Outline
● Context ● Saturation experiment Which method to estimate Kd ● Competition experiment ● Fluorescence Polarization and Ki in fluorescence ● Advantages polarization? ● Principle ● Estimation of Kd in fluorescence polarization ● Comparison of models ● Examples & Simulations Methodology and Examples ● Estimation of Ki in fluorescence polarization ● Comparison of models ● Examples & Simulations Armel Salangros (Freelance contractor) Dorothée Tamarelle (Keyrus Biopharma) ● Conclusion Véronique Onado (Sanofi)
| 2
Two basic types of ligand binding experiment Context: Ligand Binding Assay 1 – Saturation experiment ● A binding assay is used to measures the amount of binding or affinity In saturation binding assays, a labelled ligand, [L*], binds to a receptor, [R] between two molecules. There are numerous types of ligand binding k k1 1 assays. + [R] + [L*] [RL*] k k2 2 ● Widely applied in life science 1.0 ● Conservation of mass requires : 0.9 [L* ]= [L*] + [RL*] and [R ] = [R] + [RL*] 0.8 T T 0.7 with L* , total concentration of labelled ligand ● Examples T 0.6 0.5 RT, total concentration of receptor ● Targeting protein-protein interactions 0.4 0.3
• Protein–protein interaction (PPI) can contribute to many diseases, including binding Specific ● At equilibrium: k1 [L*] [R] = k2 [RL*] 0.2 Kd cancer, and plays a key role in maintaining the malignant phenotype in tumor 0.1 0.0 cells. Selective, small-molecule modulation of PPIs is therefore an area of k2 [ L* ] [ R ] 0 50 100 150 interest to pharmaceutical science. Kd = = Receptor concentration (nM) k1 [ L*R ] ● The equilibrium dissociation constant (Kd) provides a measure of affinity ● Two basic steps: saturation and competition experiments between the receptor [R] and the labelled ligand [L*]
| 3 | 4
1 Two basic types of ligand binding experiment Outline 2 – Competition experiment In competitive binding assays, an unlabelled ligand (competitor), [L], binds to a ● Context receptor [R] in competition with a labelled ligand, [L*]. ● Saturation experiment ● Competition experiment [R] + [L*] [RL*] + ● Fluorescence Polarization [L] ● Advantages 1.0 ● Principle 0.8 ● Conservation of mass requires : Estimation of Kd in fluorescence polarization 0.6 ● [L*T]= [L* ]+ [RL*] [LT] = [L] + [RL] [RL] ● Comparison of models 0.4 [RT ]= [R] + [RL*] + [RL] ● Examples & Simulations
Specific Binding 0.2 with [L*T]& [RT ],, total concentration of labelled ligand and receptor 0.0 ● Estimation of Ki in fluorescence polarization [LT ], total concentration of unlabelled ligand 1 10 100 1000 ● Comparison of models [ L ] [ R ] Unlabelled ligand (nM) ● Examples & Simulations ● At equilibrium: Ki = [ LR ] ● Conclusion ● When the Kd of the labelled ligand [L*] is known, the equilibrium inhibition constant (Ki) provides an indirect measure of affinity between receptor [R] and unlabelled ligand [L]
| 5 | 6
Why use Fluorescence Polarization? FP principle and signal expression
● Previously, traditional radioligand binding experiments were widely used for ● Fluorescence Polarization (FP) assays are based on measuring the saturation and competition experiments polarization (P) of light caused by changes in molecular size.
● Fluorescence Polarization (FP) is one alternative to the traditional binding ● The rotational speed of a molecule is decreased once it is bound to a radioligand experiments, in particular for small molecules receptor. ● Application areas of FP: • Protein/Protein interactions • Enzyme/Substrate • Antigen/Antibodies • … ● Fluorescence Polarization (FP) offers numerous advantages over the more conventional methods: ● Can be used in HTS ● Faster and highly reproducible results (low variabilities intra/inter experiment) ● No separation of bound and free ligand required ● Polarized emission can be measured by polarization and anisotropy, r. ● No radioactive materials
| 7 | 8
2 Relationship between anisotropy (r) and Fbound Outline
● In FP, there is no necessity for separation of bound and free ligand ● Context ● Saturation experiment ● Competition experiment ● The fraction of bound to free, Fbound, is directly deduced from the anisotropy, r, using the equation: ● Fluorescence Polarization ● Advantages
* ● Principle binding _ site _ occupied [RL ] r rfree Fbound * total _ ligand [L T ] rbound r Q (r rfree ) ● Estimation of Kd in fluorescence polarization ● Comparison of models ● Examples & Simulations Where rfree is the anisotropy of the free labelled ligand,
rbound is the anisotropy of the ligand-protein complex at saturation and Q is the ratio of fluorescence intensities of bound versus free ligand ● Estimation of Ki in fluorescence polarization ● Comparison of models ● Examples & Simulations ● The binding of a ligand to a receptor is expressed by the fraction of bound receptors Fbound ● Conclusion
| 9 | 10
Estimation of Kd in saturation experiment in FP Examples of estimations of Kd in FP
● Fbound = (binding sites occupied) / (total ligand) = [RL*] / [L*T] ● In FP experimental assay, when can we assume the assumption of no receptor depletion? ● Fbound allows to estimate the affinity a ligand has to a receptor (Kd): [R] + [L*] [RL] ● Example 1: ● [L*T ] =1.5 nM
Kd = [R] [L*]/ [RL*] ● [RT ] is between 0.002 nM to 257.2 nM ● Example 2:
Case 1: Specific case Case 2 : General case ● [L*T ] =10 nM ● [RT ] is between 2.5 to 1280 nM
[RT] >> [L*T] [R] ≈ [RT] [RT] not >> [L*T] [R] = [RT] - [RL*] Kd [95%CI] (nM) • Assumption of no receptor depletion Kd [95%CI] (nM) Examples Case 1: [R] ≈ [R ] T Case 2: [R] = [RL*] – [R ] No receptor depletion T * * * [RL ] [R ] [RL ] a a² 4[R ][L T ] F T F T Example 1 1.417 [1.230 ; 1.604] 0.702 [0.607 ; 0.798] bound * bound * * [L T ] Kd [RT ] [L T ] 2[L T ] Example 2 7.336 [5.774,8.898] 3.230 [1.880,4.581]
* In those examples, there is a factor around 2 between both methods to estimate with a (Kd [RT ][L T ]) ● the equilibrium dissociation constant Kd.
| 11 | 12
3 Simulations for Kd estimation Outline
● Design ● Context ● Saturation experiment ● The FP were generated using receptor L*T=100nM depletion hypothesis model (case 2) ● Competition experiment with the following factors: -4 4 Fluorescence Polarization • [RT] concentrations: 2.10 to 1.10 nM ● * ● Advantages • [L T ] concentrations: [0.1 1 10 100] nM L*T=10nM • Theoritical Kd from 0.1nM to 100nM ● Principle
Experimental example 2 ● Estimation of Kd in fluorescence polarization
L*T=1nM ● Comparison of models ● Examples & Simulations Conclusion: providing [L* ] < 10% of Experimental example 1 * ● T L*T=0.1nM [L ] T 0.1 Kd, we can assume that [R] ≈ [RT ] Kd ● Estimation of Ki in fluorescence polarization ● Comparison of models ● Examples & Simulations
● Conclusion
| 13 | 14
Estimation of Ki in competition experiment Methods based on equation
● The affinity of the competitor, unlabelled ligand [L], for the receptor [R] ● Shared assumptions can be indirectly determined by measuring its ability to compete with, ● A single class of receptor binding sites and thus inhibit, the binding of a labelled ligand [L*] to its receptor ● Assay is at equilibrium [R]+ [L*] [RL*] IC [L* ] concentration of labelled ligand [R]+ [L] [RL] ● Cheng-Prusoff equation K 50 Where i * K d dissociation cons tan t of labelled ligand [RL] + [L*] [RL*] + [L] ● [R] ≈ [RT ] [L ] * * ( 1) ● [L ] ≈ [L T ] K d ● The affinity of the unlabelled ligand for the receptor can be obtained ● Nikolovska-Coleska & al. equation from different methods: ● [R] = [RT ] - [RL] ● Estimation of constant of inhibition (Ki) * * ● [L ] = [L T ] - [RL] [R ] Initial concentration of receptor • The Cheng-Prusoff equation 0 [L ] [L] Concentration of unlabelled ligand • The Nikolovska-Coleska & all equation 50 * * 2 0.5 [R ] ((K [L ] [R ]) ((K [L ] [R ]) 4[R ]K ) ) / 2 Where 0 d1 T T d1 T T T d1 K i * • … [RL ] [R ] [R ] [L50 ] [R0 ] 0 T 0 * * ● Direct estimation of the affinity of the competitor (Kd2) ( 1) [RL ] [RL 0 ]/ 2 50 • The Wang exact mathematical expression K d [L* ] [L* ] [RL* ] 50 T 50 [L ] IC [R ] [RL* ](1 K /[L* ]) 50 50 T 50 d1 50
| 15 | 16
4 Wang model: An exact analytical treatment of Comparison of Ki competitive binding ● Wang has described an exact expression of competitive binding: ● Example 1: K K ● [L*T ] = 1.5 nM and [RT ]= 6 nM d1 d2 [RT ] [RL*][RL][R] R L* RL * R L RL ● [LT ] is between 0.51 nM to 10000 nM [R][L*] [R][L] Conservation of mass requires: * ● Kd = 1.08 nM and IC50 = 22.3 [17.5 ; 28.6] nM K (Eq.1) K (Eq. 2) [LT ] [RL*][L*] d1 [RL*] d 2 [RL] [L ] [RL][L] (Eq. 3) T ● Example 2:
● After substitution and rearrangement, this leads to the following equation: ● [L*T ] = 10.0 nM and [RT ] = 20.0 nM ● [LT ] is between 0.67 to 238 nM ● Kd = 3.23 nM and IC50 = 68.1 [40.1 ; 115.3] nM a K K [L ] [L* ] [R ] 2 a 2 3b cos a d1 d 2 T T T [RL*] 3 b K [L* ] [R ] K [L ] [R ] K K F Where d 2 T T d1 T T d1 d 2 Corrected Ki Kd2 bound * Experiment Ki [LT ] 2 3K 2 a 3b cos a c K d1 K d 2 [RT ] Cheng Prusoff Nikolovska-Coleska & al. Wang model d1 3 Example 1 9.35 2.81 3.14 [2.395 ; 3.888]
Example 2 16.62 7.33 5.34 [3.896 ; 6.778] ● [RT ] and [LT] are the experimental constants ● Kd1 must have been previously obtained from a direct binding experiment
| 17 | 18
Simulations of competition experiment (1) Simulations of competition experiment (2) Simulation & Exemple 1 Simulation & Exemple 2
● Design Exp.Cheng Exp.Cheng Prusoff Ki ● FP were generated using the Wang model under 2 experimental conditions Prusoff Ki with the following factors: Cheng-Prusoff ki Cheng-Prusoff ki Exp. Corr. Ki • [LT ] is between 0.1 nM to 10000 nM Exp. Corr. Ki • Theoretical Kd2 of competitor from 0.1nM to 10nM • 1st simulation (Example 1): L*t=1.5 nM L*t=10 nM Rt=6 nM Rt=20 nM Corr. Ki • [L* ] = 1.5 nM [R ] = 6 nM and Kd=1.08 nM Kd=1.08 nM Kd=3.23 nM T T Corr. Ki • 2nd simulation (Example 2):
• [L*T ] = 10 nM [RT ] = 20 nM and Kd=3.23 nM
● EC50, Cheng-Prusoff Ki and Coor. Ki (Nikolovska-Coleska & al.) were ● In these experimental conditions: estimated. ● the Cheng-Prusoff Ki was over estimated ● The Corr. Ki was: • always lower than the Cheng-Prusoff Ki • very close to the affinity of the competitor simulated with the Wang model (Kd2)
| 19 | 20
5 Conclusion References
● In FP, classical binding models need to be adapted to the Fbound ● Michael H A ROEHRL, Julia Y WANG, Gerhard WAGNER. “A general framework for development and data analysis of competitive high-throughput ● Which method to estimate Kd in FP? screens for small-molecule inhibitors of protein-protein interactions by
● The classical model, [R] ≈ [RT], is not well adapted: over estimation of Kd fluorescence polarization.”, Biochemistry, 2004, 43 (51), 16056-16066. The general model, taken into account the receptor depletion [R] = [R ] – [RL*], must be used in ● T ● Zhi-Xin WANG. “An exact mathematical expression for describing FP experiments competitive-binding of 2 different ligands to a protein molecule.”, FEBS Letters, 1995, 360, 111-114. ● Which method to estimate Ki in FP? ● Ki calculated with Cheng-Prusoff biaised the affinity of a competitor for a receptor ● Zaneta NIKOLOVSKA-COLESKA and al. “Development and optimization of ● The Nikolovska-Coleska equation (corr. Ki) and the exact analytical treatment of competitive a binding assay for the XIAP BIR3 domain using fluorescence polarization.”, binding (Wang model) are equivalent methods: Anal. Biochem., 2004, 332, 261-273. • Advantage of Wang model : 95% confidence interval is estimated Xinyi HUANG. “Fluorescence polarization competition assay: the range of • Advantage of Corr. Ki : equation for uncompetitive inhibition is available ● • Both methods: difficult to generalize in particular cases as dimeric models resolvable inhibitor potency is limited by the affinity of the fluorescent ligand.”, J Biomol Screen, 2003, 8, 34-38.
| 21 | 22
Back-up slides Estimation of Kd in saturation experiment in FP
● Fbound = (binding sites occupied) / (total ligand) = [RL*] / [L*T]
● Fbound allows to estimate the affinity a ligand has to a receptor (Kd): [R] + [L*] [RL]
Kd = [R] [L*]/ [RL*]
Case 1: Specific case Case 2 : General case
[RT] >> [L*T] [R] ≈ [RT] [RT] not >> [L*T] [R] = [RT] - [RL*] • Assumption of no receptor depletion
* * * [RL ] [R ] [RL ] a a² 4[R ][L T ] F T F T bound * bound * * [L T ] Kd [RT ] [L T ] 2[L T ]
* with a (Kd [RT ][L T ])
| 23 | 24
6 Estimation of Kd in saturation experiment in FP Estimation of Kd in saturation experiment in FP
● Case 1: Specific case ● Case 2: General case ● Assumption of no receptor depletion ● Assumption of receptor depletion * * * [L ][R] [R] [RT ] [L ][R] [R] [RT ] [RL ] Kd * * * Kd * * * [RL] [L ] [LT ] [RL ] [RL] [L ] [LT ] [RL ]
* ([LT ] [RL])[RT ] * * * * * * * K ([LT ][RL ])([RT ][RL ]) d K Kd [RL ] ([LT ][RL ])([RT ][RL ]) [RL] d * [RL ] * * ([LT ] [RL])[RT ] ([LT ] [RL])[RT ] [RL][RT ] Kd [RT ] [RT ] Kd [RT ] * * * * * * * * [RL] [RL] [RL] K d [RL ] ([LT ][RL ])([RT ][RL ]) 0 [RL ]² (K d [RT ] [LT ])[RL ] [RT ][LT ]) 0 * [LT ][RT ] [RL][RT ] [RL][RT ] * * * K [R ] * (Kd [RT ][LT ]) (Kd [RT ] [LT ])² 4[RT ][LT ] d T [RL] [RL ] 2 * [LT ][RT ] * * * Kd [RT ] (K [R ][L ]) (K [R ] [L ])² 4[R ][L ] [RL] [RL*] d T T d T T T T 2 * [RL ] [RT ] * * * * F [RL ] (Kd [RT ] [LT ]) (Kd [RT ][LT ])² 4[RT ][LT ] bound * F [L T ] Kd [RT ] bound * * [LT ] 2[LT ]
| 25 | 26
Wang model: An exact analytical treatment of Wang model: An exact analytical treatment of competitive binding (1) competitive binding (2) ● Wang has described an exact expression of competitive binding: ● The only meaningful solution of Eq.7 can be written as in Eq.8 and the expression K K of is given in Eq. 9. R L *d1 RL * R L d2 RL [RT ] [RL*][RL][R] * 3 [R][L*] [R][L] Conservation of mass requires: [L ] [RL*][L*] a 2 2 2a 9ab 27c Kd1 (Eq.1) Kd 2 (Eq. 2) T [R] a 3b cos where arccos (Eq.8) [RL*] [RL] [L ] [RL][L] (Eq. 3) 3 3 3 2 3 T 2 a 3b ● Expressing [RL*] and [RL] as function of total ligand (L*T) and total competitor 2 a2 3b cos a [RL*] [R] concentrations (LT) yield Eq.4 and 5 3 (Eq.9) * * [LT ] Kd1 [R] 2 [R][L ] [R][L ] 3Kd1 2 a 3b cos a RL* T (Eq. 4) RL T (Eq. 5) 3 Kd1 [R] Kd 2 [R] a K K [L ][L* ] [R ] ● Substitution of Eq.4 and 5 in Eq. 3, yields Eq. 6, which after rearrangement Where d1 d 2 T T T * corresponds to the cubic Eq. 7 b Kd 2 [LT ][RT ] Kd1 [LT ] [RT ] Kd1 Kd 2
* c Kd1 Kd 2 [RT ] [R][LT ] [R][LT ] [RT ] [R] (Eq.6) Kd1 [R] K d 2 [R] a K K [L ][L* ] [R ] d1 d 2 T T T ● [RT ] and [LT] are the experimental constants 3 2 [R] a[R] b[R] c 0 (Eq. 7) Where b K [L* ][R ] K [L ] [R ] K K d 2 T T d1 T T d1 d 2 ● Kd1 must have been previously obtained from a direct binding experiment c Kd1 Kd 2 [RT ]
| 27 | 28
7