TY - JOUR
T1 - Design principles for active transport systems
AU - Honig, Barry
AU - Stein, Wilfred D.
PY - 1978/12/7
Y1 - 1978/12/7
N2 - We have previously described simple models for active transport and have derived steady state equations for the unidirectional flux of substrate in terms of a minimal set of kinetic parameters. Here we consider how to maximize the pumping rate of a carrier-enzyme through the optimal utilization of the ATP hydrolysis reaction. The equations for net flux contain rate constants and dissociation constants and these determine the maximum velocities and affinities measured in transport kinetic analysis. It is assumed that the rate constants can evolve to the diffusion limited rate of substrate binding as has apparently occurred in the enzyme triosephosphate isomerase (Knowles & Albery, 1977). The dissociation constants of the rate limiting intermediates fit the affinities for substrates on different sides of the membrane and are dependent on the basic free energy levels (Hill, 1976) of the carrier substrate system. From our analysis it is clear that there are three ways to design a system with optimal affinities and that the choice is linked to the sequence of substrate binding. It is possible to use free energy differences of isomerization (Boyer, 1975) or ligand-ligand interactions (Weber, 1975) both of which have been described previously, but which are incorporated here into a unified treatment. A third possibility is to couple the binding step of a transported ligand to the progress of a chemical reaction as might occur, for example, if Na+ must be bound before the carrier can be phosphorylated. In this way the free energy of hydrolysis can be used not only to drive the overall pumping reaction, but also to fix differentially the affinity for substrate on either side of the membrane, as required for rapid pumping.
AB - We have previously described simple models for active transport and have derived steady state equations for the unidirectional flux of substrate in terms of a minimal set of kinetic parameters. Here we consider how to maximize the pumping rate of a carrier-enzyme through the optimal utilization of the ATP hydrolysis reaction. The equations for net flux contain rate constants and dissociation constants and these determine the maximum velocities and affinities measured in transport kinetic analysis. It is assumed that the rate constants can evolve to the diffusion limited rate of substrate binding as has apparently occurred in the enzyme triosephosphate isomerase (Knowles & Albery, 1977). The dissociation constants of the rate limiting intermediates fit the affinities for substrates on different sides of the membrane and are dependent on the basic free energy levels (Hill, 1976) of the carrier substrate system. From our analysis it is clear that there are three ways to design a system with optimal affinities and that the choice is linked to the sequence of substrate binding. It is possible to use free energy differences of isomerization (Boyer, 1975) or ligand-ligand interactions (Weber, 1975) both of which have been described previously, but which are incorporated here into a unified treatment. A third possibility is to couple the binding step of a transported ligand to the progress of a chemical reaction as might occur, for example, if Na+ must be bound before the carrier can be phosphorylated. In this way the free energy of hydrolysis can be used not only to drive the overall pumping reaction, but also to fix differentially the affinity for substrate on either side of the membrane, as required for rapid pumping.
UR - http://www.scopus.com/inward/record.url?scp=0018262939&partnerID=8YFLogxK
U2 - 10.1016/0022-5193(78)90336-3
DO - 10.1016/0022-5193(78)90336-3
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C2 - 745445
AN - SCOPUS:0018262939
SN - 0022-5193
VL - 75
SP - 299
EP - 305
JO - Journal of Theoretical Biology
JF - Journal of Theoretical Biology
IS - 3
ER -