Thermodynamics and kinetics of intracellular ice formation during freezing of biological cells

Abstract

A physicochemical model based on the modified classical heterogeneous nucleation theory was proposed to analyze the ice formation inside biological cells during freezing. According to this model, intracellular ice formation (IIF) may be catalyzed either by the plasma membrane via the effects of the external ice on the plasma membrane, called surface-catalyzed nucleation (SCN), or by the intracellular particles, called volume-catalyzed nucleation (VCN), depending on the freezing conditions. The model for IIF was coupled with the model describing the kinetics of water transport to predict the thermodynamic state of the cytoplasm. A method to estimate the nucleation frequency from the observed probability of nucleation was suggested. This method was based on the assumption that each cell has the same heteronucleating particles with identical properties to alter the nucleation kinetics in an identical way. This allowed the correlation of the experimental probability of IIF with the nucleation rate. It was suggested that the uncertainties in the experimental conditions could be minimized if cells were cooled at rapid rates to prevent water transport during freezing. The model was applied to mouse oocytes at metaphase II. Correlation of the theory with the experimental kinetics of the cumulative fraction of IIF revealed preexponentional factors of 3.56×108 (m2 s)−1 and 1.84×1050 (m3 s)−1, and exponential factors of 4.6×109 and 1.08×1012 K5 for SCN and VCN, respectively. The contact angle between the internal surface of the plasma membrane and the ice cluster for SCN, θ, was determined to be 35° for freezing in isotonic solutions (285 mosm) increasing linearly to 47° in hypertonic solutions (1035 mosm). SCN was active between ∼−5 and −20 °C in the presence of external ice. It is suggested that the presence of external ice alters the plasma membrane through its chemical, electrical, mechanical, ionic, and thermal effects, to make it an energetically favorable site for heterogeneous nucleation. For VCN, lower and upper limits for θ and R were found to be 60°<θ<100° and 10−7<R<4×10−7 cm, respectively. VCN was active between ∼−30 and −35 °C.