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Seminar Topics (PowerPoint download)


									          Seminar Topics

Evolutionary dynamics of Biological Systems
                                       Biological Switches

                                                                Multistability, the capacity to achieve multiple internal
                                                                states in response to a single set of external inputs, is the
                                                                defining characteristic of a switch. Biological switches are
                                                                essential for the determination of cell fate in multicellular
                                                                organisms, the regulation of cell-cycle oscillations during
                                                                mitosis and the maintenance of epigenetic traits in

                             Understand the biology of the system and perform a bifurcation analysis.

Multistability in the lactose utilization network of Escherichia coli, E. M. Ozbudak et al., Nature 427, 737 (2004).
          Species Body Mass Diversification
                                                             Animals—both extant and extinct—exhibit an enormously
                                                             wide range of body sizes. Among extant terrestrial mammals,
                                                             the largest is the African savannah elephant with a mass of
                                                             107g, while the smallest is Remy’s pygmy shrew at a
                                                             diminutive 1.8 g. Yet the most probable mass is 40 g, roughly
                                                             the size of the common Pacific rat, which is only a little larger
                                                             than the smallest mass. More generally, empirical surveys
                                                             suggest that such a broad but asymmetric distribution in the
                                                             number of species with adult body mass M typifies many
                                                             animal classes, including mammals, birds, fish, insects, lizards,
                                                             and possibly dinosaurs.

          Understand the biology of the system and exactly solve a convection-diffusion-
          reaction equation:

Evolutionary model of species body mass diversification, A. Clauset and S. Redner, Phys. Rev. Lett. 102, 038103 (2009).
                                        Cheating in Yeast

        Understand the biology of the system and analyze the game-theoretical model
        using methods from nonlinear dynamics.

Snowdrift games dynamics and facultative cheating in yeast, j. Gore et al., Nature 459, 253 (2009).
             Morphogen gradient formation
                                                          How morphogen gradients are formed in target tissues is a key
                                                          question for understanding the mechanisms of morphological
                                                          patterning. In 1952, Turing showed that chemical substances,
                                                          which he called morphogens (to convey the idea of “form
                                                          producers”), could self-organize into spatial patterns, starting
                                                          from homogenous distributions. There are different
                                                          mechanisms of morphogen gradient formation, the properties
                                                          of these gradients, and the implications for patterning.

        Discuss the theoretical models of morphogen gradient formation (diffusion-reaction models).

REVIEW: Morphogen gradient formation, O. Wartlick at al., Cold Spring Harbor Perspectives in Biology (2009).
                                          Bacterial Games
                                                                             Biodiversity is essential to the viability of
                                                                             ecological systems. Species diversity in
                                      C                                      ecosystems is promoted by cyclic, non-
                                                                             hierarchical interactions among competing
R outgrows C: no                                         C kills S           populations. Central features of such non-
  cost for ‘col’                                                             transitive relations are represented by the
                                                                             ‘rock–paper–scissors’ game, in which rock
                                                                             crushes scissors, scis- sors cut paper, and paper
                  R                                        S                 wraps rock. In combination with spatial
                      S outgrows R: better                                   dispersal of static populations, this type of
                                                                             competition results in the stable coexistence of
                         nutrient uptake
                                                                             all species and the long-term maintenance of

        Analyze the diffusion-reaction equation of the rsp game using normal forms.

Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games, T. Reichenbach et al., Nature 448, 1406 (2007).
       The Cytoskleton in Cell Polarization
                                                                Cell polarization is important for chemotaxis, cell
                                                                migration and cell division. The cytoskeleton is
                                                                crucial in this process. The model that will be
                                                                investigated in this project analyses two different
                                                                cytoskeletal geometries and how these influence cell
                                                                polarization. Especially interesting is the robustness
                                                                of these processes. Can cells polarize spontaneously?
                                                                And how could one possibly distinguish between
                                                                polarization due to the microtubule and the actin

                                       Reaction-diffusion model. Classical NLD Problem.

Hawkins et al. Rebuilding cytoskeleton roads: Active-transport-induced polarization of cells.
Physical Review E (2009) vol. 80 (4) pp. 040903
       Excitable Waves in Cell Locomotion
                                                                Understanding the interactions of cells with their
                                                                surrounding is essential in biology as well as in
                                                                medicin. From a physicist‘s perspective this field
                                                                offers a huge playground on which two distinct
                                                                paradigms of cell biology are brought together.
                                                                First, chemical reactions are responsible for
                                                                regulatory tasks in the cell. And second, mechanical
                                                                forces are equally important in cell regulation.
                                                                How such mechanical interactions could be
                                                                integrated into cellular signals lies in the focus of this

                                   Reaction-diffusion model. Mechano-chemical coupling.

Ali et al. Excitable waves at the margin of the contact area between a cell and a substrate.
Phys Biol (2009) vol. 6 (2) pp. 025010
         Waves in Actin Pattern Formation
                                                             The organization of the F-actin cytoskeleton relies on
                                                             many details in the cell, which are accurately tuned
                                                             in the living organism. How this accuracy can be
                                                             obtain is a micarcle. Spatial reaction-diffusion models
                                                             for the cytoskeleton can describe several dynamic
                                                             regimes which are observed in vivo. In this work
                                                             ideas from pattern formation and excitable media
                                                             combine to describe actin patterns in Dictystelium. It
                                                             is suggested that reaction-diffusion dynamics is
                                                             important in the cell, besides the traditionally known
                                                             signaling pathways.

                             Reaction-diffusion model. Excitable Media. Pattern formation.

Whitelam et al. Transformation from Spots to Waves in a Model of Actin Pattern Formation.
Physical Review Letters (2009) vol. 102 (19) pp. 1-4
         Theory of Mitotic Spindle Oscillations
                                                                    One of the main challenges in cell biology is to
                                                                    understand the mechanisms of cell division
                                                                    (mitosis). The apparatus which steers mitosis is
                                                                    the mitotic spindle. This molecular construct is
                                                                    made of stiff filaments (microtubules) which hold
                                                                    the apparatus at the center of the dividing cell
                                                                    with the help of molecular motors.
                                                                    In certain embryos it is observed that the spindle
                                                                    oszillates before the cell divides. A simple model
                                                                    predicts how these oszillations arise.

[1] Grill et al. Theory of Mitotic Spindle Oscillations.
Physical Review Letters (2005) vol. 94 (10) pp. 108104;
[2] Experiments: Pecreaux et al. Spindle oscillations during asymmetric cell division require a threshold number of active cortical force
generators. Current Biology (2006) vol. 16 (21) pp. 2111-2122
            Synchronization of globally coupled
                    phase oscillators
                                                                  One of the most fascinating cooperative phenomena
                                                                  in nature, synchronization is observed in a wide
                                                                  variety of systems. Biological examples include
                                                                  networks of pacemaker cells in the heart and
                                                                  congregations of synchronously flashing fireflies.
                                                                  In 1975, Kuramoto introduced a mathematical model
                                                                  for a system of globally coupled phase oscillators
                                                                  running at arbitrary intrinsic frequencies. Depending
                                                                  on the distribution of these frequencies, different
                                                                  synchronization scenarios can occur.

      Understand the long-term dynamics of the system and perform a bifurcation analysis.

Exact results for the Kuramoto model with a bimodal frequency distribution, EA Martens et al., PRE 79, 026204 (2009).
             Evolutionary dynamics of grammar
                                                                 Children acquire the grammar of their native
                                                                 language without formal education simply by hearing
                                                                 a number of sample sentences. They have to
                                                                 evaluate these and choose one grammar out of a
                                                                 limited set of candidate grammars. An important
                                                                 question is how accurate children have to learn the
                                                                 grammar of their parents’ language for a population
                                                                 to maintain a coherent grammatical system. By
                                                                 placing the problem in an evolutionary context, one
                                                                 can formulate equations for the population dynamics
                                                                 of communication and grammar learning.

      Analyze the population dynamics of grammar acquisition and the evolution of grammatical

The evolutionary dynamics of grammar acquisition, NL Komarova et al., J Theor Biol 209, 43-59 (2001).
                    Large Fluctuations in Stochastic
                         Population Dynamics
                                                               This project deals with dynamics of populations
                                                               experiencing intrinsic noise caused by the discreteness of
                                                               individuals and stochastic character of their interactions.
                                                               When the average size N of such population is large, the
                                                               noise-induced fluctuations in the observed number of
                                                               individuals are typically small, and only rarely large. In
                                                               many applications, however, the rare large fluctuations
                                                               can be very important. This is certainly true when their
                                                               consequences are catastrophic, such as in the case of
                                                               extinction of an isolated self-regulating population after
                                                               having maintained a long-lived metastable state.

         Derive characteristic properties of metastable populations like mean extinction time or quasi-
         stationary distribution.

Assaf et al., arXiv (2010),
                                Models of Cell Polarity in Yeast
                                                                Many cell types can spontaneously establish and
                                                                maintain asymmetric distributions of signalling
                                                                molecules on the plasma membrane. Positive
                                                                feedback circuits, found at the core of diverse
                                                                biological networks, enable signalling molecules
                                                                localized at the plasma membrane to initiate
                                                                processes that further accelerate localized
                                                                recruitment. These processes allow signalling
                                                                molecules, such as Cdc42 in budding yeast, to be
                                                                concentrated within a defined region of the plasma

   Discuss theoretical models of cell polarity (Turing-type and

Altschuler et al., On the spontaneous emergence of cell polarity. Nature (2008) vol. 454 (7206) pp. 886-9
Goryachev et al., Dynamics of Cdc42 network embodies a Turing-type mechanism of yeast cell polarity, FEBS Lett (2008) vol. 582 (10) pp.
     Dynamic Control of Cardiac Alternans

Electrical alternans are believed to be linked to the onset of life-threatening ventricular arrhythmias
and sudden cardiac death. Recent studies have shown that alternans can be suppressed temporally
by dynamic feedback control of the pacing interval. The control algorithm is adapted to drifting
system parameters, making it well suited for the control of physiological rhythms. Control of cardiac
alternans rhythms may have important clinical implications.
Understand the physiological background and discuss the control algorithm and applications
Spatiotemporal control of cardiac alternans, B. Echebarria and A. Karma, Chaos 12 (3), 923 (2002),
Dynamic Control of Cardic Alternans, K. Hall et al., PRL 78 (23), 4518 (1997).

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