀ values.

The type of energy transfer described above refers to hetero‐FRET, in which the donor and acceptor probes are distinct. A different kind of energy transfer termed homo‐FRET can occur with a single type of fluorophore (typically containing a small Stokes shift), whereby excitation energy is reversibly transferred among the probes and FRET, is typically detected by decreases in anisotropy (see Section 14.3.6).

14.3.5.1 FRET Sample Experiment: Monitoring Molecular Interactions

The ability of FRET to detect changes in the distances between D and A moieties makes this an excellent technique for monitoring alterations in interatomic distances that occur by structural dynamics and associations of macromolecules. For example, by site‐specific FRET pair labelling of two interacting proteins (incorporation of D on one protein and A on the other), one can monitor protein associations and ascertain the distance r between the probes in the interacting heterodimer. Consider a hypothetical case in which two proteins are individually labelled with extrinsic probes A and D whose R ₀ is 50 Å (Figure 14.12a). Upon mixing the two proteins, FRET‐based approaches can be used to monitor their binding kinetics in real time, their association constants, and distance between the probes in the interacting protein complex.

14.3.5.3 Data Analysis

FRET is most easily and accurately quantified by measuring the A‐dependent decrease in D fluorescence. Energy transfer causes a decrease in the donor quantum yield with the transfer efficiency quantified as

14.25

where Φ_DA and Φ_D are the donor quantum yields in the presence and absence of acceptor, respectively. Direct measurements of Φ are not practical for most FRET experiments; therefore, assuming that D absorbance is identical between the two samples, this ratiometric term can be written in terms of D fluorescence intensities in the presence and absence of A (F _DA and F _D, respectively):

14.26

In such cases, the donor emission wavelength(s) used for observation are chosen to minimise unwanted emissions from A.

Based on these relationships, the scans shown in Figure 14.12c can be used to calculate FRET efficiency. D fluorescence intensity can be measured as the integrated donor spectra for all samples; however, in cases where the D and A emission spectra overlap, this requires spectral deconvolution. For simplicity, we can take emission at a single wavelength (λ _{em max} = 566 nm) as our readout for fluorescence (F _DA, F _D, F _A and F _B). When the background signal is non‐negligible, F _B must be subtracted from F _DA, F _D and F _A to obtain the net fluorescence signal that originates solely from the probes. In the present example, we assume that the scans are background‐subtracted, which takes care of this term. Because there is no contaminating signal from A at this wavelength (no crosstalk), F _A = 0. We can then use Eq. 14.26 to calculate FRET efficiency, given relative intensity values F _D = 1.0 and F _DA = 0.4, which yields E = 0.6. From Eq. 14.24, we calculate r = 47 Å, which makes sense because at 60% FRET efficiency, r is expected to be lower than R ₀.

FRET efficiency can also be calculated from the D‐dependent increase in A fluorescence, termed ‘sensitised emission’. Here the samples are again excited at the D excitation wavelength, but the signals in the acceptor emission spectral range are analysed. However, this approach is less straightforward than using D emission for two main reasons. First, due to overlap of the D and A emission spectra, there is often a contaminating signal from D in the A spectral range, termed ‘bleed‐through’, which must be accounted for. Second, crosstalk from direct excitation of A can also contribute to the signal. In instances where D emission is negligible or can be deconvoluted from the signal, transfer efficiency is given by

14.27

where ε _A and ε _D are the extinction coefficients of A and D, respectively, at the D excitation wavelength, and F _DA and F _A are the acceptor emission intensities, respectively.

Energy transfer efficiency can also be analysed by time‐resolved techniques, for example by measuring the donor fluorescence lifetimes in the presence and absence of A (τ _DA and τ _D, respectively):

14.28

Lifetime analysis of FRET would render something similar to the pattern shown in Figure 14.12d. For the experiment described above, assuming that τ _D is 6 ns and decays as a single exponential in the absence and presence of the acceptor, then τ _DA would be 2.4 ns if we assume 60% FRET efficiency. When measuring FRET, the use of time‐resolved approaches has some advantages over using steady‐state approaches, for example when samples are not 100% labelled with a single D or A probe. Based on our assumption that every ‘D’ sample has a D probe and every ‘A’ sample has an A probe, then an emission‐based FRET efficiency of E = 0.6 can unambiguously indicate that the D–A distance r = 0.94 R ₀. However if, for instance, the ‘A’ samples were only 60% labelled with A probe and the actual D–A distance was much shorter (r < R ₀, approaching E = 1), then the same steady‐state efficiency could be obtained, significantly overestimating the D–A distance. By contrast, time‐resolved FRET measurements can help overcome difficulties associated with incomplete D–A pairing. Provided that τ _D and τ _DA are sufficiently different and have relatively straightforward decay functions (e.g. one‐ or two‐exponential decays), then one can use lifetime measurements to estimate E (Eq. 14.28) and evaluate the fraction of D that are in D–A pairs.

14.3.6 Fluorescence Anisotropy

Chromophores contain absorption transition dipole moments ( ) related to the displacement of charges that occurs upon light absorption. They are represented by vectors within the coordinate system of atoms on the molecule (Figure 14.13a). Absorption occurs when the oscillating electric field vector ( ) of light interacts with the absorption dipole moment with a particular orientation. We can also consider the emission dipole moment of a fluorophore ( ) related to by angle α. For many fluorophores, absorption and emission dipoles are collinear (α = 0°); however, they may differ in cases where the fluorophore is excited to an electronic energy level higher than the singlet state from which emission originates. These factors dictate how fluorophores absorb and emit linearly polarised light, which is analysed by fluorescence anisotropy measurements.

Consider the instrument configuration shown in Figure 14.13b. Like all natural light sources, radiation from fluorometer lamps is unpolarised, meaning that its electric vectors are in all possible orientations. An excitation polariser in the light path along the x‐axis produces plane‐polarised light with in a single orientation (here, oriented vertically or parallel to the z‐axis) prior to reaching the sample. The orientation of a single fluorophore in the sample chamber can be defined by our coordinate system such that θ and φ are the angles between the transition dipole and the z‐ and x‐axes, respectively (Figure 14.13c). The probability of photon absorption by a fluorophore is directly proportional to cos² θ, where θ is the angle between the transition dipole and , which is also the z‐axis when light is vertically polarised. Hence, fluorophores with transition dipoles parallel to (θ = 0°) will have maximal absorption, those with perpendicular orientations (θ = 90°) will not absorb light and those whose orientation is 0° < θ < 90° will absorb with intermediate efficiency (Figure 14.13d). Therefore, while fluorophores in the sample are physically oriented in all possible directions (isotropically), plane‐polarised light creates a subpopulation of excited fluorophores whose orientation is anisotropic and oriented along the z‐axis, a phenomenon termed photoselection.

The polarisation state of the resulting fluorescence can be detected using an emission polariser oriented parallel to the of polarised excitation (to detect intensity I _||) or perpendicular to the vector (to detect intensity I _⊥). These intensity values are used to calculate the dimensionless parameter, anisotropy (r):

14.29

These intensities can also be used to calculate a related parameter, polarisation (P):

14.30

The denominators in the equations for r and P, respectively, represent total emission light intensity (I _|| + 2 I_⊥) and intensity in the direction of observation (I _|| + I_⊥). Normalisation to total light intensity makes r more mathematically tractable than P; therefore, we will focus on anisotropy here. From Eq. 14.29, we see that if emitted light is completely polarised (I _⊥ = 0) then r = 1.0, and if emitted light is completely depolarised (I _|| = I_⊥) then r = 0. Note that because r is a ratiometric measure of emission intensity, it is independent of fluorophore concentration, at least for samples that are sufficiently dilute to avoid artefacts.

Several factors contribute to fluorescence anisotropy. One is of course photoselection; because the distribution of excited fluorophores is anisotropic, the emitted light will also be anisotropic, polarised in a plane defined by the emission moment. Assuming parallel transitions moments (α = 0°), the relation between emission anisotropy and the angular distribution of transition moments is r = (3 < cos² θ >  − 1)/2. Due to photoselection, the probability distribution of excited molecules <cos² θ> has a value of 3/5. This means that r has a maximal value of 0.4 (θ = 0°) and a minimal value of −0.2 (θ = 90°). A more general equation accounts for the orientation between and :

14.31

In this equation, the term r ₀ represents the fundamental anisotropy in the absence of other depolarising processes such as molecular tumbling or energy transfer (e.g. as occurs with homo‐FRET); r ₀ is measured under conditions that prevent molecular motions (e.g. by the immobilisation of molecules in clear glass or at low temperatures in glycerol solution). Values for r ₀ range from 0.4 (the theoretical maximum when emission and transition dipoles are collinear) to −0.2 (when the dipoles are perpendicular) (Figure 14.13e).

To this point we have considered factors that influence anisotropy, which are based on the nature of incident and measured light and on the photophysical properties of the fluorophores. We now turn to ways in which fluorescence anisotropy can give information about the size, shape, flexibility and associations of macromolecules in solution. We will first consider the effects of molecular motions. In contrast to the rigid system used for the measurement of fundamental anisotropy, consider the other extreme in which photoselected fluorophores can tumble very rapidly during their excited state lifetimes. In this case, their orientations become randomised prior to photon emission and emission originates from a distribution of isotropically oriented molecules so that fluorescence is completely depolarised (I _|| = I_⊥ and r = 0). Note that, in this case, it is the rate of rotational, not translational, diffusion that causes anisotropy reduction because molecular rotation alters the orientation of transition dipoles.

Now consider a macromolecule labelled with a fluorescent probe that is attached so that its dynamics are coupled to Brownian rotation of the larger molecule. When molecular rotation occurs on the same timescale as the excited state lifetime of the probe, then 0 < r < r ₀ and anisotropy measurements can reveal information about molecular motions. To illustrate this, imagine the time‐resolved decay of anisotropy following an instantaneous pulse of vertically polarised light (Figure 14.13f). Upon excitation, the population of excited probes will have their absorption transition moments biased towards the z‐axis due to photoselection. Following excitation, the molecules will randomly tumble, thereby reorienting their transition dipoles until their distributions are completely isotropic. Hence, emission anisotropy will be high immediately after excitation and will decrease over time. We can quantify the rate of molecular tumbling by the rotational correlation time (τ _C), defined as the average time it takes for a molecule to rotate cos⁻¹(1/e), or about 68.4°. Smaller molecules with τ _C in the picosecond range will show rapid anisotropy decay; larger molecules with τ _C in the nanosecond range will show slower anisotropy decay. This parameter also depends on molecular shape, as molecules that behave as spherical rotors will rotate faster than those that are elongated.

Time‐resolved anisotropy decay can be calculated as

14.32

The τ _C‐dependence of r(t) decay is shown in Figure 14.13g. Steady‐state anisotropy ( ) can be defined by the average of the anisotropy decay r(t) normalised to the total intensity decay I(t). In the case of a single exponential intensity decay:

14.33

This gives a form of the Perrin equation, which allows the calculation of τ _C from anisotropy measurements. Thus, if τ < τ _C, there is little rotation during the fluorescence lifetime and measured r values will approach r ₀; if τ > τ _C, then emission dipoles will randomly orient during the fluorescence lifetime and measured r values will approach zero. To gain insights into molecular motions, experimental conditions must be such that τ ≈ τ _C.

14.3.6.1 Anisotropy Sample Experiment: Analysis of Molecular Rotational Dynamics

As a reporter of Brownian molecular rotation, fluorescence anisotropy is an excellent technique for analysing the sizes, flexibilities and interactions of macromolecules in solution. Here we describe an experimental approach for measuring anisotropy of a fluorescent molecule in solvents of different viscosities to obtain an estimate of its hydrated volume.

For spherical particles, τ _C can be described by the Stokes–Einstein relationship:

14.34

where D _r is the rotational diffusion coefficient (in s⁻¹), η is solvent viscosity (in Poise (P), where 1 P = 0.1 kg/m s), k _B is the Boltzmann constant and V _h is the hydrated volume of the particle. This equation shows that rotational mobility is not only dependent on molecular size and shape but is also a function of solvent characteristics (greater viscosity causes higher τ _C and therefore higher r). Anisotropy measurements in solvents of known viscosity can be used to determine τ _C and therefore V _h.

14.3.6.2 Experimental Setup and Data Collection

A protein labelled with an extrinsic probe (τ = 15 ns) is prepared in glycerol solutions of different viscosities to be used for steady‐state anisotropy measurements. In this example, a series of samples (500 μl each) is prepared by mixing water, 50%(v/v) glycerol, 1M Tris‐HCl, pH 7.5 ([Tris‐HCl]^final = 20 mM) and 50 mM protein ([protein]^final = 4 μM) to produce solutions of known viscosities based on glycerol concentration (Table 14.2). Because viscosity is temperature‐dependent, all preparatory and analytical steps must be performed at a controlled temperature (here, 25 °C).

Sample	% Glycerol (v/v)	η (cP)	Sample preparation (μl)
Water	50% glycerol	1M Tris pH 7.5	50 μM protein
1	0	0.893	450	0	10	40
2	5	1.039	400	50	10	40
3	10	1.219	350	100	10	40
4	15	1.444	300	150	10	40
5	20	1.729	250	200	10	40
6	25	2.094	200	250	10	40
7	30	2.569	150	300	10	40

Sample preparation and fluorescence experiments were performed at 25 °C (298.15 K).

A fluorescence anisotropy experiment for a fluorometer in the L‐configuration equipped with polarisers is shown in Figure 14.14a. Anisotropy is determined by measuring emission intensities with P _ex and P _em (excitation and emission polarisers, respectively) in four different configurations: excitation with vertical polarisation (I _VV and I _VH) and with horizontal polarisation (I _HV and I _HH). Note that in the nomenclature for intensity readings, the first and second subscripts denote the orientations of the P _ex and P _em, respectively. Anisotropy is determined by I _|| and I _⊥ (Eq. 14.29). However, because monochromators have wavelength‐dependent transmission efficiencies for vertically and horizontally polarised light, it is important to adjust readings based on these efficiencies to obtain an unbiased measure of I _|| and I _⊥. To this end, a measured G factor accounts for these efficiencies and is usually determined as G = I _HV/I _HH. The G factor can be measured manually or automatically by the instrument. In either case, it must be known for the spectral settings of each experiment. The steady‐state anisotropy is then calculated as

14.35

In the present example, the four intensity components are used in Eq. 14.35 to determine the anisotropy of each sample. Again, this can be performed manually by rotating the in‐line polarisers for each of the four configurations or automatically by the fluorometer.

14.3.6.3 Data Analysis

Rearrangement of the Perrin equation (Eq. 14.33) and substitution with Eq. 14.34 gives

14.36

A plot of 1/r versus T/η, termed a Perrin plot, yields a straight line with a slope of τk _B/V _h r ₀ and a y‐intercept of 1/r₀. One such plot from simulated data for this experiment is shown in Figure 14.14b. Extrapolation of the linear fit of the data to the y‐axis (infinitely high viscosity) in this example shows an r ₀ value of 0.3, and evaluation of the line gives the volume of the spherical particle (V _h = τk _B/[r ₀ × slope] = 65.4 nm³). From this information, based on Eq. 14.34, τ _C is seen to range from 14.2 to 40.8 ns, going from lowest to highest viscosity. Note that if absorption and emission dipoles are collinear, a measured value of r ₀ less than the theoretical limit of 0.4 could indicate rapid rotational motions of the fluorophore that occur independently of the mobility of the macromolecule to which it is attached.

14.4.1 Site‐specific Labelling of Tim23 by Cotranslational Probe Incorporation

Purified proteins can be selectively labelled using extrinsic probes containing reactive moieties that recognise specific side chains (e.g. Figure 14.7d). An alternative to this chemical labelling approach is to incorporate the fluorescent probe as a non‐natural amino acid into a target protein during its synthesis by including aminoacyl tRNA (aa‐tRNA) analogues in the reaction [35]. To analyse Tim23, the fluorophore 7‐nitrobenz‐2‐oxa‐1,3‐diazolyl (NBD) was site‐specifically incorporated into the polypeptide during synthesis. Translation reactions were programmed with mRNA encoding monocysteine variants of Tim23 (each with unique in‐frame 5′‐UGC‐3′ codons) and reactions contained NBD‐Cys‐tRNA^Cys, which incorporate NBD‐labelled Cys at the cognate sites within Tim23 (Figure 14.15b). NBD‐labelled Tim23 variants were then imported into isolated mitochondria by the endogenous protein biogenesis machinery. NBD fluorescence properties are dependent on the polarity and hydrogen bonding capacity of its microenvironment [36,37]; hence, it is an excellent reporter of the environment of local regions within membrane proteins.

14.4.2 Fluorescence Analysis of Tim23 Structural Features

In these studies, mitochondria containing NBD‐Tim23 served as samples for spectral analysis. Due to the high scatter and endogenous fluorescence of mitochondria, it was crucial to account for signal originating from background (i.e. from sources other than NBD‐Tim23; see Sections 14.3.1 and 14.3.3). The background‐corrected emission scans of Figure 14.15c revealed: (i) that the measured emission was specific for NBD incorporated into Tim23, because Cys‐less (ΔCys) constructs gave a negligible signal and (ii) that the environment‐sensitive NBD served as a good reporter for local polarity, because sites in the N‐terminal domain (e.g. site 30) displayed red‐shifted emission with reduced intensity and sites within the membrane (e.g. site 161) displayed blue‐shifted emission with higher intensity. When NBD was incorporated at sequential sites along Tim23 TMS2, a striking periodic pattern emerged in fluorescence properties such as λ _{em max} (Figure 14.15d, left, black symbols). Fits to a harmonic wave function (dashed lines) revealed a periodicity near 3.6 residues per turn, consistent with TMS2 residing in an amphipathic environment with one helical face towards a non‐polar environment and the opposing face towards a polar region (potentially facing an aqueous channel) (Figure 14.15e). Subsequent analyses confirmed that probes on the putative channel‐facing side were indeed sensitive to the presence of substrates engaged with the complex [15].

14.4.3 Fluorescence Analysis of Tim23 Conformational Dynamics

The inner membrane of active mitochondria contains a transmembrane electric potential (Δψ _m). The TIM23 complex requires the Δψ _m to drive protein import and Tim23 is known to be a voltage‐gated channel. To address possible Δψ _m‐coupled structural changes within Tim23, NBD probes along TMS2 were again analysed following depolarisation by the protonophore CCCP, which caused two observable structural alterations (Figure 14.15d, left, compare red and black symbols) [9]. First, there was an increase in polarity of channel‐facing probes near the N‐terminus of TMS2, indicating greater exposure of the channel to the aqueous space. These results were confirmed by Stern–Volmer analyses of accessibility of dynamic quenching agents added externally, which showed much greater exposure following depolarisation (Figure 14.15d, right). Second, there was an observed disruption of the helical pattern near the C‐terminus of TMS2 following depolarisation, suggesting partial unfolding of the helix. These structural changes could also be monitored in real time by measuring time courses of NBD fluorescence following depolarisation (Figure 14.15f). Taken together, these results formed the foundation of a working model for the structural dynamics of the Tim23 channel that are coupled to the energised state of the membrane (Figure 14.15g).

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Further Reading

1. Albani, J. (2007). Principles and Applications of Fluorescence Spectroscopy. Wiley Blackwell.
2. Lakowicz, J. (2006). Principles of Fluorescence Spectroscopy, 3e. New York, NY: Springer Science+Business Media, LLC.
3. Valeur, B. (2012). Molecular Fluorescence Principles and Applications, 2e. Weinheim: Wiley‐VCH.
4. Goldys, E.A. (ed.) (2009). Fluorescence Applications in Biotechnology and the Life Sciences. Hoboken, NJ: Wiley Blackwell.
5. Gore, M.G. (ed.) (2000). Spectrophotometry and Spectrofluorimetry: A Practical Approach. Oxford: Oxford University Press.