Passive diffusion of molecules including H2O, CO2, and O2 across a cell membrane
ID: 63899 • Letter: P
Question
Passive diffusion of molecules including H2O, CO2, and O2 across a cell membrane results in movement from an area of high concentration to an area of low concentration until equilibrium is reached. Chloride ions, on the other hand, are able to move up a concentration gradient as they rely on passive transport through ion channels to maintain a lower concentration within the cytoplasm than the extracellular environment. Use your understanding of thermodynamics to explain to a college student with a strong grasp of thermodynamics and has completed general and organic chemistry (but has not taken biochemistry) how/why this is possible. A complete answer will include an explanation that ties the Cl- transport to mathematical thermodynamics.
Explanation / Answer
Ans: The movement of molecules by diffusion always proceeds spontaneously, down a gradient of concentration or chemical potential , until equilibrium is reached. The spontaneous “downhill” movement of molecules is termed passive transport. At equilibrium, no further net movements of solute can occur without the application of a driving force.
we can calculate the driving force for diffusion, or, conversely, the energy input necessary
to move substances against a gradient, by measuring the potential-energy gradient, which is often a simple function of the difference in concentration. Biological transport can be driven by four major forces: concentration, hydrostatic pressure, gravity, and electric fields.The chemical potential for any solute is defined as the sum of the concentration, electric, and hydrostatic potentials.
j = j* + RT ln Cj + zjFE + VjP
1. Chemical potential for a given solute,j
2.Chemical potential of j under standard conditions
3.Concentration (activity) component
4.Electricpotential component
5.Hydrostaticpressure component
Passive transport (diffusion) occurs spontaneously down a chemicalpotential gradient:
mj ˜A > mj˜ B
At equilibrium, mj˜ A = mj˜ B
K+, diffuse in response to both their concentration gradients ([K+]i/[K+]o) and any electric-potential difference between the two compartments (Ei – Eo). One very important implication of this equation is that ions can be driven passively against their concentration gradients if an appropriate voltage (electric field) is applied between the two compartments. Because of the importance of electric fields in biological transport, m~ is often called the electrochemical potential, and m~ is the difference in electrochemical potential between two compartments.
Nernst Equation Relates the Membrane Potential to the Distribution of an Ion at Equilibrium
When the distribution of any solute across a membrane reaches equilibrium, the passive flux, J (i.e., the amount of solute crossing a unit area of membrane per unit time), is the same in the two directions—outside to inside and inside to outside:
Joi = Jio
Fluxes are related to thus at equilibrium, the electrochemical potentials will be the same thus at equilibrium,the electrochemical potentials will be the same:
j0 = ji
mj* + RT ln Cjo + zjFEo = mj*+ RT ln Cji + zjFEi
so the difference in electric potential between the two compartments at equilibrium (Ei – Eo):
This electric-potential difference is known as the Nernst potential (Ej)
Ej = Ei – Eo
E = RT / zF [ ln Co/ C]
The Nernst equation, states that at equilibrium the difference in concentration of an ion between two compartments is balanced by the voltage difference between the compartments.The Nernst equation can be further simplified for a univalent cation at 25°C:
E = 59 log C/C
The tenfold difference in concentration corresponds to a Nernst potential of 59 mV (Co/Ci = 10/1; log 10 = 1).
That is, a membrane potential of 59 mV would maintain a tenfold concentration gradient of an ion that is transported by passive diffusion.