University of Lincoln, UK

Long ranged interactions between embedded inclusions in a membrane

In 1948 Hendrik Casimir calculated that two metallic plates in a vacuum (absence of particle of any kind…except for the plates themselves that is) would be subject to an attractive force owing to the quantum fluctuations of the electromagnetic field they are embedded in. This Force from nothing has lead to many heated speculations on the meaning of a vacuum, the reality of virtual particles and even possible contribution to the value of the cosmological constant.

The influence of Casimir’s work hasn’t stopped there. Indeed it was soon realised that Casimir forces were simply a specific case of forces arising between any two objects embedded into a field — subject to either thermal or quantum fluctuations — and whose presence would affect the field in some way. Thus we now have hydrodynamic fluctuation-induced forces, capillary fluctuation-forces, elastic fluctuation-induced forces and critical Casimir forces to name a few (apologies to those fluctuation-induced forces that I haven’t mentioned here).

But if these forces are so ubiquitous, how come we only start observing them now? Well, the thing is that these forces are often very short ranged an can only be observed over the scale of a micron or so at best. To add to the difficulty, the effect will only be consequent below a certain distance called the correlation length of the field — the distance over which a localised perturbation at one point in the field can influence the value of the field at other points — which is often very short and not easily tuneable. Some known exceptions to the rule are electromagnetic forces which have an infinite correlation length and binary mixtures that are about to phase separate which also, in principle, can have an infinite correlation length.

And this brings us to the topic of today where a new study from a collaboration between University of Durham’s J. Benet and H. Kusummatmaja and  University of Lincoln’s F. Paillusson has looked at the 2-dimensional critical Casimir interaction between compartmentalised inclusions embedded in a membrane whose constituents are on the verge of phase separation. A rich set of possible effective interactions appears to emerge from their calculations (see image below). One key finding is that these interactions can be very long ranged (much more so than in 3 dimensions) and lead to the patterning of higher order structures via the self assembling of such inclusions.

Screen Shot 2017-09-15 at 02.21.10

Since these inclusions are thought as being crude models of proteins, this study has potential relevance for the problem of protein-mediated transport in cell membranes, protein crystallisation techniques in exotic lipid phases and the micro patterning industry in general.

The paper if fully available for a quick read here.

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