Structural and Thermodynamic Studies of Synuclein Proteins Related to Parkinson’s Disease: - Metallic Systems: A Quantum Chemist's Perspective - page 43

The.most.widely.used.force.ields.include.parameters.for.the.atomic.mass,.van.
der.Waals.radius,.and.partial.charge.of.each.atom..In.addition,.force.ields.may.con-
tain.equilibrium.values.of.bond.lengths,.bond.angles,.and.dihedral.angles.for.two,.
three,.and.four.atoms,.respectively,.and.corresponding.force.constants..Most.force.
ields.have.ixed.partial.charges.on.the.atoms,.thus.the.partial.charge.of.a.speciic.
atom.does.not.correlate.with.a.change.in.the.conformation.of.a.given.biocomplex..
However,. the. newest. force. ields. incorporate. polarizability. in. their. parameteriza-
tion.and.are.able.to.describe.the.change.of.the.atomic.partial.charge.via.interactions.
with. surrounding. atoms.. The. use. of. a. polarizable. force. ield. model. is. generally.
more.expensive.(in.terms.of.CPU.time).than.the.corresponding.ixed.partial.charge.
model.
Force.ield.parameters.enable.the.calculation.of.the.potential.energy.of.the.system.
via.calculation.of.bonded.(covalent.bonds).and.nonbonded.terms.(electrostatic.and.van.
der.Waals.interactions)..Classical.MD.simulations.are.not.capable.of.bond-breaking.
and. bond-forming. interactions. due. to. the. nature. of. the. potential. energy. function..
Additionally,. dihedral. angle. potentials. and. improper. torsion. potentials,. which. are.
needed.to.represent.the.planarity.of.aromatic.and.conjugated.compounds,.are.added.
to. the. potential. energy. function.. The. van. der. Waals. term. is. calculated. using. the.
Lennard-Jones.potential.and.the.electrostatic.term.is.computed.via.Coloumb's.law. 50 .
In. our. classical. MD. simulations,. we. use. the. CHARMM27. force. ield. parameter.
set. 51 .Using.this.force.ield,.the.potential.energy.is.calculated.via

1
2

1
2

1
2

∑ ∑ ∑

( ) +

2

( ) +

2

V r ( ) = K b b − K θ θ − K [ 1 + cos( n φ δ ] − )

b 0 θ 0 φ

bonds angles torsional

⎡

12 6

⎤

σ σ q q

∑

⎛
⎜

⎞
⎟

− ⎛

⎞
⎟

∑

1 2

+ 4 ε + . (2.8)

⎢
⎢

⎥
⎥

⎜

r r r

⎣ ⎦

12

vanderWaals electrostatic

.

The. irst. three. terms. of. the. potential. function. (Equation. 2.8). are. bonded. interac-
tions,.which.represent.the.interaction.energy.between.two.(bonds),.three.(bending.
angles),.and.four.(torsion.angles).atoms.joined.by.one,.two,.and.three.bonds,.respec-
tively..The.last.two.terms.represent.the.contribution.due.to.nonbonded.interactions,.
i.e.,. van. der. Waals. and. electrostatic. interactions,. respectively.. The. parameters. in.
each.term.are.usually.obtained.via.itting.data.from.quantum.chemistry.calculations.
and/or. spectroscopic. measurements.. The. interaction. energy. between. two. atoms. is.
described.by.a.harmonic.potential.as.a.function.of.the.deviation.of.a.bond.length. b .
from.its.equilibrium.value. b 0 ..The.force.constant. K b .describes.the.interaction.of.the.
bonds,.and.is.usually.it.to.experimental.infrared.stretching.frequencies.or.frequen-
cies. calculated. using. quantum. chemistry.. The. equilibrium. bond. length. b 0 . can. be.
inferred. from. high-resolution. crystal. structures. or. determined. from. spectroscopy..
The.second.term.of.the.potential.energy.function.(Equation.2.8).describes.the.bend-
ing.interaction.between.three.bonded.atoms..The.energy.arising.due.to.the.devia-
tion.of.the.bond.angle.θ.from.its.equilibrium.angle.θ 0 .is.expressed.by.a.harmonic.
potential. function. with. a. force. constant. K θ .. The. third. term. describes. the. torsion.