Please refer to the HMMER documentation for a complete explanation of how bit score and E-values are calculated. The following is excerpted directly from the HMMER 2.3.2 User's Guide:

**Executive summary**

- The best criterion of statistical significance is the E-value. The E-value is calculated from the bit score. It tells you how many false positives you would have expected to see at or above this bit score. Therefore a low E-value is best; an E-value of 0.1, for instance, means that there's only a 10% chance that you would've seen a hit this good in a search of nonhomologous sequences. Typically, I trust the results of HMMER searches at about E=0.1 and below, and I examine the hits manually down to E=10 or so.
- HMMER bit scores are a stricter criterion: they reflect whether the sequence is a better match to the profile model (positive score) or to the null model of nonhomologous sequences (negative score). A HMMER bit score above log2 of the number of sequences in the target database is likely to be a true homologue. For current NR databases, this rule-of-thumb number is on the order of 20 bits. Whereas the E-value measures how statistically significant the bit score is, the bit score itself is telling you how well the sequence matches your HMM. Because these things should be strongly correlated, usually, true homologues will have both a good bit score and a good E-value. However, sometimes (and these are the interesting cases), you will find remote homologues which do not match the model well (and so do not have good bit scores ? possibly even negative), but which nonetheless have significant E-values, indicating that the bit score, though "bad", is still better than you would've expected by chance, so it is suggestive of homology.
- What does it mean when I have a negative bit score, but a good E-value? The negative bit score means that the sequence is not a good match to the model. The good E-value means that it's still a better score than you would've expected from a random sequence. The usual interpretation is that the sequence is homologous to the sequence family modeled by the HMM, but it's not "within" the family - it's a distant homologue of some sort. This happens most often with HMMs built from "tight" families of high sequence identity, aligned to remote homologues outside the family. For example, an actin HMM aligned to an actin-related protein will show this behavior - the bit score says the sequence isn't an actin (correct) but the E-value says it is significantly related to the actin family (also correct).