I wonder when to say two proteins are homolog. In the current example I checked the sequence of these two proteins in pfam and as you see they have some shared domains but all domains are not shared. Can I say that these proteins are homolog? How can I be confident about my decision?
Homology means shared evolutionary ancestry. Sequence similarity is often used as a proxy for homology but inferences should be made with care.
The similarity between two genes/proteins should not just be good but has to be statistically significant (metrics like E-value) for the two genes/proteins to be considered homologous.
INFERRING HOMOLOGY FROM SIMILARITY
The concept of homology – common evolutionary ancestry – is central to computational analyses of protein and DNA sequences, but the link between similarity and homology is often misunderstood. We infer homology when two sequences or structures share more similarity than would be expected by chance; when excess similarity is observed, the simplest explanation for that excess is that the two sequences did not arise independently, they arose from a common ancestor. Common ancestry explains excess similarity (other explanations require similar structures to arise independently); thus excess similarity implies common ancestry.
However, homologous sequences do not always share significant sequence similarity; there are thousands of homologous protein alignments that are not significant, but are clearly homologous based on statistically significant structural similarity or strong sequence similarity to an intermediate sequence. Thus, when a similarity search finds a statistically significant match, we can confidently infer that the two sequences are homologous; but if no statistically significant match is found in a database, we cannot be certain that no homologs are present.
Members of a protein family are descendants of a common ancestor and are hence homologous. However, in the course of evolution they would have acquired new domains or reshuffled their domains such that their sequences are no longer similar. Proteins that have full length sequence similarity are called homeomorphic (Wu et al., 2004). Therefore, members of a protein family may be homologous but not homeomorphic. However, homeomorphic proteins can evolve independently and therefore may not be considered homologous.
Identifying homologous proteins is, therefore, not a simple task. Machine learning algorithms are used for better identification of homologous proteins. Some of these algorithms are mentioned in the linked papers.
In general, global similarity, rather than local similarity should be considered for identifying homeomorphs. See What is the difference between local and global sequence alignments?
Domain is a module. Proteins are composed of one or more domains. Proteins are modular. Homology describes the relationship between domains, because domains are the primary evolutionary units. It is possible for two proteins to be homologous in one and non-homologous in another domain.
For example, alpha/beta-hydrolases (Ollis et al., 1992, Protein Eng. 5: 197-211) belonging to different families are homologous in the alpha/beta-hydrolase domain, but non-homologous in the "cap" domain.