Biology Reference
In-Depth Information
should be considered one pathway. With the complexity of cellular processes,
the uncertainty that arises from our limited ability to observe these processes
and take measurements, it becomes clear that the modelling process itself is of
interest.
In his topic
Life Itself
, Robert Rosen (1991) argues that mathematical mod-
elling in the Newtonian realm of physics - the world of mechanisms - is
inadequate to describe biological systems (organisms). The basis for his argu-
ment is a distinction between two approaches for mathematical modelling of
cellular systems: synthetic vs. analytic modelling. We are going to present the
mathematical foundation for this argument and show formally that there are ana-
lytical models which are not synthetic models. In other words, the conventional
way in which we model cells, cell function or pathways has a principal limit in
what we can know about the cell as a living organism. Rosen's discussion takes
place at a high level of abstraction, occasionally leaving the reader to fill in
details. We provide a concise summary of a formal framework in which one can
formalise the process of mathematical modelling of complex natural systems.
We maintain that such a framework is relevant for systems biology and hope
the present paper makes the work of Rosen more accessible.
2. MODELLING THE MODELLING PROCESS
Robert Rosen (1934-1998) was a theoretical biologist who focussed his career
on the question what it is that makes an organism alive. Rosen came to realise
that mathematical modelling in the Newtonian realm of physics - the world
of mechanisms - was inadequate to describe biological systems. On the basis
of the argument presented below, he introduced a class of metaphorical, rela-
tional paradigms for cellular activity, called (M,R)-systems (Rosen, 1971, 1991;
Wolkenhauer, 2001). Using concepts from category theory, he demonstrated the
minimal requirements that would have to be in place for a cell to be 'alive'. Lin-
ear systems interpretation of (M,R)-systems was assumed by Casti in the context
of engineering systems (Casti, 1988a,b). Further generalisation were considered
in the context of
Artifical Life
(Nomura, 2004) and in systems biology (Cho et al.,
2005). Letelier and coworkers related (M,R)-systems to autopoietic systems, as
well as metabolic networks (Letelier et al., 2003). Considering the fundamental
conclusions that can be drawn from Rosen's work, it is not surprising that the
concept has been challenged (e.g. Landauer & Bellman, 2002).
The discussion of how we try to understand intra- and intercellular dynamics,
using mathematical modelling and computer simulations, remains an important
question in the context of systems biology (Wolkenhauer & Mesarovic, 2005).
The purpose of the present text is, however, not a discussion of the validity of
Rosen's arguments but to provide a concise summary of the formal distinction
