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.

Designing the Next Generation of Condition Tracking and Early Warning Systems for Shellfish Aquaculture

“…This involves not only studying co-occurrences of the discrete event, but also the distribution of time between two events and the deviation from a null model. In our previous valvometry study with scallops [30], we found that under controlled constant conditions, the occurrence dynamics of single closing events could not be distinguished from a pure, stochastic process; there was an average occurrence rate of approximatively 2.4 h −1 . This was confirmed by the fact that the observed probability distribution of time intervals between two events did not deviate significantly from an exponential law.…”

“…Therefore, only one electrical cable links the HES to the data acquisition device. There are, however, some disadvantages specific to this type of sensor [1,30]:…”

“…The first task of the optimization process was to develop an accurate method to detect peaks (occurrence, frequency, and amplitude). We applied a method to detect peaks, based on the variation of speed and turning points [30]. To verify the accuracy of this method, we simulated time series using the model, then applied the method and compared the results of detection with the discrete events time imposed in the simulations.…”

“…The main challenge of the optimization process is that {Q, r, s, a} cannot be determined from valvometry measurements alone [30]. Ancillary experimental data of direct measurements of the muscle activity and related forces that are generated should be measured for the species of interest.…”

“…This system aims to assess the physiological state of the organisms, while identifying local or global sources of disturbances. For this, we use a quantitative modeling framework designed to simulate valve gape dynamics as an indicator of their physiological state [30]. In this earlier study, we quantified bivalve gape dynamics based on biophysical processes that govern opening and closing of the shell.…”