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Unformatted text preview: ".Eri'iiiiﬁ'ékinetie ________________ . Enzyme Kinetics Cataiys Catalysts reduce the activation energy necessary for a reaction to occur. This is ts Liseful in biological systems were temperature increases cannot be used to
increase the reaction rate. The equilibrium constant is unchanged by the use ofa
catalyst. For the reaction 2H:O: —> 2H:O + 0:, products are formed at a relative rate of].
without any catalyst. The inorganic catalyst Fe3‘, the rate increases 30,000 times. However. for the protein catalyst catylase. the rate increases 100.000.000
times. Denatured When heated or when pH is changed significantly enough. proteins begin to
proteins unfold (denature). This destroys the topography ofthe protein and disables
its biological function. Substrate Proteins are so selective because they have a specifically shaped bonding
specificity site with high affinity for the substrate Inducedrfit Proteins are dynamic in their shape. when a substrate binds. there is a
inodei conformational change in the protein. Cataboiic rate (vei'ocity) For the example reaction S a P, yo = k1[S] = ﬂEi'dL W k. k.
L53 E + a ﬁ ES r E + P
W k_ kw inean where E is enzyme. 8 is substrate: and P is product.
nism This mechanism assumes that only initial rates are measured. This means that the reverse reaction
with the constant k: is ignored and considered insignificant. The second assumption is that the rate—limiting step is the reaction ES —) E + P. So: the rate equation
is v0 = glad; = k:[ES]. (Equation 1) The third assumption is that there is a steadystate within the reaction: the rate of E8 formation is
equal to the rate of E8 loss. Therefore. the rate of EB formation = k1[E][S] and the rate of E8 loss =
k:[ES] + k1[ES] = [ES](<:  k.1). Combining these.
<1[E][S] = [ES]{k:  k713i
_E"S_ k. —k . :
:LJL J='.. ..=
[E51 k. m
where l<m is the michaelis constant. (Equation 2) when we write the first step ofthe mechanism. we get ES ‘57 E + S
and _ __ _
d = LEJLSJ
[E5]
where 5,1 is the dissociation constant. km Is an "apparent dissoCIation constant" {not a true one because the k: in the equation makes it
dependent on the second reaction}. and can be thought of as a repuision index. This means that
when km is large. E and 8 do not want to react (they repel each other}. Because enzyme is conserved. the concentration of enzyme remains constant. or [E]T = [E] + [E8]
{the enzyme can be free; E_. or bound up_. ES). (Equation 3a) From equations 1_. 2_. and 3a, the direct kinetic function can be derived: k.iEi
v0 = ' T From this equation. we can see that k:[E]T = m. when [S] = km; v0 = m," 2. So, “I "'
1+ k—'“ [5] (Direct Kinetic Function) The relationship between [S] and ya can be plotted on a graph: \fnnuy ' _ _'— ‘ “““ '"W_ "—_F 77 .77 QT— (Direct Plat) Ifwe invert the direct kinetic function, we get the doubfe reciprocal function: 1 1 kml
_= + V0 vm vm [S]
This reiationship between 1f[S] ancl lfvo can be piotted on a graph: (Double Reciprocal Plot) Another transformation of the direct Kinetic function yields the Eadie—Hofsfee function: v0 _ vrm _ 1 V
7 _ 7 7 ' 0
[3] km k
T.hiS._re‘.a.ti.9nshiD between. w and. VOILE]. sac b9 plotter? ..°U..§_9ra_ph_= “*6? m (Wes. Plot) Finally, another transformation of direct kinetic function is the HaynesWoolf function:
5 k 1 u = m ... v0 v This reiationship between [S] and [S],r‘vo can be plotted on a graph: max vmax (HaynesWoolf Plot) Compe In the presence of an inhibitor. 1. the Following side reaction may occur with the Emmi]
titive mechanism: inhibiti : on E + l "— El (Inhibition Mechanism 1) Inhibitor binds to the enzyme, reducing the formation ofthe ES complex, which increases the km (see
equation 2) and slows the reaction rate. when inhibition mechanism 1 is used alone. this is called competitive inhibition (8 and I are
competing to get into the active site of E to form E8 or E1). The equilibrium constant for this reaction is (Equation 4a)
kgis the repuISIon constant for this reaction. Under these conditions, the equation for [E]T also changes:
[E]T = [E] + [ES] + [EI]
(Equation 3b) Taken together. equations 3b. 4. and the direct kinetic function synthesize this new function:
V max k
l I [5] K J This can be rewritten as i '1'
v =\'"—”‘, wherek' =k 1.—u
0 k m m k
1,7!" I [5] (Competitive Inhibition Equation) Uncom The effective amount of E8 can also be reduced by the binding of it with inhibitor: Izetitiu' ES + I _. ESI
inhibm (Inhibition Mechanism 2) Oi‘l when inhibition mechanism 2 is used alone. this is called uncompetitive inhibition. i—‘igain. [E]T is changed:
[E]T = [E] + [ES] + [ESI]
(Equation 3:) And again lg; can be calculated: k=ﬁwm
1 [E51]
(Equation 4b) From these: max v:— \i'
(I
lJIM. k1 [S] (U ncompetitive Inhibition Equation) Non when both inhibition mechanisms occur. this is called noncompetitive inhibition.
compe
titive [E]T = [E] + [ES] + [EI] + [ESI]
inhibiti (Equation 3d)
on
This type ofinhibition uses both equations 4a and 4b: h:oMide saw [E1] 1 : [ESI] This equation can be derived: V . LJ
v=+ wherek=k ——
° m "l ml
k; [5] (Noncompetitive Inhibition Equation) Inhibiti A direct plot of the differentinhibition types looks like this: on
siots UﬁlﬂHIﬁl1‘Ep
' b1...“  " a a a r a — — or; is;  : 2L —/’
4 _,_.__r.t:—
_,_e=="'f CN‘F‘L'TI'FhE
/ lhuibi'flom
/”
/ f u' , HE
VD V'mm_ _ _ J / / \n\..rn u . Ann—1 u u v‘ug'ih'   .u.
Mmmwiﬂiﬁﬁ‘ivf
LNHlﬁITKbn} (Direct Inhibition Plot) A double reciprocal plot ofthe different inhibition types uses the following equations (these are
reCIprocals ofthe Kinetic functions above}: 1 1 kml
—: + V0 Vm... Vm... [5]
(Direct DR Equation) i: l + kl“ wherekﬁn=km 1+m
V0 Vm... Vm... [S] k. (Competitive DR Equation) 1 [BEE] km 1 _ = — + __
V0 vm... V... [S]
(Uncompetitive DR Equation) I
t1+¥j I I
i7—1 + k’" i wherek§n=km[1+%:
I V.) vm... vm [S]
(Noncompetitive DR Equation) This plot would look like this: m»mm11nvf m. “ , uncoMPmnw
nunsrm co” m: \NHIBJT‘lQNe 'ummu'srrzb [33'] (DR Inhibition Plot) On a double reCiprocal plot, the uninhibited graph will share 1. the vintercept (Hm) with the competitive inhibition graph, 2. the slope (kmfvm) with the uncompetitive inhibition graph, or 3. the xintercept (1fkm) with the noncompetitive inhibition graph (when we assume lgh : lg}. The same can be done with the game plot:_ UNINHFﬁJﬁD ,C23Mt’e..1T‘IVE.
l~u13mupq UNCQMEE‘K‘IT‘V‘E  __ '
\MH ramau NoNco..PEv}71. 1E
' V0 I M: ranrt: M (W Inhibition Plot)
On an Wm plot, the uninhibited graph will share
1. the xintercept (m) with the competitive inhibition graph, 2. the vW (ka) with the uncompetitive inhibition graph, or
3. the slope (1,‘km) with the noncompetitive inhibition graph (when we assume 1511 : lg). The same can be done with the HaYnES'VI'IOOll: plot: Nomivh’E‘er/L UNCQ MPET'I‘I'IUE.
IN WEN“ "4 com P5777? 1/5
In; H (:5 FUD M 'UHIAHJBITED "' kn? ‘
L31
(HaynesWoolf Inhi ' 'on Plot) On an HaynesWoolf plot, the uninhibited graph will share 1. the slope (MW) with the competitive inhibition graph, 2. the ymgrggmt (kmfym) with the uncompetitive inhibition graph, or 3. the xintercept (l(m) with the noncompetitive inhibition graph (when we assume IQ; = I51). Enzym ym is not achieved in the cell. Activity of an enzyme can be regulated by covalent modification e (usually phosphorvlationi, temperature changes, pH, and ES concentration (via an increase in enzyme
behavi or substrate concentration}.
on?)
the
cell
W Them cannot explain the behavior ofthese enzymes. An S—
enzymes shaped (First concave up then concave down: W} curve on the [S] vs v0
graph characterizes this type. All W enzymes are W (more than one identical chain, thus having more than one active site}. This behavior occurs because when one substrate molecule binds to one active
site on an allgstegc enzyme, this binding enhances the binding capabilities of
the other sites. Feedback The end—product oi‘a sequence of catalyzed reactions can sometimes inhibit
inhibitors an enzyme that is used in the reaction sequence to produce it. This is a
mode oflimiting product excess. ...
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 Fall '07
 DiIulio
 Proteins, Enzyme inhibitor, direct kinetic function, inhibition graph, noncompetitive inhibition graph

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