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Thon rings from amorphous ice and implications of beam-induced Brownian motion in single particle electron cryo-microscopy

We have recorded dose-fractionated electron cryo-microscope images of thin films of pure flash-frozen amorphous ice and pre-irradiated amorphous carbon on a Falcon~II direct electron detector using 300 keV electrons. We observe Thon rings \cite{Thon1966} in both the power spectrum of the summed frames and the sum of power spectra from the individual frames. The Thon rings from amorphous carbon images are always more visible in the power spectrum of the summed frames whereas those of amorphous ice are more visible in the sum of power spectra from the individual frames. This difference indicates that while pre-irradiated carbon behaves like a solid during the exposure, amorphous ice behaves like a fluid with the individual water molecules undergoing beam-induced motion. Using the measured variation in the power spectra amplitude with number of electrons per image we deduce that water molecules are randomly displaced by mean squared distance of $\sim$ 1.1 Å$^{2}$ for every incident 300 keV e$^{-}$/Å$^2$. The induced motion leads to an optimal exposure with 300 keV electrons of 4.0 e$^{-}$/Å$^2$ per image with which to see Thon rings centred around the strong 3.7Å scattering peak from amorphous ice. The beam-induced movement of the water molecules generates pseudo-Brownian motion of embedded macromolecules. The resulting blurring of single particle images contributes an additional term, on top of that from radiation damage, to the minimum achievable B-factor for macromolecular structure determination.