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How Entropy Affects Drug Design

Entropic Botzmann by Les Dutton, PhD

How could entropy, the basis of the second law of thermodynamics -- or simply put, the measure of disorder in a system -- have anything to do with medicine, a seemingly orderly discipline? Ask Kim Sharp, PhD, an associate professor of Biochemistry and Biophysics, and chair of the Graduate Group in Biochemistry & Molecular Biophysics in the Perelman School of Medicine at the University of Pennsylvania.

Sharp and Franz Matschinsky, MD, also a professor of Biochemistry and Biophysics, translated an 1877 article on entropy by German physicist Ludwig Boltzmann (1844 – 1906) to make sure they were getting the answer to that question right. They published their translation in the journal Entropy last spring (Penn has the complete works of Boltzmann online via the HathiTrust digital library) to inform their research on physical forces that govern molecular binding, specifically drugs binding to their cellular targets.

As Sharp puts it, Boltzmann was one of the “greatest physicists of the 19th century.” Both Max Planck and Albert Einstein acknowledged his profound influence on them. Boltzmann, in addition to many other achievements, explained for the first time, the nature of entropy. “Yet almost none of his work has been translated,” Sharp said. “It is known almost entirely through secondary sources or interpreters of his work. This has engendered considerable controversy, which persists to this day. Many of the people involved in these discussions have most likely not read Boltzmann’s work in the original. Our aim was to change that.”

Most of the paper was in the international language of mathematical equations, so translating the first draft wasn’t too difficult, and Matschinsky is a native German speaker, Sharp said.

Sharp studies the structure and function of proteins and nucleic acids at the molecular and physical chemical level using theoretical and computational methods, asking “How tight can molecules bind?” as a basis for his research on designing drugs on computers.

Drugs first need to find their target and then need to bind to that target to be effective. The Boltzmann paper, which Sharp calls “ground zero” in the German’s seminal work on entropy, is used by Sharp to inquire, “Are there fundamental physical laws constraining how drugs work, with one of the constraints being entropy?”

Two physical laws govern drug-molecule binding (well all molecular interactions, really).  That energy is conserved, the amount does not change, and that entropy increases. Entropy, which Sharp focuses on in a biomedical system, drives the direction of all chemical reactions towards disorder. Therefore, it is this phenomenon that determines how tightly a drug binds to its target. When a drug binds to its target, its entropy decreases, so disorder must increase somewhere else in the cell, usually in the abundant water molecules found in a cell, Sharp suggests. That increase in disorder can be detected as heat flowing into the water surrounding the drug-target bond.

The catalyst to translate Boltzmann’s paper started at a 2011 conference on protein dynamics during a talk Sharp was giving on how to better calculate entropy in drug design.

During the Q&A period, one participant brought up a still-current debate on how Boltzmann and 19th century American physicist Josiah Gibbs calculated entropy differently, which could ultimately affect the way biophysicists determine how drugs work.

“I decided I needed to see what Boltzmann had originally said,” Sharp recalls, which led him to the translation. With the Entropy paper now freely available in an open access journal, Kim says that Boltzmann’s original work is more accessible to a wider audience. With this, he and colleagues are better able to calculate entropy for their practical research, which he is already applying to his current work on enzymes and how mutations in associated proteins affect binding.

Although Sharp and Matschinsky base part of their research on understanding the natural inclination of biological systems to ultimately decay into disorder, their translation is an attempt to add back a small amount of order to biomedical research.

Entropic Boltzmann by Les Dutton, PhD

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