Generation of the profile_with_prior in alphafold about deepmind-research

[Augustin-Zidek]

Hi,

Here is the code for the profile_with_prior feature, I hope that helps:

def profile_with_prior(amino_acid_probs, prior_amino_probs,
                       s_ij, nc, beta=10.0):
  """Compute priors which takes into account priors and Blosum matrix.

  Args:
    amino_acid_probs: the observed amino acid probabilities in a column of MSA.
    prior_amino_probs: the prior amino acid probabilities for that column.
    s_ij: the substitution matrix going from amino acid i to j.
    nc: the mean number of different amino acid types.
    beta: weight of the prior, default set to 10.

  Returns:
    A profile of length 21.
  """
  f_j_over_g_j = np.divide(amino_acid_probs, prior_amino_probs)
  g_i = np.matmul(s_ij, f_j_over_g_j)
  alpha = nc - 1.0
  profiles = (alpha * amino_acid_probs + beta * g_i) / (alpha + beta)
  return profiles

[newtonjoo]

Hi,

Here is the code for the profile_with_prior feature, I hope that helps:

def profile_with_prior(amino_acid_probs, prior_amino_probs,
                       s_ij, nc, beta=10.0):
  """Compute priors which takes into account priors and Blosum matrix.

  Args:
    amino_acid_probs: the observed amino acid probabilities in a column of MSA.
    prior_amino_probs: the prior amino acid probabilities for that column.
    s_ij: the substitution matrix going from amino acid i to j.
    nc: the mean number of different amino acid types.
    beta: weight of the prior, default set to 10.

  Returns:
    A profile of length 21.
  """
  f_j_over_g_j = np.divide(amino_acid_probs, prior_amino_probs)
  g_i = np.matmul(s_ij, f_j_over_g_j)
  alpha = nc - 1.0
  profiles = (alpha * amino_acid_probs + beta * g_i) / (alpha + beta)
  return profiles

Hi,
Thank you, it's helpful.
But, It's for profile_with_prior_without_gaps with 21 number in the feature.
With gaps, a profile of length is 22.
Additionally, I wonder how to calculate s_ij for with gaps.
Please provide more information about the formula....
Thanks

[Augustin-Zidek]

Hi @newtonjoo,

sorry for the late reply.

But, It's for profile_with_prior_without_gaps with 21 number in the feature.

The code above should also work for profile with gaps.

Additionally, I wonder how to calculate s_ij for with gaps.

# 0.3176 from www.ncbi.nlm.nih.gov/pmc/articles/PMC146917/pdf/253389.pdf
s_ij = np.matmul(prior, prior.T) * np.exp(0.3176 * blosum)
s_ij_without_gaps = (np.matmul(prior_without_gaps, prior_without_gaps.T)
                     * np.exp(0.3176 * blosum[:-1, :-1]))

[alyosama]

Hi @Augustin-Zidek ,

I wonder how do you calculate nc (the mean number of different amino acid types) parameter that you are sending to the function.

[Augustin-Zidek]

Hi @alyosama,

You calculate nc as:

def mean_unique_aa_types(sequence_matrix):
  """Compute the average unique amino acids in a column for the MSA."""
  num_res = sequence_matrix.shape[1]
  unique_aa = np.zeros(num_res)
  for i in range(num_res):
    unique_aa[i] = len(np.unique(sequence_matrix[:, i]))
  return np.mean(unique_aa)

nc = mean_unique_aa_types(seq_matrix)

where seq_matrix is the MSA encoded as a matrix where each amino acid has been replaced with a unique integer.

[alyosama]

Hi @Augustin-Zidek Thanks for your fast response,

Also, I was wondering about prior calculations as well. Are you taking the frequencies of amino acids in the whole MSA as prior ?

[Augustin-Zidek]

Hi @alyosama, the prior is a static matrix (i.e. it does not depend on the current MSA) we calculated once over a set of high quality proteins.

[newtonjoo]

Hi @alyosama, the prior is a static matrix (i.e. it does not depend on the current MSA) we calculated once over a set of high quality proteins.

Thank you, please provide the static matrix. It will be helpful.

[Augustin-Zidek]

Hi John,

here is pseudo-code to regenerate the prior matrix from a set of proteins with their HHBlits MSAs:

prior = np.zeros((512, 22))  # 20 amino acids + unknown (X) + gap (-)
for protein in proteins:
  msa = protein.msa  # Shape: (number_of_alignments, sequence_length)
  # Iterate over all sequences in the MSA.
  for seq in msa:
    for i, aa in enumerate(seq):
      prior[i, aa] += 1

[newtonjoo]

Hi John,

here is pseudo-code to regenerate the prior matrix from a set of proteins with their HHBlits MSAs:

prior = np.zeros((512, 22))  # 20 amino acids + unknown (X) + gap (-)
for protein in proteins:
  msa = protein.msa  # Shape: (number_of_alignments, sequence_length)
  # Iterate over all sequences in the MSA.
  for seq in msa:
    for i, aa in enumerate(seq):
      prior[i, aa] += 1

Thanks for your providing.
prior matrix shape is (512, 22), does it mean you consider sequences less than 512 residues?

[Augustin-Zidek]

Does it mean you consider sequences less than 512 residues?

Correct, but that is only when we constructed the prior matrix (which we did once).