Research topics
Our
research
focuses on
non-equilibrium statistical physics,
soft matter and
theoretical biological physics, as well as physically motivated
data
science. Key topics include the theory and applications of normal and anomalous
stochastic processes, gene regulation, crowding in biological cells, (bio)polymer
physics, as well as Bayesian maximum likelihood and machine learning analyses.
Effects of disorder, annealed or quenched, interacting particles, or non-stationary
dynamics are studied. Our methods are analytics, numerics (Mathematica etc), and
simulations (Langevin dynamics, Monte Carlo, etc). We collaborate with a number of
theoretical and experimental groups worldwide.
Student projects can be found
here.
Anomalous diffusion
As one of the internationally leading groups we study stochastic processes,
in which the mean squared displacement (MSD) deviates from the linear form
<r^2(t)>∼t known from Brownian motion. Mostly we are
interested in processes following the power law form
<r^2(t)>∼t
α where
α≠1, distinguishing subdiffusion
(
0<α<1) and superdiffusion (
α>1), but we also study
ultraslow processes with
<r^2(t)>∼log
(t) such as
Sinai diffusion. In particular we are interested in the physical origins of
anomalous diffusion, but also in the inference of parameters and mechanisms
from measured data. Apart from biological systems our theories find application
in solid state physics, physical chemistry, econophysics, and movement ecology.
Ergodicity and ageing in physical systems
In standard statistical mechanics courses we learn in the spirit of Boltzmann
that the long time average of a physical observable, obtained from following
a single particle, should provide the identical information as the ensemble
average of this observable garnered from following many particles. In many
cases this ergodic behaviour is broken. Motivated by a growding body of evidence
garnered by superresolution microscopy, we study non-ergodic systems in
detail and demonstrate that the understanding of this phenomenon is pivotal
for the proper physical interpretation of the dynamics of many complex
systems. Concurrently, many of these systems are non-stationary, such that
their dynamics changes over time: they are ageing. In our analyses of ageing
systems we demonstrate interesting crossover phenomena dependening on the
length of the observation time.
Normal diffusion and first passage processes
Even for normal Brownian processes a large number of questions remains open.
One of our focus points of study is the effect of geometry and heterogeneity
on the dynamics of a test particle. In particular, we are interested in the
analytical study of first passage processes, that is the statistics of when
a particle reaches a given location in a physical space for the first time.
Our current research demonstrates that the typical analysis in terms of the
mean first passage time may provide insufficient information on specific
processes, in particular, when small concentrations of particles are
involved.
Physics of molecular crowding
The cytoplasm of biological cells is
superdense, crowded by larger
biopolymers at volume fractions of some 35%. Sometimes cells can be even
more crowded (supercrowded) by large inclusions such as granules or vesicles.
We study how such crowding affects the dynamics of both passive diffusion and
active motion propelled by molecular motors in such crowded environments.
Important clues also come from experimental collaborators.
Crowding also occurs in two-dimensional membrane systems, which are studied
by partner groups via large scale simulations and experiments. We are
interested in a systematic investigation of the physical behaviour of
crowded systems.
Soft matter physics
We study the dynamics of polymers under certain constraints, such as the
passage of a polymer chain through a nanopore (translocation), the looping
in the presence of crowding molecules, or the denaturation of double stranded
DNA due to thermal or mechanical action. More recently we also consider
charged systems, for instance, the statistics and dynamics of the attachment
of charged polymers to oppositely charged, homogeneous and inhomogeneous
surfaces.
Gene regulation
Experimentalists can by now observe the production of individual proteins in
a living biological cell, providing unprecedented evidence in specific
features of gene regulation. Based on information from experiments and
simulations we generalise the facilitated diffusion model for the search
of regulatory proteins for their specific binding spot on the cellular DNA.
In particular, we came up with a fit free model explaining experimentally
measured protein search rates in bacteria cells, and we provided a theoretical
explanation for the rapid search hypothesis: the idea that even in the small
confines of bacterial cells the distance between two communicating genes is
important for the precision of their precise control.