Phing Li

Stephen D Liew
email: stephen.bell@path.ox.ac.uk

Sir William Bell

Dunn

The interplay of DNA binding, ATP hydrolysis and helicase activities of the archaeal MCM helicase

The MCM proteins of Archaea are widely believed to be the replicative DNA helicase of these organisms. Most archaea possess a single MCM ortholog that forms homo-multimeric assemblies with a single hexamer believed to be the active form. Here we characterize the roles of highly conserved residues in the ATPase domain of the MCM of the hyperthermophilic archaeon Sulfolobus solfataricus. Our results identify a potential conduit for communicating DNA binding information to the ATPase active site.

Introduction

The homomultimeric MCM proteins of archaea have been studied for a number of years. In particular, considerable effort has been put into analyses of the MCMs encoded by Methanothermobacter thermautotrophicum (MthMCM) and Sulfolobus solfataricus (SsoMCM) (For reviews see [START_REF] Bochman | The Mcm Complex: Unwinding the Mechanism of a Replicative Helicase[END_REF][START_REF] Brewster | Insights into the MCM functional mechanism: lessons learned from the archaeal MCM complex[END_REF][START_REF] Costa | Structural biology of MCM helicases[END_REF][START_REF] Sakakibara | Unwinding the structure and function of the archaeal MCM helicase[END_REF]). In agreement with the proposed role of archaeal MCMs as the replicative helicase, SsoMCM is enriched at replication origins at the time of replication initiation in vivo [START_REF] Duggin | Chromosome replication dynamics in the archaeon Sulfolobus acidocaldarius[END_REF]. Furthermore, in vitro studies have revealed that the recombinant protein forms homohexamers and is capable of directing (d)ATPdependent melting of partially duplex DNA substrates [START_REF] Mcgeoch | Organization of the archaeal MCM complex on DNA and implications for the helicase mechanism[END_REF]. Ensemble and single-molecule FRET studies indicate that the enzyme loads onto 3' to 5' polarity single stranded DNA tails with the C-terminal proximal domains facing the duplex DNA [START_REF] Mcgeoch | Organization of the archaeal MCM complex on DNA and implications for the helicase mechanism[END_REF][START_REF] Rothenberg | MCM forked substrate specificity involves dynamic interaction with the 5 '-tail[END_REF]. This loading results in single stranded DNA passing through a central pore in the homohexameric MCM ring where it is contacted by basic residues supplied by -hairpin motifs that line the pore. One -hairpin is supplied by the N-terminal domains of the protein and a second, the presensor 1 -hairpin (PS1BH), is found in the C-terminal AAA+ ATPase domain of the MCM [START_REF] Mcgeoch | Organization of the archaeal MCM complex on DNA and implications for the helicase mechanism[END_REF][START_REF] Barry | Archaeal MCM has separable processivity, substrate choice and helicase domains[END_REF]. Interestingly, the N-terminal domains of MCM, although dispensable for helicase activity in vitro, do play significant roles in modulating substrate choice, enhancing processivity and facilitating inter-subunit communication [START_REF] Barry | Archaeal MCM has separable processivity, substrate choice and helicase domains[END_REF][START_REF] Barry | Intersubunit allosteric communication mediated by a conserved loop in the MCM helicase[END_REF]. Furthermore, the N-terminal domains have been shown to interact with the archaeal GINS complex in vivo and in vitro [START_REF] Marinsek | GINS, a central nexus in the archaeal DNA replication fork[END_REF]. The Cterminal PS1BH has been shown to be important for DNA binding and mutation of a single lysine residue at its tip results in a mutant protein with impaired DNA binding, ATPase activity that is no longer stimulated by DNA and complete loss of helicase activity [START_REF] Mcgeoch | Organization of the archaeal MCM complex on DNA and implications for the helicase mechanism[END_REF]. In addition, studies of the MthMCM have implicated a second conserved element within the AAA+ domain of the MCM in DNA melting. Deletion of this module, the H2I, a β-α-β structure in the AAA+ fold, resulted in elevated DNA binding and DNA-stimulated ATPase activity but complete loss of helicase activity [START_REF] Jenkinson | Minichromosome maintenance helicase activity is controlled by N-and C-terminal motifs and requires the ATPase domain helix-2 insert[END_REF]. Recently a 4.35 Å resolution structure of a monomeric form of SsoMCM has been reported [START_REF] Brewster | Crystal structure of a nearfull-length archaeal MCM: Functional insights for an AAA plus hexameric helicase[END_REF]. The PS1BH and H2I are adjacent to one another and modeling of a hexameric form of the protein predicts that they point in towards the central cavity of the hexameric ring. Importantly, evidence has been obtained that indicates that both the PS1BH and H2I undergo re-positioning during the ATP utilization cycle of the helicase [START_REF] Barry | Intersubunit allosteric communication mediated by a conserved loop in the MCM helicase[END_REF][START_REF] Jenkinson | Minichromosome maintenance helicase activity is controlled by N-and C-terminal motifs and requires the ATPase domain helix-2 insert[END_REF]. These observations are in agreement with structural studies of the distantly related Superfamily 3 helicases. More specifically, studies of the SV40 LTag and BPV E1 helicases have revealed that the analogous PS1BH hairpin in these helicases undergo movements of up to 17 Å during ATP binding, hydrolysis and release by the helicase, serving as the power stroke to drive the helicase along DNA [START_REF] Enemark | Mechanism of DNA translocation in a replicative hexameric helicase[END_REF][START_REF] Enemark | On helicases and other motor proteins[END_REF][START_REF] Gai | Mechanisms of conformational change for a replicative hexameric helicase of SV40 large tumor antigen[END_REF]. In MCM, the PS1BH of a given subunit is close to a conserved loop (the ACL) in the Nterminal domains of the adjacent protomer within the hexameric assembly. The ACL plays a key role in communicating information between protomers within the hexamer [START_REF] Barry | Intersubunit allosteric communication mediated by a conserved loop in the MCM helicase[END_REF]. Thus, repositioning of the PS1BH during the reaction cycle may serve dual roles -to act as the power stroke and to propagate cooperative interactions between SsoMCM monomers.

Analyses of MCM with mutations in residues predicted to play roles in the ATPase activity of the protein, coupled with mutant doping studies, have revealed that MCM has a rather unusual form of limited cooperativity between protomers [16]. Furthermore, these studies revealed an unusual architecture for the AAA+ ATPase domain of the helicase. Typical AAA+ proteins function as multimers with the ATPase active site formed at the interface between protomers [START_REF] Erzberger | Evolutionary relationships and structural mechanisms of AAA plus proteins[END_REF]. Thus, both subunits contribute residues to the active site. One subunit acts as a "cis" site and contributes sidechains such as the Walker A (K346 in SsoMCM), Walker B (D404) and Sensor 1 (N488) residues. However the neighbouring protomer also plays an active role and contributes "trans" acting residues such as the Arg finger (R473 in SsoMCM). ATP binding, hydrolysis and release can thus effect repositioning of adjacent subunits. In addition, intra-subunit motions are mediated by repositioning of the two principal domains of the AAA+ site, the lid and base domains. The Sensor 2 motif normally plays a key role in this intra-molecular repositioning event. Interestingly, however, MCM has a highly unusual configuration of the Sensor 2 residue (Arg 560 in SsoMCM). As initially predicted bioinformatically, and subsequently verified biochemically and structurally, an alpha helical insertion preceding the Sensor 2 motif in MCM results in Sensor 2 acting in trans rather than the usual cis configuration [START_REF] Brewster | Crystal structure of a nearfull-length archaeal MCM: Functional insights for an AAA plus hexameric helicase[END_REF]16,[START_REF] Erzberger | Evolutionary relationships and structural mechanisms of AAA plus proteins[END_REF]. Additionally, complementation data suggested that MCM may possess a number of additional trans-acting residues, clustered around the base of the PS1BH [16]. Precedent for multiple trans-acting residues has been found in the distantly related viral Superfamily 3 helicases such as SV40 LTag and Bovine Papilloma Virus E1. However, whether the candidate trans-acting residues in MCM do indeed directly coordinate ATP, as in the SF3 helicases, or whether they have an indirect role via facilitating the positioning of bona fide trans-acting residues is unknown.

In the current work we address the roles of a cluster of highly conserved residues that occupy a pivotal position in SsoMCM, lying at the juxtaposition of the PS1BH and the post-Sensor 2 alpha helix. We identify R329 as a key residue in the communication between the DNA binding site of SsoMCM and the trans component of the ATPase active site.

Experimental

Site-directed mutagenesis and protein purification

Site-directed mutagenesis was performed using the single primer site-directed mutagenesis method (Stratagene). The primers used for mutagenesis are shown in Table 1. Proteins were purified as described previously [START_REF] Mcgeoch | Organization of the archaeal MCM complex on DNA and implications for the helicase mechanism[END_REF]. Briefly, proteins were expressed in E. coli strain Rosetta (DE3). 1 L of transformants were grown to A 600nm =0.6 before being induced with 1 mM IPTG (Isopropyl β-D-1-thiogalactopyranoside) for 3 hours. Cells were harvested by centrifugation and resuspended in 25ml 1× TBS (10mM Tris-HCl pH 8.0, 150mM NaCl) containing 14mM β-Mercaptoethanol and one tablet of Complete EDTA-free Protease Inhibitor Cocktail (Roche). Cells were lysed using a French Press (Thermo Spectronic) followed by heat treatment at 75°C for 20 minutes and clarification by centrifugation. MCM proteins was first purified over a 5 ml HiTrap Heparin HP column (GE Healthcare) using an AKTA Prime system (Amersham Bioscience). After the column was pre-equilibrated with 1× TBS, sample was injected and unbound proteins were flushed with 5 column volumn (cv) of 1× TBS. With all the steps run at a flow rate of 2.5 ml/min, proteins were eluted with a 15 cv gradient from 150mM to 1M NaCl in 10mM Tris-HCl pH 8.0. 5 ml fractions were collected and analysed by SDS-PAGE and Coomassie staining. Protein-containing fractions were pooled and concentrated to ≤ 5 ml using a Vivaspin 20 of 30k MWCO PES (Sartorius Stedim Biotech). The concentrated proteins were then purified over a Hi-load 26-60 Superdex 200 prep grade column (Amersham Biosciences) using an AKTA Purifier system (GE Healthcare). The column was first equilibrated with 1× TBS before sample was injected. Proteins were eluted with 1 cv (≈ 350 ml) of 1× TBS and were collected after 100 ml of elution. 5 ml fractions were collected and analysed by SDS-PAGE and Coomassie staining. Proteincontaining fractions were pooled and further purified over a Mono Q 5/50 GL column (GE Healthcare) using an AKTA Purifier system (GE Healthcare). The column was first equilibrated with 1× TBS, sample was then injected and unbound proteins were flushed with 2 cv of 1× TBS at a flow rate of 1 ml/min. To elute proteins, a 15 cv gradient from 150 mM to 1M NaCl in 10mM Tris-HCl pH 8.0 was applied. Samples were collected at 0.5 ml fraction and were analysed by SDS-PAGE and Coomassie staining. Protein-containing fractions were pooled and concentrated to ≤ 0.5 ml using a Vivaspin 2 of 30k MWCO PES (Sartorius Stedim Biotech). A c c e p t e d M a n u s c r i p t Licenced copy. Copying is not permitted, except with prior permission and as allowed by law.

before the resultant partial duplex molecule probe was purified via recovery from a gel slice following electrophoresis on a 8% PAGE gel. DNA-binding was performed by mixing 10nM labelled Y-shaped DNA substrate with the indicated concentration of protein in 50 mM potassium acetate, 20 mM Tris-acetate, 10 mM magnesium acetate, 1 mM DTT pH 7.9 and 5% glycerol. Binding reactions were incubated at 50°C for 15 minutes prior to electrophoresis on a 6% polyacrylamide gel (17 cm × 17 cm × 1.5 mm) in 1× TBE at 10 V per cm. Gels were dried and analysed by phosphorimagery (Fujifilm FLA-5000). Quantitation was performed by using the Aida Image Analyzer software (Raytest Isotopenmeβgeräte GmbH, Germany).

ATPase assay

ATP hydrolysis was performed in a 20 μl reaction volume containing 50 mM potassium acetate, 20 mM Tris-acetate, 10 mM magnesium acetate, 1 mM DTT pH 7.9, 1 mM ATP (Sigma), 25 nCi γ-32 P-ATP, and 1 μM of protein.

Where DNA was added, the Y-shaped substrate described above was added to 1 μM. Reactions were incubated at 60°C for 30 minutes before termination by the addition of 1% SDS. Samples were then analyzed using thin-layer chromatography by spotting 2 μl of each sample on CEL 300 PEI TLC plates (Macherey-Nagel), which was subsequently developed with 0.8 M lithium chloride 1 M formic acid buffer. Analysis was performed by phosphorimagery (Fujifilm FLA-5000) and quantification using Aida Image Analyzer software (Raytest Isotopenmeβgeräte GmbH, Germany).

Helicase Assay

DNA unwinding was performed in a 20 μl reaction volume containing 50 mM potassium acetate, 20 mM Tris-acetate, 10 mM magnesium acetate, 1 mM DTT pH 7.9, 1 nM Y-shaped DNA probe (prepared as described above), 10 mM ATP, 2 µg BSA and indicated amount of proteins. Reactions were incubated at 65°C for 45 minutes before addition of 20 μl stop buffer (100 mM EDTA, 2% SDS, 0.1% bromophenol blue, and 40% glycerol). Samples were electrophoresed on a 8% polyacrylamide gel (17 cm × 17 cm × 1.5 mm) in 1× TBE 0.2% SDS. Gels were run for 90 minutes at 12 V per cm before drying and analysis by phosphorimagery (Fujifilm FLA-5000). Quantitation was performed by using Aida Image Analyzer software (Raytest Isotopenmeβgeräte GmbH, Germany).

ATPase Complementation assay

Reactions were preformed as described previously [16]. 1µM of indicated mutant proteins were mixed for 15 minutes prior to ATPase assays.

Results and Discussion

Examination of the sequence conservation of archaeal and eukaryotic MCMs with reference to the 4.35 Å crystal structure of SsoMCM reveals an intriguing juxtaposition of secondary structure elements within SsoMCM. Although the low resolution of the available structure precludes accurate positioning of side chains, it is apparent that the helix following the Sensor 2 Arginine residue (R 560) lies on top of the base of a feature described by Chen and colleagues as the external hairpin (EXT-HP) [START_REF] Brewster | Crystal structure of a nearfull-length archaeal MCM: Functional insights for an AAA plus hexameric helicase[END_REF]. Additionally, the EXT-HP precedes the first beta sheet of the AAA+ domain, this beta sheet is followed by the essential Walker A motif (including K346). Examination of sequence conservation reveals that there is a cluster of highly conserved residues in the vicinity of the base of the EXT-HP (Fig. 1 and Figure S1). We reasoned that this cluster might have roles in influencing the ATPase activity of the MCM. In principle this hypothetical influence could be effected by modulation of either the cis-or trans-properties of the MCM. In the case of the former, cis-, scenario the residues at the base of the EXT-HP could influence the positioning of the residues of the Walker A motif. Alternatively, the trans-acting activity of the MCM subunit could be altered, by virtue of the residues at the base of the EXT-HP influencing the positioning of the overlying alpha-helix and thereby transducing effects to the Sensor 2 R560 residue. Furthermore, the base of the EXT-HP is additionally juxtaposed to the base of the PS1BH. Thus, we speculated that there might be a route of communication from the PS1BH, via the EXT-HP to the AAA+ active site.

Previous work from our laboratory had addressed the roles of two adjacent glutamines (Q423 and Q424) at the base of PS1BH, these residues were found to act as trans-residues and to be absolutely required for ATPase and helicase activity of MCM; mutation of these residues to alanine abrogated both activities. In addition, we have revealed that R331 (at the base of the EXT-HP) was similarly essential for helicase and ATPase activities and also appeared to play a trans-role [16]. However, the molecular basis of this phenotype was not resolved in the previous work.

In the current work, we have made a further seven mutations to four conserved residues. These include E422A and E422R, E422 is a extremely highly conserved residue that precedes the previously described Q423Q424. We also generated R329E, R329 is a conserved basic residue at the base of the EXT-HP. In addition, we made R331I and R331K mutants as well as targeting L565, a conserved hydrophobic residue in the helix following the Sensor 2 residue (R560), modelling of this residue suggests it is in close physical proximity to the R331 -L565 residue was mutated to aspartate or lysine. The resultant mutant proteins were purified and found to elute as hexamers from gel filtration columns (not shown). We next subjected them to tests of their biochemical activities.

First we tested DNA binding activity, using a model Y-shaped DNA substrate in electrophoretic mobility shift assays (EMSAs). As can be seen in Figure 2 all mutant proteins retained the ability to bind DNA, albeit with affinities somewhat altered from the wild-type protein. More specifically, the E422A and R331K mutant MCMs showed up to two-fold higher affinity for the DNA substrate than the wild-type MCM; MCM (L565D), MCM (R331I) and MCM (E422R) had the same affinity as the wild-type and R329E and L565K had up to two-fold lower affinity for DNA.

Next, we tested the ability of the mutants to hydrolyse ATP in the presence and absence of DNA (Figure 3). As we have reported previously, the ATPase activity of wild-type SsoMCM is modestly stimulated (approximately 2-fold) by the presence of DNA. The MCM (R331K), MCM (E422A) and both MCM (L565D) and MCM (L565K) demonstrated ATPase properties similar to wildtype while MCM (R331I) and MCM (E422R) lost the ability to hydrolyse ATP. Interestingly, the R329E mutant MCM had significantly reduced ATPase activity and this was no longer stimulated by the addition of DNA. As MCM (R329E) displayed a 2-fold reduced DNA binding affinity when compared to the wild-type protein, we note that the concentration of DNA added to these assays was 1 µM, a 13-fold higher concentration than the Kd measured in Figure 2. Therefore we think it is unlikely that the non-responsiveness of this mutant to DNA was a simple consequence of having modestly lowered DNA binding activity compared to the wild-type enzyme.

Having established the DNA binding and ATPase activities of the mutant MCMs, we next assayed their ability to effect DNA melting using Y-shaped oligonucleotide substrates (Figure 4). In agreement with the inability of the MCM (R331I) and MCM (E422R) proteins to hydrolyse ATP, these mutants also lacked detectable helicase activity. The MCM (R331K) mutant showed helicase activity at about half the level of wild-type and interestingly, the MCM (R329E) mutant showed similar activity to MCM (R331K), despite its low and non-DNA stimulated ATPase activity. While the E422R mutant MCM had no detectable helicase activity, the potentially less invasive mutation to alanine, E422A, resulted in essentially wild-type activity. Finally, mutation of L565 to either aspartate or lysine (L565D or L565K) significantly stimulated the helicase activity of the resultant mutant protein when compared to wild-type. Significantly, these mutants do not show any elevation of either DNA binding or ATPase rates, suggesting that these alterations enhance the coupling between ATP hydrolysis and helicase activity.

The reduction of the ATPase activities of the E422R and R329E mutant MCMs could be due to the wild-type residues contributing to the ATPase active site. As detailed above, the ATPase site is generated by the juxtaposition of two MCM subunits with coordinating residues being donated by both subunits -following previous convention we have termed these cisacting residues [such as Walker A (K346), Walker B (D404) and Sensor 1 (N488) residues] or trans-acting, the classic example being the Arginine finger (R473) and additionally, in the case of MCM, Sensor 2 (R560) and other basic residues [16]. We have shown previously that while mutation of cis or trans residues affects ATPase activity in homomultimers, mixing a cis mutant and a trans mutant can regenerate activity [16]. This arises because the cis mutant has a wild-type trans site and conversely the trans mutant has a wild-type cis site. Appropriate apposition of subunits of the two mutant types can thus reconstitute a functional active site. We therefore tested the effect of mixing either E422R or R329E mutant with MCM containing the Walker A lysine cis mutant K346E or a second mutant MCM with an isoleucine substitution of the previously identified trans-residue R331. As can be seen in Figure 5A, mixing MCM (E422R) with MCM (K346E) restored ATPase activity, indeed levels were significantly higher than wild-type. In contrast, mixing MCM (E422R) with MCM (R331I) did not restore ATPase activity. Similarly, the R329E mutant is complemented by the cis mutant K346E but not by the trans mutant R331I (Figure 5B). Taken together these data reveal that both MCM (E442R) and MCM (R329E) mutants have specific impairments in the trans component of the ATPase active site.

Perhaps the simplest explanation for the "trans phenotype" of these residues would be that the residues' side chains directly coordinate ATP in the active site. This however does not appear to be the case for E422 as the E422A mutant protein, while having modestly elevated affinity for DNA, has essentially wild-type ATPase and helicase activities. This therefore indicates that the side chain of E422 is not directly involved in coordinating the ATP moiety.

The E422R and R329E mutant SsoMCMs, while both acting as trans mutants, show distinct behaviours. SsoMCM (E422R) has essentially wild-type DNA binding but no detectable ATPase or helicase activities. In contrast, R329E, while less active than the wild-type protein, nevertheless retains helicase activity despite its weak ATPase activity no longer being stimulated by the addition of DNA. Given the relatively close juxtaposition of E422 and R329 in the structure of SsoMCM, we tested whether an E422R R329E double mutant could restore activity. However, in agreement with the distinct properties of the individual mutations, the double mutant, like the E422R single mutant, lacked detectable ATPase and helicase activities (data not shown).

Our studies of the R331 residue in the EXT-HP confirm our previous data that the basic side chain of this residue is of pivotal importance for the ATPase and helicase activities of SsoMCM. Notably, however, mutation of this residue to isoleucine has no effect on the DNA binding activity of the enzyme. Interestingly, the similarly highly conserved R329 shows a different phenotype, a charge-reversal mutation of this residue to glutamate has a modest effect on DNA binding but renders the SsoMCM's ATPase activity non-responsive to the addition of DNA. This indicates that this mutation is defective in transducing information from the DNA binding site of the helicase to the ATPase active site. The behaviour of this mutant is superficially reminiscent of that of the T364E mutation of the glutamate switch [START_REF] Zhang | The 'glutamate switch' provides a link between ATPase activity and ligand binding in AAA+ proteins[END_REF][START_REF] Mogni | The Glutamate Switch is present in all seven clades of AAA+ protein[END_REF]. The glutamate switch is a conserved residue in all clades of AAA+ ATPases that plays a key role in aligning the catalytic glutamate in the Walker B motif for activation of a water molecule during ATP hydrolysis [START_REF] Zhang | The 'glutamate switch' provides a link between ATPase activity and ligand binding in AAA+ proteins[END_REF][START_REF] Mogni | The Glutamate Switch is present in all seven clades of AAA+ protein[END_REF]. Like the R329E mutant, the glutamate switch mutant SsoMCM (T364E) can still bind DNA yet displays lowered helicase activity and has reduced ATPase activity that is no longer stimulated by DNA. However, T364 exerts its influence via the cisacting Walker B motif and thus contrasts with the trans-acting R329. Given the proximity of the base of the R329-containing EXT-HP and the alpha helix preceding the trans-acting Sensor 2 R560, it is tempting to speculate that A c c e p t e d M a n u s c r i p t R329 may influence the position of the Sensor 2 residue. Furthermore, the EXT-HP is additionally juxtaposed to the DNA-binding PS1BH. In this regard, it may be significant that we have previously demonstrated that mutation of a conserved lysine (K430) located at the tip of the PS1BH results in an enzyme that, like the R329E MCM, shows lowered basal ATPase activity that is no longer stimulated by DNA [START_REF] Mcgeoch | Organization of the archaeal MCM complex on DNA and implications for the helicase mechanism[END_REF].

Taken together, these observations lead us to propose that R329 plays a key role in transducing positional information from the DNA binding PS1BH to the trans-acting face of the ATPase active site, an event at the heart of the mechanochemistry of the MCM helicase. Licenced copy. Copying is not permitted, except with prior permission and as allowed by law.

Biochemical

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Biochemical

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Biochemical

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Biochemical

  Journal Immediate Publication. Published on 01 Mar 2011 as manuscript BJ20110084 THIS IS NOT THE VERSION OF RECORD -see doi:10.1042/BJ20110084

Figure 1 :

 1 Figure 1: A Model of the hexameric form of SsoMCM (generated from PDB file 3F9V) showing the two tiered appearance of the hexamer. The upper (Cterminal) tier contains the AAA+ ATPase modules of the monomers. The two subunits closest to the viewer are coloured green and cyan. The cis-acting residues (Walker A, Walker B and Sensor 1) of the green subunit are shown as lilac spheres. The positons of residues E422, L565, R331 and R329 that were targeted for mutagenesis are indicated and the PS1BH and H2I are shown in yellow and tan. Note that because of the low resolution (4.35Å) of the structure (ref. 12) all residues are represented by alanine in this representation. Part B shows a closer view of the AAA+ domain of a single monomer, the positions of the residues targeted for mutagenesis are indicated and the resides are shown in colour stick form. Note that although this representation shows residue side chains, the 4.35Å resolution of the current SsoMCM structure precludes accurate positioning of the sidechains [12].

Figure 2 :

 2 Figure 2: DNA binding activity of WT and mutant SsoMCM to a Y-shaped DNA substrate. Quantification of EMSAs using 0, 15.6, 31.3, 65.5, 125 and 250 nM of each protein are shown. The assays were performed at least three times, and the error bars indicate the standard error of the mean. (A) DNA binding activity of WT, R331I, R331K, E422A and L565D. (B) DNA binding activity of WT, R329E, E422R and L565K.

Figure 3 :

 3 Figure 3: ATPase activity of WT and mutant SsoMCM in the presence and absence of DNA. 1 µM of MCM proteins were used. The assays were performed at least three times, and the error bars indicate the standard error of the mean.

Figure 4 :

 4 Figure 4: Helicase activity of WT and mutant SsoMCM. 0 (-), 31.3, 65.5, 125, 250, 500 and 1000 nM of each protein were used. The assays were performed at least three times, and the error bars indicate the standard error of the mean. (A) Helicase activity of WT, R331I, R331K, E422A and L565D. (B) Helicase activity of WT, R329E, E422R and L565K.

Figure 5 :

 5 Figure 5: ATPase complementation study of E422R (A) and R329E (B). ATPase activity of 1 µM WT and mixtures containing 1 µM of the indicated mutants and either 1 µM of Walker A K346E or trans-ATPase motif R331I mutant. The assays were performed at least three times, and the error bars indicate the standard error of the mean.

1

 1 Biochemical Journal Immediate Publication. Published on 01 Mar 2011 as manuscript BJ20110084 THIS IS NOT THE VERSION OF RECORD -see doi:10.1042/BJ20110084 A c c e p t e d M a n u s c r i p t Licenced copy. Copying is not permitted, except with prior permission and as allowed by law. © 2011 The Authors Journal compilation © 2011 Portland Press Limited Liew and Bell Figure 2

3 4 5 Biochemical

 345 Publication. Published on 01 Mar 2011 as manuscript BJ20110084 THIS IS NOT THE VERSION OF RECORD -see doi:10.1042/BJ20110084 A c c e p t e d M a n u s c r i p t Licenced copy. Copying is not permitted, except with prior permission and as allowed by law. © 2011 The Authors Journal compilation © 2011 Portland Press Limited Biochemical Journal Immediate Publication. Published on 01 Mar 2011 as manuscript BJ20110084 THIS IS NOT THE VERSION OF RECORD -see doi:10.1042/BJ20110084 A c c e p t e d M a n u s c r i p t Licenced copy. Copying is not permitted, except with prior permission and as allowed by law. © 2011 The Authors Journal compilation © 2011 Portland Press Limited Biochemical Journal Immediate Publication. Published on 01 Mar 2011 as manuscript BJ20110084 THIS IS NOT THE VERSION OF RECORD -see doi:10.1042/BJ20110084 A c c e p t e d M a n u s c r i p t Licenced copy. Copying is not permitted, except with prior permission and as allowed by law. © 2011 The Authors Journal compilation © 2011 Portland Press Limited Journal Immediate Publication. Published on 01 Mar 2011 as manuscript BJ20110084 THIS IS NOT THE VERSION OF RECORD -see doi:10.1042/BJ20110084 A c c e p t e d M a n u s c r i p t

Table 1 : Site-directed mutagenesis primers used in this study.

 1 Biochemical Journal Immediate Publication. Published on 01 Mar 2011 as manuscript BJ20110084 THIS IS NOT THE VERSION OF RECORD -see doi:10.1042/BJ20110084

	Mutation Primer sequence (5' to 3')
	R329E	AAGGTTCTAGAAGATACGGAAATAAGAGGAGATATTCACA
	R331I	CTAGAAGATACGAGAATAATAGGAGATATTCACATACTG
	R332K	CTAGAAGATACGAGAATAAAAGGAGATATTCACATACTG
	E422A	GCCATTCATGAGGCAATGGCACAACAGACAGTCTCAATA
	E422R	GCCATTCATGAGGCAATGAGACAACAGACAGTCTCAATA
	L565D	CCAAGACAATTAGAGGCTGATATAAGAATTTCAGAAGCC
	L565K	CCAAGACAATTAGAGGCTAAAATAAGAATTTCAGAAGCC
	EMSA
	The Y-shaped DNA substrate was prepared by radio-labelling the
	oligonucleotide
	((T) 44 GCTCGTGCAGACGTCGAGGTGAGGACGAGCTCCTCGTGACCACG)
	with γ 32 P-ATP. This radio-labelled molecule was then annealed to its
	complementary	strand
	(CGTGGTCACGAGGAGCTCGTCCTCACCTCGACGTCTGCACGAGC(T) 44 )

Licenced copy. Copying is not permitted, except with prior permission and as allowed by law.© 2011 The Authors Journal compilation © 2011 Portland Press Limited

© 2011 The Authors Journal compilation © 2011 Portland Press Limited

Acknowledgements

The work was funded by the BBSRC.


Binod Sreenivasan

On dynamo action produced by boundary thermal coupling

Rotating dynamos controlled by laterally varying thermal conditions at the boundary are investigated in this paper. A quasi-stationary, locked dynamo solution is obtained when the thermal winds produced by the non-axisymmetric lateral variations come into an approximate balance with the Coriolis forces. This force balance is verified numerically for both equatorially symmetric and antisymmetric boundary variations. The introduction of lateral variations at the boundary can excite dynamo action in a weakly convective regime that does not otherwise sustain a magnetic field with homogeneous boundary heating. A sufficiently large lateral variation drives strong radial and axial fluid motions near the equatorial plane; these flows in turn generate the helicity required for dynamo action. It is shown that a boundary-locked dynamo operates in a state of equipartition between the velocity and magnetic fields. The departure from equipartition in a partially locked dynamo allows the magnetic energy to be greater than the kinetic energy. As the balance of forces in a locked dynamo is different from that in a convection-driven dynamo, lower-mantle coupling could have a marked effect on the structure and dynamics of convection in the Earth's core.

where convection in the Earth's outer core is thought to be affected by lateral inhomogeneities in the lower mantle. As the convective turn-over time in the lower mantle is considerably larger than that in the underlying molten core, these lateral variations constitute an approximately static outer boundary condition that could organize core convection in a preferred pattern. Laboratory experiments on rotating, nonmagnetic convection (Sumita & Olson, 1999) showed how a multicolumnar, westward-drifting convection pattern gives way to a locked downwelling front, when a section of the outer boundary is cooled.

Numerical studies of rotating convection indicated that a lateral variation in heat flux at the boundary can lock a flow that would otherwise drift (Zhang & Gubbins, 1993). Several dynamo calculations with variable boundary heating [START_REF] Sarson | The influence of boundary region heterogeneities on the geodynamo[END_REF][START_REF] Glatzmaier | The role of the Earth's mantle in controlling the frequency of geomagnetic reversals[END_REF][START_REF] Olson | The time-averaged magnetic field in numerical dynamos with non-uniform boundary heat flow[END_REF][START_REF] Aubert | Detecting thermal boundary control in surface flows from numerical dynamos[END_REF] have presented evidence for a correlation between the magnetic field and boundary thermal anomalies, at least in a time-averaged sense.

Recent studies produced, for the first time, dynamos where the magnetic field was nearly locked to lateral variations in heat flux defined by seismic tomography [START_REF] Gubbins | Correlation of Earth's magnetic field with lower mantle thermal and seismic structure[END_REF][START_REF] Gubbins | Correlation of Earth's magnetic field with lower mantle thermal and seismic structure[END_REF], enabling direct comparison of a model magnetic field to the present-day geomagnetic field. Although the solution was not stationary, the characteristic four main magnetic flux lobes persisted for many diffusion times at the same sites as the main lobes of the geomagnetic field. These high-latitude magnetic flux concentrations are found to be relatively stationary during the historical period (Bloxham & Gubbins, Email address: binod@earth.leeds.ac.uk (Binod Sreenivasan).

Page 3 of 32 A c c e p t e d M a n u s c r i p t 1985; [START_REF] Jackson | Four centuries of geomagnetic secular variation from historical records[END_REF] and appear to persist in the time-averaged paleomagnetic field from the past few million years [START_REF] Johnson | The time-averaged geomagnetic field as recorded by lava flows over the past 5 Myr[END_REF].

The magnetohydrodynamic (MHD) regime that produces quasi-stationary flux lobes in a dynamo model is significant in two respects: First, it can give insights into the MHD regime that exists in the Earth's liquid iron core. Secondly, lower-mantle effects in the Earth and in different dynamo simulations can be understood with reference to a basic, locked solution. The present paper therefore examines the dynamics of boundary thermal locking in a rotating dynamo. It is shown that the balance of forces in a locked dynamo is fundamentally different from that in a classical, convection-driven dynamo with homogeneous boundary heating. The role of lateral thermal variations in supporting dynamo action under weak buoyancy-driven convection is also investigated for the first time in a computational experiment. This paper is organized as follows. In Section 2 the governing equations and operating parameters in the model are presented. In Section 3 the dynamics of the locked dynamo are investigated. This includes the behaviour of the energies and lengthscales, the principal force balances and the possible role of the lateral variations in supporting dynamo action. Comparisons with classical dynamos with homogeneous boundary heating are made where appropriate.

Finally, in Section 4 the main results of this paper and their implications for the Earth are discussed.

Governing equations

We consider a thermal convection-driven dynamo where an electrically conducting fluid is confined between two concentric, co-rotating spherical surfaces.

The radius ratio r i /r o is chosen to be that in the Earth, 0.35. In the Boussinesq approximation, the time-dependent, 3D MHD equations for the velocity u, the magnetic field B and the temperature T are solved numerically. The governing dimensionless equations are,

E P m ∂u ∂t + (∇ × u) × u + ẑ × u = -∇p + Ra q T r + (∇ × B) × B + E∇ 2 u, (1)
∂B ∂t = ∇ × (u × B) + ∇ 2 B, (2)
∂T ∂t + (u • ∇)T = P mP r -1 ∇ 2 T + Q s , (3)
∇ • u = ∇ • B = 0, ( 4
)
where p is an augmented fluid pressure that includes the irrotational part of the nonlinear inertial forces and Q s is a uniform volumetric heat source/sink.

The dimensionless groups in Equations ( 1

Basic heating modes and boundary variations

In Cases 1-4 of Table 1, convection is driven by the basic state temperature profile T 0 (r) = β i (r 2 ir 2 )/2, where r i is the inner radius and β i is related to a uniform, dimensional heat source, Q s by β i = Q s /3κ. A Y 2 2 harmonic variation in heat flux is imposed on the outer boundary. The modified Rayleigh number for these cases is given by Ra = gαβ i L 3 /2Ωκ, where g is the gravitational acceleration and α is the coefficient of thermal expansion. The ratio of the maximum (peak-to-peak) variation in heat flux to the mean heat flux at the outer boundary gives the lateral inhomogeneity factor, denoted by f . In Cases 5 & 6 of Table 1, the basic state temperature distribution is one of pure basal heating, T 0 (r) = β b /r, where β b = r i r o . A lateral variation in temperature is imposed on the outer boundary. The Rayleigh number for these cases is given by Ra = gα∆T L/2Ωκ, where ∆T is the basic state temperature In Case 7, a temperature profile that represents a combination of basal heating and intrinsic cooling is considered: T 0 (r) = -β i r 2 /2+β b /r, where β b = r i r o and

β i = -0.25. A Y 2
2 variation in temperature is imposed on the outer boundary. The Rayleigh number is defined based on the temperature drop across the layer from basal heating alone, and the inhomogeneity factor has the same definition as in Cases 5 & 6.

Results

Flow structures, energies and lengthscales

We begin the study with Cases 1-4 in Table 1 where a Y 2 2 variation in heat flux is applied at the outer boundary. The Ekman number is fixed at E = 10 -4 , for which the onset of thermal convection occurs at Ra c ≈ 22.8, where Ra c is the critical Rayleigh number. The Rayleigh number is fixed at a marginally supercritical value (Ra ≈ 1.5Ra c ). Since the convective Rayleigh number is small, the ratio of thermal to magnetic diffusivities, q is set to 10 for possible magnetic field generation. For a lateral inhomogeneity factor f ≤ 0.6, a multicolumnar flow is present as shown in Fig. 1(a); however, there is no dynamo action. Fig. 2 shows the kinetic and magnetic energies, given by

E k = 1 2 u 2 dV ; E m = P m 2E B 2 dV. ( 5
)
Page 7 of 32

A c c e p t e d M a n u s c r i p t

For f = 0.9 dynamo action is produced with the magnetic energy being greater than the kinetic energy. As f is increased to 1.6, the amplitude of oscillations in the energy is reduced. The kinetic and magnetic energies are found to be approximately equal (see Fig. 2 and also Table 2). The dominant structure of the flow for 0.9 < f < 1.6 consists of two static downwellings near φ = ±π/2, as shown in Fig. 1(b) and Fig. 3 3(a) concentrate the radial magnetic flux in four distinct lobes that are symmetric with respect to the equator, as shown in Fig. 3(b). Now, the azimuthal lengthscales of the velocity and magnetic field, l u and l B , may be estimated from a weighted average of the respective wavenumbers, m, as follows:

m u = m < u 2 m > u 2 dV ; m B = m < B 2 m > B 2 dV , (6)
where the angled brackets represent time averages and the sum is over all m.

The lengthscales l u and l B are given by 2π/m u and 2π/m B . An alternative, 'dissipative' lengthscale for u and B is also defined based on the ratio of kinetic energy to viscous dissipation and the ratio of magnetic energy to Ohmic dissipation. The ratio of l B to l u in the runs, obtained from (6), is given in Table 2 and the ratio of dissipative lengthscales is given in brackets. It is Increasing the inhomogeneity factor, f to > 1.6 causes the magnetic field to weaken considerably, and when f ≈ 2 the field decays rapidly to zero. For f = 2.4 (see Fig. 1(c) and Case 4, Table 1) strong azimuthal flows are produced by the lateral variation, causing the downwellings to be distorted from a radial into a spiral structure, similar to that observed at large f in a laboratory experiment of thermal convection (Sumita & Olson, 1999). Although the precise numerical value of f that results in dynamo failure would depend on the parameters chosen in the model, the above result is significant: where the applied inhomogeneity is either too small or too big, the dynamo fails. From

Table 1 we note that the volume-averaged root mean square value of the velocity in the model, < u > rms (which gives the magnetic Reynolds number for a dynamo calculation) increases as f is increased from 0.6 to 2.4 and all other parameters are kept fixed. Yet, dynamo action is lost at f ∼ 2. We note from

Figs. 1(b) & (c) that the transformation from a radial to spiral structure as f is increased is accompanied by a significant decrease in fluid velocity within the downwelling. As we shall see below in Section 3.3, the axial (z) velocity at f = 2.4 is also significantly lower than that at f = 1.6. This suggests that dynamo action is determined by the magnitude of the velocity within the fluid rolls, rather than the rms value of the velocity.

8

A c c e p t e d M a n u s c r i p t

Force balances in locking

The spherical surface plot of the azimuthal velocity, u φ for f = 1.6 (Fig. 3(c);

Case 3 in Tables 1 &2) may be understood from the temperature distribution imposed by the Y 2 2 boundary variation. At φ = ±π/2, ∂T /∂θ is negative in the northern hemisphere, and u φ changes sign from positive (cyclonic) near the equatorial plane to negative (anticyclonic) at high latitudes. The opposite effect is seen beneath warm regions, φ = 0, π. An similar pattern of u φ is obtained at every radius of the spherical shell except near the inner boundary (r = r i ), indicating that the boundary thermal variation has penetrated the fluid down to the inner boundary. For f = 1.6 the equatorial symmetry of the boundary condition is mapped on to the velocity field. The symmetry of the locked state forces the net kinetic helicity of the dynamo, H = u • (∇ × u)dV to decrease by 8 orders of magnitude from its value at f = 0.9, as shown in Fig. 3(d). This suggests that, while the equatorial symmetry of the dynamo solution at f = 0.9 is approximate, the symmetry at f = 1.6 is exact. (In near-complete locking, the helicities in the two hemispheres are approximately equal in magnitude and of opposite sign.) As the boundary condition appears to control the flow structure in Fig. 3, we first examine the validity of the following thermal wind-type balance in the curl of the momentum equation:

∂u ∂z = -Ra q ∇ × (T r), (7)
where the temperature gradients are dominated by the non-axisymmetric lateral variations at the boundary, rather than free convection. In The steep gradient ∂T /∂θ produced by the Y 2 2 variation for f = 1.6 is absent for f = 0.6.

The θ-component of ( 7) in spherical polar coordinates relates the latitudinal velocity, u θ to the azimuthal gradient in boundary temperature:

∂u θ ∂z = - Ra q sin θ ∂T ∂φ . ( 8
)
For an equatorially symmetric Y 2 2 variation, a positive ∂T /∂φ should be correlated to a negative u θ above the equatorial plane (z > 0). This prediction is confirmed in plots of ∂T /∂φ and u θ versus longitude φ, shown in Fig. 6(a) for Case 3 in Table 1. The dotted vertical line in this figure gives the longitude at which temperature is minimum. The profiles of u θ and ∂T /∂φ are subject to a small, finite eastward shift from φ = π/2 as seen in Fig. 6(a). This azimuthal shift shows up in plots of the radial velocity at a horizontal section near the equator [e.g. Fig. 1(b)]. The correlation between u θ and ∂T /∂φ is strongly evident for a Y 2 2 variation in temperature (Case 7 in Tables 1 &2). Here ∂T /∂φ has a smooth sin 2φ variation at the outer boundary, but its profile is transformed into a spiked structure by the profile of u θ beneath the boundary [Fig.

6(b)].

Table 2 summarizes the relative magnitudes of three forces in the momentum equation. We have a rotationally dominant regime in all calculations as the nonlinear inertial forces are small in comparison with the Coriolis forces. This is also confirmed by the small value of the local Rossby number, Ro Page 11 of 32 A c c e p t e d M a n u s c r i p t [START_REF] Christensen | Scaling properties of convection-driven dynamos in rotating spherical shells and application to planetary magnetic fields[END_REF][START_REF] Olson | Dipole moment scaling for convectiondriven planetary dynamos[END_REF]) defined based on a characteristic lengthscale of the flow. (Here the lengthscale is derived from a typical spherical harmonic degree, u obtained as a weighted average from the kinetic energy spectrum). Inertia does play a role in the momentum equation as thermal locking results in an approximate balance between the nonlinear inertial and Lorentz forces:

E P m (∇ × u) × u ≈ (∇ × B) × B, (9)
which admits the equipartition solution (see Chandrasekhar, 1961, p 157).

The equivalence of the kinetic and magnetic energies in (5) and that of the lengthscales l u and l B are consistent with (9). Note that the inertial term increases from 20% to 75% of the Lorentz force term as f is increased from 0.9 to 1.6 for the Y 2 2 variation (compare Cases 2 & 3, Table 2). This result indicates that the balance in ( 9) is enforced in the locked dynamo regime.

The global inertia-Lorentz force balance also holds for the locked solutions subject to Y 8 8 and Y 4 5 variations in temperature at the outer boundary (see Cases 5 & 6, Table 2). The above force balance is absent in convective dynamos with thermally homogeneous boundaries that produce stable, dipolar magnetic fields -for Cases 8 & 9 the inertial forces are much weaker than the Lorentz forces. These dynamos operate in an approximate balance between the magnetic, Archimedean (buoyancy) and Coriolis forces, or the MAC balance (also see Sreenivasan & Jones, 2006a). The magnetic energy for these dynamos is typically higher than the kinetic energy, and the lengthscale of the magnetic field is larger than that of the velocity field. The main differences between boundary-locked dynamos and convection-driven, dipolar dynamos are summarized in Table 3.

To test whether strong thermal coupling can be achieved in a regime of large 11 A c c e p t e d M a n u s c r i p t

Ra and q ∼ 1, a basic state temperature profile incorporating basal heating and uniform intrinsic cooling is considered in Case 7. (The basic state for this case is given in Section 2.2). Here, thermal convection is weakened as we move from the inner to the outer boundary, allowing the imposed Y 2 2 temperature variation to penetrate into the fluid. Locking is not as rigid as in Case 3, but persistent downwellings similar to those in Figs. 1(b) and 3(c) are recovered.

The velocity and magnetic field structures for this case are given in Fig. 5 of a recent paper by the author [START_REF] Sreenivasan | Dynamos with weakly convecting outer layers: implications for core-mantle boundary interaction[END_REF]. While the flow is dominated by the two downwellings, convection rolls tend to migrate towards φ = ±π/2 and clump together near these longitudes. The formation of roll clusters indicates that free convection is not negligible in the thermal wind.

The wavenumber of free convection therefore appears in the solution with the wavenumber of the imposed lateral variation. (Also see the discussion on low Ekman numbers in Section 4). From Table 2 we note that the solution in Case 7 departs from equipartition as the ratio of inertial to Lorentz forces is 0.543. Nevertheless, this ratio is much higher than that for a dynamo with homogeneous boundary heating (Case 8).

Table 2 also gives the relative magnitudes of the inductive and diffusive terms in the 'uncurled' induction equation. We find that (∇ × B) is systematically smaller than (u × B) in the locked solution, as found for dynamos with homogeneous boundaries (Cases 8 & 9).

The role of boundary thermal anomalies in dynamo action

To focus on the role of the boundary thermal inhomogeneity in dynamo action, a computational experiment is performed with the equatorially symmetric Y 2 2 boundary heating condition. The calculation begins with the locked state at Page 13 of 32 A c c e p t e d M a n u s c r i p t f = 1.6 (see Fig. 7). At time t d = 1, the magnitude of the lateral inhomogeneity is reduced to f = 0.6, following which the magnetic energy, E m falls by three orders of magnitude over one diffusion time. If left to evolve freely, the magnetic field would decay to zero in this phase. However, by setting f = 1.3 at t d = 2 and keeping all other parameters the same as before, E m increases rapidly from its low value and stabilizes at a value comparable to that at t d = 0. The eventual structure of the flow is identical to that in Fig. 1(b), and the locked regime is similar to the one reported in Case 3, Table 1. If the inhomogeneity factor, f is set to 1.6 at t d = 2 [see the dashed curve in Fig. 7(a)], rigid locking is not obtained and E m saturates at a lower value than at t d = 0. Although the precise value of f at which near-locking is realized is subject to hysteresis, the two locked states obtained in this simulation produce the same energies and lengthscales. It is evident from Fig. 7 that the thermal inhomogeneity at the boundary acts like a "switch" for dynamo action. The inhomogeneity acts on the flow by changing both the axial velocity and vorticity distributions. A sufficiently large lateral variation drives strong axial fluid motions: on azimuthal average, the axial kinetic energy at f = 1.6 is concentrated in regions near the equatorial plane which are shown magnified in Fig. 8(a).

For too small and too large lateral variations (f = 0.6 and f = 2.4) the axial energy is distinctly weak. The above effects are reflected in the axial kinetic helicity plotted in Fig. 8(b). While the strong helicity produced for f = 1.6 is consistent with dynamo action for this case, the weak helical motions for f = 0.6 and f = 2.4 do not support dynamo action. The injection of axial energy (and helicity) by the lateral variation is also observed in a nonmagnetic calculation at f = 1.6, which indicates that the dynamo magnetic field is mainly supported by boundary-induced helicity. The back-reaction of the magnetic field on the velocity field is small. The effect of the lateral variation A c c e p t e d M a n u s c r i p t on the sign of vorticity is evident from the behaviour of the axial vorticity skewness, S = ω 3 z dV /[ ω 2 z dV ] 3/2 , a diagnostic commonly used in rotating turbulence [START_REF] Bartello | Coherent structures in rotating three-dimensional turbulence[END_REF]. The value of S in Fig. 7(b) suggests that anticyclonic (negative) vorticity is dominant for f = 1.6, while cyclones and anticyclones are of comparable strength for f = 0.6. The source of the preferred negative vorticity for f = 1.6 is the Ekman layer at the upper boundary where viscous diffusion of vorticity is fed by the strong axial gradient in velocity. Since anticyclonic z-vorticity is strongly correlated to magnetic field generation in Fig. 7, the vorticity skewness could be a useful flow diagnostic for the onset of dynamo action.

Different patterns of boundary inhomogeneity

In Cases 5 & 6 of Tables 1 &2, thermal convection is produced solely by basal heating (see Section 2.2). In Case 5 (Y 8 8 boundary variation) dynamo action is lost for f < 0.5. The kinetic and magnetic energy spectra have coinciding peaks at the wavenumber m = 8 and its harmonic multiples [Fig. 4 over 5 diffusion times and saturates to within 1% of the kinetic energy, whose variation is small during the calculation. In addition, we note from Table 2 that the lengthscales of u and B are approximately equal. In short, the main force balances and the equipartition solution hold regardless of the equatorial symmetry of the applied inhomogeneity.

Discussion

In this paper we have looked at the dynamics of boundary-locked dynamos. A quasi-stationary, locked solution is obtained when the thermal winds driven 2 ) lateral variations. This regime may be simulated numerically in a low-Ra, high-q parameter space where buoyancy-driven convection is weak. Equation ( 10) is significant in that it allows fluid motion of any wavenumber to be produced by a prescribed temperature variation at the boundary. Previous studies had suggested that locking occurs when the wavenumber of convection is similar to the wavenumber of the boundary anomalies (Zhang & Gubbins, 1993); and that a small-scale flow could be converted to a large-scale flow by a self-generated magnetic field to make locking possible [START_REF] Gubbins | Correlation of Earth's magnetic field with lower mantle thermal and seismic structure[END_REF].

Clearly, neither the matching of wavenumbers nor the presence of a magnetic The secondary force balance in a locked dynamo is between the nonlinear inertial and Lorentz forces, realized approximately in all locked solutions in this paper but generally absent in buoyancy-driven dynamos with homogeneous boundary heating. The inertia-Lorentz force balance is a consequence of locking produced via Equation (10). By virtue of this balance, the locked dynamo operates in a state of equipartition between the velocity and magnetic fields. The equivalence of scaled u and B fields has been obtained in several astrophysical dynamo models; e.g. [START_REF] Dorch | On the saturation of astrophysical dynamos: numerical experiments with the no-cosines flow[END_REF][START_REF] Mininni | Dynamo regimes with a nonhelical forcing[END_REF]. These models differ from the present model in two respects: they are non-rotating; and they incorporate a forcing term in the momentum equation that corresponds to a prescribed, globally non-helical, initial velocity field. The analogy between the locked model and the astrophysical models is apparent if we note that the thermal forcing at the boundary acts to create a u field which, in turn, brings the B field into equipartition. If E k ≈ E m and l u ≈ l B , the ratio of viscous to Ohmic (resistive) dissipation rates may be shown to be of order W V /W R ∼ ν/η = P m (see Table 2 for A locked dynamo driven by lateral variations at the boundary cannot be applied directly to the Earth for two reasons: the geomagnetic field is not rigidly locked to lower-mantle inhomogeneities; and the Earth's dynamo is thought to be powered by thermal and compositional buoyancy in its fluid core. Nevertheless, the locked model provides a useful starting point in understanding core-mantle interaction in Earth-like conditions. How is locking affected by a high convective Rayleigh number and a low Ekman number? If the buoyancydriven temperature gradients are stronger than the boundary-driven gradients, the velocity field is "decoupled" from the boundary inhomogeneity and free to drift azimuthally. In other words, the thermal wind term in Equation ( 10) must contain a dominant non-axisymmetric, boundary-driven component to lock the velocity field. This would explain why a weakly convective parameter regime is crucial for obtaining a boundary-locked dynamo.

For Ekman numbers lower than the ones used in this study, locking becomes progressively difficult. Since the critical Rayleigh number for onset of nonmagnetic convection increases with decreasing Ekman number (Ra c ∼ E -1/3 ), even a marginally supercritical convective state would generate strong thermal winds that compete with the boundary-driven thermal winds in balancing the Coriolis forces. A preliminary exploration into low Ekman numbers suggests that the flow structure is different from that at higher Ekman numbers: for a sufficiently large Y 2 2 variation in temperature, the flow at E = 10 -5 is organized in clusters of small-scale rolls near φ = ±π/2, rather than isolated downwellings. For the higher Ekman numbers investigated in this paper, fluid motion is organized into two isolated downwellings as shown in Fig. 1(b). The above difference between high and low-Ekman number flows can be understood as follows. As the contribution of free convection to the thermal wind can be kept small in high-E simulations, the convective wavenumber is to-A c c e p t e d M a n u s c r i p t tally suppressed by the boundary wavenumber in the locked solution. On the other hand, as free convection becomes significant in the thermal wind in low-E simulations, the convective wavenumber will show up in the solution in addition to the boundary wavenumber. In short, numerical models with relatively large Ekman numbers are needed to demonstrate the validity of the boundary-driven force balance in (10). A systematic study of low-Ekman number dynamos controlled by lateral variations should be possible when faster computers are available.

The calculation in Case 7 produces a partially locked solution even when free convection is not small. This is achieved by suppressing convection in the outer regions through a volumetric heat sink so that boundary-driven thermal winds are allowed to balance the Coriolis forces. [The thermodynamic implications of a heat sink in a model of Boussinesq convection are discussed in [START_REF] Sreenivasan | Dynamos with weakly convecting outer layers: implications for core-mantle boundary interaction[END_REF].] The above regime could be relevant to the Earth's dynamo because the departure from equipartition does allow the magnetic energy, E m to be greater than the kinetic energy, E k . A comparison of the dynamo in Case 7 with a purely convective, dipolar dynamo suggests that mantle coupling could increase the magnitude of inertial forces in the fluid core. Note, however, that the inertial forces must be much smaller than the Coriolis forces for the Rossby number in the core to be ∼ 10 -6 . Finally, while the results in this paper are valid for individual equatorially symmetric and antisymmetric boundary heating modes, the effect of complex combinations of these modes on the dynamo needs to be investigated. Such a study would give an insight into the effects of the tomographic boundary condition [START_REF] Masters | A shear-velocity model of the mantle[END_REF] Fluid Dynam., 100, 319-339. Sumita, H. & Olson, P., 1999. A laboratory model for convection in earth's core driven by a thermally heterogeneous mantle, Science, 286, 1547-1549.

Willis, A. P., Sreenivasan, B., & Gubbins, D., 2007. Thermal A summary of the diagnostics investigated for the dynamos in Table 1. Here E k and E m are the global kinetic and magnetic energy densities given by ( 5

≈ 1 << 1 (v) Energies E m ≈ E k E m > E k (vi) Lengthscales l B ≈ l u l B > l u
Table 3 A comparative study of (a) locked dynamos controlled by inhomogeneous boundary heating and (b) convection-driven dynamos producing stable, dipolar magnetic fields.

Page 25 of 32 respectively, over one-fourth of a magnetic diffusion time. Curves (i) and (ii) are for f = 0.9 and curves (iii) and (iv) for f = 1.6. The model parameters are Ra = 1.5Ra c , E = 10 -4 , P r = 1 and q = 10 (Cases 2 & 3 in Table 1).

(i) (iii) (iv) (ii) t d E k , E m
Page 27 of 32 Evolution of the kinetic energy (solid line) and magnetic energy (dashed line) with magnetic diffusion time.

  dynamos with fluid-boundary coupling have attracted considerable attention in recent years. The problem is of interest in geophysics

  )-(3) are the Ekman number, E = ν/2ΩL 2 , the Prandtl number, P r = ν/κ, the magnetic Prandtl number, P m = ν/η and the 'modified' Rayleigh number Ra, whose definition depends on the basic state temperature profile and the thermal boundary condition in the problem. (The various cases considered in this paper are described in Section 2.2.) In the above dimensionless groups, ν is the kinematic viscosity, κ is the thermal diffusivity, η is the magnetic diffusivity, L is the gap-width of the spherical shell and Ω is the angular velocity of rotation. The Roberts number is given by q = P mP r -1 . The Ekman number is a measure of the Page 5 of 32 A c c e p t e d M a n u s c r i p t rotation rate and the Rayleigh number represents the strength of convective buoyancy in the problem. As velocity is scaled by η/L, the volume-averaged dimensionless velocity in the model directly gives the magnetic Reynolds number, R m . The standard numerical method used here involves expanding T and the poloidal and toroidal components of u and B in spherical harmonics and then timestepping the spectral coefficients(Sreenivasan & Jones, 2006a). Noslip boundary conditions are imposed on the flow. The inner core is considered to be at a fixed temperature and electrically conducting. The outer boundary is maintained electrically insulating and subject to a lateral variation in temperature or heat flux (see Section 2.2). The variation at the outer boundary is proportional to the spherical harmonic g(θ, φ) = P m l (cos θ) cos mφ, where l and m are chosen.

  layer. The ratio of the maximum variation of temperature across the outer boundary to the temperature difference across the layer gives the inhomogeneity factor, f .

  evident that the lengthscales of u and B are approximately equal in the locked regime. Indeed, we find from Fig.4(a) that the spectra of kinetic and magnetic energies have identical peaks at the boundary-imposed wavenumber m = 2 and 7 A c c e p t e d M a n u s c r i p t its large-scale multiples. The congruence between the lengthscales of u and B may further be verified from a contour plot of the radial magnetic field near the equator, which has a structure similar to that of the radial velocity shown in Fig. 1(b). The approximate equivalence of the lengthscales l u and l B and the energies E k and E m in (5) indicates an equipartition state.

  Fig. 5 the φcomponents of the forces in (7) are plotted at longitude φ = π/2. For f = 1.6 the velocity gradient ∂u φ /∂z follows the local thermal wind Ra q (1/r) ∂T /∂θ, and the two forces are of the same order of magnitude except in the Ekman 9 A c c e p t e d M a n u s c r i p t layer at the upper boundary where ∂u φ /∂z is one order of magnitude higher than that in the interior. (The Ekman layer region could not be shown in the same plot because of this large difference in magnitude.) For a weaker inhomogeneity (f = 0.6) the thermal wind term is markedly smaller; see Fig. 5(b).

  (b)], consistent with the approximate equivalence of lengthscales of u and B reported in Table 2. In Case 6 the initial state has an equatorially symmetric velocity field and a weak dipolar magnetic field. The equatorially antisymmetric Y 4 5 boundary condition produces a velocity field that locks the magnetic flux lobes beneath cold regions at the boundary, which do not lie at the same longitude in the two hemispheres; see Figs. 9(a) & (b). As the imposed temperature pattern is equatorially antisymmetric, both ∂T /∂θ and ∂u φ /∂z have equatorially symmetric distributions at φ = π/2 [Fig. 9(c)]. It is also confirmed that the magnitudes of the forces in the thermal wind balance (7) are comparable in the interior of the flow. In Fig. 9(d) the magnetic energy increases continuously Page 15 of 32 A c c e p t e d M a n u s c r i p t

  by lateral variations at the boundary are in approximate balance with the Coriolis forces in the fluid. The dimensional force balance in the curl of the momentum equation is given by 2Ω ∂u ∂z = -gα ∇ × (T r), (10) which has the same form as the classical thermal wind equation for rotating thermal convection in a Boussinesq fluid (e.g. Sreenivasan & Jones, 2006b), except that the temperature gradients are prescribed by non-axisymmetric (e.g. Y 2

  s c r i p t field is required for locking produced by the balance in (10).

  comparison). As P m = qP r ∼ 10 in the locked model, Ohmic dissipation is approximately one order of magnitude smaller than viscous dissipation. The introduction of lateral variations at the boundary can excite dynamo action for a given Ra-q combination that does not otherwise produce a dynamo with homogeneous boundary heating. While this effect was first noted in Willis et al. (2007), here we have looked at the role of lateral variations in supporting dynamo action. As shown in Figs. 1 & 8, the variations drive strong radial and axial motions which, in turn, can inject the helicity required for amplification of a seed magnetic field.

  constructed based on the Earth's lower-mantle shear wave velocity variation. s c r i p t namo action in the polar regions of planetary cores, Geophys. Astrophys.

  ), W V is the viscous dissipation given by P m (∇ × u) 2 dV , W R is the Ohmic (resistive) dissipation given by (P m/E) (∇ × B) 2 dV , l u and l B are the lengthscales of the velocity and magnetic fields and Ro is the local Rossby number. The inertial forces are given by (E/P m) < (∇ × u) × u >, Coriolis forces by <ẑ × u > and the Lorentz forces by < (∇ × B) × B >, where the angled brackets represent rms values.

Fig. 1 .

 1 Fig. 1. Equatorial section plots of the radial fluid velocity, u r for a Y 2 2 heat flux inhomogeneity at the boundary. The three cases studied are (a) f = 0.6, (b) f = 1.6 and (c) f = 2.4. The model parameters are kept fixed for all three cases (Ra = 1.5Ra c , E = 10 -4 , P r = 1 and q = 10.) The dimensionless maximum and minimum values for the three cases are [-284.8, 200], [-654.6, 281.6] and [-215.06, 103.2]. Positive values of u r are shown in red and negative values are in blue. Dynamo action is obtained only in (b).

Fig. 2 .

 2 Fig. 2. Kinetic and magnetic energies, E k and E m , shown in blue and red curves

Fig. 3 .Fig. 4 .

 34 Fig. 3. (a)-(c) are spherical surface plots with longitude φ in the range [-π, π] from left to right on the horizontal axis and colatitude θ in the range [0, π] from top to bottom on the vertical axis. (a) u r (r = 0.8r o ) with surface flow arrows superposed; (b) B r (r = r o ); (c) u φ (r = 0.8r o ), all for a Y 2 2 heat flux variation at f = 1.6. Positive values are shown in red and negative values in blue. (d) Global kinetic helicity for f = 0.9 and f = 1.6. The model parameters are Ra = 1.5Ra c , E = 10 -4 , P r = 1and q = 10.

Fig. 5 .Fig. 6 .

 56 Fig. 5. Meridional plots at azimuthal angle φ = π/2 of Ra q (1/r)∂T /∂θ (left panel) and ∂u φ /∂z (right panel). Two cases are presented for the Y 2 2 heat flux variation: (a) f = 1.6 with peak values of the two forces being [±478.1, ±542.8]; (b) f = 0.6 with peak values [±55.5, ±218.9]. The fixed model parameters are Ra = 1.5Ra c , E = 10 -4 , P r = 1 and q = 10. Positive values are shown in red and negative values in blue.

Fig. 7 .Fig. 8 .Fig. 9 .

 789 Fig. 7. (a) Variation of the magnetic energy, E m with magnetic diffusion time. At t d = 1, the inhomogeneity factor, f is switched from its initial value of 1.6 to 0.6. At t d = 2, f is set to 1.3 (solid curve) and 1.6 (dotted curve) in two separate runs. (b) The corresponding variation of the axial vorticity skewness, S. The model parameters are kept fixed at Ra = 1.5Ra c , E = 10 -4 , P r = 1 and q = 10.

Table 2

 2 core-mantle interaction: Exploring regimes for 'locked' dynamo action, Phys. Earth Planet.Case E m /E k W V /W R l B /l u

	Inter., 165, 83-92.
	Zhang, K. & Gubbins, D., 1993. Convection in a rotating spherical fluid shell
	with an inhomogeneous temperature boundary condition at infinite Prandtl
	number, J. Fluid Mech., 250, 209-232.

Table 1

 1

	). (b) Y 8 8 temperature inhomogeneity (Case 5, Table
	1).

Acknowledgement

I thank the referees for their constructive reviews which helped improve this paper. This work has been sponsored by a Research Fellowship (Grant F/00 122/AD) from the Leverhulme Trust, UK. The calculations were performed on the White Rose Grid cluster at the University of Leeds.


Zhongwen Yao

Mike L Jenkins
email: mike.jenkins@materials.ox.ac.uk

Mercedes Hernández-Mayoral

Mark A Kirk

Jenkins

The temperature dependence of heavy-ion damage in iron: a microstructural transition at elevated temperatures

Keywords: radiation damage, in-situ electron microscopy, defect analysis, microstructural characterization

published or not. The documents may come

The temperature dependence of heavy-ion damage in iron: a microstructural transition at elevated temperatures

Introduction

It has been long known that the mechanical properties of steels start to degrade at temperatures above about 500°C -a relatively low temperature (0.42T m ). According to recent theoretical calculations [1,2], a possible cause of this is an elastic instability, driven by spin fluctuations. This results in a large reduction in the shear stiffness constant C′= (C 11 -C 12 )/2 at the α → γ phase transition temperature of 912 o C, although effects on mechanical properties are manifest at temperatures well below this. The same theory predicts that dislocation loops with Burgers vector b = <100> will become relatively more stable with respect to loops with b = ½<111> with increasing temperature.

In previous papers we have described in-situ ion-irradiation experiments which followed the evolution of microstructures in thin foils of pure iron (Fe) and FeCr alloys at irradiation temperatures T irr ≤ 300 o C [3][4][5] and at 500 o C [5]. These experiments provided support for the view that dislocation loops with b = <100> increase in stability with temperature. For T irr ≤ 300 o C, the microstructures both in pure Fe and in FeCr alloys irradiated with 150 keV Fe + ions were dominated by interstitial loops with Burgers vectors b = ½<111>. These loops were frequently round or of irregular shape and had significant shear components, and sometimes coalesced into large finger-shaped loops. However, in the same materials irradiated at 500°C, only rectilinear pure-edge interstitial loops with b = <100> loops were present.

In the present paper this transition in microstructures is explored in more detail in pure Fe. All images and videos included in this paper were recorded under weak-beam diffraction conditions [6]. The weak-beam method of transmission electron microscopy has become an indispensable tool in this area of research (for a review giving full experimental details, see ref. [START_REF] Jenkins | Characterisation of Radiation Damage by Transmission Electron Microscopy[END_REF]).

Experimental method

The materials were the same as those investigated previously (annealed ultra-high purity polycrystalline Fe and a somewhat less pure Fe single crystal -see ref. [3] for details). Full details of specimen preparation and irradiation in the Argonne-IVEM Tandem Facility have been given in a previous paper [3]. Briefly, specimens were electro-polished with minimum exposure to air and introduced immediately into an Hitachi H-9000NAR transmission electron microscope interfaced to an ion implanter. They were then irradiated with 150 keV Fe + self ions at temperatures ranging 400 o C to 500 °C, with an estimated accuracy of ± 10 o C. We estimate that for this irradiation condition the peak of the damage occurs at a depth of about 28 nm [3]. The regions of foil investigated in the TEM were typically of thickness 30-40 nm, so the damage peak was close to the foil centre. We found in our previous work that in such foils small ½<111> dislocation loops were very mobile, and in some foil orientations some of these loops were lost by glide to the foil surfaces under the influence of surface image forces [3][4][5]. For this reason the single-crystal Fe used in some of the present experiments was spark-cut into slices parallel to the (110) plane in order to obtain TEM specimens with a [110] foil normal. In The evolution of radiation damage was followed by dynamic TEM observations under weak-beam diffraction conditions to doses ≤ 2 x 10 19 ions m -2 (~13 dpa). In most of the present experiments irradiations were terminated at a dose of 2 or 3 x 10 18 ions m -2 (~1.3-2 dpa). Irradiations were paused from time to time to allow detailed characterization of microstructures using standard diffraction-contrast techniques [START_REF] Jenkins | Characterisation of Radiation Damage by Transmission Electron Microscopy[END_REF]. Similar detailed characterization was performed at the end of the irradiation after specimens had cooled to room temperature.

Results

T irr = 400 o C

At doses <10 18 ions m -2 , the initial damage microstructure was similar to that seen in previous experiments at 300 o C. Small dislocation loops, visible as white dots of diameter less than about 5 nm in weak-beam images, appeared within a timescale of a few video frames. Most of these loops were extremely mobile, making large and frequent "hops" in <111> directions, consistent with ½<111> Burgers vectors. The frequencies and amplitudes of hops were much larger than those seen in the same material at 300°C [3] or in the 1-D diffusion of loops seen in similar material under electron irradiation at temperatures < 400 o C [8]. As the irradiation progressed, loops were seen to interact elastically, making coordinated hops and occasionally coalescing into larger loops. This behaviour is illustrated in video 1, which shows damage development under ion irradiation over a dose range 0 -5 × 10 17 ions m -2 . The coalescence after irradiation of a string of three ½<111> loops into a larger, but still mobile ½<111> loop which then rotates on its glide cylinder is shown in video 2, with stills from this video in figure 1. By a dose of 2 ×10 18 ions m -2 (~1.3 dpa), elastic interactions led to the formation of chains of large (30-50 nm), round loops in thicker areas, reminiscent of those seen at lower irradiation temperatures [3][4][5] but on a larger scale. The formation of loop chains under irradiation may be viewed dynamically in video 3.

In video 3, it may be seen that a number of loops appeared more gradually and were immobile, and it was surmised that these had <100> Burgers vectors. A postirradiation Burgers vector analysis was carried out at the final dose of 2 × 10 18 ions -2 , and selected micrographs from this experiment are shown in figure 2. The analysis confirmed that both ½<111> and <100> loops had formed. Large (30-50 nm) loops had Burgers vectors b = ½[ 1 1 1 ] or b = ½[ 1 11 ] (and so were out of contrast in figure 2d) or b = [001] (and so were out of contrast in figure 2a). Interestingly, no large loops of the other variants were seen in this area. Small (~ 10 nm) loops of each type and variant were also present. The number density of <100> loops was larger than that of ½<111> loops, but on average they were much smaller, so that a majority of point defects was contained in ½<111> loops. This will be quantified and discussed later. Stereo experiments showed that large loops were localized towards the foil centre, whilst smaller loops were distributed throughout the foil, regardless of their Burgers vectors. This may be seen in are seen to lie perpendicular to the diffraction vector g = 2 00 in figure 2c. Similar pure- edge <100> loops were found in our previous work at T irr = 500 o C, where their nature was determined to be interstitial [5]. Micrographs taken at other orientations showed that <100> loops larger than about 20nm were rectilinear with edges along <100> directions. Smaller ones looked more rounded. The detailed shape of loops is discussed in a separate paper [9].

The ½<111> loops are non-edge. A full Burgers vector analysis (carried out using the reflections available at both the [110] and [100] poles) showed that the predominant Burgers vector of the large loops in the area of foil shown in figure 3a was ½ [ 11 1 ]. The habit plane of these loops was found by tilting the foil from pole [110] → [310] → [100], whilst maintaining the same weak-beam diffraction condition with g = 002. The loops appear edge-on at the [310] pole, imaging as lines lying perpendicular to the [ 32 1 ] direction (figure 3a). They therefore lie on or close to the ( 32 1 ) plane, so that the angle between the loop normal n and b is about 22 o . Figures 3b and3c show experimental images of two loops recorded close to the [110] and [310] poles respectively. Image simulations using the program TEMACI [10] for circular loops with b = ½[ 11 1 ] with a ( 32 1 ) habit plane are inset at the lower left of each figure. The good match between experimental and simulated images confirms our interpretation. In our previous experiments in UHP-Fe at 300°C the large ½<111> "finger" loops which formed at high doses were also found to have significant shear components and were also found to be interstitial [4].

T irr = 450 o C

In an experiment carried out at T irr = 450 o C on an UHP Fe foil oriented about 20° from [111], early stages in damage development were similar to those seen at 400 o C, except that larger-scale microstructures appeared more slowly. Small loops were seen early in the irradiation, and were extremely mobile, and were frequently lost from the foil. As the dose increased, again chains of loops formed, interacting elastically. By a dose of 3 x 10 18 ions m -2 , long lines of large ½<111> loops had formed in thicker regions, all with the same Burgers vector, and looking similar to the microstructure examined in detail at 400°C (figure 4a). In an adjacent grain tilted close to [100], regions were found where large loops of both <100> and ½<111> types were present (figure 4b), although <100> loops were in a preponderance. In other regions of this grain large numbers of edge-on <100> loops were visible (figure 4c). The absence of ½<111> loops in figure 4c may well be a contrast effect: the large loops in figure 4b are visible in g = 1 01 and so have 11 ], but loops with these Burgers vectors would be out of contrast in figure 4c which was taken in g = 011. The average sizes of <100> loops were significantly larger than at 400°C, and a majority of point-defects was now contained in such loops, see below. This temperature seems to mark a transition from a mostly ½<111> microstructure to a microstructure dominated by <100> loops.

either b = ½ [ 1 1 1 ] or b = ½ [ 1

T irr = 460 o C -500 o C

At 500 o C, we found in our previous work that only <100> loops formed in [100] foils [5]. These loops appeared slowly over several minutes, and were immobile. Figure 5a shows the microstructure at a dose of 3 ×10 18 ions m -2 , where loops of sizes up to about 50 nm were present but well separated. As these loops grew under continuing irradiation, they coalesced with neighbouring loops with the same Burgers vector until they impinged on loops of the other variants, forming the microstructure seen in figure 5b. In this figure, loops belonging to all three <100> variants can be seen. In foils with normal [100], all variants of ½<111> loops have a component of Burgers vector pointing towards the surface. Since ½<111> loops are highly mobile at 500 o C, the possibility exists that such loops do form, but are lost by glide to the surface before they are seen. Total loss of ½<111> loops in (100) foils is known to occur in ionirradiated Mo [11]. In order to exclude this possibility, the following experiments were carried out in single-crystal foils with orientation close to [110]. In such foils, loops with b = ½[ 11 1 ] and b = ½[ 1 11 ] have little or no component of Burgers vector towards the surface, and so cannot easily be lost by glide.

First a foil was irradiated to a moderate dose (1 ×10 18 m -2 ) at 500°C. Sessile loops with b = <100> were seen to form, but no loops with b = ½<111> loops were found 2 . A further irradiation of the same foil was then performed at 482°C. A few small ½<111> loops were produced in the field of view of the CCD camera. All remained in the foil and hopped along <111> directions in the plane of the foil. Soon after irradiation, none of these ½<111> loops could be found. It was not clear by which mechanism they had disappeared.

A second foil was irradiated at 465°C. Video 6 shows this specimen under ion irradiation, and figure 6 shows a series of stills from this video. The video shows directly the fate of ½<111> loops at elevated temperatures. In the area of observation are some easily-recognized, large, sessile, near edge-on <100> loops and two small (~ 5 nm) ½<111> loops, located on either side of a larger (~ 50 nm) <100> loop (arrowed in figure 6). At first, the two ½<111> loops hopped parallel to their Burgers vector. Their glide cylinders did not intersect the <100> loop. However, within a minute both ½<111> loops had moved towards the <100> loop, this motion involving sideways steps perpendicular to their glide cylinders. On reaching the <100> loop they were subsumed, causing the 2 We have recently found the same result in a [110] Fe-C alloy irradiated at 500 o C under the same conditions. <100> loop to grow. The increase in size of the <100> loop indicates that the two ½<111> loops which it had absorbed had the same nature as the <100> loop itself, i.e. all were interstitial.

Discussion

The occurrence of <100> loops in Fe irradiated at high temperature has been known since the pioneering work of Masters [12], who carried out thin-foil irradiation experiments similar to our own. Masters found exclusively <100> loops of interstitial nature in pure Fe irradiated with 150keV Fe + ions at 550 o C. Subsequently <100> loops, or a mixture of <100> and ½<111> loops, have been found in many other elevated-temperature experiments in ferritic materials. These include, for example, experiments by Konobeev et al [13] who found <100> interstitial loops (as well as voids) in Fe and Fe 0-18%Cr irradiated with fast neutrons to doses up to 25.8 dpa at 400°C. As a further example, Gelles [14] also found that <100> loops predominated in Fe3%Cr alloys irradiated with neutrons to ~ 20dpa at temperatures between 400 o C and 450 o C, although a mixture of the two loop types was found in higher Cr alloys. In our own recent experiments in Fe irradiated in the bulk with 0.5-3 MeV Fe + ions to ~ 10 dpa at 500 o C, we also found almost exclusively interstitial <100> loops, whilst at 300 o C a mixture of <100> and ½<111> loops was present. In FeCr alloys, however, both loop types were present at 500 o C [15]. In these and other experiments there does seem a clear pattern for <100> loops to predominate in pure Fe at irradiation temperatures T irr ≥ 400 o C. In contrast, in Fe irradiated at 60 o C with neutrons, only ½<111> loops were identified, again of interstitial nature [16]. The only examples we know of <100> loops in low-temperature irradiations are found in Fe irradiated with W + ions at room temperature [START_REF] Jenkins | 2 Deleted: a/2 Deleted: a 11[END_REF] and with high doses of self-ions [START_REF] Kirk | [END_REF], and in these cases loops were considered to have formed by a process of cascade collapse and the loop nature was vacancy.

Our present work has provided further evidence that <100> loops become increasingly dominant in Fe with increasing irradiation temperature. In figure 7 we have made an attempt to quantify the proportions of interstitials contained in <100> and ½<111> at various temperatures. This figure was constructed by measuring the size distributions and number densities of the two types of loops at different irradiation temperatures. At T irr = 400°C, about 80% of loops were of the <100> type, but their mean size was only about a third that of the ½<111> loops, and so the fraction of interstitials contained in loops of the two types was comparable. At T irr = 450°C, the majority of interstitials was contained in <100> loops, but large ½<111> round loops were still present in some areas. At T irr ≥ 492°C, no <111> loops were seen during ion irradiation, whereas <100> loops formed and grew. As a rough estimate, the total number of interstitials contained in <100> loops at 500°C was comparable with the number of interstitials contained in loops at 300°C, for the same irradiation dose. No correction has been made in figure 7 for loss of mobile ½<111> loops to the surface, nor for the effects of foil orientation and thickness, nor for the variability in loop types from area to area. Discussions of these effects may be found in our previous papers [3,5]. Their neglect is likely to lead to an underestimate of the number of interstitials in ½<111> loops at all temperatures, but we believe that the trends shown are real. In parallel with our experimental work, Dudarev et al. [1,2] developed methods of calculating the self-energy of loops of different Burgers vectors and morphologies as a function of temperature. As mentioned in the introduction, they found that the reduction in the shear stiffness constant C′ with increasing temperature caused a profound effect on the anisotropic elastic self-energies of dislocations in Fe and on the relative stability of <100> and ½<111> dislocation loops. For example, for loops of perimeter P = 10 nm, hexagonal, prismatic pure-edge dislocation loops with Burgers vector ½<111> were found to be unconditionally stable at temperatures T < 350°C, whereas square <100> pure-edge loops were unconditionally stable for T > 550°C. In the intermediate temperature region, 350°C < T < 550°C, loops of this size with b = ½<111> and edges along < 10 1 > directions were thermodynamically unstable and could lower their free energy either by changing shape (with edges along < 2 11 > directions) or by transforming to <100> loops. Dudarev et al. [2] argued that in a real situation where loops of various sizes and shapes are present, the boundaries between the different regions of stability would be diffuse, leading to a gradual transition in loop types. This picture above is clearly in good qualitative accord with our observations. We found that ½<111> loops were dominant components of the microstructure at temperatures T irr ≤ 300 o C, although small <100> loops were present even at room temperature [3,4]. At temperatures T irr ≥ 400 o C, <100> loops became increasingly important components of the microstructure (figure 7). Our observations are therefore compatible with a picture that <100> loops become more energetically favoured with increasing temperature. However the mechanism by which the transition in loop types takes place is still not entirely clear. In particular, the abrupt disappearance of ½<111> loops at temperatures T irr >465°C was something of a surprise. Unlike Arakawa et al [19] we did not see ½<111> loops transform directly into <100> loops. Small mobile ½<111> loops were produced at T irr = 465°C, but were quickly subsumed by sessile <100> loops. The crabwise motion by which the ½<111> loops approached the <100> loop (video 6, figure 6) evidently involved self-climb, since the sizes of the ½<111> loops remained unchanged at the resolution of the CCD camera. Coalescence of interstitial loops by selfclimb has been observed previously during an isothermal anneal of ion-implanted UO 2 by Turnbull [20]. Turnbull considered two possible driving forces: first the mutual interaction of the loop strain fields, and second the interaction of the strain fields of loops and vacancies. He concluded that in metals both interactions were likely to be important.

Clues to the possible mechanisms underlying our observations may be gleaned from molecular dynamics simulations of displacement cascades in Fe by Bacon and coworkers [21]. In these simulations small, self-interstitial clusters formed at the cascade peripheries at the end of the displacement phase of the cascade in an essentially athermal process, or by short-range diffusion during the thermal-spike phase. Smaller clusters may be considered as bundles of <111> or <100> crowdions. These clusters are very mobile, even at low temperatures, moving by thermally-activated one-dimensional glide along the crowdion direction. Larger clusters of crowdions may be considered as small, but probably sub-microscopic ½<111> or <100> dislocation loops. We surmise that loops large enough to be seen in the TEM form by the coalescence of such small clusters, and that this process is more likely to occur in the foil interior since the surfaces act as efficient sinks. Loops with b = <100> which reach visible size become sessile, whereas b = ½<111> loops remain mobile. Both types continue to grow by absorbing mobile submicroscopic clusters and smaller loops, and by coalescing with loops of comparable size. In the case of the mobile ½<111> loops, elastic interactions play an important role in this process. The relative proportions of the two loop types are probably determined by by a combination of factors, including their stabilities at small sizes, and the increased mobility of ½<111> loops at higher temperatures. At temperatures above 450°C, small ½<111> loops are less likely to form, and those which do are quickly subsumed into <100> loops and never reach large sizes. At temperatures higher than 500 o C this process may occur before any microscopic ½<111> loops form at all, and so such loops are not seen in the high temperature regime.

A final question concerns the fate of vacancies in our experiments. We have determined the nature of larger loops using the inside-outside contrast technique, and all were found to be interstitial. Evidence presented in this paper shows that most if not all of the mobile ½<111> loops are also interstitial in nature. Vacancy-rich regions are likely to form within cascades, but calculations suggest that closed vacancy loops of size ≤ 4nm are not formed, while small open loops transform to voids [22,23]. We have looked for but not found small voids in pure Fe, suggesting that any present are of size below the resolution limit of ~ 2nm. We did find very small voids in Fe8%Cr irradiated under similar conditions [5]. It is also possible that some of the small near-surface loops might be of vacancy nature [3].

Summary and conclusions

• We have described a transition in the microstructures of pure Fe produced by heavy-ion irradiation of thin foils which took place between irradiation temperatures T irr of 300 o C and 500 o C.

• Our previous work had shown that for ≤ 300 o C, the microstructure was dominated by interstitial loops with Burgers vectors b = ½<111>. At T irr = 400 o C, about 50% of self-interstitials were still contained in ½<111> loops, which were frequently round or of irregular shape and had shear components. These loops were very mobile and frequently coalesced into larger loops. A high proportion of small, sessile, edge <100> loops was also present, also accommodating about 50% of the interstitials.

• There was a gradual transition in microstructure at temperatures greater than 400 o C. At T irr = 450 o C, loops with b = ½<111> were still present, and interacted elastically to form long chains, but loops with b = <100> of pure edge character and rectilinear shape, now dominated in most areas, and accommodated a majority of the interstitials. • At temperatures T irr ≥ 450 o C, small, mobile ½<111> loops were seen to be subsumed by sessile <100> loops, and large ½<111> loops did not form. At 500°C, <100> loops developed into large networks, and no visible ½<111> loops formed.

• A plausible explanation of these observations has been given in terms of the relative stabilities of ½<111> and <100> loops as a function of temperature, and the possible mechanism by which the microstructure develops. Chains of ½<111> loops are present together with a few large [001] loops and a large number of small loops of both types. In this field of view <001> loops outnumber ½<111> loops about in a ratio of about 2:1.

  The single-crystal Fe was spark-cut into slices parallel to the (110) plane in order to obtain TEM specimens with a [110] foil normal for reasons given in section 3.2. orientation some loop variants have their Burgers vectors in or close to the foil plane, and so cannot easily be lost by glide (see section 3.3 for details).

Formatted: 2 Deleted: a/ 2 Deleted 5 video 4 ,

 2254 Indent: First line: 18 pt Deleted: a/which shows a tilt series constructed using EM3D tomography software from a set of 7 stereo images taken over a tilt range of ~35 o with g = 002.By inspection of figure2it may be seen that the large [001] loops are of pureedge type. The foil normal in this micrograph is [100] and edge-on loops with b = [001]

  Two variants, with b = [001] and b = [010], appear edge-on, forming a quasi-regular ladder-like structure. Loops of the third variant, with b = [100], lie in the plane of the foil and are faintly visible in residual g.b × u contrast. Occasionally during irradiation loops with this Burgers vector were suddenly lost from the foil by glide, see video 5, demonstrating that <100> loops are not intrinsically sessile.

Figure 1 :

 1 Figure captionsFigure 1:Frames captured from video 2, showing loop coalescence in UHP Fe after irradiation at 400 o C to 1 × 10 18 ions m -2 . This occurred soon after ion irradiation ceased, as the specimen was being examined in the TEM and was still at 400 o C. Three small ½<111> loops towards the centre of frame A coalesce into a single ½<111> loop in frame B. The loop is seen to rotate to new habit plane, frame C, and continues to hop.

Figure 2 :

 2 Figure 2: Contrast experiment at T irr = 400 o C in UHP Fe irradiated to a dose of 2 × 10 18 ions m -2 (~1.3 dpa):(a) diffraction vector g = 020, so loops with b = [100] are out of contrast; (b) g = 1 01 so loops with b = ½[ 11 1 ] and b = ½[111] are out of contrast; (c) g = 2 00 , so loops with b = [010] are out of contrast;(d) g = 1 1 0 , so loops with b = ½[ 1 1 1 ] and b = ½[ 1 11 ] are out of contrast.

Figure 3 :

 3 Figure 3: Experiment to determine the habit plane of ½[ 11 1 ] loops: (a) the specimen shown in figure 3 has been tilted close to the [310] pole. Loops with b = ½[ 11 1 ] appear edge-on on, consistent with a ( 32 1 ) habit plane ; (b) and (c) show experimental images of a two loops with b = ½[ 11 1 ] at the [110] and [310] poles respectively. TEMACI image simulations for a circular loop with this Burgers vector lying on ( 32 1 ) are inset at the lower left in each case.

Figure 4 :

 4 Figure 4: Loops in UHP Fe at 450 o C at a dose of 3 x 10 18 ions m -2 : (a) long lines of large ½<111> loops in a grain oriented about 20 o from [111]; (b) large loops of both types in an adjacent grain oriented close to [001], with <100> loops in a preponderance; (c) edge-on <100> loops in the same grain.

Figure 5

 5 Figure 5 Formation of <100> loops in an [001] foil at 500 o C: (a) at a dose of 3 × 10 18 ions m -2 (b) the same area at a dose of 1 x 10 19 ions m -2 .

Figure 6

 6 Figure 6 Stills extracted from video 6, showing single crystal [110] Fe under irradiation at 465 o C. The large loop at the centre of the micrograph with b = <100> subsumes two smaller ½<111> loops.

Figure 7 :Deleted: a/ 2 Deleted: a/ 2 Deleted: a/ 2 Deleted: a/ 2 Deleted

 72222 Figure 7:Estimates of the fraction of interstitials contained in loops of the two types. The error bars do not take account of systematic errors due to loss of ½<111> loops to the surface.

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Acknowledgements

We thank Dr. A. Liu and P. Baldo of Argonne National Lab for their help in using this facility. The IVEM-Tandem Facility (within the Electron Microscopy Center at ANL) is supported by the US DOE Office of Science and operated under contract no. DE-AC02-06CH11357 by UChicago Argonne, LLC. We are grateful to Dr. S. L. Dudarev and Dr. S. P. Fitzgerald for helpful discussions. We thank B. Miller, D. Graham, and Prof. I M. Robertson (UIUC) for help with video 4. Part of this work was funded by the UKAEA, Culham Science Centre.