Interactions between discrete events and continuous dynamics in the regulation of scallops valve opening: insights from a biophysical model

Abstract

This study constitutes a first attempt to quantify processes that govern valve gape dynamics in bivalves. We elected to focus on the scallop, Pecten maximus, not only because of its economic importance but also because it has a complex behaviour and high sensitivity to stress, which can be inferred from valve gape dynamics. The adductor muscle is the primary organ implicated in valve movements. Scallops, as other bivalves, move their valves sharply to ensure basic physiological functions or to respond to stressing conditions; these sharp events can be perceived as discrete events within a continuous dynamic. A biophysical model, originally designed for human muscles, was first selected to simulate the adductor muscle contraction, countering the passive valve opening by the umbo ligament. However, to maintain the possibility of rapid valve movements, described as typical of bivalves behaviour, it was necessary to modify the model and propose an original formulation. The resulting hybrid modelling simulates how valve opening tends to converge continuously toward a stable steady-state angle, while being interspersed with discrete, sharp closing events, deviating values from this equilibrium. The parameters of the new model were estimated by optimization using Hall-Effect Sensor valvometry data recorded in controlled conditions. Equilibrium of the continuous regime (when fiber activation equals deactivation) was estimated for a gape angle close to ca. 15 degrees, which is ca. 45% of the maximum opening angle, hence implying a constant effort produced by the adductor muscle. The distribution of time intervals between two successive discrete events did not differ significantly from a random process, but the peak amplitudes deviated from randomness, suggesting they are regulated physiologically. These results suggest that discrete events interact with continuous dynamic regimes, regulating valve opening to minimize physiological efforts and conserve energy. However, because the overall physiological state of the scallop organism conditions the activity of the adductor muscle, a complete understanding of the physiology of bivalves will require linking a more comprehensive model of valve gape dynamics with experimental observations of physiological energy consumption under different conditions.