Membrane undulations in a structured fluid: Universal dynamics at intermediate length and time scales

The dynamics of membrane undulations inside a viscous solvent is governed by distinctive, anomalous, power laws. Inside a viscoelastic continuous medium these universal behaviors are modified by the specific bulk viscoelastic spectrum. Yet, in structured fluids the continuum limit is reached only beyond a characteristic correlation length. We study the crossover to this asymptotic bulk dynamics. The analysis relies on a recent generalization of the hydrodynamic interaction in structured fluids, which shows a slow spatial decay of the interaction toward the bulk limit. For membranes which are weakly coupled to the structured medium we find a wide crossover regime characterized by different, universal, dynamic power laws. We discuss various systems for which this behavior is relevant, and delineate the time regime over which it may be observed.Comment: 10 page

Active fractal networks with stochastic force monopoles and force dipoles unravel subdiffusion of chromosomal loci

We study the Rouse-type dynamics of elastic fractal networks with embedded, stochastically driven, active force monopoles and dipoles, that are temporally correlated. We compute, analytically -- using a general theoretical framework -- and via Langevin dynamics simulations, the mean square displacement of a network bead. Following a short-time super-diffusive behavior, force monopoles yield anomalous subdiffusion with an exponent identical to that of the thermal system. Force dipoles do not induce subdiffusion, and result in rotational motion of the whole network -- as found for micro-swimmers -- and network collapses beyond a critical force amplitude. The collapse persists with increasing system size, signifying a true first-order dynamical phase transition. We conclude that the observed identical subdiffusion exponents of chromosomal loci in normal and ATP-depleted cells are attributed to active force monopoles rather than force dipoles.Comment: 18 pages: 6 pages - main text, and 12 pages - Supplemental. 12 figues: 4 figures - main text, and 8 figures -s Supplementa

Epidemiological model for the inhomogeneous spatial spreading of COVID-19 and other diseases.

We suggest a novel mathematical framework for the in-homogeneous spatial spreading of an infectious disease in human population, with particular attention to COVID-19. Common epidemiological models, e.g., the well-known susceptible-exposed-infectious-recovered (SEIR) model, implicitly assume uniform (random) encounters between the infectious and susceptible sub-populations, resulting in homogeneous spatial distributions. However, in human population, especially under different levels of mobility restrictions, this assumption is likely to fail. Splitting the geographic region under study into areal nodes, and assuming infection kinetics within nodes and between nearest-neighbor nodes, we arrive into a continuous, "reaction-diffusion", spatial model. To account for COVID-19, the model includes five different sub-populations, in which the infectious sub-population is split into pre-symptomatic and symptomatic. Our model accounts for the spreading evolution of infectious population domains from initial epicenters, leading to different regimes of sub-exponential (e.g., power-law) growth. Importantly, we also account for the variable geographic density of the population, that can strongly enhance or suppress infection spreading. For instance, we show how weakly infected regions surrounding a densely populated area can cause rapid migration of the infection towards the populated area. Predicted infection "heat-maps" show remarkable similarity to publicly available heat-maps, e.g., from South Carolina. We further demonstrate how localized lockdown/quarantine conditions can slow down the spreading of disease from epicenters. Application of our model in different countries can provide a useful predictive tool for the authorities, in particular, for planning strong lockdown measures in localized areas-such as those underway in a few countries

Spatio-temporal spread of COVID-19: Comparison of the inhomogeneous SEPIR model and data from South Carolina.

During the COVID-19 pandemic authorities have been striving to obtain reliable predictions for the spreading dynamics of the disease. We recently developed a multi-"sub-populations" (multi-compartments: susceptible, exposed, pre-symptomatic, infectious, recovered) model, that accounts for the spatial in-homogeneous spreading of the infection and shown, for a variety of examples, how the epidemic curves are highly sensitive to location of epicenters, non-uniform population density, and local restrictions. In the present work we test our model against real-life data from South Carolina during the period May 22 to July 22 (2020). During this period, minimal restrictions have been employed, which allowed us to assume that the local basic reproduction number is constant in time. We account for the non-uniform population density in South Carolina using data from NASA's Socioeconomic Data and Applications Center (SEDAC), and predict the evolution of infection heat-maps during the studied period. Comparing the predicted heat-maps with those observed, we find high qualitative resemblance. Moreover, the Pearson's correlation coefficient is relatively high thus validating our model against real-world data. We conclude that the model accounts for the major effects controlling spatial in-homogeneous spreading of the disease. Inclusion of additional sub-populations (compartments), in the spirit of several recently developed models for COVID-19, can be easily performed within our mathematical framework

Nucleus-Targeted Drug Delivery: Theoretical Optimization of Nanoparticles Decoration for Enhanced Intracellular Active Transport

A rational design for a nanoparticle is suggested, which will maximize its arrival efficiency from the plasma membrane to the nuclear surrounding. The design is based on grafting the particle surface with polymer spacers, each ending with a motor protein associating molecule, for example, nuclear localization signal peptide. It is theoretically shown that the spacer polymer molecular weight can be adjusted to significantly increase the effective particle processivity time. This should lead to appreciable enhancement of active transport of the nanocarrier, and consequently drug delivery, to the nucleus