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# Copyright 2021 DeepMind Technologies Limited
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""Functions for processing confidence metrics."""
from typing import Dict, Optional, Tuple
import numpy as np
import scipy.special
def compute_plddt(logits: np.ndarray) -> np.ndarray:
"""Computes per-residue pLDDT from logits.
Args:
logits: [num_res, num_bins] output from the PredictedLDDTHead.
Returns:
plddt: [num_res] per-residue pLDDT.
"""
num_bins = logits.shape[-1]
bin_width = 1.0 / num_bins
bin_centers = np.arange(start=0.5 * bin_width, stop=1.0, step=bin_width)
probs = scipy.special.softmax(logits, axis=-1)
predicted_lddt_ca = np.sum(probs * bin_centers[None, :], axis=-1)
return predicted_lddt_ca * 100
def _calculate_bin_centers(breaks: np.ndarray):
"""Gets the bin centers from the bin edges.
Args:
breaks: [num_bins - 1] the error bin edges.
Returns:
bin_centers: [num_bins] the error bin centers.
"""
step = (breaks[1] - breaks[0])
# Add half-step to get the center
bin_centers = breaks + step / 2
# Add a catch-all bin at the end.
bin_centers = np.concatenate([bin_centers, [bin_centers[-1] + step]],
axis=0)
return bin_centers
def _calculate_expected_aligned_error(
alignment_confidence_breaks: np.ndarray,
aligned_distance_error_probs: np.ndarray) -> Tuple[np.ndarray, np.ndarray]:
"""Calculates expected aligned distance errors for every pair of residues.
Args:
alignment_confidence_breaks: [num_bins - 1] the error bin edges.
aligned_distance_error_probs: [num_res, num_res, num_bins] the predicted
probs for each error bin, for each pair of residues.
Returns:
predicted_aligned_error: [num_res, num_res] the expected aligned distance
error for each pair of residues.
max_predicted_aligned_error: The maximum predicted error possible.
"""
bin_centers = _calculate_bin_centers(alignment_confidence_breaks)
# Tuple of expected aligned distance error and max possible error.
return (np.sum(aligned_distance_error_probs * bin_centers, axis=-1),
np.asarray(bin_centers[-1]))
def compute_predicted_aligned_error(
logits: np.ndarray,
breaks: np.ndarray) -> Dict[str, np.ndarray]:
"""Computes aligned confidence metrics from logits.
Args:
logits: [num_res, num_res, num_bins] the logits output from
PredictedAlignedErrorHead.
breaks: [num_bins - 1] the error bin edges.
Returns:
aligned_confidence_probs: [num_res, num_res, num_bins] the predicted
aligned error probabilities over bins for each residue pair.
predicted_aligned_error: [num_res, num_res] the expected aligned distance
error for each pair of residues.
max_predicted_aligned_error: The maximum predicted error possible.
"""
aligned_confidence_probs = scipy.special.softmax(
logits,
axis=-1)
predicted_aligned_error, max_predicted_aligned_error = (
_calculate_expected_aligned_error(
alignment_confidence_breaks=breaks,
aligned_distance_error_probs=aligned_confidence_probs))
return {
'aligned_confidence_probs': aligned_confidence_probs,
'predicted_aligned_error': predicted_aligned_error,
'max_predicted_aligned_error': max_predicted_aligned_error,
}
def predicted_tm_score(
logits: np.ndarray,
breaks: np.ndarray,
residue_weights: Optional[np.ndarray] = None) -> np.ndarray:
"""Computes predicted TM alignment score.
Args:
logits: [num_res, num_res, num_bins] the logits output from
PredictedAlignedErrorHead.
breaks: [num_bins] the error bins.
residue_weights: [num_res] the per residue weights to use for the
expectation.
Returns:
ptm_score: the predicted TM alignment score.
"""
# residue_weights has to be in [0, 1], but can be floating-point, i.e. the
# exp. resolved head's probability.
if residue_weights is None:
residue_weights = np.ones(logits.shape[0])
bin_centers = _calculate_bin_centers(breaks)
num_res = np.sum(residue_weights)
# Clip num_res to avoid negative/undefined d0.
clipped_num_res = max(num_res, 19)
# Compute d_0(num_res) as defined by TM-score, eqn. (5) in
# http://zhanglab.ccmb.med.umich.edu/papers/2004_3.pdf
# Yang & Skolnick "Scoring function for automated
# assessment of protein structure template quality" 2004
d0 = 1.24 * (clipped_num_res - 15) ** (1./3) - 1.8
# Convert logits to probs
probs = scipy.special.softmax(logits, axis=-1)
# TM-Score term for every bin
tm_per_bin = 1. / (1 + np.square(bin_centers) / np.square(d0))
# E_distances tm(distance)
predicted_tm_term = np.sum(probs * tm_per_bin, axis=-1)
normed_residue_mask = residue_weights / (1e-8 + residue_weights.sum())
per_alignment = np.sum(predicted_tm_term * normed_residue_mask, axis=-1)
return np.asarray(per_alignment[(per_alignment * residue_weights).argmax()])
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