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nucleic.ml
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(***********************************************************************)
(* *)
(* Objective Caml *)
(* *)
(* Xavier Leroy, projet Cristal, INRIA Rocquencourt *)
(* *)
(* Copyright 1996 Institut National de Recherche en Informatique et *)
(* en Automatique. All rights reserved. This file is distributed *)
(* under the terms of the Q Public License version 1.0. *)
(* *)
(***********************************************************************)
(* $Id: nucleic.ml 7017 2005-08-12 09:22:04Z xleroy $ *)
[@@@ocaml.warning "-27"]
(* Use floating-point arithmetic *)
external ( + ) : float -> float -> float = "%addfloat"
external ( - ) : float -> float -> float = "%subfloat"
external ( * ) : float -> float -> float = "%mulfloat"
external ( / ) : float -> float -> float = "%divfloat"
(* -- MATH UTILITIES --------------------------------------------------------*)
let constant_pi = 3.14159265358979323846
let constant_minus_pi = -3.14159265358979323846
let constant_pi2 = 1.57079632679489661923
let constant_minus_pi2 = -1.57079632679489661923
(* -- POINTS ----------------------------------------------------------------*)
type pt =
{ x : float
; y : float
; z : float
}
let pt_sub p1 p2 = { x = p1.x - p2.x; y = p1.y - p2.y; z = p1.z - p2.z }
let pt_dist p1 p2 =
let dx = p1.x - p2.x and dy = p1.y - p2.y and dz = p1.z - p2.z in
sqrt ((dx * dx) + (dy * dy) + (dz * dz))
let pt_phi p =
let b = atan2 p.x p.z in
atan2 ((cos b * p.z) + (sin b * p.x)) p.y
let pt_theta p = atan2 p.x p.z
(* -- COORDINATE TRANSFORMATIONS --------------------------------------------*)
(*
The notation for the transformations follows "Paul, R.P. (1981) Robot
Manipulators. MIT Press." with the exception that our transformation
matrices don't have the perspective terms and are the transpose of
Paul's one. See also "M\"antyl\"a, M. (1985) An Introduction to
Solid Modeling, Computer Science Press" Appendix A.
The components of a transformation matrix are named like this:
a b c
d e f
g h i
tx ty tz
The components tx, ty, and tz are the translation vector.
*)
type tfo =
{ a : float
; b : float
; c : float
; d : float
; e : float
; f : float
; g : float
; h : float
; i : float
; tx : float
; ty : float
; tz : float
}
let tfo_id =
{ a = 1.0
; b = 0.0
; c = 0.0
; d = 0.0
; e = 1.0
; f = 0.0
; g = 0.0
; h = 0.0
; i = 1.0
; tx = 0.0
; ty = 0.0
; tz = 0.0
}
(*
The function "tfo-apply" multiplies a transformation matrix, tfo, by a
point vector, p. The result is a new point.
*)
let tfo_apply t p =
{ x = (p.x * t.a) + (p.y * t.d) + (p.z * t.g) + t.tx
; y = (p.x * t.b) + (p.y * t.e) + (p.z * t.h) + t.ty
; z = (p.x * t.c) + (p.y * t.f) + (p.z * t.i) + t.tz
}
(*
The function "tfo-combine" multiplies two transformation matrices A and B.
The result is a new matrix which cumulates the transformations described
by A and B.
*)
let tfo_combine a b =
(* <HAND_CSE> *)
(* Hand elimination of common subexpressions.
Assumes lots of float registers (32 is perfect, 16 still OK).
Loses on the I386, of course. *)
let a_a = a.a
and a_b = a.b
and a_c = a.c
and a_d = a.d
and a_e = a.e
and a_f = a.f
and a_g = a.g
and a_h = a.h
and a_i = a.i
and a_tx = a.tx
and a_ty = a.ty
and a_tz = a.tz
and b_a = b.a
and b_b = b.b
and b_c = b.c
and b_d = b.d
and b_e = b.e
and b_f = b.f
and b_g = b.g
and b_h = b.h
and b_i = b.i
and b_tx = b.tx
and b_ty = b.ty
and b_tz = b.tz in
{ a = (a_a * b_a) + (a_b * b_d) + (a_c * b_g)
; b = (a_a * b_b) + (a_b * b_e) + (a_c * b_h)
; c = (a_a * b_c) + (a_b * b_f) + (a_c * b_i)
; d = (a_d * b_a) + (a_e * b_d) + (a_f * b_g)
; e = (a_d * b_b) + (a_e * b_e) + (a_f * b_h)
; f = (a_d * b_c) + (a_e * b_f) + (a_f * b_i)
; g = (a_g * b_a) + (a_h * b_d) + (a_i * b_g)
; h = (a_g * b_b) + (a_h * b_e) + (a_i * b_h)
; i = (a_g * b_c) + (a_h * b_f) + (a_i * b_i)
; tx = (a_tx * b_a) + (a_ty * b_d) + (a_tz * b_g) + b_tx
; ty = (a_tx * b_b) + (a_ty * b_e) + (a_tz * b_h) + b_ty
; tz = (a_tx * b_c) + (a_ty * b_f) + (a_tz * b_i) + b_tz
}
(* </HAND_CSE> *)
(* Original without CSE *)
(* <NO_CSE> *)
(***
{ a = ((a.a * b.a) + (a.b * b.d) + (a.c * b.g));
b = ((a.a * b.b) + (a.b * b.e) + (a.c * b.h));
c = ((a.a * b.c) + (a.b * b.f) + (a.c * b.i));
d = ((a.d * b.a) + (a.e * b.d) + (a.f * b.g));
e = ((a.d * b.b) + (a.e * b.e) + (a.f * b.h));
f = ((a.d * b.c) + (a.e * b.f) + (a.f * b.i));
g = ((a.g * b.a) + (a.h * b.d) + (a.i * b.g));
h = ((a.g * b.b) + (a.h * b.e) + (a.i * b.h));
i = ((a.g * b.c) + (a.h * b.f) + (a.i * b.i));
tx = ((a.tx * b.a) + (a.ty * b.d) + (a.tz * b.g) + b.tx);
ty = ((a.tx * b.b) + (a.ty * b.e) + (a.tz * b.h) + b.ty);
tz = ((a.tx * b.c) + (a.ty * b.f) + (a.tz * b.i) + b.tz)
}
***)
(* </NO_CSE> *)
(*
The function "tfo-inv-ortho" computes the inverse of a homogeneous
transformation matrix.
*)
let tfo_inv_ortho t =
{ a = t.a
; b = t.d
; c = t.g
; d = t.b
; e = t.e
; f = t.h
; g = t.c
; h = t.f
; i = t.i
; tx = -.((t.a * t.tx) + (t.b * t.ty) + (t.c * t.tz))
; ty = -.((t.d * t.tx) + (t.e * t.ty) + (t.f * t.tz))
; tz = -.((t.g * t.tx) + (t.h * t.ty) + (t.i * t.tz))
}
(*
Given three points p1, p2, and p3, the function "tfo-align" computes
a transformation matrix such that point p1 gets mapped to (0,0,0), p2 gets
mapped to the Y axis and p3 gets mapped to the YZ plane.
*)
let tfo_align p1 p2 p3 =
let x31 = p3.x - p1.x in
let y31 = p3.y - p1.y in
let z31 = p3.z - p1.z in
let rotpy = pt_sub p2 p1 in
let phi = pt_phi rotpy in
let theta = pt_theta rotpy in
let sinp = sin phi in
let sint = sin theta in
let cosp = cos phi in
let cost = cos theta in
let sinpsint = sinp * sint in
let sinpcost = sinp * cost in
let cospsint = cosp * sint in
let cospcost = cosp * cost in
let rotpz =
{ x = (cost * x31) - (sint * z31)
; y = (sinpsint * x31) + (cosp * y31) + (sinpcost * z31)
; z = (cospsint * x31) + -.(sinp * y31) + (cospcost * z31)
}
in
let rho = pt_theta rotpz in
let cosr = cos rho in
let sinr = sin rho in
let x = -.(p1.x * cost) + (p1.z * sint) in
let y = -.(p1.x * sinpsint) - (p1.y * cosp) - (p1.z * sinpcost) in
let z = -.(p1.x * cospsint) + (p1.y * sinp) - (p1.z * cospcost) in
{ a = (cost * cosr) - (cospsint * sinr)
; b = sinpsint
; c = (cost * sinr) + (cospsint * cosr)
; d = sinp * sinr
; e = cosp
; f = -.(sinp * cosr)
; g = -.(sint * cosr) - (cospcost * sinr)
; h = sinpcost
; i = -.(sint * sinr) + (cospcost * cosr)
; tx = (x * cosr) - (z * sinr)
; ty = y
; tz = (x * sinr) + (z * cosr)
}
(* -- NUCLEIC ACID CONFORMATIONS DATA BASE ----------------------------------*)
(*
Numbering of atoms follows the paper:
IUPAC-IUB Joint Commission on Biochemical Nomenclature (JCBN)
(1983) Abbreviations and Symbols for the Description of
Conformations of Polynucleotide Chains. Eur. J. Biochem 131,
9-15.
*)
(* Define remaining atoms for each nucleotide type. *)
type nuc_specific =
| A of pt * pt * pt * pt * pt * pt * pt * pt
| C of pt * pt * pt * pt * pt * pt
| G of pt * pt * pt * pt * pt * pt * pt * pt * pt
| U of pt * pt * pt * pt * pt
(*
A n6 n7 n9 c8 h2 h61 h62 h8
C n4 o2 h41 h42 h5 h6
G n2 n7 n9 c8 o6 h1 h21 h22 h8
U o2 o4 h3 h5 h6
*)
(* Define part common to all 4 nucleotide types. *)
type nuc =
| N of
tfo
* tfo
* tfo
* tfo
* pt
* pt
* pt
* pt
* pt
* pt
* pt
* pt
* pt
* pt
* pt
* pt
* pt
* pt
* pt
* pt
* pt
* pt
* pt
* pt
* pt
* pt
* pt
* pt
* pt
* nuc_specific
(*
dgf_base_tfo ; defines the standard position for wc and wc_dumas
p_o3'_275_tfo ; defines the standard position for the connect function
p_o3'_180_tfo
p_o3'_60_tfo
p o1p o2p o5' c5' h5' h5'' c4' h4' o4' c1' h1' c2' h2'' o2' h2' c3'
h3' o3' n1 n3 c2 c4 c5 c6
*)
let is_A = function
| N
( dgf_base_tfo
, p_o3'_275_tfo
, p_o3'_180_tfo
, p_o3'_60_tfo
, p
, o1p
, o2p
, o5'
, c5'
, h5'
, h5''
, c4'
, h4'
, o4'
, c1'
, h1'
, c2'
, h2''
, o2'
, h2'
, c3'
, h3'
, o3'
, n1
, n3
, c2
, c4
, c5
, c6
, A (_, _, _, _, _, _, _, _) ) -> true
| _ -> false
let is_C = function
| N
( dgf_base_tfo
, p_o3'_275_tfo
, p_o3'_180_tfo
, p_o3'_60_tfo
, p
, o1p
, o2p
, o5'
, c5'
, h5'
, h5''
, c4'
, h4'
, o4'
, c1'
, h1'
, c2'
, h2''
, o2'
, h2'
, c3'
, h3'
, o3'
, n1
, n3
, c2
, c4
, c5
, c6
, C (_, _, _, _, _, _) ) -> true
| _ -> false
let is_G = function
| N
( dgf_base_tfo
, p_o3'_275_tfo
, p_o3'_180_tfo
, p_o3'_60_tfo
, p
, o1p
, o2p
, o5'
, c5'
, h5'
, h5''
, c4'
, h4'
, o4'
, c1'
, h1'
, c2'
, h2''
, o2'
, h2'
, c3'
, h3'
, o3'
, n1
, n3
, c2
, c4
, c5
, c6
, G (_, _, _, _, _, _, _, _, _) ) -> true
| _ -> false
let nuc_C1'
(N
( dgf_base_tfo
, p_o3'_275_tfo
, p_o3'_180_tfo
, p_o3'_60_tfo
, p
, o1p
, o2p
, o5'
, c5'
, h5'
, h5''
, c4'
, h4'
, o4'
, c1'
, h1'
, c2'
, h2''
, o2'
, h2'
, c3'
, h3'
, o3'
, n1
, n3
, c2
, c4
, c5
, c6
, _ )) =
c1'
let nuc_C2
(N
( dgf_base_tfo
, p_o3'_275_tfo
, p_o3'_180_tfo
, p_o3'_60_tfo
, p
, o1p
, o2p
, o5'
, c5'
, h5'
, h5''
, c4'
, h4'
, o4'
, c1'
, h1'
, c2'
, h2''
, o2'
, h2'
, c3'
, h3'
, o3'
, n1
, n3
, c2
, c4
, c5
, c6
, _ )) =
c2
let nuc_C3'
(N
( dgf_base_tfo
, p_o3'_275_tfo
, p_o3'_180_tfo
, p_o3'_60_tfo
, p
, o1p
, o2p
, o5'
, c5'
, h5'
, h5''
, c4'
, h4'
, o4'
, c1'
, h1'
, c2'
, h2''
, o2'
, h2'
, c3'
, h3'
, o3'
, n1
, n3
, c2
, c4
, c5
, c6
, _ )) =
c3'
let nuc_C4
(N
( dgf_base_tfo
, p_o3'_275_tfo
, p_o3'_180_tfo
, p_o3'_60_tfo
, p
, o1p
, o2p
, o5'
, c5'
, h5'
, h5''
, c4'
, h4'
, o4'
, c1'
, h1'
, c2'
, h2''
, o2'
, h2'
, c3'
, h3'
, o3'
, n1
, n3
, c2
, c4
, c5
, c6
, _ )) =
c4
let nuc_C4'
(N
( dgf_base_tfo
, p_o3'_275_tfo
, p_o3'_180_tfo
, p_o3'_60_tfo
, p
, o1p
, o2p
, o5'
, c5'
, h5'
, h5''
, c4'
, h4'
, o4'
, c1'
, h1'
, c2'
, h2''
, o2'
, h2'
, c3'
, h3'
, o3'
, n1
, n3
, c2
, c4
, c5
, c6
, _ )) =
c4'
let nuc_N1
(N
( dgf_base_tfo
, p_o3'_275_tfo
, p_o3'_180_tfo
, p_o3'_60_tfo
, p
, o1p
, o2p
, o5'
, c5'
, h5'
, h5''
, c4'
, h4'
, o4'
, c1'
, h1'
, c2'
, h2''
, o2'
, h2'
, c3'
, h3'
, o3'
, n1
, n3
, c2
, c4
, c5
, c6
, _ )) =
n1
let nuc_O3'
(N
( dgf_base_tfo
, p_o3'_275_tfo
, p_o3'_180_tfo
, p_o3'_60_tfo
, p
, o1p
, o2p
, o5'
, c5'
, h5'
, h5''
, c4'
, h4'
, o4'
, c1'
, h1'
, c2'
, h2''
, o2'
, h2'
, c3'
, h3'
, o3'
, n1
, n3
, c2
, c4
, c5
, c6
, _ )) =
o3'
let nuc_P
(N
( dgf_base_tfo
, p_o3'_275_tfo
, p_o3'_180_tfo
, p_o3'_60_tfo
, p
, o1p
, o2p
, o5'
, c5'
, h5'
, h5''
, c4'
, h4'
, o4'
, c1'
, h1'
, c2'
, h2''
, o2'
, h2'
, c3'
, h3'
, o3'
, n1
, n3
, c2
, c4
, c5
, c6
, _ )) =
p
let nuc_dgf_base_tfo
(N
( dgf_base_tfo
, p_o3'_275_tfo
, p_o3'_180_tfo
, p_o3'_60_tfo
, p
, o1p
, o2p
, o5'
, c5'
, h5'
, h5''
, c4'
, h4'
, o4'
, c1'
, h1'
, c2'
, h2''
, o2'
, h2'
, c3'
, h3'
, o3'
, n1
, n3
, c2
, c4
, c5
, c6
, _ )) =
dgf_base_tfo
let nuc_p_o3'_180_tfo
(N
( dgf_base_tfo
, p_o3'_275_tfo
, p_o3'_180_tfo
, p_o3'_60_tfo
, p
, o1p
, o2p
, o5'
, c5'
, h5'
, h5''
, c4'
, h4'
, o4'
, c1'
, h1'
, c2'
, h2''
, o2'
, h2'
, c3'
, h3'
, o3'
, n1
, n3
, c2
, c4
, c5
, c6
, _ )) =
p_o3'_180_tfo
let nuc_p_o3'_275_tfo
(N
( dgf_base_tfo
, p_o3'_275_tfo
, p_o3'_180_tfo
, p_o3'_60_tfo
, p
, o1p
, o2p
, o5'
, c5'
, h5'
, h5''
, c4'
, h4'
, o4'
, c1'
, h1'
, c2'
, h2''
, o2'
, h2'
, c3'
, h3'
, o3'
, n1
, n3
, c2
, c4
, c5
, c6
, _ )) =
p_o3'_275_tfo
let nuc_p_o3'_60_tfo
(N
( dgf_base_tfo
, p_o3'_275_tfo
, p_o3'_180_tfo
, p_o3'_60_tfo
, p
, o1p
, o2p
, o5'
, c5'
, h5'
, h5''
, c4'
, h4'
, o4'
, c1'
, h1'
, c2'
, h2''
, o2'
, h2'
, c3'
, h3'
, o3'
, n1
, n3
, c2
, c4
, c5
, c6
, _ )) =
p_o3'_60_tfo
let rA_N9 = function
| N
( dgf_base_tfo
, p_o3'_275_tfo
, p_o3'_180_tfo
, p_o3'_60_tfo
, p
, o1p
, o2p
, o5'
, c5'
, h5'
, h5''
, c4'
, h4'
, o4'
, c1'
, h1'
, c2'
, h2''
, o2'
, h2'
, c3'
, h3'
, o3'
, n1
, n3
, c2
, c4
, c5
, c6
, A (n6, n7, n9, c8, h2, h61, h62, h8) ) -> n9
| _ -> assert false
let rG_N9 = function
| N
( dgf_base_tfo
, p_o3'_275_tfo
, p_o3'_180_tfo
, p_o3'_60_tfo
, p
, o1p
, o2p
, o5'
, c5'
, h5'
, h5''
, c4'
, h4'
, o4'
, c1'
, h1'
, c2'
, h2''
, o2'
, h2'
, c3'
, h3'
, o3'
, n1
, n3
, c2
, c4
, c5
, c6
, G (n2, n7, n9, c8, o6, h1, h21, h22, h8) ) -> n9
| _ -> assert false
(* Database of nucleotide conformations: *)
let rA =
N
( { a = -0.0018
; b = -0.8207
; c = 0.5714
; (* dgf_base_tfo *)
d = 0.2679
; e = -0.5509
; f = -0.7904
; g = 0.9634
; h = 0.1517
; i = 0.2209
; tx = 0.0073
; ty = 8.4030
; tz = 0.6232
}
, { a = -0.8143
; b = -0.5091
; c = -0.2788
; (* P_O3'_275_tfo *)
d = -0.0433
; e = -0.4257
; f = 0.9038
; g = -0.5788
; h = 0.7480
; i = 0.3246
; tx = 1.5227
; ty = 6.9114
; tz = -7.0765
}
, { a = 0.3822
; b = -0.7477
; c = 0.5430
; (* P_O3'_180_tfo *)
d = 0.4552
; e = 0.6637
; f = 0.5935
; g = -0.8042
; h = 0.0203
; i = 0.5941
; tx = -6.9472
; ty = -4.1186
; tz = -5.9108
}
, { a = 0.5640
; b = 0.8007
; c = -0.2022
; (* P_O3'_60_tfo *)
d = -0.8247
; e = 0.5587
; f = -0.0878
; g = 0.0426
; h = 0.2162
; i = 0.9754
; tx = 6.2694
; ty = -7.0540
; tz = 3.3316
}
, { x = 2.8930; y = 8.5380; z = -3.3280 }
, (* P *)
{ x = 1.6980; y = 7.6960; z = -3.5570 }
, (* O1P *)
{ x = 3.2260; y = 9.5010; z = -4.4020 }
, (* O2P *)
{ x = 4.1590; y = 7.6040; z = -3.0340 }
, (* O5' *)
{ x = 5.4550; y = 8.2120; z = -2.8810 }
, (* C5' *)
{ x = 5.4546; y = 8.8508; z = -1.9978 }
, (* H5' *)
{ x = 5.7588; y = 8.6625; z = -3.8259 }
, (* H5'' *)
{ x = 6.4970; y = 7.1480; z = -2.5980 }
, (* C4' *)
{ x = 7.4896; y = 7.5919; z = -2.5214 }
, (* H4' *)
{ x = 6.1630; y = 6.4860; z = -1.3440 }
, (* O4' *)
{ x = 6.5400; y = 5.1200; z = -1.4190 }
, (* C1' *)
{ x = 7.2763; y = 4.9681; z = -0.6297 }
, (* H1' *)
{ x = 7.1940; y = 4.8830; z = -2.7770 }
, (* C2' *)
{ x = 6.8667; y = 3.9183; z = -3.1647 }
, (* H2'' *)
{ x = 8.5860; y = 5.0910; z = -2.6140 }
, (* O2' *)
{ x = 8.9510; y = 4.7626; z = -1.7890 }
, (* H2' *)
{ x = 6.5720; y = 6.0040; z = -3.6090 }
, (* C3' *)
{ x = 5.5636; y = 5.7066; z = -3.8966 }
, (* H3' *)
{ x = 7.3801; y = 6.3562; z = -4.7350 }
, (* O3' *)
{ x = 4.7150; y = 0.4910; z = -0.1360 }
, (* N1 *)