Reducing the complexity of mathematical models for the plant circadian clock by distributed delays

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.A major bottleneck in the modelling of biological networks is the parameter explosion problem – the exponential increase in the number of parameters that need to be optimised to data as the size of the model increases. Here, we address this problem in the context of the plant circadian clock by applying the method of distributed delays. We show that using this approach, the system architecture can be simplified efficiently – reducing the number of parameters – whilst still preserving the core mechanistic dynamics of the gene regulatory network. Compared to models with discrete time-delays, which are governed by functional differential equations, the distributed delay models can be converted into sets of equivalent ordinary differential equations, enabling the use of standard methods for numerical integration, and for stability and bifurcation analyses. We demonstrate the efficiency of our modelling approach by applying it to three exemplar mathematical models of the Arabidopsis circadian clock of varying complexity, obtaining significant reductions in complexity in each case. Moreover, we revise one of the most up-to-date Arabidopsis models, updating the regulation of the PRR9 and PRR7 genes by LHY in accordance with recent experimental data. The revised model more accurately reproduces the LHY-induction experiments of core clock genes, compared with the original model. Our work thus shows that the method of distributed delays facilitates the optimisation and reformulation of genetic network models.Engineering and Physical Sciences Research Council (EPSRC)Japan Society for the Promotion of Science (JSPS)Gatsby Foundatio

Expression of emotional arousal in two different piglet call types

Humans as well as many animal species reveal their emotional state in their voice. Vocal features show strikingly similar correlation patterns with emotional states across mammalian species, suggesting that the vocal expression of emotion follows highly conserved signalling rules. To fully understand the principles of emotional signalling in mammals it is, however, necessary to also account for any inconsistencies in the way that they are acoustically encoded. Here we investigate whether the expression of emotions differs between call types produced by the same species. We compare the acoustic structure of two common piglet calls—the scream (a distress call) and the grunt (a contact call)—across three levels of arousal in a negative situation. We find that while the central frequency of calls increases with arousal in both call types, the amplitude and tonal quality (harmonic-to-noise ratio) show contrasting patterns: as arousal increased, the intensity also increased in screams, but not in grunts, while the harmonicity increased in screams but decreased in grunts. Our results suggest that the expression of arousal depends on the function and acoustic specificity of the call type. The fact that more vocal features varied with arousal in scream calls than in grunts is consistent with the idea that distress calls have evolved to convey information about emotional arousal

Mechanism of and Threshold Biomechanical Conditions for Falsetto Voice Onset

The sound source of a voice is produced by the self-excited oscillation of the vocal folds. In modal voice production, a drastic increase in transglottal pressure after vocal fold closure works as a driving force that develops self-excitation. Another type of vocal fold oscillation with less pronounced glottal closure observed in falsetto voice production has been accounted for by the mucosal wave theory. The classical theory assumes a quasi-steady flow, and the expected driving force onto the vocal folds under wavelike motion is derived from the Bernoulli effect. However, wavelike motion is not always observed during falsetto voice production. More importantly, the application of the quasi-steady assumption to a falsetto voice with a fundamental frequency of several hundred hertz is unsupported by experiments. These considerations suggested that the mechanism of falsetto voice onset may be essentially different from that explained by the mucosal wave theory. In this paper, an alternative mechanism is submitted that explains how self-excitation reminiscent of the falsetto voice could be produced independent of the glottal closure and wavelike motion. This new explanation is derived through analytical procedures by employing only general unsteady equations of motion for flow and solids. The analysis demonstrated that a convective acceleration of a flow induced by rapid wall movement functions as a negative damping force, leading to the self-excitation of the vocal folds. The critical subglottal pressure and volume flow are expressed as functions of vocal fold biomechanical properties, geometry, and voice fundamental frequency. The analytically derived conditions are qualitatively and quantitatively reasonable in view of reported measurement data of the thresholds required for falsetto voice onset. Understanding of the voice onset mechanism and the explicit mathematical descriptions of thresholds would be beneficial for the diagnosis and treatment of voice diseases and the development of artificial vocal folds