Minimal Morphoelastic Models of Solid Tumour Spheroids: A Tutorial

Tumour spheroids have been the focus of a variety of mathematical models, ranging from Greenspan's classical study of the 1970 s through to contemporary agent-based models. Of the many factors that regulate spheroid growth, mechanical effects are perhaps some of the least studied, both theoretically and experimentally, though experimental enquiry has established their significance to tumour growth dynamics. In this tutorial, we formulate a hierarchy of mathematical models of increasing complexity to explore the role of mechanics in spheroid growth, all the while seeking to retain desirable simplicity and analytical tractability. Beginning with the theory of morphoelasticity, which combines solid mechanics and growth, we successively refine our assumptions to develop a somewhat minimal model of mechanically regulated spheroid growth that is free from many unphysical and undesirable behaviours. In doing so, we will see how iterating upon simple models can provide rigorous guarantees of emergent behaviour, which are often precluded by existing, more complex modelling approaches. Perhaps surprisingly, we also demonstrate that the final model considered in this tutorial agrees favourably with classical experimental results, highlighting the potential for simple models to provide mechanistic insight whilst also serving as mathematical examples

The prolyl-isomerase PIN1 is essential for nuclear Lamin-B structure and function and protects heterochromatin under mechanical stress

Chromatin organization plays a crucial role in tissue homeostasis. Heterochromatin relaxation and consequent unscheduled mobilization of transposable elements (TEs) are emerging as key contributors of aging and aging-related pathologies, including Alzheimer's disease (AD) and cancer. However, the mechanisms governing heterochromatin maintenance or its relaxation in pathological conditions remain poorly understood. Here we show that PIN1, the only phosphorylation-specific cis/trans prolyl isomerase, whose loss is associated with premature aging and AD, is essential to preserve heterochromatin. We demonstrate that this PIN1 function is conserved from Drosophila to humans and prevents TE mobilization-dependent neurodegeneration and cognitive defects. Mechanistically, PIN1 maintains nuclear type-B Lamin structure and anchoring function for heterochromatin protein 1\u3b1 (HP1\u3b1). This mechanism prevents nuclear envelope alterations and heterochromatin relaxation under mechanical stress, which is a key contributor to aging-related pathologies

Modelling Neutron-Star Ocean Dynamics

We re-visit the calculation of mode oscillations in the ocean of a rotating neutron star, which may be excited during thermonuclear X-ray bursts. Our present theoretical understanding of ocean modes relies heavily on the traditional approximation, commonly employed in geophysics. The approximation elegantly decouples the radial and angular sectors of the perturbation problem by neglecting the vertical contribution from the Coriolis force. However, as the implicit assumptions underlying it are not as well understood as they ought to be, we examine the traditional approximation and discuss the associated mode solutions. The results demonstrate that, while the approximation may be appropriate in certain contexts, it may not be accurate for rapidly rotating neutron stars. In addition, using the shallow-water approximation, we show analytically how the solutions that resemble r-modes change their nature in neutron-star oceans to behave like gravity waves. We also outline a simple prescription for lifting Newtonian results in a shallow ocean to general relativity, making the result more realistic.Comment: 16 pages, 2 figures. Missing text in Sec. III discovered in pres

Exploring the impact of mechanical stress in neurodegeneration

Mechanical stress has been proposed as a common denominator of different pathological conditions, including chronic inflammation and neurodegenerative disorders such as Alzheimer’s disease. While mechanical signals shape the brain development throughout morphogenesis, a role of mechanical forces in neurodegeneration has been suggested by the observed correlation of traumatic brain injury and cerebrovascular hemodynamic stress with the risk of some neurodegenerative disorders. Furthermore, neurodegenerative diseases and brain injury are associated with changes in composition and properties of the extracellular matrix. Using in vivo models, we provide genetic and molecular evidence that alterations in mechanotransduction could impact on neuronal survival and function in stressful conditions. Our findings help better understand the pathogenesis of neurodegenerative disorders and could lead to the identification of therapeutic targets