SOD1 Exhibits Allosteric Frustration to Facilitate Metal Binding Affinity

6.6 MB·English

by  Atanu Das

SOD1 Exhibits Allosteric Frustration to Facilitate
Metal Binding Affinity
Atanu Das∗ and Steven S. Plotkin∗
∗DepartmentofPhysicsandAstronomy,UniversityofBritishColumbia,Vancouver,Canada
Superoxidedismutase-1(SOD1)isaubiquitous,CuandZnbinding, tointrinsicproteinsidechainsthatcanenhanceproteinfunc-
freeradicaldefenseenzymewhosemisfoldingandaggregationplaya tionorfunctionallyimportantmotionattheexpenseofnative
potentialkeyroleinamyotrophiclateralsclerosis,aninvariablyfatal stability-akindof“self-allostery”. Someallostericactivation
neurodegenerativedisease. Over150mutationsinSOD1havebeen mechanisms involve mediation of conformational switches by
identified with a familial form of the disease, but it is presently
non-nativeintra-proteininteractions[7],aneffectpredictedby
not clear what unifying features, if any, these mutants share to
3 energylandscapeapproacheswhereinbarriersbetweenconfor-
make them pathogenic. Here, we develop several new computa-
1 mationalstatesarebuffedtolowerenergies[8]. Thepotential
tional assays for probing the thermo-mechanical properties of both
0 ALS-associatedandrationally-designedSOD1variants. Allostericin- for novel allosteric regulators may vastly broaden candidate
2 teraction free energies between residues and metals are calculated, targets for drug discovery [9]. The internal frustration re-
and a series of atomic force microscopy experiments are simulated quired for cooperative allosteric function may have deleteri-
n
with variable tether positions, to quantify mechanical rigidity “fin- ous consequences however, if protein stability is sufficiently
a gerprints” for SOD1 variants. Mechanical fingerprinting studies of penalizedinintermediatestatestoenhancethepropensityfor
J a series of C-terminally truncated mutants, along with an analysis misfoldingandsubsequentaberrantoligomerization,processes
6 ofequilibriumdynamicfluctuationswhilevaryingnativeconstraints, known to be involved in neurodegenerative disease [10]. Here
] panoatelynstiisaloefntehregycocuhpalninggebueptownemenutloatciaolnf,rufrsutsrtartaiotonmaentdermaentaallysbiisn,dainndg wdiesmshuotwaseth(aStOtDh1e)AisLeSm-absrsooicleiadteindspurcohteaincoCnufl,icZtnbestuwpeeernoxsitdae-
M interactionsforaglycinescanof90residuestogetherrevealthatthe
apo protein is internally frustrated, that these internal stresses are bility and function.
B partially relieved by mutation but at the expense of metal-binding SOD1 is a homo-dimeric antioxidant enzyme of 32kDa,
affinity, and that the frustration of a residue is directly related to wherein each monomer contains 153 amino acids, binds one
.
o its role in binding metals. This evidence points to apo SOD1 as Cu and one Zn ion, and consists largely of an eight stranded
i a strained intermediate with “self-allostery” for high metal-binding greek key β barrel with two large, functionally important
b affinity. Thus, the prerequisites for the function of SOD1 as an loops [11,12,13]. Loop VII or the electrostatic loop (ESL,
- antioxidantcompetewithapostatethermo-mechanicalstability,in-
q creasingthesusceptibilityoftheproteintomisfoldintheapostate. residues121-142)enhancestheenzymaticactivityofthepro-
[ teinbyinducinganelectrostaticfunneltowardsaredoxactive
site centered on the Cu ion [14]. Loop IV or the Zn-binding
1 allosteryandcooperativity | mechanicalstability| proteinmisfolding | frustra- loop (ZBL residues 49-83), contains histidines H63, H71, and
v tion | ALS H80 as well as D83, which coordinate the Zn ion and, along
2 withadisulfidebondbetweenC57andC146,enforceconcomi-
9 Abbreviations:(F,S)ALS,(familial,sporadic)amyotrophiclateralsclerosis;WT,wild- tant tertiary structure in the protein. The Cu on the other
9 type;ZBL,Zn-bindingloop;ESL,electrostaticloop;RMSF,rootmeansquaredfluc- hand is coordinated by H46, H48, and H120, and the bridg-
0 tuations; SASA, solvent-accessible surface area; PTM, post-translational modifica- ing histidine H63 between the Cu and Zn, which are located
. tion; Cu,Zn(SS), holo, disulfide present; E,E(SH), apo, disulfide-reduced; WHAM, primarily in the Ig-like core of the protein.
1
weightedhistogramanalysismethod;SI,SupportingInformationAppendix SALSinclusionsareimmunoreactivetomisfolding-specific
0
SOD1 antibodies [15,16]. Such misfolded aggregates may be
3 Allosteric regulation canonically involves the modulation initiated from locally (rather than globally) unfolded states
1
of a protein’s affinity for a given ligand A through the that become accessible, for example, via thermal fluctuations
:
v bindingofaseparateligandBtoadistinctspatiallocationon orrareevents[17],e.g. near-nativeaggregatesoraggregation
i the protein. The modulatory binding site at the distinct lo- precursors were found for an obligate monomeric SOD1 vari-
X cation is referred to as the allosteric site, and the interaction ant [18], and for FALS mutants S134N [19,20] and E,E(SS)
r between the allosteric site and the putative agonist binding H46R [19]. These above studies have motivated the present
a site is referred to as an allosteric interaction. Early models computational study, which focuses on the native and near-
of allostery were used to explain ligand saturation curves for nativethermo-mechanicalpropertiesofmutant,WTandpost-
hemoglobinintermsofsubunitinteractionsthatwouldinduce translationally modified SOD1.
binding cooperativity [1,2]. Cooperativity may be quantified
through the non-additivity in the binding energies of ligand
and allosteric effector [3]. More recently, allostery has been
thought to be a more generic property present even in single Results
domain proteins [4]. In this context, positive cooperativity Cumulative distributions of work values can discriminate
maybemodulatedthroughfrustratedintermediates[5],which SOD1 mutants and premature variants..Mechanical probes
may enhance the conformational changes observed upon lig- were employed by simulating tethers on the residue closest
and binding for allosteric proteins [6]. In a single domain to the center of mass of the SOD1 variant, and on various
protein, the notion of an allosteric effector can generalized residues on the protein surface. The experimental analogue
1–8
Fig. 1. (PanelA)Force(inseta),Work(mainpanel),andeffectivemodulus(insetb)asafunctionofextension. TethersareplacedattheCαatomclosesttothecenter
ofmassoftheSOD1monomer(H46),andtheCαatomofeitherresiduesG10(red)orI17(green),inseparatepullingassays. Ribbonrepresentationsoftheproteinarealso
shown;thetetheringresidueisshowninlicoricerendering(inred)andthecenterCαasaredsphere. Theinitialequilibrated(at0˚A,greenribbon)andfinal(at5˚A,blue
ribbon)structuresarealignedtoeachotherbyminimizingRMSD.(PanelB)(Inseta)WorkprofilesofCu,Zn(SS)WT(black),E,E(SH)WT(blue),andE,EG127XSOD1
(red)vs. sequenceindex. Secondarystructureschematicisshownunderneath. (Mainpanel)Cumulativedistributionsoftheworkvaluesininset(a). E,EG127Xismorestable
thanfull-lengthE,E(SH)SOD1(p=9e-7). (Insetb)Fractionofthe48incidencesthateachvarianthadeithertheweakest,strongest,ormiddleworkvalue,e.g. E,E(SH)
SOD1isweakest80%ofthetimeandisneverthestrongestvariant. (PanelC)CumulativeworkdistributionsforCu,Zn(SS)WT(black),Cu,ZnG127X(green),E,EG127X
(red),andCu,Zn(SH)WT(cyan). Cu,ZnG127Xisdestabilizedwithrespecttofull-lengthCu,Zn(SS)WT(p=6.2e-8). (Inseta)SameanalysisaspanelB,insetb,forthe
variantsCu,Zn(SS)WT,Cu,ZnG127X,andE,EG127X.(PanelD)CumulativedistributionsforserinemutantSOD1variantsdemonstratethatC-terminaltruncationstabilizes
theapoformbutdestabilizestheholoform(seetext).
stiffness moduli were observed for small perturbing distances
tosuchaninsilicoapproachwouldrequiremultipleAFM (Fig. 1A inset b). These were attributable primarily to side
oropticaltrapassaysinvolvingnumerousresiduepairsabout chain-sidechain“docking”interactionsinthenativestructure
the protein surface as tethering points. This is difficult and (SI Appendix, Fig. S2). The work to pull a given residue to
time-consumingtoachieveinpractice,whichthusprovidesan a distance sufficient to constitute an anomalously large fluc-
opportunity for the present simulation approaches. All pro- tuation, e.g. 5˚A, can be calculated as a function of sequence
teins in this study were taken in the monomeric form- many index for a given SOD1 variant, resulting in a characteristic
of them such as E,E(SH) SOD1, G127X, and G85R are ei- mechanicalprofileor“mechanicalfingerprint”forthatprotein
thernaturallymonomericorhavesignificantlyreduceddimer (Fig. 1B, inset a). The work values at 5˚A do not correlate
stability. TheALS-associatedtruncationmutantG127Xcon- with RMSF values of the corresponding residues [23]. A rep-
tains a frameshift insertion which results in 6 non-native resentativesubsetof48residueswasobtainedasdescribedin
amino acids following Gly127, after which a truncation se- the SI. We found that such a profile was independent of how
quenceterminatestheprotein20residuesshortoftheputative the protein was initially constructed before equilibration, i.e.
C-terminus[21,22]. HerePTMsrefertoprocessesinvolvedin fromwhatPDB,butwasclearlydifferentbetweenWTSOD1
thein vivomaturationofSOD1,includingdisulfidebondfor- and mutants such as G127X, as well as other PTM variants
mation, and metallation by Cu and Zn. suchasE,E(SH)SOD1(SIFig. S4). TableS1inSIgivesthe
The simulated force-extension profile may be used to ob- correlation coefficients between variants. A given PTM glob-
tain the work required to pull a given residue to a given dis- allymodulatesthemechanicalprofile,inducingbothlocaland
tance (Fig. 1A). In this assay, we found that large effective non-local changes in stability that can be both destabilizing
2
Fig. 2. (PanelA)CumulativedistributionsofworkvaluesforC-terminal-truncatedSOD1variantsofvariablesequencelengthshowanon-monotonictrendinmechanical
stability. Allvariantsaremetal-depletedandhavenodisulfidebond. Sequencesaregiveninthelegend(seetext). (Inseta)Comparingthecumulativedistributionsinthe
mainpanel,thatofthemutantG127Xismostcommonlythestrongest,full-lengthSOD1ismostcommonlytheweakest,and1-140ismostofteninthemiddle. (Insetb)
ChangeinworkvalueWMUT −WWT averagedoverresidues,asafunctiontruncationlength,fortheSOD1variantsinthemainpanel. (Insetc)Ribbonschematicsof
thevarioustruncationmutants,coloredbluetoredfromN-toC-terminus,labeledbyC-terminalresidue. (PanelB)Simulatednative-basindynamicalfluctuations(RMSF)in
explicitSPCsolvent,forCu,Zn(SS)(black)andE,E(SS)SOD1monomer(red),alongwiththeexperimentallymeasuredratioofspectraldensityfunctionsJ(ωH)/J(ωN)
ofobligatemonomericE,E(SS)F50E/G51E/E133QSOD1(bluebars)[31]. Correlationcoefficientisr =0.78. (PanelC)SimulatedRMSFforSOD1variantsE,EG127X
(black),E,E(SS)(red),E,E(SH)(blue),andE,E(SH)withtheESLconstrainedtobenativelystructured(magenta). Thepresenceofnativestressisindicatedbytheincreased
disorderoftheZBLuponstructuringtheESL(seetext). (PanelD)SnapshotsoftypicalstructuresofE,E(SH)andG127XSOD1fromequilibriumsimulations,colorcodedby
themeanRMSFforeachresidue;RMSFincreasesfrombluetoredaccordingtothescalebarsshown.
Go¯ models [28] captures the overall energy scale of the work
insomeregionsandstabilizinginothers. Adetailedstudy profilequitewellforSOD1,thoughitmustlikelybemodified
ofthemechanicalconsequencesofmutationsorPTMs,e.g. by for other proteins such as thermophilic proteins.
studying the long-range communication through interaction In support of the thermodynamic relevance of a SOD1
networksinthemutantvsWTprotein(seee.g. [24,25,26,27]) variant’s mechanical fingerprint, we found that the non-
is an interesting topic of future research. equilibrium work values obtained by pulling a residue to
Wealsofoundthatthemechanicalworkprofilewasnearly 5˚A stronglycorrelatewiththeequilibriumfreeenergychange
independent of whether an explicit or implicit solvent model forthesameprocess,ascalculatedusingtheWHAMmethod
wasusedinthesimulations,eventhoughnativebasinfluctua- (r=0.96,SIFig. S7). Thus,theworkprofilesobtainedarean
tions(RMSF)showedsignificantscatterincomparingimplicit accurate measure of the corresponding local thermodynamic
andexplicitsolventmodels(SIFig. S5). Equilibriumfluctua- stability profile, up to a scaling factor.
tionsaremuchmoresensitivetosolventmodelsthanthelarge ComparingthemechanicalfingerprintsofE,E(SH)SOD1
scale perturbations we consider here. On the other hand, a and that of G127X (Fig. 1B, inset a), we see that many dis-
structure-basedGo¯modeldoesonlyamodestjobofcapturing crepancies between SOD1 variants and WT are difficult to
the mechanical profile, and is poor in particular for residues disentangle solely from the work profile, or even from his-
where electrostatic interactions play a significant role in sta- tograms of the work values (SI Fig. S3). However, the me-
bility(SIFig. S6). Interestingly,thedefaultenergyscaleof1 chanicaldiscrepanciesemergedquitenaturallyfromthecumu-
kJ/molforeachcontactordihedralinteractionusedincurrent lativedistributionofworkvalues. Mechanicalscanswerethus
usedtoconstructthecumulativedistributions,whichthenal-
3
lowedustodistinguishstabilizingenergeticsinvariousforms C57S 1-127 is further destabilized with respect to its holo
ofPTMSOD1,e.g. betweenE,E(SH),G127X,andCu,Zn(SS) form, but is more stable than the full length apo form E,E
SOD1inFigure1B.Notallresiduesneededtobesampledto C57S/C146S1-153. ThisdemonstratesthatC-terminaltrun-
obtain the cumulative distribution- we found convergence to cation stabilizes the apo form but destabilizes the holo form.
within 1kJ/molafterasamplesizeofabout40residues(SI This conclusion is robust to changes in pulling distance (SI
≈
Fig. S8). Thisdoesnotmeanthemechanicalprofileobtained Fig. S15).
from48residuesisrepresentativeofthestabilityinthecorre-
sponding regions of the protein: the mechanical work values Short length C-terminal truncation mechanically stabilizes
wereessentiallyuncorrelatedforaminoacidsabout3residues theapoprotein,whilesufficientlylongC-terminaltruncation
apart. destabilizes it..The mechanical properties of two additional
Comparison of the cumulative work distributions shows truncated constructs, E,E 1-140 (WT sequence), and E,E 1-
that the ALS-associated mutant Cu,Zn(SS) A4V is slightly 110, were assayed to investigate the crossover from increased
more mechanically malleable than Cu,Zn(SS) WT, particu- to eventually reduced mechanical stability as the length of
larlyintheweakerregionsoftheprotein(SIFig. S13). How- truncation is increased (Fig. 2A inset b). All truncation
ever the mechanical weakening due to mutation is substan- variants are missing the putative disulfide bond. Figure 2A
tially larger in the E,E(SS) state, and largest in the E,E(SH) shows cumulative distributions for the above variants along
state (green curves in SI Fig. S13). Experimental measure- with E,E(SH) SOD and E,E G127X. The truncation E,E 1-
ments of melting temperature also have shown increased sus- 140 mechanically stabilizes E,E(SH) SOD1 (p = 1e-3), and
ceptibility to mutation in the E,E(SH) state for A4V [29]. G127X is further stabilized with respect to 1-140 (p=9e-4).
We also note from SI Figure S13 that disulfide reduction in Comparison of the triplets of rank-ordered work values cor-
the WT apo state, E,E(SS) E,E(SH), actually increases the responding to E,E(SH), E,E 1-140, and E,E G127X supports
→
rigidity of the native basin [23], even though the net ther- this conclusion (Fig. 2A inset a). We have omitted the 3
modynamic stability is decreased, primarily due to increased least stable work values for all variants in calculating statis-
unfolded entropy [30]. tical significance- these are outliers for E,E(SH) that would
dominate the result towards the conclusion that we have ar-
rived at without their inclusion. Variant E,E 1-110 has sig-
nificantly compromised mechanical rigidity and may not be
Lack of post-translational modifications mechanically desta-
thermodynamically stable- the mechanical assay only probes
bilizes SOD1, however the truncation mutant G127X stabi-
malleability of the native basin.
lizes the apo, disulfide-reduced protein..The cumulative dis-
tribution of E,E(SH) lies to the left of that for Cu,Zn(SS)
SOD1inFigure1Bforallrank-orderedworkvalues,illustrat- Simulated fluctuations correlate with experimental spectral
ingthatthatvariantismoremalleableandthusmoresuscepti- density functions for apo SOD1..Weperformed20nsequilib-
bletoperturbingforcesthatmightinducetheconformational rium simulations in explicit solvent (SPC water model) for
changes accompanying misfolding. Likewise, Cu,Zn(SH) is Cu,Zn(SS) and E,E(SS) SOD1. Native-basin RMSF values
destabilizedwithrespecttoCu,Zn(SS)inFigure1C,andthe show significant scatter between explicit and implicit solvent
otherPTMvariantsinSIFigureS14showthatlackofPTMs models compared to mechanical work values (SI Fig. S5),
reduces the mechanical rigidity. so for analysis of equilibrium fluctuations, explicit solvent is
On the other hand, the E,E G127X truncation mutant, used. Figure 2B plots the resulting equilibrium RMSF for
which lacks both metals, a disulfide bond, and part of the Cu,Zn(SS) and E,E(SS) SOD1; SI Figure S9 also gives the
sequence, shows increased mechanical stability over E,E(SH) solvent-accessible surface area of backbone amide Nitrogens
WT (p = 9e-7, Fig. 1B). Comparing the profiles, E,E(SH) (SASAN)forthesameequilibriumtrajectory. Themaineffect
ismostcommonlytheweakest,Cu,Zn(SS)ismostcommonly ofmetallossistoinducesolventexposed,disordered,anddy-
the strongest, and G127X is most commonly in the middle namic Zn-binding and electrostatic loops (loops IV and VII).
(Fig. 1B Inset b). Apparently the C-terminal region of A moderate increase in dynamics is observed for loop VI as
the protein mechanically stresses the remainder of the pro- well. The preferential increase in dynamics of the ZBL and
tein when PTMs are absent, reducing its mechanical stabil- ESLuponmetallossisconsistentwithexperimentalmeasure-
ity. However, a metastable holo variant of G127X contain- mentsoftheratioofspectraldensityfunctionsJ(ωH)/J(ωN)-
ingmetalsintheirputativepositionsislessmechanicallysta- a measure of dynamics fast compared to the tumbling rate
ble than holo WT (p = 6.2e-8, Fig. 1C). In the full-length (correlation coefficient r=0.78). The experimental measure-
holo protein, native stabilizing interactions are more apt to ments of spectral density [31] are obtained for a monomeric
be minimally frustrated, and thus C-terminal truncation in- E,E(SS) SOD1 mutant F50E/G51E/E133Q [32].
duces softening of the native structure. The metallation of
G127X only marginally stabilizes it (p = 6.7e-3, Fig. 1C in- Dynamic fluctuations in C-terminal truncation mutants re-
set a), while metallation of WT protein results in substantial veal native frustration in apo SOD..Because G127X is more
mechanicalstabilization(SIFig. S14). G127XlacksC146,so mechanicallystablethanE,E(SH)SOD1,nativebasinfluctu-
Cu,Zn(SH)WT may be a more appropriatecomparison than ationswereinvestigatedtoseeiftheextrastabilityofG127X
Cu,Zn(SS) WT. Cu,Zn(SH) SOD1 is less stable than either was recapitulated in equilibrium dynamics. Figure 2C shows
Cu,Zn G127X or E,E G127X (Fig. 1C), however Cu,Zn(SH) thatindeedtheRMSFaresubstantiallyenhancedinE,E(SH)
contains a protononated Cysteine C146, which is destabiliz- relativetoG127X,inparticularintheZBLandESL(loopsIV
ing, and not present in G127X. and VII). This is true even though β-strand 8, N-terminal to
TodeconvolutetheeffectsofprotonatedCysteines,weex- theESL,constrainsE,E(SH)andisabsentinG127X.Though
aminedasetof4serinemutantproteins: Cu,ZnC57S/C146S more dynamic and mechanically malleable, E,E(SH) is not
1-153 (full length), E,E C57S/C146S 1-153, Cu,Zn C57S 1- more solvent-exposed (by SASA ) than G127X, indicating a
N
127(truncatedatresidue127),andE,EC57S1-127. Forthis collapsed, dynamic globule with non-native interactions (SI
system of proteins, Cu,Zn C57S/C146S 1-153 is clearly the Fig. S10). As well, E,E(SH) is more dynamic than E,E(SS)
most stable over most of the range of work values (Fig. 1D), SOD1(Fig. 2C),butlesssolventexposedthanE,E(SS),par-
and Cu,Zn C57S 1-127 is destabilized with respect to it. E,E ticularlyintheZBLandESL(SIFig. S10). Collapseandnon-
4
nativeinteractionsarenothinderingthedynamicsoftheZBL both of them. Thus mutations relieve stress in the apo state,
and ESL; snapshots from simulations for E,E(SH) WT and whileinducinglossofmetalbindingfunction. Itthusappears
G127XareshowninFigure2D.Similarcondensationphenom- thatapoSOD1hasevolvedtohavehighaffinityformetalsat
enaarealsoobservedinprionprotein[33]andNHERF1[34]. the expense of native stability and increased frustration.
Inalargescalestudyof253proteinsacrossseveralfoldfami-
lies [35], RMSF and SASA showed poor correlation (r 0.35
≈
for backbone carbons).
It is intriguing that the additional constraint of structur-
ingβ8inE,E(SH)SOD1resultsinenhancedratherthansup-
presseddisorderintheZBL.Onepotentialexplanationisthat
becausethereismoreresiduesintheESLpresentinE,E(SH)
thaninG127X,theESLforcestheZBLtobemoreexpanded
by steric repulsion, and thus more dynamic, i.e. a “polymer
brush” effect. Another possible explanation is that the order
induced by structuring β8 in E,E(SH) SOD1 induces frustra-
tion and consequent strain elsewhere in the protein, result-
ing in induced disorder in the ZBL. We differentiated these
two scenarios by applying native constraints between the C
α
atoms in the ESL and the rest of protein, but excluding con-
tacts between the ESL and the ZBL: harmonic springs were Fig. 3. (A)Frustratedcontacts(inred)andunfrustratedcontacts(ingreen)for
applied to all pairs of C atoms within 4˚A in the native holo
α E,E(SS)WTSOD1,(B)Samecontactsas(A)fortheaverageover22ALSE,E(SS)
structure that involved contacts either within residues 133- mutants(seetext). (C)Themeannumberoffrustratedcontactswithinasphere
153, or between residues 133-153 and either residues 1-40 or of radius 5˚A centered on each Cα atom, is found as a function of residue index.
90-153. This procedure further constrains the ESL and β8 Ensembleaveragesaretakenfrom50snapshotsinanequilibriumsimulation. Thisis
tobenativelystructured,removinganypolymerbrusheffect, doneforboththeCu,Zn(SS)stateandtheE,E(SS)state,forboththeWTsequence,
but enhancing any native strain. Consistent with a model andfor22mutantsequences. The22mutantsequencesareaveragedtoobtainthe
involving native frustration, the ZBL loop IV becomes more ensembleandmutantaveragednumberofcontactsasafunctionofresidueindexi,
nHF(i) . Plottedisthedifferencebetween nHF(i) andthecorre-
disorderedinE,E(SH)SOD1uponimplementingESL/β8na- shpondinginMumUbTersfortheWTsequencenHF(i).AhpositiveniuMmUbTerwouldindicate
tive constraints (Fig. 2C). WT
anincreaseinfrustrationuponmutation. Holostateisshowninblueandhasan
averageof+5contacts;apostateisshowninredandhasanaverageof-22contacts.
(B)Interactionfreeenergybetweenaresidue’ssidechainandtheCuion,plottedasa
functionoftheE,E(SS)ensemble-averagednumberofhighly-frustratedcontactsthat
“Frustratometer” results and potential energy changes sup-
residuehas(r=-0.79,p=8e-21). (C)SameasinPanelBbutfortheZnion(r=-0.81,
port increased frustration in apo WT SOD1 with respect
p=2e-22).
to apo ALS-associated mutants..Typically frustrated con-
tacts, according to the “frustratometer” method developed
by Wolynes and colleagues [5], were found by averaging 50
snapshots from an equilibrium ensemble for WT SOD1, and
for each of 22 ALS-associated SOD1 mutants (SI Table S3).
Both E,E(SS), and Cu,Zn(SS) states were analyzed. Results
were averaged over the 22 mutants to yield the mean num-
ber of frustrated contacts at a given residue position, for the
“average”mutant. Takingthedifferenceofthisquantitywith
thatforWTSOD1givesthemeanchangeinfrustrationupon
mutation, which increased for holo SOD1 by about 5 total
contacts, but decreased for apo SOD1 by about 22 total con- Fig. 4. (A)Changeinpotentialenergy∆U(t)asafunctionofin silicotime,
tacts (Fig. 3A). This result again supports a frustrated apo beforeandafterimplementingthemutationG37R.(B)Distributionoftheasymptotic
state in SOD1. Direct computation shows on average about potentialenergychange∆U( )for22ALSmutants(seetext). (C)Meanpoten-
∞
38 more highly-frustrated contacts in E,E(SS) SOD1 than in tialenergychangeaveragedovermutants,forboththeholostateandtheapostate,
Cu,Zn(SS) SOD1 (SI Fig. S17). alongwiththemeandifference,WTminusmutants,inbothCuandZnbindingfree
energy.
Forthesamesetofmutants,wefoundthattheensemble-
averaged total potential energy in the native state increased
uponmutationfortheCu,Zn(SS)protein,butdecreasedupon
Frustrating residues in the apo state are allosteric effectors,
mutation in the E,E(SS) protein. This is consistent with the
and positively modulate metal affinity in proportion to their
above frustratometer results. The “time-resolved” change in
frustration.To test the extent to which the residues facilitat-
potentialenergy∆U uponinsilicomutationforarepresenta-
ingmetalbindingarefrustrated,wehavecalculatedtheinter-
tive mutant (G37R) is shown in Figure 4A. The distribution
action free energy of each WT residue with both Cu and Zn,
ofpotentialenergychangesforthe22ALS-associatedmutants
byconsideringthermodynamiccycles[3]involvingmetallation
listed in SI Table S3 is shown in Figure 4B, which shows po-
and residue “insertion” from a glycine at the corresponding
tential energy “cost” upon mutation for Cu,Zn(SS) mutants,
position(e.g. G4A).TheinteractionfreeenergyG between
int
but a significant shift towards negative stabilizing values for
each residue side-chain and either Zn or Cu is given (here
E,E(SS) mutants. The same conclusion is obtained from 30
specifically for residue Ala 4 with Zn) by
non-ALS alanine mutants (SI Fig. S18). Figure 4C shows
that the net effect of mutation on the potential energy is to G =∆G(G A,O Zn) ∆G(G A,O) ∆G(G,O Zn)
int
→ → − → − →
increase it on average in the holo state, but to decrease it on
=∆G(A,O Zn) ∆G(G,O Zn) [1]
average in the apo state, indicating stabilization. Moreover, → − →
all ALS mutants facilitate metal release [23]; the net effect of where∆G(A,O Zn)isthefreeenergychangeofZninsertion
→
mutationontheCuandZnbindingfreeenergiesistodecrease when alanine is present at position 4, and ∆G(G,O Zn) is
→
5
the free energy change of Zn insertion when glycine (no side Discussion
chain) is present at position 4. The other residues, and Cu Wehavefoundhereaconnectionbetweentheallostericdesign
interactions, are handled analogously (see SI Methods). of residues in premature superoxide dismutase towards high
Figures 3B,C plot the above interaction free energy of a metal-binding affinity, and the consequent frustration in the
residue with Cu or Zn, vs. the E,E(SS) ensemble-averaged apo state of the protein. A variety of results supported this
number of highly-frustrated contacts that residue has. Data conclusion. Mechanical profiles were obtained from in silico
are obtained for 90 glycine mutants listed in SI Table S3, for AFM assays with variable tether positions; in this context it
residues that had at least one highly-frustrated contact (see wasfoundthattheC-terminaltruncationmutantG127Xhad
SI).ThevaluesofGint forall90mutantslistedinSITableS3 highermechanicalrigiditythanE,E(SH)SOD1,implyingthe
are negative, indicating cooperative interactions, wherein the releaseofinternalstressesuponremovalofpartoftheprotein.
WT residue facilitates binding of the metal. Each of these Large truncation lengths eventually destabilized the protein.
residues can be thought of as allosteric effectors, positively The higher malleability of E,E(SH) SOD1 over G127X is
modulatingaffinityforeithermetal. ForbothCuandZn,the recapitulated by larger equilibrium dynamical fluctuations in
largerthedegreeoffrustrationintheapostate,thelargerthe the native basin. Constraining loop VII (the ESL) to be na-
role that residue has in facilitating metal binding. No such tively structured only increases fluctuations in loop IV (the
trend is seen for Cu,Zn(SS) SOD1 (SI Fig. S18). This result ZBL), ruling out polymer brush effects and supporting the
strongly supports a model of the apo state as an allosteric native stress hypothesis.
intermediate designed for high metal binding affinity at the Implementing Wolynes’s “frustratometer” method [5]
expense of structural stability. shows that, perhaps surprisingly, more frustration is present
on average in the WT apo state than is present for apo mu-
tants. For the holo state the situation is reversed however,
which is consistent with the notion that mutants facilitate
metal release. In fact every ALS-associated mutant we have
studiedloweredtheaffinityforbothCuandZn[23]. Wehave
foundherethatwhilethesemutantsraisethepotentialenergy
oftheholostate,theytendtolowerthepotentialenergyofthe
apo state and thus stabilize it, consistent with frustratome-
ter results. A general comparative analysis of the decrease in
potential energy and frustration for apo ALS-associated mu-
tants,alongwiththeresultsfromtheirindividualmechanical
scans which generally show weakening with respect to local
perturbations, is an interesting topic for future work. SI Fig-
ureS20comparestherelevantquantitiesfortheALSmutants
A4V and G127X.
Residues in apo SOD1 can be thought of as allosteric ef-
fectors for metal binding. By considering the cooperativity
in thermodynamic cycles involving mutation to glycine and
metal release, we quantified the interaction free energies be-
tween residues in the protein and either Cu or Zn. All inter-
action energies were negative, indicating positive modulation
of metal affinity, Moreover we found that function frustrates
Fig. 5. Panel (A): Residues color-coded by interaction energy with the Cu ion
stability: the stronger the interaction energy, the more frus-
(depictedasacyansphere). Theextentofinteractionisstrongestinmagnitudefor
tratedtheresidue. ForCu,thestrengthoftheinteractionsig-
redcoloredresiduesanddecreasestoblue. Panel(B):sameas(A)fortheZnion
nificantly correlates with proximity to the binding site. For
(depictedasagreysphere). Panel(C):InteractionenergywithCucorrelateswith
thedistanceoftheresiduefromtheCuion;residuesincloseproximitymorestrongly Zn however, there is no correlation with proximity, indicat-
interact. Panel(D):InteractionenergywithZndoesnotcorrelatewithdistanceof inganon-localallostericmechanisminvolvingpropagationof
theresiduetotheZnion,indicatingnon-localallostericeffects. stress-releasethroughouttheprotein,andconsistentwiththe
large structural changes accompanying Zn binding.
The above evidence points towards a paradigm wherein
Finally,wetestthedistance-dependenceoftheinteraction sequence evolution towards high metal affinity results in a
free energy with the metals, for the set of 24 ALS-associated trade-off for significant native frustration in the apo state of
mutants in SI Table S3. In the case of Cu, the allosteric reg- SOD1. A similar conclusion has been reached from studies
ulation for metal affinity is significantly correlated with the of a SOD1 variant with Zn-coordinating ligands H63, H71,
proximity of the residue to the Cu binding site (Fig. 5A,C). H80, and D83 mutated to S, which in the apo form is stabi-
Interestingly,theallostericregulationforZnbindingisuncor- lizedwithrespecttoE,EWTSOD1[38]. Inthiscontext,the
related with distance to the Zn binding site and thus nonlo- C-terminal truncation in G127X can be seen as an allosteric
cal. This finding is consistent with experimental results that inhibitionmechanismtoZnbinding,inthatfrustrationisre-
Zn binding is concomitant with large structural change (par- lievedintheaponativestate,butZn-bindingfunctionislost.
tial folding) of the protein [36]. Long-range coupling to the A similar scenario is observed for select mutants of subtil-
Zn-bindingregionhasalsobeenobservedinG93ASOD1[37]. isin, a serine protease whose function is regulated by Ca2+
Thesameconclusionisobtainedforthe90frustratedresidues binding. In this protein, the mutation M50F preferentially
given in SI Table S3 (SI Fig. S19). stabilizesaposubtilisinrelativetotheholoform,whileweak-
eningcalciumbindingandpromotinginactivationintheholo
form [39].
Native frustration in apo SOD1 as a result of allosteric
cooperativityinmetalbindinghaspotentialconsequencesfor
the misfolding of SOD1. The premature protein, or a pro-
6
teinthatperhapsduetoanexternalagenthaslostitsmetals, respectively,or90glycinemutants(SITableS3). Mechanicalprofilesareobtained
would show decreased thermal stability relative to one that after 20ns pre-equilibration from steered MD simulations (tether speed 2.5mm/s)
hadnotundergonesequenceevolutionforhighmetalaffinity. in GBSA solvent with OPLS-AA/L force field parameters. Robustness checks are
Inthissense,thetightbindingofZnandCuessentialforen- showninSIFigureS15. MonteCarlomethodsyieldthestatisticalsignifance(error
zymaticfunctionofthematureproteinasanantioxidantputs ≈2.7kJ/mol,SIFig. S21). FluctuationanalysisusedSPCexplicitsolvent. Metal
bindingfreeenergiesarefoundfromWHAMincludingpost-relaxationandvalidation
the premature form in additional peril for misfolding.
bythermodynamiccycles. Frustrationcalculationsincludeproteinconformationsand
protein-proteincontactsonly;i.e. metalsareimplicitindeterminingproteinconfor-
Materials and Methods mationbutmetal-proteininteractionsarenotexplicitlyincluded. Frustratedcontacts
AfulldescriptionofthemethodsisgivenintheSI.Missenseandtruncationmutants werecalculatedusingthefrustratometerserverhttp://frustratometer.tk.
ofSOD1,bothALS-associatedandrationallydesigned,wereequilibratedandusedfor
mechanicalforce,dynamicfluctuation,frustratometer,potentialenergy,andWHAM ACKNOWLEDGMENTS.WethankNeilCashman,WillGuest,AliMohazab,Eric
metalaffinityassays. Rationally-designedtruncationandmissensemutantsstudied Mills, Paul Whitford, and Stephen Toope for helpful and supportive discussions.
hereincludeC57S/C146S,C57S1-127,andWTsequences1-110and1-140.Frustra- We acknowledge funding from PrioNet Canada, NSERC funding to defray page
tionandmetal-bindingallosteryassaysusedeither22and24ALS-associatedmutants chargecosts,andweacknowledgecomputationalsupportfromtheWestGridhigh-
performancecomputingconsortium.
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7
SOD1 Exhibits Allosteric Frustration to Facilitate
Metal Binding Affinity (Supporting Information)
Atanu Das∗ and Steven S. Plotkin∗
∗DepartmentofPhysicsandAstronomy,UniversityofBritishColumbia,Vancouver,Canada
SI-text AtetheringpointwasplacedontheC atomatthecenter
α
Work-extension profiles provide a measure of local mechan- residue of a candidate epitope or anti-epitope (see Methods
ical stability, and have distance-dependent stiffness moduli. below), and another tethering point was placed on the Cα
We performed pulling simulations on residues taken from the atom closest to the center of mass of the protein (histidine
3 mid-points of the protein sequences of superoxide dismutase 46). A plot of the pulling force vs extension for a loading
1 predictedtobeeitherweak(referredtohereascandidateepi- rate of 2.5 10−3m/s is shown in Figure 1(A) inset (a) of
×
0 topes)orstrong(candidateanti-epitopes)thermodynamically the main text, for the residues centered at the midpoints of
2 (see Fig. S1 ). the first candidate epitopes/anti-epitope (see Methods). The
first (weak stability) epitope contains residues 5 15 so the
n −
C atom of residue 10 is taken as a tethering point. The
a α
first anti-epitope predicted to be thermo-mechanically stable
J
consists of residues 16 20 for which residue 17 is chosen as
6 representative (see Met−hods).
The forces fluctuate stochastically, however the work to
] pull to a distance x, being the integral of the force W(x) =
M
0xF(x0)dx0 results in a smooth curve (Fig. 1(A)). The work
B generallydoesnothaveaslopeofzeroasx 0onthelength
Rscale of 1˚A, because of an initial small-d→istance nonlinear
. ∼
o response corresponding to a steep rise in force within 0.1
i ˚A. That is, a force response function that appeared to∼con-
b
vergetoanon-zeroforceasx 0wouldcorrespondtoawork
- →
q function with linear behavior as x 0.
→
[ Weinterprettheinitialsteepriseinforceasbeingduethe
collective effect of numerous strong bonds which seek to pre-

1 servethenativestructure. Asdistanceisincreased,thenum-
v ber of restoring interactions, and/or the magnitude of these
2 interactions, is decreased. Thus the effective modulus of the
9 systemascalculatedby2W(x)/x2 isdistancedependent,and
9 softens with increasing distance (see Methods). A plot of the
0 effective modulus for short distances < 1˚A is given in inset
. (b) of Figure 1(A).
1
Previous measurements of force vs. extension or force vs.
0
time have shown that the force converges to non-zero values
3
atshortdistancesortimes. Thisisthecaseforligandbinding
1
(Anti)-Epitopesequence Centerresiduetaken Work(5˚A) simulations[2]wheretheforceconvergedto 50 100pNfor
v: 5 15 10 66.1 the shortest times, and in protein unfolding∼simu−lations [3,4]
i (16− 20) 17 91.5 where the force converged to 400 700 pN at the shortest
X 21−27 24 58.8 distances. These observations∼are c−onsistent with the steep
r (28−34) 31 66.3 initialrisesintheforceandcorrespondingdistance-dependent
a 35−41 38 67.1 moduli that we have resolved in the present study.
(42−49) 45 83.4 It was also observed that pulling on a given residue re-
50−59 54 85.0 sulted in large fluctuations in remote regions of the protein.
(60−85) 73 125.0 For example pulling on residue 10 disordered α-helix 2 con-
86−94 90 87.9 tainingresidues133-138,andpullingonresidue17disordered
(95 −105) 100 97.8 α-helix1containingresidues55-61(Figure1(A)insetfigures).
−
106 110 108 69.2
−
(111 131) 121 113.6
−
132 137 135 79.4
−
(138 142) 140 99.7
−
143 148 145 72.8
−
(149 153) 151 76.6
−
Fig. S1. RibbonrepresentationofmonomericSOD1structurewithCuandZn
metalsshownasorangeandgrayspheresrespectively. Candidatemisfolding-specific
epitopesaspredictedbythealgorithmofGuest,CashmanandPlotkin[1]arecolored
red,andtheirresiduenumbersareindicated. IntheTable-Epitopes,anti-epitopes,
pullingresidues,andresultingworkvaluesforCu,Zn(SS)WTSOD1.
1–16
Localmechanicalstrain,atleastbypullingaresidue,induces SOD1andvariousmodifiedSOD1proteins,includingmutant
a non-trivial stress profile that results in induced disorder at SOD1 (see Figure S13), de-metallated SOD1, and disulfide-
remote regions in the protein. Such induced disorder may reduced SOD1.
be a key ingredient in the propagation of misfolded SOD1
conformations in ALS, as well as other misfolding diseases
propagated by template directed misfolding.
The origin of large stiffness moduli at very short (sub-
Angstrom)distancesislikelyduetosidechaindocking.What
istheoriginofthishighlylocalmechanicalrigiditythatgives
rise to steep initial increases in force? From our pulling sim-
ulations, it was observed that the forces required to extend
well-structured parts of the protein were much larger than
the forces required for parts of the protein that were poorly
structured or disordered. For example, in the range of exten-
sionsfrom 0.1 0.2˚A,theforceonresidue17inβ-strand2
≈ −
of SOD1 was 83pN, and the force on residue 10 in turn 1
≈
was 67pN, while the force on residue 60 in the disordered
≈
Zn-bindingloopofZn-depletedSOD1was 52pN. Asanex-
≈
ampleofaresiduethatshouldlackanyside-chaindocking,the
forceonresidue133atthedisordered,non-nativeC-terminus
of the C-terminal truncation mutant E,E G127X is 41pN.
≈
Wethusinvestigatedthephenomenonofshort-rangemechan-
ical rigidity by calculating the components of the interaction
energy as a tethered residue was pulled.
Figure S2(a) depicts a schematic of the simulation proto-
col,andFigureS2(b)showstheresults. Fromthesepotential
energycalculations,weseethattheinitialsteepriseinforceis
duetothelossofshort-rangevanderWaalsandelectrostatic
interactions during the course of unfolding. The decrease in
interactions is mainly between side chains (SCs) rather than
backbone (Fig. S2(b) panel J): roughly 3/4 of the change Fig. S2. (Panel(a))Schematicrepresentationofthemethodofcalculationofin-
in energy arises from SC-SC interactions. This effect thus teractionenergytermsshowninpanel(b).Wehavecalculatedtheinteractionenergy
appears to be due to the many-body interactions stabilizing termsoftheatomsthatarewithin5˚A radiusfromtheCαatomofresidue10and
nativestructuresthroughSC-SCdocking,likelyformedinthe 70whenresidue10ispulled-thebluesphereindicatestheCαofresidue46which
latest stages of folding. isthecenteroftheprotein,thesmallredsphereindicatestheCα atomofresidue
10whichisthetetheringpoint,andsmallgreensphereindicatestheCα atomof
residue70. Thearrowsshowthedirectionofpulling. Thelarger,semi-transparent
Utility of making cumulative distribution.In the manuscript, redandgreensphereshaveradiiof5˚A,andenclosetheatomswithin5˚A from
wehaveanalysedthemechanicalprofilesmainlybyconstruct- therespectiveCα atomsoftheprotein. (Panel(b))Varioustermsinthepotential
energyasafunctionofdistance,whenresidue10ispulled. Theenergiesforresidue
ing cumulative distributions of the work profiles, rather than
70areinvestigatedasacontrol. Analyzingindividualtermsinthepotentialenergy
the more common probability distribution measurements.
elucidates the reason behind the initial sub-angstrom steep rise in the mechanical
The reason behind representing the work profiles in the form force. FiguresA,B,andCplottheriseinshort-rangevanderWaalsenergy,short-
ofcumulativedistributionsisthatthisrepresentationgivesthe rangecomponentoftheCoulombenergy,andtotalpotentialenergyasafunctionof
best way to differentiate between work profiles of two differ- distance. Theseshowaconcurrentriseonthelengthscaleofthesuddenriseinthe
ent variants of SOD1. The mechanical work profiles are too forceinFigure1(A)inset(a),maintext.Nosuchdistance-sensitivechangeisseenfor
noisy to compare their relative stability from the sequence- angleenergiesinresidue10(figureD),orforanyenergiesofacontrolresidue(70)far
resolved work profiles. Histograms of two work profiles also fromthepullingsite(figuresE,F,G).Decomposingthepotentialenergytermsinto
backbone-backbone(H),backbone-sidechain(I),andsidechain-sidechainterms(J)
do not clearly differentiate between two different variants of
showsthatBB-BBinteractionsplaynorole,andabout3/4ofthetotalcontribution
SOD1(seeFigureS3). However,thecumulativedistributions
arisesfromSC-SCinteractions,indicatingSCdockingplaysadominantroleinsmall
oftheworkprofilesmakethemcompletelydistinguishableand
RMSDmechanicalstability.
helptoeasilyidentifytherelativeorderofstabilityamongthe
variants.
The mechanical profiles of Cu,Zn (SS) WT and E,E (SH)
WTSOD1aredifferent, andareindependentofthestarting
PDBstructureusedtoconstructthem.Wecantakethevalue
of the work needed to pull a particular residue out to 5˚A as
a representation of the mechanical rigidity of that residue.
This value can then be scanned across the protein sequence
to obtain a mechanical profile or fingerprint for a particular
SOD1 variant. Obtaining a work value for a given residue
is computationally intensive however, so we take a subset of Fig. S3. PanelA:ProbabilitydistributionofworkvaluesofCu,Zn(SS)WTand
48 residues as a “sparse sampling” of the mechanical profile,
E,EG127X.PanelB:ProbabilitydistributionofworkvaluesofE,EG127XandE,E
inordertocomparemechanicalstabilitybetweenSOD1vari- (SH)WTSOD1.
ants. The specific residues chosen are given in the Methods
section. Mechanical profiles may be compared between WT
2
We first ensured that the mechanical profile obtained for ferent; in particular the combination of metal depletion and
a given SOD1 variant was independent of the initial condi- disulfide reduction reduces the overall mechanical stability of
tionsusedinthesimulations,inparticularforSOD1variants several regions of SOD1. We analyze this in more detail in
that currently have no PDB structure such as E,E (SH) WT the manuscript.
SOD1. Equilibrated structures were generated as described
in the Methods section below, and used as initial conditions An implicit solvent model is sufficiently accurate to obtain
for pulling simulations to generate mechanical profiles. Inset the mechanical profile.To test the accuracy of the general-
AofFigureS4showsaplotofthemechanicalscanforCu,Zn ized Born surface area (GBSA) implicit solvent model in de-
(SS) WT SOD1, and the main panel of Figure S4 shows the termining the mechanical profile, we have performed pulling
mechanical scan for E,E (SH) WT SOD1. simulationsonSOD1inexplicitsolvent,wherewatersinteract
through the SPC force field.
Fig. S4. Themechanicalworkprofileisindependentofthecrystal/NMRstructure
usedtogeneratetheinitialensembleinapullingsimulation. Themainpanelshows Fig. S5. Themainpanelshowsthattheworkprofilesagreebetweenimplicitand
themechanicalprofilethatresultsfrom2differentconstructionsoftheinitialensem-
explicitsolventsimulations. (InsetA)Scatterplotoftherootmeansquarefluctu-
bleofE,E(SH)WTSOD1. Inoneconstructionwestartfromthesolutionstructure
ation(RMSF)forheavyatomsintheproteininbothimplicitandexplicitsolvents;
ofE,E(SS)WTSOD1,reducethedisulfidebond,andequilibratethesystembefore r = 0.802, Pr = 1.2e-19. Greensolidlineisthebestfitlinewithaslopeof
startingsimulations. Inanotherconstructionwestartfromthecrystalstructureof 0.83. Bluedashedlineisthelineofslopeunity,withy=x. Reddashedlineisthe
Cu,Zn(SS)WTSOD1,removethemetalsandreducetheSS-bond,andthenequili-
median-fitlinewithanequalnumberofdatapointsaboveandbelowit,andhasa
brate.(InsetA)Themechanicalprofileobtainedfrom2differentcrystalstructuresof sloeof1.08. (InsetB)DifferenceinthedistributionsofRMSFbetweentheimplicit
Cu,Zn(SS)WTSOD1(1HL5and2C9V),equilibratedfor20nsandthensimulated
andexplicitsolventmodels. ThisshowsanenhancementofsmallRMSFvaluesand
asdescribedintheMethods. Bothmodelsgivethesamemechanicalprofiletowithin
suppressionoflargeRMSFvaluesfortheimplicitsolventmodel. (InsetC)Scatter
about2.7kJ/mol. (InsetB)WorkprofilesforCu,Zn(SS)WTandE,E(SH)WT plotofworkvaluesobtainedfromimplicitsolventvsexplicitsolventmodels;these
SOD1areseentobesignificantlydifferent,withE,E(SH)WTSOD1generallyhaving modelscorrelatewithr=0.991.
weakenedmechanicalsusceptibilityinvariousregions,butoccasionallyshowingstiffer
responseinsomelocations.
Inset A of Figure S5 plots the root mean squared fluc-
tuations of heavy atoms, obtained from 20ns simulations for
In each case, the protein was constructed from two dif-
both implicit and explicit solvent models. The two systems
ferent initial models of the protein structure, using two dif-
havecomparablethermalfluctuations,thoughthebestfitline
ferent PDB structures as starting points. We found that the
(green line in inset A of Fig. S5) has a slope less than unity,
mechanical profile of a particular SOD1 variant was nearly
indicating somewhat larger fluctuations in the explicit sol-
independent of how that variant was constructed, reinforc-
ventmodel. Interestinglyhowever,thenumberofdatapoints
ing the reliability of the mechanical scan. In inset A of Fig-
aboveandbelowthebestfitlineare624and455respectively,
ure S4, mechanical work profiles correspond to crystal struc-
indicating that there are non-Gaussian fluctuations and out-
tures1HL5[5]and2C9V[6]ofCu,Zn(SS)WTSOD1. Inthe
liers between the two models.
mainpanelofFigureS4,mechanicalworkprofilescorrespond
This skew in the data may be investigated through the
to E,E (SH) WT SOD1, obtained by modifying either the
distributions of RMSF, for both the implicit and explicit sol-
Cu,Zn (SS) WT crystal structure 1HL5, or the NMR struc-
ventmodels. Thesedistributionsaredifferent. Thedifference
ture 1RK7 of E,E (SS) WT SOD1 [7]. We note that these
in the distributions, P P , as a function of RMSF, is
PDB structures are equilibrated for 20 ns before any simula- Imp− Exp
plotted in inset B of Figure S5. This shows that the implicit
tionmeasurementsaretaken. ThemeanerrorbetweenSOD1
solvent model overestimates small fluctuations, and underes-
variants, as determined by the z-test described in the Meth-
timateslargefluctuations,ascomparedtotheexplicitsolvent
ods section, is 2.7 kJ/mol. On the other hand, the standard
model.
deviation of all 48 of the work values themselves for a given
Wecaninvestigatewhatslopelinewouldgiveequalnum-
variant(e.g. 1HL5)is18.3kJ/mol,whichisafactorofabout
bersofdatapointsaboveandbelowit,asanadditionalmea-
6.8 larger than the error. The mean error between variants
sure of the validity of the implicit solvent model. By this
usedtoconstructthesameinitialconditionindicatesthelevel
measure the implicit solvent model agrees much better with
ofaccuracyofthesimulations,sothatdifferencesinworkpro-
theexplicitsolventdata: themedianfitlinewithequalnum-
files (e.g. between mutant and WT) must generally be larger
bers of data above and below it has a slope of nearly unity
than this mean error to be significant. Inset B to Figure S4
(slope=1.08).
plots the mechanical profiles of Cu,Zn (SS) WT SOD1 and
The imperfect correlation between implicit and explicit
E,E (SH) WT SOD1. They are seen to be significantly dif-
solventfluctuationspromptsacomparisonoftheworkvalues
3