Clas Blomberg - Physics of life-Elsevier Science (2007)

Chapter 33. Origin of life 375
itself, there cannot be any stationary situation with only P. The stationary features of X are
the same as in our previous case, and this will provide stationary values X 0 , M 0 . Now, one
easily see from the P-equation above that if (K p /g p ) (K x /g x ), then P can grow from small
values. In that case, a state with X 0 is not stable. P will increase, and by that decrease
the M-concentration to levels where X decreases. Eventually both components decrease.
Such a parasite can also occur in a co-operative network like the oscillating one
described above, and then again destroy the entire system. Its growth may be catalysed by
one of the components, and then compete with one of the original ones, eventually destroying
that and by that the entire system.
What has been suggested as a remedy to parasite threats is some kind of spatial organisation
(Eigen et al., 1980). Boerlijst and Hogeweg (1991) have considered a cellular
automaton model with rules corresponding to the hypercycles, which provides an organisation
where components change by spiral waves and where parasites are eliminated unless
they appear in a spiral centre. Such models can also be formulated to provide rotating clusters
of components (Cronhjort and Blomberg, 1996a; Blomberg and Cronhjort, 1994). In
such cases, parasites may destroy some cluster but not overtake the entire system. It was
also shown (Cronhjort and Blomberg, 1996b) for a model of one component as in eq.
(33.22) that a special co-existence situation could take place where a parasite appeared at
the surface of the cluster, but the main component could move away and prevent the taking
over by the parasite. On the other hand, a calculation based on a diffusion-reaction type of
model shows that the parasites could not be avoided in that kind of model description
(Cronhjort and Blomberg 1994). This is also studied by Andrade et al. (1993) and Chacon
and Nuño (1995). These models were made for motion in two dimensions. In three dimensions,
it is found that the spiral structure is no longer stable (Cronhjort and Nyberg, 1995).
These are model descriptions, but they show important problems together with the
hypercycle dynamics, problems similar to what may also occur in population biology. In
many ways, hypercycles comprise a kind of model for a proposed RNA world-scenario,
and these questions are there at any stage of early evolution where there appear components
with several roles (information carrier as well as catalyst) and where control mechanisms
are not sufficiently developed.