Combining Two Methods of Global Sensitivity Analysis to Investigate MRSA Nasal Carriage Model

Untangling the Molecular Interactions Underlying Intracellular Phase Separation Using Combined Global Sensitivity Analyses

Liquid-liquid phase separation is an intracellular mechanism by which molecules, usually proteins and RNAs, interact and then rapidly demix from the surrounding matrix to form membrane-less compartments necessary for cellular function. Occurring in both the cytoplasm and the nucleus, properties of the resulting droplets depend on a variety of characteristics specific to the molecules involved, such as valency, density, and diffusion within the crowded environment. Capturing these complexities in a biologically relevant model is difficult. To understand the nuanced dynamics between proteins and RNAs as they interact and form droplets, as well as the impact of these interactions on the resulting droplet properties, we turn to sensitivity analysis. In this work, we examine a previously published mathematical model of two RNA species competing for the same protein-binding partner. We use the combined analyses of Morris Method and Sobol' sensitivity analysis to understand the impact of nine molecular parameters, subjected to three different initial conditions, on two observable LLPS outputs: the time of phase separation and the composition of the droplet field. Morris Method is a screening method capable of highlighting the most important parameters impacting a given output, while the variance-based Sobol' analysis can quantify both the importance of a given parameter, as well as the other model parameters it interacts with, to produce the observed phenomena. Combining these two techniques allows Morris Method to identify the most important dynamics and circumvent the large computational expense associated with Sobol', which then provides more nuanced information about parameter relationships. Together, the results of these combined methodologies highlight the complicated protein-RNA relationships underlying both the time of phase separation and the composition of the droplet field. Sobol' sensitivity analysis reveals that observed spatial and temporal dynamics are due, at least in part, to high-level interactions between multiple (3+) parameters. Ultimately, this work discourages using a single measurement to extrapolate the value of any single rate or parameter value, while simultaneously establishing a framework in which to analyze and assess the impact of these small-scale molecular interactions on large-scale droplet properties.

Exploring how ecological and epidemiological processes shape multi-host disease dynamics using global sensitivity analysis

We use global sensitivity analysis (specifically, Partial Rank Correlation Coefficients) to explore the roles of ecological and epidemiological processes in shaping the temporal dynamics of a parameterized SIR-type model of two host species and an environmentally transmitted pathogen. We compute the sensitivities of disease prevalence in each host species to model parameters. Sensitivity rankings are calculated, interpreted biologically, and contrasted for cases where the pathogen is introduced into a disease-free community and cases where a second host species is introduced into an endemic single-host community. In some cases the magnitudes and dynamics of the sensitivities can be predicted only by knowing the host species' characteristics (i.e., their competitive abilities and disease competence) whereas in other cases they can be predicted by factors independent of the species' characteristics (specifically, intraspecific versus interspecific processes or a species' roles of invader versus resident). For example, when a pathogen is initially introduced into a disease-free community, disease prevalence in both hosts is more sensitive to the burst size of the first host than the second host. In comparison, disease prevalence in each host is more sensitive to its own infection rate than the infection rate of the other host species. In total, this study illustrates that global sensitivity analysis can provide useful insight into how ecological and epidemiological processes shape disease dynamics and how those effects vary across time and system conditions. Our results show that sensitivity analysis can provide quantification and direction when exploring biological hypotheses.

Ranking non-pharmaceutical interventions against Covid-19 global pandemic using global sensitivity analysis-Effect on number of deaths

In this study, we use Global Sensitivity Analysis (GSA) to rank four non-pharmaceutical interventions (NPIs) in a deterministic compartmental model that might control Covid-19 related deaths in the United States. The NPIs are social distancing, isolation of infected individuals, identifying asymptomatically infected individuals through testing, and the use of face masks. The model uses a fear-based behavioral model that leads unmasked susceptible individuals to wear masks. The model parameters are estimated from the reported deaths for the United States of America from March 1, 2020 to November 26, 2020. Two GSA tools, the Sobol' sesntivity indices and Partial Rank Correlation Coefficient are used to obtain the rankings of the input parameters at different stages of the disease propagation. We found that social distancing and outward mask efficiency alone decreases the output uncertainty by 25-45%. Sobol' second order indices show that the combined effect of social distancing with increased mask usage and identifying and isolating asymptomatically infected individuals decreases uncertainty an additional 10%.

Sensitivity analysis methods in the biomedical sciences

Sensitivity analysis is an important part of a mathematical modeller's toolbox for model analysis. In this review paper, we describe the most frequently used sensitivity techniques, discussing their advantages and limitations, before applying each method to a simple model. Also included is a summary of current software packages, as well as a modeller's guide for carrying out sensitivity analyses. Finally, we apply the popular Morris and Sobol methods to two models with biomedical applications, with the intention of providing a deeper understanding behind both the principles of these methods and the presentation of their results.

Mechanism-Based Modeling of Tumor Growth and Treatment Response Constrained by Multiparametric Imaging Data

Multiparametric imaging is a critical tool in the noninvasive study and assessment of cancer. Imaging methods have evolved over the past several decades to provide quantitative measures of tumor and healthy tissue characteristics related to, for example, cell number, blood volume fraction, blood flow, hypoxia, and metabolism. Mechanistic models of tumor growth also have matured to a point where the incorporation of patient-specific measures could provide clinically relevant predictions of tumor growth and response. In this review, we identify and discuss approaches that use multiparametric imaging data, including diffusion-weighted magnetic resonance imaging, dynamic contrast-enhanced magnetic resonance imaging, diffusion tensor imaging, contrast-enhanced computed tomography, [18F]fluorodeoxyglucose positron emission tomography, and [18F]fluoromisonidazole positron emission tomography to initialize and calibrate mechanistic models of tumor growth and response. We focus the discussion on brain and breast cancers; however, we also identify three emerging areas of application in kidney, pancreatic, and lung cancers. We conclude with a discussion of the future directions for incorporating multiparametric imaging data and mechanistic modeling into clinical decision making for patients with cancer.