Basic Principles in Modeling Adaptive Regulation and Immunodominance - Mathematical Methods and Models in Biomedicine - page 35

1) Migration of APCs to lymph node

2) Initial T cell activation

s A

s K

kA 1 K 0
delay =

a(t)A 0

x 2 m

K 0

K

A 0

σ

A 1

A 1

3) Antigen-dependent proliferation 4) Effector cells differentiate into iTregs

kA 1 K
delay =

rK

x 2

K R

K K

ρ

A 1

5) iTregs suppress effector cells

kRK

K

R K

Fig. 1 Diagram of the iTreg model. (1) Immature APCs pick up antigen at the site of infection at a
time-dependent rate a . These APCs mature and migrate to the lymph node. (2) Mature antigen-

bearing APCs present antigen to naıve T cells causing them to activate and enter the minimal
developmental program of m divisions. (3) Effector cells that have completed the minimal program
continue to divide upon further interaction with mature APCs. (4) Effector cells differentiate into
iTregs at rate r . (5) The iTregs suppress effector cells. Although not indicated, each cell in the
diagram has a natural death rate

( t )

In both models, the number of regulatory cells is dynamically controlled. A
certain ratio of the effector cells are converted into regulatory cells. Such a process
is postulated to be controlled on the level of the individual cell possibly even in a
probabilistic way. There is no need for a central control of the number of regulatory
cells that depends on the total number of effector cells. Such a mechanism would be
biologically irrelevant. The precise means by which some of the effector cells turn
into regulatory cells is irrelevant for the present work. It is possible that asymmetric
differentiation is involved, or perhaps effector cells actually change their trait. In any
event, all that matters is that a certain fraction of the effector cells will eventually
turn into regulatory cells, due to a local process on the level of the individual cell.

2.1 Mathematical Model of Adaptive Regulation:

Feedback Loop

We start with the simple model for monoclonal T cell responses taken from [ 17 ].
This model can be summarized in five steps (illustrated in Fig. 1 ):

1. APCs mature, present relevant target antigen, and migrate from the site of
infection to the draining lymph node.