Two things should help: The author's numbering and the basic rules of English grammar. Let me explain.
The numbers in parentheses indicate that the author is in fact speaking about two distinct subjects. He could ahave lternatively used bullet points or a numbered list but chose this version to get a continuous text.
So to analyze this text, we split along these parentheses. I'm using numbers for simplicity here:
Our hypothesis is that
- many strains of rats simply cannot mount sufficiently vigorous destructive immune-response (using lymphocytes) to outstrip the liver's relatively great capacity to protect itself from immune-response damage and that
- the systemic unresponsiveness observed is due to concentration of the recipient's donor specific lymphocytes at the site of the liver transplant.
Looking closely we notice that each numbered item is basically a full sentence (with a bit of connecting stuff from the continuous original version). We may drop that surplus and get:
Our hypothesis is that
- Many strains of rats simply cannot mount sufficiently vigorous destructive immune-response (using lymphocytes) to outstrip the liver's relatively great capacity to protect itself from immune-response damage.
and that
- The systemic unresponsiveness observed is due to concentration of the recipient's donor specific lymphocytes at the site of the liver transplant.
Then we can address each item separately. Here the S-V-O structure of the English language helps:
first position: Subject: Who?
second position: Verb: Does what?
followed by Object(s) etc.
Many strains of rats
simply cannot
mount sufficiently vigorous destructive immune-response (using lymphocytes)
to outstrip
the liver's relatively great capacity
to protect itself
from immune-response damage.
The systemic unresponsiveness observed
is due to
concentration of the recipient's donor specific lymphocytes
at the site of the liver transplant.