Kelsey I. Gasior

Mathematical modeling is a powerful tool to understand biological phenomena, predict behavior, and guide experiments. Model parameters represent experimentally derived rates, and it can be challenging to understand how parameters affect the system's output(s). Global sensitivity analysis (GSA) can help determine how uncertainty in model outcomes can be attributed to parameters. Methods like Sobol' indices provide detailed analysis but at a high computational cost. Thus, it may be necessary to precede it by another method to reduce the parameter space. Morris Method Screening (MMS) is a qualitative analysis that can provide information about sensitivity and parameter interactions, making it a good partner for Sobol'. Partial Rank Correlation Coefficient (PRCC) may also be a viable option as it has a similar cost to MMS. This work tests whether a ranking (PRCC) or screening (MMS) method is better when used in combination with Sobol' analysis. Using a model of the epithelial-mesenchymal transition as a test case, this work shows that PRCC-Sobol' and MMS-Sobol' can produce diverging results, making it difficult to analyze how biological events are informed by specific rates and quantities. However, the differences between these methods mean that these techniques may be most effective when all three are used together.

Partial Rank Correlation Coefficient (PRCC), usually performed following Latin Hypercube Sampling (LHS), is a global sensitivity analysis that quantifies the monotonic relationship between model parameters and the desired output. To carry out this analysis, a range of acceptable parameter values must be known or estimated. However, within a biological context, approximating these values may be difficult. Parameter values and ranges can be taken from different organisms or systems or be estimated to produce qualitative phenomena in the model. Using a mathematical model of the epithelial mesenchymal transition (EMT) as a test case, this work examines how the parameter ranges chosen prior to analysis can influence LHS-PRCC results and shape subsequent analysis interpretations. Previous LHS-PRCC analysis of this model restricted parameters to ± 10% of their original value, which limits the scope and interpretability of parameter influence. Such a small range assumes, in the biological sense, that parameters are well-measured with little variability. Here, this work extends the previous analysis and explores several parameter ranges (± 25%, ± 50% of the original value). This work also tests whether, within the ± 10%, ± 25% and ± 50% parameter ranges, the bistable switch present in the original model are maintained. Ultimately, this work showcases how a choice made prior to analysis, such as the accepted parameter ranges for biological rates and values in complex dynamical systems can influence sensitivity analysis results and interpretability. Additionally, these choices can have hidden consequences, such as the loss of phenomenological behavior. Thus, explicit prior knowledge about the appropriate parameter values is needed before using analysis to guide future experiments and model development.

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.