From Diffraction Patterns to Crystal Structures
From Diffraction Patterns to Crystal Structures
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Crystalization
Crystalization
Image from the Starbird Lab (UNC Chapel Hill)
Macromolecule samples often already exist in their crystal form, either in nature or commercially. Protein and small molecule samples, however, need to be crystallized such that they form small crystals that we can use to perform X-ray crystallography. Crystallization techniques employ the general rule that a very highly saturated sample will not be in a stable state and will form crystals to return to a stable state.
To crystalize protein structures, researchers rely on supersaturation, leading to instability and emerging to an energetically unfavorable state. Molecules then organized into repeating lattice crystals to get back into a stable form, which we will then analyze under an Xray Diffractometer.
In this section, we will examine a computational model and fitting process for Fourier Synthesis as applied to our experimental modeling. The procedures and analytical methods used throughout this section are adapted from California State Polytechnic University, Pomona CHM 329L (Biochemistry), developed by Chantal Stieber. Using these methods, we aim to evaluate how Fourier Synthesis can be used to represent and analyze complex biochemical data through computational techniques and model fitting.
How do we go from diffraction patterns (frequency information) to a modeled electron density? Fourier Transforms!
While intensity mapping along two-θ angles gives us valuable information about diffraction peak positions and scattering intensity, it does not translate well into three-dimensional arrangement of our sample.
To reconstruct the molecular structure, amplitude and phase must be modeled using the inverse Fourier Transform. This loss of phase through experimental measurements, known as the "Phase problem," then needs to be remedied. A common solution is molecular replacement, where a molecule, similar to our crystal of study, with a known structure is rotated and translated until it matches the unknown sample. Then, the phase information can be found.
Computational Modeling
Phenix
In this simulation study, lysozyme's structure was resolved and refined. Hen Egg White Lysozyme was the first enzyme with a structure determined by X-ray crystallography with its easy abundance as a protein source and its ease of crystallization.
The software PHENIX takes in a sequence file, a reflection file containing the xray diffraction data, and a previously known search model (in this experiment, we use the 2ZIJ search model, which is the crystal structure of Lysozyme expressed in E. Coli). Phaser Molecular Replacement was then used to generate an inital sturcutre for the lysozyme and then PHENIX outputs a pdb file with atomic coordinates for us to model in a graphical program of choice
Zoomed-in Electron density map without refinement. For the molecule, green is carbon, blue is nitrogen, and red is oxygen, while the blue mesh is the electron density map
Coot
Coot was used to visualize, investigate, and remediate the output structure of Phenix. In Coot, the visualized blue electron density map is a 3 dimensional representation model of electron placement along a molecule. A difference map is a component which identifies where there's a lack of or excessive model density compared to the experimental data.
On the left, our lysozyme model after Phenix resolution can be seen. We see that the resolved structure has a good fit with the electron density map.
Ramachandran plots, such as above, provide a predictive model of where polymers are energetically allowed along dihedral angles φ and ψ.
Rotamers are a set of energetically favorable states that affect monomer placement, so researchers can conform the shape, guided by our electron density map. Peptide flips correct backbone orientation where the electron density lacks a strong fit. JED Flip and cis/trans help identify chains that may be incorrectly assigned, while backup rotamers adjusts the entire backbone rather than sidechain angles due to the location with an unfavorable position, outside the electric density map. A good rotamer improves the correlation coefficient, while not encouraging overlap with other neighboring chains.
Once the structural components are improved, the pdb file is placed back into Phenix in order to create another resolved structure. This process is continued until you can refine the molecular structure towards a desirable endpoint. To view the structure in a ribbon diagram, we transfer this data to PyMol.
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