Multiple Pareto-optimal solutions of the dissipation-adaptation trade-off

Abstract

Adaptation refers to the ability to recover and maintain ``normal'' function upon perturbations of internal or external conditions and is essential for sustaining life. Biological adaptation mechanisms are dissipative, i.e. they require a supply of energy such as the coupling to the hydrolysis of ATP. Via evolution the underlying biochemical machinery of living organisms evolved into highly optimized states. However, in the case of adaptation processes two quantities are optimized simultaneously, the adaptation speed or accuracy and the thermodynamic cost. In such cases one typically faces a trade-off, where improving one quantity implies worsening the other. The solution is no longer unique but rather a Pareto set -- the set of all physically attainable protocols along which no quantity can be improved without worsening another. Here we investigate Pareto fronts in adaptation-dissipation trade-offs for a cellular thermostat and a minimal ATP-driven receptor-ligand reaction network. We find convex sections of Pareto fronts to be interrupted by concave regions, implying the coexistence of distinct optimization mechanisms. We discuss the implications of such ``compromise-optimal'' solutions and argue that they may endow biological systems with a superior flexibility to evolve, resist, and adapt to different environments.

14 pages, 7 figures

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