Computing the Diamagnetic Susceptibility and Diamagnetic Anisotropy of Membrane Proteins from Structural Subunits

Abstract

The behavior of large, complex molecules in the presence of magnetic fields is experimentally challenging to measure and computationally intensive to predict. This work proposes a novel, mixed-methods approach for efficiently computing the principal magnetic susceptibilities and diamagnetic anisotropy of membrane proteins. The hierarchical primary (amino acid), secondary (α helical and β sheet), and tertiary (α helix and β barrel) structure of transmembrane proteins enables analysis of a complex molecule using discrete subunits of varying size and resolution. The proposed method converts the magnetic susceptibility tensor for all protein subunits to a unit coordinate system and sums them to build the magnetic susceptibility tensor for the membrane protein. Using this approach, we calculate the diamagnetic anisotropy for all transmembrane proteins of known structure and investigate the effect of different subunit resolutions on the resulting predictions of diamagnetic anisotropy. We demonstrate that amino acid residues with aromatic side groups exhibit higher diamagnetic anisotropies. On average, high percentages of aromatic amino acid subunits, a β barrel tertiary structure, and a small volume are correlated with high volumetric diamagnetic anisotropy. Finally, we demonstrate that accounting for the spatial position of the residues with respect to one another is critical to accurately computing the magnetic properties of the complex protein molecule.

Magnetic Field-Induced Alignment of Nanofibrous Supramolecular Membranes: A Molecular Design Approach to Create Tissue-like Biomaterials

“…Conveniently, the aromatic ring of phenylalanine also imparts high diamagnetic anisotropy, or susceptibility to directional alignment in a magnetic field. 15 This prior work suggests that the secondary structure of the peptide has a significant effect on its diamagnetic anisotropy. While a protein with randomly oriented phenylalanine amino acids would not exhibit directional alignment, self-assembly of these residues into secondary and tertiary structures can translate into substantial diamagnetic anisotropies at the peptide or fibril level.…”

“…The diamagnetic anisotropy (DA) of the peptides was calculated based on the magnetic susceptibility of the amino acids and their spatial position with respect to one another using a recently developed computational method. 15 Briefly, the magnetic susceptibility tensor for amino acids was transformed to a single global coordinate followed by summing the tensors to build the net magnetic susceptibility tensor for the entire peptide structure, and the diamagnetic anisotropy was calculated for the peptides based on the eigenvectors and eigenvalues of the total magnetic susceptibility tensor for the peptide structure. 15 The molar and volumetric (dimensionless) diamagnetic anisotropy for the peptides are presented in Table S1.…”

Statistical Mechanical Analysis of the Electromechanical Coupling in an Electrically-Responsive Polymer Chain

“…(3. ) While dipole effects are due to electronic and nuclear motion and hence can have interactions between monomers 34 , we assume for simplicity that the dipole induced in a monomer can be modeled without regard to the chain environment; equivalently, we assume that the electrical energy of the monomers can be decomposed additively.…”

Magnetic susceptibility increases as diamagnetic molecules breakdown: Myelin digestion during multiple sclerosis lesion formation contributes to increase on QSM

“…When a peptide bond is lost from proteolysis, the molar susceptibility of MBP will decrease by the molar susceptibility of a peptide bond. A peptide bond has the structure of glycine and molar susceptibility of cm/mol in CGS units or a volume susceptibility change in SI units of: where ρ = 1.35 g/cm 3 and M = 18,500 g/mol for the density and molar mass, respectively, of MBP . Inserting these values into Eq.…”

“…When a peptide bond is lost from proteolysis, the molar susceptibility of MBP will decrease by the molar susceptibility of a peptide bond. A peptide bond has the structure of glycine and molar susceptibility of v CGS molar 5 240:3 Á 10 26 cm 3 /mol in CGS units 15,16 or a volume susceptibility change in SI units of:…”