Engaging biological oscillators through second messenger pathways permits emergence of a robust gastric slow-wave during peristalsis

Peristalsis, the coordinated contraction—relaxation of the muscles of the stomach is important for normal gastric motility and is impaired in motility disorders. Coordinated electrical depolarizations that originate and propagate within a network of interconnected layers of interstitial cells of Cajal (ICC) and smooth muscle (SM) cells of the stomach wall as a slow-wave, underly peristalsis. Normally, the gastric slow-wave oscillates with a single period and uniform rostrocaudal lag, exhibiting network entrainment. Understanding of the integrative role of neurotransmission and intercellular coupling in the propagation of an entrained gastric slow-wave, important for understanding motility disorders, however, remains incomplete. Using a computational framework constituted of a novel gastric motility network (GMN) model we address the hypothesis that engaging biological oscillators (i.e., ICCs) by constitutive gap junction coupling mechanisms and enteric neural innervation activated signals can confer a robust entrained gastric slow-wave. We demonstrate that while a decreasing enteric neural innervation gradient that modulates the intracellular IP3 concentration in the ICCs can guide the aboral slow-wave propagation essential for peristalsis, engaging ICCs by recruiting the exchange of second messengers (inositol trisphosphate (IP3) and Ca2+) ensures a robust entrained longitudinal slow-wave, even in the presence of biological variability in electrical coupling strengths. Our GMN with the distinct intercellular coupling in conjunction with the intracellular feedback pathways and a rostrocaudal enteric neural innervation gradient allows gastric slow waves to oscillate with a moderate range of frequencies and to propagate with a broad range of velocities, thus preventing decoupling observed in motility disorders. Overall, the findings provide a mechanistic explanation for the emergence of decoupled slow waves associated with motility impairments of the stomach, offer directions for future experiments and theoretical work, and can potentially aid in the design of new interventional pharmacological and neuromodulation device treatments for addressing gastric motility disorders.

Modelling Oscillatory Patterns in the Bovine Estrous Cycle with Boolean Delay Equations

Boolean delay equations (BDEs), with their relatively simple and intuitive mode of modelling, have been used in many research areas including, for example, climate dynamics and earthquake propagation. Their application to biological systems has been scarce and limited to the molecular level. Here, we derive and present two BDE models. One is directly derived from a previously published ordinary differential equation (ODE) model for the bovine estrous cycle, whereas the second model includes a modification of a particular biological mechanism. We not only compare the simulation results from the BDE models with the trajectories of the ODE model, but also validate the BDE models with two additional numerical experiments. One experiment induces a switch in the oscillatory pattern upon changes in the model parameters, and the other simulates the administration of a hormone that is known to shift the estrous cycle in time. The models presented here are the first BDE models for hormonal oscillators, and the first BDE models for drug administration. Even though automatic parameter estimation still remains challenging, our results support the role of BDEs as a framework for the systematic modelling of complex biological oscillators.

A frequency-amplitude coordinator and its optimal energy consumption for biological oscillators

Biorhythm including neuron firing and protein-mRNA interaction are fundamental activities with diffusive effect. Their well-balanced spatiotemporal dynamics are beneficial for healthy sustainability. Therefore, calibrating both anomalous frequency and amplitude of biorhythm prevents physiological dysfunctions or diseases. However, many works were devoted to modulate frequency exclusively whereas amplitude is usually ignored, although both quantities are equally significant for coordinating biological functions and outputs. Especially, a feasible method coordinating the two quantities concurrently and precisely is still lacking. Here, for the first time, we propose a universal approach to design a frequency-amplitude coordinator rigorously via dynamical systems tools. We consider both spatial and temporal information. With a single well-designed coordinator, they can be calibrated to desired levels simultaneously and precisely. The practical usefulness and efficacy of our method are demonstrated in representative neuronal and gene regulatory models. We further reveal its fundamental mechanism and optimal energy consumption providing inspiration for biorhythm regulation in future.

Engaging Biological Oscillators through Second Messenger Pathways Permits Emergence of a Robust Gastric Slow-Wave during Peristalsis

Peristalsis, the coordinated contraction-relaxation of the muscles of the stomach, is important for normal gastric motility and is impaired in motility disorders. Coordinated electrical depolarizations that originate and propagate within a network of interconnected layers of interstitial cells of Cajal (ICC) and smooth muscle (SM) cells of the stomach wall as a slow-wave, underly peristalsis. Normally, the gastric slow-wave oscillates with a single period and uniform rostrocaudal lag, exhibiting network entrainment. Understanding of the integrative role of neurotransmission and intercellular coupling in the propagation of an entrained gastric slow-wave, important for understanding motility disorders, however, remains incomplete. Using a computational framework constituted of a novel gastric motility network (GMN) model we address the hypothesis that engaging biological oscillators (i.e., ICCs) by constitutive gap junction coupling mechanisms and enteric neural stimulus activated signals can confer a robust entrained gastric slow-wave. We demonstrate that while a decreasing enteric neural stimulus gradient that modulates the intracellular IP3 concentration in the ICCs can guide the aboral slow-wave propagation essential for peristalsis, engaging ICCs by recruiting the exchange of second messengers (inositol trisphosphate (IP3) and Ca2+) ensures a robust entrained longitudinal slow-wave, even in the presence of biological variability in coupling strengths. Our GMN with the distinct intercellular coupling in conjunction with the intracellular feedback pathways and a rostrocaudal enteric neural stimulus gradient allows gastric slow waves to oscillate with a moderate range of frequencies and to propagate with a broad range of velocities, thus preventing decoupling observed in motility disorders. Overall, the findings provide a mechanistic explanation for the emergence of decoupled slow waves associated with motility impairments of the stomach, offer directions for future experiments and theoretical work, and can potentially aid in the design of new interventional pharmacological and neuromodulation device treatments for addressing gastric motility disorders.