Closing Conference QuanTI Marie Curie-Initial Training Network – April 19-21, 2017 A unifying mathematical framework for experimental TCR-pMHC kinetic rates Jose Faro together with Carmen Molina-París & Mario Castro University of Leeds
Introduction 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 Correlation between TCR-pMHC 3D kinetics and functional activity (T-cell proliferation) at 37 ºC 1/EC 50 (M – 1 ) Effective 3D on-rate Effective 3D off-rate Effective 3D affinity ( k on , M – 1 s – 1 ) ( k off , s – 1 ) ( K a , µM – 1 ) EC 50 (M) , pMHC concentration required to reach half-maximal T-cell proliferation (symbols: ★ , OVA; , A2; × , G4; , V-OVA; ☐ , E1; , R4) J Huang et al (2010) Nature , 464:932; LJ Edwards et al (2012) Frontiers in Immunol , 3: article 86
Introduction 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) J Huang et al (2010) Nature , 464:932; JB Huppa et al (2010) Nature , 463:963
Introduction Correlation between TCR-pMHC 2D kinetics and functional activity (T-cell proliferation) at 37 ºC Zhu’s group 1/EC 50 (M – 1 ) Effective 2D on-rate Effective 2D off-rate Effective 2D affinity ( A c k on , μ m 4 s – 1 ) ( k off , s – 1 ) ( A c K a , μ m 4 ) (symbols: ★ , OVA; , A2; × , G4; , V-OVA; ☐ , E1; , R4) From J Huang et al (2010) Nature , 464:932
Introduction Comparison between TCR-pMHC 2D kinetics vs 3D kinetics and functional activity (T-cell proliferation) at 37 ºC 1/EC 50 (M – 1 ) SPR 3D Effective 3D on-rate Effective 3D off-rate Effective 3D affinity ( k on , M – 1 s – 1 ) ( k off , s – 1 ) ( K a , µM – 1 ) 1/EC 50 (M – 1 ) Zhu’s group 2D Effective 2D on-rate Effective 2D off-rate Effective 2D affinity ( A c k on , μ m 4 s – 1 ) ( k off , s – 1 ) ( A c K a , μ m 4 ) (symbols: ★ , OVA; , A2; × , G4; , V-OVA; ☐ , E1; , R4) Based on J Huang et al (2010) Nature , 464:932
Introduction 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 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 ”
Outline 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
Experimental systems: 3D assays Main 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: 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 Main 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. J Huang et al (2010) Nature , 464:932
Experimental systems: 2D assays Main 2D assays 2. Thermal fluctuation assay . Based on the reduction/resumption of 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 one or more bead pMHCs and T-cell TCRs. J Huang et al (2010) Nature , 464:932
Experimental systems: 2D assays Main 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 oriented 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. 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
Back to the classics DIVIDE AND CONQUER
Binding steps involved in 3D and 2D systems Encounte Oriented Molecular Reactants { { { r complex complex complex Diffusion Rotation Binding
Binding steps involved in 3D and 2D systems Ligand independent Dimension dependent Ligand independent Dimension dependent Ligand dependent Dimension independent 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 Encounter Oriented Molecular Reactants complex complex 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 Pre-binding model A ⟨ RL ⟩ = RL * + RL
Mathematical kinetics models Pre-binding model B ⟨ C ⟩ = C + RL
Mathematical kinetics models FRET model ⟨ R ⟩ = R + RL *, ⟨ L ⟩ = L + RL *, and ⟨ C ⟩ = C + RL
Mathematical kinetics models Single-step model This is the classical 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 L OCAL STEADY - STATE BALANCE Pre-binding model A assumptions: ⟨ RL ⟩ = RL * + RL and
Models’ reduction: formulations in terms of the intrinsic constant rates L OCAL STEADY - STATE BALANCE Pre-binding model A : Equations with effective rates Equations with intrinsic rates
YOU SAY I SAY Model rate Value D Assay PBA 2D TF assay 2D TF assay PBB 2D TF assay TF assay 2D bulk FRET 3D SMFM 3D FRET 2D SM-FRET 2D SM-FRET bulk FRET 3D Single-step AF assay 2D 2D AF assay 3D SPR SPR 3D
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 on-rates off-rates ≈ 1/EC 50 (M – 1 ) Zhu got it right!! Effective 2D on-rate Effective 2D off-rate ( A c k on , μ m 4 s – 1 ) ( k off , s – 1 ) (data is from AF assays)
Predictions Comparisons: AF vs 2D FRET on-rates off-rates ≈ 1/EC 50 (M – 1 ) ≈ Effective 2D on-rate Effective 2D off-rate ( A c k on , μ m 4 s – 1 ) ( k off , s – 1 ) (data is from AF assays)
Predictions Comparisons: FRET and 3D SPR vs 3D FRET assays are bad predicting ligand potency on-rates off-rates 3D (3D) 3D 1/EC 50 (M – 1 ) 2D (3D) 2D Effective 3D on-rate Effective 3D off-rate ( k on , M – 1 s – 1 ) ( k off , s – 1 ) (data is from SPR assays)
Predictions But … FRET can provide useful microscopic information Comparison of dimensional Indirect computation of rotational rates rotational rates
Conclusions 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
Acknowledgements Financial support:
Vigo and Cíes islands Vigo long bay T HANK Y OU !
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