codonseq.py

# Copyright 2013 by Zheng Ruan (zruan1991@gmail.com).
# All rights reserved.
# This code is part of the Biopython distribution and governed by its
# license.  Please see the LICENSE file that should have been included
# as part of this package.
"""Code for dealing with coding sequence.

CodonSeq class is inherited from Seq class. This is the core class to
deal with sequences in CodonAlignment in biopython.

"""
from itertools import permutations
from math import log

from Bio.Seq import Seq
from Bio.SeqRecord import SeqRecord
from Bio.Data import CodonTable


class CodonSeq(Seq):
    """CodonSeq is designed to be within the SeqRecords of a CodonAlignment class.

    CodonSeq is useful as it allows the user to specify
    reading frame when translate CodonSeq

    CodonSeq also accepts codon style slice by calling
    get_codon() method.

    **Important:** Ungapped CodonSeq can be any length if you
    specify the rf_table. Gapped CodonSeq should be a
    multiple of three.

    >>> codonseq = CodonSeq("AAATTTGGGCCAAATTT", rf_table=(0,3,6,8,11,14))
    >>> print(codonseq.translate())
    KFGAKF

    test get_full_rf_table method

    >>> p = CodonSeq('AAATTTCCCGG-TGGGTTTAA', rf_table=(0, 3, 6, 9, 11, 14, 17))
    >>> full_rf_table = p.get_full_rf_table()
    >>> print(full_rf_table)
    [0, 3, 6, 9, 12, 15, 18]
    >>> print(p.translate(rf_table=full_rf_table, ungap_seq=False))
    KFPPWV*
    >>> p = CodonSeq('AAATTTCCCGGGAA-TTTTAA', rf_table=(0, 3, 6, 9, 14, 17))
    >>> print(p.get_full_rf_table())
    [0, 3, 6, 9, 12.0, 15, 18]
    >>> p = CodonSeq('AAA------------TAA', rf_table=(0, 3))
    >>> print(p.get_full_rf_table())
    [0, 3.0, 6.0, 9.0, 12.0, 15]

    """

    def __init__(self, data="", gap_char="-", rf_table=None):
        """Initialize the class."""
        # rf_table should be a tuple or list indicating the every
        # codon position along the sequence. For example:
        # sequence = 'AAATTTGGGCCAAATTT'
        # rf_table = (0, 3, 6, 8, 11, 14)
        # the translated protein sequences will be
        # AAA TTT GGG GCC AAA TTT
        #  K   F   G   A   K   F
        # Notice: rf_table applies to ungapped sequence. If there
        #   are gaps in the sequence, they will be discarded. This
        #   feature ensures the rf_table is independent of where the
        #   codon sequence appears in the alignment

        Seq.__init__(self, data.upper())
        self.gap_char = gap_char

        # check the length of the alignment to be a triple
        if rf_table is None:
            length = len(self)
            if length % 3 != 0:
                raise ValueError(
                    "Sequence length is not a multiple of "
                    "three (i.e. a whole number of codons)"
                )
            self.rf_table = list(range(0, length - self.count(gap_char), 3))
        else:
            # if gap_char in self:
            #    assert  len(self) % 3 == 0, \
            #            "Gapped sequence length is not a triple number"
            if not isinstance(rf_table, (tuple, list)):
                raise TypeError("rf_table should be a tuple or list object")
            if not all(isinstance(i, int) for i in rf_table):
                raise TypeError(
                    "Elements in rf_table should be int "
                    "that specify the codon positions of "
                    "the sequence"
                )
            self.rf_table = rf_table

    def get_codon(self, index):
        """Get the index codon from the sequence."""
        if len({i % 3 for i in self.rf_table}) != 1:
            raise RuntimeError(
                "frameshift detected. CodonSeq object is not able to deal with "
                "codon sequence with frameshift. Please use normal slice option."
            )
        if isinstance(index, int):
            if index != -1:
                return str(self[index * 3 : (index + 1) * 3])
            else:
                return str(self[index * 3 :])
        else:
            # This slice ensures that codon will always be the unit
            # in slicing (it won't change to other codon if you are
            # using reverse slicing such as [::-1]).
            # The idea of the code below is to first map the slice
            # to amino acid sequence and then transform it into
            # codon sequence.
            aa_index = range(len(self) // 3)

            def cslice(p):
                aa_slice = aa_index[p]
                codon_slice = ""
                for i in aa_slice:
                    codon_slice += self[i * 3 : i * 3 + 3]
                return str(codon_slice)

            codon_slice = cslice(index)
            return CodonSeq(codon_slice)

    def get_codon_num(self):
        """Return the number of codons in the CodonSeq."""
        return len(self.rf_table)

    def translate(
        self, codon_table=None, stop_symbol="*", rf_table=None, ungap_seq=True
    ):
        """Translate the CodonSeq based on the reading frame in rf_table.

        It is possible for the user to specify
        a rf_table at this point. If you want to include
        gaps in the translated sequence, this is the only
        way. ungap_seq should be set to true for this
        purpose.
        """
        if codon_table is None:
            codon_table = CodonTable.generic_by_id[1]
        amino_acids = []
        if ungap_seq:
            tr_seq = str(self).replace(self.gap_char, "")
        else:
            tr_seq = str(self)
        if rf_table is None:
            rf_table = self.rf_table
        p = -1  # initiation
        for i in rf_table:
            if isinstance(i, float):
                amino_acids.append("-")
                continue
            # elif '---' == tr_seq[i:i+3]:
            #    amino_acids.append('-')
            #    continue
            elif "-" in tr_seq[i : i + 3]:
                # considering two types of frameshift
                if p == -1 or p - i == 3:
                    p = i
                    codon = tr_seq[i : i + 6].replace("-", "")[:3]
                elif p - i > 3:
                    codon = tr_seq[i : i + 3]
                    p = i
            else:
                # normal condition without gaps
                codon = tr_seq[i : i + 3]
                p = i
            if codon in codon_table.stop_codons:
                amino_acids.append(stop_symbol)
                continue
            try:
                amino_acids.append(codon_table.forward_table[codon])
            except KeyError:
                raise RuntimeError(
                    f"Unknown codon detected ({codon}). Did you"
                    " forget to specify the ungap_seq argument?"
                )
        return "".join(amino_acids)

    def toSeq(self):
        """Convert DNA to seq object."""
        return Seq(str(self))

    def get_full_rf_table(self):
        """Return full rf_table of the CodonSeq records.

        A full rf_table is different from a normal rf_table in that
        it translate gaps in CodonSeq. It is helpful to construct
        alignment containing frameshift.
        """
        ungap_seq = str(self).replace("-", "")
        relative_pos = [self.rf_table[0]]
        for i in range(1, len(self.rf_table[1:]) + 1):
            relative_pos.append(self.rf_table[i] - self.rf_table[i - 1])
        full_rf_table = []
        codon_num = 0
        for i in range(0, len(self), 3):
            if self[i : i + 3] == self.gap_char * 3:
                full_rf_table.append(i + 0.0)
            elif relative_pos[codon_num] == 0:
                full_rf_table.append(i)
                codon_num += 1
            elif relative_pos[codon_num] in (-1, -2):
                # check the gap status of previous codon
                gap_stat = 3 - self.count("-", i - 3, i)
                if gap_stat == 3:
                    full_rf_table.append(i + relative_pos[codon_num])
                elif gap_stat == 2:
                    full_rf_table.append(i + 1 + relative_pos[codon_num])
                elif gap_stat == 1:
                    full_rf_table.append(i + 2 + relative_pos[codon_num])
                codon_num += 1
            elif relative_pos[codon_num] > 0:
                full_rf_table.append(i + 0.0)
            try:
                this_len = 3 - self.count("-", i, i + 3)
                relative_pos[codon_num] -= this_len
            except Exception:  # TODO: IndexError?
                # we probably reached the last codon
                pass
        return full_rf_table

    def full_translate(self, codon_table=None, stop_symbol="*"):
        """Apply full translation with gaps considered."""
        if codon_table is None:
            codon_table = CodonTable.generic_by_id[1]
        full_rf_table = self.get_full_rf_table()
        return self.translate(
            codon_table=codon_table,
            stop_symbol=stop_symbol,
            rf_table=full_rf_table,
            ungap_seq=False,
        )

    def ungap(self, gap="-"):
        """Return a copy of the sequence without the gap character(s)."""
        if len(gap) != 1 or not isinstance(gap, str):
            raise ValueError("Unexpected gap character, %s" % repr(gap))
        return CodonSeq(str(self).replace(gap, ""), rf_table=self.rf_table)

    @classmethod
    def from_seq(cls, seq, rf_table=None):
        """Get codon sequence from sequence data."""
        if rf_table is None:
            return cls(str(seq))
        else:
            return cls(str(seq), rf_table=rf_table)


def _get_codon_list(codonseq):
    """List of codons according to full_rf_table for counting (PRIVATE)."""
    # if not isinstance(codonseq, CodonSeq):
    #    raise TypeError("_get_codon_list accept a CodonSeq object "
    #                    "({0} detected)".format(type(codonseq)))
    full_rf_table = codonseq.get_full_rf_table()
    codon_lst = []
    for i, k in enumerate(full_rf_table):
        if isinstance(k, int):
            start = k
            try:
                end = int(full_rf_table[i + 1])
            except IndexError:
                end = start + 3
            this_codon = str(codonseq[start:end])
            if len(this_codon) == 3:
                codon_lst.append(this_codon)
            else:
                codon_lst.append(str(this_codon.ungap()))
        elif str(codonseq[int(k) : int(k) + 3]) == "---":
            codon_lst.append("---")
        else:
            # this may be problematic, as normally no codon should
            # fall into this condition
            codon_lst.append(codonseq[int(k) : int(k) + 3])
    return codon_lst


def cal_dn_ds(codon_seq1, codon_seq2, method="NG86", codon_table=None, k=1, cfreq=None):
    """Calculate dN and dS of the given two sequences.

    Available methods:
        - NG86  - `Nei and Gojobori (1986)`_ (PMID 3444411).
        - LWL85 - `Li et al. (1985)`_ (PMID 3916709).
        - ML    - `Goldman and Yang (1994)`_ (PMID 7968486).
        - YN00  - `Yang and Nielsen (2000)`_ (PMID 10666704).

    .. _`Nei and Gojobori (1986)`: http://www.ncbi.nlm.nih.gov/pubmed/3444411
    .. _`Li et al. (1985)`: http://www.ncbi.nlm.nih.gov/pubmed/3916709
    .. _`Goldman and Yang (1994)`: http://mbe.oxfordjournals.org/content/11/5/725
    .. _`Yang and Nielsen (2000)`: https://doi.org/10.1093/oxfordjournals.molbev.a026236

    Arguments:
     - codon_seq1 - CodonSeq or or SeqRecord that contains a CodonSeq
     - codon_seq2 - CodonSeq or or SeqRecord that contains a CodonSeq
     - w  - transition/transversion ratio
     - cfreq - Current codon frequency vector can only be specified
       when you are using ML method. Possible ways of
       getting cfreq are: F1x4, F3x4 and F61.

    """
    if isinstance(codon_seq1, CodonSeq) and isinstance(codon_seq2, CodonSeq):
        pass
    elif isinstance(codon_seq1, SeqRecord) and isinstance(codon_seq2, SeqRecord):
        codon_seq1 = codon_seq1.seq
        codon_seq2 = codon_seq2.seq
    else:
        raise TypeError(
            "cal_dn_ds accepts two CodonSeq objects or SeqRecord "
            "that contains CodonSeq as its seq!"
        )
    if len(codon_seq1.get_full_rf_table()) != len(codon_seq2.get_full_rf_table()):
        raise RuntimeError(
            f"full_rf_table length of seq1 ({len(codon_seq1.get_full_rf_table())})"
            f" and seq2 ({len(codon_seq2.get_full_rf_table())}) are not the same"
        )
    if cfreq is None:
        cfreq = "F3x4"
    elif cfreq is not None and method != "ML":
        raise RuntimeError("cfreq can only be specified when you are using ML method")
    if cfreq not in ("F1x4", "F3x4", "F61"):
        import warnings

        warnings.warn(
            f"Unknown cfreq ({cfreq}). "
            "Only F1x4, F3x4 and F61 are acceptable. Used F3x4 in the following."
        )
        cfreq = "F3x4"
    if codon_table is None:
        codon_table = CodonTable.generic_by_id[1]
    seq1_codon_lst = _get_codon_list(codon_seq1)
    seq2_codon_lst = _get_codon_list(codon_seq2)
    # remove gaps in seq_codon_lst
    seq1 = []
    seq2 = []
    for i, j in zip(seq1_codon_lst, seq2_codon_lst):
        if ("-" not in i) and ("-" not in j):
            seq1.append(i)
            seq2.append(j)
    dnds_func = {"ML": _ml, "NG86": _ng86, "LWL85": _lwl85, "YN00": _yn00}
    if method == "ML":
        return dnds_func[method](seq1, seq2, cfreq, codon_table)
    else:
        return dnds_func[method](seq1, seq2, k, codon_table)


#################################################################
#              private functions for NG86 method
#################################################################


def _ng86(seq1, seq2, k, codon_table):
    """NG86 method main function (PRIVATE)."""
    S_sites1, N_sites1 = _count_site_NG86(seq1, codon_table=codon_table, k=k)
    S_sites2, N_sites2 = _count_site_NG86(seq2, codon_table=codon_table, k=k)
    S_sites = (S_sites1 + S_sites2) / 2.0
    N_sites = (N_sites1 + N_sites2) / 2.0
    SN = [0, 0]
    for i, j in zip(seq1, seq2):
        SN = [
            m + n for m, n in zip(SN, _count_diff_NG86(i, j, codon_table=codon_table))
        ]

    ps = SN[0] / S_sites
    pn = SN[1] / N_sites
    if ps < 3 / 4:
        dS = abs(-3.0 / 4 * log(1 - 4.0 / 3 * ps))
    else:
        dS = -1
    if pn < 3 / 4:
        dN = abs(-3.0 / 4 * log(1 - 4.0 / 3 * pn))
    else:
        dN = -1
    return dN, dS


def _count_site_NG86(codon_lst, codon_table, k=1):
    """Count synonymous and non-synonymous sites of a list of codons (PRIVATE).

    Arguments:
     - codon_lst - A three letter codon list from a CodonSeq object.
       This can be returned from _get_codon_list method.
     - k - transition/transversion rate ratio.

    """
    S_site = 0  # synonymous sites
    N_site = 0  # non-synonymous sites
    purine = ("A", "G")
    pyrimidine = ("T", "C")
    base_tuple = ("A", "T", "C", "G")
    for codon in codon_lst:
        neighbor_codon = {"transition": [], "transversion": []}
        # classify neighbor codons
        codon = codon.replace("U", "T")
        if codon == "---":
            continue
        for n, i in enumerate(codon):
            for j in base_tuple:
                if i == j:
                    pass
                elif i in purine and j in purine:
                    codon_chars = list(codon)
                    codon_chars[n] = j
                    this_codon = "".join(codon_chars)
                    neighbor_codon["transition"].append(this_codon)
                elif i in pyrimidine and j in pyrimidine:
                    codon_chars = list(codon)
                    codon_chars[n] = j
                    this_codon = "".join(codon_chars)
                    neighbor_codon["transition"].append(this_codon)
                else:
                    codon_chars = list(codon)
                    codon_chars[n] = j
                    this_codon = "".join(codon_chars)
                    neighbor_codon["transversion"].append(this_codon)
        # count synonymous and non-synonymous sites
        aa = codon_table.forward_table[codon]
        this_codon_N_site = this_codon_S_site = 0
        for neighbor in neighbor_codon["transition"]:
            if neighbor in codon_table.stop_codons:
                this_codon_N_site += 1
            elif codon_table.forward_table[neighbor] == aa:
                this_codon_S_site += 1
            else:
                this_codon_N_site += 1
        for neighbor in neighbor_codon["transversion"]:
            if neighbor in codon_table.stop_codons:
                this_codon_N_site += k
            elif codon_table.forward_table[neighbor] == aa:
                this_codon_S_site += k
            else:
                this_codon_N_site += k
        norm_const = (this_codon_N_site + this_codon_S_site) / 3
        S_site += this_codon_S_site / norm_const
        N_site += this_codon_N_site / norm_const
    return (S_site, N_site)


def _count_diff_NG86(codon1, codon2, codon_table):
    """Count differences between two codons, three-letter string (PRIVATE).

    The function will take multiple pathways from codon1 to codon2
    into account.
    """
    if not isinstance(codon1, str) or not isinstance(codon2, str):
        raise TypeError(
            "_count_diff_NG86 accepts string object to represent codon"
            f" ({type(codon1)}, {type(codon2)} detected)"
        )
    if len(codon1) != 3 or len(codon2) != 3:
        raise RuntimeError(
            "codon should be three letter string"
            f" ({len(codon1)}, {len(codon2)} detected)"
        )
    SN = [0, 0]  # synonymous and nonsynonymous counts
    if codon1 == "---" or codon2 == "---":
        return SN
    base_tuple = ("A", "C", "G", "T")
    if not all(i in base_tuple for i in codon1):
        raise RuntimeError(
            f"Unrecognized character detected in codon1 {codon1}"
            " (Codons consist of A, T, C or G)"
        )
    if not all(i in base_tuple for i in codon2):
        raise RuntimeError(
            f"Unrecognized character detected in codon2 {codon2}"
            " (Codons consist of A, T, C or G)"
        )
    if codon1 == codon2:
        return SN
    else:
        diff_pos = []
        for i, k in enumerate(zip(codon1, codon2)):
            if k[0] != k[1]:
                diff_pos.append(i)

        def compare_codon(codon1, codon2, codon_table, weight=1):
            """Compare two codon accounting for different pathways."""
            sd = nd = 0
            if len(set(map(codon_table.forward_table.get, [codon1, codon2]))) == 1:
                sd += weight
            else:
                nd += weight
            return (sd, nd)

        if len(diff_pos) == 1:
            SN = [
                i + j
                for i, j in zip(
                    SN, compare_codon(codon1, codon2, codon_table=codon_table)
                )
            ]
        elif len(diff_pos) == 2:
            for i in diff_pos:
                temp_codon = codon1[:i] + codon2[i] + codon1[i + 1 :]
                SN = [
                    i + j
                    for i, j in zip(
                        SN,
                        compare_codon(
                            codon1, temp_codon, codon_table=codon_table, weight=0.5
                        ),
                    )
                ]
                SN = [
                    i + j
                    for i, j in zip(
                        SN,
                        compare_codon(
                            temp_codon, codon2, codon_table=codon_table, weight=0.5
                        ),
                    )
                ]
        elif len(diff_pos) == 3:
            paths = list(permutations([0, 1, 2], 3))
            tmp_codon = []
            for p in paths:
                tmp1 = codon1[: p[0]] + codon2[p[0]] + codon1[p[0] + 1 :]
                tmp2 = tmp1[: p[1]] + codon2[p[1]] + tmp1[p[1] + 1 :]
                tmp_codon.append((tmp1, tmp2))
                SN = [
                    i + j
                    for i, j in zip(
                        SN, compare_codon(codon1, tmp1, codon_table, weight=0.5 / 3)
                    )
                ]
                SN = [
                    i + j
                    for i, j in zip(
                        SN, compare_codon(tmp1, tmp2, codon_table, weight=0.5 / 3)
                    )
                ]
                SN = [
                    i + j
                    for i, j in zip(
                        SN, compare_codon(tmp2, codon2, codon_table, weight=0.5 / 3)
                    )
                ]
    return SN


#################################################################
#               private functions for LWL85 method
#################################################################


def _lwl85(seq1, seq2, k, codon_table):
    """LWL85 method main function (PRIVATE).

    Nomenclature is according to Li et al. (1985), PMID 3916709.
    """
    codon_fold_dict = _get_codon_fold(codon_table)
    # count number of sites in different degenerate classes
    fold0 = [0, 0]
    fold2 = [0, 0]
    fold4 = [0, 0]
    for codon in seq1 + seq2:
        fold_num = codon_fold_dict[codon]
        for f in fold_num:
            if f == "0":
                fold0[0] += 1
            elif f == "2":
                fold2[0] += 1
            elif f == "4":
                fold4[0] += 1
    L = [sum(fold0) / 2.0, sum(fold2) / 2.0, sum(fold4) / 2.0]
    # count number of differences in different degenerate classes
    PQ = [0] * 6  # with P0, P2, P4, Q0, Q2, Q4 in each position
    for codon1, codon2 in zip(seq1, seq2):
        if (codon1 == "---" or codon2 == "---") or codon1 == codon2:
            continue
        else:
            PQ = [
                i + j
                for i, j in zip(
                    PQ, _diff_codon(codon1, codon2, fold_dict=codon_fold_dict)
                )
            ]
    PQ = [i / j for i, j in zip(PQ, L * 2)]
    P = PQ[:3]
    Q = PQ[3:]
    A = [
        (1.0 / 2) * log(1.0 / (1 - 2 * i - j)) - (1.0 / 4) * log(1.0 / (1 - 2 * j))
        for i, j in zip(P, Q)
    ]
    B = [(1.0 / 2) * log(1.0 / (1 - 2 * i)) for i in Q]
    dS = 3 * (L[2] * A[1] + L[2] * (A[2] + B[2])) / (L[1] + 3 * L[2])
    dN = 3 * (L[2] * B[1] + L[0] * (A[0] + B[0])) / (2 * L[1] + 3 * L[0])
    return dN, dS


def _get_codon_fold(codon_table):
    """Classify different position in a codon into different folds (PRIVATE)."""

    def find_fold_class(codon, forward_table):
        base = {"A", "T", "C", "G"}
        fold = ""
        codon_base_lst = list(codon)
        for i, b in enumerate(codon_base_lst):
            other_base = base - set(b)
            aa = []
            for j in other_base:
                codon_base_lst[i] = j
                try:
                    aa.append(forward_table["".join(codon_base_lst)])
                except KeyError:
                    aa.append("stop")
            if aa.count(forward_table[codon]) == 0:
                fold += "0"
            elif aa.count(forward_table[codon]) in (1, 2):
                fold += "2"
            elif aa.count(forward_table[codon]) == 3:
                fold += "4"
            else:
                raise RuntimeError(
                    "Unknown Error, cannot assign the position to a fold"
                )
            codon_base_lst[i] = b
        return fold

    fold_table = {}
    for codon in codon_table.forward_table:
        if "U" not in codon:
            fold_table[codon] = find_fold_class(codon, codon_table.forward_table)
    fold_table["---"] = "---"
    return fold_table


def _diff_codon(codon1, codon2, fold_dict):
    """Count number of different substitution types between two codons (PRIVATE).

    returns tuple (P0, P2, P4, Q0, Q2, Q4)

    Nomenclature is according to Li et al. (1958), PMID 3916709.
    """
    P0 = P2 = P4 = Q0 = Q2 = Q4 = 0
    fold_num = fold_dict[codon1]
    purine = ("A", "G")
    pyrimidine = ("T", "C")
    for n, (i, j) in enumerate(zip(codon1, codon2)):
        if i != j and (i in purine and j in purine):
            if fold_num[n] == "0":
                P0 += 1
            elif fold_num[n] == "2":
                P2 += 1
            elif fold_num[n] == "4":
                P4 += 1
            else:
                raise RuntimeError("Unexpected fold_num %d" % fold_num[n])
        if i != j and (i in pyrimidine and j in pyrimidine):
            if fold_num[n] == "0":
                P0 += 1
            elif fold_num[n] == "2":
                P2 += 1
            elif fold_num[n] == "4":
                P4 += 1
            else:
                raise RuntimeError("Unexpected fold_num %d" % fold_num[n])
        if i != j and (
            (i in purine and j in pyrimidine) or (i in pyrimidine and j in purine)
        ):
            if fold_num[n] == "0":
                Q0 += 1
            elif fold_num[n] == "2":
                Q2 += 1
            elif fold_num[n] == "4":
                Q4 += 1
            else:
                raise RuntimeError("Unexpected fold_num %d" % fold_num[n])
    return (P0, P2, P4, Q0, Q2, Q4)


#################################################################
#               private functions for YN00 method
#################################################################


def _yn00(seq1, seq2, k, codon_table):
    """YN00 method main function (PRIVATE).

    Nomenclature is according to Yang and Nielsen (2000), PMID 10666704.
    """
    from collections import defaultdict
    from scipy.linalg import expm

    fcodon = [
        {"A": 0, "G": 0, "C": 0, "T": 0},
        {"A": 0, "G": 0, "C": 0, "T": 0},
        {"A": 0, "G": 0, "C": 0, "T": 0},
    ]
    codon_fold_dict = _get_codon_fold(codon_table)
    fold0_cnt = defaultdict(int)
    fold4_cnt = defaultdict(int)
    for codon in seq1 + seq2:
        # count sites at different codon position
        if codon != "---":
            fcodon[0][codon[0]] += 1
            fcodon[1][codon[1]] += 1
            fcodon[2][codon[2]] += 1
        # count sites in different degenerate fold class
        fold_num = codon_fold_dict[codon]
        for i, f in enumerate(fold_num):
            if f == "0":
                fold0_cnt[codon[i]] += 1
            elif f == "4":
                fold4_cnt[codon[i]] += 1
    f0_total = sum(fold0_cnt.values())
    f4_total = sum(fold4_cnt.values())
    for i, j in zip(fold0_cnt, fold4_cnt):
        fold0_cnt[i] = fold0_cnt[i] / f0_total
        fold4_cnt[i] = fold4_cnt[i] / f4_total
    # TODO:
    # the initial kappa is different from what yn00 gives,
    # try to find the problem.
    TV = _get_TV(seq1, seq2, codon_table=codon_table)
    k04 = (_get_kappa_t(fold0_cnt, TV), _get_kappa_t(fold4_cnt, TV))
    kappa = (f0_total * k04[0] + f4_total * k04[1]) / (f0_total + f4_total)
    # kappa = 2.4285
    # count synonymous sites and non-synonymous sites
    for i in range(3):
        tot = sum(fcodon[i].values())
        fcodon[i] = {j: k / tot for j, k in fcodon[i].items()}
    pi = defaultdict(int)
    for i in list(codon_table.forward_table.keys()) + codon_table.stop_codons:
        if "U" not in i:
            pi[i] = 0
    for i in seq1 + seq2:
        pi[i] += 1
    S_sites1, N_sites1, bfreqSN1 = _count_site_YN00(
        seq1, seq2, pi, k=kappa, codon_table=codon_table
    )
    S_sites2, N_sites2, bfreqSN2 = _count_site_YN00(
        seq2, seq1, pi, k=kappa, codon_table=codon_table
    )
    N_sites = (N_sites1 + N_sites2) / 2
    S_sites = (S_sites1 + S_sites2) / 2
    bfreqSN = [{"A": 0, "T": 0, "C": 0, "G": 0}, {"A": 0, "T": 0, "C": 0, "G": 0}]
    for i in range(2):
        for b in ("A", "T", "C", "G"):
            bfreqSN[i][b] = (bfreqSN1[i][b] + bfreqSN2[i][b]) / 2
    # use NG86 method to get initial t and w
    SN = [0, 0]
    for i, j in zip(seq1, seq2):
        SN = [
            m + n for m, n in zip(SN, _count_diff_NG86(i, j, codon_table=codon_table))
        ]
    ps = SN[0] / S_sites
    pn = SN[1] / N_sites
    p = sum(SN) / (S_sites + N_sites)
    w = log(1 - 4.0 / 3 * pn) / log(1 - 4.0 / 3 * ps)
    t = -3 / 4 * log(1 - 4 / 3 * p)
    tolerance = 1e-5
    dSdN_pre = [0, 0]
    for temp in range(20):
        # count synonymous and nonsynonymous differences under kappa, w, t
        codon_lst = [
            i
            for i in list(codon_table.forward_table.keys()) + codon_table.stop_codons
            if "U" not in i
        ]
        Q = _get_Q(pi, kappa, w, codon_lst, codon_table)
        P = expm(Q * t)
        TV = [0, 0, 0, 0]  # synonymous/nonsynonymous transition/transversion
        codon_npath = {}
        for i, j in zip(seq1, seq2):
            if i != "---" and j != "---":
                codon_npath.setdefault((i, j), 0)
                codon_npath[(i, j)] += 1
        for i in codon_npath:
            tv = _count_diff_YN00(i[0], i[1], P, codon_lst, codon_table)
            TV = [m + n * codon_npath[i] for m, n in zip(TV, tv)]
        TV = (TV[0] / S_sites, TV[1] / S_sites), (TV[2] / N_sites, TV[3] / N_sites)
        # according to the DistanceF84() function of yn00.c in paml,
        # the t (e.q. 10) appears in PMID: 10666704 is dS and dN
        dSdN = []
        for f, tv in zip(bfreqSN, TV):
            dSdN.append(_get_kappa_t(f, tv, t=True))
        t = dSdN[0] * 3 * S_sites / (S_sites + N_sites) + dSdN[1] * 3 * N_sites / (
            S_sites + N_sites
        )
        w = dSdN[1] / dSdN[0]
        if all(
            map(lambda x: x < tolerance, (abs(i - j) for i, j in zip(dSdN, dSdN_pre)))
        ):
            return dSdN[1], dSdN[0]  # dN, dS
        dSdN_pre = dSdN


def _get_TV(codon_lst1, codon_lst2, codon_table):
    """Get TV (PRIVATE).

    Arguments:
     - T - proportions of transitional differences
     - V - proportions of transversional differences

    """
    purine = ("A", "G")
    pyrimidine = ("C", "T")
    TV = [0, 0]
    sites = 0
    for codon1, codon2 in zip(codon_lst1, codon_lst2):
        if "---" not in (codon1, codon2):
            for i, j in zip(codon1, codon2):
                if i == j:
                    pass
                elif i in purine and j in purine:
                    TV[0] += 1
                elif i in pyrimidine and j in pyrimidine:
                    TV[0] += 1
                else:
                    TV[1] += 1
                sites += 1
    return (TV[0] / sites, TV[1] / sites)
    # return (TV[0], TV[1])


def _get_kappa_t(pi, TV, t=False):
    """Calculate kappa (PRIVATE).

    The following formula and variable names are according to PMID: 10666704
    """
    pi["Y"] = pi["T"] + pi["C"]
    pi["R"] = pi["A"] + pi["G"]
    A = (
        2 * (pi["T"] * pi["C"] + pi["A"] * pi["G"])
        + 2
        * (
            pi["T"] * pi["C"] * pi["R"] / pi["Y"]
            + pi["A"] * pi["G"] * pi["Y"] / pi["R"]
        )
        * (1 - TV[1] / (2 * pi["Y"] * pi["R"]))
        - TV[0]
    ) / (2 * (pi["T"] * pi["C"] / pi["Y"] + pi["A"] * pi["G"] / pi["R"]))
    B = 1 - TV[1] / (2 * pi["Y"] * pi["R"])
    a = -0.5 * log(A)  # this seems to be an error in YANG's original paper
    b = -0.5 * log(B)
    kappaF84 = a / b - 1
    if t is False:
        kappaHKY85 = 1 + (
            pi["T"] * pi["C"] / pi["Y"] + pi["A"] * pi["G"] / pi["R"]
        ) * kappaF84 / (pi["T"] * pi["C"] + pi["A"] * pi["G"])
        return kappaHKY85
    else:
        t = (
            4 * pi["T"] * pi["C"] * (1 + kappaF84 / pi["Y"])
            + 4 * pi["A"] * pi["G"] * (1 + kappaF84 / pi["R"])
            + 4 * pi["Y"] * pi["R"]
        ) * b
        return t


def _count_site_YN00(codon_lst1, codon_lst2, pi, k, codon_table):
    """Site counting method from Ina / Yang and Nielsen (PRIVATE).

    Method from `Ina (1995)`_ as modified by `Yang and Nielsen (2000)`_.
    This will return the total number of synonymous and nonsynonymous sites
    and base frequencies in each category. The function is equivalent to
    the ``CountSites()`` function in ``yn00.c`` of PAML.

    .. _`Ina (1995)`: https://doi.org/10.1007/BF00167113
    .. _`Yang and Nielsen (2000)`: https://doi.org/10.1093/oxfordjournals.molbev.a026236

    """
    if len(codon_lst1) != len(codon_lst2):
        raise RuntimeError(
            "Length of two codon_lst should be the same (%d and %d detected)"
            % (len(codon_lst1), len(codon_lst2))
        )
    else:
        length = len(codon_lst1)
    purine = ("A", "G")
    pyrimidine = ("T", "C")
    base_tuple = ("A", "T", "C", "G")
    codon_dict = codon_table.forward_table
    stop = codon_table.stop_codons
    codon_npath = {}
    for i, j in zip(codon_lst1, codon_lst2):
        if i != "---" and j != "---":
            codon_npath.setdefault((i, j), 0)
            codon_npath[(i, j)] += 1
    S_sites = N_sites = 0
    freqSN = [
        {"A": 0, "T": 0, "C": 0, "G": 0},  # synonymous
        {"A": 0, "T": 0, "C": 0, "G": 0},
    ]  # nonsynonymous
    for codon_pair, npath in codon_npath.items():
        codon = codon_pair[0]
        S = N = 0
        for pos in range(3):
            for base in base_tuple:
                if codon[pos] == base:
                    continue
                neighbor_codon = codon[:pos] + base + codon[pos + 1 :]
                if neighbor_codon in stop:
                    continue
                weight = pi[neighbor_codon]
                if codon[pos] in pyrimidine and base in pyrimidine:
                    weight *= k
                elif codon[pos] in purine and base in purine:
                    weight *= k
                if codon_dict[codon] == codon_dict[neighbor_codon]:
                    S += weight
                    freqSN[0][base] += weight * npath
                else:
                    N += weight
                    freqSN[1][base] += weight * npath
        S_sites += S * npath
        N_sites += N * npath
    norm_const = 3 * length / (S_sites + N_sites)
    S_sites *= norm_const
    N_sites *= norm_const
    for i in freqSN:
        norm_const = sum(i.values())
        for b in i:
            i[b] /= norm_const
    return S_sites, N_sites, freqSN


def _count_diff_YN00(codon1, codon2, P, codon_lst, codon_table):
    """Count differences between two codons (three-letter string; PRIVATE).

    The function will weighted multiple pathways from codon1 to codon2
    according to P matrix of codon substitution. The proportion
    of transition and transversion (TV) will also be calculated in
    the function.
    """
    if not isinstance(codon1, str) or not isinstance(codon2, str):
        raise TypeError(
            "_count_diff_YN00 accepts string object to represent codon"
            f" ({type(codon1)}, {type(codon2)} detected)"
        )
    if len(codon1) != 3 or len(codon2) != 3:
        raise RuntimeError(
            "codon should be three letter string"
            f" ({len(codon1)}, {len(codon2)} detected)"
        )
    TV = [
        0,
        0,
        0,
        0,
    ]  # transition and transversion counts (synonymous and nonsynonymous)
    if codon1 == "---" or codon2 == "---":
        return TV
    base_tuple = ("A", "C", "G", "T")
    if not all(i in base_tuple for i in codon1):
        raise RuntimeError(
            f"Unrecognized character detected in codon1 {codon1}"
            " (Codons consist of A, T, C or G)"
        )
    if not all(i in base_tuple for i in codon2):
        raise RuntimeError(
            f"Unrecognized character detected in codon2 {codon2}"
            " (Codons consist of A, T, C or G)"
        )
    if codon1 == codon2:
        return TV
    else:
        diff_pos = []
        for i, k in enumerate(zip(codon1, codon2)):
            if k[0] != k[1]:
                diff_pos.append(i)

        def count_TV(codon1, codon2, diff, codon_table, weight=1):
            purine = ("A", "G")
            pyrimidine = ("T", "C")
            dic = codon_table.forward_table
            stop = codon_table.stop_codons
            if codon1 in stop or codon2 in stop:
                # stop codon is always considered as nonsynonymous
                if codon1[diff] in purine and codon2[diff] in purine:
                    return [0, 0, weight, 0]
                elif codon1[diff] in pyrimidine and codon2[diff] in pyrimidine:
                    return [0, 0, weight, 0]
                else:
                    return [0, 0, 0, weight]
            elif dic[codon1] == dic[codon2]:
                if codon1[diff] in purine and codon2[diff] in purine:
                    return [weight, 0, 0, 0]
                elif codon1[diff] in pyrimidine and codon2[diff] in pyrimidine:
                    return [weight, 0, 0, 0]
                else:
                    return [0, weight, 0, 0]
            else:
                if codon1[diff] in purine and codon2[diff] in purine:
                    return [0, 0, weight, 0]
                elif codon1[diff] in pyrimidine and codon2[diff] in pyrimidine:
                    return [0, 0, weight, 0]
                else:
                    return [0, 0, 0, weight]

        if len(diff_pos) == 1:
            TV = [
                p + q
                for p, q in zip(TV, count_TV(codon1, codon2, diff_pos[0], codon_table))
            ]
        elif len(diff_pos) == 2:
            tmp_codon = [codon1[:i] + codon2[i] + codon1[i + 1 :] for i in diff_pos]
            path_prob = []
            for i in tmp_codon:
                codon_idx = list(map(codon_lst.index, [codon1, i, codon2]))
                prob = (P[codon_idx[0], codon_idx[1]], P[codon_idx[1], codon_idx[2]])
                path_prob.append(prob[0] * prob[1])
            path_prob = [2 * i / sum(path_prob) for i in path_prob]
            for n, i in enumerate(diff_pos):
                temp_codon = codon1[:i] + codon2[i] + codon1[i + 1 :]
                TV = [
                    p + q
                    for p, q in zip(
                        TV,
                        count_TV(
                            codon1, temp_codon, i, codon_table, weight=path_prob[n] / 2
                        ),
                    )
                ]
                TV = [
                    p + q
                    for p, q in zip(
                        TV,
                        count_TV(
                            codon1, temp_codon, i, codon_table, weight=path_prob[n] / 2
                        ),
                    )
                ]
        elif len(diff_pos) == 3:
            paths = list(permutations([0, 1, 2], 3))
            path_prob = []
            tmp_codon = []
            for p in paths:
                tmp1 = codon1[: p[0]] + codon2[p[0]] + codon1[p[0] + 1 :]
                tmp2 = tmp1[: p[1]] + codon2[p[1]] + tmp1[p[1] + 1 :]
                tmp_codon.append((tmp1, tmp2))
                codon_idx = list(map(codon_lst.index, [codon1, tmp1, tmp2, codon2]))
                prob = (
                    P[codon_idx[0], codon_idx[1]],
                    P[codon_idx[1], codon_idx[2]],
                    P[codon_idx[2], codon_idx[3]],
                )
                path_prob.append(prob[0] * prob[1] * prob[2])
            path_prob = [3 * i / sum(path_prob) for i in path_prob]
            for i, j, k in zip(tmp_codon, path_prob, paths):
                TV = [
                    p + q
                    for p, q in zip(
                        TV, count_TV(codon1, i[0], k[0], codon_table, weight=j / 3)
                    )
                ]
                TV = [
                    p + q
                    for p, q in zip(
                        TV, count_TV(i[0], i[1], k[1], codon_table, weight=j / 3)
                    )
                ]
                TV = [
                    p + q
                    for p, q in zip(
                        TV, count_TV(i[1], codon2, k[1], codon_table, weight=j / 3)
                    )
                ]
    return TV


#################################################################
#        private functions for Maximum Likelihood method
#################################################################


def _ml(seq1, seq2, cmethod, codon_table):
    """ML method main function (PRIVATE)."""
    from collections import Counter
    from scipy.optimize import minimize

    codon_cnt = Counter()
    pi = _get_pi(seq1, seq2, cmethod, codon_table=codon_table)
    for i, j in zip(seq1, seq2):
        # if i != j and ('---' not in (i, j)):
        if "---" not in (i, j):
            codon_cnt[(i, j)] += 1
    codon_lst = [
        i
        for i in list(codon_table.forward_table.keys()) + codon_table.stop_codons
        if "U" not in i
    ]

    # apply optimization
    def func(
        params, pi=pi, codon_cnt=codon_cnt, codon_lst=codon_lst, codon_table=codon_table
    ):
        """Temporary function, params = [t, k, w]."""
        return -_likelihood_func(
            params[0],
            params[1],
            params[2],
            pi,
            codon_cnt,
            codon_lst=codon_lst,
            codon_table=codon_table,
        )

    # count sites
    opt_res = minimize(
        func,
        [1, 0.1, 2],
        method="L-BFGS-B",
        bounds=((1e-10, 20), (1e-10, 20), (1e-10, 10)),
        tol=1e-5,
    )
    t, k, w = opt_res.x
    Q = _get_Q(pi, k, w, codon_lst, codon_table)
    Sd = Nd = 0
    for i, c1 in enumerate(codon_lst):
        for j, c2 in enumerate(codon_lst):
            if i != j:
                try:
                    if codon_table.forward_table[c1] == codon_table.forward_table[c2]:
                        # synonymous count
                        Sd += pi[c1] * Q[i, j]
                    else:
                        # nonsynonymous count
                        Nd += pi[c1] * Q[i, j]
                except KeyError:
                    # This is probably due to stop codons
                    pass
    Sd *= t
    Nd *= t

    # count differences (with w fixed to 1)
    def func_w1(
        params, pi=pi, codon_cnt=codon_cnt, codon_lst=codon_lst, codon_table=codon_table
    ):
        """Temporary function, params = [t, k]. w is fixed to 1."""
        return -_likelihood_func(
            params[0],
            params[1],
            1.0,
            pi,
            codon_cnt,
            codon_lst=codon_lst,
            codon_table=codon_table,
        )

    opt_res = minimize(
        func_w1,
        [1, 0.1],
        method="L-BFGS-B",
        bounds=((1e-10, 20), (1e-10, 20)),
        tol=1e-5,
    )
    t, k = opt_res.x
    w = 1.0
    Q = _get_Q(pi, k, w, codon_lst, codon_table)
    rhoS = rhoN = 0
    for i, c1 in enumerate(codon_lst):
        for j, c2 in enumerate(codon_lst):
            if i != j:
                try:
                    if codon_table.forward_table[c1] == codon_table.forward_table[c2]:
                        # synonymous count
                        rhoS += pi[c1] * Q[i, j]
                    else:
                        # nonsynonymous count
                        rhoN += pi[c1] * Q[i, j]
                except KeyError:
                    # This is probably due to stop codons
                    pass
    rhoS *= 3
    rhoN *= 3
    dN = Nd / rhoN
    dS = Sd / rhoS
    return dN, dS


def _get_pi(seq1, seq2, cmethod, codon_table):
    """Obtain codon frequency dict (pi) from two codon list (PRIVATE).

    This function is designed for ML method. Available counting methods
    (cfreq) are F1x4, F3x4 and F64.
    """
    # TODO:
    # Stop codon should not be allowed according to Yang.
    # Try to modify this!
    pi = {}
    if cmethod == "F1x4":
        fcodon = {"A": 0, "G": 0, "C": 0, "T": 0}
        for i in seq1 + seq2:
            if i != "---":
                for c in i:
                    fcodon[c] += 1
        tot = sum(fcodon.values())
        fcodon = {j: k / tot for j, k in fcodon.items()}
        for i in codon_table.forward_table.keys() + codon_table.stop_codons:
            if "U" not in i:
                pi[i] = fcodon[i[0]] * fcodon[i[1]] * fcodon[i[2]]
    elif cmethod == "F3x4":
        # three codon position
        fcodon = [
            {"A": 0, "G": 0, "C": 0, "T": 0},
            {"A": 0, "G": 0, "C": 0, "T": 0},
            {"A": 0, "G": 0, "C": 0, "T": 0},
        ]
        for i in seq1 + seq2:
            if i != "---":
                fcodon[0][i[0]] += 1
                fcodon[1][i[1]] += 1
                fcodon[2][i[2]] += 1
        for i in range(3):
            tot = sum(fcodon[i].values())
            fcodon[i] = {j: k / tot for j, k in fcodon[i].items()}
        for i in list(codon_table.forward_table.keys()) + codon_table.stop_codons:
            if "U" not in i:
                pi[i] = fcodon[0][i[0]] * fcodon[1][i[1]] * fcodon[2][i[2]]
    elif cmethod == "F61":
        for i in codon_table.forward_table.keys() + codon_table.stop_codons:
            if "U" not in i:
                pi[i] = 0.1
        for i in seq1 + seq2:
            if i != "---":
                pi[i] += 1
        tot = sum(pi.values())
        pi = {j: k / tot for j, k in pi.items()}
    return pi


def _q(i, j, pi, k, w, codon_table):
    """Q matrix for codon substitution (PRIVATE).

    Arguments:
     - i, j  : three letter codon string
     - pi    : expected codon frequency
     - k     : transition/transversion ratio
     - w     : nonsynonymous/synonymous rate ratio
     - codon_table: Bio.Data.CodonTable object

    """
    if i == j:
        # diagonal elements is the sum of all other elements
        return 0
    if i in codon_table.stop_codons or j in codon_table.stop_codons:
        return 0
    if (i not in pi) or (j not in pi):
        return 0
    purine = ("A", "G")
    pyrimidine = ("T", "C")
    diff = []
    for n, (c1, c2) in enumerate(zip(i, j)):
        if c1 != c2:
            diff.append((n, c1, c2))
    if len(diff) >= 2:
        return 0
    if codon_table.forward_table[i] == codon_table.forward_table[j]:
        # synonymous substitution
        if diff[0][1] in purine and diff[0][2] in purine:
            # transition
            return k * pi[j]
        elif diff[0][1] in pyrimidine and diff[0][2] in pyrimidine:
            # transition
            return k * pi[j]
        else:
            # transversion
            return pi[j]
    else:
        # nonsynonymous substitution
        if diff[0][1] in purine and diff[0][2] in purine:
            # transition
            return w * k * pi[j]
        elif diff[0][1] in pyrimidine and diff[0][2] in pyrimidine:
            # transition
            return w * k * pi[j]
        else:
            # transversion
            return w * pi[j]


def _get_Q(pi, k, w, codon_lst, codon_table):
    """Q matrix for codon substitution (PRIVATE)."""
    import numpy as np

    codon_num = len(codon_lst)
    Q = np.zeros((codon_num, codon_num))
    for i in range(codon_num):
        for j in range(codon_num):
            if i != j:
                Q[i, j] = _q(
                    codon_lst[i], codon_lst[j], pi, k, w, codon_table=codon_table
                )
    nucl_substitutions = 0
    for i in range(codon_num):
        Q[i, i] = -sum(Q[i, :])
        try:
            nucl_substitutions += pi[codon_lst[i]] * (-Q[i, i])
        except KeyError:
            pass
    Q = Q / nucl_substitutions
    return Q


def _likelihood_func(t, k, w, pi, codon_cnt, codon_lst, codon_table):
    """Likelihood function for ML method (PRIVATE)."""
    from scipy.linalg import expm

    Q = _get_Q(pi, k, w, codon_lst, codon_table)
    P = expm(Q * t)
    likelihood = 0
    for i, c1 in enumerate(codon_lst):
        for j, c2 in enumerate(codon_lst):
            if (c1, c2) in codon_cnt:
                if P[i, j] * pi[c1] <= 0:
                    likelihood += codon_cnt[(c1, c2)] * 0
                else:
                    likelihood += codon_cnt[(c1, c2)] * log(pi[c1] * P[i, j])
    return likelihood


if __name__ == "__main__":
    from Bio._utils import run_doctest

    run_doctest()