A Model of Gastric Mucosal pH Regulation: Extending Sensitivity Analysis Using Sobol' Indices to Understand Higher Moments.

Several recent theoretical studies have indicated that a relatively simple secretion control mechanism in the epithelial cells lining the stomach may be responsible for maintaining a neutral (healthy) pH adjacent to the stomach wall, even in the face of enormous electrodiffusive acid transport from the interior of the stomach. Subsequent work used Sobol' Indices (SIs) to quantify the degree to which this secretion mechanism is "self-regulating" i.e. the degree to which the wall pH is held neutral as mathematical parameters vary. However, questions remain regarding the nature of the control that specific parameters exert over the maintenance of a healthy stomach wall pH. Studying the sensitivity of higher moments of the statistical distribution of a model output can provide useful information, for example, how one parameter may skew the distribution towards or away from a physiologically advantageous regime. In this work, we prove a relationship between SIs and the higher moments and show how it can potentially reduce the cost of computing sensitivity of said moments. We define γ -indices to quantify sensitivity of variance, skewness, and kurtosis to the choice of value of a parameter, and we propose an efficient strategy that uses both SIs and γ -indices for a more comprehensive sensitivity analysis. Our analysis uncovers a control parameter which governs the "tightness of control" that the secretion mechanism exerts on wall pH. Finally, we discuss how uncertainty in this parameter can be reduced using expert information about higher moments, and speculate about the physiological advantage conferred by this control mechanism.

A framework for model analysis across multiple experiment regimes: Investigating effects of zinc on Xylella fastidiosa as a case study.

Mathematical models are ubiquitous in analyzing dynamical biological systems. However, it might not be possible to explicitly account for the various sources of uncertainties in the model and the data if there is limited experimental data and information about the biological processes. The presence of uncertainty introduces problems with identifiability of the parameters of the model and determining appropriate regions to explore with respect to sensitivity and estimates of parameter values. Since the model analysis is likely dependent on the numerical estimates of the parameters, parameter identifiability should be addressed beforehand to capture biologically relevant parameter space. Here, we propose a framework which uses data from different experiment regimes to identify a region in the parameter space over which subsequent mathematical analysis can be conducted. Along with building confidence in the parameter estimates, it provides us with variations in the parameters due to changes in the experimental conditions. To determine significance of these variations, we conduct global sensitivity analysis, allowing us to make testable hypothesis for effects of changes in the experimental conditions on the biological system. As a case study, we develop a model for growth dynamics and biofilm formation of a bacterial plant pathogen, and use our framework to identify possible effects of zinc on the bacterial populations in different metabolic states. The framework reveals underlying issues with parameter identifiability and identifies a suitable region in the parameter space, sensitivity analysis over which informs us about the parameters that might be affected by addition of zinc. Moreover, these parameters prove to be identifiable in this region.

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

We apply two different sensitivity techniques to a model of bacterial colonization of the anterior nares to better understand the dynamics of Staphylococcus aureus nasal carriage. Specifically, we use partial rank correlation coefficients to investigate sensitivity as a function of time and identify a reduced model with fewer than half of the parameters of the full model. The reduced model is used for the calculation of Sobol' indices to identify interacting parameters by their additional effects indices. Additionally, we found that the model captures an interesting characteristic of the biological phenomenon related to the initial population size of the infection; only two parameters had any significant additional effects, and these parameters have biological evidence suggesting they are connected but not yet completely understood. Sensitivity is often applied to elucidate model robustness, but we show that combining sensitivity measures can lead to synergistic insight into both model and biological structures.

Mathematical Model for MRSA Nasal Carriage.

An interesting biological phenomenon that is a factor for the spread of antibiotic-resistant strains, such as MRSA, is human nasal carriage. Here, we evaluate several biological hypotheses for this problem in an effort to better understand and narrow the scope of the dominant factors that allow these bacteria to persist in otherwise healthy individuals. First, we set up and analyze a simple PDE model created to generally mimic the interactions of the microbes and nasal immune response. This includes looking at different types of diffusion and chemotaxis terms as well as different boundary conditions. Then, using sensitivity analysis, we walk through several biological hypotheses and compare to the model's results looking for persistent infection scenarios indicated by the model's bacteria component surviving over time.

Viscous, resistive magnetohydrodynamic stability computed by spectral techniques.

Expansions in Chebyshev polynomials are used to study the linear stability of one-dimensional magnetohydrodynamic quasiequilibria, in the presence of finite resistivity and viscosity. The method is modeled on the one used by Orszag in accurate computation of solutions of the Orr-Sommerfeld equation. Two Reynolds-like numbers involving Alfvén speeds, length scales, kinematic viscosity, and magnetic diffusivity govern the stability boundaries, which are determined by the geometric mean of the two Reynolds-like numbers. Marginal stability curves, growth rates versus Reynolds-like numbers, and growth rates versus parallel wave numbers are exhibited. A numerical result that appears general is that instability has been found to be associated with inflection points in the current profile, though no general analytical proof has emerged. It is possible that nonlinear subcritical three-dimensional instabilities may exist, similar to those in Poiseuille and Couette flow.