Scientific Foundations

synth-cryo-em is built on standard physical models used in structural biology and electron microscopy.

Density Generation

The mapping from atomic coordinates to 3D density is performed using Gemmi.

Resolution and Blur

In structural biology, the relationship between resolution ($d$) and the isotropic B-factor ($B$) is often approximated as: $$B \approx 8 d^2$$ This ensures that the information content is significantly attenuated beyond the target resolution. When --no-bfactors (default) is used, a global blur is applied to all atoms using this relationship.

Local Resolution

When --bfactors is enabled, the atomic B-factors from the input PDB/CIF file are used directly. This allows for simulating "local resolution" effects where flexible regions of a protein appear more blurred than the rigid core.

Contrast Transfer Function (CTF)

The simulation of the microscope's optics follows the standard phase-contrast model. The phase shift $\chi(k)$ at spatial frequency $k$ is given by: $$\chi(k) = \pi \lambda k^2 (\Delta f - 0.5 \lambda^2 k^2 C_s)$$ where: - $\lambda$ is the relativistic electron wavelength. - $\Delta f$ is the defocus. - $C_s$ is the spherical aberration.

The resulting CTF is: $$CTF(k) = -(\sqrt{1-w^2} \sin(\chi(k)) + w \cos(\chi(k)))$$ where $w$ is the amplitude contrast.

Envelope Function

An optional envelope function can be applied to simulate spatial and temporal incoherence: $$E(k) = e^{-B_{env} k^2 / 4}$$

Validation Metrics

Fourier Shell Correlation (FSC)

FSC measures the normalized cross-correlation between two 3D maps in shells of constant spatial frequency. It is the standard tool for assessing resolution in Cryo-EM. $$FSC(k) = \frac{\sum_{|k'|=k} F_1(k') \cdot F_2(k')^*}{\sqrt{\sum_{|k'|=k} |F_1(k')|^2 \cdot \sum_{|k'|=k} |F_2(k')|^2}}$$

Cross-Correlation Coefficient (CCC)

CCC provides a global measure of similarity between two maps in real space: $$CCC = \frac{\sum (M_1 - \bar{M_1})(M_2 - \bar{M_2})}{\sqrt{\sum (M_1 - \bar{M_1})^2 \sum (M_2 - \bar{M_2})^2}}$$