Several transcription factors (TFs) oscillate, periodically relocating between the cytoplasm and the nucleus. NF-κB, which plays key roles in inflammation and cancer, displays oscillations whose biological advantage remains unclear. Recent work indicated that NF-κB displays sustained oscillations that can be entrained, that is, reach a persistent synchronized state through small periodic perturbations. We show here that for our GFP-p65 knock-in cells NF-κB behaves as a damped oscillator able to synchronize to a variety of periodic external perturbations with no memory. We imposed synchronous dynamics to prove that transcription of NF-κB-controlled genes also oscillates, but mature transcript levels follow three distinct patterns. Two sets of transcripts accumulate fast or slowly, respectively. Another set, comprising chemokine and chemokine receptor mRNAs, oscillates and resets at each new stimulus, with no memory of the past. We propose that TF oscillatory dynamics is a means of segmenting time to provide renewing opportunity windows for decision.DOI: http://dx.doi.org/10.7554/eLife.09100.001

In this letter we discuss some properties of order patterns both in deterministic and random orbit generation. As it turns out, the orbits of one-dimensional maps have always forbidden patterns, i.e., order patterns that cannot occur, in contrast with random time series, in which any order pattern appears with probability one. However, finite random sequences may exhibit "false" forbidden patterns with non-vanishing probability. In this case, forbidden patterns decay with the sequence length, thus unveiling the random nature of the sequence. Last but not least, true forbidden patterns are robust against noise and disintegrate with a rate that depends on the noise level. These properties can be embodied in a simple method to distinguish deterministic, finite time series with very high levels of observational noise, from random ones. We present numerical evidence for white noise.

This paper deals with the distinction between white noise and deterministic chaos in multivariate noisy time series. Our method is combinatorial in the sense that it is based on the properties of topological permutation entropy, and it becomes especially interesting when the noise is so high that the standard denoising techniques fail, so a detection of determinism is the most one can hope for. It proceeds by i) counting the number of the so-called ordinal patterns in independent samples of length L from the data sequence and ii) performing a χ 2 test based on the results of i), the null hypothesis being that the data are white noise. Holds the null hypothesis, so should all possible ordinal patterns of a given length be visible and evenly distributed over sufficiently many samples, contrarily to what happens in the case of noisy deterministic data. We present numerical evidence in two dimensions for the efficiency of this method. A brief comparison with two common tests for independence, namely, the calculation of the autocorrelation function and the BDS algorithm, is also performed.

NF-κB is a transcription factor that upon activation undergoes cycles of cytoplasmic-to-nuclear and nuclear-to-cytoplasmic transport, giving rise to so called “oscillations”. In turn, oscillations tune the transcriptional output. Since a detailed understanding of oscillations requires a systems biology approach, we developed a method to acquire and analyze large volumes of data on NF-κB dynamics in single cells. We measured the time evolution of the nuclear to total ratio of GFP-p65 in knock-in mouse embryonic fibroblasts using time-lapse imaging. We automatically produced a precise segmentation of nucleus and cytoplasm based on an accurate estimation of the signal and image background. Finally, we defined a set of quantifiers that describe the oscillatory dynamics, which are internally normalized and can be used to compare data recorded by different labs. Using our method, we analyzed NF-κB dynamics in over 2000 cells exposed to different concentrations of TNF- α α. We reproduced known features of the NF-κB system, such as the heterogeneity of the response in the cell population upon stimulation and we confirmed that a fraction of the responding cells does not oscillate. We also unveiled important features: the second and third oscillatory peaks were often comparable to the first one, a basal amount of nuclear NF-κB could be detected in unstimulated cells, and at any time a small fraction of unstimulated cells showed spontaneous random activation of the NF-κB system. Our work lays the ground for systematic, high-throughput, and unbiased analysis of the dynamics of transcription factors that can shuttle between the nucleus and other cell compartments.

The genetic elements required to tune gene expression are partitioned in active and repressive nuclear condensates. Chromatin compartments include transcriptional clusters whose dynamic establishment and functioning depends on multivalent interactions occurring among transcription factors, cofactors and basal transcriptional machinery. However, how chromatin players contribute to the assembly of transcriptional condensates is poorly understood. By interrogating the effect of KMT2D (also known as MLL4 ) haploinsufficiency in Kabuki Syndrome, we found that MLL4 contributes to the assembly of transcriptional condensates through liquid-liquid phase separation. MLL4 loss-of-function (LoF) impaired Polycomb-dependent chromatin compartmentalization, altering nuclear architecture. By releasing the nuclear mechanical stress through the inhibition of the mechano-sensor ATR, we re-established the mechano-signaling of mesenchymal stem cells (MSCs) and their commitment towards chondrocytes both in vitro and in vivo. This study supports the notion that in Kabuki Syndrome the haploinsufficiency of MLL4 causes an altered functional partitioning of chromatin, which determines the architecture and mechanical properties of the nucleus.

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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.

Phase-control techniques of chaos aim to extract periodic behaviors from chaotic systems by applying weak harmonic perturbations with a suitably chosen phase. However, little is known about the best strategy for selecting adequate perturbations to reach desired states. Here we use experimental measures and numerical simulations to assess the benefits of controlling individually the three terms of a Duffing oscillator. Using a real-time analog indicator able to discriminate on-the-fly periodic behaviors from chaos, we reconstruct experimentally the phase versus perturbation strength stability areas when periodic perturbations are applied to different terms governing the oscillator. We verify the system to be more sensitive to perturbations applied to the quadratic term of the double-well Duffing oscillator and to the quartic term of the single-well Duffing oscillator.