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#@title get secondary structure (SSE) from given PDB file
#@markdown So far it seems the best solution is to steal code from biotite
#@markdown which calculates the SSE of a peptide chain based on the P-SEA algorithm (Labesse 1997)
# CODE FROM BIOKITE
# From Krypton
import numpy as np
import random
import torch
def vector_dot(v1,v2):
return (v1*v2).sum(axis=-1)
def norm_vector(v):
factor = np.linalg.norm(v, axis=-1)
if isinstance(factor, np.ndarray):
v /= factor[..., np.newaxis]
else:
v /= factor
return v
def coord(x):
return np.asarray(x)
def displacement(atoms1, atoms2):
v1 = coord(atoms1)
v2 = coord(atoms2)
if len(v1.shape) <= len(v2.shape):
diff = v2 - v1
else:
diff = -(v1 - v2)
return diff
def distance(atoms1, atoms2):
diff = displacement(atoms1, atoms2)
return np.sqrt(vector_dot(diff, diff))
def angle(atoms1, atoms2, atoms3):
v1 = displacement(atoms1, atoms2)
v2 = displacement(atoms3, atoms2)
norm_vector(v1)
norm_vector(v2)
return np.arccos(vector_dot(v1,v2))
def dihedral(atoms1, atoms2, atoms3, atoms4):
v1 = displacement(atoms1, atoms2)
v2 = displacement(atoms2, atoms3)
v3 = displacement(atoms3, atoms4)
norm_vector(v1)
norm_vector(v2)
norm_vector(v3)
n1 = np.cross(v1, v2)
n2 = np.cross(v2, v3)
# Calculation using atan2, to ensure the correct sign of the angle
x = vector_dot(n1,n2)
y = vector_dot(np.cross(n1,n2), v2)
return np.arctan2(y,x)
def replace_letters(arr):
# Create a dictionary that maps the letters 'a', 'b', and 'c' to the corresponding numbers
letter_to_number = {'a': 0, 'b': 1, 'c': 2}
# Create a new array that will hold the numbers
nums = []
# Loop through the input array and replace the letters with the corresponding numbers
for letter in arr:
if letter in letter_to_number:
nums.append(letter_to_number[letter])
else:
nums.append(letter)
return np.array(nums)
def replace_with_mask(arr, percentage, replace_loops=False):
# Make sure the percentage is between 0 and 100
percentage = min(max(percentage, 0), 100)
# Calculate the number of values to replace
num_to_replace = int(len(arr) * percentage / 100)
# Choose a random subset of the array to replace
replace_indices = random.sample(range(len(arr)), num_to_replace)
# Replace the values at the chosen indices with the number 3
for i in replace_indices:
arr[i] = 3
if replace_loops:
for i in arr:
if arr[i] == 2:
arr[i] = 3
return arr
def annotate_sse(ca_coord, percentage_mask=0, replace_loops=False):
_radians_to_angle = 2*np.pi/360
_r_helix = ((89-12)*_radians_to_angle, (89+12)*_radians_to_angle)
_a_helix = ((50-20)*_radians_to_angle, (50+20)*_radians_to_angle)
_d2_helix = ((5.5-0.5), (5.5+0.5))
_d3_helix = ((5.3-0.5), (5.3+0.5))
_d4_helix = ((6.4-0.6), (6.4+0.6))
_r_strand = ((124-14)*_radians_to_angle, (124+14)*_radians_to_angle)
_a_strand = ((-180)*_radians_to_angle, (-125)*_radians_to_angle,
(145)*_radians_to_angle, (180)*_radians_to_angle)
_d2_strand = ((6.7-0.6), (6.7+0.6))
_d3_strand = ((9.9-0.9), (9.9+0.9))
_d4_strand = ((12.4-1.1), (12.4+1.1))
# Filter all CA atoms in the relevant chain.
d2i_coord = np.full(( len(ca_coord), 2, 3 ), np.nan)
d3i_coord = np.full(( len(ca_coord), 2, 3 ), np.nan)
d4i_coord = np.full(( len(ca_coord), 2, 3 ), np.nan)
ri_coord = np.full(( len(ca_coord), 3, 3 ), np.nan)
ai_coord = np.full(( len(ca_coord), 4, 3 ), np.nan)
# The distances and angles are not defined for the entire interval,
# therefore the indices do not have the full range
# Values that are not defined are NaN
for i in range(1, len(ca_coord)-1):
d2i_coord[i] = (ca_coord[i-1], ca_coord[i+1])
for i in range(1, len(ca_coord)-2):
d3i_coord[i] = (ca_coord[i-1], ca_coord[i+2])
for i in range(1, len(ca_coord)-3):
d4i_coord[i] = (ca_coord[i-1], ca_coord[i+3])
for i in range(1, len(ca_coord)-1):
ri_coord[i] = (ca_coord[i-1], ca_coord[i], ca_coord[i+1])
for i in range(1, len(ca_coord)-2):
ai_coord[i] = (ca_coord[i-1], ca_coord[i],
ca_coord[i+1], ca_coord[i+2])
d2i = distance(d2i_coord[:,0], d2i_coord[:,1])
d3i = distance(d3i_coord[:,0], d3i_coord[:,1])
d4i = distance(d4i_coord[:,0], d4i_coord[:,1])
ri = angle(ri_coord[:,0], ri_coord[:,1], ri_coord[:,2])
ai = dihedral(ai_coord[:,0], ai_coord[:,1],
ai_coord[:,2], ai_coord[:,3])
sse = np.full(len(ca_coord), "c", dtype="U1")
# Annotate helices
# Find CA that meet criteria for potential helices
is_pot_helix = np.zeros(len(sse), dtype=bool)
for i in range(len(sse)):
if (
d3i[i] >= _d3_helix[0] and d3i[i] <= _d3_helix[1]
and d4i[i] >= _d4_helix[0] and d4i[i] <= _d4_helix[1]
) or (
ri[i] >= _r_helix[0] and ri[i] <= _r_helix[1]
and ai[i] >= _a_helix[0] and ai[i] <= _a_helix[1]
):
is_pot_helix[i] = True
# Real helices are 5 consecutive helix elements
is_helix = np.zeros(len(sse), dtype=bool)
counter = 0
for i in range(len(sse)):
if is_pot_helix[i]:
counter += 1
else:
if counter >= 5:
is_helix[i-counter : i] = True
counter = 0
# Extend the helices by one at each end if CA meets extension criteria
i = 0
while i < len(sse):
if is_helix[i]:
sse[i] = "a"
if (
d3i[i-1] >= _d3_helix[0] and d3i[i-1] <= _d3_helix[1]
) or (
ri[i-1] >= _r_helix[0] and ri[i-1] <= _r_helix[1]
):
sse[i-1] = "a"
sse[i] = "a"
if (
d3i[i+1] >= _d3_helix[0] and d3i[i+1] <= _d3_helix[1]
) or (
ri[i+1] >= _r_helix[0] and ri[i+1] <= _r_helix[1]
):
sse[i+1] = "a"
i += 1
# Annotate sheets
# Find CA that meet criteria for potential strands
is_pot_strand = np.zeros(len(sse), dtype=bool)
for i in range(len(sse)):
if ( d2i[i] >= _d2_strand[0] and d2i[i] <= _d2_strand[1]
and d3i[i] >= _d3_strand[0] and d3i[i] <= _d3_strand[1]
and d4i[i] >= _d4_strand[0] and d4i[i] <= _d4_strand[1]
) or (
ri[i] >= _r_strand[0] and ri[i] <= _r_strand[1]
and ( (ai[i] >= _a_strand[0] and ai[i] <= _a_strand[1])
or (ai[i] >= _a_strand[2] and ai[i] <= _a_strand[3]))
):
is_pot_strand[i] = True
# Real strands are 5 consecutive strand elements,
# or shorter fragments of at least 3 consecutive strand residues,
# if they are in hydrogen bond proximity to 5 other residues
pot_strand_coord = ca_coord[is_pot_strand]
is_strand = np.zeros(len(sse), dtype=bool)
counter = 0
contacts = 0
for i in range(len(sse)):
if is_pot_strand[i]:
counter += 1
coord = ca_coord[i]
for strand_coord in ca_coord:
dist = distance(coord, strand_coord)
if dist >= 4.2 and dist <= 5.2:
contacts += 1
else:
if counter >= 4:
is_strand[i-counter : i] = True
elif counter == 3 and contacts >= 5:
is_strand[i-counter : i] = True
counter = 0
contacts = 0
# Extend the strands by one at each end if CA meets extension criteria
i = 0
while i < len(sse):
if is_strand[i]:
sse[i] = "b"
if d3i[i-1] >= _d3_strand[0] and d3i[i-1] <= _d3_strand[1]:
sse[i-1] = "b"
sse[i] = "b"
if d3i[i+1] >= _d3_strand[0] and d3i[i+1] <= _d3_strand[1]:
sse[i+1] = "b"
i += 1
sse=replace_letters(sse)
sse=replace_with_mask(sse, percentage_mask, replace_loops=replace_loops)
sse=torch.nn.functional.one_hot(torch.tensor(sse), num_classes=4)
return sse
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