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

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

(implicated in MHC restriction, and sensitivity).

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

(deleting autoimmune TCR).


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: Assumepairwise 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)

Specificity of TCR comes from cooperative binding of weakly interacting amino-acids (team effort).

Verified 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 notmal 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, ...


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 sequencs:  

Extremal mean value:   

where  and  are the mean and variance of interactions of the candidateTCR sequence.

Extremal standard deviation:    

Note scaling in the large N limit;            (proteome)

Due to the shaprpness of the distibution in the large N limit, the seletion 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

   

Because of the restriction to an energy interval, there is a range of parameters where = 0.


  How well does this work for finite N? (N=5 and M=10.000)

A. Kosmrlj, A.K. Chakraborty, M.K., & E. Shakhnovich, PRL 103, 068103 (2009)

Selective enrichment of amino-acids in TCR.