How to predict the distance between two residues in a protein sequence I have some protein sequences and I need to predict the physical distance between each two residues in the protein when folded correctly in 3 dimensions; I need to predict this distances just by having the protein sequence and not the structure.

I have a group of pdb IDs and I have got homologs for them and made a multiple sequence alignment for each query sequence; But later I need to imagine that I don't have any structure for being able to predict the distance between residues in query sequences without any known structure.

There are some articles for solving this issue using machine learning methods but I don't want to train with a large numbers of structures. Any one knows any way to solve this problem by using mathematical or statistical methods?
Developments in this area over the last year are worth pointing out. All use residue-residue covariation information from a protein family so require a multiple sequence alignment to work, though it sounds like you have that.

The most accurate way to do this would be to use pre-trained machine learning methods, which would not require you to train your own version. Examples include:


DMPfold from our lab, which is freely-available open source.
The RaptorX method from the Xu lab.
The state of the art is AlphaFold from DeepMind, though this has not been published yet.


These predict the probabilities of a residue-residue distance being in various distance 'bins', e.g. the probability of being 5 - 6 Angstrom apart. They don't predict beyond ~20 Angstrom.

If you specifically wanted a statistical, non-trained method, then consider:


PSICOV from our lab.
CCMPred.
EVfold.


All of which are available in some form. The problem here is that they all predict binary contacts at 8 Angstrom, whereas it sounds like you need more fine-grained distances.

In a general sense, you can use any 3D structure prediction method and then read the distances back from the predicted structure.