My research interests evolved from a purely theoretical non-linear dynamics focus to the physics and dynamics of biological systems. What intrigues me is how living systems exploit the richness of dynamics and self-organized patterns to fulfill certain tasks efficiently, for example through the emergence of biological rhythms that allow cells or whole organisms to temporally separate incompatible functions and carry them out sequentially. I am investigating how these complex biological dynamics arise, what purpose they fulfill and how they are maintained and controlled, be it a genetic oscillator entrained by an external signal or cardiac arrhythmias terminated with electrical stimuli. As a result of working in a synthetic biology lab that cares about applications and hence the stability of genetic constructs, a recent addition to my work has been a particular aspect of population genetics, where, again, dynamics can play a crucial role in determining the fate of mutations. 

For instant complexity...
... just add dynamics!

 

Synthetic biology

Uncoupled genetic oscillators in E. coli, pulsed expression of fluorescent protein

Simple bacteria like E. coli can be equipped with synthetic gene regulatory networks that either mimic fundamental design principles of natural systems or provide entirely new functionality. Many classical systems known from nonlinear dynamics have been realized in the form of these synthetic circuits, including bistable systems ("toggle switches") and a plethora of oscillators. Despite their important role in shaping the field of synthetic biology and demonstrating what is possible, many of these circuits remained "toy models". While toggle switches have been used for numerous applications, oscillators have mainly been designed for their own sake, doing little more than expressing fluorescent proteins to verify the desired dynamics was achieved. My current research focuses on the theoretical and experimental investigation of oscillatory gene networks which provide a measurable functional advantage, thereby gaining an understanding of why similar networks might have evolved in nature and, at the same time, developing tools for biotechnological applications. In a recent publication, we showed that bacterial ecologies can be stabilized by using circuits that control population growth and lysis.

Population genetics

Serial passage
The serial passage protocol imposes periodic reductions in population size

How stable are the synthetic circuits that we design inside the host cells in an evolutionary sense? In many cases, it would be advantageous for host cells to deactivate or at least somehow impair a synthetic circuit to lessen the metabolic burden it imposes on the host machinery. In this sense, a random mutation that deactivates a synthetic construct would be a beneficial mutation and so the question arises what factors determine the spread of mutations in bacterial lab populations. Of course, the implications of this research are not limited to synthetic biology, but also apply to, e.g., experimental evolution and directed evolution experiments.

Once a mutation occurs, the mutants can either disappear due to random fluctuations or take over the population. The likelihood of the latter is called the "fixation probability". If mutations arise continuously, this fixation probability also determines the time scale on which one can expect the original genome (or some part thereof, e.g., a synthetic circuit) to be stable before it is replaced with a mutated version. Naturally, more beneficial mutations are more likely to become fixed in the population.

Over the past decades, it has become clear that variations of the population size over time can have a strong influence on the fixation probability as well. In almost any biology lab in the world, there is one particular striking example of externally imposed population size dynamics: the so-called serial passage protocol, where liquid bacterial cultures are periodically diluted into fresh growth media (see picture). As it turns out, this innocent procedure with its seemingly simple dynamics can have complex consequences for the fixation process of beneficial mutations. Read about our recent paper to find out more.

Spiral waves in excitable media

Pinned spiral FFP
A spiral wave pinned to a non-conducting heterogeneity interacting with wave induced by external stimulation

Excitable media are a class of spatially extended systems that support the propagation of non-linear waves that have prominent characteristic properties, such as annihilation of colliding wave fronts (instead of superposition) and refractoriness (the fact the system has to recover before it can be activated in the same spot). Certain chemical reactions (like the famous Belousov-Zhabotinsky reaction) belong to this type of spatio-temporal systems, but biological examples like the emergent aggregation dynamics of the amoeba dictyostelium discoideum are known as well. My interest in excitable media is mostly due to the fact that they also provide a high-level description for the cardiac muscle, where electrical activity is relayed from cell to cell to coordinate the cardiac contraction sequence.

In this abstract picture, plane waves correspond to the regular heart beat where excitation waves emitted by pacemaker cells travel across the heart once to trigger the normal cardiac contraction sequence. However, excitable also support self-sustained activity, most prominently in the form of spiral waves, which correspond to an abnormally increased heart rate as the self-sustained activity in the bulk of the muscle overrides the signal emitted by the (slower) pace makers. Spiral waves can further break up and develop into spatio-temporal chaos consisting of vigorously interacting spiral waves, which corresponds to life-threatening fibrillation in the heart and leads to sudden cardiac death when left untreated.

As spiral waves are thought to be the constitutive elements of many types of arrhythmias, they deserve special attention, and knowledge about their control is key to effectively treating arrhythmias. This is particularly true given the heterogeneity of the cardiac muscle, where spiral waves may pin to non-conducting regions, which stabilizes them and makes them harder to terminate. An important step in the control of these spiral waves therefore is the process of "unpinning". As it turns out, stimulation with electric fields can lead wave emission from the same non-conducting regions, and these induced waves can interact with the pinned wave in such a way as to cause unpinning. First, it is therefore important to understand the mechanisms governing this process and how it compares to other strategies of controlling spiral waves.

Since the success critically depends on the timing of the external stimulus, we then further investigated how reliable unpinning can be achieved with multiple, periodic electric-field pulses. It turns out that the success rate can be surprisingly well predicted with an iterated map that incorporates the phase-response of the pinned spiral to a single electric-field pulse. Due to the stability properties of this map, pacing with a frequency slower than the spiral wave frequency leads to reliable unpinning, while pacing with a higher frequency can lead to phase locking with no chance to unpin the wave. We were recently able to confirm these theoretical predictions in experiments on chicken cardiac muscle cell monolayers. A question that remains is how well these mechanisms translate to the actual situation during a cardiac arrhythmia, where the dynamics is complicated by the 3D structure of the muscle and multiple interacting waves.

Control strategies for cardiac arrhythmias

Waves triggered at tissue boundaries by electric-field stimulation. P. Bittihn, M. Hörning, S. Luther, PRL 109, 118106 (2012)

Electric shocks are used in external and implantable defibrillators to terminate life-threatening cardiac arrhythmias such as ventricular fibrillation. Today, these shocks use relatively high energies, sometimes causing intolerable pain (if delivered during consciousness), and potentially further damaging the usually already diseased muscle, although there is conflicting evidence regarding the latter. Therefore, there is a search for low-energy alternatives that use more subtle mechanisms to terminate the spatio-temporal chaos that is thought to underlie fibrillation and restore the heart's normal rhythm. During conventional defibrillation, every single cell is activated, leading to the cessation of all activity due to the tissue's refractoriness. We developed a new method that uses weak pulsed electric fields instead of one big shock and is based on our knowledge about the wave emission caused by the interaction of electric fields with heterogeneities in the tissue (see above). In isolated canine ventricular tissue and in in-vivo experiments on atrial fibrillation, it yields a huge energy reduction, which we believe is due to the presence of heterogeneities  throughout the heart and therefore the ability for newly created waves to directly interact with the waves that populate the muscle during fibrillation.

To systematically design such alternative pacing strategies, it is essential to understand how electric fields interact with the complex geometry given by cardiac anatomy. In a theoretical study, we extended the notion of "non-conducting heterogeneity" (cf. above section) to include boundaries of different shapes. It turns out that the local boundary curvature is a major determinant of the sensitivity of the tissue to electric fields, making wave induction at negative curvature boundaries particularly easy. This information can now be used to optimize the electric-field geometry and potentially create adaptive pacing strategies that adjust the number of wave emitting sites in the muscle to the complexity of the arrhythmia.