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A classification of all possible icosahedral viral capsids is proposed. It takes into account the diversity of hexamers’ compositions, leading to definite capsid size.We showhowthe self-organization of observed capsids during their production results from definite symmetries of constituting hexamers. The division of all icosahedral capsids into four symmetry classes is given. New subclasses implementing...
Polymerases select nucleotides according to a template before incorporating them for chemical synthesis during gene replication or transcription. Efficient selection to achieve sufficiently high fidelity and speed is essential for polymerase function. Due to multiple kinetic steps detected in a polymerase elongation cycle, there exist multiple selection checkpoints to allow different strategies of...
The Poisson-Boltzmann equation (PBE) is one important implicit solvent continuum model for calculating electrostatics of protein in ionic solvent. Several numerical algorithms and program packages have been developed but verification and comparison between them remains an interesting topic. In this paper, a PBE test model is presented for a protein in a spherical solute region, along with its analytical...
We investigate the relationship between a discrete version of thickness and its smooth counterpart. These discrete energies are deffned on equilateral polygons with n vertices. It will turn out that the smooth ropelength, which is the scale invariant quotient of length divided by thickness, is the Γ-limit of the discrete ropelength for n → ∞, regarding the topology induced by the Sobolev norm ‖ ·...
It is well known that genomic materials (long DNA chains) of living organisms are often packed compactly under extreme confining conditions using macromolecular self-assembly processes but the general DNA packing mechanism remains an unsolved problem. It has been proposed that the topology of the packed DNA may be used to study the DNA packing mechanism. For example, in the case of (mutant) bacteriophage...
Retrovirus capsid is a fullerene-like lattice consisting of capsid protein hexamers and pentamers. Mathematical models for the lattice structure help understand the underlying biological mechanisms in the formation of viral capsids. It is known that viral capsids could be categorized into three major types: icosahedron, tube, and cone. While the model for icosahedral capsids is established and well-received,...
Description of inhomogeneous dielectric properties of a solvent in the vicinity of ions has been attracting research interests in mathematical modeling for many years. From many experimental results, it has been concluded that the dielectric response of a solvent linearly depends on the ionic strength within a certain range. Based on this assumption, a new implicit solvent model is proposed in the...
Trypanosomatida parasites, such as Trypanosoma and Leishmania, are the cause of deadly diseases in many third world countries. The three dimensional structure of their mitochondrial DNA, known as kinetoplast DNA (kDNA), is unique since it is organized into several thousands of minicircles that are topologically linked. How and why the minicircles form such a network have remained unanswered questions...
Modeling of repulsive forces is essential to the understanding of certain bio-physical processes, especially for the motion of DNA molecules. These kinds of phenomena seem to be driven by some sort of “energy” which especially prevents the molecules from strongly bending and forming self-intersections. Inspired by a physical toy model, numerous functionals have been defined during the past twenty-five...
Gramicidin A is a small and well characterized peptide that forms an ion channel in lipid membranes. An important feature of gramicidin A (gA) pore is that its conductance is affected by the electric charges near the its entrance. This property has led to the application of gramicidin A as a biochemical sensor for monitoring and quantifying a number of chemical and enzymatic reactions. Here, a mathematical...
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