During the lock-down in the UK due to the coronavirus pandemic, I have been reading about viruses and the modelling of them. It is a multi-disciplinary and multi-scale problem; so, something that engineers should be well-equipped to tackle. It is a multi-scale because we need to understand the spread of the virus in the human population so that we can control it, we need to understand the process of infection in individuals so that we can protect them, and we need to understand the mechanisms of virus-cell interaction so that we can stop the replication of the virus. At each size scale, models capable of representing the real-world processes will help us explore different approaches to arresting the progress of the virus and will need to be calibrated and validated against measurements. This can be represented in the sort of model-test pyramid shown in the top graphic that has been used in the aerospace industry [1-2] for many years [see ‘Hierarchical modelling in engineering and biology’ on March 14th, 2018] and which we have recently introduced in the nuclear fission  and fusion  industries [see ‘Thought leadership in fusion engineering’ on October 9th, 2019]. At the top of the pyramid, the spread of the virus in the population is being modelled by epidemiologists, such as Professor Neil Ferguson , using statistical models based on infection data. However, I am more interested in the bottom of the pyramid because the particles of the coronavirus are about the same size as the nanoparticles that I have been studying for some years [see ‘Slow moving nanoparticles’ on December 13th, 2017] and their motion appears to be dominated by diffusion processes [see ‘Salt increases nanoparticle diffusion’ on April 22nd, 2020] [6-7]. The first step towards virus infection of a cell is diffusion of the virus towards the cell which is believed to be a relatively slow process and hence a good model of diffusion would assist in designing drugs that could arrest or decelerate infection of cells . Many types of virus on entering the cell make their way to the nucleus where they replicate causing the cell to die, afterwhich the virus progeny are dispersed to repeat the process. You can see part of this sequence for coronavirus (SARS-COV-2) in this sequence of images. The trafficking across the cytoplasm of the cell to the nucleus can occur in a number of ways including the formation of a capsule or endosome that moves across the cell towards the nuclear membrane where the virus particles leave the endosome and travel through microtubules into the nucleus. Holcman & Schuss  provide a good graphic illustrating these transport mechanisms. In 2019, Briane et al  reviewed models of diffusion of intracellular particles inside living eukaryotic cells, i.e. cells with a nuclear enclosed by a membrane as in all animals. Intracellular diffusion is believed to be driven by Brownian motion and by motor-proteins including dynein, kinesin and myosin that enable motion through microtubules. They observed that the density of the structure of cytoplasm, or cytoskeleton, can hinder the free displacement of a particle leading to subdiffusion; while, cytoskeleton elasticity and thermal bending can accelerate it leading to superdiffusion. These molecular and cellular interactions are happening at disparate spatial and temporal scales  which is one of the difficulties encountered in creating predictive simulations of virus-cell interactions. In other words, the bottom layers of the model-test pyramid appear to be constructed from many more strata when you start to look more closely. And, you need to add a time dimension to it. Prior to the coronavirus pandemic, more modelling efforts were perhaps focussed on understanding the process of infection by Human Immunodeficiency Virus (HIV), including by a multi-national group of scientists from Chile, France, Morocco, Russia and Spain [12-14]. However, the current coronavirus pandemic is galvanising researchers who are starting to think about novel ways of building multiscale models that encourage multidisciplinary collaboration by dispersed groups, [e.g. 15].
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