Cell Mechanics and Signalization: SARS-CoV-2 Hijacks Membrane Liquid Crystals and Cytoskeletal Fractal Topology

We highlight changes to cell signaling under virus invasion (with the example of SARS-CoV-2), involving disturbance of membranes (plasma, mitochondrial, endothelial-alveolar) and of nanodomains, modulated by the cytoskeleton. Virus alters the mechanical properties of the membranes, impairing mesophase structures mediated by the fractal architecture initiated by actomyosin. It changes the topology of the membrane and its lipid composition distribution. Mechano-transduction, self-organization and topology far from equilibrium are omnipresent. We propose that the actomyosin contractility generates the cytoskeletons fractal organization. We focus on three membranar processus: The transition from lamellar configuration in cell and viral membranes to a bi-continuous organization in the presence of ethanolamine. (The energy for this transition is provided by change of the folding of the viral fusion protein from metastable to stable state). The action of mitochondrial antiviral signaling protein on the external mitochondrial envelope in contact with mitochondrial-associated membranes, modified by viral endoribonuclease, distorting innate immune response. The increased permeability of the epithelial-alveolar-pulmonary barrier involves the cytoskeleton membranes. The pulmonary surfactant is also perturbed in its liquid crystal state. Viral subversion disorganizes membrane structure and functions and thus the metabolism of the cell. We advocate systematic multidisciplinary exploration of membrane mesophases and their links with fractal dynamics, to enable novel therapies for SARS-CoV-2 infection.

FRACTAL ARCHITECTURE: PAST, PRESENT, AND FUTURE

Architects of the past widely used the principle of fractal structure. Building designs are separate elements that are self-similar objects. The article presents examples of various unique structures of the past and present. The modern approach to the development of fractal architecture allows architects to create wonderful structures, search for the most unusual forms and harmony of orderly structures and dynamics of chaos.

A Self-Operating Time Crystal Model of the Human Brain: Can We Replace Entire Brain Hardware with a 3D Fractal Architecture of Clocks Alone?

Time crystal was conceived in the 1970s as an autonomous engine made of only clocks to explain the life-like features of a virus. Later, time crystal was extended to living cells like neurons. The brain controls most biological clocks that regenerate the living cells continuously. Most cognitive tasks and learning in the brain run by periodic clock-like oscillations. Can we integrate all cognitive tasks in terms of running clocks of the hardware? Since the existing concept of time crystal has only one clock with a singularity point, we generalize the basic idea of time crystal so that we could bond many clocks in a 3D architecture. Harvesting inside phase singularity is the key. Since clocks reset continuously in the brain–body system, during reset, other clocks take over. So, we insert clock architecture inside singularity resembling brain components bottom-up and top-down. Instead of one clock, the time crystal turns to a composite, so it is poly-time crystal. We used century-old research on brain rhythms to compile the first hardware-free pure clock reconstruction of the human brain. Similar to the global effort on connectome, a spatial reconstruction of the brain, we advocate a global effort for more intricate mapping of all brain clocks, to fill missing links with respect to the brain’s temporal map. Once made, reverse engineering the brain would remain a mere engineering challenge.

A formula for the settling velocity of cohesive sediment flocs in water

A simple formula is developed to relate the size and settling velocity of cohesive sediment flocs in both the viscous and inertial settling ranges. This formula maintains the same basic structure as the existing formula but is amended to incorporate the fact that the flocculated sediment has an internal fractal architecture and is composed of different-sized primary particles. The input parameters needed for calculating the settling velocity include the median size and size distribution of the primary particles, the fractal dimension of the floc, the density of the sediment, and two calibrated coefficients that incorporate the effects of floc shape, permeability, and flow separation on drag. The proposed formula is compared with four data sets of settling velocity–floc size collected from the published literature, and a good agreement between the model and these data can be found.