Treating diseases by steering evolution with ideas from physics

When physicians attempt to use targeted therapy against bacterial infections and cancer, one of the greatest challenges they face is the rapid evolution of the disease to resist treatment. I attended a fascinating talk yesterday afternoon about a novel approach to this problem that draws on an idea from physics: counterdiabatic driving.

Oncologist Jacob Scott of the Cleveland Clinic explained counterdiabatic driving using the analogy of a waiter carrying a full glass of water on a tray. If the waiter starts walking while holding the tray horizontally, the water might spill. But if the waiter tilts the tray forward as they start walking, they can keep the water at equilibrium and avoid spilling it.

Sequence of three pictures showing counterdiabatic driving by a waiter carrying a glass of water. First picture: glass upright. Second picture: glass tilted backward, water spilling out. Third picture: glass tilted forward, water staying inside the glass in equilibrium.

A waiter carrying a glass of water provides an analogy for counterdiabatic driving. As the waiter walks to the right, the water leaves equilibrium in situation B but stays in equilibrium in situation C.

In physics, counterdiabatic driving — this sort of preemptive tweaking of parameters to keep a system in instantaneous equilibrium — shows up in Brownian motion of a bead in an optical trap and in adiabatic quantum computing. I encountered the concept during my undergraduate research on parity-time symmetry in quantum mechanics, so the title of Scott’s talk, “Controlling the speed and trajectory of evolution with counterdiabatic driving,” immediately caught my attention.

As Scott explained, the various genetic mutations that allow a disease to evolve resistance to a drug can be thought of as forming a fitness landscape. The shape of this landscape will be different for each drug, so evolving resistance to one drug affects the sensitivity to other drugs. This leads to an important but often-overlooked fact in treating diseases: Evolution is not commutative. That is, the sequence in which drugs are administered has a big impact on the final outcome. For example, it’s possible that using Drug A followed by Drug B would render Drug C ineffective, but using Drug B followed by Drug A would cause Drug C to be highly effective. It all depends on the path that evolution takes through the fitness landscapes.

Graph showing a fitness landscape. X axis and y axis are parameters in the genotype, while the z axis is the resulting fitness. The graph has two peaks, labeled by a star and a pentagon.

A conceptual representation of fitness landscapes. Which peak (purple pentagon or green star in large figure) the disease reaches during the first treatment will determine which second-line drug (smaller figures) is most effective.

Here’s the core question of Scott’s research: Is it possible to steer evolution to maximize the effectiveness of second- and third-line drugs? It turns out that the answer is yes. Simply changing the order in which drugs are administered is a rudimentary way to accomplish this, and counterdiabatic driving provides a more sophisticated strategy. When administering the first drug, altering the dosage over time in a specific way can guide the disease genotype toward a desired point in the fitness landscape where the second-line drug will prove particularly effective. 

The details get more complicated, of course. The individual cells in a bacterial infection or a cancer tumor don’t evolve as a homogenous unit, but rather as a distribution of genotypes. As a result, the math of diffusion comes into play in the evolutionary dynamics. Plus, in the theoretical models, it takes infinite time for the disease to reach the desired point in the fitness landscape. But patients can’t wait forever before switching from the first-line drug to the second-line one, so researchers have to determine how close is close enough. 

We’re still in the early days of applying these ideas to actual diseases, but results so far have been promising. For example, Scott mentioned a study of 15 empirical fitness landscapes of E. coli that showed that it is possible to steer the bacterial population to avoid the emergence of antibiotic resistance. 

Image comparing three applications of counterdiabatic driving: in quantum computing, in optical traps, and in the probability distribution of genetic variants.

Counterdiabatic driving, an idea that originated in physics, can be used to steer the evolution of a disease and make treatment more effective.

I thought it was fascinating to see how an idea that I first encountered in the context of physics has direct applications to medicine, and I can’t wait to hear about future developments. If you want to learn more, Scott’s slides and references are available online. The talk was part of the AMS Special Session on the Mathematics of RNA and DNA.

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