"Structural Identifiability and Observability of Compartmental Models of the COVID-19 Pandemic"
The recent coronavirus disease (COVID-19) outbreak has dramatically increased the public awareness and appreciation of the utility of dynamic models. At the same time, the dissemination of contradictory model predictions has highlighted their limitations. If some parameters and/or state variables of a model cannot be determined from out-put measurements, its ability to yield correct insights – as well as the possibility of controlling the system – maybe compromised. Epidemic dynamics are commonly analysed using compartmental models, and many variations of such models have been used for analysing and predicting the evolution of the COVID-19 pandemic. In this paper we survey the different models proposed in the literature, assembling a list of 36 model structures and assessing their ability to provide reliable information. We address the problem using the control theoretic concepts of structural identifiability and observability. Since some parameters can vary during the course of an epidemic, we consider boththe constant and time-varying parameter assumptions. We analyse the structural identifiability and observability ofall of the models, considering all plausible choices of outputs and time-varying parameters, which leads us to analyse 255 different model versions. We classify the models according to their structural identifiability and observability under the different assumptions and discuss the implications of the results. We also illustrate with an example several alternative ways of remedying the lack of observability of a model. Our analyses provide guidelines for choosing the most informative model for each purpose, taking into account the available knowledge and measurements.
"Mechanosensing can enhance adaptation to maintain polarity of migrating cells"
Migratory cells are known to adapt to environments that contain wide-ranging levels of chemoattractant. While biochemical models of adaptation have been previously proposed, here we discuss a different mechanism based on mechanosensing, where the interaction between biochemical signaling and cell tension facilitates adaptation. In this talk, we develop and analyze a model of mechanochemical-based adaptation consisting of a mechanics-based physical model coupled with the wave-pinning reaction-diffusion model for Rac GTPase activity. We use Local Perturbation Analysis to predict how cells adapt signaling parameters via feedback from mechanics to maintain polarity in response to chemoattractant levels. To confirm this prediction, we simulate the mechanochemical model in moving cells, demonstrating how mechanosensing results in persistent cell polarity when cells are stimulated with wide-ranging levels of chemoattractant in silico. These results demonstrate how mechanosensing may help cells adapt to maintain polarity in variable environments.
"Length regulation of multiple flagella that self-assemble from a shared pool of components"
The single cell biflagellate Chlamydomonas reinhardtii has proven to be a very useful model organism for studies of size control. The lengths of its two flagella are tightly regulated. We study a model of flagellar length control whose key assumption is that proteins responsible for the intraflagellar transport (IFT) of tubulin are present in limiting amounts. In the case of two simultaneously assembling flagella, regardless of the details of how the flagella are coupled, we find that the widely-used assumption of a constant disassembly rate is inconsistent with experimental results. We therefore propose a model in which diffusion gives rise to a length-dependent concentration of depolymerizer at the flagellar tip. This model is found to be consistent with experimental results and generalizes to other situations such as arbitrary flagellar number.