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pknotsRG-enf.lhs
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***************************************
* pknotsRG-enf *
* *
* RNA Structures including *
* pseudoknots in O(n^4) time and *
* O(n^2) space. *
***************************************
This variant of pknotsRG computes the structure with minimum free energy
that contains at least one pseudoknot somewhere in the sequence
> module Main where
> import Data.Array
> import System.Environment(getArgs)
> import Foldingspace
> import RNACombinators
> import Energy
> import Algebras
> main :: IO()
> main = do
> args <- getArgs
> let input = head args
> pkmaxsize = case args of
> [x] -> 0
> [x,y] -> (read y)::Int
> otherwise -> error "Error: pknotsRG-enf sequence [pkmaxsize]"
> ereal :: Float
> ereal = (fromIntegral e / 100)
> (e,p) = case (pknots input pkmaxsize (energy *** pp)) of
> [] -> (0,"The input sequence contains no pseudoknot!")
> (x:xs) -> x in
> putStr (input ++"\n"++ p ++ " ( " ++ show ereal ++")\n")
> pknots :: [Char] -> Int -> ( (RNAInput -> FS_Algebra Int a b)
> ,(RNAInput -> FS_AlgebraExt Int a b)) -> [b]
> pknots sequence maxpk algebra = axiom (q struct') where
>
> tabulated = table n
> listed = table1 n
> n = length sequence
> axiom = axiom' n
> inp = mk (rna sequence)
> basepair (i,j) = basepair' (inp,(i,j))
> stackpair (i,j) = stackpair' (inp,(i,j))
> minloopsize m (i,j) = minloopsize' m (inp,(i,j))
> pkmaxsize
> | maxpk == 0 = \t -> True
> | otherwise = maxsize maxpk
> (alg, algext ) = algebra
> (sadd,cadd,is,sr,hl,bl,br, il,ml, mldl, mldr, mldlr, dl, dr, dlr, edl, edr, edlr,
> drem, cons, ul, pul, addss, ssadd, nil, h, h_l, h_s, h_i, h_p) = alg inp
> (pk, pkmldl, pkmldr, pkmldlr, pkml, pk',
> kndl, kndr, kndlr, frd, bkd, scale, unscale, emptymid,
> midbase, middlro, middl, middr, middlr, midregion, pss) = algext inp
>
> struct = listed (
> sadd <<< base +~~ q struct |||
> cadd <<< edangle ~~~ q struct |||
> empty nil ... h_s)
> struct' = listed (
> sadd <<< base +~~ q struct' |||
> cadd <<< edangle ~~~ q struct' |||
> cadd <<< edangle' ~~~ q struct |||
> cadd <<< edangle' ~~~ q struct' ... h_s)
>
> edangle = edl <<< base +~~ closed ~~. loc |||
> edr <<< loc .~~ closed ~~+ base |||
> edlr <<< base +~~ closed ~~+ base |||
> drem <<< initstem |||
> kndr <<< knot ~~+ base |||
> kndl <<< base +~~ knot |||
> kndlr<<< base +~~ knot ~~+ base |||
> pk <<< knot ... h
> edangle' = edl <<< base +~~ closed' ~~. loc |||
> edr <<< loc .~~ closed' ~~+ base |||
> edlr <<< base +~~ closed' ~~+ base |||
> drem <<< initstem' |||
> kndr <<< knot ~~+ base |||
> kndl <<< base +~~ knot |||
> kndlr<<< base +~~ knot ~~+ base |||
> pk <<< knot ... h
>
> initstem = is <<< loc .~~ closed ~~. loc
> closed = tabulated (
> stack ||| (hairpin ||| leftB ||| rightB ||| iloop ||| multiloop) `with` stackpair ... h)
> where
> stack = (sr <<< base +~~ closed ~~+ base) `with` basepair
> hairpin = (hl <<< base +~~ base ++~ (region `with` (minloopsize 3)) ~~+ base ~~+ base)
> leftB = (bl <<< base +~~ base ++~ region ~~~ initstem ~~+ base ~~+ base) ... h
> rightB = (br <<< base +~~ base ++~ initstem ~~~ region ~~+ base ~~+ base) ... h
> iloop = (il <<< base +~~ base ++~ region !~~ closed ~~! region ~~+ base ~~+ base) ... h where
> infixl 7 ~~!,!~~
> (~~!) = (~~<) 30
> (!~~) = (<~~) 32
> multiloop = (mldl <<< base +~~ base ++~ base +++ ml_components ~~+ base ~~+ base |||
> mldr <<< base +~~ base ++~ ml_components ~~+ base ~~+ base ~~+ base |||
> mldlr <<< base +~~ base ++~ base +++ ml_components ~~+ base ~~+ base ~~+ base |||
> ml <<< base +~~ base ++~ ml_components ~~+ base ~~+ base) `with` stackpair ... h
> where
> ml_components = combine <<< block ~~~ comps
> initstem' = is <<< loc .~~ closed' ~~. loc
> closed' = tabulated (
> stack' ||| (leftB' ||| rightB' ||| iloop' ||| multiloop') `with` stackpair ... h)
> where
> stack' = (sr <<< base +~~ closed' ~~+ base) `with` basepair
> leftB' = (bl <<< base +~~ base ++~ region ~~~ initstem' ~~+ base ~~+ base) ... h
> rightB' = (br <<< base +~~ base ++~ initstem' ~~~ region ~~+ base ~~+ base) ... h
> iloop' = (il <<< base +~~ base ++~ region !~~ closed' ~~! region ~~+ base ~~+ base) ... h where
> infixl 7 ~~!,!~~
> (~~!) = (~~<) 30
> (!~~) = (<~~) 32
> multiloop' = (mldl <<< base +~~ base ++~ base +++ ml_components' ~~+ base ~~+ base |||
> mldr <<< base +~~ base ++~ ml_components' ~~+ base ~~+ base ~~+ base |||
> mldlr <<< base +~~ base ++~ base +++ ml_components' ~~+ base ~~+ base ~~+ base |||
> ml <<< base +~~ base ++~ ml_components' ~~+ base ~~+ base) `with` stackpair ... h
> where
> ml_components' = combine <<< block' ~~~ comps' |||
> combine <<< block ~~~ comps' |||
> combine <<< block' ~~~ comps
> comps = tabulated (
> cons <<< block ~~~ comps |||
> block |||
> addss <<< block ~~~ region ... h_l)
>
> comps' = tabulated (
> cons <<< block ~~~ comps' |||
> cons <<< block' ~~~ comps |||
> cons <<< block' ~~~ comps' |||
> block' |||
> addss <<< block' ~~~ region ... h_l)
>
> block = tabulated (
> ul <<< dangle |||
> ssadd <<< region ~~~ dangle ... h_l)
> where
> dangle = dl <<< base +~~ initstem ~~. loc |||
> dr <<< loc .~~ initstem ~~+ base |||
> dlr <<< base +~~ initstem ~~+ base |||
> drem <<< initstem ... h
> block' = tabulated (
> ul <<< dangle' |||
> ssadd <<< region ~~~ dangle' |||
> pkmldl <<< base +~~ knot |||
> pkmldr <<< knot ~~+ base |||
> pkmldlr <<< base +~~ knot ~~+ base |||
> pkml <<< knot ... h_l) -- pk inside multiloop
> where
> dangle' = dl <<< base +~~ initstem' ~~. loc |||
> dr <<< loc .~~ initstem' ~~+ base |||
> dlr <<< base +~~ initstem' ~~+ base |||
> drem <<< initstem' ... h
> knot = tabulated (pknot `with` pkmaxsize ... h_p)
> where
> pknot (i,j) = [pk' energy a u b v a' w b' dangle| l <- [i+3 .. j-8], k <- [l+4 .. j-4],
The helices a and b should not overlap each other and not exceed [l...k]. Furthermore each helix must have
a minimum length of two bases. Due to stereochemical reasons one base in the front part and two
bases in the back part are left explicitely unpaired. These bases should brigde the stacks.
> (alpha,alpha', alphanrg,x1,y1) <- stack' (i,k) ++ stack (i,k),
> (beta, beta' , betanrg ,x2,y2) <- getbeta (l,j, k-alpha'),
> a <- region (i , i+alpha ),
> u <- front j (i+alpha+1, l ),
> b <- region (l , l+beta ),
> v <- middle (j-beta') (i+alpha) (l+beta, k-alpha'),
> a'<- region (k-alpha', k ),
> w <- back i (k , j-beta'-2),
> b'<- region (j-beta', j ),
> dangle <- [(max x1 y1, max x2 y2)],
> energy <- [alphanrg + betanrg
> + npp * fromIntegral(abs(alpha-alpha') + abs(beta-beta'))]
> ]
>
>
> front j = front2 |||
> frd j <<< front2 ~~+ base ... h_l -- one base dangling of b,b'
> front2 = pul <<< emptystrand |||
> (comps) |||
> (comps') ... h_l
>
> middle k l = emptymid k l |||
> midbase k l |||
> middlro k l |||
> middl k <<< base +~~ mid |||
> middr l <<< mid ~~+ base |||
> middlr k l <<< base +~~ mid ~~+ base |||
> midregion <<< mid ... h_l
> mid = pul <<< singlestrand |||
> comps |||
> comps' ... h_l
>
> back i = back2 |||
> bkd i <<< base +~~ back2 ... h_l -- one base dangling of a,a'
> back2 = pul <<< emptystrand |||
> comps |||
> comps' ... h_l
> singlestrand = pss <<< region
> emptystrand = pss <<< uregion
'stacklen' records the maximal helix of a (hypothetical) stem
starting at position i and ending at j. Only canonical helices are found.
the result of the parser is a list of 5-tuples:
(length of helix starting at i, lenght of helix ending at j, MFE,pos of bulge, pos of bulge)
> stack = tabulated (
> (countbp <<< base +~~ stack ~~+ base ) `with` basepair |||
> (countbl <<< base +~~ base ++~ base +++ stack' ~~+ base ~~+ base ) `with` stackpair |||
> (countbr <<< base +~~ base ++~ stack' ~~+ base ~~+ base ~~+ base ) `with` stackpair ...emin )
> stack' = tabulated(
> (countbp <<< base +~~ stack' ~~+ base ) `with` basepair |||
> (count2 <<< base +~~ base ++~ (region `with` (minloopsize 3)) ~~+ base ~~+ base ) `with` stackpair ... emin)
>
> getbeta (l, j, alphaend) = [ tup | tup <- help (stack' (l,j)) ++ help (stack (l,j))]
> where help [] = []
> help [(b,b',nrg,x,y)]
> | newb < 2 = []
> | l+b <= alphaend = [(b,b',nrg,x,y)] --no overlap
> -- overlap, without bulges
> | x==0 && y==0 = [(newb ,newb, nrg - head(stacknrg (l+newb-1, j-newb+1)),x,y)]
> -- bulge in overlap
> | x==0 && y<=j-newb = [(newb, newb, nrg - head(stack_wb (l+newb-1, j-newb+1)),x,0)]
> -- bulge not in overlap
> | x==0 && y>j-newb = [(newb, newb+1,nrg- head(stacknrg (l+newb-1, j-newb)), x,y)]
> -- bulge in overlap
> | x > alphaend = [(newb, newb, nrg - head(stack_wb (l+newb-1, j-newb+1)),0,y)]
> -- bulge adjacent to end of alpha
> | x == alphaend = [(newb-1, newb-1,nrg - head (stack_wb (x-2,j-newb+2)) ,0,y)]
> -- bulge not in overlap
> | x < alphaend = [(newb, newb-1,nrg- head (stacknrg (l+newb-1, j-newb+2)),x,y)]
> -- this case should never occur
> | otherwise = error ("no rule to score pseudoknot")
> where newb = alphaend-l
this table stores the energy of a helix of maximal length without bulge
> stacknrg = tabulated(
> (sum <<< base +~~ stacknrg ~~+ base) `with` basepair |||
> (sumend <<< base +~~ (region`with` (minloopsize 3)) ~~+ base) `with` basepair ...hmin)
> where sum lb c rb = c + sr_energy inp (lb, rb)
> sumend lb _ rb = 0
this table stores the energy of stacks that may start with a bulge (noncanonical stack)
We need this as a correction term in case of overlapping pseudoknot stems
> stack_wb = tabulated(
> bulgel <<< base +~~ stacknrg ~~. loc |||
> bulger <<< loc .~~ stacknrg ~~+ base |||
> (stack2 <<< base +~~ stack_wb ~~+ base) `with` basepair ...hmin)
Functions for all algebras necessary for
the computation of the max stem length/energy
> countbp lb (c,c',e,x,y) rb = (c+1, c'+1, e+sr_energy inp (lb, rb),x,y )
> count2 lb _ _ _ rb = (2 , 2 , sr_energy inp (lb, rb),0,0 )
> countbl llb lb bl (c,c',e,x,y) rb rrb = (c+3, c'+2, e+sr_energy inp (llb, rrb)
> + bl_energy inp lb (bl-1,bl) rb, bl ,y)
> countbr llb lb (c,c',e,x,y) br rb rrb = (c+2, c'+3, e+sr_energy inp (llb, rrb)
> + br_energy inp lb (br-1,br) rb,y,br)
>
> bulgel bl e rloc = e + bl_energy inp (bl-1) (bl-1, bl) (rloc+1)
> bulger lloc e br = e + br_energy inp (lloc ) (br-1,br) (br+1)
> stack2 lb e rb = e + sr_energy inp (lb -1, rb+1)
>
> hmin [] = []
> hmin xs = [minimum xs]