Sigmoid growth models, such as the logistic and Gompertz growth models, are widely used to study various population dynamics ranging from microscopic populations of cancer cells, to continental-scale human populations. Fundamental questions about model selection and precise parameter estimation are critical if these models are to be used to make useful inferences about underlying ecological mechanisms. However, the question of parameter identifiability for these models -- whether a data set contains sufficient information to give unique or sufficiently precise parameter estimates for the given model -- is often overlooked; We use a profile-likelihood approach to systematically explore practical parameter identifiability using data describing the re-growth of hard coral cover on a coral reef after some ecological disturbance. The relationship between parameter identifiability and checks of model misspecification is also explored. We work with three standard choices of sigmoid growth models, namely the logistic, Gompertz, and Richards' growth models; We find that the logistic growth model does not suffer identifiability issues for the type of data we consider whereas the Gompertz and Richards' models encounter practical non-identifiability issues, even with relatively-extensive data where we observe the full shape of the sigmoid growth curve. Identifiability issues with the Gompertz model lead us to consider a further model calibration exercise in which we fix the initial density to its observed value, neglecting its uncertainty. This is a common practice, but the results of this exercise suggest that parameter estimates and fundamental statistical assumptions are extremely sensitive under these conditions; Different sigmoid growth models are used within subdisciplines within the biology and ecology literature without necessarily considering whether parameters are identifiable or checking statistical assumptions underlying model family adequacy. Standard practices that do not consider parameter identifiability can lead to unreliable or imprecise parameter estimates and hence potentially misleading interpretations of the underlying mechanisms of interest. While tools in this work focus on three standard sigmoid growth models and one particular data set, our theoretical developments are applicable to any sigmoid growth model and any relevant data set. MATLAB implementations of all software available on GitHub.
Current chemotherapy against Mycobacterium tuberculosis (Mtb), an important human pathogen, requires a multidrug regimen lasting several months. While efforts have been made to optimize therapy by exploiting drug-drug synergies, testing new drug combinations in relevant host environments remains arduous. In particular, host environments profoundly affect the bacterial metabolic state and drug efficacy, limiting the accuracy of predictions based on in vitro assays alone. In this study, we utilize conditional Mtb knockdown mutants of essential genes as an experimentally tractable surrogate for drug treatment, and probe the relationship between Mtb carbon metabolism and chemical-genetic interactions (CGI). We examined the anti-tubercular drugs isoniazid, rifampicin and moxifloxacin, and found that CGI are differentially responsive to the metabolic state, defining both environment independent and dependent synergies. Specifically, growth on the in vivo relevant carbon source, cholesterol, reduced rifampicin efficacy by altering mycobacterial cell surface lipid composition. We report that a variety of perturbations in cell wall synthesis pathways restore rifampicin efficacy during growth on cholesterol, and that both environment-independent and cholesterol-dependent in vitro CGI could be leveraged to enhance bacterial clearance in the mouse infection model. Our findings present an atlas of novel chemical genetic environmental synergies that can be used to optimize drug-drug interactions as well as provide a framework for understanding in vitro correlates of in vivo efficacy.
The treatment of diabetic foot ulcerations has been a difficult task for podiatrists. Numerous methods and materials have been used in an attempt to alleviate this frustrating and complex treatment dilemma. However, there is one treatment method that has been used successfully for decades on plantar ulcerations of the neuropathic foot. Total contact casting has been an easily applicable and effective treatment modality for neuropathic ulcerations of the diabetic foot.
Transport of cells and biochemical molecules often takes place in crowded, heterogeneous environments. As such, it is important we understand how to quantify crowded transport phenomena, and the possibilities of extracting transport coefficients from limited observations. We employ a volume-excluding random walk model on a square lattice where different fractions of lattice sites are filled with inert, immobile obstacles to investigate whether it is possible to estimate parameters associated with transport when crowding is present. By collecting and analysing data obtained on multiple spatial scales we demonstrate that commonly used models of motility within crowded environments can be used to reliably predict our random walk data. However, infeasibly large amounts of data are needed to estimate transport parameters, and quantitative estimates may differ depending on the spatial scale on which they are collected. We also demonstrate that in models of crowded environments there is a relatively large region of the parameter space within which it is difficult to distinguish between the “best fit” parameter values. This suggests commonly used descriptions of transport within crowded systems may not be appropriate, and that we should be careful in choosing models to represent the effects of crowding upon motility within biochemical systems.
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