Electrochemical Potential and the Thermodynamic Basis of Solute Transport Mechanisms

Transcription

1 Electrochemical Potential and the Thermodynamic Basis of Solute Transport Mechanisms A. Electrochemical Potential The electrochemical potential arising from the distribution of a solute A across a membrane can be considered from the standpoint of an equilibrium which is written for solute uptake into a cell rather than solute loss to the environment. This is a convention that determines the /- sign convention that propagates in the following equations. The free energy change for the movement of A from out to in is given by: G A= G Ain - G Aout = nf ψ 2.3 RT log A Ain out G A : referred to as the Electrochemical Potential R: Gas Law Constant = 8.3 J K -1 mol -1 ( kj K -1 mol -1 l) T: 298 K n: electric charge on A (-1, 0, 2, etc.) F: Faraday Constant = 96 kj V -1 mol -1 ψ: "Membrane Potential" ψ = ψin - ψout ψ is measured experimentally. In metabolically active cells, or mitochondria, carrying out aerobic respiration it often has a value between -0.1 V and -0.2 V (Negative values of ψ mean there is more negative charge inside the cell.) Note that the magnitude of ψ in active cells is comparable in magnitude to the electrical potential used in agarose gel electrophoresis. Ain The RT ln term describes a chemical (mass) gradient, while the A out nf ψ term describes a gradient of electric charge. This is the reason for using the term electrochemical gradient.

2 Do not confuse the equation for electrochemical potential with the Nernst Equation. The intracellular concentration of most solutes is in the neighborhood of 1 mm, often several orders of magnitude higher than the extracellular concentration. Therefore, because [A in ] > [A out ], solute uptake is typically endergonic ( G A < 0). This is the context of the phenomenon you have learned to call active transport.

3 B. Electrochemical Potentail of a Gradient of Protons The foregoing general description of Electrochemical Potential can now be customized to describe an electrochemical gradient based specifically on protons. n = 1: therefore, nf ψ = F ψ H in RT ln H out H in 2.3 RT log H out ( ph = -logh ) ( in out ) ( in out ) 2.3 RT log H -log H -2.3 RT -log H --log H ( in out) -2.3 RT ph - ph G = F ψ RT ( ph - ph ) H in out Typical values in metabolically active bacterial cells, and in mitochondria, (where the proton gradient is maintained by electron transport) are: ψ: -0.1V phin: 7.0 phout: 6.5 You can now calculate the free energy required for transport of a single proton under such typical conditions as follows: kj kj G = V K o V mol K mol kj kj kj G = = mol mol mol o ( ) ( )( )

4 The genome of the bacterium E. coli has at least 427 genes coding for membrane transport proteins. This amounts to a startling 10% of all E. coli genes, and makes this the most frequent type of gene in the genome. By way of comparison, the second most abundant type is biosynthetic genes, at 8% of the total. The large number of transport genes reflects the omnivorous appetite of E. coli for the wide variety of organic substrates it encounters in the complex biochemical stew of the mammalian gut. Another reason there are so many transport genes in E. coli is that there are 2 or more redundant transport mechanisms for many solutes. A good example is transport of the pentose, arabinose, which is transported by the ara F,G,H multicomponent system and, independently, by the arae system. The equation for electrochemical potential, and a basic understanding of biochemical thermodynamics, properly applied, allow you to explain the existence of the two redundant arabinose transport systems.

5 We notice that the two arabinose transport systems are redundant in the sense that they both transport arabinose, but they are not identical. The ara F, G, H multi-component system couples arabinose transport to ATP hydrolysis. The ara E system couples transport to proton transport (i.e. proton symport). Both systems use an exogenous source of free energy to drive endergonic arabinose uptake, therefore both are examples of active transport. Additionally, the binding constants (K m ) of the two systems differ by several orders of magnitude. The ATP-dependent system has high affinity, and the proton symport system low affinity for arabinose. Estimate the free energy change (in kj per mole) for arabinose uptake by these two systems. Assume an intracellular concentration of 1 mm, and extracellular concentrations equal to the respective Km values of the two systems. ABC SYSTEM: kj/mole Simple Proton Symport: kj/mole