[acnash]

Hi All,

I am having a bit of difficulty visualising/calculating free energy difference from the reactants to a product over 10 intermediate steps. It is to do with balancing the number of atoms (for context, these are ab initio computational calculations).

My reactants are two amino acids and a sugar. The final product is the sugar bound to both amino acids.

The first step we see the one amino acid bind to the sugar. Over the course of 8 steps there is the removal of two water molecules and a significant rearrangement to the sugar structure. The step before last the second amino acid binds to the complex and there is also the removal of a further water molecule. The final product is a bit of rearrangement to give an aminoacid-sugar-aminoacid complex.

My question. How do I calculate the DIFFERENCE in free energy at each step? Do I need to include the free energy contribution from every atom involved through the complete reaction pathway at each intermediate even if they are not playing a part any more (for example, should I take into account the free energy contribution from the second amino acid during the first intermediate even though that second amino acid doesn't bound to the sugar until the step before last)?

e.g., DeltaG of Int1 =(AA1+Sugar AA2) - (AA1 AA2 Sugar)
...
DeltaF of Int6 = (AA1+Sugar AA2 H2O) - (AA1 AA2 Sugar)
.
DeltaG of Product = (AA1+Sugar+AA2 H2O H2O H2O) - (AA1 AA2 Sugar)

I really appreciate the help and I hope this makes sense!!
Thanks

[Babcock_Hall]

I don't know the answer, but I might try to make use of the fact that ΔG is a state function.

[acnash]

I don't know the answer, but I might try to make use of the fact that ΔG is a state function.

Hi thanks for the reply. I can see where you are going with that. Free energy is a state function, but the difference in free energy makes it relative to something else. Unfortunately, I can't find any examples beyond publications (difficult to interpret as a working example rather than a set of results) where a reaction pathway has more that one transition state and involves a series of dis/associations.

Thanks
Anthony

[Big-Daddy]

Write reaction equations for each process and try and transform, for which you have a known ΔG, the reaction equations of those reactions to form the reaction equation for which you want ΔG. This transformation should then be applied to the values of ΔG for the reactions in question, to find the value of ΔG for the desired reaction, because ΔG values are additive (from the meaning of G being a state function).

See Hess' law for more. Most problems will concern ΔH with regards to Hess' law, but ΔS, ΔG, ΔU, etc. are additive across reactions in the same way.

[acnash]

Hi Big-Daddy, thanks for your reply. It has given me some direction of thought.

If I am right, I would take the reactants, lets say aminoacid A, aminoacid B and sugar S, add their free energy as a control. This value would be subtracted from all intermediate steps and the final product. However, given there are three water molecules coming off from the intermediate steps would I need to add their free energy values during the disassociation step and all subsequent steps? e.g.

A+B+S -> A'+B+S+H2O -> A'+B'+S+2H2O -> A'+B'+S'+3H2O  (prime indicates a change a rearrangement in structure).

Thanks

Or, do I not balance the atoms, as in:
A+B+S -> A'+B+S -> A'+B'+S -> A'+B'+S'

Examples of a single disassociation i.e., reactant, product and a transition state, suggest that you DO include the free energy of the disassociated fragment when you calculate free energy differences.

[Big-Daddy]

Please specify:

1) what information (I'm talking about thermodynamic values here) you're given
2) what you're trying to find
3) all the reactions whose equations you can write