Fluorescence Spectroscopy

CHE5540 Lab exercise 9

See Lakowicz’ Book “Principles of Fluorescence Spectroscopy”Möller, M. & Denicola, A. (2002) Biochem. Mol. Bio. Ed 30(3):175-178Pain, R. H. (2004) Curr. Protocols Protein Sci. 7.7.1-7.7.20

Advantages: more selective , combines and emission spectrum and an absorption spectrum, observed on a zero background

Fluorescence(red-shifted).We minimize background by centrifuging or filtering out anything that could scatter

Incident Io

Transmitted I

The change in intensity may be slight.

Emission is observed at a 90° angle from the incident beam to separate it from transmitted light.

State 0

State 1

Absorption (excitation)

!

Internal conversion

Fluorescence (emission)

The state formed upon excitation is surrounded by solvent molecules in a configuration that is optimal for the ground state but not the excited state.Rapid internal conversion and vibrational relaxation result in a vibrational ground state of the electronic excited state. That energy is lost.Similar losses may be associated with the emissive transition.Result, the photon emitted does not retain all the energy of the absorbed photon, and is red-shifted. The “Stokes Shift”.

Fluorescence is re-emission at a longer wavelength.

vibrational substates

State 0

State 1

Absorption (excitation)Internal conversionFluorescence (emission)

Kasha’s rule, the emission spectrum does not depend on the excitation wavelength (but the intensity does).

Emission spectrum arises entirely from lowest vibrational substate of excited electronic state, regardless of which vibrational substate was created upon excitation. (Internal conversion is fast.)

Absorption (excitation)

!

State 0

State 10-5

0-4 0-3

0-2

0-1 0-0 5-0

4-0

3-0

2-0

1-0

0-0

0-5

0-4 0-3

0-2

0-1

0-0 5-0

4-0

3-0

2-0

1-00-0

Internal conversion

Fluorescence (emission)

Franck-Condon: all electronic transitions occur without changes in nuclear positions: if a particular transition is favourable in absorption (eg. 0-1), then it is also favourable in emission.

Franck-Condon principle and the ‘mirror image rule’

From Lakowicz’ Book “Principles of Fluorescence Spectroscopy”

Anthracene’s vibrationally-resolved electronic spectra.

8 INTRODUCTION TO FLUORESCENCE

Figure 1.8. Mirror-image rule and Franck-Condon factors. The ab-sorption and emission spectra are for anthracene. The numbers 0, 1, and 2 refer to vibrational energy levels. From [11].

1.3.3. Exceptions to the Mirror-Image Rule

Although often true, many exceptions to the mirror-image rule occur. This is illustrated for the pH-sensitive fluo-rophore 1-hydroxypyrene-3,6,8-trisulfonate (HPTS) in Fig-ure 1.9. At low pH the hydroxyl group is protonated. The absorption spectrum at low pH shows vibrational structure typical of an aromatic hydrocarbon. The emission spectrum shows a large Stokes shift and none of the vibrational struc-ture seen in the absorption spectrum. The difference between the absorption emission spectra is due to ionization of the hydroxyl group. The dissociation constant (pKa) of the hydroxyl group decreases in the excited state, and this group becomes ionized. The emission occurs from a differ-ent molecular species, and this ionized species displays a broad spectrum. This form of HPTS with an ionized hydroxyl group can be formed at pH 13. The emission spec-trum is a mirror image of the absorption of the high pH form of HPTS.

Changes in pKa in the excited state also occur for bio-chemical fluorophores. For example, phenol and tyrosine each show two emissions, the long-wavelength emission being favored by a high concentration of proton acceptors. The pKa of the phenolic hydroxyl group decreases from 11 in the ground state to 4 in the excited state. Following exci-tation, the phenolic proton is lost to proton acceptors in the solution. Depending upon the concentration of these accep-tors, either the phenol or the phenolate emission may dom-inate the emission spectrum.

Figure 1.9. Absorption (pH 1, 7.64, and 13) and emission spectra (pH 7) of 1-hydroxypyrene-3,6,8-trisulfonate in water. From [11].

Excited-state reactions other than proton dissociation can also result in deviations from the mirror symmetry rule. One example is shown in Figure 1.10, which shows the emission spectrum of anthracene in the presence of diethyl-aniline.13 The structured emission at shorter wavelengths is a mirror image of the absorption spectrum of anthracene. The unstructured emission at longer wavelengths is due to formation of a charge-transfer complex between the excited state of anthracene and diethylaniline. The unstructured emission is from this complex. Many polynuclear aromatic hydrocarbons, such as pyrene and perylene, also form charge-transfer complexes with amines. These excited-state complexes are referred to as exciplexes.

Some fluorophores can also form complexes with themselves. The best known example is pyrene. At low con-centrations pyrene displays a highly structured emission (Figure 1.11). At higher concentrations the previously invis-ible UV emission of pyrene becomes visible at 470 nm. This long-wavelength emission is due to excimer forma-tion. The term "excimer" is an abbreviation for an excited-state dimer.

1.4. FLUORESCENCE LIFETIMES AND QUANTUM YIELDS

The fluorescence lifetime and quantum yield are perhaps the most important characteristics of a fluorophore. Quan-tum yield is the number of emitted photons relative to the number of absorbed photons. Substances with the largest quantum yields, approaching unity, such as rhodamines, display the brightest emissions. The lifetime is also impor-tant, as it determines the time available for the fluorophore

8 INTRODUCTION TO FLUORESCENCE

Figure 1.8. Mirror-image rule and Franck-Condon factors. The ab-sorption and emission spectra are for anthracene. The numbers 0, 1, and 2 refer to vibrational energy levels. From [11].

1.3.3. Exceptions to the Mirror-Image Rule

Although often true, many exceptions to the mirror-image rule occur. This is illustrated for the pH-sensitive fluo-rophore 1-hydroxypyrene-3,6,8-trisulfonate (HPTS) in Fig-ure 1.9. At low pH the hydroxyl group is protonated. The absorption spectrum at low pH shows vibrational structure typical of an aromatic hydrocarbon. The emission spectrum shows a large Stokes shift and none of the vibrational struc-ture seen in the absorption spectrum. The difference between the absorption emission spectra is due to ionization of the hydroxyl group. The dissociation constant (pKa) of the hydroxyl group decreases in the excited state, and this group becomes ionized. The emission occurs from a differ-ent molecular species, and this ionized species displays a broad spectrum. This form of HPTS with an ionized hydroxyl group can be formed at pH 13. The emission spec-trum is a mirror image of the absorption of the high pH form of HPTS.

Changes in pKa in the excited state also occur for bio-chemical fluorophores. For example, phenol and tyrosine each show two emissions, the long-wavelength emission being favored by a high concentration of proton acceptors. The pKa of the phenolic hydroxyl group decreases from 11 in the ground state to 4 in the excited state. Following exci-tation, the phenolic proton is lost to proton acceptors in the solution. Depending upon the concentration of these accep-tors, either the phenol or the phenolate emission may dom-inate the emission spectrum.

Figure 1.9. Absorption (pH 1, 7.64, and 13) and emission spectra (pH 7) of 1-hydroxypyrene-3,6,8-trisulfonate in water. From [11].

Excited-state reactions other than proton dissociation can also result in deviations from the mirror symmetry rule. One example is shown in Figure 1.10, which shows the emission spectrum of anthracene in the presence of diethyl-aniline.13 The structured emission at shorter wavelengths is a mirror image of the absorption spectrum of anthracene. The unstructured emission at longer wavelengths is due to formation of a charge-transfer complex between the excited state of anthracene and diethylaniline. The unstructured emission is from this complex. Many polynuclear aromatic hydrocarbons, such as pyrene and perylene, also form charge-transfer complexes with amines. These excited-state complexes are referred to as exciplexes.

Some fluorophores can also form complexes with themselves. The best known example is pyrene. At low con-centrations pyrene displays a highly structured emission (Figure 1.11). At higher concentrations the previously invis-ible UV emission of pyrene becomes visible at 470 nm. This long-wavelength emission is due to excimer forma-tion. The term "excimer" is an abbreviation for an excited-state dimer.

1.4. FLUORESCENCE LIFETIMES AND QUANTUM YIELDS

The fluorescence lifetime and quantum yield are perhaps the most important characteristics of a fluorophore. Quan-tum yield is the number of emitted photons relative to the number of absorbed photons. Substances with the largest quantum yields, approaching unity, such as rhodamines, display the brightest emissions. The lifetime is also impor-tant, as it determines the time available for the fluorophore

The intensity of fluorescence depends on the fraction of excited states that decay that way, vs via alternative decay routes.

http://www.olympusmicro.com/primer/java/jablonski/jabintro/index.html

Fluorescence in context: Energy and light: electronic states of molecules.

IC

Fluorescence takes place on a much longer time scale than absorption, so it is sensitive to a much wider range of interactions and perturbations.1

kF = A10

radiative lifetime "F=1/kF

kF is the intrinsic fluorescence rate constant.

Internal conversion: kIC non-radiative decay , mediated via collisions with solvent, internal motions (vibrations). Increases w. temperature.Intersystem crossing: kIS electron spin flip to a triplet state (different manifold of states). Inefficient (forbidden) slow and usually masked by other processes. Usually need low T, rigid glass and low [O2].Quenching: kQ[Q] dissipation of energy via interactions with other molecules, or functionalities. Since the natural lifetime of most organic fluorophores is only 1 - 100 ns, only efficient quenchers are significant.I-, O2, acrylamide

!F = kF/(kIC + kIS + kQ[Q] + kF)Fraction of excited state that returns to the ground state via fluorescenceThis is the same as the fraction of photons absorbed that lead to fluorescence.

Fluorescence Quantum Yield

Because fluorescence emission is a slower process, it is more sensitive to the environment and interactions of the chromophore.This makes it more useful.

Lakowicz Figure 1.21

18 INTRODUCTION TO FLUORESCENCE

Figure 1.21. Emission spectra of TNS in water, bound to apomyoglo-bin, and bound to lipid vesicles.

ume (or molecular weight) of proteins. This measurement is possible because larger proteins rotate more slowly. Hence, if a protein binds to another protein, the rotational rate decreases, and the anisotropy(s) increases (Figure 1.23). The rotational rate of a molecule is often described by its rotational correlation time !, which is related to

"V! ! (1.17)

RT

where " is the viscosity, V is the molecular volume, R is the gas constant, and T is the temperature in EK. Suppose a pro-tein is labeled with DNS-Cl (Figure 1.23). If the protein associates with another protein, the volume increases and so does the rotational correlation time. This causes the anisotropy to increase because of the relationship between the steady-state anisotropy r to the rotational correlation time ! (eq. 1.10).

Fluorescence polarization measurements have also been used to determine the apparent viscosity of the side chain region (center) of membranes. Such measurements of microviscosity are typically performed using a hydrophobic probe like DPH (Figure 1.23), which partitions into the membrane. The viscosity of membranes is known to decrease in the presence of unsaturated fatty acid side

Figure 1.22. Accessibility of fluorophores to the quencher (Q). Reprinted with permission by Wiley-VCH, STM. From [21].

chains. Hence, an increase in the amount of unsaturated fatty acid is expected to decrease the anisotropy. The appar-ent microviscosity of the membrane is determined by com-paring the polarization of the probe measured in the mem-brane with that observed in solutions of known viscosity.

Anisotropy measurements are widely used in biochem-istry, and are even used for clinical immunoassays. One rea-son for this usage is the ease with which these absolute val-ues can be measured and compared between laboratories.

1.9.4. Resonance Energy Transfer

Resonance energy transfer (RET), sometimes called fluo-rescence resonance energy transfer (FRET), provides an opportunity to measure the distances between sites on macromolecules. Förster distances are typically in the range of 15 to 60 Å, which is comparable to the diameter of many proteins and to the thickness of membranes. According to eq. 1.12, the distance between a donor and acceptor can be calculated from the transfer efficiency.

1-Anilinonaphthalene-8-Sulfonic Acid

human

serum albumin

(HSA)

The lower polarity environment in the core of a protein is less quenching of fluorescence and less supportive of internal conversion.

Figure 1.30 from Lakowicz

22 INTRODUCTION TO FLUORESCENCE

Figure 1.32. FCS of an Alexa-labeled benzodiazepine (Alexa-Bz) in solution and on a single neuronal cell. Revised from [32].

Figure 1.30. Fluorescence image of RBL-3H3 cells stained with DAPI (blue), Patman (green), and tetramethylrhodamine (red). Courtesy of Dr. W. Zipfel and Dr. W. Webb, Cornell University. Reprinted with permission from [30].

Figure 1.31. Fluorescence correlation spectroscopy. Top: observed volume shown as a shaded area. Middle: intensity fluctuations. Bottom: correlation function.

most single-molecule experiments are performed on immo-bilized fluorophores, with fluorophores chosen for their high quantum yields and photostability (Chapter 23). A typ-ical instrument for SMD consists of laser excitation through microscope objective, a scanning stage to move the sample and confocal optics to reject unwanted signals. SMD is now being extended to include UV-absorbing fluorophores, which was considered unlikely just a short time ago. The probe 2,2'-dimethyl-p-quaterphenyl (DMQ) has an absorp-tion maximum of 275 nm and an emission maximum of 350 nm. Figure 1.33 (left) shows intensity images of DMQ on a quartz cover slip.35 The spots represent the individual DMQ molecules, which can yield signals as high as 70,000 pho-tons per second. The technology for SMD has advanced so rapidly that the lifetimes of single molecules can also be measured at the same time the intensity images are being collected (right). The individual DMQ molecules all display lifetimes near 1.1 ns.

Without the use of SMD, almost all experiments observe a large number of molecules. These measurements reveal the ensemble average of the measured properties. When observing a single molecule there is no ensemble averaging, allowing for the behavior of a single molecule to be studied. Such an experiment is shown in Figure 1.34 for a hairpin ribozyme labeled with a donor and acceptor. Steady-state measurements on a solution of the labeled ribozyme would yield the average amount of energy trans-fer, but would not reveal the presence of subpopulations showing different amounts of energy transfer. Single-mole-cule experiments show that an individual ribozyme mole-cule fluctuates between conformations with lower or high-er amounts of energy transfer.36 These conformational changes are seen from simultaneous increases and decreas-

Examples of biological uses.

More cool experiments: FRET, FRAP

DAPI or 4',6-diamidino-2-phenylindole is a fluorescent stain that

binds strongly to A-T rich regions in DNA. It is used extensively in

fluorescence microscopy

tetramethylrhodamine methyl ester

Wikipedia

Examples of commonly-used fluorophores

the local environment determines the spectral properties oftryptophan. It is also possible to insert tryptophan ana-logues into proteins. These analogues display unique spec-tral features, and are observable in the presence of othertryptophan residues.

In summary, a growing understanding of indole photo-physics, the ability to place the tryptophan residues atdesired locations, and the availability of numerous proteinstructures has resulted in increased understanding of thegeneral factors that govern protein fluorescence. The high

sensitivity of the emission from tryptophan to the details ofits local environment have provided numerous opportuni-ties for studies of protein functions, folding, and dynamics.

16.1. SPECTRAL PROPERTIES OF THE AROMATIC AMINO ACIDS

Several useful reviews and monographs have summarizedthe spectral properties of proteins.1–9 Proteins contain threeamino-acid residues that contribute to their ultraviolet fluo-

530 PROTEIN FLUORESCENCE

Figure 16.1. Absorption (A) and emission (E) spectra of the aromatic amino acids in pH 7 aqueous solution. Courtesy of Dr. I. Gryczynski, unpub-lished observations.

Figure 16.1 from Lakowicz

Proteins’ built-in fluorophores

Note

Y-a

xes

Trp h

as a

lar

ger

extinct

ion c

oef

fici

ent

riboflavin 370, 480 12 531 (0.3 - 0.37) 36 http://omlc.ogi.edu/spectra/PhotochemCAD/html/004.html

enhanced GFP 395, 475 55 509 0.6 330 http://en.wikipedia.org/wiki/Green_fluorescent_protein

Natural fluorophores in proteins

Cantor & Schimmel

http://zeiss-campus.magnet.fsu.edu/print/probes/fpintroduction-print.htmlhttp://www.scholarpedia.org/article/Fluorescent_proteins

multiple tryptophan residues, and the residues contributeunequally to the total emission. There have been attempts todivide proteins into classes based on their emission spec-tra.56–59 The basic idea is that the tryptophan emission spec-trum should reflect the average environment of the trypto-phan. For tryptophan in a completely apolar environment ablue-shifted structured emission characteristic of indole incyclohexane can be observed. As the tryptophan residuebecomes hydrogen bonded or exposed to water, the emis-sion shifts to longer wavelengths (Figure 16.11). In fact,individual proteins are known that display this wide rangeof emission spectra.60–61 For example, later in this chapterwe will see that azurin displays an emission spectrum char-acteristic of a completely shielded tryptophan residue. Theemission from adrenocorticotropin hormone (ACTH) ischaracteristic of a fully exposed tryptophan residue.

The emission maximum and quantum yield of trypto-phan can vary greatly between proteins. Denaturation ofproteins results in similar emission spectra and quantumyields for the unfolded proteins. Hence, the variations intryptophan emission are due to the structure of the protein.We are not yet able to predict the spectral properties of pro-teins using the known structures, but some efforts areunderway.61 One might expect that proteins that display ablue-shifted emission spectrum will have higher quantumyields (Q) or lifetimes (!). Such behavior is expected from

536 PROTEIN FLUORESCENCE

Figure 16.10. Emission spectra of proteins that lack tryptophanresidues. Neutral pH. Revised from [48–49].

Figure 16.11. Effect of tryptophan environment on the emission spectra. The emission spectra are those of apoazurin Pfl, ribonuclease T1, staphylo-coccal nuclease, and glucagon, for 1 to 4, respectively. Revised from [59] and [60].

Tryptophan fluorescence differs depending on exposure to solvent

It therefore reports on protein unfolding.

Figure 16.11 from Lakowicz

The Stokes shift is larger in a more polar solvent because the

energies associated with interactions with polar solvent

molecules are larger.

single-tryptophan azurin Pae. The spectrum of thequenched tryptophan residue can be seen from the differ-ence spectrum, and is characteristic of an exposed residuein a partially hydrophobic environment. In this favorablecase, one residue is quenched and the other is not, provid-ing resolution of the two emission spectra.

16.6.1. Effect of Emission Maximum on Quenching

Water-soluble quenchers, including iodide and acrylamide,do not readily penetrate the hydrophobic regions of pro-teins. There is a strong correlation between the emissionmaximum and quenching constant.101–102 Blue-shifted tryp-tophan residues are mostly inaccessible to quenching byacrylamide, and red-shifted residues are nearly as accessi-ble as tryptophan in water. This correlation can be seen inthe acrylamide quenching of several proteins (Figure

16.32). The emission of azurin is essentially unchanged inup to 0.8 M acrylamide. In contrast, the exposed tryptophanresidue in adrenocorticotropin hormone (ACTH) is almostcompletely quenched at 0.4 M acrylamide (Figure 16.32,left panel).

Quenching data are typically presented as Stern-Volmer plots, which are shown for several single-trypto-phan proteins (Figure 16.32, right panel). In these plots thelarger slopes indicate larger amounts of quenching and canbe used to calculate the bimolecular quenching constant(kq). The buried single-tryptophan residue in azurin Pae isnot affected by acrylamide. In contrast, the fully exposedresidue in ACTH is easily quenched by acrylamide. ACTHis quenched nearly as effectively as NATA. A plot of thebimolecular quenching constant (kq) for acrylamide versusemission maximum for a group of single-tryptophan pro-teins is shown in Figure 16.33. These data show that kq

PRINCIPLES OF FLUORESCENCE SPECTROSCOPY 547

Figure 16.30. Collisional quenching of buried (W1) and surface accessible (W2) tryptophan residues in proteins.

Quenching of tryptophan in proteins

Buried (blue-shifted) tryptophan is less accessible to polar quenching agents, so the quenched spectrum is blue-shifted.

Figure 16.30 from Lakowicz

16.6.3. Resolution of Emission Spectra byQuenching

Selective quenching of tryptophan residues allows resolu-tion of the emission spectra of the quenched and un-quenched components. For apomyoglobin we assumed thatsome fraction of the emission was completely inaccessibleto quenching. A more general procedure allows the emis-sion spectra to be resolved even when both residues are par-tially accessible to quenching.114–116 The basic approach isto perform a least-squares fit to the quenching data to recov-er the quenching constant and fractional intensity at eachwavelength (!):

(16.4)

In this expression the values of fi(!) represent the fractionof the total emission quenchable at wavelength ! with avalue Ki(!) (Section 8.8).

This procedure was applied to a metalloprotease fromS. aureus that contains two tryptophan residues.116 For allemission wavelengths the Stern-Volmer plot is curved dueto the different accessibilities of each residue (Figure16.38). The data are fit by least-squares methods to obtainthe values of Ki(!) and fi(!). Similar data are collected for arange of emission wavelengths. These data can be used tocalculate the emission spectra of each component:

(16.5)

where F0(!) is the unquenched emission spectrum. For met-alloprotease this procedure yielded two well-resolved emis-sion spectra (Figure 16.39).

The use of quenching-resolved spectra may not alwaysbe successful. One possible reason for failure would be if atryptophan residue was not in a unique environment. In thiscase each tryptophan residue may display more than oneemission spectrum, each of which would be quenched to adifferent extent. Quenching-resolved spectra have beenobtained for proteins that contain a single-tryptophan resi-due.116–117 These results have been interpreted as due to theprotein being present in more than a single conformational

Fi(! ) ! F0(! )fi(! )

F(! )F0

! "i

fi(! )

1 " Ki(! ) !Q"

550 PROTEIN FLUORESCENCE

Figure 16.36. Stern-Volmer and modified Stern-Volmer plots forapomyoglobin quenching by iodide or trichloroethanol (TCE). Thedata in the upper panel was reconstructed from the data in the lowerpanel. Data from [113].

Figure 16.37. Emission spectra of apomyoglobin and of the accessi-ble and inaccessible components. The lower panel shows the wave-length-dependent fractional accessibility to quenching. Revised from[113].

16.6.3. Resolution of Emission Spectra byQuenching

Selective quenching of tryptophan residues allows resolu-tion of the emission spectra of the quenched and un-quenched components. For apomyoglobin we assumed thatsome fraction of the emission was completely inaccessibleto quenching. A more general procedure allows the emis-sion spectra to be resolved even when both residues are par-tially accessible to quenching.114–116 The basic approach isto perform a least-squares fit to the quenching data to recov-er the quenching constant and fractional intensity at eachwavelength (!):

(16.4)

In this expression the values of fi(!) represent the fractionof the total emission quenchable at wavelength ! with avalue Ki(!) (Section 8.8).

This procedure was applied to a metalloprotease fromS. aureus that contains two tryptophan residues.116 For allemission wavelengths the Stern-Volmer plot is curved dueto the different accessibilities of each residue (Figure16.38). The data are fit by least-squares methods to obtainthe values of Ki(!) and fi(!). Similar data are collected for arange of emission wavelengths. These data can be used tocalculate the emission spectra of each component:

(16.5)

where F0(!) is the unquenched emission spectrum. For met-alloprotease this procedure yielded two well-resolved emis-sion spectra (Figure 16.39).

The use of quenching-resolved spectra may not alwaysbe successful. One possible reason for failure would be if atryptophan residue was not in a unique environment. In thiscase each tryptophan residue may display more than oneemission spectrum, each of which would be quenched to adifferent extent. Quenching-resolved spectra have beenobtained for proteins that contain a single-tryptophan resi-due.116–117 These results have been interpreted as due to theprotein being present in more than a single conformational

Fi(! ) ! F0(! )fi(! )

F(! )F0

! "i

fi(! )

1 " Ki(! ) !Q"

550 PROTEIN FLUORESCENCE

Figure 16.36. Stern-Volmer and modified Stern-Volmer plots forapomyoglobin quenching by iodide or trichloroethanol (TCE). Thedata in the upper panel was reconstructed from the data in the lowerpanel. Data from [113].

Figure 16.37. Emission spectra of apomyoglobin and of the accessi-ble and inaccessible components. The lower panel shows the wave-length-dependent fractional accessibility to quenching. Revised from[113].

Dependance on quencher concentration: Stern-Volmer plots

Figure 16.36 from Lakowicz

!F = kF/(kIC + kIS + kF) = kF " (" is the unperturbed life time of the excited state, also called the fluorescence life time)

In the absence of quencher

In the presence of quencher

!F = kF/(kIC + kIS + kF + kQ[Q])

The ratio of fluorescence in the absence of Q vs. in the presence of Q is

F0

F=

kF

kF + kIC + kIS

kF + kIC + kIS + kQ[Q]

kF

F0

F=kF + kIC + kIS + kQ[Q]

kF + kIC + kIS=1+

kQ[Q]

kF + kIC + kIS

F0

F=1+ kQ[Q]!

The Stern-Volmer Equation for Quenching

F0

F=1+ kQ[Q]!

The Modified Stern-Volmer Equation

F =F0

1+ kQ[Q]!

Observed fluorescence is the sum of fluorescence from exposed sides and buried sites.

F = FX+ F

BFor each type of site: F =

F0

1+ kQ[Q]!

F =FX ,0

1+ kQ[Q]!+ FB,0

F =FX ,0

1+ kQ[Q]!+ (F

0" FX ,0 )

F0 is the total fluorescence when there is no quencher.

F ! F0= (

1

1+ kQ[Q]"!1)FX ,0 = FX ,0 (

1!1! kQ[Q]"

1+ kQ[Q]")

F0! F = "F = FX ,0

kQ[Q]#

1+ kQ[Q]#

1

!F=1

FX ,0

1+ kQ[Q]"

kQ[Q]"

F0

!F=

F0

FX ,0kQ[Q]"+F0

Fx,0=1

fX

1

kQ[Q]"+1

fX

F0

!F=1

fX

1

kQ"

1

[Q]+1

fX

Intercept yields fx, the fraction of fluorescence

due to exposed sites.Slope