10. 【Lab】 Does a CD4 TCR look different from a CD8 TCR? · Prof. Kwon's TCR-HLA and CD4/CD8, First Steps

By this point an obvious question turns up.

Does a TCR that reads class I look different from one that reads class II?

It would be reasonable. The grooves are shaped differently, the fragments are different lengths, and the way a fragment overhangs is different. Surely the receptor sitting on top should differ too.

Let us count.

A difference of 0.06 residues — one fifteenth of a single amino acid.

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# CDR3 length — does it differ by class
import thla

for gene in ["TRA", "TRB"]:
    a = thla.cdr3_len("I", gene)
    b = thla.cdr3_len("II", gene)
    print(f"{gene}")
    print(f"   class I  n={len(a):>7,}  mean {a.mean():.2f}  median {a.median():.0f}")
    print(f"   class II n={len(b):>7,}  mean {b.mean():.2f}  median {b.median():.0f}")
    print(f"   difference {a.mean()-b.mean():+.2f} residues")
    print()

A difference 120,000 rows cannot catch is, at most, very small.

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# Could it be chance? A rank-sum test.
import thla
from scipy import stats

a = thla.cdr3_len("I", "TRB")
b = thla.cdr3_len("II", "TRB")
u, p = stats.mannwhitneyu(a, b)
print(f"Mann-Whitney U test  p = {p:.3f}")
print()
if p > 0.05:
    print("No grounds for saying the two distributions differ.")
else:
    print("There is a difference.")
print()
print("With samples of 116,477 and 4,098, a large p does not mean")
print("the difference is 'small'. It means it is 'not visible'.")

The two curves sit almost on top of each other.

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# Overlay the length distributions
import matplotlib.pyplot as plt
import numpy as np
import thla

fig, ax = plt.subplots(figsize=(8, 4))
bins = np.arange(8, 24) - 0.5
for cls, col, lab in [("I", "#4C7DE0", "class I  (CD8)"), ("II", "#E8863F", "class II (CD4)")]:
    v = thla.cdr3_len(cls, "TRB")
    ax.hist(v, bins=bins, density=True, histtype="step", lw=2.4, color=col, label=lab)
ax.set_xlabel("CDR3beta length (aa)")
ax.set_ylabel("fraction")
ax.legend()
plt.show()

Overlay the two distributions, then shrink the sample and see whether any difference shows.

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What about V gene usage — and here a trap appears

If CDR3 length matches, what about V genes? Except that this comparison inherits, whole, the bias we met earlier.

0.38 and 0.90. A gap that wide means one enormous lump is sitting somewhere.

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# Compare TRBV usage across the two classes — with two correlation coefficients
import pandas as pd
import thla

a = thla.vdj("I", "TRB")["v"].value_counts(normalize=True)
b = thla.vdj("II", "TRB")["v"].value_counts(normalize=True)
j = pd.concat([a, b], axis=1, keys=["I", "II"]).fillna(0)
print(f"Pearson  {j['I'].corr(j['II']):.3f}    (compares the values)")
print(f"Spearman {j['I'].corr(j['II'], method='spearman'):.3f}    (compares the ranks)")
print()
print("The ranks agree while the values do not. Why?")

Drop one fragment and 0.38 becomes 0.64. One NY-ESO-1 experiment weighs that much.

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# Find the culprit — drop one fragment and measure again
import pandas as pd
import thla

d = thla.vdj("I", "TRB")
big = d.groupby("epitope").size().idxmax()
n = int((d["epitope"] == big).sum())
print(f"biggest lump : {big}  {n:,} rows  ({100*n/len(d):.1f}%)")
print()
b = thla.vdj("II", "TRB")["v"].value_counts(normalize=True)
for label, sub in [("everything", d), (f"without {big}", d[d["epitope"] != big])]:
    a = sub["v"].value_counts(normalize=True)
    j = pd.concat([a, b], axis=1, keys=["I", "II"]).fillna(0)
    print(f"   {label:<22} Pearson {j['I'].corr(j['II']):.3f}")

🤔 Check yourself

What did comparing CDR3β length between class I and class II TCRs show?

🤔 Check yourself

When Pearson reads 0.38 and Spearman reads 0.90, what should you suspect?

🤔 Check yourself

What does this lesson conclude?