Further analysis of open-respirometry systems: an a-compartmental mechanistic approach

A system is said to be "instantaneous" when for a given constant input an equilibrium output is obtained after a while. In the meantime, the output is changing from its initial value towards the equilibrium one. This is the transient period of the system and transients are important features of open-respirometry systems. During transients, one cannot compute the input amplitude directly from the output. The existing models (e.g., first or second order dynamics) cannot account for many of the features observed in real open-respirometry systems, such as time lag. Also, these models do not explain what should be expected when a system is speeded up or slowed down. The purpose of the present study was to develop a mechanistic approach to the dynamics of open-respirometry systems, employing basic thermodynamic concepts. It is demonstrated that all the main relevant features of the output dynamics are due to and can be adequately explained by a distribution of apparent velocities within the set of molecules travelling along the system. The importance of the rate at which the molecules leave the sensor is explored for the first time. The study approaches the difference in calibrating a system with a continuous input and with a "unit impulse": the former truly reveals the dynamics of the system while the latter represents the first derivative (in time) of the former and, thus, cannot adequately be employed in the apparent time-constant determination. Also, we demonstrate why the apparent order of the output changes with volume or flow.