Debusschere earns honors
for sorting out uncertainty
(page 3 of 4)
"You have to properly define what your observable is," he adds – what molecule or reaction you want to understand. But "you can't say 'I'm interested in the number of molecules of X.' You will get a different answer each time, so you look at a distribution of the number of molecules." By running models multiple times, the researchers can get a probability distribution of reaction products.
Debusschere's main tools for understanding uncertainties are polynomial chaos expansions (PCEs). Polynomial chaos methods, developed in the 1930s by American mathematician Norbert Wiener, are a way to reduce the complexity of random variables, making them easier to work with in computations. They provide compact representations of how intrinsic noise and parametric uncertainty affect a system, making the corresponding processes easier to analyze.
"PCEs present a way to describe stochasticity with a set of deterministic coefficients," Debusschere says. "Those deterministic descriptions are a lot easier to work with."
In most cases, Debusschere and his fellow researchers have used PCEs to represent different types of variability and uncertainties. Their standard test case has been the Schlögl model, a prototype reaction network in which two chemical concentrations are stable while concentrations of other chemicals, reaction rates and other parameters change. Their PCE-based methods demonstrate good agreement with original data that show the system moving from two-activity modes to a single mode as values of a selected parameter increase.
In one case, Debusschere and his fellow researchers used PCEs to artificially perturb parameters to learn about the system's sensitivity to such changes. The researchers gave selected parameters a quantified uncertainty large enough to generate a response that would stick out over intrinsic noise. On a test using a simplified virus infection model, the researchers found the probability of failed infections, the viral reservoir (cells where the infection is latent for a long time without fully developing) and virus production rate all are very sensitive to the generation of two particular viral nucleic acids.
Such stochastic reaction networks are everywhere, Debusschere says, making the tools he and his fellow researchers develop broadly applicable. They can be used to study the interactions and feedback loops governing cell growth, gene expression and other biological activities. They can study catalytic reactions important for batteries and fuel cells. They can help understand the conditions affecting how bacteria break down environmental contaminants or plant material so scientists can tweak the bacteria and conditions to boost efficiency.
