

In [19]:

    
%matplotlib inline
import numpy as np
import pandas as pd
import scipy as sp
import scipy.stats
import matplotlib.pyplot as plt
import seaborn as sns

PhIP-Seq kinetics computations

IP reaction (1 mL)

IgG
- MW of IgG = 150 kDa
- 2 µg IgG = 13.3 pmol = 8.03e12 molecules
- 13.3 nM in the reaction
Phage
- 100k particles per clone on average
- Add ~1e10 total particles per mL reaction
- 5k - 50k of each clone per reaction
- Equiv to per clone concentration of 0.0083 fM to
Protein A/Protein G Beads
- 40 µL total => 1.2 mg beads => capture 9.6 µg Ab according to manual
- Should capture all Ab in reaction so will ignore in calculation
- Kd maybe ~10 nM

Ab in reaction

Kd = [Ab] [L] / [AbL]

Inputs: Desired Kd ability to resolve Total Ab and L (e.g., [Ab] + [AbL]) requires overwhelming Protein A/G binding sites?

Input library



In [23]:

    
df = pd.read_csv('/Users/laserson/lasersonlab/larman/libraries/T7-Pep_InputCountsComplete46M.csv', header=None, index_col=0)



In [24]:

    
counts = df.values.ravel()



In [25]:

    
sns.distplot(counts)









    Out[25]:





<matplotlib.axes._subplots.AxesSubplot at 0x10b954d30>

(min, 10%ile, 50%ile, 90%ile, max)



In [46]:

    
iles = (counts.min(), sp.stats.scoreatpercentile(counts, 10), sp.stats.scoreatpercentile(counts, 50), sp.stats.scoreatpercentile(counts, 90), counts.max())
iles









    Out[46]:





(0, 18.0, 94.0, 229.0, 1736)



In [38]:

    
cov = sum(counts)
cov









    Out[38]:





46859607

And the same values as frequencies



In [39]:

    
tuple([float(val) / cov for val in iles])









    Out[39]:





(0.0,
 3.8412614087864629e-07,
 2.0059920690329308e-06,
 4.8869381256227775e-06,
 3.704683225362944e-05)



In [41]:

    
counts.mean(), counts.std()









    Out[41]:





(113.29390901112397, 91.683612273186029)



In [47]:

    
(18. / cov) * 1e10









    Out[47]:





3841.2614087864631



In [48]:

    
(229. / cov) * 1e10









    Out[48]:





48869.381256227774



In [52]:

    
(counts > 0).sum()









    Out[52]:





404255



In [53]:

    
counts.shape









    Out[53]:





(413611,)



In [101]:

    
def equil_conc(total_antibody, total_phage, Kd):
    s = total_antibody + total_phage + Kd
    bound = 0.5 * (s - np.sqrt(s * s - 4 * total_antibody * total_phage))
    equil_antibody = total_antibody - bound
    equil_phage = total_phage - bound
    return (equil_antibody, equil_phage, bound)



In [102]:

    
equil_conc(13e-15, 8.302889405513118e-17, 1e-9)









    Out[102]:





(1.2999998920632698e-14, 8.3027814687829376e-17, 1.079367301805132e-21)



In [103]:

    
np.logspace?



In [148]:

    
antibody_concentrations = np.logspace(-15, -3, num=25)
phage_concentrations = np.logspace(-18, -12, num=13)

antibody_labels = ['{:.1e}'.format(c) for c in antibody_concentrations]
phage_labels = ['{:.1e}'.format(c) for c in phage_concentrations]

Kd = 1e-8
frac_antibody_bound = np.zeros((len(antibody_concentrations), len(phage_concentrations)))
frac_phage_bound = np.zeros((len(antibody_concentrations), len(phage_concentrations)))
for (i, a) in enumerate(antibody_concentrations):
    for (j, p) in enumerate(phage_concentrations):
        bound = equil_conc(a, p, Kd)[2]
        frac_antibody_bound[i, j] = bound / a
        frac_phage_bound[i, j] = bound / p

fig = plt.figure(figsize=(12, 6))
ax = fig.add_subplot(121)
sns.heatmap(frac_antibody_bound, xticklabels=phage_labels, yticklabels=antibody_labels, square=True, ax=ax)
ax.set_title('Fraction Antibody Bound')
ax.set_ylabel('total antibody clone conc')
ax.set_xlabel('total phage clone conc')
ax = fig.add_subplot(122)
sns.heatmap(frac_phage_bound, xticklabels=phage_labels, yticklabels=antibody_labels, square=True, ax=ax)
ax.set_title('Fraction Phage Bound')
ax.set_ylabel('total antibody clone conc')
ax.set_xlabel('total phage clone conc')









    Out[148]:





<matplotlib.text.Text at 0x11ed07ef0>

It's most important to ensure we get maximal phage capture, and this seems to be independent of the total phage concentration. Let's instead explore the fraction phage bound as a function of the antibody concentration and Kd



In [147]:

    
antibody_concentrations = np.logspace(-15, -3, num=25)
Kds = np.logspace(-15, -6, num=19)

antibody_labels = ['{:.1e}'.format(c) for c in antibody_concentrations]
Kd_labels = ['{:.1e}'.format(c) for c in Kds]

phage_concentration = 2e-15
frac_antibody_bound = np.zeros((len(antibody_concentrations), len(Kds)))
frac_phage_bound = np.zeros((len(antibody_concentrations), len(Kds)))
for (i, a) in enumerate(antibody_concentrations):
    for (j, Kd) in enumerate(Kds):
        bound = equil_conc(a, phage_concentration, Kd)[2]
        frac_antibody_bound[i, j] = bound / a
        frac_phage_bound[i, j] = bound / phage_concentration

fig = plt.figure(figsize=(9, 9))
# ax = fig.add_subplot(121)
# sns.heatmap(frac_antibody_bound, xticklabels=Kd_labels, yticklabels=antibody_labels, square=True, ax=ax)
# ax.set_title('Fraction Antibody Bound')
# ax.set_ylabel('total antibody clone conc')
# ax.set_xlabel('Kd')
ax = fig.add_subplot(111)
sns.heatmap(frac_phage_bound, xticklabels=Kd_labels, yticklabels=antibody_labels, square=True, ax=ax)
ax.set_title('Fraction Phage Bound')
ax.set_ylabel('total antibody clone conc')
ax.set_xlabel('Kd')









    Out[147]:





<matplotlib.text.Text at 0x11e1c6d68>



In [ ]:

PhIP-Seq kinetics computations

Reaction summary

Input library