Uploaded July 2026 | Updated September 2026, 2 weeks ago
X-ray crystallography maps (viewing & understanding 2Fo-Fc, Fo-Fc, etc.)… In X-ray crystallography, electrons in a crystal interact with x-rays to generate a diffraction pattern. Then crystallographers work backwards from the diffraction patterns to create an electron density map. Then they build an atomic model into that map.
blog: bit.ly/xraymaps
Sounds straight forward right? Wrong! There’s a big problem. Recreating an electron density map from diffraction data basically involves reconstructing a complicated wave through a math-y thing called a Fourier transformation. And a wave equation describing that wave requires both intensity (which we can measure from spot strength) & phases. We only can detect the intensity. Leaving us with a big “phase problem.” So in order to actually create a typical map - even a pretty bad one - we have to "guess" the phases through various methods like molecular replacement (which is just computational, basing it on similarity to a known structure) or experimental determination with techniques like SAD and MAD or heavy metal soaking that give us only rough starting points.
Scientists then compute their "best guess" models based on the initial data & calculate what the map would look like if the model were correct. Then they refine their models to make them match the data better, working back and forth between map and model.
And maps help them find their way!
There are a few kinds…
2Fo-Fc is a common way to view electron density. This map shows 2X observed signal (Fo) - modeled (calculated) signal (Fc) (so it weighs observed more highly) & you want to see continuous density. Density is typically clearest in the backbone and "stiff" areas of a protein and less clear (maybe even invisible) in side chains and flexible areas. These areas have a high “B factor” aka displacement factor.
You might see variations of this such as 2mFo-DFc which add some statistical weighting stuff to make more reliable, higher strength, data "count more."
Fo-Fc shows you where things should or shouldn't be! The Fo-Fc difference map highlights differences between the observed & the calculated-from-the-model signals. So, if they match completely, you'll see nothing! but they won't (at least not everywhere), so.… it's typically displayed in red/green on top of the 2Fo-Fc map.
A negative (red) blob tells you you've modeled in something "extra" that's not supported by the data. A positive (green) blob tells you the model is missing something - there's still signal you need to account for
Note: there will have to be an equal amount of red and green in the map so lots of it will just be noise - the 2Fo-Fc can help you sort it out by tracing the continuous density
There are also “omit maps” where you calculate maps based on structures where you’ve left out (omitted) some part of the model (such as a bound ligand (binding partner)). This is often used to show that the density supporting the ligand in your other maps is real and not just the result of model bias. This is really important because scientists often have wishful thinking that something is bound so they model it on which then contributes to the normal map - but not the omit one. So there better be density still there!
How much density you see on the screen depends in part on how you’ve set the contour level. Maps can be contoured at different levels and changing the sigma (o) level only changes how much of the data is displayed, not the data itself. o refers to the standard deviation of the strength of the signal (much of which is just noise) above the average, & you choose a factor of this at which to cut off the data. A higher o cut-off means that you only show data whose signal is further above the level of noise, but you also leave out true but weaker signal. Higher o contour is stricter. You just see the strongest signal.
It’s important not to set your contour too low when building your model or you will end up building into a bunch of noise!
Finished in comments
X-ray crystallography maps (viewing & understanding 2Fo-Fc, Fo-Fc, etc.)… In X-ray crystallography, electrons in a crystal interact with x-rays to generate a diffraction pattern. Then crystallographers work backwards from the diffraction patterns to create an electron density map. Then they build an atomic model into that map.
blog: bit.ly/xraymaps
Sounds straight forward right? Wrong! There’s a big problem. Recreating an electron density map from diffraction data basically involves reconstructing a complicated wave through a math-y thing called a Fourier transformation. And a wave equation describing that wave requires both intensity (which we can measure from spot strength) & phases. We only can detect the intensity. Leaving us with a big “phase problem.” So in order to actually create a typical map - even a pretty bad one - we have to "guess" the phases through various methods like molecular replacement (which is just computational, basing it on similarity to a known structure) or experimental determination with techniques like SAD and MAD or heavy metal soaking that give us only rough starting points.
Scientists then compute their "best guess" models based on the initial data & calculate what the map would look like if the model were correct. Then they refine their models to make them match the data better, working back and forth between map and model.
And maps help them find their way!
There are a few kinds…
2Fo-Fc is a common way to view electron density. This map shows 2X observed signal (Fo) - modeled (calculated) signal (Fc) (so it weighs observed more highly) & you want to see continuous density. Density is typically clearest in the backbone and "stiff" areas of a protein and less clear (maybe even invisible) in side chains and flexible areas. These areas have a high “B factor” aka displacement factor.
You might see variations of this such as 2mFo-DFc which add some statistical weighting stuff to make more reliable, higher strength, data "count more."
Fo-Fc shows you where things should or shouldn't be! The Fo-Fc difference map highlights differences between the observed & the calculated-from-the-model signals. So, if they match completely, you'll see nothing! but they won't (at least not everywhere), so.… it's typically displayed in red/green on top of the 2Fo-Fc map.
A negative (red) blob tells you you've modeled in something "extra" that's not supported by the data. A positive (green) blob tells you the model is missing something - there's still signal you need to account for
Note: there will have to be an equal amount of red and green in the map so lots of it will just be noise - the 2Fo-Fc can help you sort it out by tracing the continuous density
There are also “omit maps” where you calculate maps based on structures where you’ve left out (omitted) some part of the model (such as a bound ligand (binding partner)). This is often used to show that the density supporting the ligand in your other maps is real and not just the result of model bias. This is really important because scientists often have wishful thinking that something is bound so they model it on which then contributes to the normal map - but not the omit one. So there better be density still there!
How much density you see on the screen depends in part on how you’ve set the contour level. Maps can be contoured at different levels and changing the sigma (o) level only changes how much of the data is displayed, not the data itself. o refers to the standard deviation of the strength of the signal (much of which is just noise) above the average, & you choose a factor of this at which to cut off the data. A higher o cut-off means that you only show data whose signal is further above the level of noise, but you also leave out true but weaker signal. Higher o contour is stricter. You just see the strongest signal.
It’s important not to set your contour too low when building your model or you will end up building into a bunch of noise!
Finished in comments
