Two Methods for Calculating the Size Distribution of Ferritin ’ s Outer Diameter

Ferritin is a kind of iron-storage protein widely found in animals and plants. The dynamic light scattering (Dynamic Light Scattering) method is used in the laboratory to determine the ferritin size. This paper presents two methods for calculating the outer diameter size distribution of ferritin, both of which assume that ferritin is approximately spherical. The ferritin data file was obtained from the PDB website and was calculated using the coordinate data of the amino acids to which the amino acids belong. The first method is based on the calculation of the sphere center; the second method is based on the method of the farthest distance atom pair. The outer diameter size distribution curves obtained by the two methods are basically consistent with the experimental methods. The paper also compares the calculation results and performance of the two methods. Both methods are versatile and can be used to calculate the size distribution of the globular proteins.


Background and Introduction
Ferritins have been found to exist almost ubiquitously in biological systems, regulating the storage and release of iron.Molecularly, ferritins are large globular multi-subunit proteins with a central cavity in which a hydrated ferric oxide is mineralised.When produced by multiple living organisms, ferritins vary widely in their primary structures (some share as low as 14% similarity in their amino acid sequences) but share essentially the same quaternary structure.Each hollow globular protein consists of 24 subunits and can store approximately 4500 iron ions.Typically it has internal and external diameters of about 8 and 12 nm, re-X.Y. Zhao, J. H. Gao DOI: 10.4236/cmb.2018.83006116 Computational Molecular Bioscience spectively [1].
Clinically, ferritin maintains iron homeostasis and is associated with a wide range of physiologic and pathologic processes.It is predominantly utilized as a serum marker of total body iron stores, which serves a critical role in both diagnosis and management of related diseases such as coronary artery disease, malignancy, and poor outcomes following stem cell transplantation [2].
Furthermore, advances in biological nanoparticles have shown promising therapeutic applications.In particular, ferritin can self-organise in the nanometer range while meeting multiple criteria, such as biocompatibility, water solubility and high cellular uptake efficiency with minimal toxicity.They are also highly amenable through genetic and chemical modifications to suit different purposes.
This makes ferritin a suitable molecular scaffold for the targeted delivery of the drugs and other molecules by conjugation with specific ligands or for imaging purposes using dyes [3] [4] [5].
The methods introduced in this paper can be applied to related research into ferritin and be further extended to other studies about globular proteins.

The Calculation Method Based on the Center of the Sphere
Outwardly, almost all ferritin is spherical.The calculation method of the center of the ball is simple.First, read the X, Y, Z coordinates of all the atoms in the PDB file which are labeled as ATOM, and then calculate the average value of all X, Y, Z, and the calculated average value is the coordinate value of the center of the ball.Because ferritin is not spherical, we can only calculate the density distribution of its outer diameter.By keeping the atoms larger than the center of the sphere, doubling each of these distances, we get a number of samples representing the size of the outer diameter.

Calculation Method Based on the Furthest Distance Atom Pair
We first describe this method in theory.The atom B, which is the furthest away from the atomic A, is calculated, and then the atom C, which is the furthest away from the atom B, is calculated.This C may be A, or it may not be A. In this way, iterative computation is carried out until no new atom appears. is taken as a sample of the outer diameter.

The Combination of the Two Methods
First, calculate the coordinates of the center of the sphere, and keep the atoms that are larger in the center of the sphere.This step is the same as the first calculation method.The next steps are the same as the second calculation method.
For each atom, calculate the atom that is the furthest from this atom and calculate the distance between them as one of the approximate diameters.Calculate all such atom pairs.

Calculation of Outer Diameter Distribution
After obtaining a batch of data on the outside diameter, we can program to get the distribution of the outside diameter size.The specific approach is to use Python programming, using gaussian_kde and its PDF density distribution function in the scipy.statspackage, calculate the density distribution of the outer diameter size, and draw the density distribution map with matplotlib.

Results
Taking 3kx9 as an example, the outer diameter density distribution curve calculated by the two methods is shown in Figure 2.Among them, the red curve is based on the calculation method of the sphere center, and the blue curve is based on the calculation method of the farthest distance atom pair.
Structural information of various types of ferritins can be obtained from Protein Data Bank (PDB) [6]. Figure 1 shows the biological assembly of ferritin 3kx9 consisting of over 30,000 atoms.It is a mutant of Archaeoglobus fulgidus ferritin (AfFtn) formed by replacing the amino acid residues Lys-150 and Arg-151 by Alanine.It forms a typical 24-mer structure but with octahedral closed symmetry.
Now we describe the actual calculation process: traversing all the atoms in the ferritin molecule, put in List 0, calculate the atom in the farthest distance from each atom in List, put in List 1, remove the repeating atoms in List 1, and get a new List 2. In List 2, calculate the atoms that are the furthest away from each atom, put them in List 3, remove the duplicate atoms in List 3, and get the new List 4. The distance between the atomic pairs with the furthest distance in List 4