Basic assay principles for fluorescence 1 • donor transfers energy to acceptor • Result: donor fluorescence is reduced (quenced), acceptor fluorescence is increased • Main application : quenced protease substrate, fluorescence increases when protease cleaves substrate and donor and acceptor get too far separated for energy transfer 1 Fluorescence anisotropy Excitation Dipole of Dye Excitation - photoselection HN O + HN O OH OH O t • during absorption a photo- Emission: selection occurs • After average fl. Life-time molecules emits light of different orientation. • This is used as a measure for how fast molecule rotates, i.e. how big it is. Anisotropy measurment setup Anisotropy setup D vertical Fluorescence D lens beam splitter horizontal I - I Ivv - IVH vv VH P = r = I + 2 I Ivv + IVH vv VH 3 How to use Anisotropy for ligand binding Assay principle Orientation Orientation Labeled ligand of dipole of dipole at moment of protein at moment of Test ligand excitation emission 1. complex: High MW Anisotropy setup D vertical Slow rotation Fluorescence D lens beam splitter horizontal 2. ligand replaced: Low MW D vertical Fast rotation Fluorescence D lens beam splitter horizontal 4 How well does a ligand bind? Main indicators used: [R] x [L] 1. Dissociation constant, Kd: = Kd unit: concentration e.g. 1 uM [RL] If ligand is at concentration of Kd, 50% of receptor is bound to ligand. 2. IC50: Half maximum effect (any assay). unit: concentration e.g. 1 uM The relationship to the Kd is the following: IC50 Where SL is the surrogate ligand used Kd = in the assay [SL] + 1 [Kd of SL] Note: only the Kd is indipendent of the assay and can be used to compare compounds. IC50 values (e.g. for cellular assays can only be compared for the same assay). 5 Ligand-receptor interactions: Thermodynamics (Kd) + ligand Protein In reality there is a thermodynamic equilibrium between unbound and bound form of the ligand. The «better « the ligand is i.e. the stronger it’s binding, the more ligand molecules will be bound to the protein at a given ligand and protein concentration. This is expressed as «dissociation constant» Kd and is a parameter measuring the «strength « or affinity of a ligand to its protein. [P] x [L] Where P, L are free protein and free ligand Kd = PL is the complex [PL] [] denotes «concentration» thereof 6 A weak ligand: Protein + Protein Protein ligand Protein Protein Protein [2] x [5] [P] x [L] Kd = = = 10 [PL] [1] 7 A strong ligand: Protein + Protein Protein ligand Protein Protein Protein [1] x [1] [P] x [L] Kd = = = 0.5 [PL] [2] • As seen from the last two slides: the lower Kd, the better i.e. higher affinity the ligand. • Dissociation constants are expressed as concentrations [M] • Classification: Kd > 10-3 M «low affinity» Kd < 10-3 M > 10-6 «medium affinity» kd < 10-9 M «high affinity» 8 How affinites are determined: • To a solution of Ligand are added increasing amounts of P P the Protein and the protein-ligand complex formation is P detected. (or vice versa). L L -> requirement: there needs to be an «assay principle» to L L measure complex formation. • Then, the measured effect is plotted vs. concentration of added ligand and non-linear curve fitting is done Note: in reality one knows only the total amount of 0.12 ligand and protein and the amount of complex 0.1 formed during the reaction, therefore the actual free 0.08 and bound ligand and protein concentrations are not directly known. This is why the simplified calculation 0.06 shown above is not used in reality but curve-fitting is Kd = 273 +/- 8 nM Fluorescence Anisotropy Fluorescence 0.04 needed. 0.02 0 2000 4000 6000 8000 10000 Concentration of unlabeled Grb2-SH2 [nM] 9 How to determine binding Kd Normally, via a titration experiment : 2. Protein in portions [100 nM] -> final [1000 nM] readout 1. Ligand [100 nM] [c] ligand [R] x [L] = Kd Is simplified, because the true meaning [RL] of the concentrations is [R]free and [L]free However, we only know total ligand concentration and total protein concentration we put into the well [c]tot ligand, [c]tot protein Answer : non-linear curve fitting 10 Non-linear curve fitting Direct binding reaction: labeled ligand -> protein protein + protein We have to build up equations from the reaction: [R]f x [L]f / [RL]= Kd Mass balances: Substituting Rf and Lf [R]f + [RL] = [R]tot for Rtot and Ltot [L]f + [RL] = [L]tot ([R]tot – [RL] ) x ([L]tot – [RL])/[RL] = Kd -> quadratic equation as fit-function for Kd -> now Kd can be determined with fit fuction applied to data generated with total protein & ligand [c] -> same doable for inhibition testing -> leads to a cubic equation -> higher models only numerically solvable.... 11 [A] ×[B] A + B AB Kd = f f [AB] [A0 ]= [A]f +[AB] [B0 ]= [B]f +[AB] ([A ]-[AB])×([B ]-[AB]) [AB]= 0 0 Kd 2 [AB]× Kd = [A0 ]×[B0 ]- [B0 ]×[AB]- [A0 ]×[AB]+ [AB] 2 [AB] - [AB]×([A0 ]+ [B0 ]+ Kd )+ [A0 ]×[B0 ]= 0 Quadratic equation: [A ]+ [B ]+ Kd [A ]+ [B ]+ Kd [AB]= 0 0 - 0 0 -[A ]×[B ] 2 2 0 0 12 To use the equation built up before we need a system, where the Signal is linearly proportional to the amount of complex in solution. Option 1: Signal is increasing DF [AB] = DFMAX B0 [AB] F = FMIN + (FMAX - FMIN )× B0 Substitute term for [AB] 13 Option 2 Signal is decreasing DF F - F [AB] = MAX = DFMAX FMAX - FMIN [B0 ] [AB] F = FMAX - (FMAX - FMIN )× B0 Substitute term for [AB] 14 IC50 fitting Imax S = slope factor (hill coefficent) y= I max = starting value 1+( [c] Ligand )s IC50 100 80 60 signal signal 40 20 0 1 10 100 c [ligand] 15 Non-linear curve fitting Advantages: • Exact equations based on the law of mass action • Data can directly be fittet (no linearisation etc, .. ) • The end-point does not have to be reached but can be used as parameter • Simulations help to guide experimental planning • Quick Disadvantages: • For n-interaction partner equation is of n+1 order : i.e. A + B <=> AB -> quadratic equaction A + B <=> AB A + C <=> AC -> cubic equation Build-up is analogous from mass balances & interaction equations: e..g. Kd1 = [A] + [B] /[ AB] variables: Kd1, [A], [B], [C], [AC] Kd 2 = [A] + [C]/ [AC] Kd2 determined separately [C]tot = [C] + [AC] [AB] dependent variable [B]tot = [B] + [AB] [A]tot = [A] + [AB] + [AC] 16 Inhibition curve Fitting: protein 100 Direct binding 80 Kd1< Kd 2 Kd1 > Kd2 60 40 20 Fluorescence anisotropy Fluorescence 0 0 1 2 3 Concentration of unlabeled target [µM] 17 Application of nonlinear curve fitting for elucidation of binding mechansim Meisner, Hintersteiner et al. Experiment Nat. Chem. Biol. 2007, 3 (8), 508 0.24 ARE IL-2 + HuR Kd = 15.82 nM 0.2 + cpd at 1 µM + cpd at 5 µM 0.16 + cpd at 20 µM Anisotropy 0.12 0 20 40 60 80 100 HuRfl [nM] Protein RNA (fl labeled) cpd 18 19 Single molecule detection technologies Ensemble Single molecule 20 21 Principle of confocal detection Laser Optics f f Pinhole Ø = 50 µm Detector Detector 22 Fluorescence only from the confocal focus: the size of an E. coli bacterium FCS and HTS Screening • Insensitive to Miniaturisation (Volume 10-15 l) • Potential to Cover ALL Fluorescence Techniques • Improves Well to Well and • Assay to Assay Quality Control • Concentrations Free of Artefacts • On-line Mechanistic Characterisation • Throughput > 100 000 a day. 23 In general, same setup as for bulk fluorescence is used for single molecule methods except: - light source is laser/diode - detector is APD (avalanche photo detector) Two types of techniques: a) Single channel Fluorescence D Pin-hole beam splitter b) Multiple channel e.g. polarized D vertical or color Or Color 1 Fluorescence D Polarization splitter horizontal Pin-hole Or color split Or Color 2 24 FCS: Fluorescence Correlation Spectroscopy FCS provides information about intermolecular interactions from tiny fluctuations. FCS can retrieve 1/N - local concentrations tdiff - motility coefficients - rate constants: Kd, Ka - enzyme kinetics - … tdiff : transl. diffusion time 1/N 1/N : particle number tdiff • Refs: Magde et al., Phys. Rev. Let.29, 1972; Rigler et al., Eur. Biophys. J. 22, 1993 25 FIDA: Fluorescence Intensity Distribution Analysis FIDA allows identifying multiple species and their concentrations by analyzing the molecular-specific brightness FIDA Binding Study - Case 1: FIDA Binding/Aggregation Study - Case 2: binding-induced change in dye (label) fluorescence intensity binding-induced accumulation of dye fluorescence qI qI qII > qII > q : molecular brightness q q : molecular brightness II qI qII qI - fluorescence quenching / enhancement The molecular brightness parameter can be perturbed by - induced spectral shift of fluorophore • Refs: Kask et al. PNAS, 1996; Chen et al. Biophys. J. 77, 1996; - fluorescence resonance energy transfer Buehler et al., Springer Series on Fluorescence 1, 2001 - multiple binding sites for labelled molecules 26 - … - two-dimensional data acquisition - SAMPLE Possible Applications Beam expander • 1 color excitation / 2 color emission (FRET, Spectral Shift, etc.) Microscope objective LASER DICHROIC MIRROR • 2 color excitation / 2 color emission Optical filter (Coincidences like Tubus lens Cross Correlation, 2C-2D-FIDA etc.) • Polarized excitation / Polarized emission (Polarization, Anisotropy, etc.) PINHOLE Beamsplitter or DETECTOR #2 Polarization cube Color filters DETECTOR #1 2D-FIDA 27 2D-FIDA – Analysis of molecular brightness in 2 channels • 2D-FIDA is a general method that provides multi-dimensional analysis of two simultaneously recorded brightness distributions. • 2D-FIDA may be configured for - polarization► molecular rotation -> single molecule analog of Anisotropy - two-color ► molecular brightness - FRET ► molecular energy transfer • Refs: Schwille et. al., Biophys.