Phase transitions, instabilities and morphogenesis in biological systems

I am a theoretical physicist and interested in understanding mechanistic principles which underly the patterns and morphology in various kinds of biological systems. By applying concepts from non-linear dynamics, non-equilibrium thermodynamics and kinetic theory I focus on the minimal ingredients necessary to describe the dynamics of these systems. My fascination for biological systems is based on their inherent local consumption and dissipation of energy, which can power chemical reactions or give rise to active force generation on the scale of the constituent particle. These active processes can drive changes of the state of biological matter or affect its shape and even its mechanical integrity. In particular, I consider biological systems, which undergo macroscopic changes in degree of order. Examples range from the spontaneous emergence of collective motion (swarming), over the clustering of bacterial colonies, to the controlled positioning of droplets in maintained concentration gradients. The change in degree of order can often be understood as phase transitions far from equilibrium.  Phase transitions can cause dramatic changes in chemical and physical properties of biological matter. These changes often require little energy input to perturb or quench the system and in general there is no need to supply the energy costs to rearrange each particle. The molecular and mechanical interactions are sufficient to drive the change of matter. Thus phase transitions are ideal to efficiently control and switch biological functions.


Phase transitions in cells

Cells have to control and switch biological function. In some cases this is achieved by the formation of chemically distinct compartments. Recent evidence suggests that there is a class of compartments, which can be regarded as liquid-like droplets formed by phase separation from the cellular cytoplasm. Together with Prof. Frank Jülicher (Max-Planck Institute for the Physics of Complex Systems)  and Prof. Anthony Hyman (Max Planck Institute of Molecular Cell Biology & Genetics) we investigate the question of how cells use liquid phase separation to form chemically distinct non-membrane bound compartments inside cells and how cells control the position of these compartments in space using concentration gradients of regulating proteins [Annual Reviews, 30: 39–58].
In the specific case of the C. elegans embryo we could understand the mechanistic principles of how the MEX-5 protein concentration gradient spatially controls phase separation of P granule compartments [Cell, 6, 166: 1572–1584]. From a theoretical perspective, the concentration gradient leads to a spatially inhomogeneous scenario of droplet ripening, which can be described by an extension of the classical ripening theory of Lifschitz & Slyozov [Read More]. In addition, we found that the switch of position can be understood as a first order phase transition [Read More]. 
Further interests are devoted to the influence of chemical reactions and external control parameters such as temperature and pH on the stability and dynamics of these liquid-like compartments. The presence of chemical reactions can affect the stability of liquid-like drops and even drive the division of droplets [Read More]. This finding indicates that liquid droplets combined with chemical reactions might have played a fundamental role in the evolution of protocells. The stability of liquid-like compartments is also influenced by changes of pH, which affects the interactions between components and can thereby drive phase separation in region where the pH is close to the isoelectric point (manuscript in preparation).

P granules (green) segregate to the posterior of the C elegans embryo due to the presence of a concentration gradient of a protein MEX-5.


Movie - Droplets in a developing concentration gradient.mp41.45 MB
Movie - Droplet nucleation in an existing concentration gradient.mp41.09 MB
Movie - Ripening theory of droplets in a concentration gradient.mp44.6 MB

Cluster instabilities in bacterial systems

Other examples of how a living system controls biological function by the formation of chemically and physically distinct structures are biofilms. Specifically, together with Dr. Vasily Zaburdaev (Max-Planck Institute for the Physics of Complex Systems) we consider the clustering instability of N. Gonorrhea bacteria cells to colonies. These bacterial clusters can be regarded as biofilm precursors as the cluster stage represents an intermediate step during biofilm formation.  The tight neighborhood within the colony already provides a higher resistance against antibiotics to the bacterial cells. N. Gonorrhea bacteria actively move and interact by retracting polymeric appendices called pili. On a substrate these active processes can drive the formation of large-scale bacterial clusters, which we could reconstitute by a kinetic theory and the derivation of the corresponding hydrodynamic equation [Phys. Rev. E., 92: 032704]. In addition, we investigate the dynamics of shape and rheological properties of these bacterial colonies [Read More].

N. Gonorrhea bacteria cells forming colonies on a substrate (left) and patterns predicted by solving the hydrodynamic equation derived from a kinetic theory (right).

FileBacterial Colony Formation predicted by kinetic theory.mp4


Dynamics of morphogenesis
Morphogenesis refers to the early development of shape in embryos. In the early stage an embryo consists of just a few fundamental cell types, which are orchestrated such that after some time a highly complex organism develops. Over time the initially few cell types differentiate to a large variety of cells that form together with polymers and minerals all kinds of tissues (connective, muscle, nervous and epithelial tissue). Each tissue type performs a specific biological role for the organism and none could function on its own. From a physics perspective each tissue exhibits very different mechanical and chemical properties. An example is cartilage or bone, which are significantly stiffer than epithelial or muscle tissue. In the early embryo these difference in degree of physical and chemical properties had to develop first from a mixture of just a few cell types. 
Together with Prof. L. Mahadevan (Harvard University) we are interested in the question of how a soft tissue hardens during embryogenesis. As an example we consider the condensation of cartilage during the early limb bud development. In particular, we focus on the change of mechanical properties and how they relate to the shape dynamics of the limb bud.