Exploring the role of the Kölliker-Fuse nucleus in breathing variability by mathematical modelling.

The Kölliker-Fuse nucleus (KF), which is part of the parabrachial complex, participates in the generation of eupnoea under resting conditions and the control of active abdominal expiration when increased ventilation is required. Moreover, dysfunctions in KF neuronal activity are believed to play a role in the emergence of respiratory abnormalities seen in Rett syndrome (RTT), a progressive neurodevelopmental disorder associated with an irregular breathing pattern and frequent apnoeas. Relatively little is known, however, about the intrinsic dynamics of neurons within the KF and how their synaptic connections affect breathing pattern control and contribute to breathing irregularities. In this study, we use a reduced computational model to consider several dynamical regimes of KF activity paired with different input sources to determine which combinations are compatible with known experimental observations. We further build on these findings to identify possible interactions between the KF and other components of the respiratory neural circuitry. Specifically, we present two models that both simulate eupnoeic as well as RTT-like breathing phenotypes. Using nullcline analysis, we identify the types of inhibitory inputs to the KF leading to RTT-like respiratory patterns and suggest possible KF local circuit organizations. When the identified properties are present, the two models also exhibit quantal acceleration of late-expiratory activity, a hallmark of active expiration featuring forced exhalation, with increasing inhibition to KF, as reported experimentally. Hence, these models instantiate plausible hypotheses about possible KF dynamics and forms of local network interactions, thus providing a general framework as well as specific predictions for future experimental testing. KEY POINTS: The Kölliker-Fuse nucleus (KF), a part of the parabrachial complex, is involved in regulating normal breathing and controlling active abdominal expiration during increased ventilation. Dysfunction in KF neuronal activity is thought to contribute to respiratory abnormalities seen in Rett syndrome (RTT). This study utilizes computational modelling to explore different dynamical regimes of KF activity and their compatibility with experimental observations. By analysing different model configurations, the study identifies inhibitory inputs to the KF that lead to RTT-like respiratory patterns and proposes potential KF local circuit organizations. Two models are presented that simulate both normal breathing and RTT-like breathing patterns. These models provide testable hypotheses and specific predictions for future experimental investigations, offering a general framework for understanding KF dynamics and potential network interactions.

The role of Kölliker-Fuse nucleus in breathing variability.

The Kölliker-Fuse nucleus (KF), which is part of the parabrachial complex, participates in the generation of eupnea under resting conditions and the control of active abdominal expiration when increased ventilation is required. Moreover, dysfunctions in KF neuronal activity are believed to play a role in the emergence of respiratory abnormalities seen in Rett syndrome (RTT), a progressive neurodevelopmental disorder associated with an irregular breathing pattern and frequent apneas. Relatively little is known, however, about the intrinsic dynamics of neurons within the KF and how their synaptic connections affect breathing pattern control and contribute to breathing irregularities. In this study, we use a reduced computational model to consider several dynamical regimes of KF activity paired with different input sources to determine which combinations are compatible with known experimental observations. We further build on these findings to identify possible interactions between the KF and other components of the respiratory neural circuitry. Specifically, we present two models that both simulate eupneic as well as RTT-like breathing phenotypes. Using nullcline analysis, we identify the types of inhibitory inputs to the KF leading to RTT-like respiratory patterns and suggest possible KF local circuit organizations. When the identified properties are present, the two models also exhibit quantal acceleration of late-expiratory activity, a hallmark of active expiration featuring forced exhalation, with increasing inhibition to KF, as reported experimentally. Hence, these models instantiate plausible hypotheses about possible KF dynamics and forms of local network interactions, thus providing a general framework as well as specific predictions for future experimental testing. Key points: The Kölliker-Fuse nucleus (KF), a part of the parabrachial complex, is involved in regulating normal breathing and controlling active abdominal expiration during increased ventilation. Dysfunction in KF neuronal activity is thought to contribute to respiratory abnormalities seen in Rett syndrome (RTT). This study utilizes computational modeling to explore different dynamical regimes of KF activity and their compatibility with experimental observations. By analyzing different model configurations, the study identifies inhibitory inputs to the KF that lead to RTT-like respiratory patterns and proposes potential KF local circuit organizations. Two models are presented that simulate both normal breathing and RTT-like breathing patterns. These models provide plausible hypotheses and specific predictions for future experimental investigations, offering a general framework for understanding KF dynamics and potential network interactions.

Frontal plane dynamics of the centre of mass during quadrupedal locomotion on a split-belt treadmill.

Our previous study of cat locomotion demonstrated that lateral displacements of the centre of mass (COM) were strikingly similar to those of human walking and resembled the behaviour of an inverted pendulum (Park et al. 2019 J. Exp. Biol.222, 14. (doi:10.1242/jeb.198648)). Here, we tested the hypothesis that frontal plane dynamics of quadrupedal locomotion are consistent with an inverted pendulum model. We developed a simple mathematical model of balance control in the frontal plane based on an inverted pendulum and compared model behaviour with that of four cats locomoting on a split-belt treadmill. The model accurately reproduced the lateral oscillations of cats' COM vertical projection. We inferred the effects of experimental perturbations on the limits of dynamic stability using data from different split-belt speed ratios with and without ipsilateral paw anaesthesia. We found that the effect of paw anaesthesia could be explained by the induced bias in the perceived position of the COM, and the magnitude of this bias depends on the belt speed difference. Altogether, our findings suggest that the balance control system is actively involved in cat locomotion to provide dynamic stability in the frontal plane, and that paw cutaneous receptors contribute to the representation of the COM position in the nervous system.

Random dynamical models from time series.

In this work we formulate a consistent Bayesian approach to modeling stochastic (random) dynamical systems by time series and implement it by means of artificial neural networks. The feasibility of this approach for both creating models adequately reproducing the observed stationary regime of system evolution, and predicting changes in qualitative behavior of a weakly nonautonomous stochastic system, is demonstrated on model examples. In particular, a successful prognosis of stochastic system behavior as compared to the observed one is illustrated on model examples, including discrete maps disturbed by non-Gaussian and nonuniform noise and a flow system with Langevin force.

Prognosis of qualitative system behavior by noisy, nonstationary, chaotic time series.

An approach to prognosis of qualitative behavior of an unknown dynamical system (DS) from weakly nonstationary chaotic time series (TS) containing significant measurement noise is proposed. The approach is based on construction of a global time-dependent parametrized model of discrete evolution operator (EO) capable of reproducing nonstationary dynamics of a reconstructed DS. A universal model in the form of artificial neural network (ANN) with certain prior limitations is used for the approximation of the EO in the reconstructed phase space. Probabilistic prognosis of the system behavior is performed using Monte Carlo Markov chain (MCMC) analysis of the posterior Bayesian distribution of the model parameters. The classification of qualitatively different regimes is supposed to be dictated by the application, i.e., it is assumed that some classifier function is predefined that maps a point of a model parameter space to a finite set of different behavior types. The ability of the approach to provide prognosis for times comparable to the observation time interval is demonstrated. Some restrictions as well as possible advances of the proposed approach are discussed.

Investigation of nonlinear dynamical properties by the observed complex behaviour as a basis for construction of dynamical models of atmospheric photochemical systems.

The importance of the investigation of nonlinear dynamical properties (NDPs) of the atmospheric photochemical systems (PCSs) was demonstrated in ref. 1 and 2 (A. M. Feigin and I. B. Konovalov, J. Geophys. Res., 1996, 101 (D20), 26038; 1. B. Konovalov, A. M. Feigin and A. Y. Mukhina, J. Geophys. Res., 1999, 104 (D3), 3669). The only known way to study NDPs of any natural dynamical system (including atmospheric PCSs) is to construct a mathematical model of the system. The key point here is adequacy of the NDPs of the constructed model to the system observed. We propose a new approach to construction of such an adequate model for systems manifesting nonstationary chaotic behaviour and describe an algorithm based exclusively on nonlinear dynamical analysis of the observed time series (TS) without invoking any a priori knowledge about the properties of the system observed. Potentialities of the algorithm are demonstrated with the aid of a computer model of the mesospheric PCS. The duration of the "observed" TS is limited so that the system demonstrates only one--chaotic--type of behaviour, without any bifurcations throughout the observed TS. The proposed algorithm enabled us to make a correct prognosis of bifurcation sequences and calculate probabilities to reveal, at the time instant of interest, predicted regimes of the system's behaviour for times much greater than the length of the initial TS.