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Abstract Division and differentiation events by which cell populations with specific functions are generated often take place as part of a developmental programme, which can be represented by a sequence of compartments. A compartment is the set of cells with common characteristics; sharing, for instance, a spatial location or a phenotype. Differentiation events are transitions from one compartment to the next. Cells may also die or divide. We consider three different types of division events: (i) where both daughter cells inherit the mother’s phenotype (self-renewal), (ii) where only one of the daughters changes phenotype (asymmetric division), and (iii) where both daughters change phenotype (symmetric division). The self-renewal probability in each compartment determines whether the progeny of a single cell, moving through the sequence of compartments, is finite or grows without bound. We analyse the progeny stochastic dynamics with probability generating functions. In the case of self-renewal, by following one of the daughters after any division event, we may construct lifelines containing only one cell at any time. We analyse the number of divisions along such lines, and the compartment where lines terminate with a death event. Analysis and numerical simulations are applied to a five-compartment model of the gradual differentiation of hematopoietic stem cells and to a model of thymocyte development: from pre-double positive to single positive (SP) cells with a bifurcation to either SP4 or SP8 in the last compartment of the sequence.

Abstract The mechanical and magnetic properties of polycrystalline nanoframes were investigated using atomistic molecular dynamics and micromagnetic simulations. The magneto-mechanical response of Fe hollow-like nanocubes was addressed by uniaxial compression carried out by nanoindentation. Our results show that the deformation of a nanoframe is dominated at lower strains by the compression of the nanostructure due to filament bending. This leads to the nanoframe twisting perpendicular to the indentation direction for larger indentation depths. Bending and twisting reduce stress concentration and, at the same time, increase coercivity. This unexpected increase of the coercivity occurs because the mechanical deformation changes the cubic shape of the nanoframe, which in turn drives the system to more stable magnetic states. A coercivity increase of almost 100 mT is found for strains close to 0.03, which are within the elastic regime of the Fe nanoframe. Coercivity then decreases at larger strains. However, in all cases, the coercivity is higher than for the undeformed nanoframe. These results can help in the design of new magnetic devices where mechanical deformation can be used as a primary tool to tailor the magnetic response on nanoscale solids.

Abstract Endosomes are intracellular vesicles that mediate the communication of the cell with its extracellular environment. They are an essential part of the cell’s machinery regulating intracellular trafficking via the endocytic pathway. Many viruses, which in order to replicate require a host cell, attach themselves to the cellular membrane; an event which usually initiates uptake of a viral particle through the endocytic pathway. In this way viruses hijack endosomes for their journey towards intracellular sites of replication and avoid degradation without host detection by escaping the endosomal compartment. Recent experimental techniques have defined the role of endosomal maturation in the ability of enveloped viruses to release their genetic material into the cytoplasm. Endosome maturation depends on a family of small hydrolase enzymes (or GTPases) called Rab proteins, arranged on the cytoplasmic surface of its membrane. Here, we model endosomes as intracellular compartments described by two variables (its levels of active Rab5 and Rab7 proteins) and which can undergo coagulation (or fusion) and fragmentation (or fission). The key element in our approach is the “per-cell endosomal distribution” and its dynamical (Boltzmann) equation. The Boltzmann equation allows us to derive the dynamics of the total number of endosomes in a cell, as well as the mean and the standard deviation of its active Rab5 and Rab7 levels. We compare our mathematical results with experiments of Dengue viral escape from endosomes. The relationship between endosomal active Rab levels and pH suggests a mechanism that can account for the observed variability in viral escape times, which in turn regulate the viability of a viral intracellular infection.