Whip it good: how flagella help cells move

The linked article is for SIAM News, the magazine for members of the Society for Industrial and Applied Mathematics (SIAM). However, even though the main audience for this magazine is professional mathematicians, I wrote it to be understandable even if you gloss over the math.

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A Mathematical Tale of Fibers, Fluids, and Flagella

For SIAM News:

Under a microscope, a cell scoots along by its own power and hoovers up small crumbs of nutrition from the water around it. An example of such an organism is a choanoflagellate, which has a thin, whip-like appendage called a flagellum that controls its feeding and motion. While similarly proportioned apparatuses would be useless on a human scale, flagella are common among single-celled organisms like bacteria, the sometimes-toxic dinoflagellate algae, and even human sperm cells.

Motion in the microscopic world—particularly in fluids—involves an entirely different set of forces than those that govern macroscopic environments. Flagella operate efficiently under these forces and allow microscopic life to move around in fluids, where large viscous forces are present even in substances such as water. The motion of choanoflagellates and the way in which flexible fibers or strands of cells passively respond to liquid flow all constitute a set of complex problems with many potential applications in engineering and medicine.

“With the advent of microfluidic devices and computational technology, there has been an incredible resurgence in studies of the flow of tiny creatures at the microscale,” Lisa Fauci, an applied mathematician at Tulane University and a former president of SIAM, said. “There are possibilities of creating nanorobots that can be guided with external magnetic fields to break up blood clots or deliver drugs to a tumor.”

Read the rest at SIAM News

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Modeling tuberculosis from molecules to organs

The linked article is for SIAM News, the magazine for members of the Society for Industrial and Applied Mathematics (SIAM). However, even though the main audience for this magazine is professional mathematicians, I wrote it to be understandable even if you gloss over the math.

[ This blog is dedicated to tracking my most recent publications. Subscribe to the feed to keep up with all the science stories I write! ]

Multiscale Models Shed Light on Tuberculosis

For SIAM News:

As demonstrated by the ongoing COVID-19 pandemic, a thorough understanding of infectious diseases requires data and models on multiple interconnected levels. Epidemiology addresses population-level issues, transmission models describe individuals within their environments, and a variety of biomedical approaches help researchers comprehend the way in which pathogens infiltrate the body — and the body’s ability to fight back.

Tuberculosis (TB) is one of the deadliest infectious diseases in the world. It accounts for roughly 1.5 million deaths per year and causes the most HIV-related casualties. While decision-makers know in principle how to slow the spread of certain illnesses, TB is more stubborn than most.

“TB is unique compared to many other diseases and the way we treat them,” Denise Kirschner, a mathematical biologist at the University of Michigan Medical School, said. During her plenary talk at the hybrid 2022 SIAM Conference on the Life Sciences (LS22), which took place concurrently with the 2022 SIAM Annual Meeting in Pittsburgh, Pa., this July, Kirschner described the major challenges that surround TB’s characterization.

Read the rest at SIAM News

How do cells “know” to move without brains?

The linked article is for SIAM News, the magazine for members of the Society for Industrial and Applied Mathematics (SIAM). However, even though the main audience for this magazine is professional mathematicians, I wrote it to be understandable even if you gloss over the math. And it involves the word “tortuosity”, which is just fun to say.

[ This blog is dedicated to tracking my most recent publications. Subscribe to the feed to keep up with all the science stories I write! ]

The Mathematical Machinery That Makes Cells Move

For SIAM News:

A white blood cell slips through the gaps between other cells, stretching and bending as it goes. Though its movement strongly evokes that of a macroscopic creature—perhaps a rodent nosing its way through a maze—the cell is guided only by chemical signals and molecular forces. It has no need for a brain, not even the one in the human body that it shares.

Mathematical biologists have developed a number of models to understand self-organization both within and between cells. Leah Edelstein-Keshet of the University of British Columbia received SIAM’s prestigious 2022 John von Neumann Prize for her significant contributions to this field. Edelstein-Keshet has been a leader in mathematical biology research for several decades and also penned one of the earliest textbooks on the subject: Mathematical Models in Biology [1]. She delivered the associated prize lecture at the hybrid 2022 SIAM Annual Meeting (AN22), which took place in Pittsburgh, Pa., this July.

“I started off by looking at the interesting patterns that cells make,” Edelstein-Keshet said. “Fibroblasts try to align in parallel patterns, and the question was, how do they form these parallel arrays? We developed some mathematical language to deal with that. And it turns out that there are a lot of related problems of units that line up in parallel arrays.”

Read the rest at SIAM News

Finding the right math for medical problems

The linked article is for SIAM News, the magazine for members of the Society for Industrial and Applied Mathematics (SIAM). However, even though the main audience for this magazine is professional mathematicians, I wrote it to be understandable even if you gloss over the math. And it involves the word “tortuosity”, which is just fun to say.

[ This blog is dedicated to tracking my most recent publications. Subscribe to the feed to keep up with all the science stories I write! ]

A Nonparametric Swiss Army Knife for Medicine

For SIAM News:

The complexity of living things is frequently humbling for mathematicians. Even a single cell contains a plethora of processes and complicated interactions that tractable mathematical models cannot easily describe. Researchers have applied nonlinear dynamics, mechanical analogs, and numerous other techniques to understand biological systems, but the tradeoffs of modeling often err on the side of reductionism.

For this reason, Heather Harrington of the University of Oxford and her collaborators are turning to global mathematical methods and drawing on experimental data to identify the best techniques. Harrington described several of these methods during her invited talk at the 2021 SIAM Conference on Applications of Dynamical Systems, which took place virtually earlier this year.

“The way that we look at dynamical systems is usually in a small region of the parameter space,” Harrington said. This approach is helpful if one knows a lot about the model and its parameters, but it can be hard to extract detailed predictions from the model if the parameters in question range over large values. “In biology, we often don’t know if the system is very close to a value in parameter space because the variables or parameters are difficult to measure or the data is too messy,” she added.

[read the rest at SIAM News]

Gaining time for brain cancer patients with mathematics

The linked article is for SIAM News, the magazine for members of the Society for Industrial and Applied Mathematics (SIAM). The audience for this magazine, in other words, is professional mathematicians and related researchers working in a wide variety of fields. While the article contains equations, I wrote it to be understandable even if you skip over the math.

[ This blog is dedicated to tracking my most recent publications. Subscribe to the feed to keep up with all the science stories I write! ]

Mathematical Modeling Gains Days for Brain Cancer Patients

For SIAM News:

Glioblastoma, or glioblastoma multiforme, is a particularly aggressive and almost invariably fatal type of brain cancer. It is infamous for causing the deaths of U.S. Senators John McCain and Ted Kennedy, as well as former U.S. Vice President Joe Biden’s son Beau. Though glioblastoma is the second-most common type of brain tumor—affecting roughly three out of every 100,000 people—medicine has struggled to find effective remedies; the U.S. Food and Drug Administration has approved only four drugs and one device to counter the condition in 30 years of research. The median survival rate is less than two years, and only about five percent of all patients survive five years beyond the initial diagnosis.

Given these terrible odds, medical researchers strive for anything that can extend the effectiveness of treatment. The nature of glioblastoma itself is responsible for many obstacles; brain tumors are difficult to monitor noninvasively, making it challenging for physicians to determine the adequacy of a particular course of therapy.

Figure 1. Magnetic resonance imaging scan of the brain. Public domain image.
Kristin Rae Swanson and her colleagues at the Mayo Clinic believe that mathematical models can help improve patient outcomes. Using magnetic resonance imaging (MRI) data for calibration, they constructed the proliferation-invasion (PI) model — a simple deterministic equation to estimate how cancer cells divide and spread throughout the brain. Rather than pinpoint every cell’s location, the model aims to categorize the general behavior of each patient’s cancer to guide individualized treatment.

[Read the rest at SIAM News]

The knotty problem of DNA tangling

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This article is a little different from the fare you’re used to getting from me: it’s for SIAM News, which is the magazine for members of the Society for Industrial and Applied Mathematics (SIAM). The audience for this magazine, in other words, is professional mathematicians and related researchers working in a wide variety of fields. While the article contains equations, I wrote it to be understandable even if you skip over the math.

I will also have you know, I only included one of the many knot-theory puns I came up with while writing the piece. Professionalism, people. Professionalism.

Untangling DNA with Knot Theory

For SIAM News:

Long before there were sailors, nature learned to tie—and untie—knots. Certain DNA types, proteins, magnetic fields, fluid vortices, and other diverse phenomena can manifest in the form of loops, which sometimes end up tangled. But knots, kinks, and tangles are often undesirable for the system in which they occur; for instance, knotted DNA can kill its cell. In such cases, nature finds ways to restore order.

Mariel Vazquez of the University of California, Davis, uses topology to understand the knotting and unknotting of real-world molecules. Specifically, she and her colleagues employ topological concepts from knot theory to demonstrate that cells detangle DNA with optimal efficiency.

During her talk at the 2018 SIAM Annual Meeting, held in Portland, Ore., this July, Vazquez emphasized her work’s multidisciplinary nature; although she focuses on DNA, her research has applications beyond molecular biology.

[Read the rest at SIAM News]

The math behind leopard spots and chemical waves

[ This blog is dedicated to tracking my most recent publications. Subscribe to the feed to keep up with all the science stories I write! ]

This article is a little different from the fare you’re used to getting from me: it’s for SIAM News, which is the glossy magazine for members of the Society for Industrial and Applied Mathematics (SIAM). The audience for this magazine, in other words, is professional mathematicians and related researchers working in a wide variety of fields. While the article contains equations, I wrote it to be understandable even if you skip over the math.

Leopard Spots, Frog Eggs, and the Spectrum of Nonlinear Diffusion Processes

For SIAM News:

Stripes, spots, or a mix of both appear on the skin of many animals — from tigers to beetles to whale sharks. These patterns are typically unique to individual creatures, and biologists often use them for identification. While distinct patterns may seem random, they obey certain rules that suggest a common underlying description. Striping and spotting occur in many unrelated species, implying that both evolutionary advantages and simple biochemical mechanisms drive such patterns.

As Björn Sandstede of Brown University noted during his invited address at the 2018 SIAM Annual Meeting, held in Portland, Ore., this July, similar patterns appear in certain chemical reactions and granular material under vibration. Nonlinear reactions and diffusion describe biological and non-biological patterns, producing stable concentrations in this space.

Alan Turing—best known for his work in computer science and cryptography—first made the mathematical connection between nonlinear diffusion processes and animal stripes in the 1950s. Many researchers have applied the resulting model to demonstrate how various species get their spots and describe nonlinear waves in chemical reactions.

[Read the rest at SIAM News]

Using math to understand why species don’t out-eat each other

[ This blog is dedicated to tracking my most recent publications. Subscribe to the feed to keep up with all the science stories I write! ]

This article is a little different from the fare you’re used to getting from me: it’s for SIAM News, which is the glossy magazine for members of the Society for Industrial and Applied Mathematics (SIAM). The audience for this magazine, in other words, is professional mathematicians and related researchers working in a wide variety of fields. While the article contains equations, I wrote it to be understandable even if you skip over the math.

Competitive Adaptation Prevents Species from Eradicating Each Other

For SIAM News:

Evolution is frequently rough and unforgiving; individuals within a species compete for food, reproductive partners, or other resources. Species fight each other for survival, especially when preying on one another.

Mathematical biologists often simplify these dynamics to predator versus prey. Real-world populations of predator and prey species within a given ecosystem cycle between booms and busts. In various cases, multiple species—including both predators and prey—coexist with similar diets. For example, a cubic meter of seawater can harbor several species of plankton, consisting of tiny plants and animals (see Figure 1).

One would naively expect reproductive success (more offspring) or competitive performance (eating more than your neighbor) to lead to one species’ domination. But that does not occur. While many of these organisms consume the same food, one species does not out-eat the others; the plankton swarm’s overall diversity remains fairly constant. Biologists refer to this phenomenon as the “paradox of the plankton” or the “biodiversity paradox,” among similar terms.

[read the rest at SIAM News]

Swarming in time, synchronizing in space

[ This blog is dedicated to tracking my most recent publications. Subscribe to the feed to keep up with all the science stories I write! ]

This article is a little different from the fare you’re used to getting from me: it’s for SIAM News, which is the glossy magazine for members of the Society for Industrial and Applied Mathematics. The audience for this magazine, in other words, is professional mathematicians and related researchers working in a wide variety of fields. In this case, I covered research by mathematicians looking at a type of system that occurs in biology and materials science. While the article contains equations, I wrote it to be understandable if you skim that part.

Self-organization in Space and Time

For SIAM News:

Self-organization is an important topic across scientific disciplines. Be it the spontaneous flocking of birds or dramatic phase transitions like superconductivity in materials, collective behavior without underlying intelligence occurs everywhere.

Many of these behaviors involve synchronization, or self-organization in time, such as activation in heart cells or the simultaneous blinking of certain firefly species. Others are aggregations, or self-organization in space, like swarming insects, flocking birds, or the alignment of electron spins in magnetic material.

Despite their conceptual similarity, self-organization in space and time have largely been treated separately. “I was curious about whether the two fields had been wedded, and it turns out they hadn’t, at least not fully,” Kevin O’Keeffe, a postdoctoral researcher at the Massachusetts Institute of Technology, said. “I knew all these tricks and mathematical tools from synchronization, and I was looking to cross-fertilize them into the swarming world.”

[Read the rest at SIAM News]