Thymic Selection

Thymic Selection

Immunological tolerance of the T cell repertoire is shaped in the thymus gland:

thymus

where a diverse repertoire of thymocites (expressing distinct TCRs, produced by random recombination)

is culled by encounters with self pMHC, via

Negative selection: TCR must not bind any self pMHC too strongly

(deleting autoimmune TCR).

Positive selection: TCR must bind sufficiently strongly to at least one self pMHC

(implicated in MHC restriction, and sensitivity).

Model for Thymic selection [Kosmrlj, Jha, Huseby, Kardar, & Chakraborty, PNAS 105, 16671 (2008) (offlline)]

Candidate TCR, sequences of N amino-acids, are randomly generated. (This ignores potential V(D)J generation bias.)

model

The binding energy of any TCR is calculated against a repertoire of M self-peptides.

(Experimental justification)

Binding energy E: Assume pairwise interactions between aligned amino-acids of peptide and TCR (Miazawa-Jernigan matrix J)

What are characteristics of amino-acids in the post-selection TCR repertoire?

Simulations were performed for TCRs of length N=5 and varying values of M

(strong binding) (weak binding)

(Typical number of peptide encounters in thymus is 1,000-10,000)

Tolerance => Specificity: TCR recognition results from cooperative binding of weakly interacting amino-acids (team effort).

Observations in transgenic mice [Huseby, et. al, Nat Immunol 7, 1191 (2006)]

Created mice expressing only one self peptide (M=1) in their thymus!

Compared specificity of TCRs from normal and transgenic mice to mutations of a recognized peptide.

Normal mice TCR typically do not recognize peptides after single site mutations,

while transgenic mice TCR are tolerant of most single site mutations, except at a few "hot spots".

Elite controllers of HIV appear to better tolerate mutations of the virus. Is a similar mechanism at play?

A. Košmrlj, ..., A.K. Chakraborty, Nature online (5 May 2010) WebMed, ...

Selective enrichment of amino-acids in TCR.

Connection to Statistical Physics:

The selection condition is equivalent to the choice of the Extreme Value:

Characteristics of the Extreme Value Distribution:

Binding energies of a particular TCR sequences:

Extremal mean value:

where and are the mean and variance of interactions of the candidate TCR sequence.

Extremal standard deviation:

Note scaling in the large N limit;           (proteome)

Due to the sharpness of the distribution in the large N limit, the deletion condition can be written as:

The above selection condition is reminiscent of the micro-canonical rule in Statistical Physics.

The "energy" involves interactions amongst the N amino-acids in the sequence

The "interaction" depends only on the sum of variances for the individual amino-acids

As such, in the large N limit, the probability to select a sequence can be written as a product

,

where and have to be obtained self-consistently from

and .

Graphical solution for