Theoretical Models of Immune Processes - Immunological Computation: Theory and Applications - page 37

the a nity class, α L B the rate at which L B die, k r the reverse rate constant, R i the
rescued centrocytes that migrate out of GC with rate m R R i , and η a fraction that
enters the memory compartment.
Although the Kesmir-Boer model (Kesmir and Boer, 1999) includes the T cell
dynamics, it contradicts with the OP model because it allows proliferation and
selection almost simultaneously and allows the proliferation of centrocyte complex
( C * ) and T cells after centrocyte selection. h e set of diff erential equations used in
Kesmir-Boer model is as follows:

dB
dt

(2.10)

*

PC B B

0

r 0 B 0

T

dB
dt

(2.11)

i

( 1 ) B B B

Bi 1 i Bi

dC
dt

(2.12)

dB C

n

*

dC
dt

(2.13)

CC
A

*

dM
dT

*

(2.14)

( 1 pC

r

)

T

dA
dT

zA uC A (2.15)

dT
dT

*

(2.16)

pC dT

TT T

A ), S is a saturation constant, P the C * recycle probability,
µ the C disappear rate, ρ the B cell division rate, δ B the B cell death rate, δ T the T cell
death rate, d the B to C phenotype conversion rate, z the A decay rate, u the C to C *
uptake rate, σ the initial T infl ux, and p the C * proliferation rate.
Another recent model called the Dasgupta, Kozma, and Pramanik (DKP) model
modifi ed the Kesmir-Boer model and simulated the GC dynamic with a cascade of
three Hopfi eld neural networks. It assumed that the migrated centroblasts are selected
by Ag and T cells for forming a complex within the FDC network. h is complex may
dissociate into memory or plasma cells and a centrocyte complex ( C * ) that feedback
to the proliferation chamber for further production of high-a nity centroblasts.

where C A = ( C.A ) / ( S +