Free Energy Transduction in Biology: The Steady-State by Terrell L. Hill

By Terrell L. Hill

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Right, three must be added. The total number of directional diagrams is 8 x 56 = 448. The number of independent transition fluxes i s / = 10 — 7 = 3. Thus we are using the maximum possible number of phenomenological fluxes for this model (K+, Na+, ATP). Charged particles and a membrane potential are involved here. In general, all the rate constants of the model might be expected to contain electrostatic contributions (Appendix 3). But these would appear only in a very explicit molecular model. At the formal level being used in this book, we can manipulate the rate constants OLU of a model without enquiring into the molecular theory of the α0· themselves.

The case of primary interest occurs when the downhill N a + electrochemical gradient (out -* in) is large enough to drive the ligand uphill (out -► in) against its concentration gradient. The states and diagram are shown in Fig. 11. 12 exhibits the A (outside) 11 Na+ Na+ State: 1 2 FIG. 11 3 I 5 B (inside) 4 5 6 Illustrative model and diagram for active transport of L by Na + . 1 2 30 2. THE DIAGRAM METHOD! CYCLES 1 l· 1 (b) (a) ' B A " 1 t« ' ί K (c) FIG. 12 (a) Cycles for Fig. 11. (b) Flux diagrams for cycle b.

On setting this equal to {3αΣ/Ν) + (J b Z/iV), we have the desired second linear relation between ρ^Σ and ρ%Σ. 26) where s = K2 + K + 1. Then from, say, ρ™Σ and (Eq. 2°Σ. States 1, 5, and 6 are handled in similar fashion. Finally, with all the ρ*Σ available, Σ may be deduced by means of £ , p{= 1. ) + ( / ! 28) Note that Σ has 90 terms (with many degeneracies), as expected. Thus, in this example, we have deduced the state probabilities from the very simple flux diagrams (Fig. 12), without using directional diagrams.

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