Membrane free energy

Membrane pumps function by mechanisms that are simple in principle but often complex m detail. Fundamentally, each pump protein can exist in two principal conformational states, one with ion-binding sites open to one side of the membrane and the other with ion-binding sites open to the other side (Figure 13.2). To pump ions in a single direction across a membrane, free energy must be provided in a manner that can be coupled to the interconversion between these conformational states. 

The electrostatic free energy of a macromolecule embedded in a membrane in the presence of a membrane potential V can be expressed as the sum of three separate terms involving the capacitance C of the system, the reaction field Orffr), and the membrane potential field p(r) [73],... 

The first step in studying phenomenological theories (Ginzburg-Landau theories and membrane theories) has usually been to minimize the free energy functional of the model. Fluctuations are then included at a later stage, e.g., using Monte Carlo simulations. The latter will be discussed in Sec. V and Chapter 14. 

For fluid membranes, in which neighbor relations are not maintained, the free energy of a membrane is often written in the form [27,30]... 

Passive diffusion is the simplest transport process. In passive diffusion, the transported species moves across the membrane in the thermodynamically favored direction without the help of any specific transport system/molecule. For an uncharged molecule, passive diffusion is an entropic process, in which movement of molecules across the membrane proceeds until the concentration of the substance on both sides of the membrane is the same. For an uncharged molecule, the free energy difference between side 1 and side 2 of a membrane (Figure 10.1) is given by... 

Fructose is present outside a cell at 1 /iM concentration. An active transport system in the plasma membrane transports fructose into this cell, using the free energy of ATP hydrolysis to drive fructose uptake. Assume that one fructose is transported per ATP hydrolyzed, that ATP is hydrolyzed on the intracellular surface of the membrane, and that the concentrations of ATP, ADP, and Pi are 3 mM, 1 mM, and 0.5 mM, respectively. T = 298 K. What is the highest intracellular concentration of fructose that this transport system can generate Hint Kefer to Chapter 3 to recall the effects of concentration on free energy of ATP hydrolysis.)... 

The free energy difference for protons across the inner mitochondrial membrane includes a term for the concentration difference and a term for the electrical potential. This is expressed as... 

Reported values for A and ApH vary, but the membrane potential is always found to be positive outside and negative inside, and the pH is always more acidic outside and more basic inside. Taking typical values of A F = 0.18 V and ApH = 1 unit, the free energy change associated with the movement of one mole of protons from inside to outside is... 

Assume that the free energy change, AG, associated with the movement of one mole of protons from the outside to the inside of a bacterial cell is —23 kJ/mol and 3 must cross the bacterial plasma membrane per ATP formed by the bacterial FjEo-ATP synthase. ATP synthesis thus takes place by the coupled process ... 

A proton-motive force of approximately —250 mV is needed to achieve ATP synthesis. This proton-motive force, A, is composed of a membrane potential, A P, and a pH gradient, ApH (Chapter 21). The proton-motive force is defined as the free energy difference, AG, divided by S, Paraday s constant ... 

Because osmosis is a thermodynamic property, we can expect it to be related to the effect of the solute on the enthalpy and entropy of the solution solvent flows until the molar Gibbs free energy of the solvent is the same on each side of the membrane We have already seen several times that a solute lowers the molar Gibbs free energy of the solution below that of the pure solvent, and solvent therefore has a tendency to pass into the solution (Fig. 8.33). 

FIGURE 8.33 On the left of the semipermeable membrane is the pure solvent with its characteristic molar enthalpy, entropy, and Gibbs free energy. On the right is the solution. The molar Gibbs free energy of the solvent is lower in the solution (an entropy effect), and so there is a spontaneous tendency for the solvent to flow into the solution. 

Fig. 2b. The appearance of two crystal forms shows that the protein in the membrane exists in equilibrium between the protomeric aj8 unit and oligomeric (aj8>2 forms. The high rate of crystal formation of the protein in vanadate solution shows that transition to the E2 form reduces the difference in free energy required for self association of the protein. This vanadate-method for crystallization has been very reproducible [34-36] and it also leads to crystalline arrays of Ca-ATPase in sarcoplasmic reticulum [37] and H,K-ATPase from stomach mucosa [38]. 

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