Friction on the molecular scale

Friction remains an under-appreciated subject in conventional physics education. In classical mechanics classes students learn that friction (typically, between two solid objects – a concrete block on a wooden surface of a table) is proportional to the normal force. The coefficient of proportionality depends on the materials that rub, and does not change, no matter how large is the surface area of contact or the relative velocity.

The other commonly encountered friction force acts on objects that move in liquids (or gases). In the simplest possible case,  a sphere (of radius a) that is moving in a fluid (characterized by the viscosity, η) with speed V feels the drag force F=6πηaV. This textbook expression for the hydrodynamic friction, also known as Stokes’ drag, reveals a very different force – not only it depends on the size of the object, but also scales linearly with the speed.

Despite being so different, the two frictional forces have a thing in common. They both arise due to the interaction of a very large number of particles, so the surfaces (in case of the solid friction) and the liquid are treated as continuum, without much regard for their constituent molecules. In our work, we look at the friction at the molecular scale, the limit where the properties of constituents and their relative orientation matters.

To do so, we use filamentous bio-polymers – actin, microtubules and bacterial flagella. These filaments have been studied in great detail – their structure, periodicity and mechanical properties are well known. There are plenty of tools in the biochemistry toolbox to control and manipulate them. For instance, we can use laser tweezers to grab two actin polymers, drag one along the other and measure the frictional forces in the process. This is a very elaborate, miniature version of the experiment one can do on the regular (i.e. human) scale – drag a concrete block along the wooden table and measure the friction. We find that friction between the actin filaments rises rapidly, and stays roughly constant as we drag one along the other – similar to the friction between solids. The magnitude of the friction force (measured in pico-Newtons) is much larger than the predicted hydrodynamic friction, thus reaffirming the solid-like behaviour.

While friction between actin is solid-like, two other biopolymers – flagella and MTs – exhibit hydrodynamic friction, which tends to be much smaller (femto-Newtons). However, as we increase the pressure on the filaments, the friction changes abruptly from hydrodynamic to the solid-like regime. In the experiment, we use crowding agent (PEG) to push the two filaments together. We can adjust its concentration to control how much (osmotic) pressure is exerted. By doing that we push the filaments together more – and observe the increase in the maximum friction force (for actin), or even completely change the type of frictional coupling (for flagella and MTs).

Friction between actin filaments can be understood through a theoretical model that accounts for the stiffness and periodicity of the polymers. Combination of experiments with theoretical calculations helps to bridge the gap between molecular and continuum models of friction.

Read more about “Solid Friction between Soft Filaments” in Nature Materials

Laser tweezers and actin
Laser tweezers and actin
Friction force between actin filaments
Friction force between actin filaments