Related papers: An irreversible growth model for virus capsid asse…
We study the self-assembly behaviour of patchy particles with `protein-like' interactions that can be considered as a minimal model for the assembly of viral capsids and other shell-like protein complexes. We thoroughly explore the…
A random graph model with prescribed degree distribution and degree dependent edge weights is introduced. Each vertex is independently equipped with a random number of half-edges and each half-edge is assigned an integer valued weight…
Recent studies reveal that certain viruses package a portion of their genome in a manner that mirrors the icosahedral symmetry of the protein container, or capsid. Graph theoretical constraints forbid exact realization of icosahedral…
Biomolecular condensates are liquid- or gel-like droplets of proteins and nucleic acids formed at least in part through liquid-liquid phase separation. Condensates enable diverse functions of cells and the pathogens that infect them,…
We develop a clear theoretical description of radial swelling in virus-like particles which delineates the importance of electrostatic contributions to swelling in absence of any conformational changes. The model couples the elastic…
We consider a constrained version of the HL$(0)$ Hastings--Levitov model of aggregation in the complex plane, in which particles can only attach to the part of the cluster that has already been grown. Although one might expect that this…
A vital constituent of a virus is its protein shell, called the viral capsid, that encapsulates and hence provides protection for the viral genome. Viral capsids are usually spherical, and for a significant number of viruses exhibit overall…
Hydra tissue fragments excised freshly from Hydra body bend spontaneously to some quasi-stable shape in several minutes. We propose that the spontaneous bending is driven mechanically by supracellular actomyosin bundles inherited from…
We systematically study the design of simple patchy sphere models that reversibly self-assemble into monodisperse icosahedral clusters. We find that the optimal patch width is a compromise between structural specificity (the patches must be…
Cyanobacteria sequester photosynthetic enzymes into microcompartments which facilitate the conversion of carbon dioxide into sugars. Geometric similarities between these structures and self-assembling viral capsids have inspired models that…
Assembly of protein complexes like virus shells, the centriole, the nuclear pore complex or the actin cytoskeleton is strongly determined by their spatial structure. Moreover it is becoming increasingly clear that the reversible nature of…
This paper studies the construction of adaptive confidence intervals under Huber's contamination model when the contamination proportion is unknown. For the robust confidence interval of a Gaussian mean, we show that the optimal length of…
Recent high resolution structures for viral capsids with 12, 32 and 72 subunits ($T1$, $T3$ and $T7$ viruses) have confirmed theoretical predictions of an icosadeltahedral structure with 12 subunits having five nearest neighbors (pentamers)…
We define and study one-dimensional model of irreversible aggregation of particles obeying a discrete-time kinetics which is a special limit of the generalized Totally Asymmetric Simple Exclusion Process (gTASEP) on open chains. The model…
We will study a mathematical model of the human immunodeficiency virus (HIV) infection in the presence of combination therapy that includes within-host infectious dynamics. The deterministic model requires us to analyze asymptotic stability…
Single-stranded (ss) RNA viruses self-assemble spontaneously in solutions that contain the viral RNA genome molecules and viral capsid proteins. The self-assembly of empty capsids can be understood on the basis of free energy minimization.…
A simple model is proposed aimed to investigate how the amount of dissociated ions influences the mechanical stability of viral capsids. After an osmotic and mechanical equilibrium is established with the outer solution, a non-adiabatic…
Polymorphism has been observed in viral capsid assembly, demonstrating the ability of identical protein dimers to adopt multiple geometries under the same solution conditions. A well-studied example is the hepatitis B virus (HBV), which…
This paper uses combinatorics and group theory to answer questions about the assembly of icosahedral viral shells. Although the geometric structure of the capsid (shell) is fairly well understood in terms of its constituent subunits, the…
In this work we study how a viral capsid can change conformation using techniques of Large Deviations Theory for stochastic differential equations. The viral capsid is a model of a complex system in which many units - the proteins forming…