Cellular polarity in aging: role of redox regulation and nutrition

Cellular polarity concerns the spatial asymmetric organization of cellular components and structures. Such organization is important not only for biological behavior at the individual cell level, but also for the 3D organization of tissues and organs in living organisms. Processes like cell migration and motility, asymmetric inheritance, and spatial organization of daughter cells in tissues are all dependent of cell polarity. Many of these processes are compromised during aging and cellular senescence. For example, permeability epithelium barriers are leakier during aging; elderly people have impaired vascular function and increased frequency of cancer, and asymmetrical inheritance is compromised in senescent cells, including stem cells. Here, we review the cellular regulation of polarity, as well as the signaling mechanisms and respective redox regulation of the pathways involved in defining cellular polarity. Emphasis will be put on the role of cytoskeleton and the AMP-activated protein kinase pathway. We also discuss how nutrients can affect polarity-dependent processes, both by direct exposure of the gastrointestinal epithelium to nutrients and by indirect effects elicited by the metabolism of nutrients, such as activation of antioxidant response and phase-II detoxification enzymes through the transcription factor nuclear factor (erythroid-derived 2)-like 2 (Nrf2). In summary, cellular polarity emerges as a key process whose redox deregulation is hypothesized to have a central role in aging and cellular senescence.

Scaling law in Saddle-node bifurcations for one-dimensional maps: A complex variable approach

The study of transient dynamical phenomena near bifurcation thresholds has attracted the interest of many researchers due to the relevance of bifurcations in different physical or biological systems. In the context of saddle-node bifurcations, where two or more fixed points collide annihilating each other, it is known that the dynamics can suffer the so-called delayed transition. This phenomenon emerges when the system spends a lot of time before reaching the remaining stable equilibrium, found after the bifurcation, because of the presence of a saddle-remnant in phase space. Some works have analytically tackled this phenomenon, especially in time-continuous dynamical systems, showing that the time delay, tau, scales according to an inverse square-root power law, tau similar to (mu-mu (c) )(-1/2), as the bifurcation parameter mu, is driven further away from its critical value, mu (c) . In this work, we first characterize analytically this scaling law using complex variable techniques for a family of one-dimensional maps, called the normal form for the saddle-node bifurcation. We then apply our general analytic results to a single-species ecological model with harvesting given by a unimodal map, characterizing the delayed transition and the scaling law arising due to the constant of harvesting. For both analyzed systems, we show that the numerical results are in perfect agreement with the analytical solutions we are providing. The procedure presented in this work can be used to characterize the scaling laws of one-dimensional discrete dynamical systems with saddle-node bifurcations.