131 Proposal of reaction kinetic model for cell death due to extracellular freezing based on two-factor hypothesis

Abstract

Post-thaw cell viability (CV) as a function of cooling rate generally shows the bell-shaped distribution with an optimal cooling rate. The characteristic distribution is understood on the basis of a two-factor hypothesis, i.e. the cell damage is caused by two factors: the intracellular freezing (IIF) and the extracellular freezing (EIF) without IIF [Mazur, P. et al., Experimental Cell Research 71 (1972) 345–355]. Mathematical description and prediction of the cell survival curve (CSC) is one of important problems in the area of cryobiology. Contribution to the cell death by IIF was already modelled successfully based on nucleation in the cells [Toner, M. et al., J. Appl. Phys., 67(3) (1990) 1582–1593]. In the present study, a reaction kinetic model was proposed to describe the cell death caused due to EIF without IIF. According to the two-factor hypothesis, the post-thaw cells are classified by freezing pattern into two categories: those with IIF experience and those with only EIF and no IIF experience. The former is regarded as dead, and the latter consists of live and dead cells. Regarding the cells with only EIF as a population, the model to describe mathematically CV of the population as a function of cooling rate was developed on the basis of phenomenological investigation of CV without considering the mechanisms of cell damage and death. Four assumptions for the modelling were made as follows: (1) Cell damage and death are described as one overall reaction kinetic process, (2) Cells have three states: normal, damaged (but still alive) (intermediate state) and dead, (3) Cells change from normal state through damaged into dead, (4) Change rate of the number of cells is expressed by the first-order reaction. Rate constants for the changes in the number of cells were assumed to depend on the time elapsed during the freezing and thawing. Also, the simplest formulation was investigated for comparison: cells changed from normal directly into dead. Conservation equations of the number of cells in each state, were expressed by a set of simultaneous first-order linear ordinary differential equations. Under the condition that all the cells were initially normal, analytical solutions of CV of the population were found for the rate constants depending on time. On condition of constant cooling rate, the time integral of rate constant in the solutions was changed into a temperature integral of it, and a value of the latter was defined as a model constant. Therefore, a basic function of cooling rate for CSC was found. Further, three functions with cooling rate modified by another model constant for CSC were also proposed. A parameter study of model constants was performed to evaluate CSC as a function cooling rate. The model constants were also determined by inverse problem analysis based on the experiment with human erythrocytes [MAZUR, P., Am. J. Physiol. 247, C125–C142 (1984)] as the experimental data on the viability of the cells with only EIF were unavailable. The experiment and prediction by the model were compared on CSC. The result shows that EIF-induced cell death is successfully described by the reaction kinetic mode. Source of funding: Grant-in-Aid for Scientific Research #24360083 and #21360098 to H.I. from Japan Society for the Promotion of Science. Conflict of interest: None declared. ishiguro@life.kyutech.ac.jp