FLUORESCENCE BINDING ASSAY ANALYSIS

Experiment date: 2015/09/22

Protein: HSA

Fluorescent ligand : dansylamide (lig1)

Xml parsing parts adopted from Sonya's assaytools/examples/fluorescence-binding-assay/Src-gefitinib fluorescence simple.ipynb



In [1]:

    
import numpy as np
import matplotlib.pyplot as plt
from lxml import etree
import pandas as pd
import os
import matplotlib.cm as cm 
import seaborn as sns
%pylab inline









    



Populating the interactive namespace from numpy and matplotlib



In [2]:

    
# Get read and position data of each fluorescence reading section
def get_wells_from_section(path):
    reads = path.xpath("*/Well")
    wellIDs = [read.attrib['Pos'] for read in reads]

    data = [(float(s.text), r.attrib['Pos'])
         for r in reads
         for s in r]

    datalist = {
      well : value
      for (value, well) in data
    }
    
    welllist = [
                [
                 datalist[chr(64 + row) + str(col)]          
                 if chr(64 + row) + str(col) in datalist else None
                 for row in range(1,9)
                ]
                for col in range(1,13)
                ]
                
    return welllist



In [6]:

    
file_lig1="MI_FLU_hsa_lig1_20150922_150518.xml"
file_name = os.path.splitext(file_lig1)[0]
label = file_name[0:25]
print label









    



MI_FLU_hsa_lig1_20150922_



In [8]:

    
root = etree.parse(file_lig1)

#find data sections
Sections = root.xpath("/*/Section")
much = len(Sections)
print "****The xml file " + file_lig1 + " has %s data sections:****" % much
for sect in Sections:
    print sect.attrib['Name']









    



****The xml file MI_FLU_hsa_lig1_20150922_150518.xml has 3 data sections:****
ex340_em480_topRead
ex340_em480_bottomRead
Abs_600



In [9]:

    
#Work with topread
TopRead = root.xpath("/*/Section")[0]
welllist = get_wells_from_section(TopRead)

df_topread = pd.DataFrame(welllist, columns = ['A - HSA','B - Buffer','C - HSA','D - Buffer', 'E - HSA','F - Buffer','G - HSA','H - Buffer'])
df_topread.transpose()



In [10]:

    
# To generate cvs file
# df_topread.transpose().to_csv(label + Sections[0].attrib['Name']+ ".csv")

Calculating Molar Fluorescence (MF) of Free Ligand

1. Maximum likelihood curve-fitting

Find the maximum likelihood estimate, $\theta^*$, i.e. the curve that minimizes the squared error $\theta^* = \text{argmin} \sum_i |y_i - f_\theta(x_i)|^2$ (assuming i.i.d. Gaussian noise)

Y = MF*L + BKG

Y: Fluorescence read (Flu unit)

L: Total ligand concentration (uM)

BKG: background fluorescence without ligand (Flu unit)

MF: molar fluorescence of free ligand (Flu unit/ uM)



In [16]:

    
import numpy as np
from scipy import optimize
import matplotlib.pyplot as plt
%matplotlib inline

def model(x,slope,intercept):
    ''' 1D linear model in the format scipy.optimize.curve_fit expects: '''
    return x*slope + intercept

# generate some data
#X = np.random.rand(1000)
#true_slope=1.0
#true_intercept=0.0
#noise = np.random.randn(len(X))*0.1
#Y = model(X,slope=true_slope,intercept=true_intercept) + noise

#ligand titration
lig1=np.array([200.0000,86.6000,37.5000,16.2000,7.0200, 3.0400, 1.3200, 0.5700, 0.2470, 0.1070, 0.0462, 0.0200])
lig1









    Out[16]:





array([  2.00000000e+02,   8.66000000e+01,   3.75000000e+01,
         1.62000000e+01,   7.02000000e+00,   3.04000000e+00,
         1.32000000e+00,   5.70000000e-01,   2.47000000e-01,
         1.07000000e-01,   4.62000000e-02,   2.00000000e-02])



In [19]:

    
# Since I have 4 replicates
L=np.concatenate((lig1, lig1, lig1, lig1))
len(L)









    Out[19]:





48



In [36]:

    
# Fluorescence read
df_topread.loc[:,("B - Buffer", "D - Buffer", "F - Buffer", "H - Buffer")]



In [41]:

    
B=df_topread.loc[:,("B - Buffer")]
D=df_topread.loc[:,("D - Buffer")]
F=df_topread.loc[:,("F - Buffer")]
H=df_topread.loc[:,("H - Buffer")]

Y = np.concatenate((B.as_matrix(),D.as_matrix(),F.as_matrix(),H.as_matrix()))



In [44]:

    
(MF,BKG),_ = optimize.curve_fit(model,L,Y)
print('MF: {0:.3f}, BKG: {1:.3f}'.format(MF,BKG))
print('y = {0:.3f} * L + {1:.3f}'.format(MF, BKG))









    



MF: 2.517, BKG: 86.201
y = 2.517 * L + 86.201

Curve-fitting to binding saturation curve

Fluorescence intensity vs added ligand

LR= ((X+Rtot+KD)-SQRT((X+Rtot+KD)^2-4XRtot))/2

L= X - LR

Y= BKG + MFL + FRMF*LR

Constants

Rtot: receptor concentration (uM)

BKG: background fluorescence without ligand (Flu unit)

MF: molar fluorescence of free ligand (Flu unit/ uM)

Parameters to fit

Kd: dissociation constant (uM)

FR: Molar fluorescence ratio of complex to free ligand (unitless) complex flurescence = FRMFLR

Experimental data

Y: fluorescence measurement X: total ligand concentration L: free ligand concentration



In [82]:

    
def model2(x,kd,fr):
    ''' 1D linear model in the format scipy.optimize.curve_fit expects: '''
    # lr =((x+rtot+kd)-((x+rtot+kd)**2-4*x*rtot)**(1/2))/2
    # y = bkg + mf*(x - lr) + fr*mf*lr
    bkg = 86.2
    mf = 2.517
    rtot = 0.5
    return bkg + mf*(x - ((x+rtot+kd)-((x+rtot+kd)**2-4*x*rtot)**(1/2))/2) + fr*mf*(((x+rtot+kd)-((x+rtot+kd)**2-4*x*rtot)**(1/2))/2)



In [78]:

    
# Total HSA concentration (uM)
Rtot = 0.5
#Total ligand titration
X = L
len(X)









    Out[78]:





48



In [79]:

    
# Fluorescence read
df_topread.loc[:,("A - HSA", "C - HSA", "E - HSA", "G - HSA")]



In [80]:

    
A=df_topread.loc[:,("A - HSA")]
C=df_topread.loc[:,("C - HSA")]
E=df_topread.loc[:,("E - HSA")]
G=df_topread.loc[:,("G - HSA")]

Y = np.concatenate((A.as_matrix(),C.as_matrix(),E.as_matrix(),G.as_matrix()))
len(Y)









    Out[80]:





48



In [81]:

    
(Kd,FR),_ = optimize.curve_fit(model2, X, Y, p0=(5,1))

print('Kd: {0:.3f}, Fr: {1:.3f}'.format(Kd,FR))









    



Kd: 30.691, Fr: 2.510



In [ ]:

	0	1	2	3	4	5	6	7	8	9	10	11
A - HSA	947	636	434	296	212	152	114	92	78	70	70	67
B - Buffer	540	306	184	122	95	96	84	78	83	80	81	84
C - HSA	934	646	435	314	221	150	114	91	75	71	71	70
D - Buffer	572	311	182	130	98	86	80	82	85	78	81	80
E - HSA	935	652	457	307	267	157	108	86	78	71	70	71
F - Buffer	557	310	183	121	99	87	82	82	79	80	80	81
G - HSA	946	631	486	336	245	174	130	102	92	86	197	78
H - Buffer	651	364	210	139	113	107	96	98	93	89	97	93

	B - Buffer	D - Buffer	F - Buffer	H - Buffer
0	540	572	557	651
1	306	311	310	364
2	184	182	183	210
3	122	130	121	139
4	95	98	99	113
5	96	86	87	107
6	84	80	82	96
7	78	82	82	98
8	83	85	79	93
9	80	78	80	89
10	81	81	80	97
11	84	80	81	93

	A - HSA	C - HSA	E - HSA	G - HSA
0	947	934	935	946
1	636	646	652	631
2	434	435	457	486
3	296	314	307	336
4	212	221	267	245
5	152	150	157	174
6	114	114	108	130
7	92	91	86	102
8	78	75	78	92
9	70	71	71	86
10	70	71	70	197
11	67	70	71	78

	B - Buffer	D - Buffer	F - Buffer	H - Buffer
0	540	572	557	651
1	306	311	310	364
2	184	182	183	210
3	122	130	121	139
4	95	98	99	113
5	96	86	87	107
6	84	80	82	96
7	78	82	82	98
8	83	85	79	93
9	80	78	80	89
10	81	81	80	97
11	84	80	81	93

	A - HSA	C - HSA	E - HSA	G - HSA
0	947	934	935	946
1	636	646	652	631
2	434	435	457	486
3	296	314	307	336
4	212	221	267	245
5	152	150	157	174
6	114	114	108	130
7	92	91	86	102
8	78	75	78	92
9	70	71	71	86
10	70	71	70	197
11	67	70	71	78

	B - Buffer	D - Buffer	F - Buffer	H - Buffer
0	540	572	557	651
1	306	311	310	364
2	184	182	183	210
3	122	130	121	139
4	95	98	99	113
5	96	86	87	107
6	84	80	82	96
7	78	82	82	98
8	83	85	79	93
9	80	78	80	89
10	81	81	80	97
11	84	80	81	93

	A - HSA	C - HSA	E - HSA	G - HSA
0	947	934	935	946
1	636	646	652	631
2	434	435	457	486
3	296	314	307	336
4	212	221	267	245
5	152	150	157	174
6	114	114	108	130
7	92	91	86	102
8	78	75	78	92
9	70	71	71	86
10	70	71	70	197
11	67	70	71	78

	B - Buffer	D - Buffer	F - Buffer	H - Buffer
0	540	572	557	651
1	306	311	310	364
2	184	182	183	210
3	122	130	121	139
4	95	98	99	113
5	96	86	87	107
6	84	80	82	96
7	78	82	82	98
8	83	85	79	93
9	80	78	80	89
10	81	81	80	97
11	84	80	81	93

	A - HSA	C - HSA	E - HSA	G - HSA
0	947	934	935	946
1	636	646	652	631
2	434	435	457	486
3	296	314	307	336
4	212	221	267	245
5	152	150	157	174
6	114	114	108	130
7	92	91	86	102
8	78	75	78	92
9	70	71	71	86
10	70	71	70	197
11	67	70	71	78