Processing Temporal Growth Factor Patterns by an Epidermal Growth Factor Receptor Network Dynamically Established in Space.

The proto-oncogenic epidermal growth factor (EGF) receptor (EGFR) is a tyrosine kinase whose sensitivity and response to growth factor signals that vary over time and space determine cellular behavior within a developing tissue. The molecular reorganization of the receptors on the plasma membrane and the enzyme-kinetic mechanisms of phosphorylation are key determinants that couple growth factor binding to EGFR signaling. To enable signal initiation and termination while simultaneously accounting for suppression of aberrant signaling, a coordinated coupling of EGFR kinase and protein tyrosine phosphatase activity is established through space by vesicular dynamics. The dynamical operation mode of this network enables not only time-varying growth factor sensing but also adaptation of the response depending on cellular context. By connecting spatially coupled enzymatic kinase/phosphatase processes and the corresponding dynamical systems description of the EGFR network, we elaborate on the general principles necessary for processing complex growth factor signals.

Fast quantum interference of a nanoparticle via optical potential control.

We introduce and theoretically analyze a scheme to prepare and detect non-Gaussian quantum states of an optically levitated particle via the interaction with light pulses that generate cubic and inverted potentials. We show that this approach allows to operate on sufficiently short time- and length scales to beat decoherence in a regime accessible in state-of-the-art experiments. Specifically, we predict the observation of single-particle interference of a nanoparticle with a mass above 108 atomic mass units delocalized by several nanometers, on timescales of milliseconds. The proposed experiment uses only optical and electrostatic control, and can be performed at about 10-10 mbar and at room temperature. We discuss the prospect of this method for coherently splitting the wavepacket of massive dielectric objects without using either projective measurements or an internal level structure.

Nonreciprocal synchronization in embryonic oscillator ensembles.

Synchronization of coupled oscillators is a universal phenomenon encountered across different scales and contexts, e.g., chemical wave patterns, superconductors, and the unison applause we witness in concert halls. The existence of common underlying coupling rules defines universality classes, revealing a fundamental sameness between seemingly distinct systems. Identifying rules of synchronization in any particular setting is hence of paramount relevance. Here, we address the coupling rules within an embryonic oscillator ensemble linked to vertebrate embryo body axis segmentation. In vertebrates, the periodic segmentation of the body axis involves synchronized signaling oscillations in cells within the presomitic mesoderm (PSM), from which somites, the prevertebrae, form. At the molecular level, it is known that intact Notch-signaling and cell-to-cell contact are required for synchronization between PSM cells. However, an understanding of the coupling rules is still lacking. To identify these, we develop an experimental assay that enables direct quantification of synchronization dynamics within mixtures of oscillating cell ensembles, for which the initial input frequency and phase distribution are known. Our results reveal a "winner-takes-it-all" synchronization outcome, i.e., the emerging collective rhythm matches one of the input rhythms. Using a combination of theory and experimental validation, we develop a coupling model, the "Rectified Kuramoto" (ReKu) model, characterized by a phase-dependent, nonreciprocal interaction in the coupling of oscillatory cells. Such nonreciprocal synchronization rules reveal fundamental similarities between embryonic oscillators and a class of collective behaviors seen in neurons and fireflies, where higher-level computations are performed and linked to nonreciprocal synchronization.

Cell reprogramming design by transfer learning of functional transcriptional networks.

Recent developments in synthetic biology, next-generation sequencing, and machine learning provide an unprecedented opportunity to rationally design new disease treatments based on measured responses to gene perturbations and drugs to reprogram cells. The main challenges to seizing this opportunity are the incomplete knowledge of the cellular network and the combinatorial explosion of possible interventions, both of which are insurmountable by experiments. To address these challenges, we develop a transfer learning approach to control cell behavior that is pre-trained on transcriptomic data associated with human cell fates, thereby generating a model of the network dynamics that can be transferred to specific reprogramming goals. The approach combines transcriptional responses to gene perturbations to minimize the difference between a given pair of initial and target transcriptional states. We demonstrate our approach's versatility by applying it to a microarray dataset comprising >9,000 microarrays across 54 cell types and 227 unique perturbations, and an RNASeq dataset consisting of >10,000 sequencing runs across 36 cell types and 138 perturbations. Our approach reproduces known reprogramming protocols with an AUROC of 0.91 while innovating over existing methods by pre-training an adaptable model that can be tailored to specific reprogramming transitions. We show that the number of gene perturbations required to steer from one fate to another increases with decreasing developmental relatedness and that fewer genes are needed to progress along developmental paths than to regress. These findings establish a proof-of-concept for our approach to computationally design control strategies and provide insights into how gene regulatory networks govern phenotype.

A Markovian dynamics for Caenorhabditis elegans behavior across scales.

How do we capture the breadth of behavior in animal movement, from rapid body twitches to aging? Using high-resolution videos of the nematode worm Caenorhabditis elegans, we show that a single dynamics connects posture-scale fluctuations with trajectory diffusion and longer-lived behavioral states. We take short posture sequences as an instantaneous behavioral measure, fixing the sequence length for maximal prediction. Within the space of posture sequences, we construct a fine-scale, maximum entropy partition so that transitions among microstates define a high-fidelity Markov model, which we also use as a means of principled coarse-graining. We translate these dynamics into movement using resistive force theory, capturing the statistical properties of foraging trajectories. Predictive across scales, we leverage the longest-lived eigenvectors of the inferred Markov chain to perform a top-down subdivision of the worm's foraging behavior, revealing both "runs-and-pirouettes" as well as previously uncharacterized finer-scale behaviors. We use our model to investigate the relevance of these fine-scale behaviors for foraging success, recovering a trade-off between local and global search strategies.

Emergent programmable behavior and chaos in dynamically driven active filaments.

How the behavior of cells emerges from their constituent subcellular biochemical and physical parts is an outstanding challenge at the intersection of biology and physics. A remarkable example of single-cell behavior occurs in the ciliate Lacrymaria olor, which hunts for its prey via rapid movements and protrusions of a slender neck, many times the size of the original cell body. The dynamics of this cell neck is powered by a coat of cilia across its length and tip. How a cell can program this active filamentous structure to produce desirable behaviors like search and homing to a target remains unknown. Here, we present an active filament model that allows us to uncover how a "program" (time sequence of active forcing) leads to "behavior" (filament shape dynamics). Our model captures two key features of this system-time-varying activity patterns (extension and compression cycles) and active stresses that are uniquely aligned with the filament geometry-a "follower force" constraint. We show that active filaments under deterministic, time-varying follower forces display rich behaviors including periodic and aperiodic dynamics over long times. We further show that aperiodicity occurs due to a transition to chaos in regions of a biologically accessible parameter space. We also identify a simple nonlinear iterated map of filament shape that approximately predicts long-term behavior suggesting simple, artificial "programs" for filament functions such as homing and searching space. Last, we directly measure the statistical properties of biological programs in L. olor, enabling comparisons between model predictions and experiments.

Emergent structure and dynamics of tropical forest-grassland landscapes.

Previous work indicates that tropical forest can exist as an alternative stable state to savanna. Therefore, perturbation by climate change or human impact may lead to crossing of a tipping point beyond which there is rapid forest dieback that is not easily reversed. A hypothesized mechanism for such bistability is feedback between fire and vegetation, where fire spreads as a contagion process on grass patches. Theoretical models have largely implemented this mechanism implicitly, by assuming a threshold dependence of fire spread on flammable vegetation. Here, we show how the nonlinear dynamics and bistability emerge spontaneously, without assuming equations or thresholds for fire spread. We find that the forest geometry causes the nonlinearity that induces bistability. We demonstrate this in three steps. First, we model forest and fire as interacting contagion processes on grass patches, showing that spatial structure emerges due to two counteracting effects on the forest perimeter: forest expansion by dispersal and forest erosion by fires originating in adjacent grassland. Then, we derive a landscape-scale balance equation in which these two effects link forest geometry and dynamics: Forest expands proportionally to its perimeter, while it shrinks proportionally to its perimeter weighted by adjacent grassland area. Finally, we show that these perimeter quantities introduce nonlinearity in our balance equation and lead to bistability. Relying on the link between structure and dynamics, we propose a forest resilience indicator that could be used for targeted conservation or restoration.

Rate-induced tipping in complex high-dimensional ecological networks.

In an ecosystem, environmental changes as a result of natural and human processes can cause some key parameters of the system to change with time. Depending on how fast such a parameter changes, a tipping point can occur. Existing works on rate-induced tipping, or R-tipping, offered a theoretical way to study this phenomenon but from a local dynamical point of view, revealing, e.g., the existence of a critical rate for some specific initial condition above which a tipping point will occur. As ecosystems are subject to constant disturbances and can drift away from their equilibrium point, it is necessary to study R-tipping from a global perspective in terms of the initial conditions in the entire relevant phase space region. In particular, we introduce the notion of the probability of R-tipping defined for initial conditions taken from the whole relevant phase space. Using a number of real-world, complex mutualistic networks as a paradigm, we find a scaling law between this probability and the rate of parameter change and provide a geometric theory to explain the law. The real-world implication is that even a slow parameter change can lead to a system collapse with catastrophic consequences. In fact, to mitigate the environmental changes by merely slowing down the parameter drift may not always be effective: Only when the rate of parameter change is reduced to practically zero would the tipping be avoided. Our global dynamics approach offers a more complete and physically meaningful way to understand the important phenomenon of R-tipping.

Predicting chromosomal compartments directly from the nucleotide sequence with DNA-DDA.

Three-dimensional (3D) genome architecture is characterized by multi-scale patterns and plays an essential role in gene regulation. Chromatin conformation capturing experiments have revealed many properties underlying 3D genome architecture, such as the compartmentalization of chromatin based on transcriptional states. However, they are complex, costly and time consuming, and therefore only a limited number of cell types have been examined using these techniques. Increasing effort is being directed towards deriving computational methods that can predict chromatin conformation and associated structures. Here we present DNA-delay differential analysis (DDA), a purely sequence-based method based on chaos theory to predict genome-wide A and B compartments. We show that DNA-DDA models derived from a 20 Mb sequence are sufficient to predict genome wide compartmentalization at the scale of 100 kb in four different cell types. Although this is a proof-of-concept study, our method shows promise in elucidating the mechanisms responsible for genome folding as well as modeling the impact of genetic variation on 3D genome architecture and the processes regulated thereby.

Turbulence tracks recurrent solutions.

Despite a long and rich history of scientific investigation, fluid turbulence remains one of the most challenging problems in science and engineering. One of the key outstanding questions concerns the role of coherent structures that describe frequently observed patterns embedded in turbulence. It has been suggested, but not proved, that coherent structures correspond to unstable, recurrent solutions of the governing equation of fluid dynamics. Here, we present experimental and numerical evidence that three-dimensional turbulent flow tracks, episodically but repeatedly, the spatial and temporal structure of multiple such solutions. Our results provide compelling evidence that coherent structures, grounded in the governing equations, can be harnessed to predict how turbulent flows evolve.

Prevalence and scalable control of localized networks.

The ability to control network dynamics is essential for ensuring desirable functionality of many technological, biological, and social systems. Such systems often consist of a large number of network elements, and controlling large-scale networks remains challenging because the computation and communication requirements increase prohibitively fast with network size. Here, we introduce a notion of network locality that can be exploited to make the control of networks scalable, even when the dynamics are nonlinear. We show that network locality is captured by an information metric and is almost universally observed across real and model networks. In localized networks, the optimal control actions and system responses are both shown to be necessarily concentrated in small neighborhoods induced by the information metric. This allows us to develop localized algorithms for determining network controllability and optimizing the placement of driver nodes. This also allows us to develop a localized algorithm for designing local feedback controllers that approach the performance of the corresponding best global controllers, while incurring a computational cost orders-of-magnitude lower. We validate the locality, performance, and efficiency of the algorithms in Kuramoto oscillator networks, as well as three large empirical networks: synchronization dynamics in the Eastern US power grid, epidemic spreading mediated by the global air-transportation network, and Alzheimer's disease dynamics in a human brain network. Taken together, our results establish that large networks can be controlled with computation and communication costs comparable to those for small networks.

Intrinsic nonlinear dynamics drive single-species systems.

The importance of oscillations and deterministic chaos in natural biological systems has been discussed for several decades and was originally based on discrete-time population growth models (May 1974). Recently, all types of nonlinear dynamics were shown for experimental communities where several species interact. Yet, there are no data exhibiting the whole range of nonlinear dynamics for single-species systems without trophic interactions. Up until now, ecological experiments and models ignored the intracellular dimension, which includes multiple nonlinear processes even within one cell type. Here, we show that dynamics of single-species systems of protists in continuous experimental chemostat systems and corresponding continuous-time models reveal typical characteristics of nonlinear dynamics and even deterministic chaos, a very rare discovery. An automatic cell registration enabled a continuous and undisturbed analysis of dynamic behavior with a high temporal resolution. Our simple and general model considering the cell cycle exhibits a remarkable spectrum of dynamic behavior. Chaos-like dynamics were shown in continuous single-species populations in experimental and modeling data on the level of a single type of cells without any external forcing. This study demonstrates how complex processes occurring in single cells influence dynamics on the population level. Nonlinearity should be considered as an important phenomenon in cell biology and single-species dynamics and also, for the maintenance of high biodiversity in nature, a prerequisite for nature conservation.

Environmental context dependency in species interactions.

Ecological interactions are not uniform across time and can vary with environmental conditions. Yet, interactions among species are often measured with short-term controlled experiments whose outcomes can depend greatly on the particular environmental conditions under which they are performed. As an alternative, we use empirical dynamic modeling to estimate species interactions across a wide range of environmental conditions directly from existing long-term monitoring data. In our case study from a southern California kelp forest, we test whether interactions between multiple kelp and sea urchin species can be reliably reconstructed from time-series data and whether those interactions vary predictably in strength and direction across observed fluctuations in temperature, disturbance, and low-frequency oceanographic regimes. We show that environmental context greatly alters the strength and direction of species interactions. In particular, the state of the North Pacific Gyre Oscillation seems to drive the competitive balance between kelp species, asserting bottom-up control on kelp ecosystem dynamics. We show the importance of specifically studying variation in interaction strength, rather than mean interaction outcomes, when trying to understand the dynamics of complex ecosystems. The significant context dependency in species interactions found in this study argues for a greater utilization of long-term data and empirical dynamic modeling in studies of the dynamics of other ecosystems.

Inspiratory and sigh breathing rhythms depend on distinct cellular signalling mechanisms in the preBötzinger complex.

Breathing behaviour involves the generation of normal breaths (eupnoea) on a timescale of seconds and sigh breaths on the order of minutes. Both rhythms emerge in tandem from a single brainstem site, but whether and how a single cell population can generate two disparate rhythms remains unclear. We posit that recurrent synaptic excitation in concert with synaptic depression and cellular refractoriness gives rise to the eupnoea rhythm, whereas an intracellular calcium oscillation that is slower by orders of magnitude gives rise to the sigh rhythm. A mathematical model capturing these dynamics simultaneously generates eupnoea and sigh rhythms with disparate frequencies, which can be separately regulated by physiological parameters. We experimentally validated key model predictions regarding intracellular calcium signalling. All vertebrate brains feature a network oscillator that drives the breathing pump for regular respiration. However, in air-breathing mammals with compliant lungs susceptible to collapse, the breathing rhythmogenic network may have refashioned ubiquitous intracellular signalling systems to produce a second slower rhythm (for sighs) that prevents atelectasis without impeding eupnoea. KEY POINTS: A simplified activity-based model of the preBötC generates inspiratory and sigh rhythms from a single neuron population. Inspiration is attributable to a canonical excitatory network oscillator mechanism. Sigh emerges from intracellular calcium signalling. The model predicts that perturbations of calcium uptake and release across the endoplasmic reticulum counterintuitively accelerate and decelerate sigh rhythmicity, respectively, which was experimentally validated. Vertebrate evolution may have adapted existing intracellular signalling mechanisms to produce slow oscillations needed to optimize pulmonary function in mammals.

Kinematic and neuromuscular characterization of cognitive involvement in gait control in healthy young adults.

The signature of cognitive involvement in gait control has rarely been studied using both kinematic and neuromuscular features. The present study aimed to address this gap. Twenty-four healthy young adults walked on an instrumented treadmill in a virtual environment under two optic flow conditions: normal (NOF) and perturbed (POF, continuous mediolateral pseudorandom oscillations). Each condition was performed under single-task and dual-task conditions of increasing difficulty (1-, 2-, 3-back). Subjective mental workload (raw NASA-TLX), cognitive performance (mean reaction time and d-prime), kinematic (steadiness, variability and complexity in the mediolateral and anteroposterior directions) and neuromuscular (duration and variability of motor primitives) control of gait were assessed. The cognitive performance and the number and composition of motor modules were unaffected by simultaneous walking, regardless of the optic flow condition. Kinematic and neuromuscular variability was greater under POF compared to NOF conditions. Young adults sought to counteract POF by rapidly correcting task-relevant gait fluctuations. The depletion of cognitive resources through dual-tasking led to reduced kinematic and neuromuscular variability and this occurred to the same extent regardless of simultaneous working memory (WM) load. Increasing WM load led to a prioritization of gait control in the mediolateral direction over the anteroposterior direction. The impact of POF on kinematic variability (step velocity) was reduced when a cognitive task was performed simultaneously, but this phenomenon was no modulated by WM load. Collectively, these results shed important light on how young adults adjust the processes involved in goal-directed locomotion when exposed to varying levels of task and environmental constraints.

Dynamics of pH Oscillators in Continuous Stirred Tanks in Series.

Complex reaction networks with positive and negative feedback can produce diverse nonlinear phenomena in open reactors, such as multistability and oscillations. pH oscillators driven by hydrogen or hydroxide autocatalytic processes show sustained oscillations in continuously stirred tank reactors (CSTR) but only a sharp pH switch in batch. Here, we present a numerical study on the dynamics of pH oscillators in a series of CSTRs. We show a critical residence time under which bistability and above which oscillations develop. The dynamics of the CSTR cascade show the cross-shaped phase diagram of nonlinear activatory inhibitory systems. In the domain of oscillations, one reactor starts to oscillate autonomously and induces forced complex oscillations in the following tanks with damped amplitudes. These results, with their practical implications, may contribute to understanding the recent experimental observations of nonlinear phenomena in the presence of a residence time ramp and inspire further research in this area.

Early warning signals observed in motor activity preceding mood state change in bipolar disorder.

INTRODUCTION: Alterations in motor activity are well-established symptoms of bipolar disorder, and time series of motor activity can be considered complex dynamical systems. In such systems, early warning signals (EWS) occur in a critical transition period preceding a sudden shift (tipping point) in the system. EWS are statistical observations occurring due to a system's declining ability to maintain homeostasis when approaching a tipping point. The aim was to identify critical transition periods preceding bipolar mood state changes. METHODS: Participants with a validated bipolar diagnosis were included to a one-year follow-up study, with repeated assessments of the participants' mood. Motor activity was recorded continuously by a wrist-worn actigraph. Participants assessed to have relapsed during follow-up were analyzed. Recognized EWS features were extracted from the motor activity data and analyzed by an unsupervised change point detection algorithm, capable of processing multi-dimensional data and developed to identify when the statistical property of a time series changes. RESULTS: Of 49 participants, four depressive and four hypomanic/manic relapses among six individuals occurred, recording actigraphy for 23.8 ± 0.2 h/day, for 39.8 ± 4.6 days. The algorithm detected change points in the time series and identified critical transition periods spanning 13.5 ± 7.2 days. For depressions 11.4 ± 1.8, and hypomania/mania 15.6 ± 10.2 days. CONCLUSION: The change point detection algorithm seems capable of recognizing impending mood episodes in continuous flowing data streams. Hence, we present an innovative method for forecasting approaching relapses to improve the clinical management of bipolar disorder.

Potential of coupled array harvester in enhanced energy harvesting.

Harvesting energy from nonlinear systems has been at the centre of research in the energy harvesting community. Many such proposed systems are single nonlinear harvester. While these systems show an increase in bandwidth of harvesting frequency, overall, they are not effective enough in power generation. This article studies power harvesting and frequency bandwidth characteristics of an array of harvesters. Multiple harvesters are considered with linear and nonlinear coupling between the harvesters. The phenomena of internal resonance (IR) and stochastic resonance (SR) are reported. The IR in multiple coupled nonlinear harvesters is explored using multiple-scale analysis. A parametric study is conducted to demonstrate the effect of coupling strength, frequency mistuning, innate nonlinearity and other parameters. The parametric study helped establish effective ways to increase bandwidth. Moreover, a stochastically loaded linearly coupled bistable harvester array is numerically analysed to find the effect of coupling strength and array size on the phenomenon of SR and on the system's harvesting performance. Through these studies, the potential of multiple coupled nonlinear harvesters in enhanced energy harvesting is demonstrated under both harmonic and stochastic excitation.This article is part of the theme issue 'Celebrating the 15th anniversary of the Royal Society Newton International Fellowship'.

Evaluating dynamic models for rigid-foldable origami: unveiling intricate bistable dynamics of stacked-Miura-origami structures as a case study.

Recent advances in origami science and engineering have particularly focused on the challenges of dynamics. While research has primarily focused on statics and kinematics, the need for effective and processable dynamic models has become apparent. This paper evaluates various dynamic modelling techniques for rigid-foldable origami, particularly focusing on their ability to capture nonlinear dynamic behaviours. Two primary methods, the lumped mass-spring-damper approach and the energy-based method, are examined using a bistable stacked Miura-origami (SMO) structure as a case study. Through systematic dynamic experiments, we analyse the effectiveness of these models in predicting bistable dynamic responses, including intra- and interwell oscillations, in different loading conditions. Our findings reveal that the energy-based approach, which considers the structure's inertia and utilizes dynamic experimental data for parameter identification, outperforms other models in terms of validity and accuracy. This model effectively predicts the dynamic response types, the rich and complex nonlinear characteristics and the critical frequency where interwell oscillations occur. Despite its relatively increased complexity in model derivation, it maintains computational efficiency and shows promise for broader applications in origami dynamics. By comparing model predictions with experimental results, this study enhances our understanding of origami dynamics and contributes valuable insights for future research and applications. This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'.

Information, Coding, and Biological Function: The Dynamics of Life.

In the mid-20th century, two new scientific disciplines emerged forcefully: molecular biology and information-communication theory. At the beginning, cross-fertilization was so deep that the term genetic code was universally accepted for describing the meaning of triplets of mRNA (codons) as amino acids. However, today, such synergy has not taken advantage of the vertiginous advances in the two disciplines and presents more challenges than answers. These challenges not only are of great theoretical relevance but also represent unavoidable milestones for next-generation biology: from personalized genetic therapy and diagnosis to Artificial Life to the production of biologically active proteins. Moreover, the matter is intimately connected to a paradigm shift needed in theoretical biology, pioneered a long time ago, that requires combined contributions from disciplines well beyond the biological realm. The use of information as a conceptual metaphor needs to be turned into quantitative and predictive models that can be tested empirically and integrated in a unified view. Successfully achieving these tasks requires a wide multidisciplinary approach, including Artificial Life researchers, to address such an endeavour.