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4 Cellular Frustration Can Establish the Principles of an Immune
System
The purpose of this work is to show that cellular frustration provides an alternative
framework that explains self-nonself discrimination not as a two-cell process, but as
an emerging principle of the whole system. Cellular frustration is compatible with a
somatically generated immunological repertoire; it avoids the existence of holes in
shape space, while maintaining perfect specific tolerance.
To understand why this can happen we question whether there can be a system of
mutually interacting elements, which can all potentially react but never reach this
state because they are frustrated due to interactions with other elements in the system?
Here by interaction we mean the process during which two cells sense each others
ligands through their receptors and by reaction it is meant an effector function that
only takes place if two cells interact for a time longer than a characteristic time T.
As it is known from the study of the stable roommate problem [44], it is possible to
define a set of mutually interacting elements that never reach the reaction state
described above. To exemplify this, consider a simple system made of 3 cells, A, B and
C. Assume that each of these cells promote interactions according to an interaction list
(Table 1), in such a way that, if given a chance, they always promote interactions with
cells that are on upper positions in their interaction list (IL). Then it is easy to verify that
all associations are unstable due to the possibility of contacting with the third cell.
Table 1.
Interaction List (IL) for a system of three frustrated cells. In each column the IL of the
cell on the top line is defined. According to this list, cell A tries to bind to cell C, if it is
unbound: however,if given the opportunity, it would bind to cell B and detach from cell C. This
sequence of interactions corresponds to the one described in Fig.1.
A
B
C
B
C
A
C
A
B
Consider a simple algorithm in which at each time-step each cell is given an
opportunity to interact with another cell. Thus, in each time-step, a new conjugate can
be established and a former one terminated. In the simple case in Table 1, at each time-
step the probability that a new interaction is established at the expense of a former
interaction, is 1, because there is always one bound cell that interacts but prefers another
cell. In this particular system, provided interactions do not lead to instantaneous
reactions, the system is frustrated, and thus in a tolerant or homeostatic state.
An interesting situation arises when one adds a new cell into the frustrated system.
If one considers that there are no identical cells, then cell D has to appear on the
bottom of the ILs of all the other cells, otherwise the system comes out of the tolerant
state. Hence, to keep the system in the tolerant state, the fourth cell D has very
specific ligands. Yet, the IL of cell D is arbitrary. Hence, tolerance or 'foreignness' is
determined by the system itself and the system is very sensitive relatively to the
introduction of new cells. In fact, from all the possible ILs for cell D, only
1/27<4%
keep the system frustrated in this simple system.
