Global Analysis of a Time Fractional Order Spatio-Temporal SIR Model

We deal in this paper with a diffusive SIR epidemic model described by reaction-diffusion equations involving a fractional derivative. The existence and uniqueness of the solution are shown, next to the boundedness of the solution. Further, it has been shown that the global behavior of the solution is governed by the value of R0 , which is known in epidemiology by the basic reproduction number. Indeed, using the Lyapunov direct method it has been proved that the disease will extinct for R0 < 1 for any value of the diffusion constants. For R0 > 1, the disease will persist and the unique positive equilibrium is globally stable. Some numerical illustrations have been used to confirm our theoretical results.Subject classification: 26A33; 34A08; 92D30; 35K57.

Selective excitation enables encoding and measurement of multiple diffusion parameters in a single experiment

Band selectivity to address specific resonances in a spectrum enables one to encode individual settings for diffusion experiments. In a single experiment, this could include different gradient strengths (enabling coverage of a larger range of diffusion constants), different diffusion delays, or different gradient directions (enabling anisotropic diffusion measurement). In this report, a selective variant of the bipolar pulsed gradient eddy current delay (BPP-LED) experiment, enabling selective encoding of three resonances, was implemented. As proof of principle, the diffusion encoding gradient amplitude was assigned a range dependent on the selected signal, thereby allowing the extraction of the diffusion coefficient for water and a tripeptide (Met-Ala-Ser) with optimal settings in a single experiment.

Real-Time Messenger RNA Dynamics in Bacillus subtilis

Messenger RNA molecules have been localized to different positions in cells and have been followed by time-lapse microscopy. We have used MS2-mVenus–labeled mRNA and single-particle tracking to obtain information on the dynamics of single-mRNA molecules in real time. Using single-molecule tracking, we show that several mRNA molecules visualized via two MS2-binding sites and MS2-mVenus expressed in Bacillus subtilis cells show free diffusion through the entire cell and constrained motion predominantly close to the cell membrane and at the polar regions of the cells. Because constrained motion of mRNAs likely reflects molecules complexed with ribosomes, our data support the idea that translation occurs at sites surrounding the nucleoids. Squared displacement analyses show the existence of at least two distinct populations of molecules with different diffusion constants or possibly of three populations, for example, freely mobile mRNAs, mRNAs in transition complexes, or in complex with polysomes. Diffusion constants between differently sized mRNAs did not differ dramatically and were much lower than that of cytosolic proteins. These data agree with the large size of mRNA molecules and suggest that, within the viscous cytoplasm, size variations do not translate into mobility differences. However, at observed diffusion constants, mRNA molecules would be able to reach all positions within cells in a frame of seconds. We did not observe strong differences in the location of confined motion for mRNAs encoding mostly soluble or membrane proteins, indicating that there is no strong bias for localization of membrane protein-encoding transcripts for the cell membrane.

First-principles model of optimal translation factors stoichiometry

Enzymatic pathways have evolved uniquely preferred protein expression stoichiometry in living cells, but our ability to predict the optimal abundances from basic properties remains underdeveloped. Here we report a biophysical, first-principles model of growth optimization for core mRNA translation, a multi-enzyme system that involves proteins with a broadly conserved stoichiometry spanning two orders of magnitude. We show that predictions from maximization of ribosome usage in a parsimonious flux model constrained by proteome allocation agree with the conserved ratios of translation factors. The analytical solutions, without free parameters, provide an interpretable framework for the observed hierarchy of expression levels based on simple biophysical properties, such as diffusion constants and protein sizes. Our results provide an intuitive and quantitative understanding for the construction of a central process of life, as well as a path toward rational design of pathway-specific enzyme expression stoichiometry.

Hi-C Contacts Encode Heterogeneity in Sub-diffusive Motion of E. coli Chromosomal Loci

Underneath its apparently simple architecture, the circular chromosome of E. coli is known for displaying complex dynamics in its cytoplasm. Recent experiments have hinted at an inherently heterogeneous dynamics of chromosomal loci, the origin of which has largely been elusive. In this regard, here we investigate the loci dynamics of E. coli chromosome in a minimally growing condition at 30°C by integrating the experimentally derived Hi-C interaction matrix within a computer model. Our quantitative analysis demonstrates that, while the dynamics of the chromosome is sub-diffusive in a viscoelastic media in general, the diffusion constants and the diffusive exponents are strongly dependent on the spatial coordinates of chromosomal loci. In particular, the loci in Ter Macro-domain display slower mobility compared to the others. The result is found to be robust even in the presence of active noise. Interestingly, a series of control investigations reveal that the absence of Hi-C interactions in the model would have abolished the heterogeneity in loci diffusion, indicating that the observed coordinate-dependent chromosome dynamics is heavily dictated via Hi-C-guided long-range inter-loci communications. Overall, the study underscores the key role of Hi-C interactions in guiding the inter-loci encounter and in modulating the underlying heterogeneity of the loci diffusion.

Selective excitation enables encoding and measurement of multiple diffusion parameters in a single experiment

Band selectivity to address specific resonances in a spectrum enables one to encode individual settings for diffusion experiments. In a single experiment, this could include different gradient strengths (enabling coverage of a larger range of diffusion constants), different diffusion delays, or different gradient directions (enabling anisotropic diffusion measurement). In this report a selective variant of the bipolar pulsed gradient, eddy-current delay (BPP-LED) experiment enabling selective encoding of three resonances was implemented. As proof-of-principle, the diffusion encoding gradient amplitude was assigned a range dependent on the selected signal, thereby allowing the extraction of the diffusion coefficient for water and a tripeptide (Met-Ala-Ser) with optimal settings in a single experiment.

Bound of diffusion constants from pole-skipping points: spontaneous symmetry breaking and magnetic field

We investigate the properties of pole-skipping of the sound channel in which the translational symmetry is broken explicitly or spontaneously. For this purpose, we analyze, in detail, not only the holographic axion model, but also the magnetically charged black holes with two methods: the near-horizon analysis and quasi-normal mode computations. We find that the pole-skipping points are related with the chaotic properties, Lyapunov exponent (λL) and butterfly velocity (vB), independently of the symmetry breaking patterns. We show that the diffusion constant (D) is bounded by $$ D\ge {v}_B^2/{\lambda}_L $$ D ≥ v B 2 / λ L , where D is the energy diffusion (crystal diffusion) bound for explicit (spontaneous) symmetry breaking. We confirm that the lower bound is obtained by the pole-skipping analysis in the low temperature limit.

First-principles model of optimal translation factors stoichiometry

Enzymatic pathways have evolved uniquely preferred protein expression stoichiometry in living cells, but our ability to predict the optimal abundances from basic properties remains underdeveloped. Here we report a biophysical, first-principles model of growth optimization for core mRNA translation, a multi-enzyme system that involves proteins with a broadly conserved stoichiometry spanning two orders of magnitude. We show that a parsimonious flux model constrained by proteome allocation is sufficient to predict the conserved ratios of translation factors through maximization of ribosome usage The analytical solutions, without free parameters, provide an interpretable framework for the observed hierarchy of expression levels based on simple biophysical properties, such as diffusion constants and protein sizes. Our results provide an intuitive and quantitative understanding for the construction of a central process of life, as well as a path toward rational design of pathway-specific enzyme expression stoichiometry.

Multicellular Spatial Model of RNA Virus Replication and Interferon Responses Reveals Factors Controlling Plaque Growth Dynamics

Respiratory viruses present major health challenges, as evidenced by the 2009 influenza pandemic and the ongoing severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic. Severe RNA virus respiratory infections often correlate with high viral load and excessive inflammation. Understanding the dynamics of the innate immune response and its manifestation at the cell and tissue levels are vital to understanding the mechanisms of immunopathology and developing improved, strain independent treatments. Here, we present a novel spatialized multicellular spatial computational model of two principal components of tissue infection and response: RNA virus replication and type-I interferon mediated antiviral response to infection within lung epithelial cells. The model is parameterized using data from influenza virus infected cell cultures and, consistent with experimental observations, exhibits either linear radial growth of viral plaques or arrested plaque growth depending on the local concentration of type I interferons. Modulating the phosphorylation of STAT or altering the ratio of the diffusion constants of interferon and virus in the cell culture could lead to plaque growth arrest. The dependence of arrest on diffusion constants highlights the importance of developing validated spatial models of cytokine signaling and the need for in vitro experiments to measure these diffusion constants. Sensitivity analyses were performed under conditions creating both continuous plaque growth and arrested plaque growth. Findings suggest that plaque growth and cytokine assay measurements should be collected during arrested plaque growth, as the model parameters are significantly more sensitive and more likely to be identifiable. The model’s metrics replicate experimental immunostaining imaging and titer based sampling assays. The model is easy to extend to include SARS-CoV-2-specific mechanisms as they are discovered or to include as a component linking epithelial cell signaling to systemic immune models.

Superstatistical modelling of protein diffusion dynamics in bacteria

A recent experiment (Sadoon AA, Wang Y. 2018 Phys. Rev. E 98 , 042411. ( doi:10.1103/PhysRevE.98.042411 )) has revealed that nucleoid-associated proteins (i.e. DNA-binding proteins) exhibit highly heterogeneous diffusion processes in bacteria where not only the diffusion constant but also the anomalous diffusion exponent fluctuates for the various proteins. The distribution of displacements of such proteins is observed to take a q -Gaussian form, which decays as a power law. Here, a statistical model is developed for the diffusive motion of the proteins within the bacterium, based on a superstatistics with two variables. This model hierarchically takes into account the joint fluctuations of both the anomalous diffusion exponents and the diffusion constants. A fractional Brownian motion is discussed as a possible local model. Good agreement with the experimental data is obtained.