How lambda parameter works in BLAST?

Question

[jqg44605]

How lambda parameter works in BLAST? It is calculated using the following equation (https://doi.org/10.1073/pnas.87.6.2264):

Scoring matrix is calculated using:

While bit score using:

My questions:

1. To calculate lambda we need scoring matrix, and to calculate scoring matrix we need lambda. How does it work?
2. To calculate scoring matrix we divide logarithm by lambda, and to calculate bit score we multiply raw alignment score by lambda. Therefore, lambda parameter has no effect. Is it correct?

[biofalconch]

Found something that might be related to the values of lambda and K, perhaps you could check this?

https://bioinformatics.stackexchange.com/questions/5145/calculating-bit-score-how-do-you-find-lambda-and-k

From the post:

NCBI BLAST uses tables of pre-computed values for lambda/K for gapped protein and nucleotide comparison and their values depend on the amino acid substitution matrix or the substitution scores + gap penalties.