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The effect of noise on entropy
1Department of Biochemistry and Biophysics, Texas A & M University, College Station, Texas 77843-2128, USA.
Acta Crystallographica. Section D, Biological Crystallography
|January 1, 1993
Summary
Noise in electron-density maps surprisingly decreases entropy (S), a finding supported by a new entropy-variance relationship. This relationship aids in interpreting macromolecular maps by justifying entropy maximization.
Area of Science:
- Crystallography
- Biophysics
- Computational Biology
Background:
- Electron-density maps are crucial for determining molecular structures.
- Map quality is often limited by noise, complicating interpretation.
- Entropy (S) is a measure of map complexity and interpretability.
Purpose of the Study:
- To derive a complementary relationship between entropy (S) and variance (sigma(2)) for electron-density maps.
- To provide a theoretical basis for understanding the effect of noise on map entropy.
- To justify maximizing map entropy for improved macromolecular structure determination.
Main Methods:
- Approximating the logarithmic term in the entropy expression using series expansion.
- Deriving an algebraic expression: S ≈ ln N - 1/2σ(2).
- Analyzing the impact of noise-induced variance on map entropy.
Main Results:
- A novel entropy-variance relationship (S ≈ ln N - 1/2σ(2)) was established.
- Noise was shown to increase map variance, thereby decreasing map entropy.
- The relationship is particularly useful for experimental maps with low structure definition.
Conclusions:
- The derived relationship supports the counterintuitive idea that noise reduces map entropy.
- Maximizing electron-density map entropy is a valid strategy for enhancing interpretability.
- This entropy-variance concept broadens the application of entropy analysis to maps with negative density regions.