A computational model of insect discontinuous gas exchange: A two-sensor, control systems approach

- We model insect respiration using interacting O2 and CO2/pH control systems.
- Realistic respiration patterns and pH and CO2 fluctuations are generated.
- A prolonged open spiracle phase cannot be governed by a single pH threshold.
- Hysteresis in the CO2/pH system is key to generating realistic model results.

The insect gas exchange system is characterised by branching air-filled tubes (tracheae/tracheoles) and valve-like structures in their outer integument (spiracles) which allow for a periodic gas exchange pattern known as the discontinuous gas exchange cycle (DGC). The DGC facilitates the temporal decoupling of whole animal gas exchange from cellular respiration rates and may confer several physiological benefits, which are nevertheless highly controversial (primarily reduction of cellular oxidative damage and/or respiratory water saving). The intrinsic and extrinsic factors influencing DGCs are the focus of extensive ongoing research and little consensus has been reached on the evolutionary genesis or mechanistic costs and benefits of the pattern. Despite several hypotheses and much experimental and evolutionary biology research, a mechanistic physical model, which captures various key elements of the DGC pattern, is currently lacking. Here, we present a biologically realistic computational, two-sensor DGC model (pH/carbon dioxide and oxygen setpoints) for an Orthopteran gas exchange system, and show computationally for the first time that a control system of two interacting feedback loops is capable of generating a full DGC pattern with outputs which are physiologically realistic, quantitatively matching experimental results found in this taxonomic model elsewhere. A finite-element mathematical approach is employed and various trigger sets are considered. Parameter sensitivity analyses suggest that various aspects of insect DGC are adequately captured in this model. In particular, with physiologically relevant input parameters, the full DGC pattern is induced; and the phase durations, endotracheal carbon dioxide partial pressure ranges, and pH fluctuations which arise are physically realistic. The model results support the emergent property hypothesis for the existence of DGC, and indicate that asymmetric loading and off-loading (hysteresis) in one of the sensor feedback loops, which is a novel inclusion here, is a critical aspect of the insect spiracle-tracheal gas exchange system.