Heat transfer from protein crystals: implications for flash-cooling and X-ray beam heating

Abstract

Three problems involving heat transfer from a protein crystal to a cooling agent are analyzed: flash-cooling in a cold nitrogen- or helium-gas stream, plunge-cooling into liquid nitrogen, propane or ethane and crystal heating in a cold gas stream owing to X-ray absorption. Heat transfer occurs by conduction inside the crystal and by convection from the crystal's outer surface to the cooling fluid. For flash-cooling in cold gas streams, heat transfer is limited by the rate of external convection; internal temperature gradients and crystal strains during cooling are very small. Helium gas provides only a threefold improvement in cooling rates relative to nitrogen because its much larger thermal conductivity is offset by its larger kinematic viscosity. Characteristic cooling times vary with crystal size L as L(3/2) and theoretical estimates of these times are consistent with experiments. Plunge-cooling into liquid cryogens, which can give much smaller convective thermal resistances provided that surface boiling is eliminated, can increase cooling rates by more than an order of magnitude. However, the internal conduction resistance is no longer negligible, producing much larger internal temperature gradients and strains that may damage larger crystals. Based on this analysis, factors affecting the success of flash-cooling experiments can be ordered from most to least important as follows: (1) crystal solvent content and solvent composition, (2) crystal size and shape, (3) amount of residual liquid around the crystal, (4) cooling method (liquid plunge versus gas stream), (5) choice of gas/liquid and (6) relative speed between cooling fluid and crystal. Crystal heating by X-ray absorption on present high-flux beamlines should be small. For a fixed flux and illuminated area, heating can be reduced by using crystals with areas normal to the beam that are much larger than the beam area.

Protein hydration dynamics in solution: a critical survey

“…However, this adiabatic limit is not realized in practical flash-cooling protocols, which, even for small protein crystals, yield characteristic cooling times on the order of 0.1-1 s (Kriminski et al 2003). There is thus ample time for thermal averaging during the cooling process.…”

X-ray absorption by macromolecular crystals: the effects of wavelength and crystal composition on absorbed dose

“…Additionally, if the temperature rise takes the sample above the phase transition of the solvent glass in the crystal at around 155 K (Weik et al, 2001), crystalline ice will form and the diffraction pattern will be degraded. For the calculations of the temperature rise induced by the X-ray beam in the sample using the isothermal`lumped model' of Kuzay et al (2001) in RADDOSE, two parameters are required to specify the thermal properties of the crystal: the heat capacity, c p of the protein, estimated to be 5 Â 10 2 J K À1 kg À1 , and the heattransfer coef®cient, h, taken to be 320 W m À2 K À1 after Kriminski et al (2003). In the examples below, the initial temperature of the crystal has been taken as 100 K.…”

“…Thermal gradients within the crystal are neglected; this is not valid for highly absorbing crystals or for a non-uniform beam-intensity pro®le. However, although the model makes a number of simplifying assumptions, it is realistic enough to give an idea of relative temperature rises, and results from it have been born out by more sophisticated treatments (Kriminski et al, 2003).…”

Progress in rational methods of cryoprotection in macromolecular crystallography

“…Each of these aspects of the domain structure can become exaggerated with cooling, causing broadening of the Bragg spots (Nave, 1998;Dobrianov et al, 1999;Kriminski et al, 2002;Vahedi-Faridi et al, 2003 The underlying cause of the domain exaggerations is under investigation. In some cases, especially for large plunge-cooled crystals, temperature gradients can develop within the crystal as it is cooled (Kriminski et al, 2003). If one part of the crystal undergoes its cooling-induced change before another part, defects may be produced between these two regions.…”

“…Even if the crystal is cooled uniformly without large temperature gradients, as is common for cooling in cold gas streams (Kriminski et al, 2003), damage can still result. In this context, an important factor appears to be thermal contraction compensation among the different constituents of the crystal (Juers & Matthews, 2001;Kriminski et al, 2002;Juers & Matthews, 2004a,b;Lovelace et al, 2006;Fig.…”