Molecular machines are responsible for a variety of non-equilibrium actions. They can make cells themselves move about, and perhaps exhibit fascinating collective motion, and the are responsible, amongst other things, for the transportation of cargo, or play a role in the tightening of the contractile ring during cells division.
A range of molecular motors move along the filamentous structures, microtubules and actin filaments, in the cell. It is interesting and challenging to ask and understand how molecular motors when connected in different ways start modifying the properties of the networks of filaments, or how their functioning alters the mechanical and conformational, and other dynamical properties of a variety of structures.
There is a wide range of interesting introductory articles by various authors, for example, check out this one http://www.nature.com/news/the-physics-of-life-1.19105?WT.mc_id=FBK_NatureNews.
A system with a relatively simple set-up is an array of filaments that move on top of a flat bed of molecular motors, a so-called motility assay. When a large number of motor heads grabs, moves, detaches to a filament, they cause it to move, but also to respond to an applied force. Under certain conditions, we found that an instability occurs [Banerjee, et al.]. Current work is related to dealing with interactions of filaments.
Above: A single filament moving on a surface with tethered motors. Cartoon for physical content of Banerjee paper. (Copyright Kristian Müller-Nedebock)
Stepping mechanism formalism
In the project with Janusz Meylahn we introduced novel ways to formulate the stepping action of motor heads using ideas from dynamical networking theories. We hope to present these results very soon.
Can we think about the tension in contractile rings, given the latest, fascinating experiment on filament orientation and the motors linking the rings? This is part of the project Stanard Mebwe Pachong is investigating in her research.
Contractile rings are formed of actin filaments and molecular machines (and possible other components) to actively pinch of the cell membrane after the division of genetic material. A ring of these filaments forms and then contracts ever more tightly.
We are have studied these systems using analytical dynamical approaches. These are complemented by some simple Langevin dynamics simulations. See Pachong and Müller-Nedebock paper.
Above: A simulations of the motions of actin filaments (some oriented clockwise and others counter-clockwise) under the action of networking and active forces. Two filaments with opposite orientations have been highlighted. (Copyright Kristian Müller-Nedebock)
When networks of filaments are formed (which is typical of the cytoskeleton) pairs of molecular motor heads, for example, can link different strands in addition (perhaps) to other crosslinks, forming an active gel. In past years two MSc theses on these topics have been completed in the group: a general network formalism (using ideas from equilibrium networks in polymer physics) and a dynamical perspective. The work was done by former members Mohau Mateyisi and Karl Möller.