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Флуоресцентная корреляционная спектроскопия Флуоресцентная корреляционная спектроскопия

Флуоресцентные параметры и методы 1. Спектры возбуждения и люминесценции • Полярность локального окружения, концентрация Флуоресцентные параметры и методы 1. Спектры возбуждения и люминесценции • Полярность локального окружения, концентрация люминесциирующих молекул 2. Анизотропия и поляризация • вращательная диффузия 3. Тушение флуоресценции • «активность» растворителя • характер локального окружения (локального поля) 4. Время жизни флуоресценции • Динамическиеипроцессы (наносекунды) 5. Резонансный перенос энергии электронного возбуждения • измерение расстояния между взаимодействующими молекулами 6. Флуоресцентная микроскопия • локализация 7. Флуоресцентная корреляционная спектроскопия • Трансляционная и вращательная диффузия • концентрация • динамика

В ФКС Флуктуации дают сигнал Диффузия Флуктуации фазы Конформационная динамика Вращательное движение Процессы вызывающие В ФКС Флуктуации дают сигнал Диффузия Флуктуации фазы Конформационная динамика Вращательное движение Процессы вызывающие флуктуации

Генерация флуктуаций из-за движения Что мы наблюдаем? 1. Скорость вращения Наблюдаемый объем Пространство образца Генерация флуктуаций из-за движения Что мы наблюдаем? 1. Скорость вращения Наблюдаемый объем Пространство образца 2. Концентрацию частиц 3. Изменения во флуоресценции частиц во время регистрации, например из-за конформационных переходов

Одно- и двух фотонное возбуждение 2 - фотонное 1 - фотонное Определены диафрагма малого Одно- и двух фотонное возбуждение 2 - фотонное 1 - фотонное Определены диафрагма малого размера, длина волны, увеличение и численная апертура объектива Примерно 1 um 3 Определены длиной волны и численной апертурой объектива

1 -фотон 2 -фотон 1 -фотон 2 -фотон

Обработка данных и анализ Временная гистограмма Гистограмма счета фотонов (ГСФ) автокорреляция Автокорреляционные параметры: G(0) Обработка данных и анализ Временная гистограмма Гистограмма счета фотонов (ГСФ) автокорреляция Автокорреляционные параметры: G(0) & kaction ГСФ параметры: & e

Автокорреляционная функция Факторы, влияющие на сигнал флуоресценции : k. Q = quantum yield and Автокорреляционная функция Факторы, влияющие на сигнал флуоресценции : k. Q = quantum yield and detector sensitivity (how bright is our probe). This term could contain W(r) describes our the fluctuation of the observation volume fluorescence intensity due to internal processes C(r, t) is a function of the fluorophore concentration over time. This is the term that contains the “physics” of the diffusion processes

Calculating the Autocorrelation Function Fluorescence Fluctuation F(t) in photon counts time Average Fluorescence t Calculating the Autocorrelation Function Fluorescence Fluctuation F(t) in photon counts time Average Fluorescence t t+t

The Autocorrelation Function t 3 t 5 t 4 t 2 t 1 G(0) The Autocorrelation Function t 3 t 5 t 4 t 2 t 1 G(0) 1/N As time (tau) approaches 0 Diffusion

The Effects of Particle Concentration on the Autocorrelation Curve <N> = 2 <N> = The Effects of Particle Concentration on the Autocorrelation Curve = 2 = 4

Why Is G(0) Proportional to 1/Particle Number? A Poisson distribution describes the statistics of Why Is G(0) Proportional to 1/Particle Number? A Poisson distribution describes the statistics of particle occupancy fluctuations. In a Poissonian system the variance is proportional to the average number of fluctuating species:

What about the excitation (or observation) volume shape? What about the excitation (or observation) volume shape?

Effect of Shape on the (Two-Photon) Autocorrelation Functions: For a 2 -dimensional Gaussian excitation Effect of Shape on the (Two-Photon) Autocorrelation Functions: For a 2 -dimensional Gaussian excitation volume: 1 -photon equation contains a 4, instead of 8 For a 3 -dimensional Gaussian excitation volume:

Additional Equations: 3 D Gaussian Confocor analysis: . . . where N is the Additional Equations: 3 D Gaussian Confocor analysis: . . . where N is the average particle number, t. D is the diffusion time (related to D, t. D=w 2/8 D, for two photon and t. D=w 2/4 D for 1 -photon excitation), and S is a shape parameter, equivalent to w/z in the previous equations. Note: The offset of one is caused by a different definition of G( ) : Triplet state term: . . where T is the triplet state amplitude and t. T is the triplet lifetime.

Orders of magnitude (for 1 μM solution, small molecule, water) Volume Device Size(μm) Molecules Orders of magnitude (for 1 μM solution, small molecule, water) Volume Device Size(μm) Molecules millilitercuvette 10000 6 x 1014 104 microliter plate well 1000 6 x 1011 nanoliter microfabrication 100 6 x 108 picoliter typical cell 10 6 x 105 femtoliter confocal volume 1 6 x 102 attoliter nanofabrication 0. 1 6 x 10 -1 Time 102 1 10 -2 10 -4 10 -6

The Effects of Particle Size on the Autocorrelation Curve Diffusion Constants 300 um 2/s The Effects of Particle Size on the Autocorrelation Curve Diffusion Constants 300 um 2/s 90 um 2/s 71 um 2/s Slow Diffusion Fast Diffusion Stokes-Einstein Equation: and Monomer --> Dimer Only a change in D by a factor of 21/3, or 1. 26

FCS inside living cells Two-Photon Spot Correlation Analysis Dsolution Dnucleus Coverslip = 3. 3 FCS inside living cells Two-Photon Spot Correlation Analysis Dsolution Dnucleus Coverslip = 3. 3 objective Measure the diffusion coefficient of Green Fluorescent Protein (GFP) in aqueous solution in inside the nucleus of a cell.

Autocorrelation Adenylate Kinase -EGFP Chimeric Protein in He. La Cells Examples of different Hela Autocorrelation Adenylate Kinase -EGFP Chimeric Protein in He. La Cells Examples of different Hela cells transfected with AK 1 b -EGFP Qiao Ruan, Y. Chen, M. Glaser & W. Mantulin Dept. Biochem & Dept Physics- LFD Univ Il, USA Fluorescence Intensity Examples of different Hela cells transfected with AK 1 -EGFP

Autocorrelation of EGFP & Adenylate Kinase -EGFP G(t) EGFP-AK in the cytosol EGFP-AKb in Autocorrelation of EGFP & Adenylate Kinase -EGFP G(t) EGFP-AK in the cytosol EGFP-AKb in the cytosol EGFPsolution EGFPcell Time (s) Normalized autocorrelation curve of EGFP in solution ( • ), EGFP in the cell ( • ), AK 1 -EGFP in the cell( • ), AK 1 b-EGFP in the cytoplasm of the cell( • ).

Autocorrelation of Adenylate Kinase –EGFP on the Membrane Clearly more than one diffusion time Autocorrelation of Adenylate Kinase –EGFP on the Membrane Clearly more than one diffusion time A mixture of AK 1 b-EGFP in the cytoplasm and membrane of the cell.

Multiple Species Case 1: Species vary by a difference in diffusion constant, D. Autocorrelation Multiple Species Case 1: Species vary by a difference in diffusion constant, D. Autocorrelation function can be used: (2 D-Gaussian Shape) ! G(0)sample is no longer g/N ! fi is the fractional fluorescence intensity of species i.

Antibody - Hapten Interactions Binding site carb 2 Mouse Ig. G: The two heavy Antibody - Hapten Interactions Binding site carb 2 Mouse Ig. G: The two heavy chains are shown in yellow and light blue. The two light chains are shown in green and dark blue. . J. Harris, S. B. Larson, K. W. Hasel, A. Mc. Pherson, "Refined structure of an intact Ig. G 2 a monoclonal antibody", Biochemistry 36: 1581, (1997). Digoxin: a cardiac glycoside used to treat congestive heart failure. Digoxin competes with potassium for a binding site on an enzyme, referred to as potassium-ATPase. Digoxin inhibits the Na-K ATPase pump in the myocardial cell membrane.

Anti-Digoxin Antibody (Ig. G) Binding to Digoxin-Fluorescein triplet state Digoxin-Fl • Ig. G (99% Anti-Digoxin Antibody (Ig. G) Binding to Digoxin-Fluorescein triplet state Digoxin-Fl • Ig. G (99% bound) Autocorrelation curves: Digoxin-Fl • Ig. G (50% Bound) Digoxin-Fl Binding titration from the autocorrelation analyses: Kd=12 n. M S. Tetin, K. Swift, & , E, Matayoshi , 2003

Two Binding Site Model Ig. G • 2 Ligand-Fl Ig. G • Ligand-Fl + Two Binding Site Model Ig. G • 2 Ligand-Fl Ig. G • Ligand-Fl + Ligand-Fl Ig. G + 2 Ligand-Fl 50% quenching Kd Ig. G • Ligand Ig. G • 2 Ligand [Ligand]=1, G(0)=1/N, Kd=1. 0 No quenching

Multiple Species Case 1: Species vary by a difference in diffusion constant, D. Autocorrelation Multiple Species Case 1: Species vary by a difference in diffusion constant, D. Autocorrelation function can be used: (2 D-Gaussian Shape) ! G(0)sample is no longer g/N ! fi is the fractional fluorescence intensity of species i.

Antibody - Hapten Interactions Binding site carb 2 Mouse Ig. G: The two heavy Antibody - Hapten Interactions Binding site carb 2 Mouse Ig. G: The two heavy chains are shown in yellow and light blue. The two light chains are shown in green and dark blue. . J. Harris, S. B. Larson, K. W. Hasel, A. Mc. Pherson, "Refined structure of an intact Ig. G 2 a monoclonal antibody", Biochemistry 36: 1581, (1997). Digoxin: a cardiac glycoside used to treat congestive heart failure. Digoxin competes with potassium for a binding site on an enzyme, referred to as potassium-ATPase. Digoxin inhibits the Na-K ATPase pump in the myocardial cell membrane.

Case 2: Species vary by a difference in brightness assuming that The quantity G(0) Case 2: Species vary by a difference in brightness assuming that The quantity G(0) becomes the only parameter to distinguish species, but we know that: The autocorrelation function is not suitable for analysis of this kind of data without additional information. We need a different type of analysis

Photon Counting Histogram (PCH) Aim: To resolve species from differences in their molecular brightness Photon Counting Histogram (PCH) Aim: To resolve species from differences in their molecular brightness Molecular brightness ε : The average photon count rate of a single fluorophore PCH: where p(k) is the probability of observing k photon counts probability distribution function p(k) Single Species: Note: PCH is Non-Poissonian! Sources of Non-Poissonian Noise • Detector Noise • Diffusing Particles in an Inhomogeneous Excitation Beam* • Particle Number Fluctuations* • Multiple Species*

frequency PCH Example: Differences in Brightness (en=1. 0) (en=2. 2) (en=3. 7) Increasing Brightness frequency PCH Example: Differences in Brightness (en=1. 0) (en=2. 2) (en=3. 7) Increasing Brightness Photon Counts

Single Species PCH: Concentration 5. 5 n. M Fluorescein Fit: e = 16, 000 Single Species PCH: Concentration 5. 5 n. M Fluorescein Fit: e = 16, 000 cpsm N = 0. 3 550 n. M Fluorescein Fit: e = 16, 000 cpsm N = 33 As particle concentration increases the PCH approaches a Poisson distribution

Photon Counting Histogram: Multispecies Binary Mixture: Molecular Brightness Concentration Intensity Snapshots of the excitation Photon Counting Histogram: Multispecies Binary Mixture: Molecular Brightness Concentration Intensity Snapshots of the excitation volume Time

Photon Counting Histogram: Multispecies Sample 2: many but dim (23 n. M fluorescein at Photon Counting Histogram: Multispecies Sample 2: many but dim (23 n. M fluorescein at p. H 6. 3) Sample 1: fewer but brighter fluors (10 n. M Rhodamine) Sample 3: The mixture The occupancy fluctuations for each specie in the mixture becomes a convolution of the individual specie histograms. The resulting histogram is then broader than expected for a single species.

Resolve a protein mixture with a brightness ratio of two Alcohol dehydrogenase labeling experiments Resolve a protein mixture with a brightness ratio of two Alcohol dehydrogenase labeling experiments Singly labeled proteins Mixture of singly or doubly labeled proteins + Both species have same • color • fluorescence lifetime • diffusion coefficient • polarization kcpsm

Distinguish Homo- and Hetero-interactions in living cells ECFP: EYFP: Apparent Brightness A B + Distinguish Homo- and Hetero-interactions in living cells ECFP: EYFP: Apparent Brightness A B + B A A B ε ε 2ε A B ε 0 ε ε 2ε • single detection channel experiment • distinguish between CFP and YFP by excitation (not by emission)! • brightness of CFP and YFP is identical at 905 nm (with the appropriate filters) • you can choose conditions so that the brightness is not changed by FRET between CFP and YFP • determine the expressed protein concentrations of each cell!

Two Channel Detection: Cross-correlation Sample Excitation Volume 1. 2. Beam Splitter Increases signal to Two Channel Detection: Cross-correlation Sample Excitation Volume 1. 2. Beam Splitter Increases signal to noise by isolating correlated signals. Corrects for PMT noise Detector 1 Detector 2 Each detector observes the same particles

Removal of Detector Noise by Cross-correlation Detector 1 11. 5 n. M Fluorescein Detector Removal of Detector Noise by Cross-correlation Detector 1 11. 5 n. M Fluorescein Detector 2 Detector after-pulsing Cross-correlation

Calculating the Cross-correlation Function Detector 1: Fi time t t+t Detector 2: Fj time Calculating the Cross-correlation Function Detector 1: Fi time t t+t Detector 2: Fj time

Cross-correlation Calculations One uses the same fitting functions you would use for the standard Cross-correlation Calculations One uses the same fitting functions you would use for the standard autocorrelation curves. Thus, for a 3 -dimensional Gaussian excitation volume one uses: G 12 is commonly used to denote the cross-correlation and G 1 and G 2 for the autocorrelation of the individual detectors. Sometimes you will see Gx(0) or C(0) used for the cross-correlation.

Two-Color Cross-correlation The cross-correlation ONLY if particles are observed in both channels Red filter Two-Color Cross-correlation The cross-correlation ONLY if particles are observed in both channels Red filter Each detector observes particles with a particular color The cross-correlation signal: Only the green-red molecules are observed!! Sample Green filter

Two-color Cross-correlation Equations are similar to those for the cross correlation using a simple Two-color Cross-correlation Equations are similar to those for the cross correlation using a simple beam splitter: Information Content Correlated signal from particles having both colors. Autocorrelation from channel 1 on the green particles. Autocorrelation from channel 2 on the red particles. Signal

Two-Color Fluctuation Correlation Spectroscopy Uncorrelated Correlated Interconverting Ch. 2 Ch. 1 For two uncorrelated Two-Color Fluctuation Correlation Spectroscopy Uncorrelated Correlated Interconverting Ch. 2 Ch. 1 For two uncorrelated species, the amplitude of the cross-correlation is proportional to:

A Monomer G 12(0) G 1(0) B = 0. 22 Minimum Dimer G 12(0) A Monomer G 12(0) G 1(0) B = 0. 22 Minimum Dimer G 12(0) G 1(0) = 0. 71 Maximum

Fluorescence F(t) Dual-color PCH analysis (1) FA <FA> Time t Cross-Correlation Fluorescence F(t) Dual-Color Fluorescence F(t) Dual-color PCH analysis (1) FA Time t Cross-Correlation Fluorescence F(t) Dual-Color PCH FB Time t

Signal A Tsample Brightness in each channel: e. A, e. B Signal B Average Signal A Tsample Brightness in each channel: e. A, e. B Signal B Average number of molecules: N Tsample

In vitro Cameleon Data Ca 2+ Saturated Crystallization And Preliminary X-Ray Analysis Of Two In vitro Cameleon Data Ca 2+ Saturated Crystallization And Preliminary X-Ray Analysis Of Two New Crystal Forms Of Calmodulin, B. Rupp, D. Marshak and S. Parkin, Acta Crystallogr. D 52, 411 (1996) Are the fast kinetics (~20 s) due to conformational changes or to fluorophore blinking?