question about TLS cryptosuite and x.509 fields

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I am trying to understand the relationship between parameters in the tls cryptosuite and fields in x.509.  

from rfc3279 (x.509)  

-Signature Algorithms   (section 2.2)
-Subject Public Key Algorithms (section 2.3)

From TLS cryptosuite:
-key exchange algorithms
-authentication algorithms

Are the selected algorithms for these parameters related or independent? Can someone explain how each are used.  

Thank you.

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