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Undergraduate Research Journal

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Molecular Analysis of the Interaction Between Staphylococcus aureus Protein Sbi and Immune System Protein C3d<br />

Wilson Rodriguez<br />

collection of independent and communicating scripts and<br />

is written in the R software environment for statistical<br />

computing. AESOP performs alanine scans, calculates<br />

electrostatic potentials using the Poisson-Boltzmann<br />

equation, determines electrostatic similarity distances<br />

(ESD), performs hierarchical electrostatic clustering of<br />

ESDs, calculates electrostatic free energies of association,<br />

and provides a graphical representation of electrostatic<br />

potentials. AESOP’s centralized functions have facilitated<br />

the study of electrostatics in the function of protein-protein<br />

interactions. 5-9<br />

The AESOP protocol begins with acquiring a file with<br />

the coordinates of the crystal structure from the Protein<br />

Data Bank (PDB), which is visually inspected for missing<br />

or duplicate residues. Duplicates were removed and no<br />

missing residues were found. It is then cleaned by removing<br />

the header and footer of the file and any heteroatoms<br />

and water atoms the structure may have. Once the PDB<br />

file is processed, AESOP performs the aforementioned<br />

automated tasks. It starts by reading in the coordinates of<br />

the PDB file and changes its format into a PQR file, using<br />

the PDB2PQR program. 1,2,4 PQR files are very similar<br />

to PDB files except that in addition to coordinates, they<br />

contain atomic charges and radii. If hydrogen atoms are<br />

missing in PDB files, which are typical of crystallographic<br />

structures, PDB2PQR also adds hydrogen atoms. The next<br />

step is to generate a family of mutants from the parent<br />

PQR file. AESOP does so by reading the protein sequence<br />

residues one at a time in order to locate one of the five<br />

charged residues of interest, histidines, arginines, lysines,<br />

aspartates or glutamates, and then truncates the side chain<br />

to the beta carbon, shortens the gamma carbon’s bond and<br />

changes it into a hydrogen with correct bond length and<br />

atomic charge. Once the mutation is made, a new PQR<br />

file is saved and stored for further calculations. The script<br />

then returns to the parent PQR to search and locate the<br />

next available charged residue to mutate to alanine until<br />

it has checked and mutated all the residues in the parent<br />

sequence. This process is called computational alanine<br />

scan and each of the mutant proteins has a single residue<br />

mutation generated from the parent protein. In the C3d-<br />

Sbi complex there were 94 total residue mutations, 64<br />

belonging to C3d and 30 belonging to Sbi.<br />

Following the computational mutations we calculated<br />

electrostatic potentials using the Adaptive Poisson-<br />

Boltzmann Solver (APBS)2,6. APBS is called by AESOP to<br />

solve the Poisson-Boltzmann equation, which accounts for<br />

the fixed and mobile charges and dielectric environment of<br />

the protein and solvent. The linearized Poisson-Boltzmann<br />

equation is shown below<br />

In equation (1), ε(r) = ε 0<br />

ε r<br />

(r) represents the distance<br />

dependent permittivity of the medium (ε 0<br />

being the<br />

vacuum permittivity and ε r<br />

being the relative permittivity<br />

with respect to vacuum or dielectric coefficient as referred<br />

below), φ(r) represents electrostatic potential in units of<br />

k B<br />

T/e c<br />

(k B<br />

being the Boltzmann constant, T the temperature,<br />

and e c<br />

the electron charge), and к 2 (r) is the ion accessibility<br />

function that incorporates ionic strength and distribution<br />

of ions into the equation. Finally, the sum of fixed charges<br />

found in the protein are expressed by Q i<br />

δ(r - r i<br />

), where<br />

Q i<br />

represents the protein’s fixed charge at atom position<br />

r i<br />

. The calculations were conducted using a 129 x 129 x<br />

129 grid of dimensions 114 x 140 x 122 Å 3 , a dielectric<br />

coefficient of 20 for protein interior and 78.54 for solvent,<br />

ionic strength of 150mM all at room temperature 298.15K.<br />

Visual representations of the electrostatic potentials were<br />

generated with Chimera. 10 The visual representations play<br />

a key role in analysis and understanding of the mechanism<br />

behind the binding and stability of an interaction.<br />

We further obtained a quantitative calculation of the<br />

interaction by calculating free energies of association of<br />

the mutants to find how a particular residue affected the<br />

complex, according to<br />

(1)<br />

∆G = 1<br />

2 q i φ i<br />

(2)<br />

In equation (2) the free energies of association ∆G are<br />

described by q i<br />

and φ i<br />

which represents the charge and<br />

electrostatic potential, respectively, when calculated<br />

through APBS. Using the theoretical thermodynamic<br />

cycle shown in Fig. 2, both the free energies of association<br />

(horizontal processes) and of solvation (vertical processes)<br />

can be calculated. 5-7<br />

U C R U n d e r g r a d u a t e R e s e a r c h J o u r n a l 2 5

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