Space and time on the membrane: modelling Type VI secretion system dynamics as a state-dependent random walk

The type six secretion system (T6SS) is a transmembrane protein complex that mediates bacterial cell killing. The T6SS comprises three main components (transmembrane, baseplate and sheath/tube complexes) that are sequentially assembled in order to enable an attacking cell to transport payloads into neighbouring cells. A T6SS attack disrupts the function of essential cellular components of target cells, typically resulting in their death. While the assembled T6SS adopts a fixed position in the cell membrane of the attacking cell, the location of the firing site varies between firing events. In Serratia marcescens, a post-translational regulatory network regulates the assembly and firing kinetics of the T6SS in a manner that affects the attacking cell's ability to kill target cells. Moreover, when the ability of membrane complexes to reorient is reduced, an attacking cell's competitiveness is also reduced. In this study, we will develop a mathematical model that describes both the spatial motion and assembly/disassembly of a firing T6SS. The model represents the motion of a T6SS on the cell membrane as a state-dependent random walk. Using the model, we will explore how both spatial and temporal effects can combine to give rise to different firing phenotypes. Using parameters inferred from the available literature, we show that variation in estimated diffusion coefficients is sufficient to give rise to either spatially local or global firers.

Environmental risk factors of airborne viral transmission: Humidity, Influenza and SARS-CoV-2 in the Netherlands

OBJECTIVE

The relationship between specific humidity and influenza/SARS-CoV-2 in the Netherlands is evaluated over time and at regional level.

DESIGN

Parametric and non-parametric correlation coefficients are calculated to quantify the relationship between humidity and influenza, using five years of weekly data. Bayesian spatio-temporal models-with a Poisson and a Gaussian likelihood-are estimated to find the relationship between regional humidity and the daily cases of SARS-CoV-2 in the municipalities and provinces of the Netherlands.

RESULTS

An inverse (negative) relationship is observed between specific humidity and the incidence of influenza between 2015 and 2019. The space-time analysis indicates that an increase of specific humidity of one gram of water vapor per kilogram of air (1 g/kg) is related to a reduction of approximately 5% in the risk of COVID-19 infections.

CONCLUSIONS

The increase in humidity during the outbreak of the SARS-CoV-2 in the Netherlands may have helped to reduce the risk of regional COVID-19 infections. Policies that lead to an increase in household specific humidity to over 6g/Kg will help reduce the spread of respiratory viruses such as influenza and SARS-CoV-2.

Spatio-temporal disease risk estimation using clustering-based adjacency modelling

Conditional autoregressive models are typically used to capture the spatial autocorrelation present in areal unit disease count data when estimating the spatial pattern in disease risk. This correlation is represented by a binary neighbourhood matrix based on a border sharing specification, which enforces spatial correlation between geographically neighbouring areas. However, enforcing such correlation will mask any discontinuities in the disease risk surface, thus impeding the detection of clusters of areas that exhibit higher or lower risks compared to their neighbours. Here we propose novel methodology to account for these clusters and discontinuities in disease risk via a two-stage modelling approach, which either forces the clusters/discontinuities to be the same for all time periods or allows them to evolve dynamically over time. Stage one constructs a set of candidate neighbourhood matrices to represent a range of possible cluster/discontinuity structures in the data, and stage two estimates an appropriate structure(s) by treating the neighbourhood matrix as an additional parameter to estimate within a Bayesian spatio-temporal disease mapping model. The effectiveness of our novel methodology is evidenced by simulation, before being applied to a new study of respiratory disease risk in Greater Glasgow, Scotland from 2011 to 2017.

A spatio-temporal model reveals self-limiting FcɛRI cross-linking by multivalent antigens

Aggregation of cell surface receptor proteins by multivalent antigens is an essential early step for immune cell signalling. A number of experimental and modelling studies in the past have investigated multivalent ligand-mediated aggregation of IgE receptors (FcɛRI) in the plasma membrane of mast cells. However, understanding of the mechanisms of FcɛRI aggregation remains incomplete. Experimental reports indicate that FcɛRI forms relatively small and finite-sized clusters when stimulated by a multivalent ligand. By contrast, modelling studies have shown that receptor cross-linking by a trivalent ligand may lead to the formation of large receptor superaggregates that may potentially give rise to hyperactive cellular responses. In this work, we have developed a Brownian dynamics-based spatio-temporal model to analyse FcɛRI aggregation by a trivalent antigen. Unlike the existing models, which implemented non-spatial simulation approaches, our model explicitly accounts for the coarse-grained site-specific features of the multivalent species (molecules and complexes). The model incorporates membrane diffusion, steric collisions and sub-nanometre-scale site-specific interaction of the time-evolving species of arbitrary structures. Using the model, we investigated temporal evolution of the species and their diffusivities. Consistent with a recent experimental report, our model predicted sharp decay in species mobility in the plasma membrane in response receptor cross-linking by a multivalent antigen. We show that, due to such decay in the species mobility, post-stimulation receptor aggregation may become self-limiting. Our analysis reveals a potential regulatory mechanism suppressing hyperactivation of immune cells in response to multivalent antigens.

A Comparison of Spatio-Temporal Disease Mapping Approaches Including an Application to Ischaemic Heart Disease in New South Wales, Australia

The field of spatio-temporal modelling has witnessed a recent surge as a result of developments in computational power and increased data collection. These developments allow analysts to model the evolution of health outcomes in both space and time simultaneously. This paper models the trends in ischaemic heart disease (IHD) in New South Wales, Australia over an eight-year period between 2006 and 2013. A number of spatio-temporal models are considered, and we propose a novel method for determining the goodness-of-fit for these models by outlining a spatio-temporal extension of the Moran's I statistic. We identify an overall decrease in the rates of IHD, but note that the extent of this health improvement varies across the state. In particular, we identified a number of remote areas in the north and west of the state where the risk stayed constant or even increased slightly.