Nernst equation

A different conc of ions on either side of the membrane, wants to reach equilibrium so if you openup a channel ions will flow down the conc grad and the flow can be used to do work. 

A seperate effect is that difference in charge across a membrane creates a membrane potential and this provides a source of energy. 

The two effects often combine to a greater effect. 

These are used in various ways in biology: 

• transmit nerve signals
• generate ATP from H+ grad
• Transport a variety of molecules against a conc grad

Free energy difference related to membrane potential 

delta G = zFE 

• delta G - free energy 
• z - charge on ion 
• E - membrane potential (in volts - most potentials in mV so be careful) 
• F - Faraday constant = 96485 Jmol^-1V^-1

Relates membrane potential to the concentrations outside and inside 

E= RT/zF x ln([out]/[in]) 

• E - membrane potential 
• R - gas constant = 8.31 JK^-1mol^-1
• T - absolute temperature (in Kelvin) 
• z - charge on ion 
• F - Faraday constant = 96485 Jmol^-1V^-1
  
• ln - natural log
• [out] concentration of ions outside the membrane 
• [in] concentration of ions inside the membrane 

This equation comes from combining delta G = RTln([out]/[in]) with equation 1 

If there is different conc of ions outside and inside the membrane then total free energy depends on both equations added togther 

delta G = RTln([out]/[in]) +/- zFE 

The difficult bit here is getting the sign right. This can be done for membrane potential (equation 1) by looking at whether the ion is positive or negative and whether is going to an area of positive or negative charge and decidcing if this is favourable (add the energy(may actually be taking off as free energy tends to be negative)) or not. For concentrations you can look at whether the ion in that you are calculating the free energy for is moving with or against the concentration gradient. 

It is always a good idea wuth calculations to see if the value you have got makes sense. For these sort of equations you would be looking for a reasonaby small number but to have roughly the same amount of energy as a hydrogen bond in water (20 KJmol^-1). Another good comparison is thermal energy which is about 1.2 KJmol^-1) and is enough energy to so something usefu. Answers that too large should be obvious. 

For some practice or more examples see notes. 

Some examples in there include calculating the energy to move a sodium ion moves into the cell, calculating the energy to move a sodium out of the cell via the leak channels. 

More complicated examples include looking at the glucose sodium symporter and working out the glucose gradient created, doing the same with common calcium pumps and looking at ATPase. 

Questions with information needed to put into the equations and the answers are in notes.