ON THE INTERPRETATION

SIMONI, R. D., NAKAZAWA, T., HAYS, J. B., AND ROSEMAN, S. (1973) J. Biol. Chem. 248, 932-940 HAYS, J. B., SIMONI, R. D., AND ROSEM.~N, S. (1973) J. Biol. Chem. 248, 941-956 SIMONI, R. D., HAYS, J. B., NAKAZAWA, T., AND ROSEMAN, S. (1973) J. B&Z. Chem. 248; 957-965 ROSEMAN, S. (1969) J. Gen. Phusiol. 64, 138s TANSKA, s., AND FIN, E. C. C: (1967) .Proc. iVat. Acad. Sci. U. S. A. 62, 913 20. TANAKA, S., FRAENICEL, D., AND LIN, E. C. C. (1967) Biochem. Biophys. Res. Commun. 27, 63 Fox, C. F., AND WILSON, G. (1968) Proc. Nat. Acad. Sci. U. S. A. 69, 988 21.

Correlations between the dissociation constant of a solute for a specific solute-binding protein and the apparent Michaelis constant for the transport of the solute into intact cells have been invoked to provide evidence for the hypothesis that the solute-binding protein is a rate-limiting component of the transport process (1). However, the accompanying papers (2-4) show little or no correlation between constants derived from the following three types of measurement: (a) the dissociation constant (K,) of the lactose-Enzyme IIlac complex (the Kn values for the lactose analogues TMG and IPTG could not be accurately determined), (b) the apparent Michaelis constants for lactose and its analogues in the phosphotransferase system, and (c) the apparent Michaelis constants for the transport of these sugars into intact cells. It will be shown below that kinetic analysis in fact predicts that these constants should not correlate with one another.
Enzymatic Phosphorylation-The sugar phosphorylation step of the phosphotransferase system is catalyzed by Enzyme IIlsc and involves the transfer of phosphate from phospho-Factor III1ac to sugar with the production of sugar-phosphate and Factor III1ac. This is a two substrate-two product reaction. Further, kinetic analysis has been presented in the accompanying papers (2-4) that indicates that this reaction is not random (branched), i.e. it is an ordered (linear) reaction.
Finally, the 1 /vi versus 1 /S plots for this reaction are not parallel but intersect at a single point indicating that the reaction is Ordered Bi Bi rather than Ping Pong Bi Bi (5, 6). The mechanism for such a linear reaction can be represented as follows: Binding Coonstunt-Isolated Enzyme II'"" has been used to determine a dissociation constant K. for lactose. If the binding reaction is defined as follows: where S is concentration of sugar (i.e. lactose) and kl and Ic-i are the respective rate constants, then: (2) Let Et represent the total enzyme concentration: (3) by guest on March 23, 2020 http://www.jbc.org/ Downloaded from El = E + ES1 + ESuS'z + EPz (4) Enzyme II'"" complex is 2.5 x lop7 M. Thus, If one makes the steady state assumption (5, 6), the following (K laotosc)P-III'SC~~ N KD general rate equation for Reaction 3 can be derived.
This result is compatible with Equation 14 if it is assumed that (klkgkak&Sz -k-,k-zk-8k-aP1Pz)Et v= (5) Si represents lactose and SP represents phospho-III1aO. It will A be assumed in all subsequent equations that lactose adds to Enzyme II lae before phospho-III lttc although this order of subwhere v is the rate of reaction through the system at time t (see strate addition has not been rigorously established. It is there-Equation 6 for value of A).
fore possible to write the following equations for the apparent A = klkz (k3 + k4)S1S2 + k,ka (k-2 + k&S1 + k2k3kd& + k--lk4 (k-z + k3) + k-3ke-4 (k-1 + k-z)PlPz + k-lk-zk-sP1 + k-&d(k--2 + kz)Pz + kxkzk--3&SzP1 + kzk--3k-&P1P2 + klk_zk-&P1 + k2k&&P2 (6) If it is assumed that PI = Pz = 0 at time t = 0,' then from Equations 5 and 6: v, = k~knk,k&S& E A where A = klkz (k3 + ki) SW% + klk4 (k-z + kd Sl + where KS1 and Ks2 represent the apparent Michaelis constants for Si and SZ, respectively. Now, it has been shown in the accompanying papers (2-4) that the apparent Michaelis constant for phosphorylation of lactose, as the concentration of phospho-1111"" approaches zero, is 4 x lo-' M, and that the dissociation constant for the lactose-1 When the reaction is initiated by addition of substrates Si and St, t s 0, v = vi (initial velocity), and P1 and Pt are both essentially zero. However, the phosphorylation assays in the accompanying papers were conduct,ed by adding Factor III'ac and a phosphorylating system to generate the substrate, phospho-TII'*c. Thus at t = 0, one of the products (sugar-phosphate) was essentially absent but the other product (Factor IIIlac) may not have been at zero concentration, and either PI = 0, PZ # 0, or, PI # 0, Pt = 0. If one plots l/v; versus l/S1 (or ~/SZ) and then plots both the slopes and intercepts against l/St (or l/Si), linear plots will result provided both PI and Pg are zero. Such plots were made for the phosphorylation of lactose and its analogues TMG and IPTG by Enzyme IIrac: the plots were essentially linear indicating that it is probably a reasonable approximation to assume that most of the added Factor IIIiac was phosphorylated at time t = 0. It is clear that these two apparent Michaelis constants need not be the same.
In addition to the assumptions already mentioned, there is yet another assumption implicit in the above derivations, namely, that the phospho-IIIrac substrate represents monophospho-IIIlac; it will be recalled that Factor III'"" consists of 3 subunits each of which can carry an active phosphate group (3).

Group Translocatim via Phosphotransjerase
System-The mechanism whereby the PTS effects group translocation is not known. However, a likely mechanism is shown in Scheme 1 in which Enzyme II lac serves not only as the catalyst for phosphorylation of sugar but also as the carrier whereby sugar is transported through the membrane.
The fact that Enzyme IInc binds lactose probably before the addition of phospho-III'"" (see above) is compatible with Scheme 1.
If one now assumes that the rate-limiting step in this transport process is the reaction catalyzed by Enzyme IIiac, and not the phosphotransfer steps to Enzyme I, to HPr, or to Factor IIIiac, then the rate equation for Enzyme IIlac would in fact represent the rate equation for transport.
In the above scheme below, S represents extracellular concentration of the sugar transported (e.g. lactose), S-P represents intracellular sugarphosphate concentration, IIlac refers to concentration of Enzyme IIrac, P-IIIiac refers to concentration of monophospho-IIIiac, and ki to kg and k-i to k-6 refer to the individual rate constants Ouf I A' = (s)(p-1111ac)[klk3(k4ksks + k&&s + k&&E + k&&)1 + Shbb(Lk4 + k-d-3 + k&4 + kzk-dl + p-III'~e[k3k4ks(k_lks + kzks + kzk-6 + k--lk-6)1 + k--lk-zks(k-skG + k4k6 + k4k--6 + k-sk--6) c22) of each process. The concentrations of the complexes between IIrac and sugar, sugar-P, and sugar plus phospho-III*"" are designated IInc. S, II'"". X-P, and II'"" e S .P-III'"", respectively. One can now use the steady state assumption and the procedure of King and Altman (7) to derive the general rate equation for movement of S from outside to inside the cell at any time t: where A' is a complex expression that can be determined as described by Wong and Hanes (6), and where IIt"" is the total Enzyme IP"" concentration (free and substituted enzyme). If transport studies are conducted under conditions where progress curves are linear, i.e. within seconds of adding external sugar, then S-P is essentially zero with sugars such as TMG and IPTG, and v = vi (initial velocity), where : and where A' is a somewhat simpler expression because (S-P) is zero. If one makes the further assumption that III'"" concentration is zero, the expression for A' is given in Equation 22. Therefore, the apparent Michaelis constants for transport will be given by Since the intracellular concentration of III'ac is probably not zero, the actual expressions for transport may be even more complex than given above. It is obvious that the apparent Michaelis constants for transport given by Equations 23 and 24 are far more complex than the apparent Michaelis constants for phosphorylation given by Equations 18 and 19.
Since the above expressions were derived with certain assumptions that may not be wholly valid, the actual differences between the phosphorylation constants and the transport constants may be even more marked than indicated by Equations 18, 19, 23, and 24. Thus, for example, if the concentration of IIInc is not zero, or if phospho-III1ac actually exists in several forms (mono-, di-, and triphospho-IIIiac), or if the intracellular concentration of phospho-IIIiac is neither infinitely small nor large as assumed in Equations 23 and 24, or if the PTS in vitro does not function in the same manner as the PTS in viva, both the phosphorylation and transport kinetics become more complex. It is thus evident that any agreement between the phosphorylation and transport constants must be fortuitous, or due to rather special conditions. For example, if kz = k-2 = ks = k-6 (a commonly used assumption), Equation 23 becomes identical with Equation 18 although Equation 24 remains more complex than Equation 19.