One of the central goals in our institute is a better understanding of the spreading of cancer. In this often deadly disease, individual cancer cells are migrating through the body to form secondary tumors in distant organs. For a better treatment of cancer, it is crucial to have a detailed model about how these cells are crawling across the dense bio-materials that comprise most of the body's connective tissue and how they find a passable path to their target organs.
Cell migration, even when ignoring the possibility of collective cell-cell interactions, is an extremely complex phenomenon. The connective tissue itself, such as collagen, is already a network of bio-polymers with a highly irregular structure and many nonlinear material properties. The cells are constantly changing their shape by forming and retreating protrusions that locally explore this surrounding material. At certain points the cells adhere to the external bio-polymer matrix via transmembrane receptors and exert forces onto the matrix by building contractile stress fibers between these focal adhesion points. By releasing adhesions at the rear part, the center of mass of the pre-stressed cell is moving forward. The stress fibers, mainly consisting of actin filaments crosslinked by myosin motor proteines, and the focal adhesions form together the most important part of the so-called cytoskeleton. This sub-structure of the cell is highly dynamic. Microscopic building blocks are constantly added to (and removed from) the cytoskeleton at different rates. Those biochemical remodelling processes, in turn, are regulated by a complex biochemical signaling network. Using signals transduced by the focal adhesion complexes, this reaction network is somehow processing information about the local environment and on this basis is guiding the cytoskeletal remodelling in a goal-directed way.
Selforganization by adaptive, explorative processes
How can a cell orchestrate the many microscopic structural changes of its cytoskeleton, from moment to moment, in such a way that there results on the macroscopic level a goal-directed migration towards its target site ? Or, on a somewhat shorter time-scale, how does the cell evaluate the local possibilites offered by the surrounding bio-polymer network and achieves at least a short move that brings it closer to the goal ?
One can generate some initial hypothesis for this unsolved problem by looking at similar selforganization processes in biology. A re-occuring pattern of adaptive selforganization is the method of blind trial and error, which also underlies evolution: Instead of executing a detailed, prescribed plan (that would fail anyway when encountering a novel situation) adaptive systems create many random alternatives and then select the ones which show the best signs of being useful in the present situation.
Applying this general mechanisms to our special case of cell migration, one might speculate, for example, that the cell is forming explorative protrusions into random directions. Only those protrusions that find a resilient fiber of the tissue matrix connect to this fiber via focal adhesions and are stabilized that way. All other protrusions are recycled. Similar explorative adaption processes may also occur on the more microscopic levels of cytoskeletal structure formation. Thus, a picture of the cell emerges as a multi-level hierarchy of adaptive processes. Each element of the system is autonomously trying out new ways to connect itself with the whole (variation). Elements that find a niche that is useful for the cell as a whole remain stable for a longer time (selection).
In traditional physics, non-linear many-particle systems have been studied for a long time, and complex phenomena such as out-of-equilibrium phase transitions could be successfully explained in that context. More recently, the new field of Complex Systems (CS) has emerged as a natural extension of many-particle systems. The particles are now frequently replaced by "agents", for which reason some CS are also called multi-agent systems. In contrast to the particles of traditional physics, agents can be sub-systems of arbitrary complexity by themselves, such as bio-polymers, stress fibers, organelles, cells, humans, or firms. Inteactions between agents can be much more complicated than the simple force-laws between traditional point particles. However, in order to do theory for such systems, the behaviour of each agent and all interactions must be described in the respective models by clear rules (which may be stochastic). In this case, standard methods of theoretical physics can be applied to CS.
The theory of complex systems can explain the emergence of global patterns by a causal loop between the micro- and macro-level:
CS can also be used to model adaptive, explorative processes. In the language of physics, "variation" corresponds to the fluctuations of variables in a population of agents and selection corresponds to some performance-dependent growth rates of the different agents within this population.
Physics approach to reaction networks, cytoskeletal reorganization and cell migration
We try to describe the process of cell migration using the methods and concepts of Complex Systems Theory. While our dream goal would be the development of a true, integrative multi-level model of cell migration, the complexity of the problem demands to focus on the different levels and aspects of the process hierarchy one at a time:
- Self-organization and signal processing in biochemical reaction networks
- Spontaneous fluctuations of the cytoskeleton and long-time correlations
- Cell migration as a random walk of adaptive agents in complex potential landscapes
We are also working on
- Image processing methods for detecting the deformation of the bio-polymer networks caused by migrating cells.