Structural and Thermodynamic Studies of Synuclein Proteins Related to Parkinson’s Disease: - Metallic Systems: A Quantum Chemist's Perspective - page 50

entropy.calculations.based.on.the.Schlitter.method.were.employed.for.calculating.the.
entropy.for.each.protein.using.separate.simulations. 63 .The.Schlitter.formula.yields.an.
upper.bound.to.the.true.entropy.( S true )

⎡
⎢

⎤
⎥

1
2

k Te M

2

B

S < S = k ln det 1 + σ . (2.22d)

true B

h 2

.

where
k B .is.the.Boltzmann.constant
T .is.the.temperature
e .is.Euler's.number
h .is.Planck's.constant
M .is.a.diagonal.matrix.of.masses.associated.with.the.atomic.degree.of.freedom
σ. is. the. covariance. matrix. of. atom. luctuations. deined. as.

( )

( )

σ ij = x − x x − x

i i j j

x i . are. the. coordinates. after. least. squares. superposition. of. the. trajectory. with.
respect. to. all.protein. backbone. atoms.. Even. though. the. selection. of. protein. atoms.
in. these. calculations. might. inluence. the. translational. and. rotational. calculations.
of.the.entropy,.it.is.shown.that.this.inluence.is.negligible.for.relative.comparisons..
The.energies.and.entropies.were.calculated.using.all.trajectories.for.gaining.insights.
into. the. convergence. and. the. impact. of. simulation. time. on. these. thermodynamic.
properties.

2.3 RESULTS AND DISCUSSION
The. structures. of. aqueous. and. micelle-bound. α-synuclein. have. been. determined.
experimentally.using.NMR.techniques.by.Ulmer.et.al. 29,64 .The.micelle-bound.struc-
ture. shows. anti-parallel. α-helical. conformation. from. residues. 3. to. 37. (which. has.
been. termed. as. the. N-helix). and. 45. to. 92. (which. has. been. termed. as. the. C-helix).
with.a.short.extended.region.from.93.to.97. 29 .The.rest.of.the.protein.is.unstructured.
according.to.the.experimental.observations. 29 .The.structure.of.the.free.α-synuclein.
protein.has.also.been.investigated.experimentally.by.Ulmer.et.al..as.well.as.Elsevier.
et.al..using. NMR.techniques. 64,65 .Both.experiments.showed. that. the.irst.100.resi-
dues.have.a.preference.toward.a.helical.structure.while.the.40.C-terminal.residues.
lack.any.secondary.structural.conformation. 64,65 .The.structure.of.the.A53T.mutant.
has.also.been.determined.experimentally.via.NMR.techniques.by.Ulmer.et.al..and.
the. results. show. that. the. structure. of. the. micelle-bound. A53T. mutant. is. indistin-
guishable. from. the. wild-type. by. NMR. techniques. 64 . Uversky. et. al.. characterized.
wild-type.α-synuclein.and.the.A53T.and.A30P.mutants.in.free.solution.through.far-
ultraviolet-circular. dichroism. (far-UV-CD). and. Fourier. transform. infrared. (FTIR).
measurements.and.found.that.at.physiological.pH,.the.structures.of.the.three.varia-
tions. of. the. proteins. are. virtually. indistinguishable. 30,31 . However,. our. simulations.
show.that.there.are.differences.in.the.structures.of.the.wild-type.and.A53T.mutant.