Stochastic dynamics of virus capsid formation: direct versus hierarchical self-assembly

Background: In order to replicate within their cellular host, many viruses have developed self-assembly strategies for their capsids which are sufficiently robust as to be reconstituted in vitro. Mathematical models for virus self-assembly usually assume that the bonds leading to cluster formation have constant reactivity over the time course of assembly (direct assembly). In some cases, however, binding sites between the capsomers have been reported to be activated during the self-assembly process (hierarchical assembly). Results: In order to study possible advantages of such hierarchical schemes for icosahedral virus capsid assembly, we use Brownian dynamics simulations of a patchy particle model that allows us to switch binding sites on and off during assembly. For T1 viruses, we implement a hierarchical assembly scheme where inter-capsomer bonds become active only if a complete pentamer has been assembled. We find direct assembly to be favorable for reversible bonds allowing for repeated structural reorganizations, while hierarchical assembly is favorable for strong bonds with small dissociation rate, as this situation is less prone to kinetic trapping. However, at the same time it is more vulnerable to monomer starvation during the final phase. Increasing the number of initial monomers does have only a weak effect on these general features. The differences between the two assembly schemes become more pronounced for more complex virus geometries, as shown here for T3 viruses, which assemble through homogeneous pentamers and heterogeneous hexamers in the hierarchical scheme. In order to complement the simulations for this more complicated case, we introduce a master equation approach that agrees well with the simulation results. Conclusions: Our analysis shows for which molecular parameters hierarchical assembly schemes can outperform direct ones and suggests that viruses with high bond stability might prefer hierarchical assembly schemes. These insights increase our physical understanding of an essential biological process, with many interesting potential applications in medicine and materials science

A reflexão como um instrumento de formação no PFCM

O Programa de Formação Contínua em Matemática para Professores dos 1.º e 2.º Ciclos do Ensino Básico (PFCM), com o objectivo de melhorar o ensino e as aprendizagens em Matemática e desenvolver atitudes mais positivas face a esta área do saber, pretende responder às necessidades dos professores participantes, partindo de questões relativas à concretização do currículo de Matemática na sala de aula e tendo um carácter continuado ao longo do ano lectivo. O PFCM constitui, assim, um instrumento de apoio e ajuda aos professores participantes na sua prática lectiva (planificação do trabalho, condução da aula, reflexão sobre o que foi feito) de modo a melhorar as suas actuações profissionais e, consequentemente, as aprendizagens matemáticas dos seus alunos. No anterior ano lectivo, o plano de formação desenvolvido pela Escola Superior de Educação de Bragança (ESEB), embora possibilitasse a abordagem de qualquer conteúdo de formação previsto, centrou-se em alguns domínios, nomeadamente, na clarificação ou aprofundamento de temas matemáticos, na discussão dos tipos e natureza das tarefas (exercícios, explorações, problemas, investigações; jogos, projectos), em aspectos da comunicação matemática, na utilização de materiais curriculares, e na construção dos portefólios, valorizando os registos escritos e reflexão. Nesta comunicação pretendemos discutir, com base na observação participante e na análise documental, situações e episódios ocorridos nas salas de aula que fundamentem aspectos do ensino e aprendizagem da Matemática destacados pelo plano de formação da ESEB e evidenciados quer pelos formadores quer pelos professores participantes, dando especial relevância à reflexão (pessoal e partilhada) sobre as experiências profissionais

Computational support for a scaffolding mechanism of centriole assembly

Centrioles are essential for forming cilia, flagella and centrosomes. Successful centriole assembly requires proteins of the SAS-6 family, which can form oligomeric ring structures with ninefold symmetry in vitro. While important progress has been made in understanding SAS-6 protein biophysics, the mechanisms enabling ring formation in vivo remain elusive. Likewise, the mechanisms by which a nascent centriole forms near-orthogonal to an existing one are not known. Here, we investigate possible mechanisms of centriole assembly using coarse-grained Brownian dynamics computer simulations in combination with a rate equation approach. Our results suggest that without any external factors, strong stabilization associated with ring closure would be needed to enable efficient ring formation. Strikingly, our simulations reveal that a scaffold-assisted assembly mechanism can trigger robust ring formation owing to local cooperativity, and that this mechanism can also impart orthogonalilty to centriole assembly. Overall, our findings provide novel insights into the organizing principles governing the assembly of this important organelle

Period- and mirror-maps for the quartic K3

We study in detail mirror symmetry for the quartic K3 surface in P3 and the mirror family obtained by the orbifold construction. As explained by Aspinwall and Morrison, mirror symmetry for K3 surfaces can be entirely described in terms of Hodge structures. (1) We give an explicit computation of the Hodge structures and period maps for these families of K3 surfaces. (2) We identify a mirror map, i.e. an isomorphism between the complex and symplectic deformation parameters, and explicit isomorphisms between the Hodge structures at these points. (3) We show compatibility of our mirror map with the one defined by Morrison near the point of maximal unipotent monodromy. Our results rely on earlier work by Narumiyah-Shiga, Dolgachev and Nagura-Sugiyama.Comment: 29 pages, 3 figure

Synthesis of N-Substituted phosphoramidic acid esters as “reverse” fosmidomycin analogues

An efficient synthetic pathway to a series of novel “reverse” fosmidomycin analogues has been developed, commencing from substituted benzylamines. In these analogues, the fosmidomycin hydroxamate moiety is reversed and the tetrahedral methylene carbon adjacent to the phosphonate moiety is replaced by a nitrogen atom bearing different benzyl groups. The resulting phosphonate esters were designed as potential antimalarial “pro-drugs”

Порядок исчисления и уплаты НДС ( на примере ООО «АйПиЭм групп»)

Изучение экономического содержания налогаThe study of the economic content of the ta