A mathematical model for the reaction mechanism of the enzyme alcohol dehydrogenase

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A MATHEMATICAT MODEL FOR THE REACTION MECHANISM

OF T}IE ENZVME ALCüIOL DEI{YOROÊENASE

by

MncAwr

J)AII ATKINffiN, B.Sè.

A

thesls

submitted

for

adm{ssion

to the

degrce

of

^t*laster

of Agricultural

^Sclence

June

¹⁹⁷²

rABLE OF CONTENTS

&lþfulAW

Deelantíon

^.

..

Aelotot'tLedgements

Intnoduction .,.

I

PaÞe

I

L 1,7,1,

iv

u

t0

l2 l2

13

t4 r6

L7

t8 t9

20 CTTAPÎER

I

l. Early

development

of

ldeas about enzyriles

2.

FornuLatLon

of reactlon

^mechauLsm

...

3.

^PhysLcal fmpllcatf.ons

of the sfnple

^model

4. Derfvatlon of the Mlchaells equatfon ...

5.

Steady

state

theory

6.

Study

of tra¡rslent behavlour ...

7. Integrated rate equatlons ...

CIIAPTER

II

I

3

4 6

I I

2

3 4

Enzlmlc

reactfons

Lnvolvlng two substrates ^and two

products ...

Liver alcohol dehydrogenase ...

The Theorell-Chance mecha¡rÍen

Mathenatfcal formulatLon

of the

Theorell-Chance

mechanfsm ...

Estfmatfon

of the velocfty constants ...

5

CHAPTER

III

l.

Spectrophotonetrlc ^methods

2.

^Foru

of data ...

3.

Erçerlmeotal

urethod ...

4.

Sources

of error ...

IABLE OF CONTEN?S (eontiruted)

CHAPTER IV

Page

2l

24 24 25

27

...

²⁷

29

l.

Duratfon

of translent phase ...

2.

Steady

gtate solutfon ...

3,

A modiftcaÈlon

to the

steady

Btate

^eolutfon

4.

Least squares

estlnatlon of the

Parameters

4.I

Three-parameter equatlon

4.2

Four-parameter

equatlon ...

25 26

CHAPÎER V

l.

Nr¡r¡erical

eolutl.on

^{. . .}

2.

llethod

of estf¡atLon of the velocÍty

conetants

3. Results ...

CHAPTER VI

1.

l[echanlsm

of actlon of yeast

^alcohol

dehydrogenase ...

2.

ExperÍrnental

nethod '.

^.

3.

Estfmatlon

of the velocl.ty

constarits

GTAPTER

VII

l. Flttlng of e:çonentfal

curves

to the daÈa ...

2. Dfrect

estfnatLon

of the velocLty

^{constants by}

nuuerlcal eolution of the differentfal

equatÍone ...

3.

l"fechanisn

of actfoo of lfver

^alcohol

dehydrogenase ...

4.

Mechanisn

of actlon of

^yeaeÈ alcohol

dehydrogenase ...

5.

^Value

of cmputer

technlqr-res

in

^aseeeel.ng

reactÍon models ...

30 31 32

33

35

37

38 40

IABLE OF C1N?ENIS (eantínued)

APPE¡IDIX

I

Form

of solutlon of

^equaÈfons

I.3 - I.5

APPENDIX

II

Reductlon

of reactlon

model equatlone

Page

4L

43

46

57 58

61

70 APPENDIX

III

Experimental

results

and

predicted

concenÈratÍons

of

^NADH obtalned

by the

methods described

ln

Chapters

IV

and V

APPEI'{¡DIX IV

1. Solutlon of

equatlon

IV.ll 2. SolutÍon of

equatlon IV.16

APPENDIX V

tomputer programs

BIBLIOGRAPHY

7r.

I

2.

3.

SUNITTARY

A

set of

slmultaneouE non-l1near

dlfferentlal

^{equatlons !'tas}

derived

from

stoichLonetrlc

eguatfons !ühlch descrLbe the Theorell-Ctrance ^mechanlsm

for lÍver alcohol

dehydrogenase'

Assumlng

that the

coricenËratfons

of the Ínternedlate

complexes renalned constanË, an

e:çlÍcft solutlon

^fnvolvLng

three

^unknown paraneters !üas obtafned

for the dlfferentLal equatl-ons.

Relaxatfon

of the

assumptfons ^Ëo

permft

the concentratlon

of

one

of the

fncemedlaÈes

to

change

llnearly rvlth ttne

^gave

rLse to a

four-Parameter

solutf-on'

^The

values

of the

unknon Parameters Ln

the

two types

of

solutlon

were estfmated from experfmental data

by the

nethod

of least

^squafes.

A computer ^program ¡¡as

wrltten to

^provfde a numerÍcal

solutlon of the differentlal

^{equatlons and}

the solutfon

^was

used

to obtafn

estlmstes

of the veloclty

^constants

for

the Theorell-Chance

nechanlsn.

^The

valtdfty of thfs

^model

for

llver alcohol

dehydrogenaÉ¡e lùas checked under

different

erçerlmental condltfons.

^{ThÍs nechanisu aPpears}

to

be

valfd

for the reactlon

^{when NAÐ} cofrcentrations ^{between 80 UM and} 240 uM

are

used.

T'L¿

4. The reacÈlon

of yeast alcohol

dehydrogenaee was elso exanÍoed 1n

relatl.on to the

Theorell-Cha¡rce mechanlsm.

Estfmates

of velocl.ty

constanÈa lüere obtained and nunerl'cal

solutfons fro¡r the cotputer

_Progran ^compared

wlth

experÍmental

data.

^Ttre

resulte of thfs

lnveaÈtgatfon appeer

to

support a¡r

alternstlve

mecha¡rlsm

lnvolvlng

the

fonratlon of a ternary

conplex as propoSed by

Theorell

and Ctrance.

LL7..

DECLARA?TON

L

hereby

deelare that the

work presented

ln this thesis

hae been performed by

nyself

excePt where

other- wise stated,

and

that Ít

hae

not

been subDl.tted 1n any

prevfous

applfcatlon for

any degree.

T,T.

J.

^ATTøNSON

June 1972

L0t

A C

KN

O ^W

LEDGEMENTS

I wlsh to

^thank

ny

guPervfsors, Professor D.J'D' Nfcholas (bfoche'n'letry) arid Profe8sor

A.T.

James and

!lr.

^Ì'1.8.

Taylor (sÈatfstlcs), for thefr help

^{and advLce}

wfth thLs

^work.

Thanke

are also

due

to Mrs. llelen

Brereton

for

Ëechnfcal asslstance ¡¿fth

the

blochenfcal work.

7).

rNTR ODUCTTON

Enz¡mres

are naturally

occurrlnS orgaoÍc ^{compounds whfch} fûcrease

the rates of

^cerÈaln chemfcal reactLons whl1e themselves remalnfng unchanged.

the

study

of

enz¡¡mes 1s

of great lnterest slnce, to

^{quote DIXON and I^IEBB}

(f964):

"Llfe

^{depends on}

a

^{comPlex network}

of

chenlcaL

reactlons

brought about

by speciflc

enzymes, and any ^nrodlf

lcation of the

^enz)me

pattern

uray have

far

^reachfng consequences

for the llvlng

organÍsm."

usually

an enzyme La detected

by its reactfons wlth

^a

substrate.

^The æount present

ls

estimated from

the

reacÈfon ve1oc1ty.

Many workers have sÈudfed

the relatlonshlps

between the

rate of

enzymlc reactlOn and

varlous

envlronmental

fact6rs,

^such

as concentration

of

^{enzlme and}

of subetrate,

temPerature and ^pH.

These observatlons may be used

to

formulate

kinetfc

^equatLons

whfch descrlbe

the reactlon.

This lnvestlgatÍon ls

^concerned

wlth the

formul.atlon

of

mathenatl'cal models

of

enzyufc

reactfons'

and

htfth the testlng of

these models

by

couparlng predlctLons based upon ^Èhem

with

daÈa obtalned

fron actual

o<periments.