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.

The ups and downs of S. aureus nasal carriage.

Staphylococcus aureus infections are a growing concern worldwide due to the increasing number of strains that exhibit antibiotic resistance. Recent studies have indicated that some percentage of people carry the bacteria in the nasal cavity and therefore are at a higher risk of subsequent, and more serious, infections in other parts of the body. However, individuals carrying the infection can be classified as only intermittent carriers versus persistent carriers, being able to eliminate the bacteria and later colonized again. Using a model of bacterial colonization of the anterior nares, we investigate oscillatory patterns related to intermittent carriage of S. aureus. Following several studies using global sensitivity analysis techniques, various insights into the model's behaviour were made including interacting effects of the bacteria's growth rate and movement in the mucus, suggesting parameter connections associated with biofilm-like behaviour. Here the bacterial growth rate and bacterial movement are explicitly connected, leading to expanded oscillatory behaviour in the model. We suggest possible implications that this oscillatory behaviour can have on the definition of intermittent carriage and discuss differences in the bacterial virulence dependent upon individual host health. Furthermore, we show that connecting the bacterial growth and movement also expands the region of the parameter space for which the bacteria are able to survive and persist.

Computational Investigation of Ripple Dynamics in Biofilms in Flowing Systems.

Biofilms are collections of microorganisms that aggregate using a self-produced matrix of extracellular polymeric substance. It has been broadly demonstrated that many microbial infections in the body, including dental plaque, involve biofilms. While studying experimental models of biofilms relevant to mechanical removal of oral biofilms, distinct ripple patterns have been observed. In this work, we describe a multiphase model used to approximate the dynamics of the biofilm removal process. We show that the fully nonlinear model provides a better representation of the experimental data than the linear stability analysis. In particular, we show that the full model more accurately reflects the relationship between the apparent wavelength and the external forcing velocities, especially at mid-to-low velocities at which the linear theory neglects important interactions. Finally, the model provides a framework by which the removal process (presumably governed by highly nonlinear behavior) can be studied.

A mathematical model for the determination of mouse excisional wound healing parameters from photographic data.

We present a mathematical model to quantify parameters of mouse excisional wound healing from photographic data. The equation is a piecewise linear function in log scale that includes key parameters of initial wound radius (R0 ), an initial wound stasis phase (Ti ), and time to wound closure (Tc ); subsequently, these terms permit calculation of a latter active proliferative phase (Tp ), and the healing rate (HR) during this active phase. A daily photographic record of wound healing (utilizing 6 mm diameter splinted excisional wounds) permits the necessary sampling for robust parameter refinement. When implemented with an automated nonlinear fitting routine, the healing parameters are determined in an operator-independent (i.e., unbiased) manner. The model was evaluated using photographic data from a splinted excisional surgical procedure involving several different mouse cohorts. Model fitting demonstrates excellent coefficients of determination (R2 ) in each case. The model, thus, permits quantitation of key parameters of excisional wound healing, from initial wounding through to wound closure, from photographic data.

Fluid-driven interfacial instabilities and turbulence in bacterial biofilms.

Biofilms are thin layers of bacteria embedded within a slime matrix that live on surfaces. They are ubiquitous in nature and responsible for many medical and dental infections, industrial fouling and are also evident in ancient fossils. A biofilm structure is shaped by growth, detachment and response to mechanical forces acting on them. The main contribution to biofilm versatility in response to physical forces is the matrix that provides a platform for the bacteria to grow. The interaction between biofilm structure and hydrodynamics remains a fundamental question concerning biofilm dynamics. Here, we document the appearance of ripples and wrinkles in biofilms grown from three species of bacteria when subjected to high-velocity fluid flows. Linear stability analysis suggested that the ripples were Kelvin-Helmholtz Instabilities. The analysis also predicted a strong dependence of the instability formation on biofilm viscosity explaining the different surface corrugations observed. Turbulence through Kelvin-Helmholtz instabilities occurring at the interface demonstrated that the biofilm flows like a viscous liquid under high flow velocities applied within milliseconds. Biofilm fluid-like behavior may have important implications for our understanding of how fluid flow influences biofilm biology since turbulence will likely disrupt metabolite and signal gradients as well as community stratification.

Sensitivity Analysis of a Pharmacokinetic Model of Vaginal Anti-HIV Microbicide Drug Delivery.

Uncertainties in parameter values in microbicide pharmacokinetics (PK) models confound the models' use in understanding the determinants of drug delivery and in designing and interpreting dosing and sampling in PK studies. A global sensitivity analysis (Sobol' indices) was performed for a compartmental model of the pharmacokinetics of gel delivery of tenofovir to the vaginal mucosa. The model's parameter space was explored to quantify model output sensitivities to parameters characterizing properties for the gel-drug product (volume, drug transport, initial loading) and host environment (thicknesses of the mucosal epithelium and stroma and the role of ambient vaginal fluid in diluting gel). Greatest sensitivities overall were to the initial drug concentration in gel, gel-epithelium partition coefficient for drug, and rate constant for gel dilution by vaginal fluid. Sensitivities for 3 PK measures of drug concentration values were somewhat different than those for the kinetic PK measure. Sensitivities in the stromal compartment (where tenofovir acts against host cells) and a simulated biopsy also depended on thicknesses of epithelium and stroma. This methodology and results here contribute an approach to help interpret uncertainties in measures of vaginal microbicide gel properties and their host environment. In turn, this will inform rational gel design and optimization.