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gel_old.py
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gel_old.py
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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
# doctest: +NORMALIZE_WHITESPACE
# doctest: +SKIP
# Copyright 2015 by Bruno Silva <bruno.phoenix@gmail.com>, Björn Johansson.
# All rights reserved.
# This code is part of the Python-dna distribution and governed by its
# license. Please see the LICENSE.txt file that should have been included
# as part of this package.
# from pint import UnitRegistry #, DimensionalityError
# Hacky fix for a python3 problem I don't understand
# https://github.com/pallets/flask/issues/1680
# UnitRegistry.__wrapped__ = None
# ureg = UnitRegistry()
"""Provides the class `Gel` for the simulation of agarose slab-gel
electrophoresis of DNA at constant electric field.
Note
----
This code is at an early stage of development and documentation.
"""
import numpy as _np
import matplotlib.ticker as _mtick
import matplotlib.pyplot as _plt
import matplotlib.cm as _cm
from matplotlib.ticker import FixedLocator as _FixedLocator
# from mpldatacursor import datacursor as _datacursor #, HighlightingDataCursor # version 0.5.0
from scipy.interpolate import griddata as _griddata
from scipy.optimize import leastsq as _leastsq
from scipy.optimize import fsolve as _fsolve
from scipy import stats as _stats
from pint import UnitRegistry as _UnitRegistry
from io import BytesIO as _BytesIO
from pydna.dseq import Dseq as _Dseq
from pydna.dseqrecord import Dseqrecord as _Dseqrecord
# Hacky fix for a python3 problem I don't understand
# https://github.com/pallets/flask/issues/1680
_UnitRegistry.__wrapped__ = None
# Unit registry
ureg = _UnitRegistry()
Q_ = ureg.Quantity
ureg.define("base_pair = [] = bp = basepair")
# ureg.define('base_pair = 3.4 angstrom = bp = basepair')
ureg.define("pixel = [] = px")
ureg.default_format = "~"
# Variable mapping
Vars = {
"E": {
"synonyms": ("field", "electric field"),
"units": "V/cm",
"details": (
"Electric field intensity as given by the applied "
"voltage divided by the distance between the "
"electrodes."
),
},
"quantities": {
"synonyms": (),
"units": "ng",
"details": "Mass of DNA in a sample or a band.",
},
"volume": {"synonyms": (), "units": "ul", "details": ""},
}
# Weight standards
weight_standards = {
"1kb_GeneRuler": {
"sizes": Q_(
[
10000,
8000,
6000,
5000,
4000,
3500,
3000,
2500,
2000,
1500,
1000,
750,
500,
250,
],
"bp",
),
"percent": Q_(
[
0.06,
0.06,
0.14,
0.06,
0.06,
0.06,
0.14,
0.05,
0.05,
0.05,
0.12,
0.05,
0.05,
0.05,
]
),
},
"1kb+_GeneRuler": {
"sizes": Q_(
[
20000,
10000,
7000,
5000,
4000,
3000,
2000,
1500,
1000,
700,
500,
400,
300,
200,
75,
],
"bp",
),
"percent": Q_(
[
0.04,
0.04,
0.04,
0.15,
0.04,
0.04,
0.04,
0.16,
0.05,
0.05,
0.15,
0.05,
0.05,
0.05,
0.05,
]
),
},
"Mix_GeneRuler": {
"sizes": Q_(
[
10000,
8000,
6000,
5000,
4000,
3500,
3000,
2500,
2000,
1500,
1200,
1000,
900,
800,
700,
600,
500,
400,
300,
200,
100,
],
"bp",
),
"percent": Q_(
[
0.036,
0.036,
0.036,
0.036,
0.036,
0.036,
0.12,
0.032,
0.032,
0.032,
0.032,
0.12,
0.034,
0.034,
0.034,
0.034,
0.12,
0.04,
0.04,
0.04,
0.04,
]
),
},
"High_Range_GeneRuler": {
"sizes": Q_([48502, 24508, 20555, 17000, 15258, 13825, 12119, 10171], "bp"),
"percent": Q_([0.16, 0.176, 0.16, 0.118, 0.118, 0.1, 0.094, 0.074]),
},
}
# Data
hor_str = """
+------+-----+-------+-------+-----------+-----------+----------+--------+-------+--------+
| E | %T | L_max | L_min | mu_S*10^8 | mu_L*10^8 | gamma | chi^2 | L'max | chi^2' |
|(V/cm)| | (bp) | (bp) |(m^2/V.sec)|(m^2/V.sec)| (kbp) | | (bp) | |
+------+-----+-------+-------+-----------+-----------+----------+--------+-------+--------+
| 0.71 | 0.5 | 35000 | 1000 | 2.61 | 0.42 | 29.70 | 0.9999 | | |
| 0.71 | 1.0 | 20000 | 300 | 2.54 | 1.64E-07 | 2.81E+07 | 0.9981 | 5000 | 0.9992 |
| 0.71 | 1.3 | 20000 | 200 | 2.49 | 2.60E-09 | 1.06E+09 | 0.9647 | 2600 | 0.9990 |
| 1.00 | 1.0 | 48502 | 400 | 2.37 | 0.23 | 29.99 | 0.9997 | | |
| 1.00 | 1.1 | 30000 | 200 | 2.21 | 0.05 | 74.08 | 0.9987 | 25000 | 0.9991 |
| 1.00 | 1.2 | 27500 | 200 | 2.14 | 0.01 | 144.40 | 0.9964 | 1300 | 0.9990 |
| 1.23 | 0.7 | 47500 | 1000 | 2.60 | 0.66 | 19.86 | 0.9997 | | |
| 1.23 | 0.8 | 35000 | 200 | 2.55 | 0.23 | 23.84 | 0.9988 | 27500 | 0.9990 |
| 1.23 | 0.9 | 25000 | 200 | 2.44 | 0.08 | 49.58 | 0.9971 | 3000 | 0.9992 |
| 1.31 | 0.5 | 35000 | 400 | 2.54 | 0.39 | 19.69 | 0.9999 | | |
| 1.31 | 1.0 | 25000 | 200 | 2.52 | 0.15 | 25.75 | 0.9986 | 17500 | 0.9992 |
| 1.31 | 1.3 | 48502 | 200 | 2.48 | 0.05 | 46.75 | 0.9967 | 14000 | 0.9991 |
| 1.51 | 1.0 | 35000 | 200 | 2.24 | 0.29 | 17.86 | 0.9997 | | |
| 1.51 | 1.1 | 32500 | 300 | 2.26 | 0.14 | 23.78 | 0.9980 | 20000 | 0.9989 |
| 1.51 | 1.2 | 48502 | 200 | 2.17 | 0.04 | 64.31 | 0.9974 | 15000 | 0.9991 |
| 1.80 | 0.5 | 47500 | 300 | 2.48 | 0.51 | 17.23 | 0.9998 | | |
| 1.80 | 1.3 | 30000 | 200 | 2.39 | 0.22 | 11.93 | 0.9980 | 13000 | 0.9991 |
| 2.00 | 1.0 | 48502 | 200 | 2.22 | 0.23 | 13.96 | 0.9982 | 20000 | 0.9992 |
| 2.00 | 1.1 | 48502 | 200 | 2.24 | 0.16 | 13.06 | 0.9971 | 10000 | 0.9991 |
| 2.00 | 1.2 | 17500 | 200 | 2.15 | 0.07 | 30.99 | 0.9979 | 10000 | 0.9990 |
| 2.22 | 0.5 | 35000 | 300 | 2.68 | 0.65 | 12.90 | 0.9995 | | |
| 2.22 | 1.0 | 35000 | 200 | 2.64 | 0.43 | 9.56 | 0.9994 | | |
| 2.22 | 1.3 | 32500 | 200 | 2.56 | 0.29 | 8.42 | 0.9981 | 17500 | 0.9991 |
| 2.47 | 0.7 | 32500 | 200 | 2.59 | 0.51 | 9.50 | 0.9997 | | |
| 2.47 | 0.8 | 35000 | 500 | 2.64 | 0.47 | 8.77 | 0.9998 | | |
| 2.47 | 0.9 | 48502 | 200 | 2.57 | 0.39 | 8.98 | 0.9992 | | |
| 2.51 | 0.7 | 35000 | 200 | 2.44 | 0.45 | 14.19 | 0.9999 | | |
| 2.51 | 0.8 | 35000 | 200 | 2.44 | 0.39 | 12.41 | 0.9996 | | |
| 2.51 | 0.9 | 48502 | 200 | 2.43 | 0.27 | 11.03 | 0.9986 | 15000 | 0.9991 |
| 2.78 | 0.5 | 10000 | 200 | 3.32 | 0.92 | 9.30 | 0.9999 | | |
| 2.78 | 0.6 | 10000 | 200 | 3.25 | 0.80 | 8.47 | 1.0000 | | |
| 2.78 | 0.7 | 10000 | 200 | 3.18 | 0.66 | 9.80 | 0.9998 | | |
| 2.78 | 0.8 | 10000 | 200 | 3.06 | 0.55 | 9.84 | 0.9997 | | |
| 2.78 | 0.9 | 10000 | 200 | 2.93 | 0.46 | 9.64 | 0.9997 | | |
| 2.78 | 1.0 | 10000 | 200 | 2.93 | 0.39 | 10.40 | 0.9997 | | |
| 2.78 | 1.1 | 10000 | 200 | 2.93 | 0.33 | 10.35 | 0.9993 | | |
| 2.78 | 1.2 | 10000 | 200 | 2.85 | 0.30 | 10.82 | 0.9995 | | |
| 2.78 | 1.3 | 10000 | 200 | 2.84 | 0.25 | 11.14 | 0.9996 | | |
| 2.78 | 1.4 | 10000 | 200 | 2.79 | 0.22 | 11.52 | 0.9994 | | |
| 2.78 | 1.5 | 10000 | 200 | 2.70 | 0.19 | 11.63 | 0.9993 | | |
| 3.10 | 1.0 | 32500 | 200 | 2.65 | 0.58 | 8.61 | 0.9999 | | |
| 3.10 | 1.1 | 30000 | 200 | 2.62 | 0.55 | 7.99 | 0.9998 | | |
| 3.10 | 1.2 | 27500 | 200 | 2.56 | 0.33 | 6.06 | 0.9980 | 5000 | 0.9994 |
| 3.51 | 0.5 | 35000 | 900 | 2.58 | 0.75 | 13.34 | 0.9993 | | |
| 3.51 | 1.0 | 48502 | 200 | 2.58 | 0.52 | 6.82 | 0.9997 | | |
| 3.51 | 1.3 | 25000 | 200 | 2.51 | 0.38 | 6.05 | 0.9989 | 8000 | 0.9990 |
| 5.00 | 0.5 | 22500 | 1000 | 2.53 | 0.75 | 18.15 | 0.9996 | | |
| 5.00 | 1.0 | 20000 | 400 | 2.55 | 0.67 | 5.78 | 0.9995 | | |
| 5.00 | 1.3 | 17500 | 200 | 2.51 | 0.50 | 4.22 | 0.9995 | | |
+------+-----+-------+-------+-----------+-----------+----------+--------+-------+--------+
"""
ver_str = """
+------+-----+--------+-------+-----------+-----------+----------+--------+-------+--------+
| E | %T | L_max | L_min | mu_S*10^8 | mu_L*10^8 | gamma | chi^2 | L'max | chi^2' |
|(V/cm)| | (bp) | (bp) |(m^2/V.sec)|(m^2/V.sec)| (kbp) | | (bp) | |
+------+-----+--------+-------+-----------+-----------+----------+--------+-------+--------+
| 0.62 | 0.4 | 48502 | 1000 | 2.67 | 0.21 | 52.799 | 0.9993 | | |
| 0.93 | 0.4 | 194000 | 1000 | 2.54 | 0.34 | 25.304 | 0.9992 | | |
| 1.24 | 0.4 | 48502 | 200 | 3.67 | 0.81 | 14.922 | 0.9997 | | |
| 1.55 | 0.4 | 194000 | 200 | 3.18 | 0.77 | 14.488 | 0.9992 | | |
| 1.86 | 0.4 | 194000 | 200 | 3.12 | 0.78 | 12.603 | 0.9990 | | |
| 2.17 | 0.4 | 194000 | 200 | 3.07 | 0.89 | 11.911 | 0.9971 | 17500 | 0.9992 |
| 2.48 | 0.4 | 194000 | 200 | 3.13 | 0.90 | 12.648 | 0.9979 | 15000 | 0.9991 |
| 3.10 | 0.4 | 194000 | 200 | 3.14 | 0.98 | 9.423 | 0.9964 | 12000 | 0.9991 |
| 4.97 | 0.4 | 194000 | 200 | 3.34 | 1.22 | 9.630 | 0.9983 | 8000 | 0.9990 |
| 6.21 | 0.4 | 194000 | 200 | 3.11 | 1.20 | 9.214 | 0.9959 | 4400 | 0.9993 |
| 0.62 | 0.7 | 48502 | 200 | 2.86 | 8.36E-06 | 7.32E+05 | 0.9973 | 2700 | 0.9990 |
| 0.93 | 0.7 | 194000 | 200 | 2.38 | 0.09 | 54.264 | 0.9968 | 25000 | 0.9990 |
| 1.24 | 0.7 | 48502 | 200 | 3.71 | 0.49 | 15.255 | 0.9993 | | |
| 1.55 | 0.7 | 194000 | 200 | 3.61 | 0.53 | 13.125 | 0.9994 | | |
| 1.86 | 0.7 | 47500 | 300 | 3.61 | 0.62 | 9.834 | 0.9997 | | |
| 2.17 | 0.7 | 194000 | 200 | 3.07 | 0.55 | 10.151 | 0.9998 | | |
| 2.48 | 0.7 | 194000 | 200 | 3.42 | 0.72 | 9.036 | 0.9997 | | |
| 3.10 | 0.7 | 194000 | 200 | 3.14 | 0.69 | 7.713 | 0.9996 | | |
| 4.97 | 0.7 | 194000 | 200 | 3.08 | 0.93 | 6.188 | 0.9984 | 15000 | 0.9990 |
| 6.21 | 0.7 | 194000 | 200 | 3.24 | 1.03 | 6.371 | 0.9987 | 10000 | 0.9991 |
| 0.62 | 1.0 | 48502 | 200 | 2.48 | 1.82E-14 | 1.83E+14 | 0.9938 | 2900 | 0.9990 |
| 0.93 | 1.0 | 194000 | 300 | 2.41 | 1.37E-13 | 2.33E+13 | 0.9947 | 2900 | 0.9990 |
| 1.24 | 1.0 | 48502 | 200 | 3.34 | 0.17 | 25.855 | 0.9974 | 14000 | 0.9990 |
| 1.55 | 1.0 | 47500 | 200 | 3.25 | 0.33 | 12.773 | 0.9977 | 14000 | 0.9990 |
| 1.86 | 1.0 | 47500 | 400 | 3.69 | 0.47 | 8.502 | 0.9984 | 10000 | 0.9991 |
| 2.17 | 1.0 | 194000 | 200 | 2.87 | 0.38 | 9.372 | 0.9989 | 15000 | 0.9990 |
| 2.48 | 1.0 | 194000 | 200 | 3.39 | 0.52 | 7.209 | 0.9990 | | |
| 3.10 | 1.0 | 19400 | 300 | 3.36 | 0.61 | 5.852 | 0.9994 | | |
| 4.97 | 1.0 | 48502 | 200 | 3.04 | 0.77 | 4.749 | 0.9989 | 48502 | 0.9991 |
| 6.21 | 1.0 | 194000 | 200 | 3.13 | 0.88 | 4.417 | 0.9975 | 12500 | 0.9991 |
| 0.62 | 1.3 | 48502 | 200 | 2.12 | 1.87E-10 | 1.11E+10 | 0.9904 | 1800 | 0.9991 |
| 0.93 | 1.3 | 194000 | 300 | 1.96 | 3.80E-06 | 6.10E+05 | 0.9928 | 2600 | 0.9992 |
| 1.24 | 1.3 | 48502 | 300 | 3.32 | 0.02 | 179.189 | 0.9967 | 2600 | 0.9991 |
| 1.55 | 1.3 | 194000 | 200 | 3.47 | 0.27 | 11.920 | 0.9958 | 9000 | 0.9990 |
| 1.86 | 1.3 | 47500 | 400 | 3.97 | 0.36 | 8.594 | 0.9970 | 7000 | 0.9991 |
| 2.17 | 1.3 | 194000 | 200 | 2.76 | 0.21 | 12.412 | 0.9966 | 10000 | 0.9990 |
| 2.48 | 1.3 | 194000 | 200 | 3.26 | 0.45 | 7.464 | 0.9985 | 11000 | 0.9990 |
| 3.10 | 1.3 | 47500 | 200 | 3.37 | 0.50 | 5.159 | 0.9984 | 6000 | 0.9992 |
| 4.97 | 1.3 | 48502 | 200 | 2.68 | 0.49 | 4.048 | 0.9983 | 4000 | 0.9993 |
| 6.21 | 1.3 | 194000 | 200 | 2.70 | 0.59 | 3.555 | 0.9991 | | |
+------+-----+--------+-------+-----------+-----------+----------+--------+-------+--------+
"""
# Strings of data as text files
data_as_file = {
"horizontal": _BytesIO(hor_str.replace("\n|", "\n").replace("|\n", "\n").encode()),
"vertical": _BytesIO(ver_str.replace("\n|", "\n").replace("|\n", "\n").encode()),
}
# Load data into numpy arrays
datasets = {}
for name in data_as_file:
datasets[name] = {}
data_source = data_as_file[name]
temp_dset = _np.genfromtxt(
data_source,
delimiter="|",
dtype=None,
skip_header=5,
skip_footer=1,
usecols=(0, 1, 4, 5, 6),
names=("E", "T", "muS", "muL", "gamma"),
)
datasets[name]["E"] = temp_dset["E"] * ureg("V/cm")
datasets[name]["T"] = temp_dset["T"] * ureg("(g/(100 mL))*100")
datasets[name]["muS"] = temp_dset["muS"] * ureg("1.0E-8 m**2/(V*s)")
datasets[name]["muL"] = temp_dset["muL"] * ureg("1.0E-8 m**2/(V*s)")
datasets[name]["gamma"] = temp_dset["gamma"] * ureg("kbp")
# vWBR equation
def vWBR(muS, muL, gamma):
"""vWBR equation"""
alpha = 1 / muL - 1 / muS
beta = 1 / muS
return lambda L: 1 / (beta + alpha * (1 - _np.exp(-L / gamma)))
# Mobility function: mu(L) = f(muS, muL, gamma)
mu_funcs = {}
for name in datasets:
mu_funcs[name] = vWBR(
datasets[name]["muS"].to("cm**2/V/s"),
datasets[name]["muL"].to("cm**2/V/s"),
datasets[name]["gamma"].to("bp"),
)
# Constants
kB = (1 * ureg.boltzmann_constant).to("m**2 * kg / s**2 / K") # Boltzmann constant
lp = 50 * ureg("nm") # persistence length of dsDNA (nm)
l = 2 * lp # Kuhn length (nm)
b = 0.34 * ureg("nm/bp") # curvilinear length dsDNA (nm/bp)
e = (1 * ureg.e).to("A*s") # elementary charge (1.602176565E-19 A.s)
qeff = e / Q_(7, "bp") # effective charge per dsDNA base pair (A.s/bp)
constants = {"kB": kB, "lp": lp, "l": l, "b": b, "qeff": qeff}
# mobility = distance/(time*field)
def runtime(distance, mobility, field):
return distance / (mobility * field)
def rundistance(time, mobility, field):
return time * mobility * field
# Intrinsic band broadening as function of the diffusion coefficient and time
def bandbroadening(D, time):
return _np.sqrt(2 * D * time)
def pore_size(gamma, muL, mu0, lp, b):
return (gamma * muL * lp * b / mu0) ** (1 / 2)
def pore_size_fit(C):
return 143 * ureg("nm*g**0.59/mL**0.59") * C ** (-0.59)
def radius_gyration(L, lp):
return (lp * L / 3 * (1 - lp / L + lp / L * _np.exp(-L / lp))) ** (1 / 2)
H2Oviscosity = (
lambda T: 2.414e-5 * ureg("kg/m/s") * 10 ** (247.8 * ureg.K / (T - 140 * ureg.K))
) # (Pa.s)=(kg/(m.s)) accurate to within 2.5% from 0 °C to 370 °C
def contour_length(Nbp, b):
return Nbp * b
def reduced_field(eta, a, mu0, E, kB, T):
return eta * a**2 * mu0 * E / (kB * T)
def reduced_field_Kuhn(eta, l, mu0, E, kB, T):
return eta * l**2 * mu0 * E / (kB * T)
# Diffusion coefficient of a blob
def Dblob(kB, T, eta, a):
return kB * T / (eta * a)
# Diffusion coefficient of a Kuhn segment
def DKuhn(kB, T, eta, l):
return kB * T / (eta * l)
# Relations between basepairs (Nbp), Kuhn segments (NKuhn) and blobs (N)
# number of Kuhn segments (~= Nbp/300)
def Nbp_to_NKuhn(Nbp, b, l):
return Nbp * b / l
def NKuhn_to_Nbp(NKuhn, b, l):
return NKuhn * l / b # number of base pairs (bp)
def NKuhn_to_N(NKuhn, l, a):
return NKuhn * (l / a) ** 2 # number of occupied pores
def N_to_NKuhn(N, a, l):
return N * (a / l) ** 2 # number of Kuhn segments
def N_to_Nbp(N, a, b, l):
return N * (l / b) * (a / l) ** 2 # number of base pairs (bp)
def Nbp_to_N(Nbp, a, b, l):
return Nbp * (b / l) * (l / a) ** 2 # number of occupied pores
# Individual diffusion regimes
def reptation_equilibrium(Dblob, N):
return Dblob / N**2
def reptation_accelerated(Dblob, epsilon, N):
return Dblob * epsilon * N ** (-1 / 2)
def reptation_plateau(Dblob, epsilon):
return Dblob * epsilon ** (3 / 2)
def free_solution(kB, T, eta, Rh):
return kB * T / (6 * _np.pi * eta * Rh)
def Zimm_g(Nbp, DRouse, qeff, mu0, kB, T):
return DRouse * Nbp * qeff / (mu0 * kB * T)
def Ogston_Zimm(D0, g):
return D0 * g
Ogston_Rouse = lambda Nbp, kB, T, a, eta, b, l: kB * T * a**3 / (eta * b**2 * l**2 * Nbp**2)
# Diffusion regime frontiers (in number of occupied pores)
def Zimm_Rouse(x0, args):
return Nbp_to_N(_fsolve(diff_Zimm_Rouse, x0, args)[0] * ureg.bp, args[5], args[6], args[7])
def equil_accel(epsilon):
return epsilon ** (-2 / 3)
def accel_plateau(epsilon):
return epsilon ** (-1)
def diff_Zimm_Rouse(Nbp, args):
kB, T, qeff, eta, mu0, a, b, l, lp = args
Nbp = Q_(Nbp[0], "bp")
L = contour_length(Nbp, b)
Rg = radius_gyration(L, lp)
D0 = free_solution(kB, T, eta, Rg)
DRouse = Ogston_Rouse(Nbp, kB, T, a, eta, b, l)
g = Zimm_g(Nbp, DRouse, qeff, mu0, kB, T)
g = g.to_base_units()
DZimm = Ogston_Zimm(D0, g)
# print 'Nbp =\t', Nbp
# print 'kB =\t', kB
# print 'T =\t', T
# print 'qeff =\t', qeff
# print 'eta =\t', eta
# print 'mu0 =\t', mu0
# print 'a =\t', a
# print 'b =\t', b
# print 'l =\t', l
# print 'lp =\t', lp
# print 'L =\t', L
# print 'Rg =\t', Rg
# print 'D0 =\t', D0
# print 'DRouse =\t', DRouse
# print 'g =\t', g
# print 'DZimm =\t', DZimm
# print 'DZimm - DRouse =\t', DZimm - DRouse
# print 70*'#'
return DZimm - DRouse
# Diffusion coefficient
def diffusion_coefficient(Nbp, N_lim1, N_lim2, N_lim3, args):
kB, T, qeff, eta, mu0, a, b, l, lp = args
N = Nbp_to_N(Nbp, a, b, l)
if N < N_lim3:
# Ogston-Zimm
L = contour_length(Nbp, b)
Rg = radius_gyration(L, lp)
D0 = free_solution(kB, T, eta, Rg)
DRouse = Ogston_Rouse(Nbp, kB, T, a, eta, b, l)
g = Zimm_g(Nbp, DRouse, qeff, mu0, kB, T)
D = Ogston_Zimm(D0, g)
elif N < N_lim2:
# Rouse/Reptation-equilibrium
D = Db / N**2
elif N > N_lim1:
# Reptation-plateau (reptation with orientation)
D = Db * epsilon ** (3 / 2)
else:
# Accelerated-reptation
D = Db * epsilon * N ** (-1 / 2)
return D
# def rand_str(sample, length):
# """
# Return a random string of given length built from the chars in sample.
# """
# rnd_str = ''
# for i in xrange(length):
# r = randint(0, len(sample)-1)
# rnd_str += sample[r]
# return rnd_str
def random_Dseqs(sizes):
"""
Return a list of pydna Dseqs of given sizes and random sequences.
"""
sample = []
for size in sizes:
seq = _Dseq("n" * size) # _Dseq(rand_str('actg', size))
sample.append(seq)
return sample
class Fakeseq(object):
def __init__(self, l, n=10e-12):
self._length = l
self.n = n
def __len__(self):
return self._length
def gen_sample(sizes, quantities):
"""Return list of pydna Dseqrecords of given size and quantity.
If a single quantity is given it is divided by the DNA fragments
in proportion to their length.
Parameters
----------
sizes : iterable of pint.unit.Quantity objects or ints
List of DNA sizes in base pairs (bp).
quantities : iterable of pint.unit.Quantity objects, floats or ints
List of DNA weights in nanograms (ng).
If a single quantity is given (pint.unit.Quantity object, float
or int) it is divided linearly by the DNA fragments length.
Examples
--------
Direct quantity assignment without declared units.
>>> sizes = [3000, 500, 1500] # bp
>>> qts = [70.0, 11.7, 35.0] # ng
>>> sample = gen_sample(sizes, qts)
>>> sample
[Dseqrecord(-3000), Dseqrecord(-500), Dseqrecord(-1500)]
>>> float("{0:.2f}".format(sample[0].m() * 1E6)) # µg
0.07
>>> Q_([dna.m() for dna in sample], 'g').to('ng') # doctest: +SKIP
<Quantity([70. 11.7 35. ], 'nanogram')>
>>> Q_([dna.n for dna in sample], 'mol').to('pmol') # doctest: +SKIP
<Quantity([0.03776682 0.03786665 0.03776521], 'picomole')>
Direct quantity assignment with declared units.
>>> sizes = Q_([3000, 500, 1500], 'bp')
>>> qts = Q_([70.0, 11.7, 35.0], 'ng')
>>> sample = gen_sample(sizes, qts)
>>> sample
[Dseqrecord(-3000), Dseqrecord(-500), Dseqrecord(-1500)]
>>> Q_([dna.m() for dna in sample], 'g').to('ng') # doctest: +SKIP
<Quantity([70. 11.7 35. ], 'nanogram')>
>>> Q_([dna.n for dna in sample], 'mol').to('pmol') # doctest: +SKIP
<Quantity([0.03776682 0.03786665 0.03776521], 'picomole')>
Assignment of total quantity (with declared units).
>>> sample = gen_sample(Q_([3000, 500, 1500], 'bp'), Q_(200, 'ng'))
>>> sample
[Dseqrecord(-3000), Dseqrecord(-500), Dseqrecord(-1500)]
>>> Q_([dna.m() for dna in sample], 'g').to('ng') # doctest: +SKIP
<Quantity([120. 20. 60.], 'nanogram')>
>>> Q_([dna.n for dna in sample], 'mol').to('pmol') # doctest: +SKIP
<Quantity([0.06474311 0.06472932 0.06474035], 'picomole')>
"""
frags = random_Dseqs([int(s.magnitude) for s in to_units(sizes, "bp")])
quantities = to_units(quantities, "ng")
quantities = quantities.to("g").magnitude
if not hasattr(quantities, "__iter__"):
quantities = lin_div_Qty(frags, quantities, criteria=len)
return [_Dseqrecord(seq, n=quantities[i] / seq.mw()) for i, seq in enumerate(frags)]
def weight_standard_sample(key, qty=Q_(500, "ng")):
assert key in weight_standards, "Key not recognized. Choose from: %s" % list(weight_standards.keys())
qty = to_units(qty, Vars["quantities"]["units"], var_name="qty")
sizes = weight_standards[key]["sizes"]
fracs = weight_standards[key]["percent"]
quantities = qty * fracs
return gen_sample(sizes, quantities)
def logspace_int(minimum, maximum, divs):
space = _np.logspace(_np.log10(minimum), _np.log10(maximum), divs)
return _np.array([round(val, 0) for val in space])
def flatten(List):
if List == []:
return List
flatL = []
for elem in List:
if not isinstance(elem, Q_) and hasattr(elem, "__iter__"):
flatE = flatten(elem)
[flatL.append(E) for E in flatE]
else:
flatL.append(elem)
return flatL
# Gaussian function
def Gaussian(x, hgt, ctr, dev):
return hgt * _np.exp(-((x - ctr) ** 2) / (2 * dev**2))
def Gauss_hgt(auc, dev):
return auc / (dev * _np.sqrt(2 * _np.pi))
def Gauss_dev(FWHM):
return FWHM / (2 * _np.sqrt(2 * _np.log(2)))
# Gauss_dev = lambda FWTM: FWTM/(2*_np.sqrt(2*_np.log(10)))
def Gauss_FWHM(FWTM):
return FWTM * _np.sqrt(2 * _np.log(2)) / _np.sqrt(2 * _np.log(10))
def _to_units(quantity, units, var_name=None):
"""Asserts that the quantity has the proper dimensions
(inferred from the default units) if the quantity is an instance of
pint.unit.Quantity or assigns the default units if it's not.
"""
if isinstance(quantity, Q_):
try:
quantity = quantity.to(units)
except TypeError as error:
quantity = [q.to(units) for q in quantity]
except Exception as error:
if var_name:
error.extra_msg = " for variable '%s'" % var_name
raise error
else:
quantity = Q_(quantity, units)
return quantity
def to_units(quantity, units, var_name=None):
"""Asserts that the quantity has the proper dimensions
(inferred from the default units) if the quantity is an instance of
pint.unit.Quantity or assigns the default units if it's not.
"""
if (
not isinstance(quantity, Q_)
and hasattr(quantity, "__iter__")
and len(quantity) > 0
and sum([isinstance(q, Q_) for q in flatten(quantity)]) > 0
):
temp_qty = [to_units(q, units, var_name) for q in quantity]
quantity = Q_([q.magnitude for q in temp_qty], units)
else:
quantity = _to_units(quantity, units, var_name)
return quantity
def dim_or_units(quantity, reference):
"""If <quantity> is not an instance of <Quantity>, instantiate a <Quantity>
object with <quantity> as magnitude and as <reference.units> as units.
If <quantity> is an instance of <Quantity>, check whether it has the same
dimensionality as <reference>.
"""
if not isinstance(quantity, Q_):
quantity = to_units(quantity, reference.units)
else:
assert quantity.dimensionality == reference.dimensionality, "Dimension mismatch: (%s) != (%s)" % (
quantity.dimensionality,
reference.dimensionality,
)
return quantity
def assign_quantitiesB(samples, maxdef=Q_(150, "ng")):
"""
Assigns quantities (masses in nanograms) to the DNA fragments without
corresponding quantity assuming a linear relationship between the DNA
length (in basepairs) and its mass. As if the fragments originated in
a restriction procedure.
For each sample takes the maximum quantity (either from the other samples
or from the default) and assigns it to the fragment with greater length.
"""
quantities = []
units = Vars["quantities"]["units"]
maxQ = Q_(0, units)
# Preprocessing and straightforward cases
for sample in samples:
sample_qts = []
for qty in sample.quantities:
if not _np.isnan(qty.magnitude) and qty.magnitude is not None:
sample_qts.append(qty)
if qty > maxQ:
maxQ = qty
quantities.append(sample_qts)
# Quantity assignment - missing values
if maxQ.magnitude == 0:
maxQ = to_units(maxdef, units, "maxdef")
maxQ = maxQ.magnitude
for i, sample in enumerate(samples):
if quantities[i] == []:
# Linearly extrapolates each DNA fragment's quantity taking as
# reference the maximum quantity registered (or the default)
sizes = [len(dna) for dna in sample.solutes]
maxL = max(sizes)
quantities[i] = [size * maxQ / maxL for size in sizes]
quantities = to_units(quantities, units, "quantities")
return quantities
def lin_div_Qty(sample, quantity, criteria=len):
"""
Linearly divides a quantity by the elements of sample considering a
criteria. Criteria must by a function that returns a number upon being
applied to each element of sample.
"""
sizes = [criteria(dna) for dna in sample]
return [size * quantity / sum(sizes) for size in sizes]
def size_to_mobility(
dna_len,
field,
percentage,
mu_func=mu_funcs["vertical"],
dataset=datasets["vertical"],
method="linear",
replNANs=True,
):
mobility = _griddata((dataset["E"], dataset["T"]), mu_func(dna_len), (field, percentage), method)
if replNANs and _np.isnan(mobility):
# Replace NANs by 'nearest' interpolation
print("WARNING: NAN replaced by 'nearest' interpolation.") # #### ! ###
mobility = _griddata(
(dataset["E"], dataset["T"]),
mu_func(dna_len),
(field, percentage),
method="nearest",
)
return mobility.item()
def vWBRfit(
field,
percentage,
DNAvals=_np.linspace(100, 50000, 100),
dataset=datasets["vertical"],
mu_func=mu_funcs["vertical"],
method="linear",
replNANs=True,
plot=True,
):
mu = _np.zeros(len(DNAvals))
vWBR = lambda L, muS, muL, gamma: (1 / muS + (1 / muL - 1 / muS) * (1 - _np.exp(-L / gamma))) ** -1
for i, Li in enumerate(DNAvals):
mu[i] = size_to_mobility(Li, field, percentage, mu_func, dataset, method, replNANs)
def residuals(pars, L, mu):
return mu - vWBR(L, *pars)
muS0 = 3.5e-4 # cm^2/(V.sec) ############################################
muL0 = 1.0e-4 # cm^2/(V.sec) ############################################
gamma0 = 8000 # bp ############################################
pars, cov, infodict, mesg, ier = _leastsq(residuals, [muS0, muL0, gamma0], args=(DNAvals, mu), full_output=True)
muS, muL, gamma = pars
# print ('E=%.2f V/cm, T=%.1f %%, muS=%.3e, muL=%.3e cm^2/(V.s), '
# 'gamma=%s bp' % (field, percentage, muS, muL, gamma))
if plot:
DNAmin = min(DNAvals)
DNAmax = max(DNAvals)
fig = _plt.figure()
ax = fig.add_subplot(111)
ax.scatter(DNAvals, mu * 1e4, color="blue")
ax.plot(
DNAvals,
vWBR(DNAvals, muS, muL, gamma) * 1e4,
label="fit",
linestyle="--",
color="red",
)
ax.set_xlim(DNAmin - 0.1 * DNAmin, DNAmax + 0.1 * DNAmax)
ax.set_ylim((min(mu) - 0.1 * min(mu)) * 1e4, (max(mu) + 0.1 * max(mu)) * 1e4)
ax.set_xscale("log")
ax.xaxis.set_major_formatter(_mtick.FormatStrFormatter("%d"))
ax.tick_params(which="both", top="off", right="off")
ax.set_xlabel(r"$\mathrm{DNA\,length\,(bp)}$", fontsize=14)
ax.set_ylabel(r"$\mu\times{10^{8}}\,(\mathrm{m^{2}/V\cdot s})$", fontsize=14)
ax.set_title(r"$\mu_S=%.2e,\,\mu_L=%.2e\,\mathrm{cm^2/(V.s)},\," r"\gamma=%d \mathrm{bp}$" % (muS, muL, gamma))
ax.legend().draggable()
_plt.show()
return pars, cov, infodict, mesg, ier
def ferguson_to_mu0(
field,
Tvals,
DNAvals,
dataset,
mu_func,
adjmethod="linear",
replNANs=True,
plot=True,
):
"""
This function extrapolates the free solution mobility (mu0)
for a specified electric field intensity (field), via Ferguson plot
(ln(mobility) vs. %agarose).
Mobiliy calculation method:
[E,T,muS,muL,gamma] -> [E,T,mu(L)] -(L*)-> [E,T,mu] -(E*,T*,interp.)-> mu*
"""
# Mobility dependence on size (mu(L)) for each agarose percentage (Ti)
ln_mu_LxT = []
for Lj in DNAvals:
ln_mu_T = []
for Ti in Tvals:
mu = size_to_mobility(Lj, field, Ti, mu_func, dataset, adjmethod, replNANs)
ln_mu_T.append(_np.log(mu))
ln_mu_LxT.append(ln_mu_T)
ln_mu_LxT = _np.array(ln_mu_LxT)
# Linear regression for each DNA size
lregr_stats = []
exclude = []
for l in range(len(DNAvals)):
not_nan = _np.logical_not(_np.isnan(ln_mu_LxT[l]))
if sum(not_nan) > 1:
# (enough points for linear regression)
gradient, intercept, r_value, p_value, std_err = _stats.linregress(Tvals[not_nan], ln_mu_LxT[l][not_nan])
lregr_stats.append((gradient, intercept, r_value, p_value, std_err))
exclude.append(False)
else:
exclude.append(True)
exclude = _np.array(exclude)
DNAvals = DNAvals[~exclude]
ln_mu_LxT = ln_mu_LxT[~exclude]
if len(lregr_stats) > 0:
# Free solution mobility determination
ln_mu0 = _np.mean([row[1] for row in lregr_stats]) # mean of intercepts
mu0 = _np.exp(ln_mu0) # cm^2/(V.seg)
else:
mu0 = None
if plot and len(ln_mu_LxT) > 0:
# Ferguson Plot (ln(mu) vs. %T) --> mu0
def regline(m, b, x):
return m * x + b # Line function (for the plot)
colors = _cm.rainbow(_np.linspace(0, 1, len(DNAvals)))
Tvals0 = _np.concatenate([[0], Tvals])
fig = _plt.figure()
ax = fig.add_subplot(111)
for l in range(len(DNAvals)):
ax.scatter(Tvals, ln_mu_LxT[l], label=DNAvals[l], color=colors[l])
m = lregr_stats[l][0]
b = lregr_stats[l][1]
ax.plot(Tvals0, [regline(m, b, t) for t in Tvals0], color=colors[l])
ax.set_xlim(0)
# ax.set_ylim(-10, -7.5)
ax.legend(title=r"$\mathrm{DNA size (bp)}$", prop={"size": 10}).draggable()
ax.tick_params(which="both", top="off", right="off")
ax.set_xlabel(r"$\%\,agarose$", fontsize=14)
ax.set_ylabel(r"$\mathrm{ln(mobility\,[cm^{2}/V sec])}$", fontsize=14)
ax.set_title(
r"$\mathrm{Ferguson\,plot}$"
+ "\n"
+ r"$\mathrm{ln(mobility)\,vs.\,\%\,agarose\,}$"
+ r"$\mathrm{(field=%.3f\,V/cm)}$" % field.magnitude
)
_plt.show()
return mu0 # cm^2/(V.seg)
def gelplot_imshow(
distances,
bandwidths,
intensities,
lanes,
names,
gel_len,
wellx,
welly,
wellsep,
res,
cursor_ovr,
back_col,
band_col,
well_col,
noise,
Itol,
detectlim,
title,
FWTM,
show=True,
):
nlanes = len(lanes)
gel_width = sum(wellx) + (nlanes + 1) * wellsep # cm
res = res.to("px/cm")
pxl_x = int(round((gel_width * res).magnitude))
pxl_y = int(round((gel_len * res).magnitude))
lane_centers = [(l + 1) * wellsep + sum(wellx[:l]) + 0.5 * wellx[l] for l in range(nlanes)]
rgb_arr = _np.zeros(shape=(pxl_y, pxl_x, 3), dtype=_np.float32)
bandlengths = wellx
bands_pxlXYmid = []
# Paint the bands
for i in range(nlanes):
distXmid = lane_centers[i]
pxlXmid = int(round((distXmid * res).magnitude))
bandlength = bandlengths[i]
from_x = int(round(((distXmid - bandlength / 2.0) * res).magnitude))
to_x = int(round(((distXmid + bandlength / 2.0) * res).magnitude))