Thermal hysteresis of antifreeze proteins considering Fragilariopsis cylindrus

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The diatom species Fragilariopsis cylindrus produces antifreeze proteins (AFPs) of moderate thermal hysteresis. Two concepts are often used in order to describe a thermal hysteresis, on the one hand the irreversible nucleation growth described by the Gibbs-Thomson relation and on the other hand a nonlinear adsorption kinetics of the ice-binding proteins. We refer to the Landau's phase transition theory and predict a saturation concentration of AFPs for the maximal freezing depression. The derived functional relation between temperature and AFP concentration is more complex than a simple power law as suggested by thermal hysteresis experiments. With the parameter set obtained for Fragilariopsis cylindrus the modelled curve is comparable with the often used square root law.