Nuclear Instruments and Methods in Physics Research A 467–468 (2001) 1380–1383

Modelling heating effects in cryocooled protein crystals

James Nicholsona,*, Colin Navea, Khalid Fayzb, Barry Fellb, Elspeth Garmanc

aSynchrotron Radiation Department, Daresbury Laboratory, Warrington, Cheshire, WA4 4AD, UKbEngineering Department, Daresbury Laboratory, Warrington, Cheshire, WA4 4AD, UKcLaboratory of Molecular Biophysics, Oxford University, Oxfordshire, OX1 3QU, UK

Abstract

With the application of intense X-ray beams from third generation synchrotron sources, damage to cryocooledmacromolecular crystals is being observed more commonly [1]. In order to fully utilize synchrotron facilities nowavailable for studying biological crystals, it is essential to understand the processes involved in radiation damage and

beam heating so that, if possible, action can be taken to slow the rate of damage. Finite Element Analysis (FEA) hasbeen applied to model the heating effects of X-rays on cryocooled protein crystals, and to compare the relative coolingefficiencies of nitrogen and helium. # 2001 Elsevier Science B.V. All rights reserved.

PACS: 07.85.Qe; 61.10.Nz; 61.82.Pv

Keywords: Synchrotron; Modelling; Protein; Crystal; Radiation; Damage

1. Introduction

Protein crystals are routinely frozen in fibreloops [2], with the crystal surrounded by a thin filmof frozen cryoprotectant. A schematic diagram ofthe typical set-up is shown in Fig. 1. On secondgeneration sources, such as the SRS at Daresbury,freezing in this way effectively negates radiationdamage due to beam heating and free radicaldiffusion for the duration of data collection [3,4].However, the extremely intense X-ray beams fromthird generation sources, such as the ESRF andthe proposed new UK source DIAMOND, causenoticeable damage to frozen crystals.

This can have serious detrimental effects onboth the quantity and quality of data collected,

especially in MAD experiments where it may benecessary to collect several datasets from a singlecrystal. At present there is insufficient informationavailable about radiation damage and beamheating, and their relationship to incident dose,dose rate, cooling medium and wavelength. Abetter understanding of these processes is vital sothat, if possible, evasive action can be taken toslow the damage rate. Some anecdotal evidenceexists about the temperature fluctuations inirradiated protein crystals. However, these experi-ments tend to be based on measurements withmetal temperature probes which are not accuratemodels for protein crystals.

2. Modelling protein crystals

If accurate parameters for protein crystals,such as density, thermal conductivity and specific

*Corresponding author. Tel.: +44-1925-603-905; fax: +44-

1925-603-124.

E-mail address: j.nicholson@dl.ac.uk (J. Nicholson).

0168-9002/01/$ - see front matter # 2001 Elsevier Science B.V. All rights reserved.

PII: S 0 1 6 8 - 9 0 0 2 ( 0 1 ) 0 0 7 3 5 - 5

heat capacity, were known, it would be straight-forward to calculate temperature fluctuations.However, as these parameters are not wellestablished a suitable model for a protein crystalmust be used. Clathrate hydrates are molecularlattices in which small molecules of one com-pound or element and water molecules aretrapped in holes in the crystal lattice of anothersubstance [5]. Clathrate hydrates are sometimescalled enclosure or cage compounds. They are nottrue compounds, i.e. the molecules are not heldby chemical bonds, but they make a reasonablemodel for protein crystals.

3. Finite element analysis

The objectives of the Finite Element Analysis(FEA) study were to determine the maximum andminimum temperatures generated in protein crys-tals under two different cooling conditions. AllFEA was performed using PTC Mechanica v20.The beam parameters used were based on anESRF multipole wiggler beamline with the X-raybeam (50 mm diameter) smaller than the crystal(100 mm diameter). In this scenario the intensity at

the sample is approximately 1015 photons/s/mm2,giving an absorbed power of 1.02W/mm3 alongthe beam path [6].

The cryoprotectant film surrounding the crystalwas modelled as a lens of ice 300 mm longand 100 mm at its widest point, i.e. at the positionof the crystal. The X-ray beam hits the crystalperpendicular to the plane of the ice lens wherethe thickness of the cryoprotectant is almostzero. Therefore, it is assumed that the powerabsorbed in the surrounding ice and fibre loop isnegligible.

A 3D model was constructed usingregular meshed elements for the crystal andautomesh generated tetra solid elements forthe ice ellipsoid volume. The convergencecriteria, which are a measure of numericalaccuracy of results, were set at 10%. The twodifferent cooling media were nitrogen and helium,which have heat transfer coefficients of300� 10�6W/mm2/K and 800� 10�6W/mm2/K,respectively [7].

4. Results

Steady state temperature distributions forboth nitrogen and helium gas flows show thatthe temperature variation across the crystal isonly 0.098C in each case. When the ice film ofcryoprotectant is added to the model the totaltemperature variation across the system is0.168C and 0.138C for nitrogen and helium gas,respectively.

More significant is the bulk temperature risefrom no beam power up to steady state, which is4.18C and 1.68C for nitrogen and helium gas,respectively. Fig. 2 shows graphs of peak tempera-ture in the crystal with time after the beam is‘‘switched on’’. It is evident that the temperaturerise to steady state is very rapid; approximately400 and 100ms in order to reach �169.08C and�231.48C for nitrogen and helium, respectively.Earlier modelling studies [8] without the cryopro-tectant film, but otherwise under exactly the sameconditions, showed a maximum temperatureincrease to 5.68C in approximately 200ms, with

Fig. 1. Schematic illustration of a 100mm cube protein crystal

surrounded by an ellipsoid film of frozen cryoprotectant. The

focused beam size shown is 0.05mm, as used in the finite

element analysis. The ellipsoid film surrounding the crystal is

300mm long and 100mm at its widest point, i.e. at the position

of the crystal. The X-ray beam hits the crystal perpendicular to

the plane of the film where the thickness of the cryoprotectant is

almost zero.

J. Nicholson et al. / Nuclear Instruments and Methods in Physics Research A 467–468 (2001) 1380–1383 1381

a temperature gradient across the crystal of 1.58C,for nitrogen gas.

5. Conclusions

From the study we can make the followinggeneral conclusions.

1. There are no significant temperature differenceswithin the protein crystal and ice structure andany modelling in future may proceed on thebasis of a ‘‘lumped mass’’ approximation usingsimple hand calculation models rather thanFEA.

2. The temperature gradient within the proteincrystal and ice film is small. In the scenariodescribed, with the beam smaller than thecrystal, it is anticipated that any temperaturedifferences would be most noticeable, therefore,with an X-ray beam comparable in size to thecrystal the temperature gradients across thesystem will be even smaller.

3. If the material properties of the crystal and icefilm are assumed to be fixed, the final steadystate temperature rise depends on the following:

(a) Heat absorbed in the crystal.(b) Surface area of the ice film surrounding the

crystal.(c) The heat transfer coefficient.

Assuming (a) is constant there are two ways toreduce the temperature rise.

The first is to increase the size of the ice filmaround the crystal (b). There will be an optimumsize when the temperature gradient across the icejacket will balance the gains made by increasing thesurface area. However another factor, that of powerabsorption in the ice (assumed to be zero in theanalysis), should also be re-appraised, if thisapproach were to be further investigated. The heattransfer will also be linked, although not verystrongly, to change the surface area since it dependson the diameter of the ellipsoid. The earliermodelling studies, without the ice film, showed agreater overall temperature rise in the crystal and atemperature gradient of 1.58C. This suggests thatthe presence of the ice film facilitates heat removalfrom the crystal in this example. However, increas-ing the size of the ice film may eventually bedetrimental if the effect of the increased tempera-ture gradient across the ice outweighs the gains dueto the increased surface area. In this scenario theeffect of the ice film would be to prevent heat lossthus, effectively insulating the crystal.

Also, in practice increasing the size of the cryo-protectant film, and thus the loop, is problematic.

Fig. 2. Transient temperature increase in the crystal when the

beam is ‘‘switched on’’, using (a) nitrogen and (b) helium gas as

the cooling medium. The bulk temperature rise from no beam

power up to steady state is 4.18C and 1.68C for nitrogen and

helium gas, respectively.

J. Nicholson et al. / Nuclear Instruments and Methods in Physics Research A 467–468 (2001) 1380–13831382

Not only it is difficult to retrieve a proteincrystal with an oversized loop but a largercryoprotectant film could slow down the freezingprocess, leading to ice formation and reduced dataquality [4].

The other option is to increase the heat transfer.This is dictated by (1) the gas properties, (2) theeffective aerodynamic ‘‘size’’ of the crystal (effectsdiscussed above) and (3) the speed of flow.

The importance of (1) gas properties is evidentin the enhanced coefficient provided by heliumover nitrogen. However, helium is well known as a‘‘good’’ thermal gas in many ways, so it is unlikelyto be much improved upon by using other typicalbottled gases. Alternatively, (3) the flow rate maybe increased, but the equations dictate that thespeed (or volumetric rate) must be increasedapproximately four-fold for a two-fold increasein the heat transfer coefficient.

Further modelling studies are planned with avariety of crystal and ice film dimensions andbeam parameters to investigate the potentialeffects of beam heating of protein crystals onhigher intensity beamlines and sources, such asfree-electron lasers.

Acknowledgements

The authors wish to thank the organisers andparticipants of the workshop on X-ray damage tocrystalline biological samples, held at the ESRF inJune 1999, for an extremely stimulating exchangeof information and ideas. It is hoped that furtherworkshops covering this topic will be held in thenear future.

References

[1] C. Nave, Radiat. Phys. Chem. 45 (1995) 483.

[2] T. Teng, J. Appl. Crystallogr. 23 (1990) 387.

[3] H. Hope, Acta. Crystallogr. B 44 (1988) 22.

[4] E.F. Garman, T.R. Schneider, J. Appl. Crystallogr. 30

(1997) 211.

[5] D.F. Shriver, P.W. Atkins, Inorganic Chemistry, 3rd

Edition, Oxford University Press, Oxford, 1999, pp.

262–263.

[6] J.R. Helliwell, From Macromolecular Crystallography

with Synchrotron Radiation, Cambridge University Press,

Cambridge, 1992, pp. 260–268.

[7] Handbook of Physics & Chemistry, 79th Edition, CRC

Press, Boca Raton, FL, pp. 12–197.

[8] J. Nicholson, C. Nave, K. Fayz, B. Fell, E. Garman, 1999,

unpublished results.

J. Nicholson et al. / Nuclear Instruments and Methods in Physics Research A 467–468 (2001) 1380–1383 1383