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 microbes.

Multistability in the lactose utilization network of Escherichia coli, E. M. Ozbudak et al., Nature 427, 737 (2004).

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

Species Body Mass Diversification

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

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:

Cheating in Yeast

Snowdrift games dynamics and facultative cheating in yeast, j. Gore et al., Nature 459, 253 (2009).

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

Morphogen gradient formationHow 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.

REVIEW: Morphogen gradient formation, O. Wartlick at al., Cold Spring Harbor Perspectives in Biology (2009).

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

Bacterial Games

RR SS

CC

C kills SC kills S

S outgrows R: better S outgrows R: better nutrient uptakenutrient uptake

R outgrows C: no R outgrows C: no cost for ‘col’cost for ‘col’

Biodiversity is essential to the viability of ecological systems. Species diversity in ecosystems is promoted by cyclic, non- hierarchical interactions among competing populations. Central features of such non-transitive relations are represented by the ‘rock–paper–scissors’ game, in which rock crushes scissors, scis- sors cut paper, and paper wraps rock. In combination with spatial dispersal of static populations, this type of competition results in the stable coexistence of all species and the long-term maintenance of biodiversity.

Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games, T. Reichenbach et al., Nature 448, 1406 (2007).

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

The Cytoskleton in Cell PolarizationCell 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 cytoskeleton?

Hawkins et al. Rebuilding cytoskeleton roads: Active-transport-induced polarization of cells. Physical Review E (2009) vol. 80 (4) pp. 040903

Reaction-diffusion model. Classical NLD Problem.

Excitable Waves in Cell LocomotionUnderstanding 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 project.

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

Reaction-diffusion model. Mechano-chemical coupling.

Waves in Actin Pattern FormationThe 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.

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

Reaction-diffusion model. Excitable Media. Pattern formation.

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

Theory of Mitotic Spindle Oscillations

[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

Nonlinear oszillator. Hopf bifurcation.

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.

Synchronization of globally coupled phase oscillators

Exact results for the Kuramoto model with a bimodal frequency distribution, EA Martens et al., PRE 79, 026204 (2009).

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

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.

Evolutionary dynamics of grammar acquisition

The evolutionary dynamics of grammar acquisition, NL Komarova et al., J Theor Biol 209, 43-59 (2001).

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

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.

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.

Assaf et al., arXiv (2010), http://arxiv.org/abs/1003.1019v1

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

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 membrane.

Altschuler et al., On the spontaneous emergence of cell polarity. Nature (2008) vol. 454 (7206) pp. 886-9Goryachev et al., Dynamics of Cdc42 network embodies a Turing-type mechanism of yeast cell polarity, FEBS Lett (2008) vol. 582 (10) pp. 1437-43

Discuss theoretical models of cell polarity (Turing-type and stochastic).

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.

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).

Understand the physiological background and discuss the control algorithm and applications thereof.