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The E-value estimates the expected number of random alignments with at least a comparable score in a database search.
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Formula
E dimensionless as expected hit count · m,n effective search lengths · S alignment score · λ per score unit · K depends on scoring model
| Symbol | Meaning | Unit |
|---|---|---|
| Expected number of random hits at least this score high | dimensionless expected hit count | |
| Calibration constant for the scoring and background distribution | model-dependent | |
| Effective query-sequence length | positions | |
| Effective total database length | positions | |
| Scale parameter of the score-distribution model | 1/score unit | |
| Alignment score | score unit |
E\approx Kmn e^{-\lambda S}The Karlin-Altschul approximation estimates random local alignments above a score for suitable scoring systems and background models. With model and search space fixed, E decreases exponentially with higher score and grows with search-space size. An E-value is not the probability that a biological hypothesis is true, and it proves neither homology nor function. Database size, compositional bias and parameters matter.
The local scoring model meets statistical assumptions and search-space parameters are known.
E estimates random hits that reach at least the observed score.
Score from E-value
Use with positive model parameters K, m and n.
Given Kmn=106, λ=0.5 per score unit and S=40, estimate E.
E≈106·e−20≈2.06×10−3.
Interpreting E as the probability of the biological hypothesis.
E is an expected random-hit count under the search and scoring model.
Formula cluster
a smaller E-value is more unusual under a comparable search space.
For illustrative parameters Kmn=106, λ=0.5 per score unit and S=40, E≈106·e−20≈2.06×10−3 expected random hits. Check: increasing S by ln(2)/λ≈1.386 halves E under the same model. Interpret only if scoring parameters and search space stay unchanged.
Interpret the significance of local DNA and protein alignments in BLAST searches
Here is how to work through a typical BLAST E-value in Sequence Searches (E ≈ Kmn·e^(−λS)) task step by step:
Task
Given Kmn=106, λ=0.5 per score unit and S=40, estimate E.
Solution path
E≈106·e−20≈2.06×10−3.
the expected number of random local alignments at least this score high. Its output is an expected hit count, not a probability that a biological function is true.. a smaller E-value is more unusual under a comparable search space. The quantity answers a specific biological or statistical question, not automatically the full cause of an observed pattern. Tie it to the population, sample or model level from which inputs came. A number without that reference can be misleading across studies. Keep description separate from explanation: the metric summarizes data but does not by itself establish the underlying mechanism.
Use K and λ come from the scoring model, m and n from effective search lengths. The units are E is dimensionless; λ balances score units in the exponent.. Check that numerator and denominator refer to the same time interval, target population and scale. Proportions entered as percentages usually need conversion to values between zero and one. Write units and definitions beside the observations. This helps catch swapped groups, mismatched age intervals or a wrong denominator before they distort the result. Also document measurement definitions and preprocessing, because studies can operationalize the same symbols differently.
The central assumption is: local alignments and a suitable background model are described. database size and compositional bias change the statistical expectation. If model violations prevent direct transfer of the theoretical E-value., interpretation changes or the formula no longer fits. State sampling, measurement method and biological scale. A model is useful because it simplifies a question, but its limits belong in the report. Do not automatically transfer parameters to different species, populations, laboratories or sampling conditions. Report these assumptions with the result so readers can judge which populations and conditions the conclusion can cover.
In the example, the stated parameters give about 2.06×10−3 expected random hits. The check is: raising score lowers E exponentially when other values stay fixed. Substitute calculated values back into the original relation and check whether ranges and units are biologically plausible. Rounded data can create a small discrepancy, but should not change direction or order of magnitude. Also test a simple limiting case, such as zero, complete detection or equal groups. This separates arithmetic errors from model limitations. Round intermediate values only at the end, and check the order of magnitude against the biological question.
A nearby quantity is alignment score and sequence identity. The substantive distinction is that score and identity describe the observed alignment; E estimates random hits in the search space. Both can appear in the same biological analysis, but they use different inputs and answer different questions. Choose by the requested output and verify the data definition before comparing values. A related name does not imply identical units or interchangeable interpretation. This matters when a descriptive statistic is reported alongside a model parameter. Before comparing values, align definitions, populations, observation periods and analysis rules; otherwise the difference may be methodological.
Quanta exam set
Curated exam set for "BLAST E-value in Sequence Searches":
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Which formula describes BLAST E-value in Sequence Searches?
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How do you rearrange BLAST E-value in Sequence Searches for Score from E-value?
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Which common mistake happens with BLAST E-value in Sequence Searches?
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