021 Cost functional dependence of optimal CPA equilibration trajectories

Abstract

Rapid and safe equilibration of cells with and from high concentrations of permeating solutes is of great interest to cryobiologists. This equilibration is limited by at least two competing factors: cells and tissues have volume or concentration constraints (known as osmotic tolerance limits) and the toxicity of permeating solutes is considered to be a monotonically increasing function of exposure time. Because of this, there has been considerable effort to establish equilibration protocols that minimize time of exposure while keeping cells within known bounds. Our approach has been to define the concept of an equilibration damage cost function that depends on the cellular state during the entire equilibration protocol, namely its CPA equilibration state space trajectory. We recently cast and solved this problem formally in terms of the mathematical theory of optimal control, determining extracellular CPA and nonpermeating solute concentrations that minimize a cost function of total protocol time. While it has been hypothesized that the equilibration damage cost function should also depend on intracellular concentration, the precise dependence has not yet been determined. Here we extend our recent work by mathematically determining the dependence of optimal CPA equilibration state space trajectories for classes of cost functions, defining optimal extracellular CPA and nonpermeating solute concentrations. We are able to show that there are fundamental classes of toxicity cost functions that correspond to a limited number of optimal equilibration trajectories, indicating that the precise determination of the toxicity cost function (e.g. cellular damage as a function of concentration and time) is not as important as its class membership (e.g. does the damage depend super or sublinearly as a function of concentration). In other words, we are able to mathematically determine optimal CPA equilibration protocols given relatively few cell specific parameters. Source of funding: None declared. Conflict of interest: None declared. benson@math.niu.edu