New Treatment of Enzyme Kinetics Applied to Human Dihydrofolate Reductase

Abstract

This paper presents a new procedure for the derivation of steady-state rate calculations by computer for enzyme kinetics using data on strains of human dihydrofolate reductase (DHFR) reported in the literature. This enzyme continues to command the attention of scientists since its discovery in the late 1950s in connection with applications to cancer therapy. Kinetics of nonhuman strains previously reported (Happel, J.; Sellers, P. H. J. Phys. Chem. 1995, 99, 6595) appears to be much simpler. In the present case it is necessary to introduce the concepts that an elementary step should be treated as a vector possessing the same direction in each submechanism that it occurs.

Wiring Diagrams for Complex Reaction Networks

“…As an example, we consider the conversion of 7,8-dihydrofolate (A) and NADPH (B) into 5,6,7,8-tetrahydrofolate (C) and NADP + (D), catalyzed by the enzyme dihydrofolate reductase (E). This system has been well-investigated experimentally and theoretically ,− and is represented by the OR: …”

“…By comparing the resistances in the various pathways shown in Figure , we were able to reduce the network to one comprising 11 elementary reaction steps and only 3 parallel pathways . Further, a comparison of the sequential resistances in the three parallel pathways revealed the bottleneck steps (RDS) in each of the three parallel routes .…”

Reaction Route Graphs. II. Examples of Enzyme- and Surface-Catalyzed Single Overall Reactions

“…The mechanism that describes the conversion of 7,8-dihydrofolate (A) and NADPH (B) to 5,6,7,8-tetrahydrofolate (C) and NADP + (D), as catalyzed by the enzyme dihydrofolate reductase (E), along with a set of rate constants is presented in Table . This is a single OR of the type that involves multiple RRs.…”

“…This is a single OR of the type that involves multiple RRs. The kinetics of this reaction has been intensively investigated both experimentally − and theoretically, using the theory of direct RRs ,, and the conventional King−Altman formalism. − The enumeration of direct RRs in this system has been considered by Happel and Sellers. ,, Their results are presented in Table . Of course, alternately, these RRs may be enumerated, as per the algorithm that was described in Part I …”

“…Of course, alternately, these RRs may be enumerated, as per the algorithm that was described in Part I 1 Elementary Reaction Steps and Their Rates in the Dihydrofolate Reductase (DHFR) System a stepreactionsimplified rate s 1 E + B = EB r 1 = 38.0[E][B] − 1.7[EB] s 2 EB + A = EAB r 2 = 100.2[A][EB] − 94.0[EAB] s 3 E + A = EA r 3 = 264.0[A][E] − 14.0[EA] s 4 EA+ B = EAB r 4 = 24.0[B][EA] − 19.0[EAB] s 5 EAB = ECD r 5 = 1360.0[EAB] − 37.0[ECD] s 6 EC = E + C r 6 = 5.1[EC] − 117.0[C][E] s 7 ECD = D + EC r 7 = 57.9[ECD] − 0.7[D][EC] s 8 ECD = C + ED r 8 = 46.0[ECD] − 24.0[C][ED] s 9 ED = D + E r 9 = 32.0[ED] − 17.0[D][E] s 10 EB + C = EBC r 10 = 14.0[C][EB] − 225.0[EBC] s 11 EC + B = EBC r 11 = 4.4[B][EC] − 72.6[EBC] s 12 EA + D = EAD r 12 = 11.0[D][EA] − 4.6[EAD] s 13 ED + A = EAD r 13 = 110.0[A][ED] − 1.3[EAD] a From ref . 2 Stoichiometrically Distinct RRs for the DFHS System a reaction routeexpressionFull RRs RR 1 OR = s 3 + s 4 + s 5 + s 8 + s 9 RR 2 OR = s 3 + s 4 + s 5 + s 6 + s 7 RR 3 OR = s 2 + s 5 + s 7 − s 10 + s 11 RR 4 OR = s 2 + s 5 − s 6 + s 8 + s 9 − s 10 + s 11 RR 5 OR = s 1 + s 2 + s 5 + s 8 + s 9 RR 6 OR = s 1 + s 2 + s 5 + s 6 + s 7 RR 7 OR = − s 1 + s 3 + s 4 + s 5 + s 7 − s 10 + s 11 RR 8 OR = s 4 + s 5 + s 8 − s 12 + s 13 RR 9 OR = s 4 + s 5 + s 6 + s 7 − s 9 − s 12 + s 13 RR 10 OR = − s 1 + s 4 + s 5 + s 7 − s 9 − s 10 + s 11 − s 12 + s 13 RR 11 OR = s 2 − s 3 + s 5 − s 6 + s 8 − s 10 + s 11 − s 12 + s 13 RR 12 OR = s 1 + s 2 − s 3 + s 5 + s 8 − s 12 + s 13 ...…”