Historical research guide · 0850 · 2024
Universal Casimir attraction between filaments at the cell scale
Benjamin Spreng · Hélène Berthoumieux · Astrid Lambrecht · Anne-Florence Bitbol · Paulo Maia Neto · Serge Reynaud
In one minute
The Casimir force is usually told as a story about two mirrors in a vacuum, pulled together because the field’s own fluctuations are partly excluded from the gap between them. Spreng, Berthoumieux, Lambrecht, Bitbol, Maia Neto and Reynaud follow that force into salty water, where you would expect dissolved ions to screen it out of existence. Using molecular dynamics simulations backed by field theory, they show that salt screens only half the field: the longitudinal part dies within a Debye length, while the transverse part is left untouched — and it is the transverse part that carries a long-range force. They then compute exactly the Casimir attraction between two long parallel dielectric cylinders in that fluid, and find it is universal: it does not depend on what the cylinders are made of, only on their length, radii and spacing. Put in the numbers for actin filaments and microtubules and the pull comes out several times the thermal jostling energy inside a living cell.
Connection
Chapter 2 rests on the Casimir force as the plainest evidence that the vacuum is a real medium with structure you can act on. This paper takes that same force out of the ultra-high-vacuum apparatus and finds it doing measurable work inside a cell, through salty water, at distances of tens of nanometres — a reminder that vacuum fluctuations are not a laboratory curiosity but an everyday player.
From the source
Salt screens only part of the electromagnetic field in water: molecular dynamics simulations of pure water and of a 0.2 mole per litre potassium bromide solution, matched by nonlocal-electrostatics field theory, show the longitudinal susceptibility acquiring a Debye-screened decay while the transverse susceptibility is unchanged by the salt — and it is the unscreened transverse modes that allow a long-range Casimir force in an electrolyte.Sect. 2, figure 2; appendices A and B
For two long parallel dielectric cylinders in salted water the zero-frequency Casimir free energy is minus the thermal energy scale times the ratio of cylinder length to separation times a dimensionless function of the geometry alone — because the permittivity of salted water diverges at zero frequency, the result does not depend on the dielectric response of the cylinders or of the fluid. That is what universal means here.Sect. 3, free-energy relation (5) and the geometric parameters (6)
The exact scattering calculation is bracketed by two analytic limits: at short range the proximity force approximation with an effective Hamaker coefficient of about nine tenths of the thermal energy scale, and at long range a fourth-power falloff for two cylinders against a second-power falloff for cylinder-and-plane. In the crossover region that matters biologically, both limits overestimate the true energy by roughly an order of magnitude.Sect. 3, approximations (7) and (8); figure 4
For actin filaments of radius 3 nanometres held 6 nanometres apart, as in the parallel bundles that support microvilli, microspikes and filopodia, the Casimir binding energy is 0.33 thermal units per micrometre — 5 thermal units for a 15 micrometre filament, comfortably above Brownian jostling; in contractile bundles at 33 nanometres it drops to about a hundredth of a thermal unit and stops mattering.Sect. 4, actin paragraph; figure 5
For microtubules of radius 12 nanometres at the 22 nanometre spacing measured in parallel fibre axons, the binding energy is 0.112 thermal units per micrometre, giving 5.6 thermal units for a 50 micrometre microtubule; the interaction exceeds thermal fluctuations out to about 35 nanometres, which covers parallel fibre axons, white-matter spinal cord axons and plant-cell arrays, though not Purkinje cell dendrites.Sect. 4, microtubule paragraph; figure 6
What sets this force apart from every other equilibrium interaction in a cell is its range — electrostatics is screened and depletion reaches only about 5 nanometres — and the authors point onward to out-of-equilibrium fluctuation-induced forces in an active cytoskeleton, and to stacks of lipid membranes where the same attraction should oppose the repulsive Helfrich and hydration interactions.Sect. 5, Discussion
The way in
https://doi.org/10.1088/1367-2630/ad1846How to cite it
Benjamin Spreng, Hélène Berthoumieux, Astrid Lambrecht, Anne-Florence Bitbol, Paulo Maia Neto, Serge Reynaud (2024) Universal Casimir attraction between filaments at the cell scale doi:10.1088/1367-2630/ad1846