Editorial: Network Physiology, Insights
in Dynamical Systems: 2021
Eckehard Schöll
1
,
2
,
3
*
1
Institut für Theoretische Physik, Technische Universität Berlin, Berlin, Germany,
2
Potsdam Institute for Climate Impact Research,
Potsdam, Germany,
3
Bernstein Center for Computational Neuroscience Berlin, Humboldt-Universität, Berlin, Germany
Keywords: dynamical systems, complex networks, network physiology, synchronization, coupled oscillators
Editorial on the Research Topic
Network Physiology, Insights in Dynamical Systems: 2021
The field of network physiology considers all aspects of collective dynamics of and on complex
networks with application to functions and mechanisms in living systems (Ivanov, 2021;
Schöll, 2021;Gosak et al., 2022). Complex networks are an ubiquitous paradigm in nature, with
awidefield of applications ranging from physics, chemistry, biology, neuroscience,
physiology, medicine to socio-economic systems. The human organism is an integrated
network of organ systems, individual organs, cells, biomolecules, which all interact with
each other on various levels. Rather than attempting to study the individual, isolated parts, the
network perspective of dynamical systems focusses on the interaction between the different
units which leads to the emergence of novel collective behavior not present in the isolated
systems. Central to the physiological functioning are nonlinear, dynamic or adaptive
biophysical and biochemical interactions, control mechanisms, communication and
information exchange between cells and organs. This applies to the normal physiological
state as well as to pathological states including diseases. Recent research on dynamical
networks has revealed a plethora of collective dynamic phenomena. Synchronization is an
important universal feature of the dynamics in networks of coupled nonlinear oscillators.
Various synchronization patterns are known, like cluster synchronization where the network
splits into groups of synchronous elements, or partial synchronization patterns such as
chimera states where the system splits into coexisting domains of coherent (synchronized)
and incoherent (desynchronized) states.
Phase transitions and critical phenomena in nonlinear dynamical systems far from
thermodynamic equilibrium have been investigated since the 1970s and 1980s, and concepts
from thermodynamics and statistical physics have been applied to describe self-organization,
spatio-temporal pattern formation, phase coexistence, critical phenomena, and first and second
order nonequilibrium phase transitions (Schlögl, 1972;Haken, 1978;Schöll, 1987). But only in
recent times, phase transitions and critical phenomena have been studied in dynamical
networks, where synchronization transitions may arise, giving birth to a plethora of partial
synchronization patterns and complex collective behavior. These recent developments include
connections of tipping transitions, explosive synchronization, nucleation, critical slowing down,
critical correlations and fluctuations, critical exponents, etc. with nonequilibrium
thermodynamics.
This Research Topic of Frontiers in Network Physiology –Networks of Dynamical Systems, is
focused on new insights, novel developments, current challenges, latest discoveries, recent
advances and future perspectives in the field. It features contributions from leading experts that
describe the state of the art, outlining recent developments and major accomplishments that
have been achieved and that need to occur to move the field forward. They deal with healthy as
Edited and reviewed by:
Wei Lin,
Fudan University, China
*Correspondence:
Eckehard Schöll
[email protected]erlin.de
Specialty section:
This article was submitted to
Networks of Dynamical Systems,
a section of the journal
Frontiers in Network Physiology
Received: 04 June 2022
Accepted: 20 June 2022
Published: 15 July 2022
Citation:
Schöll E (2022) Editorial: Network
Physiology, Insights in Dynamical
Systems: 2021.
Front. Netw. Physiol. 2:961339.
doi: 10.3389/fnetp.2022.961339
Frontiers in Network Physiology | www.frontiersin.org July 2022 | Volume 2 | Article 9613391
EDITORIAL
published: 15 July 2022
doi: 10.3389/fnetp.2022.961339
well as pathological states in brain networks, in general
multistable networks, and in physiological networks
describing the interaction of organs and the immune
system, and are linked up with data-driven network
approaches.
In the first contribution by Jifan Shi et al. it is suggested that
criticality plays an important role in the healthy brain. The brain
exhibits remarkable robustness under various types of noise and
flexibility under various environments. However, how the brain
works is still a mystery. The authors support the critical brain
hypothesis by a dynamical network analysis using an
electroencephalography dataset obtained from patients with
psychotic disorders, ultra-high risk individuals, and healthy
controls. The authors show that the brain of healthy controls
remains around a critical state, whereas that of patients with
psychotic disorders falls into more stable states. The brain of
ultra-high risk individuals is similar to that of psychotic disorders
in terms of entropy, but is analogous to that of healthy controls in
causality patterns. These results not only provide evidence for the
criticality of the normal brain but also highlight the practicability
of using an analytic biophysical tool to study the dynamical
properties of mental diseases.
Tobias Fischer et al. propose a data-driven estimation of
resilience in multistable networked dynamical systems as a
versatile testbed for normal and aberrant states. Estimating
resilience of adaptive, networked dynamical systems remains a
challenge for the analysis of empirical data, such as for
example time series of physiological observables of the
human organism. Resilience refers to the ability to absorb
disturbances and still retain essentially the same functioning.
The authors develop a data-driven approach and test it with a
network of networks of diffusively coupled FitzHugh–Nagumo
oscillators by modifying resilience in a controlled manner. For
this purpose they simulate a multistable system with a number
of system states and with self-induced switching between
them. The testbed also enables generation of multivariate
time series of system observables to evaluate the suitability
of data-driven estimators of resilience.
M. Madadi Asl et al. consider Parkinson’s disease as a multi-
systemic neurodegenerative brain disorder. Motor symptoms
of Parkinson’s disease are linked to significant dopamine loss
followed by basal ganglia circuit dysfunction. Increasing
experimental and computational evidence indicates that
synaptic plasticity plays a key role in the emergence of
Parkinson’s disease-related pathological changes. Spike-
timing-dependent plasticity (STDP) mediated by dopamine
provides a mechanistic model for synaptic plasticity to modify
synaptic connections within the basal ganglia according to the
neuronal activity. This paper reviews experimental pre-
clinical, clinical, and computational findings on the
modulatory effect of dopamine on STDP as well as other
plasticity mechanisms and discusses their potential role in
Parkinson’s disease pathophysiology from the viewpoint of
network dynamics. This review may provide further insights
into the abnormal structure-function relationship within the
basal ganglia contributing to the emergence of pathological
states in Parkinson’s disease. Specifically, this review is
intended to provide detailed information for the
development of computational network models for
Parkinson’s disease, serving as testbeds for the development
and optimization of invasive and non-invasive brain
stimulation techniques. Computationally derived hypotheses
may accelerate the development of therapeutic stimulation
techniques and potentially reduce the number of related
animal experiments.
The last paper by Rico Berner et al. presents a novel
approach to modeling healthy and pathological states in a
functional physiological network of organs and the immune
system. In this work, they propose a dynamical systems
perspective on the modeling of sepsis and its organ-
damaging consequences. They develop a functional two-
layer network model for sepsis based upon the interaction
of parenchymal cells and immune cells via cytokines, and the
coevolutionary dynamics of parenchymal, immune cells, and
cytokines. By means of the simple paradigmatic model of
adaptively coupled phase oscillators, the emergence of organ
threatening interactions between the dysregulated immune
system and the parenchyma is analyzed. It is demonstrated
that the complex cellular cooperation between parenchyma
and stroma (immune layer) either in the physiological or in the
pathological case can be related to dynamical patterns of the
network, i.e., either a healthy frequency synchronized state, or
a pathological multifrequency cluster state. Thus insight is
provided into the complex stabilizing and destabilizing
interplay of parenchyma and stroma by determining critical
interaction parameters. Moreover, the simulated probability
for the emergence of pathological states is compared with
empirical data for the hospitalization incidence of sepsis in
Germany as a function of age.
AUTHOR CONTRIBUTIONS
The author confirms being the sole contributor of this work and
has approved it for publication.
FUNDING
This work was supported by the Deutsche
Forschungsgemeinschaft (DFG, German Research Foundation,
project Nos. 163436311—SFB 910, 429685422 and 440145547).
Frontiers in Network Physiology | www.frontiersin.org July 2022 | Volume 2 | Article 9613392
Schöll Editorial: Network Physiology, Insights
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Conflict of Interest: The authors declare that the research was conducted in the
absence of any commercial or financial relationships that could be construed as a
potential conflict of interest.
Publisher’s Note: All claims expressed in this article are solely those of the authors
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Copyright © 2022 Schöll. This is an open-access article distributed under the terms of
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Frontiers in Network Physiology | www.frontiersin.org July 2022 | Volume 2 | Article 9613393
Schöll Editorial: Network Physiology, Insights
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