# How was the energy bonus determined for the new RNA switches?

How was the additional energy bonus of -2.1 kcal determined for the RNA switch, when the FMN aptamer is in it’s bound state?

Hi Brourd,

The energy depends on the concentration of the FMN molecule.

We use the following formula,

-RT ln([concentration]/0.3uM)

when the concentration is at 10uM, the bonus is approximately -2.1kcal

To clarify a bit, in Jee’s expression above 0.3 uM (micromolar) is the ‘intrinsic’ dissociation constant for the FMN aptamer sequence when presented in a small hairpin. In other words, as we add more and more FMN, when we reach that ‘midpoint’ concentration we achieve 50% FMN binding to the aptamer.

At that FMN concentration, a state in which the RNA binds the FMN has equal probability to a state in which the RNA binds the FMN. At higher or lower concentrations the relative probability of the bound state changes in proportion to [FMN], in accordance with the basics of statistical mechanics.

Then, in terms of energy, the probabilities are related to energy by:

E = -ln( probability/ RT )

[See stat mech wikipedia page. The value R (ideal gas constant) is equal to the Boltzmann constant but in different units].

“At that FMN concentration, a state in which the RNA binds the FMN has equal probability to a state in which the RNA binds the FMN”

For clarification’s sake: isn’t it always the case that a state in which the RNA binds to the FMN has equal probability to a state in which the RNA binds the FMN? I don’t understand how this could ever not be the case. Do you mean to say another state in which it binds the FMN? Or that it has equal probability to a state in which the RNA doesn’t bind the FMN?

I’m not sure what is actually happening at that 50% concentration

Yes, that was confusing. The two states that I meant are (1) the RNA in the ‘FMN-ready’ secondary structure but with FMN free, and (2) the RNA in the same secondary structure but with FMN bound:

RNA + FMN RNA*FMN

so, if anyone else is making a bot for EteRNA:
* -RT is approximated to -0.6
* concentration is divided by 3.0, not 0.3

Thanks Jee for clarifying this in the dev. chat yesterday

[I don’t like reviving zombie threads, but this one seems appropriate]

I’m trying to figure out what is the binding energy of FMN at a different temperature. If my admittedly fresh understanding of some thermodynamics basics is correct, the formula ΔG = -RT ln K cannot be used directly. I looked into the van 't Hoff equation and that seems to have a better chance to be correct (please confirm)

But in that case, I would need to know the ΔH at 37°C, or equivalently, to know the measure of K at a different temperature. Do we happen to have these values somewhere? Or is it possible to find these informations about the FMN aptamer somewhere in the literature (Google didn’t help much me there)?

Try this search term: ΔG = -RT ln K theoretical physical chemistry tables

and this site http://chemwiki.ucdavis.edu/Wikitexts…

or any of the several that may return in the search.

Oh,

EteRNA SELEX FMN binding aptamer isothermal titration calorimetry data is what you want.

You need the name or catalog number of the RNA aptamer and then see if the above experiment has been done and results published.

Thanks for all your efforts Chris, I couldn’t find a direct hit from the links you provided, but I revisited the papers of that team that played with “minimizing” (making the shortest possible sequence while keeping most of the functionality) various aptamers, like Theophylline and FMN.

http://nar.oxfordjournals.org/content…

In the “In vitro study of FMN binding” paragraph, there is mention of an experimental result from an earlier study which I cannot access. But if I take those numbers and if I assume that they represent measures in a standard state (298.15°K), I’m getting some numerical results, that don’t look obviously wrong, but that I can’t really confirm either. For instance, a prediction from this extrapolation says that the binding affinity should disappear above 52°C…

There’s a very non-negligible chance that I may have got my math wrong here, so I’ll keep waiting for a “pro” to shed some light

This may interest you though it’s protein-ligand based:

http://digitalcommons.sacredheart.edu…

you must be using the ΔGassociation of (-31)and −36 kJ mol−1 numbers then?

-31 kJ/mol is what they get for their own “reduced” aptamer, -36 kJ/mol (which is roughly -8.6 kcal/mol) is the value for the original aptamer, the one we’re working with in EteRNA. The value -8.6 may seem strange, but I’m assuming that it’s the binding energy in the standard state at 25°C, while the -4.867 that we see in our lab interfaces would be the binding energy scaled to the temperature normally used to simulate RNA folding, 37°C. But I could very well be wrong on all accounts…

Thanks for the pointer