Recently, it has been successfully shown that the temporal evolution of the fraction of COVID-19 infected people possesses the same dynamics as the ones demonstrated by a self-organizing diffusion model over a lattice, in the frame of universality. In this brief, the relevant emerging dynamics are further investigated. Evidence that this nonlinear model demonstrates critical dynamics is scrutinized within the frame of the physics of critical phenomena. Additionally, the concept of criticality over the infected population fraction in epidemics (or a pandemic) is introduced and its importance is discussed, highlighting the emergence of the critical slowdown phenomenon. A simple method is proposed for estimating how far away a population is from this “singular” state, by utilizing the theory of critical phenomena. Finally, a dynamic approach applying the self-organized diffusion model is proposed, resulting in more accurate simulations, which can verify the effectiveness of restrictive measures. All the above are supported by real epidemic data case studies.

The axonal translocation of two commonly used nanoparticles in medicine, namely CeO₂ and SiO₂, is investigated. The study was conducted on frog sciatic nerve fibers in an ex vivo preparation. Nanoparticles were applied at the proximal end of the excised nerve. A nerve stimulation protocol was followed for over 35 hours. Nerve vitality curve comparison between control and exposed nerves showed that CeO₂ has no neurotoxic effect at the concentrations tested. After exposure, specimens were fixed and then screen scanned every 1 mm along their length for nanoparticle presence by means of Fourier transform infrared microscopy. We demonstrated that both nanoparticles translocate within the nerve by formation of narrow bands in the Fourier transform infrared spectrum. For the CeO₂, we also demonstrated that the translocation depends on both axonal integrity and electrical activity. The speed of translocation for the two species was estimated in the range of 0.45–0.58 mm/h, close to slow axonal transportation rate. Transmission electron microscopy provided direct evidence for the presence of SiO₂ in the treated nerves.

The EGF-induced MAP kinase cascade is one of the most important and best characterized networks in intracellular signalling. It has a vital role in the development and maturation of living organisms. However, when deregulated, it is involved in the onset of a number of diseases. Based on a computational model describing a “surface” and an “internalized” parallel route, we use systems biology techniques to characterize aspects of the network’s functional organization. We examine the re-organization of protein groups from low to high external stimulation, define functional groups of proteins within the network, determine the parameter best encoding for input intensity and predict the effect of protein removal to the system’s output response. Extensive functional re-organization of proteins is observed in the lower end of stimulus concentrations. As we move to higher concentrations the variability is less pronounced. 6 functional groups have emerged from a consensus clustering approach, reflecting different dynamical aspects of the network. Mutual information investigation revealed that the maximum activation rate of the two output proteins best encodes for stimulus intensity. Removal of each protein of the network resulted in a range of graded effects, from complete silencing to intense activation. Our results provide a new “vista” of the EGF-induced MAP kinase cascade, from the perspective of complex self-organizing systems. Functional grouping of the proteins reveals an organizational scheme contrasting the current understanding of modular topology. The six identified groups may provide the means to experimentally follow the dynamics of this complex network. Also, the vulnerability analysis approach may be used for the development of novel therapeutic targets in the context of personalized medicine.