University of Colorado Boulder
As an undergraduate studying chemical and biological engineering at Tufts University, Jay Stotsky helped pay his way by working as a piano accompanist for aspiring vocalists. But while music is a pastime, math and science are his vocation.
"I've been interested in math for as long as I can remember," says Stotsky, a native of the Boston suburb of South Easton. As a Department of Energy Computational Science Graduate Fellowship (DOE CSGF) recipient at the University of Colorado Boulder, he’s applied his zest for attentive problem-solving to models of how colonies of bacteria, or biofilms, move when water flows over them.
Stotsky's advisor, David Bortz, began working on the problem as a postdoctoral researcher at the University of Michigan in the early 2000s, studying the behavior of bacterial aggregates in the bloodstream. Soon he was researching a central problem in this field: the dynamics of potentially life-threatening biofilms growing in catheters and IV (intravenous therapy) lines.
Soon after Bortz arrived in Colorado in 2006, he was introduced to researchers at the nearby National Institute of Standards and Technology who were concerned about bacterial growth in biofuel pipelines.
"It was a similar problem in the two cases," Bortz says. "You had a biofilm growing in a pipe, and you wanted to know the stress-strain relationships of the biofilm. How easy would it be to break it apart and get rid of it, and what could you do to the surface of the pipe that would make it harder to grow on?"
A biofilm consists of bacteria physically interconnected via a web of polysaccharide, or sugar, chains – the extracellular matrix – to create a viscoelastic fluid with "the consistency of mucus," Bortz says.
To tackle the problem, Bortz adapted the immersed boundary (IB) method, a technique first developed in cardiology to solve fluid-structure interaction questions.
His Michigan collaborators identified the three-dimensional positions of the bacteria. Bortz used that information to create a prototype model that treated the biofilm's macroscale rheology (deformation and flow properties) as a feature that results from the bacterial interactions. He called it the heterogeneous rheology IB method, or hrIBM.
Stotsky began improving the model’s computational performance in October 2013. Running it on Janus, CU Boulder’s supercomputer (since decommissioned and replaced by Summit), Stotsky applied highly efficient methods and computational techniques for solving the equations governing biofilm-fluid interactions. By early January he'd sped up the simulations by an order of magnitude.
He next worked on validating the model using detailed experimental results from live biofilms of Staphylococcus epidermidis, a skin bacterium that turns deadly when it infects catheters. The University of Michigan collaborators grew the biofilm and tested its rheological properties.
Stotsky explored a half-dozen mathematical models for the stress-strain relationships and ran simulations of several seconds of 3-D biofilm movement, each one requiring a full day on Janus. He discovered that when the spring-like connections between the bacteria were modeled in a particular way, nearly all of the computed data points hewed to the experimental data.
"Nobody before was able to hit the values of an experiment so precisely," Bortz says.
Having validated the hrIBM model, Stotsky set out to develop a statistical model that links biofilm rheology to how the bacteria are distributed in space.
"With the statistical model, the idea is to be able to create artificial biofilms that have similar properties as a real biofilm would," says Stotsky, who brought to the work insights in applied mathematics techniques gained during his 2016 DOE CSGF practicum at Lawrence Berkeley National Laboratory under Dan Martin and Phil Colella.
Stotsky developed a spatial statistics model using data sets of 4,000 or so bacterial positions as input. It characterizes fundamental statistical interactions between bacteria using various means of calculating the dependence of that interaction on their proximity.
After using the statistical model to simulate a biofilm colony bacterium by bacterium, Stotsky paused to overlay his simulated data on the experimental data points. They overlapped with "close approximation." The model revealed that the bacteria have a "favorite distance" by which they're separated, and that in biofilms there's strength in disorder.
"The most surprising thing is that I found that having just a little bit of non-uniformity, for example not having the bacteria aligned on a grid, tends to make the biofilms a little stronger. I thought it would be the other way around."
As Stotsky prepares to graduate in the spring 2018, he’s applying for postdoctoral positions and still performing music.
Read the entire article in DEIXIS, the DOE CSGF annual. [PDF, pages 19-21]
Image caption: Viscosity increases around each biofilm organism. The blue and green isosurfaces around each bacterium depict viscosity of 100 and 250 times that of the surrounding media. The coloration along the walls corresponds to the z-component of the fluid velocity field. Credit: Jay Stotsky.