Hyperhidrosis in sleep disorders - A narrative review of mechanisms and clinical significance

Hyperhidrosis is characterized by excessive sweating beyond thermoregulatory needs that affects patients' quality of life. It results from an excessive stimulation of eccrine sweat glands in the skin by the sympathetic nervous system. Hyperhidrosis may be primary or secondary to an underlying cause. Nocturnal hyperhidrosis is associated with different sleep disorders, such as obstructive sleep apnea, insomnia, restless legs syndrome/periodic limb movement during sleep and narcolepsy. The major cause of the hyperhidrosis is sympathetic overactivity and, in the case of narcolepsy type 1, orexin deficiency may also contribute. In this narrative review, we will provide an outline of the possible mechanisms underlying sudomotor dysfunction and the resulting nocturnal hyperhidrosis in these different sleep disorders and explore its clinical relevance.

The Sleep Revolution project: the concept and objectives

Obstructive sleep apnea is linked to severe health consequences such as hypertension, daytime sleepiness, and cardiovascular disease. Nearly a billion people are estimated to have obstructive sleep apnea with a substantial economic burden. However, the current diagnostic parameter of obstructive sleep apnea, the apnea-hypopnea index, correlates poorly with related comorbidities and symptoms. Obstructive sleep apnea severity is measured by counting respiratory events, while other physiologically relevant consequences are ignored. Furthermore, as the clinical methods for analysing polysomnographic signals are outdated, laborious, and expensive, most patients with obstructive sleep apnea remain undiagnosed. Therefore, more personalised diagnostic approaches are urgently needed. The Sleep Revolution, funded by the European Union's Horizon 2020 Research and Innovation Programme, aims to tackle these shortcomings by developing machine learning tools to better estimate obstructive sleep apnea severity and phenotypes. This allows for improved personalised treatment options, including increased patient participation. Also, implementing these tools will alleviate the costs and increase the availability of sleep studies by decreasing manual scoring labour. Finally, the project aims to design a digital platform that functions as a bridge between researchers, patients, and clinicians, with an electronic sleep diary, objective cognitive tests, and questionnaires in a mobile application. These ambitious goals will be achieved through extensive collaboration between 39 centres, including expertise from sleep medicine, computer science, and industry and by utilising tens of thousands of retrospectively and prospectively collected sleep recordings. With the commitment of the European Sleep Research Society and Assembly of National Sleep Societies, the Sleep Revolution has the unique possibility to create new standardised guidelines for sleep medicine.

Importance of Getting Enough Sleep and Daily Activity Data to Assess Variability: Longitudinal Observational Study

Background

The gold standard measurement for recording sleep is polysomnography performed in a hospital environment for 1 night. This requires individuals to sleep with a device and several sensors attached to their face, scalp, and body, which is both cumbersome and expensive. Self-trackers, such as wearable sensors (eg, smartwatch) and nearable sensors (eg, sleep mattress), can measure a broad range of physiological parameters related to free-living sleep conditions; however, the optimal duration of such a self-tracker measurement is not known. For such free-living sleep studies with actigraphy, 3 to 14 days of data collection are typically used.

Objective

The primary goal of this study is to investigate if 3 to 14 days of sleep data collection is sufficient while using self-trackers. The secondary goal is to investigate whether there is a relationship among sleep quality, physical activity, and heart rate. Specifically, we study whether individuals who exhibit similar activity can be clustered together and to what extent the sleep patterns of individuals in relation to seasonality vary.

Methods

Data on sleep, physical activity, and heart rate were collected over 6 months from 54 individuals aged 52 to 86 years. The Withings Aura sleep mattress (nearable; Withings Inc) and Withings Steel HR smartwatch (wearable; Withings Inc) were used. At the individual level, we investigated the consistency of various physical activities and sleep metrics over different time spans to illustrate how sensor data from self-trackers can be used to illuminate trends. We used exploratory data analysis and unsupervised machine learning at both the cohort and individual levels.

Results

Significant variability in standard metrics of sleep quality was found between different periods throughout the study. We showed specifically that to obtain more robust individual assessments of sleep and physical activity patterns through self-trackers, an evaluation period of >3 to 14 days is necessary. In addition, we found seasonal patterns in sleep data related to the changing of the clock for daylight saving time.

Conclusions

We demonstrate that >2 months’ worth of self-tracking data are needed to provide a representative summary of daily activity and sleep patterns. By doing so, we challenge the current standard of 3 to 14 days for sleep quality assessment and call for the rethinking of standards when collecting data for research purposes. Seasonal patterns and daylight saving time clock change are also important aspects that need to be taken into consideration when choosing a period for collecting data and designing studies on sleep. Furthermore, we suggest using self-trackers (wearable and nearable ones) to support longer-term evaluations of sleep and physical activity for research purposes and, possibly, clinical purposes in the future.

Computing enclosures for uncertain biochemical systems

In this study, the authors present a novel method that provides enclosures for state trajectories of a non-linear dynamical system with uncertainties in initial conditions and parameter values. It is based on solving positivity conditions by means of semi-definite programmes and sum of squares decompositions. The method accounts for the indeterminacy of kinetic parameters, measurement uncertainties and fluctuations in the reaction rates because of extrinsic noise. This is particularly useful in the field of systems biology when one seeks to determine model behaviour quantitatively or, if this is not possible, semiquantitatively. The authors also demonstrate the significance of the proposed method to model selection in biology. The authors illustrate the applicability of their method on the mitogen-activated protein kinase signalling pathway, which is an important and reoccurring network motif that apparently also plays a crucial role in the development of cancer.

Using noise for model-testing

For realistic models in molecular biology, you need to consider the noise in the cellular and intracellular environments. In this article, we present a novel approach for testing the validity of nonlinear models representing a biological system affected by noise. Our approach is based on results by Kushner and Øksendal and uses computational techniques that rely on efficient solvers. By providing analytically upper bounds for the exit probability of solution trajectories of a system from a particular set in the phase space, we can compare measurement data with this prediction and try to invalidate models with certain parameter values or noise properties. Thus, our approach complements the usual methods that are based on deterministic models. It is particularly useful in the field of reverse engineering in systems biology, when one seeks to determine model parameters and noise properties as we show in the Results section, where we applied the approach to examples of increasing complexity and to the Hog1 signalling pathway.

Feedback control architecture and the bacterial chemotaxis network

Bacteria move towards favourable and away from toxic environments by changing their swimming pattern. This response is regulated by the chemotaxis signalling pathway, which has an important feature: it uses feedback to ‘reset’ (adapt) the bacterial sensing ability, which allows the bacteria to sense a range of background environmental changes. The role of this feedback has been studied extensively in the simple chemotaxis pathway of Escherichia coli. However it has been recently found that the majority of bacteria have multiple chemotaxis homologues of the E. coli proteins, resulting in more complex pathways. In this paper we investigate the configuration and role of feedback in Rhodobacter sphaeroides, a bacterium containing multiple homologues of the chemotaxis proteins found in E. coli. Multiple proteins could produce different possible feedback configurations, each having different chemotactic performance qualities and levels of robustness to variations and uncertainties in biological parameters and to intracellular noise. We develop four models corresponding to different feedback configurations. Using a series of carefully designed experiments we discriminate between these models and invalidate three of them. When these models are examined in terms of robustness to noise and parametric uncertainties, we find that the non-invalidated model is superior to the others. Moreover, it has a ‘cascade control’ feedback architecture which is used extensively in engineering to improve system performance, including robustness. Given that the majority of bacteria are known to have multiple chemotaxis pathways, in this paper we show that some feedback architectures allow them to have better performance than others. In particular, cascade control may be an important feature in achieving robust functionality in more complex signalling pathways and in improving their performance.

Bacteria move towards favourable environments by changing their swimming pattern. An important feature of this response, which is called bacterial chemotaxis, is that their sensing ability remains independent of the background environment in which they find themselves. This feature has been studied extensively in the bacterium E. coli, which has a simple chemotaxis decision mechanism. However, it has been recently found that most bacteria could potentially have a much more complicated decision mechanism for this response. In this paper, we look at the chemotaxis behaviour of one such bacterium, R. sphaeroides. We develop mathematical models of possible decision mechanisms and undertake an experimental procedure to investigate their validity. We find that only one of four such models can explain the chemotaxis response in R. sphaeroides. Compared to the other models, this model corresponds to a decision mechanism that provides the bacterium with improved swimming performance over the others. Moreover, this decision mechanism has been used extensively to improve performance in several engineering systems. We suggest that this mechanism may play an important role in improving chemotactic performance in other bacteria and in other signalling pathways.

Discriminating between rival biochemical network models: three approaches to optimal experiment design

BACKGROUND

The success of molecular systems biology hinges on the ability to use computational models to design predictive experiments, and ultimately unravel underlying biological mechanisms. A problem commonly encountered in the computational modelling of biological networks is that alternative, structurally different models of similar complexity fit a set of experimental data equally well. In this case, more than one molecular mechanism can explain available data. In order to rule out the incorrect mechanisms, one needs to invalidate incorrect models. At this point, new experiments maximizing the difference between the measured values of alternative models should be proposed and conducted. Such experiments should be optimally designed to produce data that are most likely to invalidate incorrect model structures.

RESULTS

In this paper we develop methodologies for the optimal design of experiments with the aim of discriminating between different mathematical models of the same biological system. The first approach determines the 'best' initial condition that maximizes the L2 (energy) distance between the outputs of the rival models. In the second approach, we maximize the L2-distance of the outputs by designing the optimal external stimulus (input) profile of unit L2-norm. Our third method uses optimized structural changes (corresponding, for example, to parameter value changes reflecting gene knock-outs) to achieve the same goal. The numerical implementation of each method is considered in an example, signal processing in starving Dictyostelium amoebae.

CONCLUSIONS

Model-based design of experiments improves both the reliability and the efficiency of biochemical network model discrimination. This opens the way to model invalidation, which can be used to perfect our understanding of biochemical networks. Our general problem formulation together with the three proposed experiment design methods give the practitioner new tools for a systems biology approach to experiment design.

A model invalidation-based approach for elucidating biological signalling pathways, applied to the chemotaxis pathway in R. sphaeroides

Background

Developing methods for understanding the connectivity of signalling pathways is a major challenge in biological research. For this purpose, mathematical models are routinely developed based on experimental observations, which also allow the prediction of the system behaviour under different experimental conditions. Often, however, the same experimental data can be represented by several competing network models.

Results

In this paper, we developed a novel mathematical model/experiment design cycle to help determine the probable network connectivity by iteratively invalidating models corresponding to competing signalling pathways. To do this, we systematically design experiments in silico that discriminate best between models of the competing signalling pathways. The method determines the inputs and parameter perturbations that will differentiate best between model outputs, corresponding to what can be measured/observed experimentally. We applied our method to the unknown connectivities in the chemotaxis pathway of the bacterium Rhodobacter sphaeroides. We first developed several models of R. sphaeroides chemotaxis corresponding to different signalling networks, all of which are biologically plausible. Parameters in these models were fitted so that they all represented wild type data equally well. The models were then compared to current mutant data and some were invalidated. To discriminate between the remaining models we used ideas from control systems theory to determine efficiently in silico an input profile that would result in the biggest difference in model outputs. However, when we applied this input to the models, we found it to be insufficient for discrimination in silico. Thus, to achieve better discrimination, we determined the best change in initial conditions (total protein concentrations) as well as the best change in the input profile. The designed experiments were then performed on live cells and the resulting data used to invalidate all but one of the remaining candidate models.

Conclusion

We successfully applied our method to chemotaxis in R. sphaeroides and the results from the experiments designed using this methodology allowed us to invalidate all but one of the proposed network models. The methodology we present is general and can be applied to a range of other biological networks.

A new computational tool for establishing model parameter identifiability

We describe a novel method to establish a priori whether the parameters of a nonlinear dynamical system are identifiable--that is, whether they can be deduced from output data (experimental observations). This is an important question as usually identifiability is assumed, and parameters are sought without first establishing whether these can be inferred from a set of measurements. We highlight the connections between parameter identifiability and state observability. We show how observability criteria can be used to check for identifiability, and we use new, state of the art computational tools to implement our approach. Nonlinear dynamical systems are prevalent in systems biology, where they are often used to represent a biological system. Thus, examples from biology are used to illustrate our method.

Efficient, sparse biological network determination

BACKGROUND

Determining the interaction topology of biological systems is a topic that currently attracts significant research interest. Typical models for such systems take the form of differential equations that involve polynomial and rational functions. Such nonlinear models make the problem of determining the connectivity of biochemical networks from time-series experimental data much harder. The use of linear dynamics and linearization techniques that have been proposed in the past can circumvent this, but the general problem of developing efficient algorithms for models that provide more accurate system descriptions remains open.

RESULTS

We present a network determination algorithm that can treat model descriptions with polynomial and rational functions and which does not make use of linearization. For this purpose, we make use of the observation that biochemical networks are in general 'sparse' and minimize the 1-norm of the decision variables (sum of weighted network connections) while constraints keep the error between data and the network dynamics small. The emphasis of our methodology is on determining the interconnection topology rather than the specific reaction constants and it takes into account the necessary properties that a chemical reaction network should have - something that techniques based on linearization can not. The problem can be formulated as a Linear Program, a convex optimization problem, for which efficient algorithms are available that can treat large data sets efficiently and uncertainties in data or model parameters.

CONCLUSION

The presented methodology is able to predict with accuracy and efficiency the connectivity structure of a chemical reaction network with mass action kinetics and of a gene regulatory network from simulation data even if the dynamics of these systems are non-polynomial (rational) and uncertainties in the data are taken into account. It also produces a network structure that can explain the real experimental data of L. lactis and is similar to the one found in the literature. Numerical methods based on Linear Programming can therefore help determine efficiently the network structure of biological systems from large data sets. The overall objective of this work is to provide methods to increase our understanding of complex biochemical systems, particularly through their interconnection and their non-equilibrium behavior.

A dynamical model of lipoprotein metabolism

We present a dynamical model of lipoprotein metabolism derived by combining a cascading process in the blood stream and cellular level regulatory dynamics. We analyse the existence and stability of equilibria and show that this low-dimensional, nonlinear model exhibits bistability between a low and a high cholesterol state. A sensitivity analysis indicates that the intracellular concentration of cholesterol is robust to parametric variations while the plasma cholesterol can vary widely. We show how the dynamical response to time-dependent inputs can be used to diagnose the state of the system. We also establish the connection between parameters in the system and medical and genetic conditions.