Identifiability analysis for stochastic differential equation models in systems biology

Researchers rely on mathematical models to explain many biological processes. But how can they ensure their experimental data is sufficient to estimate the parameters that characterise a biological process?

Right now, there are well-established techniques to diagnose parameter Identifiability for deterministic, ordinary differential equation models. However, these models neglect the variability ubiquitous to many biological processes, meaning that information in this noise is often ignored. Another type of model, a stochastic model, is better suited to explain these volatile processes. 


(a–d) Cell proliferation and death observed in vitro over 36 h in a proliferation assay. Each snapshot has a field-of-view of 1440 × 1440 μm and the location of each cell is indicated with a yellow marker. (e) Data from the early stages of the coronavirus pandemic comprising the observed number of (i) infected individuals, deaths, and (ii) daily new case count in Australia during 2020. (f) Continuous glucose monitoring data from a single individual over three consecutive days.

For the first time, new work provides the guidance needed to take the established techniques used in deterministic models and apply them to diagnose whether model parameters can be identified in stochastic models. The work, led by ACEMS researchers at QUT, was just published in the Journal of the Royal Society Interface.

“The question of parameter identifiability is critical for tailoring model complexity to the available data,” says Alex Browning, a PhD Candidate with ACEMS at QUT.

Many volatile biological processes rely on mathematical models for interpretation and application. For example, diabetic patients rely on the rapid interpretation of highly volatile blood glucose measurements to determine insulin input. Data from the COVID-19 pandemic is also volatile, and researchers must often draw inferences from epidemic data from a single set of observations.

“Data from these processes is very stochastic or random. So, if you have something like coronavirus data, it doesn’t look nice and smooth. It looks like it jumps around a lot,” says Alex.

“Stochastic models capture that. They show how it’s likely that the data will jump all over the place.”

In the team’s review paper, the team took a Bayesian approach to parameter estimation to establish identifiability through four case studies.

"Our review explicitly demonstrates for the first time that identifiability analysis for stochastic differential equation models in biology. In fact, we show how often stochastic models can extract more information about a process than a deterministic description,” says Alex.

Alex says questions about parameter identifiability are often overlooked but have important ramifications for a model's predictive power and the biological insights it can obtain.