[Shagbark]

I moved this here from the general chemistry board.

Here's the application:  I have a cell with mRNA.  I want to add some siRNA that will bind to a specific mRNA sequence, but interfere minimally with the other mRNA in the cell.  I have a choice of m possible siRNA sequences to use, any of which will bind with the long target mRNA sequence.   I want to figure out which siRNA sequence will generate the least interference - meaning, will combine with the fewest other, non-target mRNA sequences.

For each possible siRNA sequence R_r, r in 1..m_r, I find all of its sub-sequences S_r,i that occur in non-target mRNA.  It will react with all of these sub-sequences.  The Gibbs free energy of formation for binding to a sub-sequence changes by around -1 for each base you add, but there are many, many more short matching sequences than long matching sequences.  I don't know whether interference from the many short subsequences or the fewer longer, stronger-binding subsequences predominates.

I want to take each possible siRNA sequence r, and calculate how much of it will get bound up with the non-target matching mRNA subsequences.  For each sequence r, there are n_r of these matching subsequences, giving rise to n_r equilibrium equations.  Also, each matching subsequence occurs a different number of times in the genome

So, for each r, I can write the series of equations

R_r + S_r,1 <-> R_rS_r,1
R_r + S_r,2 <-> R_rS_r,2
...
R_r + S_{r,n_r} <-> R_rS_{r,n_r}

I don't know the initial or final concentrations of anything.
I do know the relative proportions of each of the S_r,i, which are integers, and I know the Gibbs free energy of formation for each equation, as well as the enthalpy and entropy change.
I want to find out which Rr has the greatest final concentration after binding with all of its various S_r,i.
I'm pretty stuck at this point.

There is an additional complication, in that it is physiologically more dangerous for R_r to bind 2n times with S_r,i than to bind n times with S_r,j and n times with S_r,k.  However, dealing with that would probably require a lot of experimentation; I don't think anyone knows how much worse it is.

- Phil

[Shagbark]

In the other thread on the general board, Yggdrasil then responded:

This is an interesting question you pose.  I guess you can transform these equations in to several serries of equations since Keq = exp(-(Delta)G/RT).  Since for R + S <--> RS, K = [RS] / [R]ff (where the f denotes free), you get the (nonlinear) system of  equations:

Kr,i = [RrSr,i] / [R]r,freer,i,free

where
Kr,i = exp(-(Delta)Gr,i/RT)
r,i,free = r,i,total + [RS]r,i, and
[R]r,total = [R]r,free + Sumni=1 [RS]r,i

Maybe these equations would help.

Do people really have specificity problems like this with RNAi?  The silencing complex uses about a ~20 nt long siRNA which should allow specific knockdown of only one gene.

I wrote back:

Quote from: Yggdrasil on Yesterday at 10:40:50 PM
[R]_r,total = [R]_r,free + Sumⁿ_i=1 [RS]_r,i

There are two problems with this equation:
1. We don't know the concentrations being used in any particular experiment.
2. If you simply add up all of the values of [RS]_r,i, that sum can be greater than is possible.  For instance, you can have 5 different matching S_r,i, each of which, by itself, would bind up half of the R_r.

Do people really have specificity problems like this with RNAi?  The silencing complex uses about a ~20 nt long siRNA which should allow specific knockdown of only one gene.

In the literature, there is no mention of this problem.  In the lab, there is.  An siRNA can knock down a gene with a match of as few as 7 sequential base pairs, although this hasn't been reported in the literature.  I suspect that some of the unknown variation in effectiveness of siRNAs lies in the number of off-target interactions they partake in.

- Phil