2.2 Marco teórico
2.2.1 Evaluación del impacto ambiental EIA
Chemical.kinetics.describe.the.rates.at.which.reactants.disappear.and.products.appear.in.chemical.
reactions.under.idealized.conditions..Chemical.kinetics.are.based.on.the.law of mass action,.which,.
in.turn,.is.based.on.the.assumptions.that.the.reacting.and.product.molecular.species.are.well.mixed.
and.free.to.move.in.a.closed.vessel.(i.e.,.they.are.not.bound.to.a.surface.similar.to.a.mitochondrial.
membrane.or.a.cell.surface),.and.there.are.no.diffusion.barriers..Furthermore,.we.assume.that.the.
molecules.and.ions.in.the.vessel.are.in.solution.in.weak.concentrations.and.move.randomly.because.
of.thermal.energy.and.momentum.exchanges.due.to.collisions.with.themselves.and.one.another..The.
law.of.mass.action.is.based.on.the.probabilities.that.molecular.species.will.collide.and.react;.that.
is,.bonds.will.be.broken.and.made..Basically,.it.states.that.the.rate.at.which.a.chemical.is.produced.
in.a.reaction.(at.a.constant.temperature).is.proportional.to.the.product.of.the.concentrations.of.the.
reactants..Thus,.a.chemical.reaction.described.by.mass.action.kinetics.can.be.expressed.as.a.set.of.
first-order.ordinary differential equations (ODEs)..These.ODEs.are.generally.nonlinear.and.can.
have.time-varying.coefficients.
For.example,.if.two.reactants.combine.and.form.a.product,.C:
A + B → C (4.4)
Introduction to Physical Biochemistry and Biochemical Systems Modeling
Then.by.mass.action.the.rate.of.appearance.of.C.is.given.by.the.simple.first-order.nonlinear.ODE:
. d C
dt k A B
[ ]= [ ][ ]. (4.5)
Also,.it.is.easy.to.see.that.both.the.reactants.behave.as
. d A
dt d B
dt k A B
[ ]= [ ]= − [ ][ ]. (4.6)
In.these.simple.ODEs,.brackets.[*].denote.a.concentration,.such.as.moles/liter..k.is.the.reaction rate constant,.given.by.the.Arrhenius relation [Maron.&.Prutton.1958]..Note.that.k.has.temperature.
dependence.given.by.Equation.4.7:
. k.=.ko.exp(−Ea/RT). (4.7)
where.ko.is.a.positive.constant.(prefactor),.Ea.is.the.activation energy of.the.reaction.in.joules.per.
mole.(recall.that.Ea.is.lowered.by.enzymes),.T.is.the.Kelvin.temperature,.and.R.is.the.SI.gas con-stant.=.8.31441.J/(mole.K).
Another.way.of.writing.Equation.4.5.is.to.let.a.=.the.initial.concentration.of.A,.b.=.the.initial.
concentration.of.B,.and.x.=.the.number.of.moles.of.C.made.at.time.t.(a.“running”.concentration)..
Thus,.for.t.≥.0:
. x.=.k.(a.−.x)(b.−.x).=.k.[ab.−.x(a.+.b).+.x2].(moles/liter)/sec,.where.x.≡.dx/dt. (4.8) Note.that.a.reaction.may.be.reversible..For.example,.a.product,.C,.can.spontaneously.dissociate.
back.into.the.two.reactants,.A.and.B..Reversibility.is.represented.by.Reaction.4.9.in.the.following.
text..Note.that.the.forward.reaction.rate.constant,.k1 ,.is.in.general.different.from.the.reverse.con-stant,.k−1.
A B+ →← kk−11 C (4.9)
Now.we.can.write.three.ODEs.based.on.mass.action:
. d A
dt[ ]=k C k A B−1[ ]− 1[ ][ ]. (4.10)
d Bdt[ ]=k C k A B−1[ ]− 1[ ][ ]. (4.11)
. d C
dt k C k A B
[ ]= − −1[ ]+ 1[ ][ ]. (4.12)
Note.that.the.ODE.for.[A].is.identical.to.that.for.[B]..Also,.the.rate.constants.k1.and.k−1.do.not.have.
the.same.units..k−1.has.the.units.of.T−1,.and.k1.has.the.units.of.T−1.mole−1.=.(MT)−1L3.
Now.let.us.examine.a.reaction.in.which.two.molecules.of.B.must.combine.with.one.molecule.
of.A to.make.one.molecule.of.C:
A+2B →kC (4.13)
Mass.action.tells.us.that.the.rate.of.increase.of.the.molar.concentration.of.the.product,.C,.is.given.
by.the.ODE:
. d C
dt k A B
[ ]= [ ][ ]2. (4.14)
Note.that.the.concentration.of.B.is.squared.in.the.ODE.
In another example,.consider.the.physiologically.important.formation.and.decomposition.of.
carbonic acid..This.reaction.figures.in.the.regulation.of.the.acid–base.balance.in.body.fluids.and.
the.elimination.of.CO2.as.a.metabolic.waste.gas.[Guyton.1991,.Chapter.30].
H CO2 3 k H O CO2 2 k
1 1
−
→
← + . (4.15)
We.assume.that.water.is.present.in.excess;.let.x.=.the.concentration.of.carbonic.acid,.and.g.=.the.
concentration.of.dissolved.CO2.gas..Thus,.the.chemical.kinetic.ODE.is
. x .=.−k1.x.+.k−1.g. (4.16)
As a final example,.we.consider.the.important.Michaelis–Menton reaction (MMR)..The.MMR.
is.representative.of.a.typical.enzyme-catalyzed.reaction,.where.a.substrate.molecule,.S,.combines.
with.an.active.site.on.the.enzyme.to.form.a.complex,.S*E..In.the.complex,.the.enzyme.cleaves.off.
part.of.S.to.form.the.product,.P..(The.remainder.of.S.is.not.shown.in.the.reaction.).P.is.released.from.
the.intact.enzyme..The.product,.P,.is.assumed.to.be.removed.from.the.compartment.by.first-order.
kinetics.with.rate.constant,.k3..The.MMR.is.expressed.as.a.chemical.equation:
S E+ →← S E∗ → P E+
− ↓
k k
k k 1
1
2
* 3
(4.17)
Let.e.=.the.running.concentration.of.free.enzyme.at.time.t.>.0,.s.=.the.running.concentration.of.
the.substrate,.c.=.the.running.concentration.of.the.complex,.and.p.=.the.running.concentration.of.
the.product..Because.the.system.is.closed.and.the.enzyme.is.conserved,.we.can.write.the.auxiliary.
equation,.eo = e + c,.where.eo.is.the.total.(initial).concentration.of.enzyme.at.t.=.0..Note.that.the.
reactants.(S,.C,.and.P).all.have.initial.conditions.when.doing.a.simulation..The.mass.action.ODEs.
for.the.MMR.are
. s =.−.k1.(eo.−.c).s.+.k−1.c. (4.18A)
. c.=.k1.(eo.−.c).s.−.(k−1.+.k2).c. (4.18B)
. p .=.k2.c.−.k3.p. (4.18C)
Introduction to Physical Biochemistry and Biochemical Systems Modeling 0
Note.that.the.ODEs.for.s.and.c.are.nonlinear;.the.p.ODE.is.linear.
It.is.clear.that.complete.dynamic.solutions.of.the.three.Michaelis–Menton.ODEs.are.best.done.
by.computer,.using.a.program.such.as.Simnon® .(a.product.of.SSPA,.Sweden,.and.a.registered.trade- mark.of.Department.of.Automatic.Control,.Lund.Institute.of.Technology,.Sweden).or.Matlab/Simu-link.(Matlab.and.Simulink.are.trademarks.of.MathWorks,.Inc.,.Natick,.Massachusetts).
From.enzyme.conservation,.we.see.that.c = − e..In.the.steady state,.we.can.set.s = c = p
= 0,.because.no.concentration.is.changing..Now.we.can.solve.for.the.steady-state.concentration.of.
the.complex,.css:
. c k e s
where.KM≡ (k−1 + k2)/k1.is.the.well-known.Michaelis constant,.and.sss .is.the.steady-state.concentra-tion.of.the.substrate.(for.t.→.∞).
Under.conditions.of.constant.substrate.concentration.(S.is.replaced.as.fast.as.it.is.used.up),.s = so,.and.in.the.steady.state,.pss = (k2.css)/k3,.and.we.can.finally.write
. p k e s
be.modulated.in.time.by.allosteric.(feedback).regulation.and.competitive inhibition.
. impoRtant coupleD Reactions 4.2.1 introduction
A.characteristic.of.life.is.that.its.sustaining.biochemical.reactions.are.coupled..That.is,.these.vital.
reactions. tend. to. be. concatenated,. that. is,. joined. one. to. another. in. a. complex. topology.. There.
are.exceptions;. for.example,.shunt reactions.that.take. “shortcuts”. from. one. chemical. species. to.
another..The.linear.topology.makes.closed-loop.parametric.control.of.the.reactions.simpler.through.
complex. regulatory. networks.. Available. on. the. Internet,. the. Kyoto Encyclopedia of Genes and Genomes.(KEGG).contains.all.known.metabolic.pathways.and.some.of.the.known.regulatory.path-ways.in.about.100.hypermedia.diagrams.(click.on.a.section.of.a.diagram.and.download.details.of.
that.section)..The.metabolic.pathways.were.derived.in.part.from.the.Roche.Applied.Science.Bio-chemical Pathways.charts,.Parts.1.and.2,.and.the.Metabolic Maps.book.by.the.Japanese.Biochemi-cal.Society..A.KEGG.diagram.is.intended.as.a.reference.map.of.all.chemically feasible.pathways,.
not.a.consensus.of.known.pathways.in.different.genomes..“The.genome-specific.pathways.are.then.
automatically.generated.by.matching.the.enzyme.genes.in.the.gene.catalog.with.the.enzymes.on.the.
reference.pathway.diagrams”.[JGI.2004].
In.the.following.text,.we.describe.two.of.the.more.important.biochemical.energy-producing.
pathways.
4.2.2 glycolysis
Probably.one.of.the.more-studied.and.better-known.systems.of.coupled.reactions.is.glycolysis,.the.
first.step.in.the.complex.reactions.of.cellular.metabolism..Glycolysis.is.the.initial.reaction.pathway.
for.the.conversion.of.the.monosaccharide,.d-glucose,.into.chemical.energy..It.describes.the.anaero-bic.catabolism.of.glucose..Glycolysis.is.also.known.as.the.Embden–Meyerhoff Pathway.
Glycolysis.is.found.in.all.cells.(with.some.variations)..In.eukaryotes,.glycolysis.occurs.in.the.
cytosol;. a. “soup”. of. ions,. reactants,. products,. enzymes,. coenzymes,. redox,. and. energy-source.
molecules.(ATP,.GTP)..The.“input”.molecule.to.the.glycolysis.pathway.is.d-glucose..d-Glucose.
itself.can.come.from.enzymatic.transformation.of.other.monosaccharides.that,.in.turn,.can.arise.
from. enzymatic. cleavage. of. disaccharide. sugars. (e.g.,. sucrose). or. the. enzymatic. digestion. of.
starches.or.cellulose.
In. the. first step. of. glycolysis,. one. molecule. of. d-glucose. is. phosphorylated. by. the. enzyme.
hexokinase (HK),.using.the.energy.from.one.phosphate.bond.in.ATP..The.products.are.glucose-6-phosphate.(G6P),.ADP,.and.free.hexokinase..The.second step.in.glycolysis.is.the.conversion.of.G6P.
to.fructose-6-phosphate (F6P).by.the.enzyme.phosphoglucose isomerase.(PGI)..In.the.third reac-tion,.F6P.is.given.a.second.phosphate.group.by.the.enzyme.phosphofructokinase.(PFK).to.form.
fructose-1,6, biphosphate.(F1,6-BP)..ATP.is.also.used.in.this.reaction.for.its.energy..Next,.in.the.
fourth reaction,.the.hexose.sugar.F1,6-BP.is.lysed.by.the.enzyme.aldolase.to.form.two.triose sugars.
called.dihydroxyacetone phosphate.(DHAP)..(Now.we.have.two,.identical,.parallel.pathways..All.
the.reactions.described.in.the.following.paragraph.take.place.at.the.same.time..For.example,.one.
molecule.of.d-glucose.leads.to.two.GADP.molecules,.etc.)
In.the.fifth reaction,.in.each.of.two.parallel.pathways,.a.DHAP.molecule.is.acted.on.by.the.
enzyme.triose phosphate isomerase.to.form.glyceraldehyde-3-phosphate (GADP)..In.the.sixth reaction,.a.GADP is.acted.on.by.the.oxidoreductase.enzyme.glyceraldehyde-3-phosphate dehy-drogenase (GAP).to.become.1,3-biphosphoglycerate.(1,3BPG)..This.reaction.is.important.because.
the.hydrogen.displaced.by.the.phosphate.radical.is.used.to.reduce.a.molecule.of.nicotinamide adenine dinucleotide. (NAD+). to. NADH.. The. seventh reaction. in. glycolysis. yields. metabolic.
energy:.1,3BPG.reacts.with.the.enzyme.phosphoglycerate kinase (PGK).to.form.3-phosphoglyc-erate.(3PG),.plus.an.enzymatic.coupling.of.a.phosphate.to.ADP,.producing.one.molecule.of.ATP..
In.the.eighth reaction,.the.enzyme.phosphoglyceromutase.(PGAM).makes.3PG.into.2-phospho-glycerate.(2PG)..In.the.ninth reaction,.2PG.is.acted.on.by.enolase.to.form.phosphoenolpyruvate (PEP).. In. the. tenth step. in. glycolysis,. PEP. is. converted. by. pyruvate kinase (PK) into. the. end.
product,.pyruvic acid.(PA).or.pyruvate..In.this.last.step,.substrate-level.phosphorylation.makes.
another.ATP.molecule.from.ADP..Now,.because.there.are.two.parallel.DHAP.→.PA.pathways,.
the.glycolysis.system.of.coupled.reactions.yields.a.total.of.2(2.−.1).=.2.ATP.molecules.per.glucose.
molecule.input.[Farabee.2001].
In.yeasts,.an.extension.of.the.glycolysis.pathway.leads.to.fermentation..In.reaction eleven,.PA.
is.converted.to.acetaldehyde.by.pyruvate decarboxylase..One.molecule.of.CO2.gas.is.produced.in.
this.reaction..In.reaction twelve,.acetaldehyde.is.converted.to.ethanol.by.the.alcohol dehydrogenase enzyme..NADH.is.converted.to.NAD+.in.this.final.step..Note.that.one.molecule.of.glucose.produces.
two.molecules.of.CO2.and.two.molecules.of.ethanol.
Other.variations.of.fermentation.exist;.certain.bacteria.can.produce.methanol.or.methane gas.
by.similar.steps..Lactobacillus.sp..converts.two.PAs.to.two.lactic acids..Figure.4.1.illustrates.sche-matically.the.10.reactions.that.comprise.glycolysis,.as.well.as.one.form.of.fermentation.
Introduction to Physical Biochemistry and Biochemical Systems Modeling 0
OH
(Hexokinase) H
H OH
Glucose-6-phosphate Fructose-6-phosphate
ATP
Dihydroxyacetone phosphate Glyceraldehyde-3-phosphate (Triose phosphate
isomerase)
kinase) OH
OH
3-phosphoglycerate 2-phosphoglycerate 1,3-Biphosphoglycerate
Ethanol Acetaldehyde
Fermentation (2) Pyruvate
H C OH
Glucose + 2 ADP + 2 NAD++ 2 Pi 2 Pyruvate + 2 ATP + 2 NADH + 2 H++ 2 H2O
figuRe . Schematic.of.the.glycolysis.pathway.showing.one.fermentation.pathway..One.glucose.is.changed.to.two.pyruvates..Two.ATP.and.two.NADH.molecules.
are.produced.per.glucose.metabolized..In.the.fermentation,.one.pyruvate.produced.one.molecule.of.ethanol.at.the.expense.of.one.NADH.molecule.
The.overall.glycolysis.reaction.is.[Saccharomyces.2005]:
D-Glucose + 2 NAD+ + 2 ADP + 2 Pi.→ 2 Pyruvate
+ 2 NADH + 2 ATP + 2 H2O + 2 H+. (4.21)
Thus,.two.pyruvates.are.supplied.to.the.oxidative.citric.acid.(Krebs).cycle.for.every.glucose.mol-ecule.metabolized.in.glycolysis..Pyruvate kinase is.the.enzyme.that.attaches.the.Pi.(phosphate).to.
ADP.to.make.ATP.