Recent achievements in nonlinear dynamics, synchronization, and networks.

This Focus Issue covers recent developments in the broad areas of nonlinear dynamics, synchronization, and emergent behavior in dynamical networks. It targets current progress on issues such as time series analysis and data-driven modeling from real data such as climate, brain, and social dynamics. Predicting and detecting early warning signals of extreme climate conditions, epileptic seizures, or other catastrophic conditions are the primary tasks from real or experimental data.

Biological computations: Limitations of attractor-based formalisms and the need for transients.

Living systems, from single cells to higher vertebrates, receive a continuous stream of non-stationary inputs that they sense, for e.g. via cell surface receptors or sensory organs.

Non-asymptotic transients away from steady states determine cellular responsiveness to dynamic spatial-temporal signals.

Majority of the theory on cell polarization and the understanding of cellular sensing and responsiveness to localized chemical cues has been based on the idea that non-polarized and polarized cell states can be represented by stable asymptotic switching between them. The existing model classes that describe the dynamics of signaling networks underlying polarization are formulated within the framework of autonomous systems. However these models do not simultaneously capture both, robust maintenance of polarized state longer than the signal duration, and retained responsiveness to signals with complex spatial-temporal distribution.

Cells use molecular working memory to navigate in changing chemoattractant fields.

In order to migrate over large distances, cells within tissues and organisms rely on sensing local gradient cues which are irregular, conflicting, and changing over time and space. The mechanism how they generate persistent directional migration when signals are disrupted, while still remaining adaptive to signal's localization changes remain unknown. Here, we find that single cells utilize a molecular mechanism akin to a working memory to satisfy these two opposing demands.

Cell-cell communication through FGF4 generates and maintains robust proportions of differentiated cell types in embryonic stem cells.

During embryonic development and tissue homeostasis, reproducible proportions of differentiated cell types are specified from populations of multipotent precursor cells. Molecular mechanisms that enable both robust cell-type proportioning despite variable initial conditions in the precursor cells, and the re-establishment of these proportions upon perturbations in a developing tissue remain to be characterized. Here, we report that the differentiation of robust proportions of epiblast-like and primitive endoderm-like cells in mouse embryonic stem cell cultures emerges at the population level through cell-cell communication via a short-range fibroblast growth factor 4 (FGF4) signal.

A self-organized synthetic morphogenic liposome responds with shape changes to local light cues.

Reconstituting artificial proto-cells capable of transducing extracellular signals into cytoskeletal changes can reveal fundamental principles of how non-equilibrium phenomena in cellular signal transduction affect morphogenesis. Here, we generated a Synthetic Morphogenic Membrane System (SynMMS) by encapsulating a dynamic microtubule (MT) aster and a light-inducible signaling system driven by GTP/ATP chemical potential into cell-sized liposomes. Responding to light cues in analogy to morphogens, this biomimetic design embodies basic principles of localized Rho-GTPase signal transduction that generate an intracellular MT-regulator signaling gradient.

Robustness and timing of cellular differentiation through population-based symmetry breaking.

During mammalian development and homeostasis, cells often transition from a multilineage primed state to one of several differentiated cell types that are marked by the expression of mutually exclusive genetic markers. These observations have been classically explained by single-cell multistability as the dynamical basis of differentiation, where robust cell-type proportioning relies on pre-existing cell-to-cell differences. We propose a conceptually different dynamical mechanism in which cell types emerge and are maintained collectively by cell-cell communication as a novel inhomogeneous state of the coupled system.

Organization at criticality enables processing of time-varying signals by receptor networks.

How cells utilize surface receptors for chemoreception is a recurrent question spanning between physics and biology over the past few decades. However, the dynamical mechanism for processing time-varying signals is still unclear. Using dynamical systems formalism to describe criticality in non-equilibrium systems, we propose generic principle for temporal information processing through phase space trajectories using dynamic transient memory.

Interdependence between EGFR and Phosphatases Spatially Established by Vesicular Dynamics Generates a Growth Factor Sensing and Responding Network.

The proto-oncogenic epidermal growth factor receptor (EGFR) is a tyrosine kinase whose sensitivity to growth factors and signal duration determines cellular behavior. We resolve how EGFR's response to epidermal growth factor (EGF) originates from dynamically established recursive interactions with spatially organized protein tyrosine phosphatases (PTPs). Reciprocal genetic PTP perturbations enabled identification of receptor-like PTPRG/J at the plasma membrane and ER-associated PTPN2 as the major EGFR dephosphorylating activities.

Cell signaling as a cognitive process.

Cellular identity as defined through morphology and function emerges from intracellular signaling networks that communicate between cells. Based on recursive interactions within and among these intracellular networks, dynamical solutions in terms of biochemical behavior are generated that can differ from those in isolated cells. In this way, cellular heterogeneity in tissues can be established, implying that cell identity is not intrinsically predetermined by the genetic code but is rather dynamically maintained in a cognitive manner.

Restoration of rhythmicity in diffusively coupled dynamical networks.

Oscillatory behaviour is essential for proper functioning of various physical and biological processes. However, diffusive coupling is capable of suppressing intrinsic oscillations due to the manifestation of the phenomena of amplitude and oscillation deaths. Here we present a scheme to revoke these quenching states in diffusively coupled dynamical networks, and demonstrate the approach in experiments with an oscillatory chemical reaction.

Generalizing the transition from amplitude to oscillation death in coupled oscillators.

Amplitude death (AD) and oscillation death (OD) are two structurally different oscillation quenching types in coupled nonlinear oscillators. The transition from AD to OD has been recently realized due to the interplay between heterogeneity and coupling strength [A. Koseska et al.

Genome-wide identification of regulatory elements and reconstruction of gene regulatory networks of the green alga Chlamydomonas reinhardtii under carbon deprivation.

The unicellular green alga Chlamydomonas reinhardtii is a long-established model organism for studies on photosynthesis and carbon metabolism-related physiology. Under conditions of air-level carbon dioxide concentration [CO2], a carbon concentrating mechanism (CCM) is induced to facilitate cellular carbon uptake. CCM increases the availability of carbon dioxide at the site of cellular carbon fixation.

Transition from amplitude to oscillation death via Turing bifurcation.

Coupled oscillators are shown to experience two structurally different oscillation quenching types: amplitude death (AD) and oscillation death (OD). We demonstrate that both AD and OD can occur in one system and find that the transition between them underlies a classical, Turing-type bifurcation, providing a clear classification of these significantly different dynamical regimes. The implications of obtaining a homogeneous (AD) or inhomogeneous (OD) steady state, as well as their significance for physical and biological applications and control studies, are also pointed out.

Unraveling gene regulatory networks from time-resolved gene expression data - a measures comparison study.

Background: Inferring regulatory interactions between genes from transcriptomics time-resolved data, yielding reverse engineered gene regulatory networks, is of paramount importance to systems biology and bioinformatics studies. Accurate methods to address this problem can ultimately provide a deeper insight into the complexity, behavior, and functions of the underlying biological systems. However, the large number of interacting genes coupled with short and often noisy time-resolved read-outs of the system renders the reverse engineering a challenging task.

Analysing dynamical behavior of cellular networks via stochastic bifurcations.

The dynamical structure of genetic networks determines the occurrence of various biological mechanisms, such as cellular differentiation. However, the question of how cellular diversity evolves in relation to the inherent stochasticity and intercellular communication remains still to be understood. Here, we define a concept of stochastic bifurcations suitable to investigate the dynamical structure of genetic networks, and show that under stochastic influence, the expression of given proteins of interest is defined via the probability distribution of the phase variable, representing one of the genes constituting the system.

Spatiotemporal dynamics of the Calvin cycle: multistationarity and symmetry breaking instabilities.

The possibility of controlling the Calvin cycle has paramount implications for increasing the production of biomass. Multistationarity, as a dynamical feature of systems, is the first obvious candidate whose control could find biotechnological applications. Here we set out to resolve the debate on the multistationarity of the Calvin cycle.

Timing cellular decision making under noise via cell-cell communication.

Many cellular processes require decision making mechanisms, which must act reliably even in the unavoidable presence of substantial amounts of noise. However, the multistable genetic switches that underlie most decision-making processes are dominated by fluctuations that can induce random jumps between alternative cellular states. Here we show, via theoretical modeling of a population of noise-driven bistable genetic switches, that reliable timing of decision-making processes can be accomplished for large enough population sizes, as long as cells are globally coupled by chemical means.

Multistability of synthetic genetic networks with repressive cell-to-cell communication.

We investigate an experimentally feasible synthetic genetic network consisting of two phase repulsively coupled repressilators, which evokes multiple coexisting stable attractors with different features. We perform a bifurcation analysis to determine and classify the dynamical structure of the system. Moreover, some of the dynamical regimes found, such as inhomogeneous steady states and inhomogeneous limit cycles can further be associated with artificial cell differentiation.

Quantized cycling time in artificial gene networks induced by noise and intercell communication.

We propose a mechanism for the quantized cycling time based on the interplay of cell-to-cell communication and stochasticity, by investigating a model of coupled genetic oscillators with known topology. In addition, we discuss how inhomogeneity can be used to enhance such quantizing effects, while the degree of variability obtained can be controlled using the noise intensity or adequate system parameters.