902:. For example, in a linear chain of reactions at steady-state, all steps carry the same flux. That is, there is no slow or fast step with respect to the rate or speed of a reaction. The flux control coefficient, instead, measures how much influence a given step has on the steady-state flux. A step with a high flux control coefficient means that changing the activity of the step (by changing the expression level of the enzyme) will have a large effect on the steady-state flux through the pathway and vice versa.
795:
604:
16:
In chemistry, control coefficients are used to describe how much influence (i.e., control) a given reaction step has on the steady-state flux or species concentration level. In practice, this can be accomplished by changing the expression level of a given enzyme and measuring the resulting changes in
417:
One criticism of the concept of the control coefficient as defined above is that it is dependent on being described relative to a change in enzyme activity. Instead, the Berlin school defined control coefficients in terms of changes to local rates brought about by any suitable parameter, which could
820:
could be any convenient parameter. For example, a drug, changes in enzyme expression etc. The advantage is that the control coefficient becomes independent of the applied perturbation. For control coefficients defined in terms of changes in enzyme expression, it is often assumed that the effect on
391:
194:
615:
424:
408:
It is important to note that control coefficients are not fixed values but will change depending on the state of the pathway or organism. If an organism shifts to a new nutritional source, then the control coefficients in the pathway will change.
35:
The simplest way to look at control coefficients is as the scaled derivatives of the steady-state change in an observable with respect to a change in enzyme activity. For example, the flux control coefficients can be written as:
203:
398:
In theory, other observables, such as growth rate, or even combinations of observables, can be defined using a control coefficient. But flux and concentration control coefficients are by far the most commonly used.
395:
Control coefficients can have any value that includes negative and positive values. A negative value indicates that the observable in question decreases as a result of the change in enzyme activity.
905:
Historically the concept of the rate-limiting steps was also related to the notion of the master step. However, this drew much criticism due to a misunderstanding of the concept of the steady-state.
41:
885:
898:
is defined as the slowest step of a chemical reaction that determines the speed (rate) at which the overall reaction proceeds. The flux control coefficients do not measure this kind of
790:{\displaystyle C_{v_{i}}^{s}=\left({\frac {ds}{dp}}{\frac {p}{s}}\right){\bigg /}\left({\frac {\partial v_{i}}{\partial p}}{\frac {p}{v_{i}}}\right)={\frac {d\ln s}{d\ln v_{i}}}}
599:{\displaystyle C_{v_{i}}^{J}=\left({\frac {dJ}{dp}}{\frac {p}{J}}\right){\bigg /}\left({\frac {\partial v_{i}}{\partial p}}{\frac {p}{v_{i}}}\right)={\frac {d\ln J}{d\ln v_{i}}}}
1117:
818:
386:{\displaystyle C_{e_{i}}^{s_{j}}={\frac {ds_{j}}{de_{i}}}{\frac {e_{i}}{s_{j}}}={\frac {d\ln s_{j}}{d\ln e_{i}}}\approx {\frac {s_{j}\%}{e_{i}\%}}}
405:
Control coefficients are useful because they tell us how much influence each enzyme or protein has in a biochemical reaction network.
924:
899:
418:
include changes to enzyme levels or the action of drugs. Hence a more general definition is given by the following expressions:
189:{\displaystyle C_{e_{i}}^{J}={\frac {dJ}{de_{i}}}{\frac {e_{i}}{J}}={\frac {d\ln J}{d\ln e_{i}}}\approx {\frac {J\%}{e_{i}\%}}}
402:
The approximation in terms of percentages makes control coefficients easier to measure and more intuitively understandable.
1107:
919:
18:
826:
1122:
914:
973:"A Linear Steady-State Treatment of Enzymatic Chains. General Properties, Control and Effector Strength"
895:
1112:
1047:
Burton, Alan C. (December 1936). "The basis of the principle of the master reaction in biology".
686:
495:
1029:
994:
953:
1083:
1056:
1021:
984:
1074:
Hearon, John Z. (September 1981). "Transient times in enzyme and coupled enzyme systems".
989:
972:
803:
1101:
1087:
1025:
17:
flux and metabolite levels. Control coefficients form a central component of
1060:
1033:
998:
957:
821:
the local rate by changes to the enzyme activity is proportional so that:
1012:
Hearon, John Z. (1 October 1952). "Rate
Behavior of Metabolic Systems".
198:
while the concentration control coefficients can be written as:
971:
Heinrich, Reinhart; Rapoport, Tom A. (February 1974).
829:
806:
618:
427:
206:
44:
944:
Kacser, H; Burns, JA (1973). "The control of flux".
879:
812:
789:
598:
385:
188:
946:Symposia of the Society for Experimental Biology
1049:Journal of Cellular and Comparative Physiology
8:
24:There are two primary control coefficients:
894:In normal usage, the rate-limiting step or
880:{\displaystyle C_{v_{i}}^{X}=C_{e_{i}}^{X}}
609:and concentration control coefficients by
988:
871:
864:
859:
846:
839:
834:
828:
805:
778:
748:
732:
723:
706:
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628:
623:
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587:
557:
541:
532:
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478:
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371:
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174:
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117:
103:
97:
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70:
61:
54:
49:
43:
936:
7:
1118:Mathematical and theoretical biology
890:Relationship to rate-limiting steps
31:Concentration Control Coefficients.
990:10.1111/j.1432-1033.1974.tb03318.x
714:
699:
523:
508:
377:
362:
180:
165:
14:
925:Summation theorems (biochemistry)
977:European Journal of Biochemistry
1:
1026:10.1152/physrev.1952.32.4.499
1088:10.1016/0025-5564(81)90031-6
1139:
920:Metabolic control analysis
19:metabolic control analysis
800:In the above expression,
28:Flux Control Coefficients
1076:Mathematical Biosciences
1061:10.1002/jcp.1030090102
915:Elasticity coefficient
881:
814:
791:
600:
387:
190:
1014:Physiological Reviews
896:rate-determining step
882:
815:
792:
601:
388:
191:
1108:Biochemistry methods
827:
804:
616:
425:
204:
42:
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235:
66:
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830:
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383:
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45:
900:rate-limitingness
813:{\displaystyle p}
785:
738:
721:
677:
667:
594:
547:
530:
486:
476:
413:Formal Definition
381:
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295:
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154:
112:
95:
1130:
1092:
1091:
1082:(1–2): 129–140.
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1123:Systems biology
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1039:
1020:(4): 499–523.
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62:
55:
51:
46:
37:
30:
27:
26:
25:
22:
20:
1079:
1075:
1069:
1052:
1048:
1042:
1017:
1013:
1007:
983:(1): 89–95.
980:
976:
966:
949:
945:
939:
904:
893:
823:
799:
608:
416:
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404:
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397:
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200:
197:
38:
34:
23:
15:
1055:(1): 1–14.
1113:Metabolism
1102:Categories
952:: 65–104.
931:References
772:
758:
715:∂
700:∂
581:
567:
524:∂
509:∂
378:%
363:%
347:≈
331:
310:
181:%
166:%
157:≈
141:
127:
1034:13003538
909:See also
999:4830198
958:4148886
1032:
997:
956:
1030:PMID
995:PMID
954:PMID
1084:doi
1057:doi
1022:doi
985:doi
1104::
1080:56
1078:.
1051:.
1028:.
1018:32
1016:.
993:.
981:42
979:.
975:.
950:27
948:.
769:ln
755:ln
578:ln
564:ln
328:ln
307:ln
138:ln
124:ln
21:.
1090:.
1086::
1063:.
1059::
1053:9
1036:.
1024::
1001:.
987::
960:.
873:X
866:i
862:e
857:C
853:=
848:X
841:i
837:v
832:C
808:p
780:i
776:v
766:d
761:s
752:d
746:=
742:)
734:i
730:v
726:p
718:p
708:i
704:v
693:(
687:/
681:)
675:s
672:p
664:p
661:d
656:s
653:d
646:(
642:=
637:s
630:i
626:v
621:C
589:i
585:v
575:d
570:J
561:d
555:=
551:)
543:i
539:v
535:p
527:p
517:i
513:v
502:(
496:/
490:)
484:J
481:p
473:p
470:d
465:J
462:d
455:(
451:=
446:J
439:i
435:v
430:C
373:i
369:e
358:j
354:s
339:i
335:e
325:d
318:j
314:s
304:d
298:=
291:j
287:s
281:i
277:e
266:i
262:e
258:d
251:j
247:s
243:d
237:=
230:j
226:s
218:i
214:e
209:C
176:i
172:e
163:J
149:i
145:e
135:d
130:J
121:d
115:=
110:J
105:i
101:e
90:i
86:e
82:d
77:J
74:d
68:=
63:J
56:i
52:e
47:C
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