University of Cambridge > > Biological and Biomedical Physics > Controlling the speed and trajectory of evolution with counterdiabatic driving: applications to human disease and expanding populations

Controlling the speed and trajectory of evolution with counterdiabatic driving: applications to human disease and expanding populations

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Most mature models of disease evolution have had the stated end-goal of predicting evolutionary trajectories, and have not even approached the problem of fine grained control. Part of the problem has been a relative lack of formal connections of classical models of population genetics to systems which permit even a degree of control. To address this, we have worked to formally transform one of the governing models in population genetics—the multi-type Wright-Fisher Model—into a Fokker-Planck approximation: a fully resolved, time dependent partial differential equation on a realistic genotype space. This approximation has allowed us to borrow results originally developed in a completely different context – counterdiabatic driving to control the behavior of quantum states for applications like quantum computing and manipulating ultra-cold atoms—and apply them to a cancer or pathogens searching for a fitness optima under therapy. Implementing these ideas for the first time in a biological context, we show how a set of external control parameters (i.e. varying drug concentrations / types, temperature, nutrients) can guide the probability distribution of genotypes in a population along a specified path and on a finite, clinically-relevant timescale. We develop a closed form ‘control protocol’ from real world data derived from a genetically engineered yeast system under the selective pressure of anti-microbial agents, and show that in individual based simulations, and numerical solutions, the control protocol allows us to control the speed and trajectory of evolution in a 4-allele system.

In order to approach applicability to real-world, spatially distributed populations, in the second part of the talk, I will describe our efforts to study the changing evolutionary dynamics along the front of an advancing wave of unicellular organisms (or cells) as they expand their population in space. Using stochastic partial differential equations, we explore the length scales at which various characteristic evolutionary regimes are concurrently maintained. The ramifications of these changing evolutionary dynamics in spreading populations on evolutionary control will be discussed as well.

This talk is part of the Biological and Biomedical Physics series.

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