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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 the action of symmetry groups Z2, Z3 and S3 are found and described. They concern special cases...
Für die Lösungen seminlinearer parabolischer Differentialgleichungen werden Einschliessungsaussagen hergeleitet. Hierbei werden Aussagen zur Stabilität von Lösungen ermittelt. Die Resultate werden am Beispiel der Fitzhugh-Nagumo Gleichungen diskutiert.
RNA viruses replicate as complex and dynamic mutant distributions. They are termed viral
quasispecies, in recognition of the fundamental contribution of quasispecies theory in our
understanding of error-prone replicative entities. Viral quasispecies have launched a
fertile field of transdiciplinary research, both experimental and theoretical. Here we
review the origin and some implications of the quasispecies concept, with emphasis on
internal interactions...
The Poisson-Boltzmann (PB) model is an effective approach for the electrostatics analysis of solvated biomolecules. The nonlinearity associated with the PB equation is critical when the underlying electrostatic potential is strong, but is extremely difficult to solve numerically. In this paper, we construct two operator splitting alternating direction implicit (ADI) schemes to efficiently and stably solve the nonlinear PB equation in a pseudo-transient continuation approach. The operator splitting...
Determining amino acid sequences of protein molecules is one of the most important issues in molecular biology. These
sequences determine protein structure and functionality. Unfortunately, direct biochemical methods for reading amino
acid sequences can be used for reading short sequences only. This is the reason, which makes peptide assembly algorithms
an important complement of these methods. In this paper, a genetic algorithm solving the problem of short amino acid sequence
assembly is presented....
Polymerization of proteins is a biochemical process involved in different diseases.
Mathematically, it is generally modeled by aggregation-fragmentation-type equations. In
this paper we consider a general polymerization model and propose a high-order numerical
scheme to investigate the behavior of the solution. An important property of the equation
is the mass conservation. The WENO scheme is built to preserve the total mass of proteins
along time....
Recently the effect of a quiescent phase (or dormant/resting phase in applications) on
the dynamics of a system of differential equations has been investigated, in particular with respect
to stability properties of stationary points. It has been shown that there is a general phenomenon
of stabilization against oscillations which can be cast in rigorous form. Here we investigate, for
homogeneous systems, the effect of a quiescent phase, and more generally, a phase with slower
dynamics. We show that...
Viruses are obligate intracellular parasites that rely on the host cell for expansion.
With the development of global analyses techniques like transcriptomics, proteomics and
siRNA library screening of complete cellular gene sets, a large range of host cell factors
have been discovered that either support or restrict virus growth. Here we summarize some
of the recent findings and focus our discussion on the hepatitis C virus and the human
immunodeficiency...
When invading the tissue, malignant tumour cells (i.e. cancer cells) need to detach from
neighbouring cells, degrade the basement membrane, and migrate through the extracellular
matrix. These processes require loss of cell-cell adhesion and enhancement of cell-matrix
adhesion. In this paper we present a mathematical model of an intracellular pathway for
the interactions between a cancer cell and the extracellular matrix. Cancer cells use
similar...
High-dimensional data models abound in genomics studies, where often inadequately small sample sizes create impasses for incorporation of standard statistical tools. Conventional assumptions of linearity of regression, homoscedasticity and (multi-) normality of errors may not be tenable in many such interdisciplinary setups. In this study, Kendall's tau-type rank statistics are employed for statistical inference, avoiding most of parametric assumptions to a greater extent. The proposed procedures...
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