framework for experimental TCR-pMHC kinetic rates Jose Faro - - PowerPoint PPT Presentation

A unifying mathematical framework for experimental TCR-pMHC kinetic rates

Jose Faro

together with Carmen Molina-París & Mario Castro

University of Leeds Closing Conference QuanTI Marie Curie-Initial Training Network – April 19-21, 2017

Recognition of pMHC molecules by TCRs determines T-cell selection, development, differentiation, fate, and function. Despite intensive studies on kinetic rates, classification of T-cell ligands was inconsistent with the biological outcome of that interaction.

Introduction

Introduction

Effective 3D affinity (Ka, µM–1) Effective 3D on-rate (kon, M–1s–1) Effective 3D off-rate (koff, s–1)

1/EC50 (M–1)

EC50 (M), pMHC concentration required to reach half-maximal T-cell proliferation

J Huang et al (2010) Nature, 464:932; LJ Edwards et al (2012) Frontiers in Immunol, 3: article 86

Correlation between TCR-pMHC 3D kinetics and functional activity (T-cell proliferation) at 37 ºC

(symbols: ★, OVA; , A2; ×, G4; , V-OVA; ☐, E1; , R4)

Two landmark papers in 2010 disclosed essential differences between classical, 3D assays and assays in which TCRs and their pMHC ligands are confined into a membrane (2D assays)

Introduction

J Huang et al (2010) Nature, 464:932; JB Huppa et al (2010) Nature, 463:963

Introduction

From J Huang et al (2010) Nature, 464:932 Effective 2D affinity (AcKa, μm4) Effective 2D on-rate (Ackon, μm4 s–1) Effective 2D off-rate (koff, s–1)

1/EC50 (M–1)

Correlation between TCR-pMHC 2D kinetics and functional activity (T-cell proliferation) at 37 ºC

(symbols: ★, OVA; , A2; ×, G4; , V-OVA; ☐, E1; , R4)

Zhu’s group

Introduction

Based on J Huang et al (2010) Nature, 464:932

Comparison between TCR-pMHC 2D kinetics vs 3D kinetics and functional activity (T-cell proliferation) at 37 ºC

(symbols: ★, OVA; , A2; ×, G4; , V-OVA; ☐, E1; , R4)

1/EC50 (M–1)

Effective 3D affinity (Ka, µM–1) Effective 3D on-rate (kon, M–1s–1) Effective 3D off-rate (koff, s–1) Effective 2D affinity (AcKa, μm4) Effective 2D on-rate (Ackon, μm4 s–1) Effective 2D off-rate (koff, s–1)

1/EC50 (M–1)

SPR 3D Zhu’s group 2D

Large impact of dimensionality in the kinetics of those reversible chemical reactions.

• An inherent potential pitfall of 3D assays?
• Should we throw away all the previous 3D data?
• Are the new experimental methods the holy grail?

Are they free of interpretation?

Introduction

Introduction

The experimental conumdrum

• All experimental methods use “underlying models” to

extract data

– Langmuir – Probabilities of engagement – …

• Most of the methods are “binary”

– “Free reactants” → “Bound complexes”

 Experimental setups of 3D and 2D assays  Reformulate the problem (mathematically)  Analysis and clarification of kinetic models  Derivation of formulations in terms of the intrinsic constant rates  Predictions

Outline

Experimental systems: 3D assays

• 1. Surface Plasmon Resonance (SPR). The interaction of the linked

molecule and the analyte are assumed to be well described by a simple Langmuir model:

Main 3D assays

• 2. FRET in solution. In this technique specific MHC-peptide complex and

TCR molecules, labeled with donor and acceptor fluorochromes, respectively, are mixed in solution in a small reaction chamber of a stopped-flow instrument. When the TCR and MHC-peptide are close enough and properly oriented the donor and acceptor dyes can generate a FRET signal. where C is the bound complex of A and B

Experimental systems: 2D assays

• 1. Adhesion frequency assay. A micropipette holds an erythrocyte

decorated with univalent pMHC molecules or an erythrocyte with a attached bead decorated with pMHC. With the help of another micropipette a T cell was positioned to touch the erythrocyte or the bead.

Main 2D assays

J Huang et al (2010) Nature, 464:932

Experimental systems: 2D assays

• 2. Thermal fluctuation assay. Based on the reduction/resumption
• f thermal position fluctuations of a pMHC-decorated bead

touching a TCR-transgenic T cell held in a fixed position. Beads’ fluctuation reduction is caused by bond formation between

• ne or more bead pMHCs and T-cell TCRs.

Main 2D assays

J Huang et al (2010) Nature, 464:932

Experimental systems: 2D assays

• 3. FRET on cell membrane. This experimental setting uses TCR-

transgenic T cells with the V-regions stained with a donor fluorochrome, MHC-peptide complexes tagged with an acceptor fluorochrome, and total internal reflection microscopy to allow single molecule FRET. When the TCR and MHC-peptide are close enough and properly

• riented the donor and acceptor dyes can generate a FRET
• signal. The duration in single synapses of FRET signals that

started and finished during an experiment recording was considered to correspond to bound time periods.

Main 2D assays

JB Huppa et al (2010) Nature, 463:963

 Experimental setups of 3D and 2D assays  Reformulate the problem (mathematically)  Analysis and clarification of kinetic models  Derivation of formulations in terms of the intrinsic constant rates  Predictions

DIVIDE AND CONQUER

Back to the classics

Binding steps involved in 3D and 2D systems Reactants Encounte r complex Oriented complex Molecular complex

     

{ { {

Diffusion Rotation Binding

Binding steps involved in 3D and 2D systems Ligand dependent Dimension independent Ligand independent Dimension dependent Ligand independent Dimension dependent

Only the binding step and molecular complex formation can potentially lead to an allosteric conformational change in the TCR

Mathematical kinetics models

The general model

Reactants Encounter complex Oriented complex Molecular complex

Kinetics models Reactions and chemical species assumed in different experimental systems Effective rates mean different things in different contexts…

 Experimental setups of 3D and 2D assays  Reformulate the problem (mathematically)  Analysis and clarification of kinetic models  Derivation of formulations in terms of the intrinsic constant rates  Predictions

Mathematical kinetics models ⟨RL⟩ = RL* + RL

Pre-binding model A

Mathematical kinetics models ⟨C⟩ = C + RL

Pre-binding model B

Mathematical kinetics models ⟨R⟩ = R + RL*, ⟨L⟩ = L + RL*, and ⟨C⟩ = C + RL

FRET model

Mathematical kinetics models

This is the classical model Single-step model

 Experimental setups of 3D and 2D assays  Reformulate the problem (mathematically)  Analysis and clarification of kinetic models  Derivation of formulations in terms of the intrinsic constant rates  Predictions

Models’ reduction: formulations in terms of the intrinsic constant rates

Pre-binding model A assumptions:

LOCAL STEADY-STATE BALANCE

⟨RL⟩ = RL* + RL

and

Models’ reduction: formulations in terms of the intrinsic constant rates

Pre-binding model A :

LOCAL STEADY-STATE BALANCE

Equations with effective rates Equations with intrinsic rates

YOU SAY I SAY

2D 3D 2D 2D 2D 3D 3D 2D 2D 3D 2D 2D 3D

TF assay TF assay TF assay TF assay bulk FRET SMFM SM-FRET SM-FRET bulk FRET AF assay AF assay SPR SPR

Assay D Value rate Model PBA PBB FRET Single-step

 Experimental setups of 3D and 2D assays  Reformulate the problem (mathematically)  Analysis and clarification of kinetic models  Derivation of formulations in terms of the intrinsic constant rates  Predictions

Predictions

Comparisons: AF vs true binding

• n-rates

Effective 2D on-rate (Ackon, μm4 s–1)

1/EC50 (M–1)

• ff-rates

Effective 2D off-rate (koff, s–1)

(data is from AF assays)

Zhu got it right!!

≈

Predictions

Comparisons: AF vs 2D FRET

Effective 2D on-rate (Ackon, μm4 s–1)

1/EC50 (M–1)

• n-rates

Effective 2D off-rate (koff, s–1)

• ff-rates

(data is from AF assays)

≈ ≈

Effective 3D off-rate (koff, s–1)

• ff-rates

Predictions

Comparisons: SPR vs 3D FRET

Effective 3D on-rate (kon, M–1s–1)

1/EC50 (M–1)

(3D)

• n-rates

(3D)

(data is from SPR assays)

FRET and 3D assays are bad predicting ligand potency

2D 2D 3D 3D

But…

FRET can provide useful microscopic information

Comparison of dimensional rotational rates Indirect computation of rotational rates

Predictions

This framework allows us to rationalize and compare the different experimental results in the literature

• 2D AF assay is best (with caveats)
• FRET can be misleading but also unexpectedly

useful

• 3D Assays are also misleading

Conclusions

Financial support:

Acknowledgements

THANK YOU!

Vigo and Cíes islands Vigo long bay