CD69 response explorer

How to read the plot

• Each colored line is one peptide: the fraction of CD69+ cells as the pMHC concentration rises.
• The lines sit at their peptide's KD along the depth axis. Higher KD means weaker binding.
• The dashed line on the floor is the potency P₁₅: the pMHC concentration that makes 15% of cells CD69+. It has gaps where the response never reaches 15%.
• The dots are the P₁₅ of the five peptides, and the red line is a straight-line fit through them on log scales.
• Rotate to look straight down on the floor to see that line's true slope.

Discrimination power

Pettmann et al. measured how sharply T cells tell peptides apart by fitting a straight line to log P₁₅ against log KD across a panel of peptides (eLife 2021). The slope is the discrimination power. A receptor that only counted bound peptides would give 1; they found about 2 for T cells.

The dashed line is curved, so its local slope also changes along the panel. Where binding is tight, almost every receptor stays bound whatever the KD, and the slope is low. Where binding is weak, proofreading filters out short contacts, and the slope is high. The slope also climbs steeply wherever a peptide's top response falls close to 15%.

The model

The model passes the signal through four stages, each in closed form.

1. Binding. Receptors and peptides bind in the contact between cells, giving the density of bound complexes $$C_T=f_A\frac{b-\sqrt{b^2-4\alpha x{T}_T}}{2},b=\alpha x+T_T+\frac{{\tilde{g}}_1{K}_D}{k_{\text{on}}^{\text{2d}}}$$ where x is the pMHC concentration.
2. Proofreading. A bound complex must pass several steps before it signals, and it may let go at each one: $$C_N={(1+\frac{{\tilde{g}}_1{K}_D}{k_P})}^{-n_{\text{KP}}}{C}_T$$
3. Switch. Inside the cell, the signal flips a switch once enough complexes finish: $$X=\frac{C_N^{n_C}}{C_N^{n_C}+{\lambda }_X^{n_C}}$$
4. Output. The switch sets the fraction of cells that show CD69: $$O_1=O_1^{\text{max}}\frac{X}{X_{O_1}+X}$$

The five peptides and their KDs (7.97 to 299 µM) are from Aleksic et al. (Immunity 2010). The model is from a manuscript in preparation.

What the parameters mean