Statistical properties of microbial phenotypes and colony growth

Cells are the fundamental units of which all life forms are
composed. To understand the elementary organization of life, it is
therefore meaningful to start the investigation on the single cell
level.Modern microscopy permits the examination of both subcellular
processes and collective microbial behavior. In this microscopic
regime, fluctuations are of eminent importance. As this noise is an
inherent property of such systems, life evolved robust systems,
which work effectively in spite of severe fluctuations. Moreover,
life also makes use of these fluctuations for its benefit. For
modeling purposes in this field of research, concepts from
statistical mechanics and from the analysis of stochastic processes
can be applied to account for the fluctuations. This work is
roughly divided into two parts, which also address the background,
concepts and literature of the corresponding topics. The first part
is concerned with the modeling of intracellular processes, for
which noise is important. In this context two publications, which
arose from collaborations with experimental biophysicists, are
discussed: In gene therapy external genetic material is injected
into cells to remedy deficient behavior. To characterize this
process, fluorophore encoding plasmids were administered to
eukaryotic cells by means of two chemical transfection methods. The
distribution of expression levels is explained by several strongly
stochastic steps during transfection and subsequent
quasi-deterministic gene expression. The second collaboration
addresses the switching kinetics between different phenotypes in
bacteria. In the case at hand, the emergence of "competence" in B.
subtilis is studied. This ability (to take up genetic material from
the extracellular medium) is strongly regulated by a network of
interacting genes. While the different phenotypes are associated
with stable fixed points of non-linear differential equations,
switching between phenotypes relies on fluctuations in the small
number of mRNA molecules. The second part of this work elaborates
on collective, stochastic growth of many cells in an expanding
colony. The corresponding manuscript analyzes a theoretical model
with methods from statistical mechanics. Microbial colony growth is
sometimes seen as a model system for range expansion or
colonization processes. Inspired by experiments, a stochastic
surface growth process, in the form of a generalized Eden model, is
set up and analyzed. The model explicitly takes into account
selection between two strains, irreversible mutations, and the
roughness of the propagating colony front. The asymmetric character
of mutations implies the existence of an absorbing state, where
only the mutant strain is at the front of the expanding population.
Hence, the model combines two interesting branches of
non-equilibrium statistical mechanics: phase transitions to
absorbing states and dynamic surface roughening. As usual for these
processes, one can define critical exponents, which describe the
divergence of observables near the phase transition, and admit
organization of models into universality classes. It turns out that
the coupling between roughening dynamics and population dynamics
induces qualitative different behavior. As a consequence, the model
cannot be assigned to any universality class currently known.