Download Sequence Entropy and the Absolute Rate of Amino Acid Substitutions

bioRxiv preprint first posted online May. 31, 2016; doi: http://dx.doi.org/10.1101/056325. The copyright holder for this preprint (which was not
peer-reviewed) is the author/funder. It is made available under a CC-BY-NC-ND 4.0 International license.
SequenceEntropyandtheAbsoluteRateofAminoAcidSubstitutions
RichardA.Goldstein1andDavidD.Pollock2
1
DivisionofInfection&Immunity,UniversityCollegeLondon,London,WC1E6BT,UK.
DepartmentofBiochemistryandMolecularGenetics,UniversityofColoradoSchoolofMedicine,Aurora,CO
80045USA.
2
Theevolutionofmodelproteinsunderselectionforthermodynamicstabilitysuggestsparallels
between evolutionary behavior and chemical reaction kinetics. We developed a statistical
mechanicstheoryofproteinevolutionbydividingaminoacidinteractionsintosite-specificand
‘bath’ components, and show that substitutions between two amino acids occur when their
site-specific contributions to stability are nearly identical. Fluctuating epistatic interactions
drive stabilities into and out of these regions of near neutrality, with the time spent in the
neutral region and thus the rate of substitution governed by physicochemical similarities
between the amino acids. We derive a theoretical framework for how site-specific stabilities
are determined, and demonstrate that substitution rates and the magnitude of the
evolutionaryStokesshiftcanbepredictedfrombiophysicsandtheeffectofsequenceentropy
alone.Populationgeneticsunderlaysouranalysis,butpopulationsizedoesnotdeterminethe
absoluterateofaminoacidsubstitutions.
Introduction
Modelingtherateatwhichproteinsequenceschangeiscentraltounderstandinghowproteins
adapt to their structural, functional, and thermodynamic requirements. It is also key to
decipheringthepatternsofconservationandvariationthatreflectevolutionaryprocessesand
the properties of specific proteins. An important step was Kimura’s calculation of the
probabilityoffixationofasinglemutationgivenconstantrelativefitnessesofthewildtypeand
mutant (1-3). Fixation probabilities alone, however, do not address how or why fitness
differencescometobe,andthereforecannotexplainobservedsubstitutionrates.Empirically
derived substitution rates have long been obtained by analyzing differences between related
protein sequences (4-6), providing estimates of average rates but not explaining them.
Althoughthisapproachhasbeenextremelyuseful,itssuccesseswereachievedbyignoringthe
underlyingbiophysics,molecularbiology,andpopulationdynamics,aswellashowtheserates
varyamongstsitesandtime.
Inrecentyears,thenumberofproteinsequences,computationalspeeds,andourknowledge
ofproteinbiophysicshaveincreasedsubstantially.Thishasledtoanexpansioninthepotential
scope of evolutionary analyzes and a growing awareness of the limitations of standard
empirical models. Proteins are under selection for traits – function, foldability, stability,
solubility – that depend on a complex network of interacting amino acids. These forms of
selectioninduceepistaticinteractions(orcoevolution)amongsitesintheprotein,resultingin
substantial effects on the evolutionary process (7-12). Models that ignore this epistasis can
seriously compromise evolutionary analyzes by misrepresenting the frequency and time
bioRxiv preprint first posted online May. 31, 2016; doi: http://dx.doi.org/10.1101/056325. The copyright holder for this preprint (which was not
peer-reviewed) is the author/funder. It is made available under a CC-BY-NC-ND 4.0 International license.
dependence of convergence and homoplasy (13). Empirical models can be modified to allow
thesubstitutionprocesstovaryamongsites(14,15)andovertime(6,16-20),butinformation
available from sequences to obtain accurate site- and time-dependent substitution rates is
fundamentallylimited.Effortstouseproteinstructuretopredictsubstitutionrates(21,22)are
compromised by our lack of understanding of the relationship between protein sequence,
proteinproperties,andorganismalfitness,andourinabilitytopredicttheeffectofmutations
asdifferencesaccumulate.
Thedevelopmentofmoreaccurateandpowerfulmodelsofproteinevolutiondependsonour
abilitytorepresenttheprocessofmolecularevolutionatamechanisticlevel,ideallyenabling
ustocalculatesubstitutionratesbasedontheprotein’ssequenceandbiophysicalproperties.
Ourpurposehereistodevelopfromfirstprinciplesatheoryofhowproteinsevolveandhow
substitution rates are determined. We approach the problem by building a conceptual
framework to translate protein evolution into the formalisms of statistical mechanics,
demonstrating the primacy of sequence entropy. Using evolutionary simulations of model
proteins, with fitness determined by thermodynamic stability, we demonstrate that
substitutionratesdependonhowaminoacidenergycontributionsfluctuateastherestofthe
protein sequence evolves. We show that substitution rates can be predicted based on 1) the
stability distributions at a site in the absence of selection on that site; and 2) the relative
numbersofsequenceswithdifferentproteinstabilities;nootheradjustableparameters,such
asexpectedpopulationsize,areneeded.Thisformsamechanisticframeworkforconstructing
improvedmodelsofaminoacidsubstitutionrates.
Results
Site-specificstabilitiesandrelativesubstitutionrates
To develop a mechanical theory of the evolutionary process, we consider the relationship
between protein stability and substitution rates at a site. The stability Ξ(𝐗) of a protein
sequence 𝐗 = {𝑥! , 𝑥! , 𝑥! … 𝑥! } was defined as the negative of the free energy difference
between the sequence in the native structure and in the ensemble of possible alternative
structures,sothatmorepositivevaluesindicategreaterstability.TheMalthusianfitness𝑚(𝐗)
wassetequaltothefractionofsuchsequencesthatwouldbefoldedinapre-specifiednative
conformation at thermodynamic equilibrium (Equation (2, Methods) (11, 23, 24). Thus,
increasesinstabilityleadtoincreasesinfitness.
Tounderstandhowtherestoftheproteininfluencesthesubstitutionrateatindividualsites,
wefocusourattentiononanaminoacidαataspecificfocalsitek,andpartitionthestability
into Ξ(𝐗) = ξ!,! (𝐗 ∌ ! ) + ξ!,!"#$ (𝐗 ∌ ! ). The first term, ξ!,! (𝐗 ∌ ! ), is the site-specific stability
contribution due to interactions (in both the folded and unfolded states) between α at site k
and the amino acids at all other sites excluding k. The second term, ξ!,!"#$ (𝐗 ∌ ! ), is the
‘background’contributionresultingfrominteractionsamongaminoacidsatsitesexcludingthe
focal site. Because only a small fraction of contacts involve site k, we assume that the site-
bioRxiv preprint first posted online May. 31, 2016; doi: http://dx.doi.org/10.1101/056325. The copyright holder for this preprint (which was not
peer-reviewed) is the author/funder. It is made available under a CC-BY-NC-ND 4.0 International license.
specific stability contribution is small relative to the background contribution, so that this
secondtermfulfillstheroleofthe‘thermalbath’instatisticalphysics.
This statistical mechanics formalism can now be applied to modeling the amino acid
substitutionrate.Consider𝑄!,!→! 𝐗 ∌ ! ,theinstantaneousrateofanαtoβsubstitutionatsite
k,equaltothemutationratetimesthefixationprobability.Thefixationprobabilitydependson
the difference in fitnesses ∆𝑚!,!→! , which is a function of the initial stability Ξ(𝐗) and the
stabilityofthemutantΞ 𝐗′ = Ξ 𝐗 + ΔΞ!,!→! (𝐗 ∌ ! ).Wecansimplifythesituationbynoting
that sequences from real proteins, as well as proteins from evolutionary simulations under
selection for thermostability, tend to have a narrow range of stability values(23, 25-28). This
stability range occurs where the decreasing effectiveness of selection for greater stability is
balanced by destabilizing mutations fixed by genetic drift. The precise value depends on a
varietyoffactorssuchastemperature,effectivepopulationsize,sequencelengthandprotein
function. As long as these factors are approximately constant, we can assume that a given
protein will evolve to the mean of this narrow range Ξ(𝐗) = Ξ. If Ξ is a known constant,
calculating the fixation probability requires only the difference in site-specific stabilities
ΔΞ!,!→! (𝐗 ∌ ! ) = ξ!,! (𝐗 ∌ ! ) − ξ!,! (𝐗 ∌ ! ); the bath component, ξ!,!"#$ (𝐗 ∌ ! ) is independent of
theaminoacidatfocalsitek,andisthereforeunchangedbythesubstitution.
From this perspective, the key distribution determining the substitution rate from α to β is
ρ!,! (ξ!,! , ξ!,! ),thejointprobabilitydensityofξ!,! (𝐗 ∌ ! )andξ!,! (𝐗 ∌ ! )giventhataminoacidα
is resident at site k, integrating over the distributions of amino acids at other locations. The
distributiondependsonwhichaminoacidoccupiespositionkbecausethataminoacidwillhave
affected the evolution in the rest of the protein; in this case, ξ!,! is the local stability
contributionthatwouldresultifβweretoreplaceαatthatsitewithnootherchangesinthe
sequence. For simplicity, we will consider that the rest of the protein sequence has evolved
sufficientlythatρ!,! ξ!,! , ξ!,! hasreachedastationarydistribution;theeffectofabreakdown
inthisassumptionwillbeconsideredbelow.
To help visualize these distributions, and evaluate our theoretical results, we modeled the
evolution of real proteins using the simulated evolution of a 300-residue protein under
selectionforthermodynamicstability.Thismodelisnotmeanttomakequantitativepredictions
in particular cases. Instead, it is meant to predict general characteristics of evolutionary
behaviorforproteinsthatrequirethenativeconfirmationtocarryoutsomecriticalbiological
function, and has demonstrated its ability to reproduce fundamental aspects of the
evolutionary process (11, 23, 24). By using a simple pair-contact model of protein
thermodynamics, we were able to perform replicate simulations over long periods of
evolutionary time, corresponding to approximately 5 billion years given typical substitution
rates.
Wegroupedsiteswithsimilarsubstitutionpatternsintofourdifferentsiteclasses,whereclass
1 is the most exposed and 4 is the most buried. Figures 1A-D shows the observed joint
probabilitydistributionsofthesesiteclassesforglutamicacidandlysine,aswellasthestability
L
L
s pos ed on ne May 31 2016 do h p dx do o g 10 1101 056325 The copy gh ho de o h s p ep n wh ch was no
pee ev ewed s he au ho unde
s made ava ab e unde a CC BY NC ND 4 0 n e na ona cense
L
L
b oRx v p ep n
●●
● ●
●
5
●
●
●
ξ(Glu)
LT0
L
●
● ●
●
●
● ● ●●●●●
●
●
●●
●
●●
● ●●
● ●●
●
● ● ●
●●
●● ●
● ●●
● ●●● ●
●
●●
●● ●●● ●●
●● ●
●
●
● ●
● ●
● ●●
●
●●●●● ●
●
●●●
●●
●
●
●
●
●●
●● ● ●●
●
●●
●
●
●●
● ● ●
●
●
●
●
●
●●●
●
●
●
●
●
●●●
●
●
●●
●
●
●
● ●●
●● ●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●●●
●
●●
●●
●●
●
●●
●
●
●
●
●●
●●
●
●
● ●●
●
●
●
●●●
●●●
●●
●●●
●
●
●
●
●
●
●
●● ●
●
●●
●
●
●
●●
●
●
●
●●
●
●●
●●●
●
● ●● ●
●●● ●
● ●
●●
●
●
●●
●
●●
●
●●
●●
●
●
●
●
●
●● ●●
●
●
●
●
●●
●
●
● ● ●●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●●● ●●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●● ●
●●
●
●
●
●
●
●
● ●●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●● ●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●●
●●
●
●●
●
●
●●●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●● ●
●
●
●
●
●
●
●
●
●
●
●
●
● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●● ● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
● ●●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●●●
●
●
●
●
●
●
● ●●●●●
●
●
●
●
● ●●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●●
●
●●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●● ●
●
●
●
●
●
●
●
●
●●
●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
● ●●
●
●
●
●
●●
●
●
●
●
●
●● ●●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
● ●●
●●
●
●● ●
●
●
●
●●
●●
●
●● ●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●● ●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●●
●
●
●●●
●
●
●
●
●
●
●
●
●●●
●
● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
● ●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
● ●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●● ●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
● ●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●●
●
●
●●
●
●
● ●●
●
●
●
●
●●
● ●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
● ●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
● ●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●●
●
●
●
●
●●●
●
●
●
●●
●
●
●
●●
●
●
●● ●
●
●
●
●
●●
●
●
●
●
●●
●
●
●●●
●
● ●●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
● ●●
●
●
●
● ●
●●●
●
●
●
●
●
●
●
●
●
●
●●●● ●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
● ●
●●
●●
●
● ●●
●●
●●
●
●●
●
●●●
● ●
●●● ●
●●
●
●●
●●
●●
● ●
●● ●●●
●
● ●●
● ●●
●
●● ●
● ●● ●●●●
●●● ●●● ●
●●
●●● ●●●
●
●
●
● ●
●
● ●● ●●●
●
●
●
●
●
●
●
●
●●
Ca
2
C ass 4
●
●
●
●
●
●
●●● ●
●●
●●●
●
●
●
● ●●
●
● ●● ●
●
●
●
● ● ● ● ● ●●
●
●● ●
● ●●
●●
●
●
●●
●
●
●
● ●●● ● ●
●
● ●●
●
●●
●
●● ● ● ● ●
● ● ●●● ● ● ● ●
● ●● ●●●●●
●●
●●
●●
●
●
● ●●
●
●●●
●●●●
●
●●●
●
●
●●
● ●●
●●●● ●
●
●●
● ●
●
●● ● ● ●●
●
●●●●
● ●●
●●
●●
●
●
●
●
●●●
●● ●●●
●
●●
●
●●
●●●
●
●
●
●●●
●
●
●●
●●
●
●
●●
●●●
●
● ●●●●
●●
●
●●
●● ●
●
●
●● ●●●●●
●
●
● ●
●
●
●
●●●
●
●
●●
●
●
●
●●● ●●
●
●
●
●
●
●●
●●●
●
●
●
●
●●● ● ●
●
●
●
●●● ●
●
●
●
●●
●
●●
●●
●
●●●
●
●●
●
●
● ●● ●●
●
●
●
●●
●
●
●● ● ●●
●
●●●
●●
●
●
●
●●
●
●
●
●
●
●
●
●●
●●●●
●● ●
●
●
●
● ● ● ●●
●
●
●●
●
● ●●●
●
●
●●
●
●
●●
●
●
●
●●●
●
●
●
●●●
●
●
●
●
●●
●●
●
●●
●
● ●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●●
●
●
●●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●●
●●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
● ●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●● ●●
●
●●
●
●●
●
●
●● ●
●
●
●
●
●●
●
●
●
●●
●
●
●
●●●●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●●●
● ●●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●●
●
●
●
●● ●
●
●
●
●●
●●●
●
●
●
●
●
●
●
●
●●
●
●●●
●
● ●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
● ●●●
●
●
●●
●●●
●●●
●●
●
●
●
●●●
●●
●
●
●●
●
●●
●●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●●●
●
●
●
●●
●●●
●●
●
●
●
●
●
●●
●
●
●
●
●●
●
●● ● ●
●
●
●
●●
●
●● ●●
●
●
●
●
●
●
●●● ●●
●
●●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●● ●● ●
●●
●
●
●
●● ●
●
●
●●
●
●●
●
●●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●● ●
●
●
●
● ●
●●
●
●
●
●
●
●
●●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●●
● ●●
●
●
●
●
●
●
●●●
●●●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●●
●
●●
●
●
●● ●
●
●
●
●●
●●
●●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●●
●●
●
●
●
●
●
●
●●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●●
●
●
●
●
●
● ●●●
●
●●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●●●
●
●●
●
●
●●
●
●●
●
●
●
●●●●
●
●
● ●
●
●
●
●
●
●
●
●●●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●●●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●● ●●●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●●
●●●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●● ●● ●
●●
●
●
●
●●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●● ●
●
●
●
●●
●
●●
●●
●
●
●●
●
●
●
●
●
●
●
●●●
●●
●
●
●●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●●
● ●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
● ●
●
●
●
●
●●
●
●
●
●
●
●
●
●● ●
●
●
●
●
●●
●
●
●
●●●
●
●
●●
●
●●
●●
●●
●●
●●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●●
●
●●●
●
●●
●● ●
●
●●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
● ●●
●
●
●
●
●●●●
●
●
●
●
●
●
●● ●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
● ●
●
●
●
●
●
●●
●
●
●●●●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●●
●
●
●
●●●
●
●●
●
●
●
●● ●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
● ●
●
●●
●
●●
●●
●●
●
●
●
●
●
●
●
●
●●
●
●●
●
●●
●
●
●
●●
●
●
●●●
●
●
●
●
●
●●●
●
●
● ●
●●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●● ● ●
●●
●
●●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●●
●●
●
●
●●
●
●
●
●
●
●●
●
●
●●
●●●
●
●
●
●
●
●●●
● ●
●●
●
●
●
●
●
●
●
●●●●
●
●
●
●
● ● ●● ●●
●
●●●
●
●●●
●
●●
●
●
●
●
●●
●
●
●
● ●
●●
●
●●●
●
●●●
●
●
● ●●●
●
●
●
●
●● ● ●
●●
●
●
●
●
● ●● ●
●●
● ●●
●
●●
●● ● ●●●
●
●
●●●
●●●
●
●●
●●
●
● ●
●●
●●
● ●●●
●●● ●
●
●
● ●●
●
● ●●
● ●
●
●
●●● ● ●
●
●
●●
●●
● ●
●●
●●●
●● ●
●
●
●
Leu
●
●
−5
C ass 3
●
● ●
●
●
0
LG u
L
●
●
GGu u
C
aa
21
DC
Ca
a 3
3
C
●
●
●
●
C ass 2
Class
CCa
aa 22
12
CC
LT
LLeu
10
●
LG u
ξL(Glu)
5
C ass 1
CClass
BCaaa 1211
C
−5
10
GGu u
Ca 1
AC
Caa 00
−10
10
Se
A
Gu g
u
G
●
C ass 3
●
● ●
●
●
●●
●
●
●
●
●
●
●●● ●
●●
●●●
●
●
●
● ●●
●
● ●● ●
●
●
●
● ● ● ● ● ●●
●
●● ●
● ●●
●●
●
●
●●
●
●
●
● ●●● ● ●
●
● ●●
●
●●
●
●● ● ● ● ●
● ● ●●● ● ● ● ●
● ●● ●●●●●
●●
●●
●●
●
●
● ●●
●
●●●
●●●●
●
●●●
●
●
●●
● ●●
●●●● ●
●
●●
● ●
●
●● ● ● ●●
●
●●●●
● ●●
●●
●●
●
●
●
●
●●●
●● ●●●
●
●●
●
●●
●●●
●
●
●
●●●
●
●
●●
●●
●
●
●●
●●●
●
● ●●●●
●●
●
●●
●● ●
●
●
●● ●●●●●
●
●
● ●
●
●
●
●●●
●
●
●●
●
●
●
●●● ●●
●
●
●
●
●●
●●●
●
●
●
●●●
●●● ● ●
●
●
●
●●● ●
●
●
●
●
●●
●●
●
●●●
●
●●
●
●
● ●● ●●
●
●
●
●
●
●● ● ●●
●
●●●
●●
●
●
●
●●
●●●
●
●
●
●
●
●
●●
●●●●
●● ●
●
●
●
● ● ● ●●
●
●
●●
●
● ●●●
●
●
●●
●
●
●●
●
●
●
●●●
●
●
●
●●●
●
●
●
●
●●
●●
●
●●
●
● ●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●●
●
●
●●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●●
●●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
● ●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●● ●●
●
●●
●
●●
●
●
●● ●
●
●
●
●
●●
●
●
●
●●
●
●
●
●●●●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●●●
●●●●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●●
●
●
●
●● ●
●
●
●
●●
●●●
●
●
●
●
●
●
●
●
●●
●
●●●
●
● ●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
● ●●●
●
●
●●
●●●
●●●
●●
●
●
●
●●●
●●
●
●
●●
●
●●
●●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●●●
●
●
●
●
●●
●●●
●●
●
●
●
●
●
●●
●
●
●
●
●●
●
●●●● ●● ●
●
●
●
●
●●
●
●● ●●
●
●
●
●
●
●
●●● ●●
●
●●
●
●
●
●
●●
●
●
●
●
●
● ●
●●
●●
●●
●
●
●
●●
●● ●
●
● ●●●
●
●
●● ●
●
●●
●
●
●●●
●●
●
●
●●
● ●
●
●
●
●●
●●
●
●
●
●
●
●
●
●●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●●
●●
●
●
●
●
●
●●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●● ●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
● ●●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●● ● ●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●● ●●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●● ●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
● ●●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
● ●●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●●●●
●●
●● ●
●●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●●
●
●
●
●
●●●
●
●●
●● ●
●
●
●
●
●
●●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
● ●●
●
●
●
●
●●●●
●
●
●
●
●
●
●● ●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
● ●
●
●
●
●
●
●●
●
●
●●●●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●●●
●
●●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
● ●
●
●
●
●
●
●
●●
●
●
●●
●●
●
●
●
●●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●●
●●
●●●
●●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●●
●
●
●
●●●
●
●
●
●
●
●●●
●
●
● ●
●●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●● ● ●
●●
●
●●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●●
●●
●
●
●●
●
●
●
●
●
●●
●
●
●●
●●●
●
●
●
●
●
●●●
● ●
●●
●
●
●
●
●
●
●●●●
●●
●●
●
● ● ●
●
●●●●●
●●●
●●
●
●
●
●
●
●
●
●
●
●
●
● ●● ●●
●●
●
●●●
●●●
●
●
● ●●
●
●
●
●
●● ● ●
●●
●
●
●
●
● ●● ●
●●
● ●●
●
●●
●● ● ●●●
●
●
●●●
●●●
●
●●
●●
●
● ●
●●
●●
● ●●●
●●● ●
●
●
● ●●
●
● ●●
● ●
●
●
●●● ● ●
●
●
●●
●●
● ●
●●
●●●
●● ●
●
●
●
●
●
●
●
●
● ●●
●
●●
●
● ●
●
●
●●●
● ●●
●
● ●
●
●●
●
● ●● ●●●
●
●●●● ●
●
● ●
●
●
●
●
●●
●
●
●
●
● ●●● ●
●●●
●●
●●
●
●● ● ● ●
● ● ● ● ●●
●●● ●
●
● ●●
●
● ●
●● ●
●●
●●●●●
●
●
●●
●
●
●●
●
● ●●
●
●
●●●
●●
●
●●
●
●● ●
●
●●
●
●
●●●●●●
●
●
● ●● ●●●●
●
●
●●
●
●●
●●●
●●
● ●● ●●●●
●
●
● ●
●
●
●
●
●
●
●●
● ●●
●
●
●
●●
●
●●
●●
●●
●● ● ●
●
● ●● ● ●
●●
●●
●
● ●
●●
●●
●
●
●
●
●
●●
●
●
● ●●●●
●
●●
●
●
●●
●
●●
●●●●
●
●
●●
●●●● ●●
●
●●
●●
●●
●
●●
●
●●
●
●●
●
●
●
●
●
●
●●
●●●●●
●
●
●●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●●
●●
●●●
●
●
●
●●●●
●
●
●
●
●
●
●
●●
●●●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●●
●●
●
●●
●
●
●
●
●●●
●
●● ●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
● ●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●●●
●
●
●
●
●
●●●
●
● ● ●● ●●
●●
●●
●
●
●●
●
●
●●●
●
●
●●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●●●
●
●●
●●●
●
●
●
●
●
●
●
●
●
●●
●
●
●● ● ●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
● ●●
●
●●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●●
●
●●
●
●
●
●●
●
●
● ●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●●●
●
●
●
●
●
●●●●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●●
●
●●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ● ●●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●●●●●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●● ●
●
●●
●
●
●
●
●
●
●
●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●● ●●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●● ● ● ●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
● ●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
● ●● ● ●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●●●
●
● ●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●●
●
●
●
●
●
●
●
●
● ●● ● ●● ● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●●
●
●
● ●●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ● ●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
● ●●●●
●
●
●
●
●●●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●● ●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●● ●●
●
●
●●●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
● ●● ●● ●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●●
●
●●
●
●●
●
●
●
●●
●
● ●●●●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●●
●●
●
●
●
●●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ● ●
●
●●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●●
●
●
●●
●●●
●
●
●●
●
●
●●●
●
●●
●
●
●
●
●
●
●
●
●●●
●
●
●
●●
●●
●
●
●
●
●● ●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●●●●
●
●
●
●
●●●● ●● ●
●●
●
● ●● ●●● ●
●
●●
●●
●●
●
●
●
●
●●●
●●
●●
●●
●●
●
●
●
●●
●
●●
●● ●
●
●
●
●
●●●
●
●
●
●
●●
●●
●
●●
●
●
●
●
●
●
●
●●
●●
●●
●●●
●
●● ●●● ●●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
● ●●
●
●
●●
●
●●
●
●
●
●
●●
●●
●
●
●●●●
●
●
●
●
●
●
●
●
●
●
●●●● ●
●
●
●
●
●
●
●
●
●
●● ●
●
●
●
●
●
●
●
●●●
●●
●
●●●
●
●
●
●
● ●●●
●
●
●
●●
●
●
●
●
●●
● ●
●
●
●
●
●●
●
● ●
●●●●
●●
● ●●
●●●
●●
●●●
●●
● ● ●● ●●●● ●
●
● ●●●
●●
●
●
●
●●● ●
●
● ●
●
●
●
●
●●
●
●●
● ●●
●
●●●●
● ●●●●
●
●
●
●
●
● ● ● ●●● ●●●
●
●
●
●●●●●●● ●
● ● ● ● ●● ●
● ●●
●
●
●
●
●● ●
●
●
●
●
●
●●●●●
● ●●
●
● ● ●
● ●
●●
●
●● ● ●
● ●●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●●
0
Class
Ca 2
4
●
●
●
● ●
●
●
10
C ass 3
●
●
Ag
Class
HClass
C
41
Caa 2
3
5
●
●
●
●
●
●●
● ●
●●●
●
●● ●
●●
●
● ●
●●●
● ●
● ●
●
●
● ● ● ●
●●●
●
●●
●● ●●●
●
● ●●
● ●●
●
●
●●●●
●
●● ●
●●
●
●●
●● ●●
●●
●●● ●●
●●
●
●●
●
● ●●● ●
●●
●●●
●
●
●●● ● ●●
●
● ●●●●
●
●
●
●●●
● ●●
●●
●● ● ●●
●
●●●●●
●
●
●
● ●
●● ●
●● ●
● ●
● ●●●●
●
●●●●
● ●●● ●
●●●
●
●●
● ●
● ●● ●
●●
● ●●●●●
●
●
●●
●
●●
●
●
●● ●
●
●●
●●●●●
●●● ●●
●
●● ●
●
●● ●
●
●
● ● ●●●
●
●
●
●
●
●● ●
●
●
●
●●
●
● ●●● ●●●●●
●
●● ●● ●●
●
●
●
●
●
● ●●
● ●
●
●●
●●
●
●
●●
●●
●●
●
●
●●
●●●
●●
●
●●
●
●●
●
●
●●● ●
●
●
●
●●
●●●
● ● ●●
●
●
●●
●
●
●
●●
●●
●
●●●●
●
●
●
●
●
●● ● ●
●
●
●
●●
●
●●
●●●●
●●●
●
● ●●
●●
●
●
● ●
●●●● ●
●●●
●●
●
●
● ●
●
●●
●
●
●
●
●
●
●●
● ●
●
●
●
● ●
●●
●●
●●●
●
●
●
●●●●
●●
●●●●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●● ●●
●
●
●
●
●
● ●●●●
●●
●● ●
●
●
●●
●
●
●
●
●●●
●●●●●
●
●●
●● ●
●
●
● ●
●
●
●
●
●
●
●
●●
●
● ●●
●
●
●
●
●●
●●
●
●
●
●● ● ●● ●
●
●●
●
●
●
●
●
●●●
●●
●
●●
●
●
●
●
● ●
●
●
● ●
●
●
●●
●
●●●●
●●
●
●●●●
●
●
●
● ●● ●●●●● ●●●●●●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●●●●● ● ● ●
●●
●
●
●
● ●
●
●●
●●
●
●●
●
●
●●
●
●●
●●● ● ●● ●● ● ●
●●●
●●
●
● ●
●
●
●
●
●●●● ●
●
●
●●
●
●
●
●
●
●
●●
●
●●
●
●
●●
●
●●
● ●
●
●●
●
●
●
●●
●
●
●●
●●
●
●
●
●
● ● ●●
●
●
●
●
●
●●●
●●
●
●●●
●●
●●
●
●
●●
●●●
●
●●●
●●●●●●●
●
●●
●
●
●
●
●●
●
●
● ●●●
●
● ● ● ● ●●●
●●●●●
●
●
●
●
●
●●
●●●●●● ●
●
●
●
● ●●●
●●
●
●
●
●●
●
●●
●
●●●●●
●
●
●
●
● ● ● ●●●
●
●
●
●
●
●
●
● ●
●●●
●
●●
●
●●●
●
●●
●●
●●
●
●●
●●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
● ●●●
●●●●
●
●
●●●
●
●●
●
●
●●
●
● ● ●●
● ● ●
●
●
●
●
●
●
●
●●
●
●●
●●
●
●
●
●
●
●
●● ●
●
●
●●●
●
●
●
●
●
●
●
●●
●
●
●●●
●●● ●●●
●●
●
● ●
●●●● ●●
●
●●● ●
●●
●
●●
●●
●
●
●●●●
●
● ●●
●●
●
●
●
●●
●
●●●
● ●● ● ●● ● ● ●●
●
●●●
●
●
●●●
●
●
●●
●●●●
●●
●
●●
● ●
●
●
●
●●
●
●
●
●
●
●●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●●● ●●
●
●
●●● ●●
●
●
●●
●
●
●
●●
●
●
●●●
● ● ●
●
●●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●●
●
●
●
●●●
●
●
●
●
●
●
●●
●
● ●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
● ●●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
● ●●●
●
●
●
●
●●●
●
●
●
●
●●
●
●
●●
● ● ●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●●
●
● ●●
●
●●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
● ●
●●●
●
●
●
●●●
●
●
●
● ●●
●
●
●
●
●
●
●
●
●●
●
● ●
●●●
●
●
●
●
●●
●
●
●
●
●●
●
●
● ● ●●
●
●
●●
●●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●●
●●●
●
●●
●
●
●
●
●
●
●
●●
●●●
●
●
●
●
●●●●●●
●●
●●
●
●●
●
●●●
●
●
●
●
●
●
●
●
●●●●
●
●
●●●
●
●●
●
●●
●●
●● ●
●
●●
●
●●
●
●
●
●
●
●
●●●
●
●
●
●●
●
●●
● ● ● ●●
●
●
●
●●
●●
●
●
●●
●●●
●
●
●
●●
●●
●●
●●●
●
●● ●●
●●●●
●
●●
●
●●
●
●● ●
●
●
●●
●
●
●
●
●
●
●●●●
●
●● ●
●●
●● ●
●●●
●
●
●
● ● ●●
● ● ●●●
●●
● ●
●
●
●●●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●● ●●●
●
●
●
●
●●
●
●
●
●●●●
●●●●●●
●●
●
●
●●
●
●●●
●
●
●
●●
●
● ●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●●
●
●
●
●● ●
●
●●
●
●
●
●
● ●● ●
●● ●●●
●
●●
●
●●
●●
●
● ●●
●
●
●●
●
●
●
●●●
●
●●
●●
●
●
●●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●●●●
●
●
●
●
●●
●
●●●
● ● ● ●●● ●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●● ●
●
●
●
●
●
●
●
●●
●
●
●●
●●
●●
●
●●
●
●
●
●
●
●●●
●
●
●●●●●●●
●●●●
●
●
●●
●●●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●●
●●
●
●
●
●●
●
● ●●●
●
●●
●
●●
●
●
●
●
●
●
●●
●●
●●
●
●
●●
●
●
●
●●●
●
●
●
●
●
●●●
●
●
●● ● ●● ●
●
●
●
●●
●●
●
●●
●
●●
● ● ●● ●
● ●●
●
●● ●
●
●●●
●●●●
●●
●
●
●●●
●
●
●●●●
●●
●●● ●●●● ●
● ● ● ● ●● ●
●●
●
●
●
●●
●
● ●●
●
●
●
●●
●
●
●
●
●
●●●●
●●
●
●
●
●
●
●●
●
●●●
●●●
●
●●
●
●
●
●●
●●
●●●
●
●●●●●
●
●
●
●● ●●
●
●
●●
●
●
●●
●
●
●
● ● ●
●●
●
●●●●
●
●●●
●
●●
●●●
●●
●●●
●
●
●
●●
●
●
●●● ●●●
●
●
● ●●
●●● ●
●● ●
● ●●●●
●● ●
● ●
●●
●
●●● ●●●
●●
●●●
●
●
●
●
●
●●
●●●
●● ●
●●●●
● ● ●●
● ●
●●●
●
●●●
●
● ●
●●
●●
●● ●
●
●
●
●●●●●
●●
●
●
●●
●●●●
●
●●
●
●
●●●
●
●
●
●● ●
●
●●
●●●
●
● ●
●●
● ●
●●
●● ●●
●●
●●● ● ● ●
●
●●●●
●● ● ●● ●
●
●
●
●
●
●
●
●
●
●
●●●●
●
●
●
●
●●
●●●
●
●
●● ●
●
●●
● ●●● ●
●
● ●●
● ●
● ●
●
●
●
●●● ● ●● ●●
●● ●
●
●
●● ●
●●●
● ●
●
●
●
●
●●
● ● ● ●
● ● ● ● ●●
●
●
●●
● ● ●
●●
●● ●
●
●
●
0
Class
2
C
GClass
Caa 41
3
ξLeu
(Leu)
10
10
10
10
●
●●
●
●
●
●
●
●
●
●
● ● ●●
●
●
●
● ● ●●●●
●
●●
●
●● ●
●
●●● ● ●
●●● ● ●
● ●●
●●
●●
● ●
●
●●
●
●
● ● ● ●
● ●● ●●●
● ●●
●
●●
●
●●● ●
●●●
●●
●
● ● ●
● ● ●
●
●
●
●●
●● ●●●● ● ●
●
●● ●
●
●
●●●
●●
●
●●●●
● ●●● ●
●
● ●
●
●● ●
●
●
● ● ●●●
●●●●
●
●
●● ●
● ●
●●
●●● ●●●
●
●
● ●
●● ●
●
●
●
●
●●
●
●
● ●
● ●●
●
● ●●
●
●
● ● ● ● ●
●
●●
●
●
●
●
●●
●●
●
●●● ●
●
●
●
● ●●●
●●
●
●
●
●
●
●●●
●
●
●●
●
●●
●
●
●
●
●
●
●
● ●
●
●
●
●●
●
●
●●
●
●●
●●● ●
●
●●●●
●●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●●
●
●● ●●● ●●
●
●●
●
●
●
●
●●
●●
●●
● ●
●
● ●●●
●●●
●●
●
●●
●
●
●
●●
●
●
● ●
●
●●
●
●
●●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●●●●
●
●
●
●
●
●
● ●
●
●●
●
●
●●
●
●
●
●●
●
●●
●●● ● ●
●●
●
●
● ●
●
●
●
●
●
●
●
●
●● ●● ●
●● ●
●●
●
●
●
●●
●
●
●
●●
●
●●●
●
●
●
●●●●
●
●
●
● ● ●●
●
●
●
●
●●
●
●●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●● ● ●
●
● ●
●
●
●●
●
●
●
●
●● ●
●
●
●●
●●
●
●
●
●●
●●
●
●
●
● ●●●●
●
●●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●● ●●
●●
●
●●
●
●●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●●
●
●
●
●●●
●
●
●
●
●
●●
●
● ●●
●
●
●
●
●● ●
●
●●
●
●
●
●
● ●
●
●●
●●
●
●
●
●
●
●● ●
●●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
● ●●●●●●
●●● ●
●
●
●
●● ●
●
●●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ● ●● ●●
●
●
●●
●
●
●
●
●
●
●
●
●●●
●
●
●●
●
●●
●
●●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
● ●●●●
●● ●●●●●●
●
●●
●
●
● ●●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
● ●
●
●●
●●
●
●
●
●
●
●
●
●
●●
●
●●●●
●●●
●
●●
●
●
●
●
●●●●●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●●
●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●●
●
●●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●● ●
●
●●●●
●
●
●
● ●
●●
●
●●
●
●
●●
●●●
●
●
●
●
●
●●
●
●
●
●
●
●●●
●
●●
●
●
●●●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●●●● ●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●● ●●●●●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
● ●●
●
●
●
●
●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●● ●●●
●
●
●
●
●
●●
●
●●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●●●●
●
●
●
●
●
●
●
●
●
●●●●
●
●
●
●
●●●●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●●●●●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●●●
●
●● ●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●●
●
●
●● ●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●●
●●
●
●
●
●
● ●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●●●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
● ●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●●● ●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●●
●
●
●●
●
● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
● ● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
● ● ●●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●●●●
●
●
●
●●
●
●
●
●
●
●
●● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●● ●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●● ●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
● ● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ● ●
●
●
●
●
●
●●
●●
●
●
●
●● ●
●
●
●
●●●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●●
●●
●
●
●
●
●
●● ●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●●● ●●
●
●
●
●
●
●
●
●
●
●
● ●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●●
●
●●
●●
●
●
●
●●
●
●
●
●●● ●
●
●
●
●
●
●
●
●
●
●●● ●
●
●●●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●●
● ●● ●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●● ● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
● ● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
● ●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●● ●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●● ●●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●● ●
●●
●●
●●
●
●
●
●●
●
● ●●
●
●
●●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●●●
●●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●●●
●
●
●
●
●
●●
●●
●
●
●
●
●●
●●
●
●●
●
●
●
●
●
●●●●●●
●
●
●
●●●
●●
●●●
●●
●
●
●●
●●
●
●
●● ●
●●●
●●●
●
●
●●●●
●
●●●
●●●
●● ●●
●
●●
●
●
●
●●
●
●
●● ●
●●
●
●
●●
●●
●
●
●●
●
●
●●
●
●●
●
●
●
●
●●
●●●
●●●
●●
●
●●
●●
●●
● ●
●
● ●● ●
●
●
●●
●
●●
●
●
●●
●
●
●●
●
●●
●●
●
●
●●
●
●● ●
●●
●
●
●●
●
●●● ●
●
●●
●●●
●●●
●●●● ●
●
● ●●●
●
●
●
●● ●
●
●●
● ●●
●
●● ●
●●
●
●
●
●
5
−5
−5
0
ξ(Ala
)
Se
Gu u
G
●
●
●
●
●
−5
ξT
Tyr)
ξLeu
((Leu
0 )
C ass 3
●
5
5
5
55
●
●
●
●
●
●
−10
0
●
●
●
00
●
Class21
Class
Caa 43
C
FC
C
aa 33
−5
−5−5
●
●
●●
10
ξG
Glu
u )
ξT
((Tyr
0 )
●
●
●
● ●
●
● ●
● ●
●
●●●
●
●● ●●
●● ●●●●
● ●● ●
● ●
●● ● ●
●
●●●●●● ●
●
●●
● ●●
●●
●●
●
●
●●
●●●●●
●
●●
● ●
● ●
●
● ●●
●●
●
●
●●●
● ●
●●
●
●
●●
●
●●
● ●● ●●
●
●
●●
●
●●●
●
●● ●
●●
●
●
●
●●●●●
●●
●●
●●
●●●
●● ●
●
●● ●
●●
●
●●
●
●●●
●
●
●
●
●●
●●
●
●●●
●
●● ●
●●●
●
●
●
●
●
●●●●
●
●
●
●
●
●●●
●●
● ●
●
●
●●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●●
●
●●
●
●
●
●● ●
●
●●
●
● ●●
●
●
●
●
●
●
●
●
●
●●
●●
●●●
●●●
●
●●
●
● ●●●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●●
●●
●
●
●
●
●●
●
●
●
●
●
● ●● ●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●●●
●●
●
●
●●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●●
●
●
●● ●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●●
●
●●●
●
●
●
● ●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
● ●● ●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●●●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●● ●●
●
●
●
●
●●
●
●
●
● ●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
● ●●●
●
●
●
●
●
●
●
●
●
●
●
● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●● ●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●● ●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●● ●
●
●
●
●
●
●
●
●●●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
● ●●● ● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
● ●
●
●● ●
●
●
● ●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●●
●
●
●
●
●
●
●
●
●
●●
●●●●
●
●
●●
●
●●
●
●●●
●
●
●
●
●●●
●
●
●●
●
●
●●●
●
●
●
●
●
●●
●
● ●
●
●
●
●
●
●
●
●
●
●
●●
● ●●
●
●
●●● ●●
●
●
●●
●
● ●●
●●●
●
●
● ● ●●
●●
● ●●● ●● ●
● ●● ●
●●
●●
●●●
● ● ●●
●●●●●● ●
●●●
●●
●
●
●
●● ●
●
● ● ● ● ● ●● ●●
●●
●● ● ●
●●
●●
● ●
●
5
−5
−5
10
1010
●
0
ξA(Ala
p )
GGu u
LξG
((Glu
u )
Glu
ξL(ξGlu
0 ))
10
5
(Glu
LξG
u )
L 0
1
CCa
aa 2
32
EClass
C
C ass 3
−5
−5
−5
−10
A p
GGu u
5
5
−10
●
●
●
−5
−5
−5
●
●
−5−5
00
55
ξ(ξSer
))
(Arg
Se
Ag
1010
−10
Class
LClass43
C ass 3
●
●● ●
● ●●
●
●● ●
● ● ● ●●
●● ● ●
●
●●
●●
● ●●
●
●
●
● ●●
●
●●
● ● ●
● ●●
● ●●
●●
●
●
● ●●
● ●
●
●●
● ●●
●●
●
●●
●●●● ●●
●
● ●●● ●
● ● ● ● ●●
●●●
● ●
●
●●
●● ●
●●
●
● ●
●●●●
●● ●
●●●
●●
●
●
●
● ● ●●
●
●
●
●
●
●
●
●● ●
●●●●
●● ●●
●
●
●
●
●
●●
●
●
●
● ● ●●
●
●●
●●●
●●
●●
●
● ●●
●●●
●
●●●
●●
●
●●
●●●●
● ●●● ●
● ●●
●●
●
●
● ●●
● ●●
●
●●
●● ● ●
●●●●
●
●● ●
●
●
●
●● ●●●
● ●●
●●●●
●●
●●
●●●
●
●●
● ●●
●●
● ●
●● ●●●
●●
●
●
●●
●● ●●●
●
●
●●●●
●
●
●
●
●
●●
●● ●
●●● ●● ●
●
●
●
●
●
●
●
●●●
●
●●
●●●
●
●
● ●●
●
●
●
●
●
●
●
●
●●●
●
●
●●
●●●
●●●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●●
●
●
●
●
●●●
●●●●
●
●●
●●●
●
●●● ●
●
●
●●●
●
●
●
●●
● ●●●
●
●●
●
●
●
●
●
●
●
●●●●● ●● ● ●
●
●●
●●
●
●●
●●●
●
●
●
●
●
●
●
●●
●●●
●
●
●●●
●● ●●
●●●●
●
●
●
●
●●
●
●●
●
●
●●
●
●●
●
●
●
●●
●●
●
●
●
●●
●
●
●●
●
● ●● ●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●● ●● ●
●●
●
●
●
●
●
●
●●
●●
●
●
●●
●
●●
● ●
●
●
●●
●
●
●
●●●
●●
●
●● ● ●
●
●
●●
●
●●
●
●●●●
●●
●●●
●
●
●
●●
●
●
●
●●
●●
●
●
●
●
●●
●●●
●●
●
●
● ●
●●
●
●
● ●●● ●
●
●
●
●●
●
●●
●
●●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●●
●●●
●
●●
●
●
●●
●
●
●
●
●
● ●●
●
●●●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●●
●
●
●
●● ●● ●●
●
●●
●●
●
●
●
●●
●●
●
●
●
●●
●
●
●
●
●
●●
●
●
●●
●● ● ●●●●
●
●●
●
●
●●
●
● ●●
●●
●●
●
●●●●
●●●
●
●
●●
●
●●● ●
●
●●●●●
●●
●●
●
●
●
●●
●●
● ●●●
●
●
●
●●●●
●
●
●
●
●
●
●
●
● ●● ●●
●● ●
●●●
● ●●
● ●●●
●
●●
●
●
●
●
●
●●
●
●●●
●
● ●
●
●● ●
● ●●
●● ● ●
● ●●
● ● ● ●● ●
●
●
●
●
● ●●
●●●●● ● ●
● ●
● ●● ●
● ●
●
●
●●●
●●
●●
●● ● ●
● ● ● ●●
● ●● ●●● ●
●●● ●●
● ●●
●●
●●
●
● ●
●
●
●●● ● ●
●
●
●●
●
●
●
●
●●
●●
●
●
●
●
●●
●● ●
● ●
● ●●
●
●
●
●
●●
●●
●●
●●●●
●●●
●
●
●
● ●●● ●● ●
●
●●
●
●
●
●●
●
●
●
●●
●●●
●
●
●
●●
●
●
●
●●●
●
●
●
●
●
●●
●
●●
●●●
●
●
●●
● ● ● ●●●●
●
●●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●●
●
● ● ● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●● ●
●
●
●● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●●●● ●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●●● ●
●
●
●
●
●
●
●
●
●
●●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●● ●●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●●●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●●●●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●● ●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
● ●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●●●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●●
●
●
●●
●
●●
●
●●
●●
●
●● ●
●
●●
●● ●
●●
●
●
●●●
●
●
●
●●●
●
●
●
●
●●
●
● ● ●● ●
●
●
●●
●●
●●
●●
●●
●
●
●
●
●●●
●
●
●●
●
●●
●
●
●●●
●●
●
●●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●●●
●
●
●
●
●
●●
●
●
●●
●
●●
●●
●
●
●
●●
●
●
●●●
●
●●● ●
●
● ●
●
●
●
●●
●
●
●●●
●●
●●
●
●●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●● ●●
●●
●
●● ●
●
●
●●
●●
●
●● ●●●
●●
●
●
●
●
●
●●
●
●
●
●
●●
●
●●
●
●
●●●●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
● ●●
●
●
●
●
●
●
●
●
●●
● ●
●
●
●
●●
●
●
●
●●●
●
●
●
●●●
●
●
●
●●
●
●●
●●
●
●●
●
●
●
●
●●
●
● ●●
● ●●●
●
●●
●
●
●
●
●●●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●●
●●
●
●
●
●●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●● ●
●
●
●
●●●
●
●●●●●
●●●
●
●
●
●
●
●●
● ●
●●
●
●
●●
●
●
●
●●
● ● ●● ●●●
●
● ●●●
●
●
●
●
●
●
●
●
●
● ●●●
●●
●
●
●
●
●
●
● ●●
●
●●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●●
● ●●
●
●
●●
●
● ●●
●
●
●
●●●
●
●●
●
●
●●
● ●●
●●
●
●●●
●
●
●
●
●
●
●●●●●●
●
●
●●
●●
●
●
●
●
●●
●
●●
●
●
●
●●
●●●●●●
●
●
●●
●
●●
●
●●●
●●
●● ●●
●
● ●
●●●
●
● ●●
●●
●●
●●
●
●
●
●
●
●
●
●
●
●● ●
●●●●● ● ●
●
●●
●
● ●● ●●
●
●●
●●
●
●●
●
●●
●
●
●
●●
●●
●
●●●●
●
●●
●
● ●●
●
●
●●●
●
●●
●
●●● ●
●
●●
●●
● ● ●●
●●●●● ● ●●● ●
●●
●
●
●●●●
●
●
●
●
● ● ●● ● ●
● ●● ●
● ●●
●
● ●● ●
●
●
●
●
●●
●
●
●
●
● ●●
●
●
●
●
0
5
10
Class 4
●
●
●
●
●
●
●
●
●
●
●●
●
●● ●
●● ●
●
●
●
●● ●
●
●●
●
● ●●
●
●
● ●●
● ● ●●● ● ● ● ●●
● ●● ● ●● ●● ●
● ● ●
●
●
●●
●
●
● ●
●
● ●
●● ●
●● ●●●
●● ●●●
●
●
●
●
●● ●●●
●
●
● ● ● ●
●
● ●
●
● ● ● ●●● ●●●●●
●●
●●●
● ●●
● ● ●
●●● ●●
●
●
● ●
●
●●●
●●●●
● ●
●
●
●●●
●
●●●●
●●● ●
●
●●●
●
●
●
●
●
●●●
●
●
●
●
●●●●● ● ●
●●
●
●
●●
● ●
●
●
●●
● ●●
●●
●
●
●
●
●●
●
●●●●
●
●
●● ●
●
● ●
●
●
●● ● ●
●
●●●●
●●
●●
●●●
●
●● ●
●
●
●
●●
●
●●
●
●
●●●
● ●●
●●●
● ●●●
●
●
●
●●
●●
●
●●
●●
●
●
●●
●
●●
●
●
●
●●●
●●●
●
●
●
● ●
●
●
●
●
●
●●
●●●●●
●
●
●
●
●
●●
●
●
●●
●
●●
●●
●●
●
●
●●
●
●
●
●
●
●●
● ●● ●●●
●●
●
●
●
●
●
●
●● ●●
●
●
●
●
●●
● ●
●
●
●
●
●
●
●●
●
●●
● ●●
●
●●
●
●●●
●●●● ●●●
●●
●
●●
●
●●
●
●●
●
● ●
●●●
●
●
●●●
●
●
●
●●
●
● ●●●●
●
● ●
●
●
●
●
●
● ●●
●
●
●
●
●
●● ●
● ●●
●
● ●
●
●
●
●●●●
●
●
●● ●
●
●
●
●● ●
●
●
●
●
●●
●
●
●●
●
●
●
●
●●●
● ●●●●●● ●●●●
●●●
●●
●●
●
●
●●
●
●
●●●●
●
●
●
●
●●
●
●
● ●●
●●●●
●●●
●
●
●
●
●●
●
●
●
●
●●●
●
●●●●
●
●
●●● ●
●
●
●●
●●
●● ●
●
●●
●
● ● ●●
●
●●
●●●
●
●
● ●● ● ● ● ● ●●●
●●
●
●
●
●●●●●
●●●●●
●
●●
●●
●●●
● ●● ●
● ●● ● ● ●●●
●●●
● ●
●
●
●
●
●
●●
●●●
●●
●
●
● ●
●
●
●
●●●●●●
●
●● ●
●● ●●
●
●● ● ●
●●●●●● ●●●
●●
●
●
●
●
●
● ●
●
●●
●
● ●●●
●
●
●
●
●● ●●●
●●
●
●
●●
● ●●
●●●●●●
●
●
●●
●
●
●●
●
●●●●
●●
●●●●
●●●
●
●
●
●
●
●
●
● ●
●
●
●●
●●●
●
●●●● ●
●
●
●
●
●
●
●
●
● ● ●●● ●
●●
●
●● ●● ● ●●
●●
●
● ●●
●
●
●●●
● ●● ●
●
●
●●
●●●
● ●
● ●●
●● ●
●
●●
●
● ● ●●
●
●●
● ●●
●
●
●● ●●
●
●
●
●
●
●●
●● ●
●
●
●●
● ●
●
● ●●
●
●
●
●
● ●●
● ●●
●
●●
● ●
●
●●●
●
●●
●
●
●
●
●●
● ●
●
●
●
● ●●●
●● ●
● ●●
●
●●●
●
●
●
●●
●●
●●●● ● ●
● ●●
● ●● ● ●
●●
●
●
● ●● ●
●
● ●
●●
●
●●● ● ●●● ●
●●
●
●● ● ●
●
●
● ● ●●
●
●
● ●●
●●●● ● ● ●
●● ●
● ●
●
● ●●●
● ●●
●● ● ●
●●
●●
●
●
●
●
● ● ●●● ●●● ●● ●●
● ● ●
●
●●
●
●
●
●● ●
●●
●●
●●
● ●●
● ●
●
●●●
●● ●
●●
●
● ●
●
●●
●●●●●●● ● ● ●
●●
●●
●
●
●● ●
●●
●
●
●
●● ● ●
●●
●
●●
●●
● ●
●
●
●
●
●
● ●●●
●●
● ●
●● ●● ●
●●●● ●
●
●
●
●
●●
●●●●●● ●
●●●
● ●
● ●
●
● ● ● ●●
●●●
●●
●
● ●
● ●●
●● ●
●●
●●
●●
● ●●●●
●●
●●●
●
●
●
●
● ●●
●
●
●● ●
●●
●●
●●
●●●
● ●●●
●●● ●●
●
●●
● ●●
●●●●
●●
●
●
●● ●●●●● ● ●
●
●
●
● ● ●●●●● ●
●
●
●
● ●●
● ●
●●
● ●
●●● ●
●
●
●
●●●
●●●
●
●
●●●
● ● ●● ● ●
●●●●●
●●●●●
● ● ●●
●
●● ●
●●
●
●
●
● ●
●
●
●
●●●●
●
●●● ●
●
●●
●●
●●●
●
●
●●
●
●
●●●●
●
●●
●
● ●●
●
●
●
●
● ● ●●
●
●
●●●
●●
● ●●
●●
●●
●●
●
●
●●●
●
●● ● ●
●●
●
●
● ●●
●
●
●
●●
●●
●
●
●●
●
●●
●
●● ●
●●
●
● ●●●●
●●
●
●
●●● ●●
● ● ●● ●●
●
●●
●
●●
●●
●●
●●
●●
●
●●
●●
●
●●
●
● ● ●
●●●
●
●
●
●
●● ●●● ●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●●
●● ●
●●●
●
●
●
●
●
●●●
●
●
●
●
●
●●
●
●
●
●●
●●
●
●
●
●●
●
●●●
●
● ●
●
●
● ●●●●
●●
●
●
●
●●
●●
●●●
●●
●●
●
●●
●
●
●●
●●
●●
●● ● ●
●●● ●
●●●
●
●
●
● ●● ●
●●
●● ●●●
●
●
●●●●●
●●
●● ●●●
●●●●
●
●
●
●
●
●
● ●● ●
● ● ●● ● ●●
●
●●
●●
●●●
●
●
●
●
●
●
●●
●
●
●● ●
●●
●
●
●●●
●●
●●
●●
●
●●
●
●
●●●
●
●
●
●
●
●●●● ●
●
● ●●● ● ● ●
●●
●
●●●
●●
●
●
● ●●●●● ●
●●
●● ● ● ●
● ●●
● ●●●●
●●
●
●●
●
●
●
●●
●
●●●●
● ● ● ●●
●
●
●●
● ● ●●
●
●
●
●
● ●
●● ●● ●●
●
●
●●● ●
●
●●
● ● ●●
●●● ●●●
● ●
●●
●●● ●●●●
●●
● ●● ●●●
●●
● ●●
●
●
●
●● ●
●●●
● ●● ●●
●
● ●●
●●
● ●●●
● ●● ●● ●
●●
●●● ●●● ● ● ●●●●
●
●
●
●●
● ●
●
●
●●
●
●
●●
●
● ● ●●●● ●● ●
●
●
●
● ● ●●
●●
●
●
●●
● ●●
● ●● ●
●●
● ●● ● ● ●●
● ●●
●
●
●●●
●●
●●● ●
●● ● ●
●
●
●
● ●●
● ●
●
● ●●
●
●
●
●
●
●
●
● ● ●
●● ●
●
●●
●●
●
●●
●
●
●
●
●
● ●
● ● ● ●●●
●
● ●
●
●
●
●
●
● ●
● ● ●
●
● ●
●●●
● ●●
●●
●
●
●
● ●●
●
●●
●●●
●
●
●●
● ●
●●
● ●
●●
●●
● ●●
●
● ● ●●● ● ●
●
●
● ●●
●
●
● ● ●● ●
● ●
●●●
●●
● ●●●
●
●●
●●
●
●
●
●
●
●●●
●●●
●
●●
●
●●
●
● ● ●●●●●
●● ● ● ●
●●●●●
●●
●●●
●
●
●● ●
●● ●● ●●●●
●
●
●
●●
●●
●●
●●
●
●
●● ●●●●●●● ●
●
●
●
● ● ●
●●●
●●
●
●
●
●● ●
●●●
●
●
●
● ●
●●●
●
●
●● ●
●
●
●●
●●
●●
●
●
●
●●●
●
● ●●
●●●●
●●●
●
●
●
●●
●●
● ●
● ●●
●
● ●
●
● ●●●●
● ●
●●●
●
●● ●
●
●
●
●
● ● ●
●
●●
●
●
●
●●●●
●
●
●
●
●●
●
●
●
●●
●
●●
●
●●
●●
●●
● ●●●●● ●
●
●●●
●
●
●
●
●●●
●
● ●
●
●● ●
●●●
●
●
●
●
●●●
●
●
●●
●
●●●
●●
●
●
●●
●
●●
●
●
●
●● ●
●●
●
●●
●
●●
●
●●
●●
●
● ●●
● ●
●●
●
●●
● ●
●●●
●
●●
●
●●
●●
●
●
● ● ●●
●
●● ● ●●
●
●
●
●
●
●●
●
● ● ● ●●●●
●●●
●
●● ●
●●
●
●
●
●●
●
●
●●
●
●●●●
●
●
●
●●
● ●
●●●●●●
●
●
●●
●
●●● ●●
●●● ●
●●● ●
●
●
●
●●●●
●
●●
●●
●●
● ●
●●
●
●
●●●
●●
●
●●●
●
● ●
●
●●●●
●
●
●
●
●●
●●●● ● ●
●●●
●●●● ●
●●
●●●
●
●
●
●
●
●
●●
●●
●
●
●
●
●●●
●●
●
●
●
●
●
●
●
●
●●●
●
●
●
●●
●
●
●
●
●
●
●●
●●●●
●
●
●●●
●
●●
●●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●● ●
●
●
●
●
● ● ●●
●
●
●
●
●●
●
●
●●
●
●
●●●●●●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●●
●
●
●
●●
●●●
●●●
●
●
●
● ● ●● ●
●
●
●
●
●
●
●
●
●
●●
● ●●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●● ● ●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●●
●
●●●
●
●
●●
●
●
●
●
●
●
●
●
●●●●●
●
●
●●
●
●
●
●
●
●
●●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●●
●
●
●
●
●
●
●
●●
●
●
● ●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●●
●
●
●
●●
●
●● ●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●● ●
●
●●●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●● ●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●●
●
●
●
● ●●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●●● ●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ● ●● ●●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
● ●● ●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●●● ●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
● ●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●● ●
●●●
●
●
● ●
●
●●
●● ●
●
●
●
●
●
●●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●● ●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●●
●●
●
●
●
●
●
●●
●
●
●
● ●●
●
●●●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●●
●
●
●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●●
●●●●●
●
●
●
●
●
●
●
●
●
● ● ●
●
●
●
●
●
●●
●
●●
●
●
●
●●
●●●●
● ●
●
●
●●●
●
●
● ●
●●
●
●
●●
●
●
●
●●
●
●
●●
●
●●
●●
● ●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●● ●
● ● ●●
●
●
●
●●●
●
●
●
●●●
●
● ●●
●
● ●●
●
●●
●●●
● ● ●●
● ●●●●
●●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
● ●●
●●
●
●
●
●
●
●●●
●
●
●
● ●●
●●
●
●
●●
●
● ●
●
●
●
●
●●●●●●●
● ●● ●
●● ●●
●●●
●●
● ●
●
●● ●
●●
●
●
●
●●
●●
●● ●●
●●
●●● ●
● ● ●
●
●
●
●
●
●
●●●
●
●
● ●● ● ● ●
●●
●●●●
●● ●
●
● ●●
●●
●
●● ●
●● ●
●●
●●
● ● ●●
●●
●
●
● ●
●
●
●
●●●
●●
●
●●
● ● ●●
●●
●●
●●
●●●
●●●
●●●●
●
●●
●●●
●
●●● ●● ● ● ● ●
●
●
● ●●
●●
●
●●
●●●●
●● ●
●
●
●●
●
●●
●
●
●●
●●●
●●
● ●●● ●
●●
●
●●
●
●
●
●
●
●●●
●
●●
●
●
●
●
●
●
●●
●●●
●
●●●
●
●●
●
●
●●●●●
●●
●
●
●
●
●
●●
●
●●
●
●
●
●●● ●
●
●
●
●
● ●●
●
●
●
●●●
●●●
●
●
●
●
●●
●
●●● ●●
●
●
●●●●
●● ●
●
●
●
●●●
●
●
●
●●
●●
●●
●●
●
●
●
●
●
●
●●●
●
●
●
●
● ●●●
●
●
●
●
●●●
●
●●●
●●
●
●●
● ●● ● ●
●
●
●●
●
●
●
●
●●
● ●●●
●
●
●
●
●
●
●●
●● ●
●
●
●●
●●
●●
●
●●
●
●●
●
●
●●
●●
●● ●●
●●
●●
●●
●●
●
●●
●
● ●●
●
●
●
●
●
●
●●
●●●
●
●●
●
●
●●
●●●
●
●
●●
●●
●
●
●
● ●●●
●
●●
●
●
●
●●
●●
●
●
●
●
●
●●
●
●
●
●●●
● ●●● ●
●
●
●
●
●
●
●
●
●
● ●● ● ●
●●●
●●
●
●●
●
●●
●
●
●
●
●●
●●●●
●
●
●●●●●
●
●●
●
●
●●
●
●
●●
●●
●
●
●
● ●●●●
●
● ●●
●
●●●
●
●
●
●
●●
●
●
●●
●
●
●●
●● ●
●●
●●
●●
●●
●●
●●
●
●
●
●●
● ●●
●
●●●
●
●
●●
●●
●●●
●
●●
●●
●●
●
●●●
●
● ●
●
●●●
●
●
●
●●
●
●
●
●
●
●●
●
●●
●●
●
●●●● ●● ● ● ●
●●
●
●
●●
● ● ●● ● ●● ●
●
●●
●
●●
●●●
●
●
●
●
●
●●
●
●●
● ●
● ● ● ●●●
●●
● ●●
●●●
●
●●
●●●
●
●●
●
● ●●●●● ● ● ●
●
●
●● ●
●● ●
●●●
●
●●●
●● ● ●●
●●●
●
●
●●
●
●●
●
●
●
●●●●●
●●
●● ●●
●●
● ●●●●●
●
●●●
●●●
●● ● ●● ●
●
●●
●
●
●
●
●●●● ●●●●● ● ●
●●●● ●● ●●●
●
●
●●● ● ●
●
● ●●
●●● ●●●
●
●
● ●●
●●
● ● ●
● ●●●
●●
●
●● ●●
●
●● ●●
●●●
●●
●●
●
●
●
●
●● ● ●●● ● ●
●
● ● ●
●
● ●
●
● ●
●
●
● ●●
●
●
●
●
●
●
●
●
−5
ξ(Arg)
Ag
10
●
●
●
C ass 3
●
−10
−10
−10
Class
KClass43
−10
−10
5
●
1010
0
● ●
●
●
55
10
10
●
●
●●
00
ξ(ξAla
)
(Ser
A
a )
Se
ξ(Leu)
●
●
●
● ● ●
●
●
● ●
●
●
●
● ●●
●
●
●
●
●
● ● ●
● ●●
● ●● ●
●
●
● ● ●●
●●
●●
●●
●
● ● ●●
●
●
●
●●●
● ● ●●
●● ●
●●
●
●
● ●● ●●● ●
● ●● ●
●
●●● ● ●
●●
● ●●●●
●
●
●
●●
●
●●
●
●
●●
●●●
●
●
●
●
●
●● ●
● ●
●●
●●●●
●●
●●
●
●●●
●●●
●●
●●
●●
●
●
●●
●● ●
●●
●●●●
●●● ●● ●
●●
●●
●●
●●
●
●
●● ●
●
●
●
●
●●
●●
● ● ●● ●
●
● ●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●●
●●●
●●
● ●
●
●●●
●●
●●
●
●
●
●
●
●●●●
●
●
●
●
●
●
●
●
●
●
●●●●●
●
●
●
●● ●
●
●
●● ●
● ●●
●
●
●●
●
●
●
●
●
● ●● ●
●
●
●
●
●
●
●●
●●
●
●
●
●
● ●●
●
●
●● ●●
●● ●
● ● ●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
● ●
●
● ●
●
●●
●
●
●
●
●
●
●
● ●●
●●
●
● ●●●
●
●
●●
●
●●
●
●
●●
●
●
●
●
●●
●●
●
●
●●
●
●
● ●
●
●
● ●●
●
●
●
●
●
● ● ●
●
●
●●
●
●
●
●
●
●
●
●
●●
●●
●
●
●●●
●
●
●●●
● ●●●
●
●
●
●
●
●
●●
●●
●
● ●●
●
●●●
●
●
●●
●
●● ●
●
●
●
●
● ●
●
●
●●
●
●●
●●
●
●
●
●●●
●●●
●●
●
●●●
●
●
●●
●
●
●
●
●●
●
●
●● ●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
● ●●●
●
● ● ●
●
●
●
●●●
●
●●
●
●
●●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
● ●
●●
●
●
●●
●
●
● ●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●●●●
●
●
●
●●
● ●●●●
●
●
●●
●
●
●
●
●
●
●
● ●●
●
●
●
●
●●
●
●
●
●
●
●
●● ●● ●
●
●
●●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
● ●
●●
●●●●●
●
●
●
●
●●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●● ●
● ●●● ●●
●●
●●
●●
●●
●
●
●
●
●●
●
●
●●
● ●
●
●
●
●
●●
●
●
●
●●
●●
●
●●
●●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●● ●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
● ●●
●
●●
●●
●
●●
●
●
●
●● ●
●
●
●
●●●●
●
●
●
●
●
●
●
●
● ●
●
●● ●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
● ●●
●
●●
●
●
●
●
●
●
●
●
●●
●●
● ● ●●
●
●
●
●
●
●●● ●
●
●
●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
● ●● ●●
●
●
●
●● ●
●
●
●
●
●
●●
●●
●
●
●
●
●
●●
●
●
●
●
●●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
● ●
●
●
●●●● ● ●● ●
●
●
●
● ●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
● ●●●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
● ●
●
●
●
●
●
●●
●
●
●
● ●●
●●●
● ●●●
●
●●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
● ●●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
● ●●
●●●●
●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
● ● ●●
●
●
●●
●
●
●
●
●
●● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
● ●●●●●●●
●
●●●
●
●
●
●
●
●
●
●
●
● ●●●
●
●
●
●
●
●●● ●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●● ●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●●
●
●
●●
●
●
●
●
●
●
●
● ●●
●
●
●● ●●● ●
●
●
●
●
●
●
●
●
●
●
●● ●●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●● ●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●●
●
●
●●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
● ●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●●
●
●●
●●
● ●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●● ● ●
●●
●
●
●
●
●
●
●
●
●
●
●
●● ●
●
●
●
●
●
●●
●●●●
●
●
●
●
●●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●● ● ●●●●●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
● ●●
●
●●
●
●●
●●
●●
●●●●●
●●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●● ●
●
●
●
●
●
●
●
●
●●
● ●●
●
●
●●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
● ●●
●
●
●
●
●
●
●
●
●●
●
●
●
● ●
●
●
●
●●
●
●●●●
●
●●●
●●●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●●●● ●
●
●
●
●●●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
● ●●●
●
●
●
●
●
●
●●
●
● ● ●●●●●●
●
●●
●
●
●
●●●●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●●
●●
●●
●
●
●●
●
●
●●
● ●
● ●
●
●●
●
● ●
●●
●
●
●
●
●
●●●
●
●
●
●
●●
●
●
●
●
●
● ●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●●
●
●
●●
●
●
●
●●
●● ●●●
●●
●●●
●●●
●● ●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●● ●●
●●
●●
●
●●
●
●
●
●
●
●● ●
●●
●
●●
●
●
●
●●●
●
●
●
●●
●
●
●
●
●
●●
●
●
●●
●●●
●●
●
●●●
●
●●
●
●
●
●
●●
●●
●●●
● ●●
●
●●
●●
●
●
●
●
●
●●
●
●
●●
●●
●
●●
●
●
●
●●
●
●●
●●
●
●
●
●●
●
●
●●●
●●
●
●
●
●
●
●●
●
●
●
●
●●
●
●●●
●
●
●
●
●●
●
●
●●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●●●● ●
●
●● ●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●●
●● ●
●
●●●●●
●●
●●●
●●●
●
●
●
●
●
●
●●
●
●
●
●●
●●●
●
●●●
●● ●
●●
●
●●
●
●●
●●
●
● ●●●●
●
● ●
●
●
●
●●
●●
●
●
●●
●
●
●
●
●●
●
●
●
●●●
●●● ● ●
●
●
●
● ●●
●
●
●●
●
●
●
●●
●●
●
●●●
●●
●
●
●
●
●
●
●
●● ●●●●
●●●
●●
●
●
●
●●
●
●
●
●
●
● ●
●●
●
●
●●
●
●● ●
●
●
● ●●
●●
●●
●
●●
●●
●
●
●
●
●●
●
●●
●●
● ●
●
● ●
●
●●
●
●
●
●
●
●●
●●●
●●
●
●●
●●●
●
●
●●●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
● ● ●●
●
●
● ● ●●
●
●
●●
●
● ●
●
●●
●
●
●●
●
●
●● ●
●
●●●
●●●●● ●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●●
●
●
●
●●
●
●●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●●●
●●
● ●●
●
●
●
●
●●●
●
●
●●
●●●
●
●
●
●
●
●
●
●
●●
●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●●●
●
●
●●
●
●
● ●
●
●●
●●
●
●
●
●
●
●
●
●●
●
●●●●
●●
●
●
●
●
●
●● ●●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
● ●●●
●
●●
●
●
●
●
●
●
●
●
●●
●●●
●
●●●●●●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
● ●● ●
●
●
●
●
●
●
●
● ●
●
●●
●●●●
●
●●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●● ● ●
●
●
●●
●
●
●
●●
●●●
●
●
●
●●
● ●● ●
●
●
●
●●
●
●●
●● ●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
● ●
●
● ●●
●●●●
●●
●
●
●
●
●
●
●●
●●●
●
●
●●
●
●
●
●●
●
●
●●
●
●
●
●●●
●
●
●●
●●
●
●●●●●
●●● ●●●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
● ●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●●
● ●●
●
●●
●●
●
●
●
●
●●
●
●
●
●
●●●
●
●
●
●
●
●●
●●●
●
●
●● ●
●●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●●
●● ●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●●
●
●●●●
●
●
●●● ●●
●
●
●
●
●
●
●
●
●●
●●●
●
●
●
●●
●
●●
●
●●●
●
●●
●
●
●
●
●●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●●
●●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●●
●
●●
●
●
●
●●●
●
●
●
●●
●●
●
●
●●
●● ●
●●
●●●
●●
●
●
●
●
●●
●
●●●
●●●
●
●
●●●
●
●
● ●●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●●
●
●●●
●
●
●●
●
●
●
●
●
●
●●
●●
●
●
●●
●●
●●●
●
●
●
●
●
●
●
●●
●
●●●
●
●●
●
●●
●
●
●●●
●
●●
●●
●
●●●●●●
●
●
●
●●●
●
●●
●●
●● ●
●●●
●
●●●
●●●●
●
●
●
●●●
●
● ●● ●● ●
●
●
●●
●
●
●●
●● ●●
●
●●
●
●
●
●●
●●
●
●
●
● ● ●●
●
●●●
● ●●
● ●
●
● ●● ●
●
●
●●
●
● ●
●
●
●●●
●
●●
●
● ●●●
●● ●●
●
●
●● ●
●●
●
● ●● ●
●
●●●
●●●
●●●● ●
●
● ●●●
●
●
●
●● ●
●
●●
● ●●
●
●● ●
●●
●
●
●
●
−5−5
−5
5
5
●
●
●
−10
−10
5
5
●
1010
10
0
C ass 3
55
5
ξ(Tyr)
ξ(Leu
0 )
●
●
Class43
Class
0
5
0
ξ(Glu)
●
●
●
●● ●
●
●
●
●
●
● ●●
● ● ●
●
●●
● ●●
●
●
●
●
●
●
● ●
● ●● ●● ● ●
●
●● ● ●
●
● ●
●
●
● ●
● ●●●●
●
● ●
●●
●
●● ●
●●
●
● ● ●● ● ●
● ●● ●
● ●● ●
●
●●●
●●
● ●● ●
●●
●
●
●
●
●
●●
●●
●
●
● ● ●●●
●●
●
●
●
●
●
● ● ●
●
●●
●
●
●
●
●●
●
●●
●
●
●●
●
●● ●
●
●
●● ●
●
●
●
●
●
●●
●●
●●
●●
●●
●
● ●●●
●
●
● ●●
●
●
●
●
●●
●
●●
●●
●
●
●
●●●
●
●
● ●
●
●
● ●
●
●●●
●●●
●
●
●
●●
●
●
●
●
●
●●
●●
●
●
●
●
●
●● ●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●●
● ●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●●●
●
●
●
●●●
●
●
●
●
●●●
●●●
●
●●● ●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●●
●
●●● ●
●
●
●
●
●
●●●
●
●
●
●
●●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●●●●● ●●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●● ●
●
●
●
●
●●
●●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
● ● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●●
●
●
●
●●
●
●●
● ●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
● ●● ●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ● ●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
● ● ●●●
●
●
●
●●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●● ● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●● ●● ●
●
●
●
●
●
●
●
●
●
●●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
● ●●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●● ●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●●● ●
●
●
●
●● ●
●
●
●●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●●●●● ●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●●●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●●
●
●
●
●●
●
●
●
●
●
● ● ●
●
●●●
●●
●
●
●
●
●
●
●
●●●● ● ●
●
●
●
●●
●●
●
●
●
●
●●
●●
●●●
●●
● ●
● ●●●
●●
●
●●
●●●●● ●●●
●● ●
● ●●
●● ●
●●
●
●●
●●●●●
●● ● ● ●● ●
●
●
●
● ●
●● ●●
●
●
●
●
●
●●●
●
●
●●
●
● ●●●●●
●
●
●●
●
●
●● ● ●
●
●
●
●
●
●
●
●
●
●
● ●
● ●●
● ●
●
●
● ●
●
00
0
((Ala
ξ(ξξAsp
))
Ala)
A
GGupu
−5
−5
10
10
●
−5−5
−5
ξ(Glu)
ξ(Glu
0 )
10
Class 3
C ass 3
−10
−10
−10
−10
−10
10
10
10
5
5
5
0
ξ(Asp)
A
GGupu
0
−5
ξ(Glu)
ξ(Tyr
0 )
−10
−5
−5
−10
−10
−10
−10
●
●
●
●
●
●
●
●
−10
−5
0
5
10
−10
−10
−5−5
00
(Ala) )
ξ(ξAsp
55
1010
−10
−10
−5−5
00
ξ(ξAla
))
(Ser
55
1010
−10
−10
−10
−10
−10
−10
−10
−10
●
−10
−10
−5−5
00
55
1010
ξ(ξSer
(Arg) )
F gure 1 A-H) Re a ve oca con bu ons o s ab y o pa o am no ac ds n d e en s e g oups (A-D) o d e en
pa s o am no ac ds n he same s e g oup (E-H) Po n s a e samp ed e he when he am no ac d n he absc ssa s
es den (b
when
he am no
ac d contributions
n he o d na e stoesstability
den (g een)
du of
ng amino
ans ons
be ween
he wo site
Figure
1:ue)
A-H)
Relative
local
for opair
acids
in different
(ye ow) -L: D s bu ons o oca con bu ons o s ab y when non- n e ac ng am no ac d s p esen (magen a)
classes
(A-D)
or
different
pairs
of
amino
acids
in
the
same
site
class
(E-H).
Points
were
sampled
and when am no ac d n he absc ssa s p esen (cyan: p ed c ed; b ue: obse ved)
ξ(Asp)
−10
either when the amino acid in the abscissa is resident (blue), when the amino acid in the ordinate is
resident (green), or during transitions between the two (yellow). I-L: Distributions of local
contributions to stability in reference state when the non-interacting null amino acid was present
(ρ!,∅ !ξ!,! , ξ!,! !, magenta), when the amino acid in the abscissa was present as predicted using
Equation (1 (ρ! !,! !ξ!,! , ξ!,! !, cyan), or as observed (𝜌!,! !ξ!,! , ξ!,! !, blue).
distributionswhensubstitutionsbetweenthesetwoaminoacidsoccurred.Figures1E-Hshows
thesedistributionsforfourdifferentpairsofaminoacidsinsiteclass3.Therearewideranges
of values for ξ!,! and ξ!,! , consistent with earlier results demonstrating fluctuating selective
pressures at sites due to substitutions elsewhere in the protein (11). The distributions of ξ!,! andξ!,! stronglydependontheresidentaminoacid.Inparticular,thepotentialcontributionof
anaminoacidtotheproteinstabilitytendstobegreaterwhenthataminoacidisresidentata
site, a phenomenon we previously named the ‘evolutionary Stokes shift’ (11). The amount of
thisincreaseappearstobecorrelatedwiththeobservedvarianceinξ!,! .
Rapidly evolving sites with few selective constraints tend to have compact distributions with
smaller variances in ξ!,! and ξ!,! than slowly evolving sites (Figures 1A-D). Distributions for
physicochemicallysimilaraminoacids(e.g.,asparticacidversusglutamicacid,Figure1E)appear
highly correlated, while those for dissimilar amino acids (e.g., arginine versus leucine, Figure
1H)seemanti-correlated.Thisisbecausebackgroundsequencesthatconferahighsite-specific
stability on aspartic acid tend to do the same for the highly similar glutamic acid, while
background sequences that stabilize arginine tend to destabilize the dissimilar leucine (29). A
−5
0
ξ(Arg)
5
10
bioRxiv preprint first posted online May. 31, 2016; doi: http://dx.doi.org/10.1101/056325. The copyright holder for this preprint (which was not
peer-reviewed) is the author/funder. It is made available under a CC-BY-NC-ND 4.0 International license.
non-resident amino acid is generally stabilized if the
distributions are correlated (e.g. glutamic acid when
aspartic acid is present, Figure 1E), but destabilized if
thedistributionsareanti-correlated(e.g.glutamicacid
whenalanineispresent,Figure1F).
To determine whether substitution rates can be
predicted from ρ!,! (ξ!,! , ξ!,! ), class-specific stability
distributions were modeled with the best fitting
bivariate normal distribution for each pair of amino
acids
ρ!,! (ξ!,! , ξ!,! ) =
Figure 2: Comparison of observed and
!
!
𝒩{ξ!,!|! , ξ!,!|! , σ!,!|! , σ!,!|! , φ!,!"|! }. The expected predicted substitution rates. Blue: predicted
substitution rates calculated by integrating
substitution rates between each pair were then over ρ (ξ , ξ ), Red: Predicted
!,α
!,α
!,β
estimated by numerical integration over these substitution rates calculated using
distributionsusingKimura’sformulafortheprobability transition state theory (Equation(7),
offixation(30-32)(seeEquation(3,Methods).Thereis which assumes only near-neutral
extremely good agreement between expected substitutions occur.
substitutionratesderivedfromthisapproximationand
substitution rates obtained by counting substitutions that occurred during the simulations
(Figure2).Thisvalidatestheutilityofthebivariatenormalapproximationandtheassumption
thatvariationinΞ(𝐗)haslittleeffectonsubstitutionrates.
A striking feature of Figure 1 is the strong tendency for substitutions to occur in the overlap
region between ρ!,! (ξ!,! , ξ!,! ) and ρ!,! (ξ!,! , ξ!,! ), centred on the diagonal ΔΞ!,!→! = ξ!,! −
ξ!,! = 0 where substitutions are neutral. This suggests the possible applicability of transition
state theory (TST), a method for predicting the rate of chemical reactions (33). In TST, the
reactionrateisgivenbythefractionofreactantsina‘transitionstate’inwhichtheenergiesof
reactant and product are approximately equal, times the rate of conversion from transition
statetoproducts.Adaptingthistheory,wemodelthesubstitutionrateasequaltothefraction
ofjointstabilitiesforwhichthefitnessofwildtypeandmutantareapproximatelyequal,times
therateofsubstitutionunderneutralconditions.
Theprobabilitythatthebackgroundsequenceresultsinnearlyequalfitnessesbetweenαandβ
at site k was estimated as the density ρ!,! ξ!,! , ξ!,! integrated along the neutral line ξ!,! =
ξ!,! ,multipliedbythewidthoftheneutralzoneonbothsidesoftheneutralline,2ε,theregion
inwhichtheeffectofselectionissmall.Theneutralsubstitutionrateisequaltothemutation
rate υ!→! , allowing us to write a closed-form expression for the average substitution rate
(Equation(7,Methods).
AsdescribedintheMethodssection,theextentoftheneutralzone,ε,canbenaturallydefined
bythefalloffinthenumberofsequenceswithgreaterstabilities.BecausethestabilityvaluesΞ
forfoldedproteinsrepresentthefartailofadistributiondominatedbyunstablesequences,we
bioRxiv preprint first posted online May. 31, 2016; doi: http://dx.doi.org/10.1101/056325. The copyright holder for this preprint (which was not
peer-reviewed) is the author/funder. It is made available under a CC-BY-NC-ND 4.0 International license.
modeledΩ Ξ , thenumberofsequenceswithstabilityΞ,asanexponentialΩ Ξ ∝ exp(−γΞ),
whereγcharacterizesthedecreaseinnumberofsequencewithincreasingstability;thus,the
!
biasofthedrifteffectdoesnotdependonΞ.Thescaleoftheneutralzoneisgivenby!,which
!
is equal to the range of stabilities at which the fitness changes by less than !! regardless of
!
populationsize(seeMethods).Tocalculatesubstitutionrates,weestimatedγ=1.26(kcalmol1)-1basedontherelativenumbersofdestabilizingandstabilizingmutations,yieldingε=0.79
kcal mol-1. Notably, because this calculation considers only neutral substitutions, it produces
strikinglyaccuratepredictions(Figure2)withouttheneedforKimura’sformula.
The equilibrium distributions of site-specific stabilities: The mechanism behind the
evolutionary‘StokesShift’
It appears that the rate of amino acid substitutions is substantially determined by
ρ!,! ξ!,! , ξ!,! intheregionswhereξ!,! ≈ ξ!,! .Ourgoalfortherestofthepaperistoshow
the degree to which these distributions, and therefore substitution rates, can be explained
usingtheprinciplesofstatisticalmechanics.
Asabove,weassumethatproteinsevolvetoaspecificstabilityvalueΞ(𝐗) = Ξ.Allsequences
withstabilityΞhave,inourmodel,identicalfitnesses,sononearepreferredoveranotherby
selection. If evolution has had sufficient time to sample from the stationary distribution, the
fractionofsequenceswithanypropertyθisproportionaltoΩ(θ, Ξ),thenumberofsequences
with property θ and stability Ξ = Ξ. The log of this quantity, 𝑆(θ, Ξ) = ln[Ω(θ, Ξ)], is the
‘sequence entropy’ of such sequences, analogous to thermodynamic entropy. Under these
conditions,theprobabilityofpropertyθ is givenbyρ!" (θ) =
!(!,!)
!(!)
= e!
!,! !! !
,whereΩ(Ξ)
andS(Ξ)arethenumberofsequenceswithstabilityΞ = Ξandthelogofthisquantity.
Tocalculateρ!,! (ξ!,! , ξ!,! ),anestimateofρ!,! (ξ!,! , ξ!,! ),wefirstconsideredΩ!,! (ξ!, ! , ξ!,! , Ξ),
the number of sequences with stability Ξ = Ξ, α resident at site k, and site-specific stability
contributions ξ!,! and ξ!,! at that location. We approximated this number as the product of
Ω!"#
! (ξ!, ! , ξ!,! ), the number of amino acid arrangements resulting in the site-specific
ξ!,! and ξ!,! , times Ω!"#$
(ξ!,!"#$ = Ξ − ξ!, ! ). The latter term is the number of sequences
!
furnishing the background stability required to complement the site-specific contribution
furnishedbyξ!, ! ,foratotalstabilityequaltoΞ.Thiscalculationassumesindependenceofthe
bathandlocalcontributionstototalstability;althoughnotstrictlyaccurate(therelevantsites
in the protein overlap), it is likely to be approximately true because the interactions involved
aredifferent.
We note that Ω!"#
! (ξ!, ! , ξ!,! ) does not depend on selection, so to characterize it requires
removing selection at site k. To do this we performed simulations with the focal site
permanently occupied by a non-interacting amino acid, ∅, and with all other sites evolving
freely. The resulting distributions ρ!,∅ (ξ!, ! , ξ!,! ) are proportional to Ω!"#
! (ξ!, ! , ξ!,! ), and
bioRxiv preprint first posted online May. 31, 2016; doi: http://dx.doi.org/10.1101/056325. The copyright holder for this preprint (which was not
peer-reviewed) is the author/funder. It is made available under a CC-BY-NC-ND 4.0 International license.
representthenulldistributionsoflocalstabilitycontributionsthatwouldoccurifinteractions
between amino acids at site k and the rest of the protein did not affect the evolutionary
dynamics.Becausethenumberofpossiblesequencesisimmense,andbecauseξ!,! andξ!,! are
theresultofmanyinteractions,thecentrallimittheoremsuggeststhatρ!,∅ (ξ!, ! , ξ!,! ) canbe
approximated
by
a
bivariate
normal
distribution
ρ!,∅ (ξ!, ! , ξ!,! ) ∝ 𝒩{ξ!,!|∅ , ξ!,!|∅ , σ!!,!|∅ , σ!!,!|∅ , φ!,!"|∅ } . Interactions involving the focal amino
acid represent a small fraction of total interactions, allowing us to approximate
Ω!"#$
(ξ!,!"#$ ) ∝ Ω Ξ = ξ ,!"#$ .Thenormalizedproductofρ!,∅ (ξ!, ! , ξ!,! ) andtheexponential
!
Ω(Ξ = ξ!,!"#$ = Ξ − ξ!, ! ) results in a shifted bivariate normal distribution ρ!,! ξ!,! , ξ!,! =
𝒩 ξ!,!|! , ξ!,!|! , σ!!,!|! , σ!!,!|! , φ!,!"|! with
ξ!,!|! = ξ!,!|∅ + γσ!!,!|∅
σ!!,!|! = σ!!,!|∅
ξ!,!|! = ξ!,!|∅ + γ φ!,!"|∅ σ!,!|∅ σ!,!|∅ (1)
σ!!,!|! = σ!!,!|∅
φ!,!"|! = φ!,!"|∅
Selection in the presence of amino acid α at site k shifts the average local contribution to
stabilitybyanamountζ!,!|! = γσ!!,!|∅ comparedtoitscontributiontostabilityintheabsence
of interactions; this stabilization can be viewed as the basis for the evolutionary Stokes shift.
Themechanismfortheshiftisthelargeincreaseinsequenceentropygainedfromadecreasein
ξ!,!"#$ ,combinedwiththetrade-offbetweenξ!,! andξ!,!"#$ = Ξ − ξ!, ! .
Thefitbetweenestimatedequilibriumvaluesofξ!,!|! foreachaminoacidandvaluesofξ!,!|! calculated directly from the simulations is surprisingly good given the approximations made
!
(Figure 3A). The entropic stabilization as a function of 𝜎!,!|∅
is linear (correlation coefficient
0.857; Figure 3B) as predicted by Equation (1. The slope of 1.00 (kcal mol-1)-1 (95% CI: 0.87 –
1.14)isclosetotheexpectedvalueofγ=1.26(kcalmol-1)-1,confirmingthetrendsevidentin
Figure1.Theobservedentropicstabilizationissmallerthanpredictedforthetwolargestshifts
in the slowest rate class, involving the negatively charged aspartic acid and glutamic acid.
Earlier work demonstrated that equilibration for the most buried states can be extremely
slow(11),andtheseoutliersmayrepresentcaseswheretheproteinhashadinsufficienttimeto
adjusttothepresenceofthenewaminoacid.
The key result here is that the magnitude of the entropic stabilization that drives the
evolutionaryStokesshiftdependsonlyonthenumberofproteinsequenceswithgivenprotein
stabilities and on the underlying distributions of interactions in the absence of selection: the
effectcanbeunderstoodpurelyintermsofbiophysicsandsequenceentropy.
bioRxiv preprint first posted online May. 31, 2016; doi: http://dx.doi.org/10.1101/056325. The copyright holder for this preprint (which was not
peer-reviewed) is the author/funder. It is made available under a CC-BY-NC-ND 4.0 International license.
Figure 3: Accuracy of site-specific stability and evolutionary Stokes shift predictions. A)
Estimated values of ξ!!,!|! versus observed values ξ̅ !,!|! for all four site rate classes (from most
exposed to most buried: Class 1, blue; Class 2, red; Class 3, black; and Class 4, purple). B) The
linear relationship between the observed evolutionary Stokes shift and the variance in amino
acid-specific stability contributions in the absence of selection on the site. The lines shown are
theoretical predictions with gamma = 1.26.
Thepredictedandobserveddistributionsofρ!,! ξ!,! , ξ!,! areshowninFigures1I-L.Thevalues
ofξ!,! areshiftedbyanamountζ!,!|! = γ φ!,!"|∅ σ!,!|∅ σ!,!|∅ toeitherhigherorlowervalues
dependingonthephysicochemicalsimilaritiesbetweentheaminoacids.FromEquation(1we
canseethattherealizedevolutionary‘Stokesshift’afterasubstitution,theexpectedaverage
difference in stability before and after the protein adjusts to the new resident amino acid, is
equal to ζ!,!|! − ζ!,!|! = γ(σ!!,!|∅ −φ!,!"|∅ σ!,!|∅ σ!,!|∅ ). The full entropic stabilization is
reduced by ζ!,!|! , which can be viewed as the
averageamountofpreadaptation(orlackthereof)
toaminoacidβcausedbytheresidencyofamino
acidα.Aswwiththeaverageentropicstabilization,
the realized evolutionary Stokes shifts depend
deterministically on the site-specific stability
distributions in the absence of selection with no
adjustable parameters. Substitution rates
estimatedwiththeTSTapproximation(Equation(7)
using the site-specific stabilities calculated from
Equation(1areremarkablyaccurateforallfoursite
classes and over four orders of magnitude of rate
variation(Figure4).
Discussion
The understanding of evolutionary mechanics
developed here represents a fundamental shift in
Figure 4: Predicted and observed values of
substitution rates based on transition state
theory. Rates were computed using estimated
values compared with observed values for all
four classes (Class 1, blue; Class 2, red; Class
3, black; Class 4, purple).
bioRxiv preprint first posted online May. 31, 2016; doi: http://dx.doi.org/10.1101/056325. The copyright holder for this preprint (which was not
peer-reviewed) is the author/funder. It is made available under a CC-BY-NC-ND 4.0 International license.
how we conceptualize the process of amino acid substitution. Although stability is
approximately constant, the way this stability is partitioned among various interactions
fluctuates as a protein evolves. In particular, the contribution that a resident amino acid at a
sitemakestothestabilityoftheprotein,aswellasthecontributionanon-residentaminoacid
would make if substituted in, will fluctuate. Occasionally, these fluctuations lead to
approximatelyequalstabilitiesforapairofaminoacidssothatsubstitutionsfromonetothe
other are nearly neutral. The frequencies of these nearly neutral states then determine the
relativesubstitutionrates.Thefluctuationsinstabilizingcontributionsofdifferentaminoacids
at a site are not superfluous or unwanted complications in the construction of substitution
models,butratherarecentraltothesubstitutionprocess.Inevolutionarytheoryitiscommon
toevoketheideaofafixed‘adaptivelandscape’,butforasingleaminoacidpositionamore
appropriate analogy may be a fluctuating adaptive seascape; the site explores the space of
possibleaminoacidsbymovingalongfluctuatinglocalcontoursinthecontextofapproximately
constantoverallfitness.
By developing a statistical mechanics view of protein evolution, the evolutionary Stokes shift
can be seen as a direct consequence of sequence entropy. Increases in the stabilizing
contributions of an amino acid occupying a given site reduce the amount of stabilization
requiredbytherestofthesequence,increasingthenumberofsequencesthatcancontribute
this reduced stability. Our theoretical analysis of the balance between the number of states
availabletothesystem(theaminoacidatthefocalsiteanditsinteractions)andthe‘bath’(the
restofthesequence)yieldsanexpectationthattherelativemagnitudeofentropicstabilization
of an amino acid at a site is proportional to the variance of the underlying null site-specific
stabilitydistribution.Furthermore,thestabilizationofallaminoacidsatallsitesarescaledbya
protein-wide proportionality constant determined by the decline in the number of available
sequences as protein stability increases. Thus, surprisingly, the strength of selection and the
effectivepopulationsizedonotaffecttheevolutionaryStokesshiftorsubstitutionratesifthe
protein is in a steady state(34, 35). Thus, although our evolutionary mechanics theory fully
incorporates population genetics theory and Kimura’s equation for the probability of a
substitution,ifthesystemisnearequilibriumwedonotneedKimura’sformulatopredictand
explainsubstitutionratesamongaminoacids.
Correlations in the fluctuations between amino acids with similar physicochemical properties
increasetheprobabilityofnear-neutrality,providingamechanisticexplanationforhigherrates
of conservative change, a general phenomenon rationalized by Fisher with his geometric
argument(36).Theprobabilityofoccupyingtheneutralzoneisloweratinteriorsites,wherethe
multiplicityofinteractionswiththefocalsiteincreasethedistancebetweenξ!,! andξ!,! ,and
correspondinglyhigheratsurfacesites;thisisconsistentwithobservedslowerinternal(buried)
thanexternal(surface)substitutionrates.
For dissimilar amino acids, the probability of achieving the near-neutrality required for a
substitution can be unlikely. However, if such a substitution occurs the protein will
subsequently evolve to sequences that partition a larger stability contribution to the newly
residentaminoacid,causinganincreasedaffinityforthisresidue.Thisincreasedaffinityiswhat
bioRxiv preprint first posted online May. 31, 2016; doi: http://dx.doi.org/10.1101/056325. The copyright holder for this preprint (which was not
peer-reviewed) is the author/funder. It is made available under a CC-BY-NC-ND 4.0 International license.
we have called the evolutionary Stokes shift. This evolutionary mechanism can be fully
reversible,asisinourevolutionarysimulations,withthereversibilitycomingfromthesimilarity
intheprocessesofmovingintoandawayfromtheneutralzone(11).Theseprocesses,called
‘contingency’and‘entrenchment’byPlotkinandcolleagues(12),aremirrorsofeachother,so
that if the substitution were reversed the dissipation process, played backwards, would have
the same statistical properties as the pre-adaptation process played forwards. Where
previously we might have assumed that the amino acid found at the site had adapted to the
requirementsofthesite,thesitemayhaveinsteadadaptedtotheresidentaminoacid.
The fluctuations and the relaxation of the protein are explicitly time-dependent. Here we
addressedonlythetheoreticalequilibriumpredictionsandtheresultofsimulationsthatwere
designedtobenearequilibrium.Thisneglectofthistimedependencemayexplainsomeofthe
errors in the predicted Stokes shift for charged residues in buried sites. Individual sites at
specific time points might be further constrained by conserved neighboring sites in the
structureaswellastheconservedstructuralcontextoftheirinteractionswiththosesites.Such
effectsmayinfluencethetime-dependentprobabilityofbackmutationsaswellassubsequent
substitutions,animportanttopicforfurtherinvestigation.
Thesimulationspresentedherealsoconsideronlythefitnesseffectsofstability,butfitnessis
alsousuallydeterminedbyothereffectssuchasinteractionswithsubstrates,ligandsorother
proteins.Suchalternativefitnesscomponentswilladdadditionalconstraintstothesystem,and
may force non-neutral substitutions if outside selective pressures change. Previous analyzes
indicated that when a substitution is compelled by an outside force, an evolutionary Stokes
shiftoccursinlargelythesamefashion,exceptthattheprocessisnolongerreversible(11).In
this context, evolution can be seen as occurring in a ‘memory foam’ made up by the bath of
interactionsthatoccuramongallsitesotherthantheselectedfocalsite.
In conclusion, the work described here sets up a theory of evolutionary mechanics, and
demonstrates that this theory can be used to predict substitution rates from the basic
propertiesofhowaminoacidsinteract.Althoughthecurrentworkisfocusedonfitnessdefined
bytheproteinstability,weexpectthatotherkindsofselectionwillfitwellintothisframework,
either by defining a large nearly neutral landscape in their own right, or by constraining the
stability-basednearlyneutralnetwork.
Methods
Simulationsofproteinevolution
Themethodsusedtosimulateproteinevolutionhavebeendescribedpreviously(11,23,24).
The free energy 𝐺(𝐗, 𝐫) of a protein sequence 𝐗 = {𝑥! , 𝑥! , 𝑥! … 𝑥! } in conformation 𝐫 was
calculatedbysummingthepair-wiseenergiesofaminoacidsincontactinthatconformation,
using the contact potentials derived by Miyazawa and Jernigan (37). We computed the free
energy of folding Δ𝐺Folding (𝐗) by first determining the free energy of the sequence in a prechosennativestate,theconformationofthe300-residuepurpleacidphosphatase,PDB1QHW
bioRxiv preprint first posted online May. 31, 2016; doi: http://dx.doi.org/10.1101/056325. The copyright holder for this preprint (which was not
peer-reviewed) is the author/funder. It is made available under a CC-BY-NC-ND 4.0 International license.
(38)).TheenergiesoftheunfoldedstateswereassumedtofollowaGaussiandistributionwith
parameters estimated by calculating the free energy of the sequence in an ensemble of 55
different structurally diverse protein structures. The energy of the unfolded state was then
calculated by assuming a large set (10160) of possible unfolded structures with free energies
drawn from that distribution. The free energy of folding Δ𝐺!"#$%&' (𝐗) was calculated as the
differencebetweenthetwo,andstabilitywasΞ 𝐗 = −Δ𝐺!"#$%&' (𝐗).TheMalthusianfitnessof
a sequence m 𝐗 was defined as the fraction of that sequence that would be folded to the
nativestateatequilibrium
Ξ(𝐗)
𝑇
𝑚(𝐗) = Ξ(𝐗)
1 + exp 𝑇
exp
(2)
whereTisthetemperatureinunitsofenergy,0.6kcalmol-1.
Startingfromarandomlychosennucleotidesequenceencodinga300amino-acidprotein,we
simulated evolution by considering in each step all possible nucleotide mutations with rates
givenbytheK80nucleotidemodel(κ = 2)(39).Thefixationprobabilityofeachmutationwas
calculatedbasedontheKimuraformulafordiploidorganisms(30-32),
!
𝑃!"#
1 − e!!(!(!(𝐗 ))!!(!(!)))
𝐗, 𝐗′ =
!
1 − e!!!! (!(!(𝐗 ))!!(!(!)))
(3)
where𝐗and𝐗 ! arethesequencesbeforeandafterthemutation,withtheeffectivepopulation
size𝑁! setto106.Onesubstitutionwaschosentobefixedatrandomwithrelativeprobabilities
determinedbytheproductofthemutationratestimestheacceptanceprobabilities.
Sequenceevolutionwassimulatedforasufficientnumberofgenerationssuchthatthestability
of the protein was roughly constant, representing mutation-drift selection balance. 100 such
equilibrated proteins were chosen, and three longer simulations were performed using each
these equilibrated proteins as initial starting sequences, for a total of 300 simulations. We
simulated the evolution of each lineage for an evolutionary distance of approximately seven
aminoacidreplacementsperaminoacidposition.
Groupingofsites
For ease of analysis, we divided the sites in the protein into four classes with similar
substitution rates. Substitution matrices were calculated individually for each site; due to the
length of the simulations, we had on average over 2000 substitutions at each site. We then
clustered the sites based on the off-diagonal elements of the substitution matrices using Kmeans clustering (40, 41). The resulting clusters were approximately of equal size, and class
bioRxiv preprint first posted online May. 31, 2016; doi: http://dx.doi.org/10.1101/056325. The copyright holder for this preprint (which was not
peer-reviewed) is the author/funder. It is made available under a CC-BY-NC-ND 4.0 International license.
membershipstronglydependentonhowburiedorexposedthesiteswereinthenativestate
(asindicatedbynumberofcontacts).Werankedtheclustersbysurfaceexposure,whereclass
1isthemostexposedand4isthemostburied.
Calculatingthesite-specificcontributiontoproteinstability
The site-specific contribution ξ!,! 𝐗 ∌ ! of amino acid α at focal site k as a function of the
amino acids 𝐗 ∌ ! at all sites excluding k is equal to Ξ{𝑥! , 𝑥! , 𝑥! … 𝑥!!! , α, 𝑥!!! … 𝑥! }, the
stability when the focal site is occupied by α, minus Ξ{𝑥! , 𝑥! , 𝑥! … 𝑥!!! , ∅, 𝑥!!! … 𝑥! } , the
stabilityofareferencestatewhenbyαisreplacedbyanon-interactingaminoacid∅,whilethe
rest of the sequence and thus all other interactions, are unchanged. The part of the stability
unaffected by this replacement is represented by the ‘bath’ interactions ξ!,Bath (𝐗 ∌ ! ) so that
Ξ(𝐗) = ξ!,! (𝐗 ∌ ! ) + ξ!,Bath (𝐗 ∌ ! ).
Calculatingthesubstitutionrateintegratingoverdistributionsoflocalcontributions
Theaveragerateforthesubstitutionα → βatsitek,𝑄!,!→! ,isequaltotheneutralsubstitution
rate υ!→! times the average probability of fixation, which is a function of the stability of the
proteinbeforeandafterthesubstitution.ThestandarddeviationofobservedvaluesofΞ,0.71
kcalmol-1,wassmallcomparedwiththerangeofvaluesofξ!,! (asshowninFigure1),allowing
ustorepresentthedistributionΞbyitsaverage,Ξ ≃ Ξ=9.27kcalmol-1.Weassumedthatthe
stabilitybeforethesubstitutionwasequaltoΞandafterthesubstitutionwasΞ + (ξ!,! − ξ!,! ).
Theaveragesubstitutionratewasthenestimatedas
𝑄!,!→! = υ!→! ∬
!!!
!!!
!! ! !! !!,! !!!,!
!!!! ! !! !!,! !!!,!
!! !
!! !
ρ!,! ξ!,! , ξ!,! dξ!,! dξ!,! ,
(4)
whereρ!,! ξ!,! , ξ!,! isthejointdistributionofξ!,! andξ!,! observedwhenαoccupiessitek.
Based on the observations in Figure 1, we modeled ρ!,! ξ!,! , ξ!,! as a bivariate normal
distribution of the form ρ!,! (ξ!,! , ξ!,! ) = 𝒩(ξ!,!|! , ξ!,!|! , σ!!,!|! , σ!!,!|! , φ!,!"|! ), where the
parametersarerepresentedasexplicitlydependingontheaminoacidoccupyingsitek.These
parameters were calculated directly from the evolutionary simulation, and Equation (4 was
integrated numerically. The neutral substitution rate was calculated using the same K80
nucleotide model (κ = 2)(39) as used in the simulation, with all non-nonsense codons
consideredequallylikely.
Calculatingthesubstitutionrateintegratingassumingonlyneutralsubstitutions
As observed in Figure 1, substitutions generally occur in a neutral region in which ΔΞ!,!→! =
ξ!,! − ξ!,! ≈ 0,sothat
bioRxiv preprint first posted online May. 31, 2016; doi: http://dx.doi.org/10.1101/056325. The copyright holder for this preprint (which was not
peer-reviewed) is the author/funder. It is made available under a CC-BY-NC-ND 4.0 International license.
1 − e!!(!(!!(!!,! !!!,! ))!!(!))
1 − e!!!! (!(!!(!!,! !!!,! ))!!(!))
≈ 1.
(5)
Thisconditionissatisfiedinabandofwidth2εcentredonξ!,! = ξ!,! ,whereεrepresentsthe
deviation from strict neutrality that is still sufficiently close for Equation (5 to be sufficiently
accurate.
We can obtain a natural scale for ε by considering the concept of ‘free fitness’ Φ Ξ of the
! !
protein equal to Φ Ξ = 𝑚 Ξ + !! (42, 43). Free fitness, analogous to its thermodynamic
!
equivalent ‘free energy’ where 𝑇 is replaced by 4𝑁! , encompasses the contributions of both
fitnessandsequenceentropyindeterminingthedistributionofstates;evolutionarydynamics
movestowardsmaximisingthisquantity.Assuming𝑆 Ξ = ln Ω! 𝑒 !γ! whereΩ! isaconstant,
andnotingthatthesystemisatequilibriumwith
!" Ξ
!!
𝜕 4𝑁! 𝑚 Ξ
𝜕Ξ
= 0whenΞ=Ξ,wecanseethat
= γ
(6)
!!Ξ
Thus,γdefinestherateofchangeofthepopulation-weightedfitness4𝑁! 𝑚 Ξ withstability.
!
Alternatively,achangeinstabilityof γ correspondstoaunitchangeinthepopulation-weighted
!
fitness.Inourcalculations,weequatedε = γ ;theestimationofγisdescribedbelow.Notethat
this calculation demonstrates that ε is, surprisingly, independent of effective population size
𝑁! . This is a result of the balance between selection and mutational drift at equilibrium; for
!" !
fixedeffectofmutationaldrift,thedegreeofselection(
populationsizesothattheirproductisconstant(34,35).
!!
)adjuststochangesineffective
Ifweassumethatρ!,! ξ!,! , ξ!,! isbroaderthanε,andthatEquation(5issatisfied,Equation(4
becomes
!"!
𝑄!,!→!
= 2ε υ!→! ∬ ρ!,! ξ!,! , ξ!,! δ ξ!,! − ξ!,! dξ!,! dξ!,! (ξ!,!|! − ξ!,!|! )!
exp −
2(σ!!,!|! + σ!!,!|! − 2φ!,!"|! σ!,!|! σ!,!|! )
= υ!→! ε
!
!
2π σ!,!|! + σ!,!|! − 2φ!,!"|! σ!,!|! σ!,!|!
where δ ξ!,! − ξ!,! istheDiracdeltafunction.
(7)
bioRxiv preprint first posted online May. 31, 2016; doi: http://dx.doi.org/10.1101/056325. The copyright holder for this preprint (which was not
peer-reviewed) is the author/funder. It is made available under a CC-BY-NC-ND 4.0 International license.
For highly similar amino acids the entire distribution of ρ!,! ξ!,! , ξ!,! may be contained in a
regionsignificantlynarrowerthantheneutralzone,resultinginanoverestimationof𝑄!,!→! >
υ!→! .Forthisreason,theestimatedratewascappedattheneutralrateυ!→! .
Characterisingthebathstatedistribution
Asdescribedabove,weassumethatthenumberofproteinsequenceswithagivenvalueofΞin
the range of interest around Ξ = Ξ is approximately exponential Ω(Ξ)~ 𝑒 !!" . To estimate γ,
weconsiderthedistributionofchangesinstabilityresultingfromrandommutations,ρ!"# ΔΞ .
Theaveragechangeinstability ρ!"# ΔΞ isnegativeduetothegreaternumberofsequences
codingforproteinswithlowerstability.ThissuggeststhatifwecorrectforthedependenceofΩ
on Ξ by multiplying ρ!"# ΔΞ by 𝑒 !"# , this bias would disappear. We adjusted γ so that
ΔΞ𝑒 !"# = 0 where the average was over all possible mutations during the simulations,
yieldingγ = 1.26(kcalmol-1)-1.
LiteratureCited
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
M.Kimura,Someproblemsofstochasticprocessesingenetics.Ann.Math.Stat.28,
882–901(1957).
M.Kimura,Ontheprobabilityoffixationofmutantgenesinapopulation.Genetics47,
713-719(1962).
J.F.Crow,M.Kimura,Anintroductiontopopulationgeneticstheory.(Harper&Row,
NewYork,1970).
S.V.Muse,B.S.Gaut,Alikelihoodapproachforcomparingsynonymousand
nonsynonymousnucleotidesubstitutionrates,withapplicationtothechloroplast
genome.MolBiolEvol11,715-724(1994).
R.Nielsen,Z.Yang,Likelihoodmodelsfordetectingpositivelyselectedaminoacidsites
andapplicationstotheHIV-1envelopegene.Genetics148,929-936(1998).
A.U.Tamuri,M.DosReis,A.J.Hay,R.A.Goldstein,Identifyingchangesinselective
constraints:hostshiftsininfluenza.PLoSComputBiol5,e1000564(2009).
G.A.Bazykin,Changingpreferences:deformationofsinglepositionaminoacidfitness
landscapesandevolutionofproteins.BiolLett11,(2015).
M.Figliuzzi,H.Jacquier,A.Schug,O.Tenaillon,M.Weigt,CoevolutionaryLandscape
InferenceandtheContext-DependenceofMutationsinBeta-LactamaseTEM-1.MolBiol
Evol33,268-280(2016).
D.M.McCandlish,E.Rajon,P.Shah,Y.Ding,J.B.Plotkin,Theroleofepistasisinprotein
evolution.Nature497,E1-2;discussionE2-3(2013).
D.D.Pollock,R.A.Goldstein,Strongevidenceforproteinepistasis,weakevidence
againstit.ProcNatlAcadSciUSA111,E1450(2014).
D.D.Pollock,G.Thiltgen,R.A.Goldstein,Aminoacidcoevolutioninducesan
evolutionaryStokesshift.ProcNatlAcadSciUSA109,E1352-1359(2012).
P.Shah,D.M.McCandlish,J.B.Plotkin,Contingencyandentrenchmentinprotein
evolutionunderpurifyingselection.ProcNatlAcadSciUSA112,E3226-3235(2015).
bioRxiv preprint first posted online May. 31, 2016; doi: http://dx.doi.org/10.1101/056325. The copyright holder for this preprint (which was not
peer-reviewed) is the author/funder. It is made available under a CC-BY-NC-ND 4.0 International license.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
R.A.Goldstein,S.T.Pollard,S.D.Shah,D.D.Pollock,NonadaptiveAminoAcid
ConvergenceRatesDecreaseoverTime.MolBiolEvol32,1373-1381(2015).
J.M.Koshi,R.A.Goldstein,Modelsofnaturalmutationsincludingsiteheterogeneity.
Proteins32,289-295(1998).
N.Lartillot,H.Philippe,ABayesianmixturemodelforacross-siteheterogeneitiesinthe
amino-acidreplacementprocess.MolBiolEvol21,1095-1109(2004).
T.Pupko,N.Galtier,Acovarion-basedmethodfordetectingmolecularadaptation:
applicationtotheevolutionofprimatemitochondrialgenomes.ProcRSocLondB269,
1313-1316(2002).
D.Penny,B.J.McComish,M.A.Charleston,M.D.Hendy,Mathematicalelegancewith
biochemicalrealism:thecovarionmodelofmolecularevolution.JournalofMolecular
Evolution53,711-723(2001).
M.M.Miyamoto,W.M.Fitch,Testingthecovarionhypothesisofmolecularevolution.
MolBiolEvol12,503-513(1995).
N.Galtier,Maximum-likelihoodphylogeneticanalysisunderacovarion-likemodel.Mol
BiolEvol18,866-873(2001).
B.P.Blackburne,A.J.Hay,R.A.Goldstein,ChangingSelectivePressureduringAntigenic
ChangesinHumanInfluenzaH3.PLoSPathogens4,e1000058(2008).
D.M.Robinson,D.T.Jones,H.Kishino,N.Goldman,J.L.Thorne,Proteinevolutionwith
dependenceamongcodonsduetotertiarystructure.MolBiolEvol20,1692-1704
(2003).
N.Rodrigue,N.Lartillot,D.Bryant,H.Philippe,Siteinterdependenceattributedto
tertiarystructureinaminoacidsequenceevolution.Gene347,207-217(2005).
R.A.Goldstein,Theevolutionandevolutionaryconsequencesofmarginal
thermostabilityinproteins.Proteins79,1396-1407(2011).
P.D.Williams,D.D.Pollock,B.P.Blackburne,R.A.Goldstein,Assessingtheaccuracyof
ancestralproteinreconstructionmethods.PLoSComputBiol2,e69(2006).
P.L.Privalov,Stabilityofproteins:smallglobularproteins.AdvProteinChem33,167241(1979).
P.L.Privalov,S.J.Gill,Stabilityofprotein-structureandhydrophobocinteraction.
AdvancesinProteinChemistry39,191-234(1988).
D.M.Taverna,R.A.Goldstein,Whyareproteinsmarginallystable?Proteins46,105-109
(2002).
K.B.Zeldovich,E.I.Shakhnovich,Understandingproteinevolution:fromproteinphysics
toDarwinianselection.AnnuRevPhysChem59,105-127(2008).
R.A.Goldstein,D.D.Pollock,Thetangledbankofaminoacids.ProteinSci,(2016).
J.F.Crow,M.Kimura,others,Anintroductiontopopulationgeneticstheory.An
introductiontopopulationgeneticstheory.,(1970).
M.Kimura,Someproblemsofstochasticprocessesingenetics.TheAnnalsof
MathematicalStatistics,882–901(1957).
M.Kimura,Ontheprobabilityoffixationofmutantgenesinapopulation.Genetics47,
(1962).
H.Eyring,TheActivatedComplexinChemicalReactions.JChemPhys3,107-115(1935).
bioRxiv preprint first posted online May. 31, 2016; doi: http://dx.doi.org/10.1101/056325. The copyright holder for this preprint (which was not
peer-reviewed) is the author/funder. It is made available under a CC-BY-NC-ND 4.0 International license.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
J.L.Cherry,Shouldweexpectsubstitutionratetodependonpopulationsize?Genetics
150,911-919(1998).
R.A.Goldstein,Populationsizedependenceoffitnesseffectdistributionand
substitutionrateprobedbybiophysicalmodelofproteinthermostability.GenomeBiol
Evol5,1584-1593(2013).
R.Fisher,TheGeneticTheoryofNaturalSelection.(OxfordUniversityPress,Oxford,
1930).
S.Miyazawa,R.L.Jernigan,Estimationofeffectiveinterresiduecontactenergiesfrom
proteincrystalstructures:quasi-chemicalapproximation.Macromolecules18,534–552
(1985).
Y.Lindqvist,E.Johansson,H.Kaija,P.Vihko,G.Schneider,Three-dimensionalstructure
ofamammalianpurpleacidphosphataseat2.2\AAresolutionwithaμ-(hydr)oxo
bridgeddi-ironcenter.Journalofmolecularbiology291,135–147(1999).
M.Kimura,Asimplemethodforestimatingevolutionaryratesofbasesubstitutions
throughcomparativestudiesofnucleotidesequences.Journalofmolecularevolution
16,111–120(1980).
E.W.Forgy,Clusteranalysisofmultivariatedata:efficiencyversusinterpretabilityof
classifications.Biometrics21,768-769(1965).
S.Lloyd,LeastsquaresquantizationinPCM.IEEETransactionsonInformationTheory28,
129-137(1982).
Y.Iwasa,Freefitnessthatalwaysincreasesinevolution.JTheorBiol135,265-281
(1988).
G.Sella,A.E.Hirsh,Theapplicationofstatisticalphysicstoevolutionarybiology.Proc
NatlAcadSciUSA102,9541-9546(2005).