Structural and Thermodynamic Studies of Synuclein Proteins Related to Parkinson’s Disease: - Metallic Systems: A Quantum Chemist's Perspective - page 46

and.thus.the.electrostatic.energy.is.approximated.via.integration.of.values.on.those.
grid.points. using. interpolation. functions.. The. summation. can. be. eficiently.calcu-
lated.using.the.fast.Fourier.transform.(FFT),.reducing.the.calculation.time.depen-
dence.from. O ( N 2 ).of.Ewald.summation.to. O ( N .log. N ).of.PME,.where. N .is.the.number.
of.atoms.in.the.periodic.box. 54 .The.method.of.PME.has.been.widely.applied.due.to.
its.high.eficiency.and.accuracy.
Speciic.details.about.the.simulations.are.now.presented..The.initial.α-synuclein.
structure.was.taken.from.the.protein.data.bank.(PDBID.1XQ8).and.was.placed.in.
a. box. with. dimension. 104.9.×.204.5.×.90.Å. containing. 61,921. water. molecules.. In.
order.to.neutralize.the.charge.of.the.system,.nine.sodium.ions.were.randomly.placed.
within.the.box..For.the.simulations.of.A53T,.the.structure.was.initially.placed.in.a.
box.containing.water.molecules.of.the.same.dimensions.as.for.α-synuclein.simula-
tions,. but. the. protein. shifted. out. of. the. box. during. the. initial. simulations. so. the.
dimensions.of.the.box.were.expanded.to.124.9.×.224.5.×.110.Å,.which.increased.the.
number.of.water.molecules.to.98,784..Again,.nine.sodium.ions.were.randomly.placed.
to.neutralize.the.system..Both.systems.were.minimized.for.10,000.steps.(20.ps).and.
then.the.system.was.gradually.heated.to.310.K.over.500.ps..The.simulations.then.ran.
for.an.additional.3.5.ns..The.integration.time.step.was.set.to.2.fs..The.simulation.was.
performed.using.periodic.boundary.conditions.as.described.in.detail.earlier..The.cut-
off.value.for.the.nonbonded.interactions.was.set.to.12.Å..The.full.long-range.electro-
static.interactions.were.calculated.using.the.PME.method.as.explained.earlier..The.
simulations.were.performed.using.the.isobaric-isothermal.ensemble.using.Langevin.
dynamics.to.control.the.temperature.and.the.Langevin.piston.method.to.maintain.the.
pressure.at.1.bar..The.RATTLE.algorithm.was.used.to.restrain.the.bonds.between.
the.hydrogen.atoms.and.heavy.atoms. 55 .For.simulations.in.the.gas.phase,.both.sys-
tems. were. minimized. for. 1000. steps. and. then. the. system. was. heated. to. 50.K. for.
200.ps..The.simulations.ran.for.an.additional.19.8.ns..The.gas-phase.simulations.were.
performed.using.the.canonical.ensemble.
Classical.MD.simulations.are.extremely.valuable.in.studies.of.biocomplexes.and.
biometallic. species. in. water,. though. their. accuracy. depends. on. the. quality. of. the.
force. ield. parameters. as. described. above.. The. classical. nature. of. the. simulations.
means.that.quantum.effects.that.are.not.accounted.for.in.the.parameterization.are.
ignored,. which. can. lead. to. errors. in. predicting. structure-function. relationships. of.
biometallic. species.. Despite. the. success. achieved. in. simulations. of. biomolecules,.
force.ield.parameters.cannot.give.an.accurate.representation.of.the.electronic.struc-
ture.of.metals.that.are.necessary.for.accurate.studies.of.the.coordination.chemistry.
between.biomolecules.and.transition.metal.ions..In.addition,.prediction.of.the.types.
of.bonding,.especially.π-bonding,.between.biomolecules.and.transition.metal.ions.is.
dificult.to.derive.from.classical.MD.simulations.
Recently,.multiscale.simulations.have.become.an.extensively.researched.area.in.
which.a.chemically.active.region.is.represented.using.quantum.mechanics,.a.region.
surrounding. the. quantum. mechanical. region. is. represented. using. force. ields,. and.
the.outermost.part.of.the.system.is.represented.using.coarse-grained.models. 47,56 .The.
positions. of. all. atoms. in. the. system. are. then. propagated. according. to. MD.. Here.
we. briely. introduce. the. concept. of. quantum. mechanical. (QM). calculations,. as.
well. as. the. combination. QM/MM,. which. is. used. to. investigate. the. mechanism. of.