The Genesis of Helper T cells and the Self-Nonself Model of Immune Regulation |

## Calculating the parameters and boundary conditions for the antigen independent pathway for the origin of effector T-helpers |

Link to Math details.

We use the symbol "**i**" to describe the **initial** state of
cells when they are incapable of expressing effector activity upon antigen
binding. An **i**-state cell is capable of responding to antigen, but
the response is not an expression of effector function. Antigen drives
**i**-state
cells to an **anticipatory** state (**a**Th), which in the absence
of further signals collapses into cell death. Under appropriate conditions
**a**-state
cells can become functional effectors, or **e**-state cells. The initial
decision to activate or inactivate is made when **i**-state cells fail
to progress to the **a**-state. In the unique case of **i**Th cells
after a sufficient lag, they become **e**Th. Of course the usual class
of antigens unavailable to drive **i**Th to **a**Th are antigens
that are not self. In contrast, persistent self antigens invariably drive
**i**Th
to **a**Th, and this leads to cell death because there are no **e**Th
that can give permission for **a**Th to become **e**Th.

We propose an antigen-independent pathway in which there is an antigen-independent differentiation of iTh to eTh, meaning that prior and persistent self antigen would block this pathway. A kinetic formulation is modeled here.

There is a steady state **N** = (**k1**x**G**) of newly
arriving **i**Th per unit time from the thymus. These cells are a mixture
of anti-Self (S) and anti-Nonself (NS) such that **SI** is the proportion
that are anti-S and (1.0 - **SI**) is the proportion anti-NS. There
is, therefore, a steady state production of **i**Th anti-S, **I**s
in number, that is equal to** SI**x**N** and of **i**Th anti-NS,
**I**ns**
**in
number, that is equal to (1.0 - **SI**)x**N**. We consider here the
steady state levels of each component in the absence of nonself and in
the presence of self.

The model is that **i**Th cells are generated at a steady state.
Those that are iTh anti-S interact with Self and are blocked (eventually
die through k6 pathway) from entering the antigen-independent pathway to
effectors. If the time to encounter Self is short compared to the time
to become an effector then a S-NS discrimination at the level of primer
eTh can be achieved in the absence of Nonself. The various pathways and
their rate constants,
**k**, are diagrammed.

The rate equations were derived and summed. This computer program allows
the user to vary the rate constants (**k**), the size of the Protecton
(**T**), the number of APCs per peptide, the repertoire size (**R**),
and the probability that an **i**Th cell will be anti-S is **SI**.
The rate constant, **k** per unit time, is related to the half
life of the cell, **k** = (ln2) / (t_{1/2}).

The output of the calculation is the steady state level of **I**s,**
A**s,
**E**s,** I**ns, **E**ns, and
**N **=** K1**x**G**
in the absence of Nonself. The decision as to whether the choice of parameters
are acceptable depends on the boundary conditions chosen to permit an effective
response to Nonself and a negligible response to Self.

A set of default input values are provided to illustrate what appears
to be an acceptable output. The choice of **SI**, as well as the basis
for choosing boundary conditions is discussed in:

References

- Cohn M., Langman R.E., and Mata J.J. (2002) A Computerized model for the self - non-self discrimination at the level of the Th (Th genesis). I. The origin of 'primer' effector Th cells. International Immunol. 14:1105-1112.
- Langman, R.E. and Cohn, M. (1999) The Standard Model of T-cell Receptor Function: A Critical Reassessment. Scand.J. Immunol. 49:570-577.
- Cohn, M. (1997) A New Concept of Immune Specificity Emerges from a Consideration of the Self-Nonself Discrimination. Cell. Immunol. 181:103-108.
- Langman, R.E. (1992) Was Everyone a "Little-bit-right" After All? Res. Immunol. 143-316-322.
- Cohn, M. (1992) The Self-Nonself Discrimination: Reconstructing a Cabbage from a Sauerkraut. Res. Immunol. 143:323-334.
- Cohn, M. and Langman, R.E. (1990) The Protecton: the evolutionarily selected unit of humoral immunity. Immunol.Reviews 115:1-131.

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