A model has 20 parameters. Local sensitivity analysis shows that the output is insensitive to parameter k7 at the current parameter values. Can you conclude k7 is universally unimportant?
AYes — if the output is insensitive at the current values, it will be insensitive everywhere
BNo — local sensitivity is computed at a single point in parameter space and can change dramatically at different parameter values; a parameter that is unimportant near one operating point may become critical in another regime
CYes — parameters are either important or not, regardless of their values
DNo — but only because local sensitivity analysis has computational errors
Local sensitivity is the partial derivative at a specific point — it describes the behavior in the immediate neighborhood of the current parameter values. Nonlinear systems can have very different sensitivity structures in different regions of parameter space. A parameter might be insensitive near steady state but critically important during a transient response, or unimportant at low concentrations but rate-limiting at high concentrations. Global sensitivity analysis addresses this by sampling across the entire plausible parameter range and computing variance-based indices (like Sobol indices) that capture importance across the full parameter space.
Question 2 True / False
In metabolic control analysis, the sum of all flux control coefficients for a given flux equals 1 (the summation theorem). This means control of a pathway is always distributed across multiple enzymes.
TTrue
FFalse
Answer: True
The summation theorem (sum of all flux control coefficients = 1) is one of the foundational results of metabolic control analysis. It means that if one enzyme has a high control coefficient (close to 1), all other enzymes must have coefficients close to 0 — but the total must sum to 1. In practice, control is typically distributed: several enzymes each contribute partial control, and no single enzyme is 'the' rate-limiting step. This overturned the classical concept of a single rate-limiting enzyme per pathway and has important implications for metabolic engineering (overexpressing one enzyme rarely increases flux proportionally because other enzymes share control).
Question 3 Short Answer
Why is global sensitivity analysis preferred over local sensitivity analysis for complex biological models with uncertain parameters?
Think about your answer, then reveal below.
Model answer: Complex biological models have uncertain parameters (estimated from noisy data, not measured directly), so there is no single 'correct' operating point at which to evaluate local sensitivities. Global sensitivity analysis samples across the entire plausible parameter range and quantifies each parameter's contribution to output variance, accounting for nonlinear effects and parameter interactions that local analysis misses. Sobol indices decompose the total output variance into contributions from individual parameters (first-order) and parameter interactions (higher-order), providing a complete picture of which parameters and parameter combinations drive model uncertainty. This information directly guides experimental prioritization: measure the parameters with the highest Sobol indices first.
Morris screening (elementary effects method) provides a computationally cheaper alternative for high-dimensional models by classifying parameters as negligible, linear, or nonlinear/interacting. It serves as a useful first pass before the more computationally expensive variance-based Sobol analysis.