Article No. jmbi.1998.2497 available online at http://www.idealibrary.com on J. Mol. Biol. (1999) 286, 593±606

Thermodynamics of Model and its Implications for the Problem of Folding

PaulM.Harrison1,HueSunChan2,StanleyB.Prusiner3,5 andFredE.Cohen1,2,3,4*

Departments of 1Cellular & Prion disease is caused by the propagation of a particle containing PrPSc, Molecular Pharmacology a misfolded form of the normal cellular prion protein (PrPC). PrPC can re- 2Pharmaceutical Chemistry fold to form PrPSc with loss of a-helical structure and formation of exten- 3Biochemistry & Biophysics sive b-sheet structure. Here, we model this prion folding problem with a 4Medicine and 5Neurology simple, low-resolution lattice model of . If model University of California are allowed to re-fold upon dimerization, a minor proportion of them San Francisco, 513 Parnassus (up to 17 %) encrypts an alternative native state as a homodimer. The Ave, San Francisco structures in this homodimeric native state re-arrange so that they are CA 94143, USA very different in conformation from the monomeric native state. We ®nd that model proteins that are relatively less stable as monomers are more susceptible to the formation of alternative native states as homodimers. These results suggest that less-stable proteins have a greater need for a well-designed energy landscape for protein folding to overcome an increased chance of encrypting substantially different native confor- mations stabilized by multimeric interactions. This conceptual framework for aberrant folding should be relevant in Alzheimer's disease and other disorders associated with protein aggregation. # 1999 Academic Press *Corresponding author Keywords: prion; protein folding; lattice model; PrP; protein stability

Introduction The kinetics and thermodynamics of prion misfold- ing and their relationship to the three forms of A substantial body of evidence demonstrates prion diseases have been discussed extensively (for that the neurodegenerative disorders known as reviews,seeCohen&Prusiner,1998;Prusineretal., prion diseases are caused by an agent composed 1998).Thelinkbetweenthemisfoldingoftheprion largely, if not entirely, of a misfolded form (PrPSc) protein and the actual molecular pathologic events ofthecellularprionprotein(PrPC)(Prusiner& that give rise to prion disease remains to be eluci- DeArmond,1994;Cohenetal.,1994;Harrisonetal., datedfully(Hegdeetal.,1998;Prusineretal., 1997).Threeformsofpriondiseaseoccur:inherited 1998). (e.g. familial Creutzfeldt-Jakob disease (CJD), PrPC is a predominantly a-helical molecule, Gerstmann-Straussler-Scheinker syndrome and whereasPrPScisrichinb-sheetstructure(Panetal., fatal familial insomnia in humans), infectious (e.g. 1994).Nochemicalmodi®cationhasyetbeen kuru and iatrogenic CJD in humans, bovine spon- identi®edbywhichPrPCandPrPScdiffer(Stahl giform encephalopathy in cattle and scrapie in etal.,1992).Experimentalstudiesofarecombinant sheep) and sporadic (e.g. sporadic CJD in humans). molecule corresponding to residues 90-231 of PrP indicate that PrPC is marginally stable relative to a Present address: Professor Hue Sun Chan, foldingintermediate(Jamesetal.,1997;Zhangetal., Departments of and of Medical Genetics & 1997).Athighconcentrationsat35C,recombinant Microbiology, Faculty of Medicine, University of PrP(90-231) forms a multimeric complex with sub- Toronto, Toronto, Ontario, Canada, M5S 1A8. stantialb-sheetstructure(Jamesetal.,1997;Zhang Abbreviations used: PrPC, cellular form of the prion etal.,1997).Ionizingradiationstudiessuggestthat Sc protein; PrP , scrapie (disease-causing) form of the the minimally infectious multimer of PrPSc is a prion protein; PrP, prion protein; CJD, Creutzfeldt-Jakob disease; 2D, two-dimensional or two dimensions; 3D, dimer(Bellinger-Kawaharaetal.,1988).Thesedata three-dimensional or three dimensions. together with an array of transgenic animal exper- E-mail address of the corresponding author: imentsandscrapieinactivationstudies(Prusiner, [email protected] etal.,1990;Oeschetal.,1994;Tellingetal.,1996a)

0022-2836/99/070593±14 $30.00/0 # 1999 Academic Press 594 The Thermodynamics of Being a Model Prion imply that multimeric PrPSc is more stable than strated many of the characteristics of protein fold- PrPC. Models for prion propagation have argued ing and has been useful in understanding the that PrPSc is stabilized by multimeric interactions energy landscapes that govern how a protein folds either upon conversion and/or through subsequent (Dilletal.,1995).Modelproteinsarede®nedas multimerization(Cohenetal.,1994;Lansbury& sequences that have a unique monomeric native Caughey,1995).Ahost-speci®cco-factor,dubbed conformation. Those model proteins that have protein X (which may act as a chaperone), is conformationally distinct monomeric and homo- requiredforconversionofPrPCtoPrPSc(Telling dimeric native states are used as model prions. etal.,1996a;Kanekoetal.,1997).Strainsofprions When the number of conformations in the homodi- for PrPSc have been identi®ed with distinct incu- meric native state is >1, it is said to comprise a set bation times that result in different neurohisto- of prion strain conformations. All other model pathology(Prusiner&DeArmond,1994).Recent proteins are treated as canonical or An®nsenian work has shown that the biological properties of proteins. An®nsen's hypothesis states that ``the prion strains are likely to be enciphered in the ter- three-dimensional structure of a native protein in tiarystructureofPrPSc(Tellingetal.,1996a; its normal physiological milieu is the one in which Collingeetal.,1996).Thereareatleasttwotofour the Gibbs free energy of the whole system is low- PrPSc strain conformations and possibly more est; that is, the native conformation is determined (Bessenetal.,1995;Collingeetal.,1996;Parchietal., by the totality of inter-atomic interactions and 1996;Safaretal.,1998). hence by the amino-acid sequence in a given Further examples of prions, the [PSI] and [URE3] environment.``(An®nsen,1973).Prionsarenon- non-Mendelian inheritance phenomena, have been An®nsenian because they are sensitive to ¯uctu- found in the yeast Saccharomyces cerevisiae ations in their ``physiological milieu'' that may (Lindquist,1997),andalikelyprioncandidate make dimerization/multimerization more likely. [Het-s] has been observed in the fungus Podospora For conditions of the prion sequence where dimeri- anserina(Wickner,1997).Experimentalevidence zation may be more unlikely (such as low concen- suggests that the [PSI] and [URE3] phenomena in tration), prions will adopt their monomeric native yeast are caused by propagatable isoforms of nor- state. malfunctioningcellularproteins(Sup35pand Our goal is not to study the speci®c features of Ure2p,respectively;Lindquist,1997).Despitethe prion protein folding, but rather to take a more very different biological contexts, there are some general perspective and examine unexpected notable speci®c similarities between mammalian observations that arise from our initial model PrP prion and yeast prion propagation. As in PrP design. Re-folded homodimeric conformations are prion propagation, the [PSI] phenomenon requires studied in particular, but we believe that the effects a co-factor in vivo. Intermediate concentrations of of higher-order multimerization would, in prin- the Hsp104 chaperone protein are necessary for ciple, be similar. We examine properties such as ef®cientpropagationof[PSI]invivo(Chernoffetal., conformational similarity and thermodynamic 1995).Invitro,theSup35p/[PSI]priondomain stability for An®nsenian and prion model proteins converts into b-sheet-rich -like ®laments withuniquestablemonomericconformations{. (Kingetal.,1997).Furthermore,thereisevidence The biological relevance of our results is examined. for different strains of [PSI] that can be induced by Thermodynamic stability is found to be a key fac- overproduction of the same Sup35p protein tor in determining susceptibility to an alternative (Derkatchetal.,1996).Forthe[URE3]prion,partial native state. protease resistance is observed as in the case of PrPSc, but not for the non-prion phenotype of the Ure2pprotein(Masisonetal.,1997). Results and Discussion To understand prion propagation better, we have designed the simplest thermodynamic situ- To de®ne our model proteins and prions, we ation that applies to any prion propagation model: have studied 3D 27-mer maximally compact cubic monomeric native conformations and re-folded conformations(Chan&Dill,1990;Shakhnovich& dimeric native conformations stabilized by inter- Gutin,1990;Salietal.,1994;Lietal.,1996)and2D facial interactions for the same protein sequence. n-mers for a range of chain lengths n from 11 to 16 This thermodynamic situation is implemented (Chan&Dill,1990,1991,1996).Thesesystems using a simple model of protein folding, the HP have previously been examined extensively with lattice model. While this model is low-resolution regardtootherpropertiesofproteinfolding(Dill both spatially and energetically, it has demon- etal.,1995).The2Dstudiesallowustoexamine the effects of variation of chain length and of sur- face complementarity in the dimer, whereas the { Here the term unique refers to the existence of a cubic conformations have the dimensionality of single lowest-energy native conformation for a sequence. It does not imply that the sequence always real proteins but the possible dimer packing geo- adopts that particular conformation. Even under metries are much more limited. Unless speci®ed strongly folding conditions, conformational ¯uctuation otherwise, results below are for the 27-mer cubes. is possible and the sequence can sometimes adopt non- For the 3D cubic conformations, 14,906 model nativeconformations(Dill&Chan,1997). proteins were found in a sample of 250,000 ran- The Thermodynamics of Being a Model Prion 595 domly generated HP sequences. When these model proteins were re-evaluated to ®nd homodimeric native conformations, 1110 prions were found, with the remainder of the model proteins compris- ing An®nsenian sequences. Similarly in 2D, all of the model proteins for a particular chain length were re-evaluated for homodimer native confor- mations (the enumeration procedures are described in Methods). These enumeration results are detailedinfullinTable1.TheprionandAn®nse- nian sequences have been analyzed and compared for the properties of hydrophobicity, secondary structure, conformational similarity and thermo- dynamic stability.

Proportion of sequences that are prions

Model protein sequences that exhibit prion-like Figure 1. Example of a 3D model cubic prion. behaviour make up a minor fraction of all possible A model prion from the 3D 27-mer cube enumerations sequencesintheHPmodel(2to17%;Table1). in the HP lattice model in its (a) native monomeric and Those that encrypt a single strain conformation (b) re-folded homodimeric conformations. The H(ydro- account for 2 to 7 % of model-protein sequences. phobic) residues are represented as red beads and the Interestingly, in the present model, this is of the P(olar) residues as blue beads. same order as the percentage of all possible sequences that turn out to have unique native-state conformationsasmonomers(Table1).Examplesof model3Dand2DprionsaredepictedinFigures1 sample of protein sequences from the PDB data- and2,respectively. base(Bernsteinetal.,1977;Table2).Theminimal infectious sequence fragment of PrP (residues 90- Hydrophobicity of the sequences 231) is not particularly hydrophobic or hydrophilic, compared to the representative sample of protein Is a predominantly hydrophobic or hydrophilic sequences(Table2).ThemonomericformofPrPC sequence more likely to form an alternative native is soluble at concentrations suf®cient for NMR state? Fractional hydrophobicities (È) were calcu- spectroscopy(Donneetal.,1997;Rieketal.,1997), lated for the prion-determinant sequence fragments but the PrPSc aggregate is highly insoluble. By con- of PrP, Sup35p and Ure2p, and for a representative trast, the yeast prion sequence fragments for

Table 1. Numbers of model prions for 2D 11 to 16-mers and 3D 27-mers and their hydrophobicities

Chain length nbNumberof  g (minimum NM,numberofprionswithÈ numberofTotalnumbermodel-proteinonlyone(allÈ i c d e f  h contactsofsequences sequences Nprions strain AnfinsenianÈ (prions, a considered) (Ntotal)(%ofNtotal)(%ofNM)(%ofNM) proteins) (all prions) strains ˆ 1) A. 3D data Random sample of 27 (28) 250,000 14,906 (6.0) 1110/14,906 (7.4) 236/14,906 (1.6) 0.48 Æ 0.08 0.47 Æ 0.06 0.48 Æ 0.06

B. 2D data 16 (7) 216 ˆ 65,536 1539 (2.3) 250/1539 (16.2) 100/1539 (6.5) 0.54 Æ 0.12 0.56 Æ 0.12 0.53 Æ 0.11 15 (6) 215 ˆ 32,768 857 (2.6) 147/857 (17.2) 50/857 (5.8) 0.55 Æ 0.09 0.58 Æ 0.13 0.53 Æ 0.13 14 (6) 214 ˆ 16,384 386 (2.4) 51/386 (13.2) 28/386 (7.3) 0.51 Æ 0.11 0.58 Æ 0.12 0.55 Æ 0.12 13 (5) 213 ˆ 8192 173 (2.1) 28/173 (16.2) 8/173 (4.6) 0.49 Æ 0.09 0.59 Æ 0.10 0.50 Æ 0.04 12 (5) 212 ˆ 4096 87 (2.1) 2/87 (2.3) 2/87 (2.3) 0.53 Æ 0.11 0.33 Æ 0.00 0.33 Æ 0.00 11 (4) 211 ˆ 2048 62 (3.0) 0/62 (-) 0/62 (-) 0.52 Æ 0.09 - - a For n ˆ 11, 12 and 13 in 2D, homodimer enumerations have also been extended to include all possible conformations. For these, the prion fraction of model-protein sequences increases to: 12 % (11-mers), 13 % (12-mers) and 25 % (13-mers). b Chain length n and (in parentheses) minimum number of intra-chain contacts in the unique monomeric native conformations. c Total number of HP sequences (for 3D 27-mers a random sample of 250,000 is taken; Ntotal). d The number of these that are model-protein sequences (NM). e The number of the model-protein sequences that are prions (Nprions). f The number of the model-protein sequences that are prions with number of strains ˆ 1. g Mean fractional hydrophobicity (È ) for model proteins. h È for all prions. i È for prions with number of strains ˆ 1. 596 The Thermodynamics of Being a Model Prion

Figure 2. Example of 2D model 15-mer prion in its (a) native mono- meric and (b) re-folded native homodimeric conformations. Resi- duecolouringisasforFigure1.

Sup35p and Ure2p are dominated by polar/charged Conformational similarity of the monomeric residues. These sequences have very high pro- and homodimeric native states portions of glutamine (27 % for Sup35p and 11 % for Ure2p) and asparagine (18 % for Sup35p and Spectroscopic and immunologic studies have shown that there is an extensive conformational 37 % for Ure2p), giving them a hydrophilicity that C Sc isunusualforglobularproteindomains(Table2). rearrangement between PrP and PrP that is Thus, the composition of the small set of currently largely con®ned to the middle third of the PrP sequence(Panetal.,1994;Peretzetal.,1997).The known sequences capable of forming prions shows conformational rearrangement of our lattice no general obvious distinction in terms of sequence prions on going from the monomeric native state hydrophobicity. to the homodimeric native state has been exam- We also examined the model prion and An®nse- ined.Figure3(a)showsthetrendinconfor- nian sequences for compositional bias. The mational similarity (de®ned in Methods) between fractional hydrophobicity (È)ofanHPmodel the monomeric and homodimeric native states sequence is simply the number of H residues in 3D (Smono-di) for the 3D 27-mer sequences, with a the sequence divided by the chain length. Mean single homodimeric native-state (degeneracy ˆ 1). hydrophobicity values (È ) for the prions and 3D The ®rst peak at Smono-di ˆ 1.0 is for the An®nse- for the An®nsenian proteins as populations were nian proteins, whereas the second, much smaller calculated(Table1).Theprionsequencesaregen- peak is for the prions. The lattice prion mono- erally no more or less hydrophobic than An®nse- meric and homodimeric native-state confor- nian protein sequences. However, each model mations tend to be substantially different. In 3D, prion sequence uses what hydrophobic residues it they are almost as dissimilar as any two ran- possesses to stabilize its homodimeric native-state domlychosencompactconformations(Table3). conformations by forming more hydrophobic con- 3D This trend in Smono-di, with a peak at close to ran- tacts at a binding interface. For example, for the dom values, changes little for the prions with 3D model prions with a single strain, on average multiple stable dimeric native-state conformations 24(Æ3)% of the hydrophobic contacts in prion 3D or strains. The mean Smono-di values range homodimers are interfacial, compared to 18(Æ3)% between 0.28 and 0.31 for sequences capable of for lowest-energy homodimers made from the forming two to eight strains. A similar trend in 2D monomeric native-state conformation. conformational similarity (Smono-di) was observed

Table 2. Fractional hydrophobicities (È) for the prion-determinant sequence fragments and the PDB

Protein or protein set È (Miyazawa & Jernigan, 1996) È (Fauchere & Pliska, 1983) PDB July 1997 (non-redundant set) (mean) 0.411(Æ0.037) 0.416(Æ0.036) PrPC (90-231) 0.370 0.372 Sup35p(1-125)0.269a0.335a Ure2p (1-90) 0.282 0.286 a The values differ here because of the proportion of proline in the sequence, which is ranked differently in the two scales because of its secondary-structure propensities. The Thermodynamics of Being a Model Prion 597

Table 3. Conformational similarities between the mono- meric and homodimeric native states for 3D 27-mer cubes and the longer 2D chains

A. 3D 3D Chain length nSmono-di 27-mer cubes (native) 0.31(Æ0.10) 27-mer cubes (random) 0.19(Æ0.08)

B. 2D 2D Chain length nSmono-di 15-mers (native) 0.57(Æ0.19) 15-mers (random) 0.18(Æ0.16) 16-mers (native) 0.59(Æ0.17) 16-mers (random) 0.18(Æ0.15)

the spectroscopic results on the structures of PrPC andPrPSc(Panetal.,1994).

Conformational similarity of prion strain conformations The PrPSc molecules in different prion strains are conformationally distinct as judged by their stab- ilitytolimitedproteolysis(Collingeetal.,1996; Tellingetal.,1996a).PrPScisolatedafterproteolysis and deglycosylation of infectious material derived from patients with Creutzfeldt-Jakob disease and fatal familial insomnia, had different sizes (19 kDa and 21 kDa, respectively) that bred true upon sub- sequent passage through mice carrying identical priontransgenes(Tellingetal.,1996a).Collinge etal.(1996)haveshownthat,aftertreatmentwith proteinase K, PrPSc from the new variant CJD strain in humans was smaller than PrPSc from pre- viously characterised prion strains. How similar do multiple lattice prion strain con-

formations tend to be? The trend in Sdi-di (de®ned in Methods) for lattice prion strain conformations isillustratedbyFigure3(b).Thedistributionshows two major peaks, one for slight relative rearrange- Figure 3. Conformational similarity. (a) Similarity ments of conformation and the other for alternative 3D (Smono-di) of the monomeric and homodimeric native- packings of the same conformation. When com- state conformations, for prions with number of strains paredwithFigure3(a),thisshowsthatlattice ˆ 1 for the 27-mer cube model proteins. The left-hand prion strains tend to be substantially more similar axis is for the random distribution (curve) and the right- in conformation with each other than with the hand axis for the observed distribution (histogram). 3D monomeric native structure. For the 3D cubic con- Interval [x-y] is for x < Smono-di 4 y. (b) Conformational 3D 3D formations, the distributions for Sdi-di for prions similarity (Sdi-di) for 3D model prions with two strains. 3D capable of forming three to eight strains were also The ®rst peak at Sdi-di ˆ 1.0 (dark gray bar) arises from homodimers that have the same conformation differ- derived. These also demonstrate two major peaks. 3D Ignoring the example of alternative half-dimer ently packed. Interval [x-y] is for x < Sdi-di 4 y. 3D 3D packing, where Sdi-di ˆ 1.0, Sdi-di consistently tends 3D 3D toward larger mean values than Smono-di (Sdi-di in the range 0.48 Æ 0.19 to 0.64 Æ 0.19 for two to eight for the longer 2D chains (15-mers and 16-mers) strains). examined. However, the similarity values for the The nucleated polymerization model for prion prions in 2D are not as close to the random propagation suggests that different strains arise valuesastheir3Dcounterparts(Table3).In2D, from different alternative packings of PrPSc mol- some sequences that form distinct conformations ecules(Lansbury&Caughey,1995).Ingeneral can have the same contact maps. This situation here, strains do not arise solely from alternative occurs only for enantiomeric pairs in 3D. Also, packing arrangements of the same half-dimer con- there may be a dimensionality effect for this simi- formation(Figure3(b)).Thepeakforalternative 2D larity measure. These changes in conformation packing arrangements (at Sdi-di ˆ 1.0) is virtually observed in the lattice setting are consistent with absent for the 2D investigations, because they 598 The Thermodynamics of Being a Model Prion entail more complex surface complementarity. We with the corresponding segment of a second pro- expect that the surface complementarity of proteins tein chain, and vice versa. This has been suggested that dimerize will be better represented by the irre- as an explanation of some protein aggregation gular interfaces seen in 2D, rather than by the phenomena(Bennettetal.,1995),wherealternative smooth packing of two cubes. For sequences that conformations that arise in aggregates are formed support two strains, there are two examples for the from various domain-swapping arrangements. It 2D 16-mers (out of 60, 3.3 %) and no example for also arises for lattice prion strains, as indicated in the 15-mers (out of 25). To the extent that this theexampleinFigure4.However,differentlattice model is relevant, it seems unlikely that multiple prion strain conformations may also involve differ- packing arrangements that differ at a low degree ent overall shapes for the dimerized structures that of resolution can solely explain the existence of entail some other form of symmetric rearrange- multiple prion strains. A more likely scenario to ment(Figure4). explaintheexperimentalobservationthatsome prion strains have distinct proteolytic degradation Secondary structure patterns is that a local rearrangement of the chain preserves the overall morphology of the multimer Substantially increased b-sheet content is (Cohen&Prusiner,1998). observed in the PrPC-PrPSc conversion. The A well-described example of conformational change in b-sheet is from 3 % to 43 % for convert- degeneracy in multimeric proteins is domain- ing PrPC to PrPSc as determined by FTIR spec- swapping(Bennettetal.,1995).Indomainswap- troscopy. There is a concomitant loss of a-helical ping, a segment of one protein chain is replaced structure from 42 % to 30 % during the transform-

Figure 4. A 2D prion-strain set example with six conformations that demonstrates two ways to make distinct native-state strain conformations (domain or residue- swapping, or some other form of symmetric rearrangement within the homodimer). The monomeric native-state conformation is also illustrated in (a) and the set of six strain conformations is illustrated in (b). This example was found by exhaustive enumerations over all possible chain conformations for 13-mers (see Methods). The Thermodynamics of Being a Model Prion 599 ation(Panetal.,1994).Inothercasesofmono- Thermodynamic stability mer-multimer dimorphism, such as inclusion body formation with b-lactamase or in amyloido- We have evaluated the importance of stability genesis of mutant lysozymes, an increase in for the behaviour of our model proteins and 0 b-sheetformationisnoted(Przybycienetal., prions. Stabilities (ÁGmonomer, de®ned in Methods) 1994;Boothetal.,1997). were calculated for the 27-mer cubes for the mono- Sheet formation was examined for the lattice meric native states of all of the model proteins prions(Figure5).De®nitionsofsheetcontactsare (Figure6).Thestabilityresultspresentedhereare takenfrompreviouslatticework(Chan&Dill, independent of the value of the weighting factor a 1990,1991).Asheetissimplyde®nedastwo (de®ned in Methods), which is inversely pro- consecutive parallel or antiparallel contacts on the portional to the simulation temperature as used in latticein2Dandthreein3D(Chan&Dill,1990, folding simulations such as those performed by 1991).Forthe3D27-mercubes,theprionhomo- Salietal.(1994)andUnger&Moult(1996). dimer binding interfaces exhibit a modest For An®nsenian lattice proteins, the energy increase in sheet content (3.4 Æ 2.3 sheet contacts difference between the native state and the lower- per nine-contact interface). The distribution of the energy non-native conformations is substantial change in sheet content for the remainder of the (Figure6).However,thelatticeprionsintheir conformation is approximately Gaussian about monomeric native state tend to be less stable than zero (data not shown). However, examination of theirAn®nseniancounterparts(Figure6).Thevast the data for the longer 2D chains (15 and 16-mer) majority (98.0 %) of the homodimeric native states indicates that extensive dimer sheet is enabled by have their conformations residing in the lowest formation of a large dimer interface and the non-native energy level (Enative ‡ 1) of their changeinshapethataccompaniesit(Figure5). respective monomeric native-state energy spectra. The mean change in the percentage of total sheet Also, stabilities in this model are predominantly from the monomer to the homodimer half-dimer determined by the number of conformations in the conformation is ‡26(Æ26) % for the 16-mers, and lowest non-native energy levels (particularly the

‡27(Æ24) % for the 15-mers. Enative‡1level;Shortleetal.,1992).

Figure 5. The change in the total proportion of sheet contacts (Ásheet) for the monomer and half-dimer confor- mations, for the 2D 16-mers, including the interface contacts. This is calculated as: Ásheet ˆ (number of sheet contacts made by the half-dimer/total number of contacts made by the half-dimer) (number of sheet contacts made by the monomer/total number of contacts made by the monomer). Sheets have a minimum size of two parallel or antiparal- lelconsecutivecontacts(seeChan&Dill,1991).Asimilartrendisobservedforthe2D15-mers. 600 The Thermodynamics of Being a Model Prion

0 Figure 6. Stability for the 27-mer cubic model proteins. The distribution of stabilities (ÁGmonomer) for all model-pro- tein sequences, split into An®nsenian sequences (totalling 13,796 sequences, black bar) and prions (1110 sequences, 0 white bar), using a ˆ 5.0. Interval [x] contains all values such that [x 0.02] < ÁGmonomer 4 x. Every second interval is labeled. In the inset, the distribution of the sample mean for samples of the size of the prions as a subpopulation is shown as a curve, the sample mean for the prion subpopulation is indicated by an arrow. Mean stability trends for these An®nsenian sequences and for prions are 0.25 Æ 0.21 and 0.13 Æ 0.15, respectively. Student's t-test for com- parison of the prions and the An®nsenian sequences shows that this difference in stability is highly signi®cant (p(t)50.005).

These observations taken together imply that patternofinheritance(Prusiner&DeArmond, sequences are more likely to form prions if the 1994).ThesimplicityoftheHPmodelenables lowest non-native energy levels are relatively examination of all possible single-site mutations highly populated. There is therefore a statistical for a sequence (27 in total for the cubic model pro- link between monomeric native-state stability and teins). The effect of these mutations on stability has susceptibility to the prion phenomenon. Although been studied for the model cubic prions and An®n- we do not include kinetic simulation in the current senian proteins. Only coding mutations for the study, previous studies using similar models show monomericnativestateareexamined(Figure7). that these low-energy non-native conformations Coding mutations for the monomeric native state (i.e.conformationallydistantrelatives;seeDill& are mutations that maintain this conformation as Chan,1997)wouldlikelycorrespondtokinetic the unique native state conformation. A minor traps in which relatively poorly designed fraction (15-16 %) of all single-site mutations are sequences tend to accumulate during folding coding in this model. (Thirumalai&Woodson,1996).Therefore,well- For monomeric native states of the prion designed folding kinetics for the monomers is sequences studied, 70.0 % of the coding single- necessary to avoid these low-energy conformations sitemutationsarestabilizingand30.0%are that tend to be substantially different from the destabilizing(Figure7).FortheAn®nsenian monomer, but may be encryptable in a multimeric sequences,50.0%arestabilizing(Figure7).Stabi- form with the formation of a few intermolecular lizing mutations for prions are linked to loss of interactions. A dynamic evaluation of the kinetic prion status (and conversely, destabilizing barriers on this landscape will be required to mutations for An®nsenian sequences predispose address this issue. towardsprionformation;Figure7).Mutations from prion to prion and from An®nsenian Comprehensive analysis of single- sequence to An®nsenian sequence tend to be site mutations equallystabilizing/destabilizing(Table4).Conver- sely, mutations from prion to An®nsenian Point mutations to the PrP gene are known to sequence tend to be stabilizing 70 % of the time cause prion diseases with an autosomal dominant and mutations from An®nsenian sequence to prion The Thermodynamics of Being a Model Prion 601

Figure 7. Single-site mutations data for prion sequences and for An®nsenian sequences separated into stabilizing and destabilizing 0 mutations. Stabilities (ÁGmonomer) are calculated for the complete set of single-site mutations for four sets of sequences: (i) the prion sequences with a unique strain (236 in total); (ii) all prion sequences (number of strains 51, 1110 in total); (iii) a random sample of 1200 model-protein sequences of any sort; and (iv) a random sample of 1200 An®nsenian sequences that have homodimeric native-state degeneracy ˆ 1. The number of coding mutations for each popu- lation is indicated at the top of each bar (denoted m). Tests of the signi®cance of these data as sets of Bernoulli trials were performed to compare the proportion of (de)stabilizing mutations between either of the prions populations (i) and (ii), and either of populations (iii) and (iv). They show that the difference in this proportion is highly signi®cant (p50.005, where p is the probability that the proportions are the same). These proportions are not dependent on the number of strain conformations (as the percentages for number of strains ˆ 1 and > 1 are similar). tendtobedestabilizing70%ofthetime(Table4). simple model of protein folding. In the HP model, Because the prions form a 7.6 % subpopulation of a minor proportion of model proteins can encrypt the model-protein sequences, the number of An®n- an alternative native multimeric state and do not senian protein-to-prion mutations in this Table are necessarily need a very hydrophobic or hydrophi- relatively small. Binomial distribution tests to com- lic sequence to effect this change. This is consistent pare the proportion of (de)stabilizing mutations for with observations on real prions: while PrP is of the prion-to-An®nsenian protein and prion-to- intermediate hydrophobicity, the yeast prions prion categories show that the difference is highly Ure2p and Sup35p are more hydrophilic than the signi®cant (p 5 0.005). Thus, in real proteins we average protein of known structure. would expect that destabilizing mutations predis- We have shown that model prion monomeric pose towards the prion phenomenon and, in gener- native states tend to be less stable. Since lack of al, toward the existence of alternative native states. stability implies the existence of more low-energy Alterations of the kinetic barriers to prion for- meta-stable conformations, there is a greater mation are also likely to play a role in the disease- chance that some of these meta-stable confor- causing properties of these mutations. An mations will be stabilized by multimeric inter- examination of this possibility is beyond the scope actions. This implies that susceptibility to prion of the present article. formation has a probabilistic basis and that more Destabilizing mutations have been experimen- examples of prion-like behaviour are likely to be tally demonstrated to cause lysozyme amyloid for- found for real proteins, particularly those of mation, which arises in hereditary non-neuropathic marginal stability. Prion sequences may sample systemicamyloidosis(Boothetal.,1997).Lysozyme non-native/unfolded conformations with greater mutants that are less stable have a greater ten- frequency. Factors that increase the likelihood of dencytoformamyloid®brils(Boothetal.,1997). multimer formation, including the introduction of Similar links between destabilizing mutations and a multimeric template, or mutations or the amyloid formation have been observed for immu- expressionofhighconcentrationsoftheprotein, noglobulinlightchainamyloidosis(Hurleetal., willdistorttheenergylandscape(Dill&Chan, 1994)andtransthyretin-basedamyloidoses 1997)forthefolding/refoldingofthechainfor (McCutcheonetal.,1995).ForPrP,itissuggested prion sequences. An experimental analogy for PrP that the mutations that cause inherited prion dis- would be that inoculation of PrPSc and overexpres- ease either destabilize the monomeric native state sion of PrP in transgenic animals lead to exper- of PrP or stabilize a transition state that is critical imentaldisease(Cohen&Prusiner,1998). totheformationofPrPSc(Cohenetal.,1994;Cohen Surprisingly, the monomeric native-state confor- &Prusiner,1998). mations of the prions tend to undergo substantial rearrangement to form the conformations of their Conclusions homodimeric native states. There is thus a greater need for a well-designed energy landscape for the The substantial conformational change that folding of the normal monomeric form of a less- underlies prion diseases arises quite logically in a stable protein, so that the greater chance of becom- Table 4. Classi®cation of mutations that demonstrates the connection between stabilizing/destabilizing mutations and prion status

Class of Number and percentage that Number and percentage that Number and percentage that Number and percentage that mutation are stabilizing for prion-to- are stabilizing for prion-to- are stabilizing for Anfinsenian are stabilizing for Anfinsenian Sequence group prion mutations Anfinsenian protein mutations protein-to-prion mutations protein-to-Anfinsenian protein mutations Prions forming a single strain conformation 97/188 (51.6%) 592/807 (73.4%) N/A N/A All prions 519/997 (52.1%) 2556/3514 (72.7%) N/A N/A Random sample of 1200 model-protein sequences 35/76 (46.0%) 181/263 (68.8%) 91/285 (31.9%) 2384/4769 (50.0%) Random sample of 1200 Anfinsenian proteins with a single N/A N/A 72/187 (38.5%) 2462/5030 (48.9%) dimer in the homodimeric native state The Thermodynamics of Being a Model Prion 603 ing a prion can be overcome. In a sense, the nor- ground adhesion or sticking energy is assumed so that mal functioning native form of a protein can be one has to consider only the maximally compact confor- seen as a kinetic trap on the energy landscape of mations. the alternative multimeric native form. Additionally, exhaustive enumerations over all poss- ArecentlatticeinvestigationbyAbkevichetal. ible conformations (not just the compact conformations) (1998)hasrelevancetoprions.Intheirstudy,they for very short 2D HP chains (11-mers to 13-mers) were performed. It has been demonstrated that restricting the envision the misfolded form of prion proteins as conformational ensemble to the maximally compact con- originating from kinetic partitioning into possible formations for computational ef®ciency as performed in iso-energetic conformations (i.e. the cellular and our 3D studies here can modify the thermodynamic and misfolded forms), which in their model are kinetic properties of a model system relative to the corre- assumed to have essentially the same energetic sponding model that accounts for all possible confor- favorability. In contrast to the present analysis, mations(Chan&Dill,1996;Klimov&Thirumalai,1996). Abkevichetal.(1998)donotconsiderdimerization However, we believe that our 3D approach is adequate or aggregation as mechanisms for enhancing the for the general, low-resolution thermodynamic trend we thermodynamic favorabilities of the disease-caus- aim to determine here. This is con®rmed by the qualitat- ing forms of prion proteins. ively similar trends exhibited by our 3D results and cor- responding 2D results that are obtained using more extensive conformational ensembles. Methods Model definitions Enumerations to find the native states for sequences as a monomer and as a homodimer A model-protein sequence is de®ned as a prion if each and every conformation in the homodimeric In the HP lattice model, sequences that are made from native state is distinct from the monomeric native state. two residue types (hydrophobic H and polar P) are con- Other model-protein sequences are termed An®nsenian ®gured on a three-dimensional (3D) cubic or two-dimen- sequences. We suggest that, under conditions condu- sional (2D) square lattice. The HP lattice model is cive to dimerization, these sequences may transiently implementedaspreviouslydescribed(Chan&Dill,1991). form homodimers made from the monomeric native For the HP model, in both 2D and 3D, interactions H-H, state conformation to avoid encrypting an alternative H-P and P-P are scored energetically as {e ˆ (1); HH native state. e ˆ 0; e ˆ 0}, where e is the score assigned to the HP PP AB For a prion sequence, when the number of confor- interaction/contact between residue types A and B. The mations in the homodimeric native state is >1, it is total energy for a conformation, E is Æ (e ), where the AB said to comprise a set of prion strain conformations sum is over all interactions for the conformation. HP (Tellingetal.,1996a).Prionstrainsarethusaccommo- sequences that have a single native-state conformation as dated in this energetically low-resolution model as a monomer are used as model proteins. multiple conformations in the homodimeric native In 2D, these model protein sequences have state. At low concentrations of the prion sequence previously been determined by exhaustive enumeration where dimerization is unlikely, prions will adopt their overallpossibleconformers(Chan&Dill,1991,1996). monomeric native state. However, the homodimeric Here, all 2D HP model-protein sequences with chain native state is said to be encrypted by the model-pro- length (n) ˆ 11-16 are submitted to a second set of tein sequence under these conditions that favor the homodimer enumerations to determine native re-folded monomeric folding landscape. homodimeric conformations. The individual chain con- Analysis of the model proteins and prions arising formation within the dimer is termed the half-dimer. from the 2D 15-mer and 16-mer enumerations and (par- All possible dimer conformations that comprise a con- ticularly) from the 3D cubic 27-mer enumerations is dis- formation docked against a copy of itself are enumer- cussed in more detail below. ated to generate an ensemble of possible native homodimers. These homodimer enumerations are per- formed only for all conformations that have at least Fractional sequence hydrophobicities (ÈÈÈ) the minimum number of contacts for conformations coded for by model-protein sequences. The fractional hydrophobicity (È) of a lattice HP In 3D, enumerations are performed for a random sequence is the proportion of H residues in it. È is cal- sample of 250,000 HP 27-mer sequences over the maxi- culated for all of the prion and model protein lattice mally compact conformations to identify sequences that HP sequences. Fractional sequence hydrophobicities for have unique monomeric native-state conformations, i.e. real proteins are similarly de®ned. Here, È values are that can be used as model proteins. These sequences are calculated for the prion-determinant sequence frag- then submitted to enumerations, again only over the mentsforPrP,Ure2pandSup35p.TheMiyazawa& maximally compact conformations to ®nd the lowest- Jernigan(1996)andFauchere&Pliska(1983)hydro- energy re-folded homodimer. For 3D 27-mers, all of the phobicity scales have been normalized to the interval maximally compact conformations (i.e. those with the 0.0 to 1.0, with the most hydrophobic residue type maximum number of contacts ˆ 28) are cubic. There are given a value of 1.0 and the least hydrophobic residue 103,346 cubic conformations that are unrelated to each type given a value of 0.0. The value of È for each otherbyrotationalorre¯ectivesymmetry(Chan&Dill, sequence is calculated as the sum of the individual 1990;Shakhnovich&Gutin,1990;Lietal.,1996).Forthe residue hydrophobicities divided by the number of homodimerization enumeration stage, all possible cube residues in the sequence. These fractional hydrophobi- dockings that do not entail an offset of the cube faces are cities are analogous to (though not directly comparable included. This 3D model is a perturbed homopolymer to) those calculated for the lattice HP sequences. A model(Chan&Dill,1990,1996),whereinastrongback- representative set of 756 protein chains taken from the 604 The Thermodynamics of Being a Model Prion

July 1997 version of the PDB (with a maximum of where gE is the number of conformations with energy E 25 % identity between protein chains) and chosen using as de®ned above. The summation for the partition func- amodi®cationofthealgorithmdescribedbySander& tion is over the enumerated energy levels of a monomer. Schneider(1992)wasanalyzedforhydrophobicityin The probability of the non-native state is given by: this way. "# X0 P -native ˆ gE exp aE† Q Conformational similarity non E ˆ Enative‡1† The conformational similarity of the monomeric and homodimericnative-stateconformationsisanalyzed. Stability results are calculated using a ˆ 5.0, which 3D 0 Smono-di is the proportion of residue-residue contacts that gives an overall negative trend for ÁG values. are the same for the monomer and half-dimer confor- Since only relatively compact conformations are mations for the cubic enumerations (as originally de®ned enumerated for most of the chain lengths in 2D and 3D byShakhnovich&Gutin,1990):

3D Smono-di ˆ number of contacts that are the same between the two conformations†=28

There is a one-to-one correspondence between the 0 103,346 maximally compact 3D 27-mer conformations studied here, the stability (ÁG ) calculated here is not and their contact maps. For the 2D enumerations, equal to the free energy difference between the ground different conformations can have identical contact state and all other conformations, but is expected to cor- maps and not all conformations have the same num- relate with it, as the equilibrium is dominated by that ber of contacts. The 2D similarity measure is termed between the native and low-lying non-native confor- 2D mations(Shortleetal.,1992). Smono-di and is given by:

2  number of contacts are the same for the two conformations† S2D ˆ mono-di number of contacts in conformation 1 ‡ number of contacts in conformation 2†

The conformational similarity of multiple confor- Acknowledgments mations in the homodimeric native state is examined and is termed Sdi-di for both 2D and 3D. The similarity Figures1,2and4weremadeusingthegraphicspro- Sdi-di is de®ned as the proportion of contacts that are the gram PREPI (supplied by Suhail Islam and Michael same between the conformations of two half-dimers and Sternberg, Biomolecular Modelling Laboratory, Imperial is calculated in the same manner as Smono-di in both 2D Cancer Research Fund, UK). Thanks to Kinkead Reiling and 3D. for assistance with calculations and to Andrew Wallace In both 2D and 3D, random similarity values are cal- and Marcin Joachimiak for comments on the manuscript. culated from a sample of 10,000 comparisons between H.S.C. thanks Professor Ken Dill for support and encour- conformations that have the minimum number of con- agement. This work was supported by grants from the tacts that are observed in the monomeric native-state National Institutes of Health to F.E.C. and S.B.P. conformations.

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Edited by A. R. Fersht

(Received 14 August 1998; received in revised form 9 December 1998; accepted 21 December 1998)