Noise Induces Hopping between NF-κB Entrainment Modes

Entrainment and multi-stability of the p53 oscillator in human cells

The tumor suppressor p53 responds to cellular stress and activates transcription programs critical for regulating cell fate. DNA damage triggers oscillations in p53 levels with a robust period. Guided by the theory of synchronization and entrainment, we developed a mathematical model and experimental system to test the ability of the p53 oscillator to entrain to external drug pulses of various periods and strengths. We found that the p53 oscillator can be locked and entrained to a wide range of entrainment modes. External periods far from p53's natural oscillations increased the heterogeneity between individual cells whereas stronger inputs reduced it. Single-cell measurements allowed deriving the phase response curves (PRCs) and multiple Arnold tongues of p53. In addition, multi-stability and non-linear behaviors were mathematically predicted and experimentally detected, including mode hopping, period doubling, and chaos. Our work revealed critical dynamical properties of the p53 oscillator and provided insights into understanding and controlling it. A record of this paper's transparent peer review process is included in the supplemental information.

Light-driven synchronization of optogenetic clocks

Synthetic genetic oscillators can serve as internal clocks within engineered cells to program periodic expression. However, cell-to-cell variability introduces a dispersion in the characteristics of these clocks that drives the population to complete desynchronization. Here, we introduce the optorepressilator, an optically controllable genetic clock that combines the repressilator, a three-node synthetic network in E. coli, with an optogenetic module enabling to reset, delay, or advance its phase using optical inputs. We demonstrate that a population of optorepressilators can be synchronized by transient green light exposure or entrained to oscillate indefinitely by a train of short pulses, through a mechanism reminiscent of natural circadian clocks. Furthermore, we investigate the system's response to detuned external stimuli observing multiple regimes of global synchronization. Integrating experiments and mathematical modeling, we show that the entrainment mechanism is robust and can be understood quantitatively from single cell to population level.

Co-imaging of RelA and c-Rel reveals features of NF-κB signaling for ligand discrimination

Individual cell sensing of external cues has evolved through the temporal patterns in signaling. Since nuclear factor κB (NF-κB) signaling dynamics have been examined using a single subunit, RelA, it remains unclear whether more information might be transmitted via other subunits. Using NF-κB double-knockin reporter mice, we monitored both canonical NF-κB subunits, RelA and c-Rel, simultaneously in single macrophages by quantitative live-cell imaging. We show that signaling features of RelA and c-Rel convey more information about the stimuli than those of either subunit alone. Machine learning is used to predict the ligand identity accurately based on RelA and c-Rel signaling features without considering the co-activated factors. Ligand discrimination is achieved through selective non-redundancy of RelA and c-Rel signaling dynamics, as well as their temporal coordination. These results suggest a potential role of c-Rel in fine-tuning immune responses and highlight the need for approaches that will elucidate the mechanisms regulating NF-κB subunit specificity.

Processing stimulus dynamics by the NF-κB network in single cells

Cells at the site of an infection experience numerous biochemical signals that vary in amplitude, space, and time. Despite the diversity of dynamic signals produced by pathogens and sentinel cells, information-processing pathways converge on a limited number of central signaling nodes to ultimately control cellular responses. In particular, the NF-κB pathway responds to dozens of signals from pathogens and self, and plays a vital role in processing proinflammatory inputs. Studies addressing the influence of stimulus dynamics on NF-κB signaling are rare due to technical limitations with live-cell measurements. However, recent advances in microfluidics, automation, and image analysis have enabled investigations that yield high temporal resolution at the single-cell level. Here, we summarize the recent research which measures and models the NF-κB response to pulsatile and fluctuating stimulus concentrations, as well as different combinations and sequences of signaling molecules. Collectively, these studies show that the NF-κB network integrates external inflammatory signals and translates these into downstream transcriptional responses.

The multiple activations in budding yeast S-phase checkpoint are Poisson processes

Eukaryotic cells activate the S-phase checkpoint signal transduction pathway in response to DNA replication stress. Affected by the noise in biochemical reactions, such activation process demonstrates cell-to-cell variability. Here, through the analysis of microfluidics-integrated time-lapse imaging, we found multiple S-phase checkpoint activations in a certain budding yeast cell cycle. Yeast cells not only varied in their activation moments but also differed in the number of activations within the cell cycle, resulting in a stochastic multiple activation process. By investigating dynamics at the single-cell level, we showed that stochastic waiting times between consecutive activations are exponentially distributed and independent from each other. Finite DNA replication time provides a robust upper time limit to the duration of multiple activations. The mathematical model, together with further experimental evidence from the mutant strain, revealed that the number of activations under different levels of replication stress agreed well with Poisson distribution. Therefore, the activation events of S-phase checkpoint meet the criterion of Poisson process during DNA replication. In sum, the observed Poisson activation process may provide new insights into the complex stochastic dynamics of signal transduction pathways.

A plausible identifiable model of the canonical NF-κB signaling pathway

An overwhelming majority of mathematical models of regulatory pathways, including the intensively studied NF-κB pathway, remains non-identifiable, meaning that their parameters may not be determined by existing data. The existing NF-κB models that are capable of reproducing experimental data contain non-identifiable parameters, whereas simplified models with a smaller number of parameters exhibit dynamics that differs from that observed in experiments. Here, we reduced an existing model of the canonical NF-κB pathway by decreasing the number of equations from 15 to 6. The reduced model retains two negative feedback loops mediated by IκBα and A20, and in response to both tonic and pulsatile TNF stimulation exhibits dynamics that closely follow that of the original model. We carried out the sensitivity-based linear analysis and Monte Carlo-based analysis to demonstrate that the resulting model is both structurally and practically identifiable given measurements of 5 model variables from a simple TNF stimulation protocol. The reduced model is capable of reproducing different types of responses that are characteristic to regulatory motifs controlled by negative feedback loops: nearly-perfect adaptation as well as damped and sustained oscillations. It can serve as a building block of more comprehensive models of the immune response and cancer, where NF-κB plays a decisive role. Our approach, although may not be automatically generalized, suggests that models of other regulatory pathways can be transformed to identifiable, while retaining their dynamical features.

Coupled oscillator cooperativity as a control mechanism in chronobiology

Control of dynamical processes is vital for maintaining correct cell regulation and cell-fate decisions. Numerous regulatory networks show oscillatory behavior; however, our knowledge of how one oscillator behaves when stimulated by two or more external oscillatory signals is still missing. We explore this problem by constructing a synthetic oscillatory system in yeast and stimulate it with two external oscillatory signals. Letting model verification and prediction operate in a tight interplay with experimental observations, we find that stimulation with two external signals expands the plateau of entrainment and reduces the fluctuations of oscillations. Furthermore, by adjusting the phase differences of external signals, one can control the amplitude of oscillations, which is understood through the signal delay of the unperturbed oscillatory network. With this we reveal a direct amplitude dependency of downstream gene transcription. Taken together, these results suggest a new path to control oscillatory systems by coupled oscillator cooperativity.

Enhanced DNA repair through droplet formation and p53 oscillations

Living organisms are constantly exposed to DNA damage, and optimal repair is therefore crucial. A characteristic hallmark of the response is the formation of sub-compartments around the site of damage, known as foci. Following multiple DNA breaks, the transcription factor p53 exhibits oscillations in its nuclear concentration, but how this dynamics can affect the repair remains unknown. Here, we formulate a theory for foci formation through droplet condensation and discover how oscillations in p53, with its specific periodicity and amplitude, optimize the repair process by preventing Ostwald ripening and distributing protein material in space and time. Based on the theory predictions, we reveal experimentally that the oscillatory dynamics of p53 does enhance the repair efficiency. These results connect the dynamical signaling of p53 with the microscopic repair process and create a new paradigm for the interplay of complex dynamics and phase transitions in biology.

Dissecting cell fate dynamics in pediatric glioblastoma through the lens of complex systems and cellular cybernetics

Cancers are complex dynamic ecosystems. Reductionist approaches to science are inadequate in characterizing their self-organized patterns and collective emergent behaviors. Since current approaches to single-cell analysis in cancer systems rely primarily on single time-point multiomics, many of the temporal features and causal adaptive behaviors in cancer dynamics are vastly ignored. As such, tools and concepts from the interdisciplinary paradigm of complex systems theory are introduced herein to decode the cellular cybernetics of cancer differentiation dynamics and behavioral patterns. An intuition for the attractors and complex networks underlying cancer processes such as cell fate decision-making, multiscale pattern formation systems, and epigenetic state-transitions is developed. The applications of complex systems physics in paving targeted therapies and causal pattern discovery in precision oncology are discussed. Pediatric high-grade gliomas are discussed as a model-system to demonstrate that cancers are complex adaptive systems, in which the emergence and selection of heterogeneous cellular states and phenotypic plasticity are driven by complex multiscale network dynamics. In specific, pediatric glioblastoma (GBM) is used as a proof-of-concept model to illustrate the applications of the complex systems framework in understanding GBM cell fate decisions and decoding their adaptive cellular dynamics. The scope of these tools in forecasting cancer cell fate dynamics in the emerging field of computational oncology and patient-centered systems medicine is highlighted.

Microfluidic chip for precise trapping of single cells and temporal analysis of signaling dynamics

Microfluidic designs are versatile examples of technology miniaturisation that find their applications in various cell biology research, especially to investigate the influence of environmental signals on cellular response dynamics. Multicellular systems operate in intricate cellular microenvironments where environmental signals govern well-orchestrated and robust responses, the understanding of which can be realized with integrated microfluidic systems. In this study, we present a fully automated and integrated microfluidic chip that can deliver input signals to single and isolated suspension or adherent cells in a precisely controlled manner. In respective analyses of different single cell types, we observe, in real-time, the temporal dynamics of caspase 3 activation during DMSO-induced apoptosis in single cancer cells (K562) and the translocation of STAT-1 triggered by interferon γ (IFNγ) in single fibroblasts (NIH3T3). Our investigations establish the employment of our versatile microfluidic system in probing temporal single cell signaling networks where alternations in outputs uncover signal processing mechanisms.

Nidhi Sinha, Haowen Yang and colleagues report a microfluidic large-scale integration chip to probe temporal single-cell signalling networks via the delivery of patterns of input signalling molecules. The researchers use their device to investigate drug-induced cancer cell apoptosis and single cell transcription (STAT-1) protein signalling dynamics.

A Review of Mathematical and Computational Methods in Cancer Dynamics

Cancers are complex adaptive diseases regulated by the nonlinear feedback systems between genetic instabilities, environmental signals, cellular protein flows, and gene regulatory networks. Understanding the cybernetics of cancer requires the integration of information dynamics across multidimensional spatiotemporal scales, including genetic, transcriptional, metabolic, proteomic, epigenetic, and multi-cellular networks. However, the time-series analysis of these complex networks remains vastly absent in cancer research. With longitudinal screening and time-series analysis of cellular dynamics, universally observed causal patterns pertaining to dynamical systems, may self-organize in the signaling or gene expression state-space of cancer triggering processes. A class of these patterns, strange attractors, may be mathematical biomarkers of cancer progression. The emergence of intracellular chaos and chaotic cell population dynamics remains a new paradigm in systems medicine. As such, chaotic and complex dynamics are discussed as mathematical hallmarks of cancer cell fate dynamics herein. Given the assumption that time-resolved single-cell datasets are made available, a survey of interdisciplinary tools and algorithms from complexity theory, are hereby reviewed to investigate critical phenomena and chaotic dynamics in cancer ecosystems. To conclude, the perspective cultivates an intuition for computational systems oncology in terms of nonlinear dynamics, information theory, inverse problems, and complexity. We highlight the limitations we see in the area of statistical machine learning but the opportunity at combining it with the symbolic computational power offered by the mathematical tools explored.

Insights on the NF-κB System Using Live Cell Imaging: Recent Developments and Future Perspectives

The transcription factor family of nuclear factor kappa B (NF-κB) proteins is widely recognized as a key player in inflammation and the immune responses, where it plays a fundamental role in translating external inflammatory cues into precise transcriptional programs, including the timely expression of a wide variety of cytokines/chemokines. Live cell imaging in single cells showed approximately 15 years ago that the canonical activation of NF-κB upon stimulus is very dynamic, including oscillations of its nuclear localization with a period close to 1.5 hours. This observation has triggered a fruitful interdisciplinary research line that has provided novel insights on the NF-κB system: how its heterogeneous response differs between cell types but also within homogeneous populations; how NF-κB dynamics translate external cues into intracellular signals and how NF-κB dynamics affects gene expression. Here we review the main features of this live cell imaging approach to the study of NF-κB, highlighting the key findings, the existing gaps of knowledge and hinting towards some of the potential future steps of this thriving research field.

Temperature Controls Onset and Period of NF-κB Oscillations and can Lead to Chaotic Dynamics

The transcription factor NF-κB plays a vital role in the control of the immune system, and following stimulation with TNF-α its nuclear concentration shows oscillatory behaviour. How environmental factors, in particular temperature, can control the oscillations and thereby affect gene stimulation is still remains to be resolved question. In this work, we reveal that the period of the oscillations decreases with increasing temperature. We investigate this using a mathematical model, and by applying results from statistical physics, we introduce temperature dependency to all rates, resulting in a remarkable correspondence between model and experiments. Our model predicts how temperature affects downstream protein production and find a crossover, where high affinity genes upregulates at high temperatures. Finally, we show how or that oscillatory temperatures can entrain NF-κB oscillations and lead to chaotic dynamics presenting a simple path to chaotic conditions in cellular biology.

The emergence of polyglot entrainment responses to periodic inputs in vicinities of Hopf bifurcations in slow-fast systems

Several distinct entrainment patterns can occur in the FitzHugh-Nagumo (FHN) model under external periodic forcing. Investigating the FHN model under different types of periodic forcing reveals the existence of multiple disconnected 1:1 entrainment segments for constant, low enough values of the input amplitude when the unforced system is in the vicinity of a Hopf bifurcation. This entrainment structure is termed polyglot to distinguish it from the single 1:1 entrainment region (monoglot) structure typically observed in Arnold tongue diagrams. The emergence of polyglot entrainment is then explained using phase-plane analysis and other dynamical system tools. Entrainment results are investigated for other slow-fast systems of neuronal, circadian, and glycolytic oscillations. Exploring these models, we found that polyglot entrainment structure (multiple 1:1 regions) is observed when the unforced system is in the vicinity of a Hopf bifurcation and the Hopf point is located near a knee of a cubic-like nullcline.

Multi-synchronization and other patterns of multi-rhythmicity in oscillatory biological systems

While experimental and theoretical studies have established the prevalence of rhythmic behaviour at all levels of biological organization, less common is the coexistence between multiple oscillatory regimes (multi-rhythmicity), which has been predicted by a variety of models for biological oscillators. The phenomenon of multi-rhythmicity involves, most commonly, the coexistence between two (birhythmicity) or three (trirhythmicity) distinct regimes of self-sustained oscillations. Birhythmicity has been observed experimentally in a few chemical reactions and in biological examples pertaining to cardiac cell physiology, neurobiology, human voice patterns and ecology. The present study consists of two parts. We first review the mechanisms underlying multi-rhythmicity in models for biochemical and cellular oscillations in which the phenomenon was investigated over the years. In the second part, we focus on the coupling of the cell cycle and the circadian clock and show how an additional source of multi-rhythmicity arises from the bidirectional coupling of these two cellular oscillators. Upon bidirectional coupling, the two oscillatory networks generally synchronize in a unique manner characterized by a single, common period. In some conditions, however, the two oscillators may synchronize in two or three different ways characterized by distinct waveforms and periods. We refer to this type of multi-rhythmicity as ‘multi-synchronization’.

The onset of dissipative chaos driven by nonequilibrium conditions

Dissipative chaos appears widely in various nonequilibrium systems; however, it is not clear how dissipative chaos originates from nonequilibrium. We discuss a framework based on the potential-flux approach to study chaos from the perspective of nonequilibrium dynamics. In this framework, chaotic systems possess a wide basin on the potential landscape, in which the rotational flux dominates the system dynamics, and chaos occurs with the appearance of this basin. In contrast, the probability flux is particularly associated with the detailed balance-breaking in nonequilibrium systems. This implies that the appearance of dissipative chaos is driven by nonequilibrium conditions.

Unraveling the stochastic transition mechanism between oscillation states by landscape and minimum action path theory

Cell fate transitions have been studied from various perspectives, such as the transition between stable states, or the transition between stable states and oscillation states. However, there is a lack...

Quantifying the optimal strategy of population control of quorum sensing network in Escherichia coli

Biological functions of bacteria can be regulated by monitoring their own population density induced by the quorum sensing system. However, quantitative insight into the system’s dynamics and regulatory mechanism remain challenging. Here, we construct a comprehensive mathematical model of the synthetic quorum sensing circuit that controls population density in Escherichia coli. Simulations agree well with experimental results obtained under different ribosome-binding site (RBS) efficiencies. We present a quantitative description of the component dynamics and show how the components respond to isopropyl-β-D-1-thiogalactopyranoside (IPTG) induction. The optimal IPTG-induction range for efficiently controlling population density is quantified. The controllable area of population density by acyl-homoserine lactone (AHL) permeability is quantified as well, indicating that high AHL permeability should be treated with a high dose of IPTG, while low AHL permeability should be induced with low dose for efficiently controlling. Unexpectedly, an oscillatory behavior of the growth curve is observed with proper RBS-binding strengths and the oscillation is greatly restricted by the bacterial death induced by toxic metabolic by-products. Moreover, we identify that the mechanism underlying the emergence of oscillation is determined by the negative feedback loop structure within the signaling. Bifurcation analysis and landscape theory are further employed to study the stochastic dynamic and global stability of the system, revealing two faces of toxic metabolic by-products in controlling oscillatory behavior. Overall, our study presents a quantitative basis for understanding and new insights into the control mechanism of quorum sensing system, providing possible clues to guide the development of more rational control strategy.

Analyzing signaling activity and function in hematopoietic cells

Cells constantly sense their environment, allowing the adaption of cell behavior to changing needs. Fine-tuned responses to complex inputs are computed by signaling pathways, which are wired in complex connected networks. Their activity is highly context-dependent, dynamic, and heterogeneous even between closely related individual cells. Despite lots of progress, our understanding of the precise implementation, relevance, and possible manipulation of cellular signaling in health and disease therefore remains limited. Here, we discuss the requirements, potential, and limitations of the different current technologies for the analysis of hematopoietic stem and progenitor cell signaling and its effect on cell fates.

A review of dynamical systems approaches for the detection of chaotic attractors in cancer networks

Cancers are complex dynamical systems. They remain the leading cause of disease-related pediatric mortality in North America. To overcome this burden, we must decipher the state-space attractor dynamics of gene expression patterns and protein oscillations orchestrated by cancer stemness networks. The review provides an overview of dynamical systems theory to steer cancer research in pattern science. While most of our current tools in network medicine rely on statistical correlation methods, causality inference remains primitively developed. As such, a survey of attractor reconstruction methods and machine algorithms for the detection of causal structures applicable in experimentally derived time series cancer datasets is presented. A toolbox of complex systems approaches are discussed for reconstructing the signaling state space of cancer networks, interpreting causal relationships in their time series gene expression patterns, and assisting clinical decision making in computational oncology. As a proof of concept, the applicability of some algorithms are demonstrated on pediatric brain cancer datasets and the requirement of their time series analysis is highlighted.

A tale of two rhythms: Locked clocks and chaos in biology

The fundamental mechanisms that control and regulate biological organisms exhibit a surprising level of complexity. Oscillators are perhaps the simplest motifs that produce time-varying dynamics and are ubiquitous in biological systems. It is also known that such biological oscillators interact with each other-for instance, circadian oscillators affect the cell cycle, and somitogenesis clock proteins in adjacent cells affect each other in developing embryos. Therefore, it is vital to understand the effects that can emerge from non-linear interaction between oscillations. Here, we show how oscillations typically arise in biology and take the reader on a tour through the great variety in dynamics that can emerge even from a single pair of coupled oscillators. We explain how chaotic dynamics can emerge and outline the methods of detecting this in experimental time traces. Finally, we discuss the potential role of such complex dynamical features in biological systems.

Active fluidic chip produced using 3D-printing for combinatorial therapeutic screening on liver tumor spheroid

Known for their capabilities in automated fluid manipulation, microfluidic devices integrated with pneumatic valves are broadly used for researches in life science and clinical practice. The application is, however, hindered by the high cost and overly complex fabrication procedure. Here, we present an approach for fabricating molds of active fluidic devices using a benchtop 3D printer and a simple 2-step protocol (i.e. 3D printing and polishing). The entire workflow can be completed within 6 h, costing less than US$ 5 to produce all necessary templates for PDMS replica molding, which have smooth surface and round-shaped pneumatic valve structures. Moreover, 3D printing can create unique bespoke on-off objects of a wide range of dimensions. The millimeter- and centimeter-sized features allow examination of large-scale biological samples. Our results demonstrate that the 3D-printed active fluidic device has valve control capacities on par with those made by photolithography. Controlled nutrients and ligands delivery by on-off active valves allows generation of dynamic signals mimicking the ever-changing environmental stimuli, and combinatorial/sequential drug inputs for therapeutic screening on liver tumor spheroid. We believe that the proposed methodology can pave the way for integration of active fluidic systems in research labs, clinical settings and even household appliances for a broad range of application.

Inferring Leading Interactions in the p53/Mdm2/Mdmx Circuit through Live-Cell Imaging and Modeling

The tumor-suppressive transcription factor p53 is a master regulator of stress responses. In non-stressed conditions, p53 is maintained at low levels by the ubiquitin ligase Mdm2 and its binding partner Mdmx. Mdmx depletion leads to a biphasic p53 response, with an initial post-mitotic pulse followed by oscillations. The mechanism underlying this dynamical behavior is unknown. Two different roles for Mdmx have been proposed: enhancing p53 ubiquitination by Mdm2 and inhibiting p53 activity. Here, we developed a mathematical model of the p53/Mdm2/Mdmx network to investigate which Mdmx functions quantitatively affect specific features of p53 dynamics under various conditions. We found that enhancement of Mdm2 activity was the most critical role of Mdmx under unstressed conditions. The model also accurately predicted p53 dynamics in Mdmx-depleted cells following DNA damage. This work outlines a strategy for rapidly testing possible network interactions to reveal those most impactful in regulating the dynamics of key proteins.

Landscape and flux govern cellular mode-hopping between oscillations

Recently, a "mode-hopping" phenomenon has been observed in a NF-κB gene regulatory network with oscillatory tumor necrosis factor (TNF) inputs. It was suggested that noise facilitates the switch between different oscillation modes. However, the underlying mechanism of this noise-induced "cellular mode-hopping" behavior remains elusive. We employed a landscape and flux approach to study the stochastic dynamics and global stability of the NF-κB regulatory system. We used a truncated moment equation approach to calculate the probability distribution and potential landscape for gene regulatory systems. The potential landscape of the NF-κB system exhibits a "double ring valley" shape. Barrier heights from landscape topography provide quantitative measures of the global stability and transition feasibility of the double oscillation system. We found that the landscape and flux jointly govern the dynamical "mode-hopping" behavior of the NF-κB regulatory system. The landscape attracts the system into a "double ring valley," and the flux drives the system to move cyclically. As the external noise increases, relevant barrier heights decrease, and the flux increases. As the amplitude of the TNF input increases, the flux contribution, from the total driving force, increases and the system behavior changes from one to two cycles and ultimately to chaotic dynamics. Therefore, the probabilistic flux may provide an origin of chaotic behavior. We found that the height of the peak of the power spectrum of autocorrelation functions and phase coherence is correlated with barrier heights of the landscape and provides quantitative measures of global stability of the system under intrinsic fluctuations.

Low-dimensional Dynamics of Two Coupled Biological Oscillators

The circadian clock and the cell cycle are two biological oscillatory processes that coexist within individual cells. These two oscillators were found to interact, which can lead to their synchronization. Here, we develop a method to identify a low-dimensional stochastic model of the coupled system directly from time-lapse imaging in single cells. In particular, we infer the coupling and non-linear dynamics of the two oscillators from thousands of mouse and human single-cell fluorescence microscopy traces. This coupling predicts multiple phase-locked states showing different degrees of robustness against molecular fluctuations inherent to cellular-scale biological oscillators. For the 1:1 state, the predicted phase-shifts upon period perturbations were validated experimentally. Moreover, the phase-locked states are temperature-independent and evolutionarily conserved from mouse to human, hinting at a common underlying dynamical mechanism. Finally, we detect a signature of the coupled dynamics in a physiological context, explaining why tissues with different proliferation states exhibited shifted circadian clock phases.

Techniques for Studying Decoding of Single Cell Dynamics

Cells must be able to interpret signals they encounter and reliably generate an appropriate response. It has long been known that the dynamics of transcription factor and kinase activation can play a crucial role in selecting an individual cell's response. The study of cellular dynamics has expanded dramatically in the last few years, with dynamics being discovered in novel pathways, new insights being revealed about the importance of dynamics, and technological improvements increasing the throughput and capabilities of single cell measurements. In this review, we highlight the important developments in this field, with a focus on the methods used to make new discoveries. We also include a discussion on improvements in methods for engineering and measuring single cell dynamics and responses. Finally, we will briefly highlight some of the many challenges and avenues of research that are still open.

NF-κB Signaling in Macrophages: Dynamics, Crosstalk, and Signal Integration

The nuclear factor-κB (NF-κB) signaling pathway is one of the best understood immune-related pathways thanks to almost four decades of intense research. NF-κB signaling is activated by numerous discrete stimuli and is a master regulator of the inflammatory response to pathogens and cancerous cells, as well as a key regulator of autoimmune diseases. In this regard, the role of NF-κB signaling in immunity is not unlike that of the macrophage. The dynamics by which NF-κB proteins shuttle between the cytoplasm and the nucleus to initiate transcription have been studied rigorously in fibroblasts and other non-hematopoietic cells, but many questions remain as to how current models of NF-κB signaling and dynamics can be translated to innate immune cells such as macrophages. In this review, we will present recent research on the dynamics of NF-κB signaling and focus especially on how these dynamics vary in different cell types, while discussing why these characteristics may be important. We will end by looking ahead to how new techniques and technologies should allow us to analyze these signaling processes with greater clarity, bringing us closer to a more complete understanding of inflammatory transcription factor dynamics and how different cellular contexts might allow for appropriate control of innate immune responses.

On chaotic dynamics in transcription factors and the associated effects in differential gene regulation

The control of proteins by a transcription factor with periodically varying concentration exhibits intriguing dynamical behaviour. Even though it is accepted that transcription factors vary their dynamics in response to different situations, insight into how this affects downstream genes is lacking. Here, we investigate how oscillations and chaotic dynamics in the transcription factor NF-κB can affect downstream protein production. We describe how it is possible to control the effective dynamics of the transcription factor by stimulating it with an oscillating ligand. We find that chaotic dynamics modulates gene expression and up-regulates certain families of low-affinity genes, even in the presence of extrinsic and intrinsic noise. Furthermore, this leads to an increase in the production of protein complexes and the efficiency of their assembly. Finally, we show how chaotic dynamics creates a heterogeneous population of cell states, and describe how this can be beneficial in multi-toxic environments.

It is becoming clear that the dynamics of transcription factors may be important for gene regulation. Here, the authors study the implications of oscillatory and chaotic dynamics of NF-κB and demonstrate that it allows a degree of control of gene expression and can generate phenotypic heterogeneity.

Analog Signaling With the "Digital" Molecular Switch CaMKII

Molecular switches, such as the protein kinase CaMKII, play a fundamental role in cell signaling by decoding inputs into either high or low states of activity; because the high activation state can be turned on and persist after the input ceases, these switches have earned a reputation as "digital." Although this on/off, binary perspective has been valuable for understanding long timescale synaptic plasticity, accumulating experimental evidence suggests that the CaMKII switch can also control plasticity on short timescales. To investigate this idea further, a non-autonomous, nonlinear ordinary differential equation, representative of a general bistable molecular switch, is analyzed. The results suggest that switch activity in regions surrounding either the high- or low-stable states of activation could act as a reliable analog signal, whose short timescale fluctuations relative to equilibrium track instantaneous input frequency. The model makes intriguing predictions and is validated against previous work demonstrating its suitability as a minimal representation of switch dynamics; in combination with existing experimental evidence, the theory suggests a multiplexed encoding of instantaneous frequency information over short timescales, with integration of total activity over longer timescales.

NF-κB, the Importance of Being Dynamic: Role and Insights in Cancer

In this review, we aim at describing the results obtained in the past years on dynamics features defining NF-κB regulatory functions, as we believe that these developments might have a transformative effect on the way in which NF-κB involvement in cancer is studied. We will also describe technical aspects of the studies performed in this context, including the use of different cellular models, culture conditions, microscopy approaches and quantification of the imaging data, balancing their strengths and limitations and pointing out to common features and to some open questions. Our emphasis in the methodology will allow a critical overview of literature and will show how these cutting-edge approaches can contribute to shed light on the involvement of NF-κB deregulation in tumour onset and progression. We hypothesize that this “dynamic point of view” can be fruitfully applied to untangle the complex relationship between NF-κB and cancer and to find new targets to restrain cancer growth.

Oscillatory stimuli differentiate adapting circuit topologies

Adapting pathways consist of negative feedback loops (NFLs) or incoherent feedforward loops (IFFLs), which we show can be differentiated using oscillatory stimulation: NFLs but not IFFLs generically show ‘refractory period stabilization’ or ‘period skipping’. Using these signatures and genetic rewiring we identified the circuit dominating cell cycle timing in yeast. In C. elegans AWA neurons we uncovered a Ca2+-NFL, diffcult to find by other means, especially in wild-type, intact animals. (70 words)

Universal signal generator for dynamic cell stimulation

Dynamic cell stimulation is a powerful technique for probing gene networks and for applications in stem cell differentiation, immunomodulation and signaling. We developed a robust and flexible method and associated microfluidic devices to generate a wide-range of precisely formulated dynamic chemical signals to stimulate live cells and measure their dynamic response. This signal generator is capable of digital to analog conversion (DAC) through combinatoric selection of discrete input concentrations, and outperforms existing methods by both achievable resolution, dynamic range and simplicity in design. It requires no calibration, has minimal space requirements and can be easily integrated into microfluidic cell culture devices. The signal generator hardware and software we developed allows to choose the waveform, period and amplitude of chemical input signals and features addition of well-defined chemical noise to study the role of stochasticity in cellular information processing.

Entraining Oscillations in the NF-κB Signaling System: With a Little Help from Noise

Two studies show that noise is a key ingredient of new mechanisms for entraining the NF-κB system.