In nature’s math, freedoms are fundamental

(Press-News.org) Numbers have a funny way about them. Young math students are taught various strategies to make problem-solving easier. Comparing fractions? Find a common denominator or convert to decimals. The strategies get more complex when doing the kind of math used to describe the activities of DNA, RNA, or protein sequences.

In science, when you make a model, its parameters determine its predictions. But what do you do when different sets of parameters result in the same predictions? Call one half 2/4 or 3/6—either way, the result’s the same. In physics, such parameter sets are called gauge freedoms. They play a key role in how we understand electromagnetism and quantum mechanics. Surprisingly, gauge freedoms also arise in computational biology when trying to model how different mutations interact.

Now, Cold Spring Harbor Laboratory (CSHL) quantitative biologists have developed a unified theory for gauge freedoms in models of biological sequences. Their solution could have countless applications, from plant breeding to drug development.

Granted, most folks have never heard of gauge freedoms. So, how common are they? When it comes to computer models used to describe massive genetic datasets, they’re basically everywhere, says CSHL Associate Professor Justin Kinney, who co-led this study with Associate Professor David McCandlish.

“Gauge freedoms are ubiquitous in computational models of how biological sequences work,” Kinney says. “Historically, they’ve been dealt with as annoying technicalities. We’re the first to study them directly in order to get a deeper understanding of where they come from and how to handle them.”

Until now, computational biologists have accounted for gauge freedoms using a variety of ad hoc approaches. Kinney, McCandlish, and their colleagues were looking for a better way. Together, they developed a unified approach. Their new mathematical theory provides efficient formulas scientists can use for all sorts of biological applications. These formulas will allow scientists to interpret research results much faster and with greater confidence.

The investigators also published a companion paper that reveals where these gauge freedoms ultimately come from. It turns out they’re needed for models to reflect symmetries in real biological sequences. Perhaps counterintuitively, making biological models behave in a simple and intuitive way requires them to be larger and more complex. “We prove that gauge freedoms are necessary to interpret the contributions of particular genetic sequences,” McCandlish adds.

Together, the studies strongly suggest that Kinney and McCandlish’s unified approach isn’t just a new strategy for solving theoretical problems. It may prove fundamental for future efforts in agriculture, drug discovery, and beyond.

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