# Kappa – Lambda light chain ratio

**MATHEMATICS IN MEDICINE**, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)

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Few days back I was going through the development of immunoglobulin receptors on B cells. I came across a few facts:

1. The ratio between kappa (K) and lambda (L) light chain attached with immunoglobulin (Ig) receptor is approximately 2:1. (I was surprised, as the expected ratio should have been 1:1, assuming random activation of K or L genes). It is different from free light chain ratio (as they are also affected by differential catabolism of K and L light chains). I assumed that the metabolism of intact kappa Ig and lambda Ig receptor will be same and will depend on the degradation of respective B cell (there should not be differential destruction of K and L Ig B cells).

I got the answer to the above fact after a few hours when I came across the following fact:

*“K LIGHT CHAIN GENE IS ACTIVATED IN ALL THE B CELLS INITIALLY, L LIGHT CHAIN GENE IS EXPRESSED ONLY WHEN THE TRANSLATED K CHAIN IS NOT ABLE TO BIND TO THE MU HEAVY CHAIN. IF L CHAIN PRODUCT IS ALSO NOT ABLE TO BIND TO THE HEAVY CHAIN, B CELL UNDERGOES APOPTOSIS.”*

**K/L (p=0.5) = 2**

**Implications:**

**1. K/L can never be less than 1 (if you come across any < 1 value, inform me with reference). If this happens, our model is wrong, something else may be happening.**

**2. K/L of 2 means that half of the K light chain and L light chains are incompatible with heavy chain.**

**3. K/L of 2 means that 25% of the pro (pre) B cells are undergoing apoptosis due to incompatible light chain synthesis.**

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**MATHEMATICS IN MEDICINE**.

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