Download Models and Theory in Molecular Cell Biology

Models and Theory in Molecular Cell Biology
Reinhart Heinrich
Dept. of Theoretical Biophysics, Humboldt University Berlin
Invalidenstrasse 42, D-10115 Berlin
At present mathematical modelling in systems biology focusses to a large extent on
supramolecular processes taking place within individual cells. These processes are generally
organised in the form of reaction networks, such as metabolic pathways, signal transduction
networks and gene regulatory networks. In contrast to chemical reactions of inanimate nature
the biochemical processes are the outcome of evolutionary selection and are therefore
assumed to display specific structural and dynamical properties.
I will give an introductory overview on different networks which are of central biological
interest and are amenable to detailed mathematical treatment. These are two signal
transduction pathways called MAPK pathway and Wnt pathway which, upon stimulation by
extracellular ligands (hormones, growth factors etc.), control cell division and cell
differentiation, respectively. While these processes rely on mutual activation and inhibition of
interacting proteins, other processes are based on transiently assembled multiprotein
complexes, which perform, for example, DNA repair after damaging. All these processes are
of strong medical interest, since erroneous functioning may result in tumor formation, for
example colorectal cancer (Wnt pathway). I will demonstrate how the deterministic and
stochastic properties of such networks as observed experimentally can be adequately
simulated on the basis of systems of nonlinear differential equations (1-3) or systems of
Master equations. Only very recently intracellular transport and sorting of proteins taking
place via vesicular transport between different organelles (endoplasmic reticulum, Golgi
apparatus etc. ) became a subject of mathematical modelling (4).
Whereas modelling of specific cellular processes is already prevailing there are only a few
attempts to arrive at more general conclusions concerning structure and dynamics of cellular
processes. One theoretical approach applies optimization principles which may explain, for
example, the specific kinetic characteristics of single enzymes allowing high catalytic rates,
the most efficient distribution of enzyme amounts along pathways, special topological
properties, such as the location of ATP - consuming and ATP - producing reactions for fast
energy interconversion, or the specifics of temporal gene expression ("just-in-time
transcription of genes"). Several problems of that kind can be treated by evolutionary
algorithms (5). Recently, we developed a method for analysing the structural design of large
scale metabolic networks (6, 7). It is based on a network expansion which starts from a set of
seed compounds and ends in the scope of this seed, that is, all metabolites which can be
synthesized from these initial compounds. The method allows to identify critical compounds
and reactions, to characterize the robustness of the network against enzyme deletions, to
quantify distances between thousands of reactions or compounds etc. When starting from
small chemical building blocks network expansions allow to formulate hypotheses concerning
the temporal order of the emergence of metabolic pathways in the early phase of evolution
(7).
(1) Heinrich, R., Neel, B.G., and Rapoport, T.A. (2002) Mathematical models of protein kinase signal
transduction. Mol. Cell 9, 957-970.
(2) Lee, E., Salic, A., Krüger, R., Heinrich, R., and Kirschner, M. W. (2003) The roles of APC and axin derived
from experimental and theoretical analysis of the Wnt pathway. PLOS Biology 1, 116-132.
(3) Politi, A., Moné, M.J., Houtsmuller, A.B., Hoogstraten, D., Vermeulen, W., Heinrich, R., and van Driel, R.
(2005) Mathematical Modeling of Nucleotide Excision Repair Reveals Efficiency of Sequential Assembly
Strategies. Mol. Cell 19, 679-690.
(4) Heinrich, R. and Rapoport, T. (2005) Generation of nonidentical compartments in vesicular transport
systems. J. Cell Biol. 168, 271-280.
(5) Klipp, E., Heinrich, R., and Holzhütter, H.-G. (2002) Prediction of temporal gene expression. Metabolic
optimization by re-distribution of enzyme activities. Eur. J. Biochem. 269, 5406-5413.
(6) Binder, B. and Heinrich, R. (2005) Structural and Dynamical Analyses of the Kinase Network Derived from
the Transpath Database. Genome Informatics 16, 164-173
(7) Handorf, T., Ebenhöh, and Heinrich, R. (2005) Expanding Metabolic Networks: Scopes of Compounds,
Robustness, and Evolution. Journal of Molecular Evolution 61, 498-512.