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Semiflexible polymers and cytoskeletal filaments

Semiflexible polymers are governed by their bending energy in contrast to flexible polymers, which are governed by entropic tension. Whereas typical synthetic polymers have diameters in the nm-range and are connected by carbon-carbon backbone, which is very flexible, many biopolymers - such as DNA, cytoskeletal filaments (F-actin and microtubules), protein fibers - are relatively large and thick molecules which leads to considerable bending rigidity. The bending rigidity of a polymer can be characterized by its persistence length, which is the ratio of the bending rigidity κ of the polymer and the thermal energy: Lp=κ/kBT. It can be visualized as the typical length scale over which a thermally fluctuating semiflexible polymer changes its orientation; fragments smaller than the persistence length essentially behave as rigid rods. Typical persistence lengths are 50nm for DNA (mechanical contribution, electrostatics increases the stiffness), 10μm for F-actin, or several mm for microtubules.

The reason for a large bending rigidity often is (according to isotropic elasticity theory) the "thickness" of a polymer. Therefore, semiflexible polymers are typically "thick", which makes them suitable for single polymer manipulation and observation. The theoretical description of such single polymer experiments is an important research area.

Another fascinating aspect of the cytoskeletal filaments F-actin and microtubules is their dynamic polymerization behavior which is fueled by the hydrolysis of ATP or GTP. This chemically driven polymerization dynamics provides the basis for cellular force generation and motion and allows for a constant remodelling and, thus, shape changes of the cytoskeleton. This property makes the difference between "dead" synthetic polymers and polymers, which provide the basis for active motion - a basic feature of living matter.

Our research spans from the polymer physics of single semiflexible polymers to structures containing many interacting polymers and from polymers in equilibrium to "living" cytoskeletal polymers with a chemically driven polymerization dynamics:

Single Semiflexible Polymers

The bending rigidity of semiflexible polymers gives rise to some interesting new polymer physics because thermal fluctuations, external forces, or fluctuations in a random potential are also competing with the bending energy. In "conventional" flexible synthetic polymers there would only be competition with the entropic elasticity of a flexible chain.

This has consequences, for example, if semiflexible polymers adsorb on structured curved substrates, where adsorption then also involves bending energy.

Because many semiflexible polymers are quite "large and thick" (as compared to a typical synthetic polymer), such as cytoskeletal filaments (F-actin, microtubules) or DNA, they are often well suited to be observed and manipulated on a single molecule level. In order to interpret such experiments quantitatively, detailed theoretical models are helpful. Examples are the analysis of thermal fluctuations of single polymers in straight or curved microchannels, the forced desorption from an adhesive substrate, or the dynamic behavior if a polymers is driven over a surface with potential or topographic barriers.

Finally, the fluctuation behavior of semiflexible polymers can provide interesting statistical physics connecting very different problems. For directed lines there exists a mapping from the problem of a single line in a random potential onto the so-called Kardar-Parisi-Zhang (KPZ) equation, which is a very important non-linear equation describing surface growth and whose dynamic critical properties are still not completely clear. We have studied this mapping for stiff lines, which gives some new insight into the problem.

References

Bundles and networks of filaments

In the cytoskeleton of a cell F-actin filaments typically form bundles or network structures which are hold together by crosslinkers with two "sticky" ends. Here, we study the question, how semiflexible polymers bundle or unbundle from a statistical physics view point. We found that the bundling transition is discontinuous and, thus, rather sharp for stiff polymers.

Moreover, the adhesive energy that is gained in forming a bundle can also be used to exert pushing or zipping forces onto obstacles.

We also investigated networks of semiflexible polymers with respect to wrinkle formation.

References

Polymerization kinetics of actin and microtrubules

Cytoskeletal filaments are constantly polymerizing and depolymerizing within the cell. The polymerization dynamics is also chemically driven because ATP (F-actin) or GTP (microtubules) is hydrolyzed within a filament.

An additional aspect in microtubule polymerization dynamics is their dynamical instability, i.e., the occurence of catastrophes, where the microtubule switches stochastically from a growing state into a state of rapid depolymerization, and rescue events, where it switches back to growth. Catastrophes are associated with a loss of the GTP-cap, which stabilizes the microtubule structure mechanically. We develop models to understand the origin of catastrophe chemomechanically on the dimer level. The dynamic instability has interesting consequences for their ability to generate pushing forces, which becomes limited by catastrophes. It also leads to characteristic collective catastrophes or rescue events if many microtubules cooperate in pushing an obstacle. A cooperative "tug-of-war" of polmerizing and depolyreizing microtrubule ensembles also causes stochastic oscillations in the mitotic spindle.

The polymerization of actin filaments is coupled to their hydrolysis, which determines the ATP-cap strucutre,  and to regulating proteins such as profilin, which determines growth speeds. Regulating proteins such as stathmin also play an important role in microtubule dynamics and length regulation.

References

Interaction with molecular motors (gliding assays)

Cytoskeletal filaments also serve as tracks for molecular motor proteins. In gliding assays the motor proteins are immobilized on a surface and pull filaments over the surface. Such gliding assays can be used to study the stepping behavior of single motors, the competittion between different motor types (for exmaple slow and fast motors) transporting a filament, or collective effects from interactions between filaments.

References

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Location & approach

The campus of TU Dort­mund University is located close to interstate junction Dort­mund West, where the Sauerlandlinie A 45 (Frankfurt-Dort­mund) crosses the Ruhrschnellweg B 1 / A 40. The best interstate exit to take from A 45 is “Dort­mund-Eichlinghofen” (closer to South Campus), and from B 1 / A 40 “Dort­mund-Dorstfeld” (closer to North Campus). Signs for the uni­ver­si­ty are located at both exits. Also, there is a new exit before you pass over the B 1-bridge leading into Dort­mund.

To get from North Campus to South Campus by car, there is the connection via Vogelpothsweg/Baroper Straße. We recommend you leave your car on one of the parking lots at North Campus and use the H-Bahn (suspended monorail system), which conveniently connects the two campuses.

TU Dort­mund University has its own train station (“Dort­mund Uni­ver­si­tät”). From there, suburban trains (S-Bahn) leave for Dort­mund main station (“Dort­mund Hauptbahnhof”) and Düsseldorf main station via the “Düsseldorf Airport Train Station” (take S-Bahn number 1, which leaves every 20 or 30 minutes). The uni­ver­si­ty is easily reached from Bochum, Essen, Mülheim an der Ruhr and Duisburg.

You can also take the bus or subway train from Dort­mund city to the uni­ver­si­ty: From Dort­mund main station, you can take any train bound for the Station “Stadtgarten”, usually lines U41, U45, U 47 and U49. At “Stadtgarten” you switch trains and get on line U42 towards “Hombruch”. Look out for the Station “An der Palmweide”. From the bus stop just across the road, busses bound for TU Dort­mund University leave every ten minutes (445, 447 and 462). Another option is to take the subway routes U41, U45, U47 and U49 from Dort­mund main station to the stop “Dort­mund Kampstraße”. From there, take U43 or U44 to the stop “Dort­mund Wittener Straße”. Switch to bus line 447 and get off at “Dort­mund Uni­ver­si­tät S”.

The AirportExpress is a fast and convenient means of transport from Dortmund Airport (DTM) to Dortmund Central Station, taking you there in little more than 20 minutes. From Dortmund Central Station, you can continue to the university campus by interurban railway (S-Bahn). A larger range of international flight connections is offered at Düsseldorf Airport (DUS), which is about 60 kilometres away and can be directly reached by S-Bahn from the university station.

The H-Bahn is one of the hallmarks of TU Dort­mund University. There are two stations on North Campus. One (“Dort­mund Uni­ver­si­tät S”) is directly located at the suburban train stop, which connects the uni­ver­si­ty directly with the city of Dort­mund and the rest of the Ruhr Area. Also from this station, there are connections to the “Technologiepark” and (via South Campus) Eichlinghofen. The other station is located at the dining hall at North Campus and offers a direct connection to South Campus every five minutes.

The facilities of TU Dortmund University are spread over two campuses, the larger Campus North and the smaller Campus South. Additionally, some areas of the university are located in the adjacent “Technologiepark”.

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