Chemical space

Chemical space is the space spanned by all chemical compounds. As of January 2012, there are more than 64 million organic and inorganic substances reported in the scientific literature (link). This is, however, still only a vanishing fraction of the total number of possible small organic molecules, which has been estimated to exceed 10⁶⁰ (read: 10 to the power of 60) (link). Drug discoverers have to navigate the mind-boggling vastness of this chemical space to identify those few compounds that can be used as drugs.  In some cases, knowledge about the drug target and the chemistry involved in drug-target binding allows rational drug design principles to be applied. That is, drug space is truly navigated in the sense of purposeful steering. In many cases, as with for example high-throughput screening, however, the discovery process is more like drifting through space on a random-walk-like trajectory.

For the RNA drug subspace, sequence information allow us to estimate the number of possible oligos that can be designed against a given target. In this blog I will focus on oligos consisting of only DNA and LNA nucleotides. Also, I will consider only two types of general designs: gapmers against mRNA targets and mixmers against miRNA targets.

Gapmers

Gapmers are oligos that have a stretch of DNAs in the middle and LNAs in the flanks. A shorthand notation for a 10nt gapmer with 3 LNAs in each flank and 4 DNAs in the middle (the gap) is LLLDDDDLLL. When a gapmer oligo binds to the region of its RNA target transcript where it has perfect complementarity, the DNAs in the gap forms a DNA:RNA double strand with the target transcript which can recruit RNAse H. Upon RNAse H binding the transcript is cleaved (link) and the cleaved fragments degraded by exonucleases.

So, for a given target, how many gapmers can be designed? Say that the transcript is n nucleotides long, and that the oligo is l nucleotides long. Then we can tile n−l+1 oligos along the transcript. For n >> l, n-l+1 is approximately equal to n. For example, a transcript that is 1000nt long can have 987 oligos of length 15 tiled along its length.

Concerning gapmer length, say that oligos between n_min and n_max in length are relevant to consider. That is, at each starting position, the oligo length can be between n_min and n_max, and there are  therefore n_min−n_max+1 different lengths that needs to be evaluated. Also, several (k) gapmer designs may be relevant. For example, the number of LNAs in each flank may vary between 2 and 3, giving k=4 (e.g. LLDDDDLL, LLLDDLLL, LLDDDLLL, LLLDDDLL).

The total number of oligos then equals

{ Σ(n-l+1) } × k , where the sum (Σ) is over n, from n_min to n_max

For the example used here with a 1000nt transcript, oligos between 10nt and 20nt in length, and four different gapmer designs, the total number of oligos that can be designed is 43384. A simple approximation is to say that at each position in the 1000nt long transcript, we can design 11 × 4 = 44 different gapmers (varying length and design), giving 44000 in all.

Mixmers

A mixmer binding to a miRNA hinders the binding of the RISC-incorporated miRNA mature strand to its mRNA targets. Effectively, it can be seen as an antagonist to the miRNAs natural “ligands”. For a mixmer, DNA and LNA nucleotides are mixed to optimize binding affinity and transport. A 10nt mixmer could for example be written LDLDLDLDLL.

In contract to gapmers, the length of the miRNA targets are usually only around 22nt in length – much shorther than the mRNA targets for gapmers. On the other hand, the possibility of mixing LNA and DNA in the oligos, make the number of different designs explode, as is shown in the following.

In its most simple form, for a mixmer of length l, where at each position we can have either a DNA or a LNA, the total number of possibilities is 2^l. For a 10mer, for example, there are 2¹⁰ = 1024 possibilities. Three design considerations constrain the possibilities: (1) There has to be at least one LNA in each flank to protect against degradation by endonucleases, (2) depending on the oligo length, the LNA/DNA ratio is usually constrained to a certain interval, e.g. between 20% and 80% for a 16mer, since both too high- and low affinity is unwanted, and (3) there should be no more than 3 DNAs in a row to avoid RNAse H recruitment.

I will skip the equations for the total number of possibilities under these constraints for now (perhaps a topic for a separate blog), and simply tabulate the possibilities for mixmers between 8nt and 23nt

8   2

9   16

10   74

11   92

12   352

13   1108

14   3024

15   7432

16   16862

17   39882

18   78280

19   152782

20   294270

21   567524

22   1091972

23   1053464

For this example I furthermore assumed that the seed portion (nucleotides 2-7 counting from the 5′-end) of the miRNA should be covered by the mimxer and that the LNA/DNA ratio interval went linearly from 100% LNA for 8mers to max 80% and min 20% for 23mers. All in all there are a bit more than 3.3 million possibilities. Notice that the even with these constraints, the number of mixmers that can be designed scales exponentially with the mixmer length.

Gapmer vs mixmer space

With design criteria as specified here, the number of gapmers that can be designed scales linearly with the length of the target mRNA, whereas the number of mixmers scales exponentially with the length of the mixmer. Perhaps surprisingly, this means that the mixmer space quickly becomes much larger than the gapmer space. For both mixmer and gapmer spaces, however, it seems reasonable that the number of oligos are <10¹⁰, even when allowing other nucleotide modifications besides LNA. This is still a relatively small number compared to small molecule compounds, where, just for derivatives of n-hexane, for example, there are more than 10²⁹ possibilities (Weininger, pp 425–530 in Encyclopedia of Computational Chemistry).

UPDATE: This project is filled.

Background

At the Center for Computational and Applied Transcriptomics (COAT), experimental and computational methods are being used to investigate RNA structure and RNA-protein interactions on a transcriptome wide scale to enable the design of effective and safe RNA drugs (more information at rna.dk). As part of COAT, Santaris Pharma is looking for a bioinformatics masters student to work on a project as described below.

Outline of project

RNA molecules are single-stranded molecules with a strong tendency to fold back on themselves and form Watson-Crick pairs, leading to secondary structural motifs of various lengths and complexities. These motifs can further assemble into intricate three-dimensional architectures. RNA structure is a key element in many regulatory processes (Westhof and Romby, Nat Methods, 2010), and, more pragmatically, may limit the accessibility of RNA drugs (modified oligonucleotides designed to be reverse complementary to their target RNAs).

Experimentally, high-throughput sequencing technology have recently been used to determine RNA secondary structure in full transcriptomes of yeast (Kertesz et al., Nature, 2010) and mouse (Underwood et al., Nat Methods, 2010) cells.

Computationally, RNA structure prediction can be based on deriving minimal free energy structures that maximizes the number of base pairs and uses empirical estimates of thermodynamic parameters for neighbouring interactions and loop entropies (Zuker and Stiegler, NAR, 1981, and Hofacker et al., 1994). Alternatively, comparative genomics methods that assume different evolutionary pressures on single-stranded and double-stranded parts of a folded RNA molecule can be used (Pedersen et al., PLoS Comput Biol, 2006). The thesis project will compare the experimentally observed structures derived from the sequencing data with the predictions made from these methods.

Based on this work, possible accessibility limitations due to secondary structure will be evaluated for a number of RNA molecules and compared with Santaris Pharma’s experimentally observed performances of sets of LNA-modified oligonucleotides designed against each of them.

Requirements

• Fluency in R and perhaps also in Python or similar.
• Solid understanding of RNA biology.
• Experience with analysing sequencing data is a plus

For information about how to apply, please see this post.