Rhythms and vibrations represent the quintessence of life, they are ubiquitous (systemic) in all living systems. Recognising, unfolding these rhythms is paramount in medicine, for example in the physiology of the heart, lung, hearing, speech, brain, the cellular and molecular processes involved in biological clocks. The importance of the commensurability of the frequencies in different rhythms has been thoroughly studied in music. We define a log-frequency correlation measure on spectral densities that gives the temporal evolution of the distribution of frequency ratios (rational or irrational) in between two signals, using analytic wavelets. We illustrate these concepts on numerical signals (sums of sine functions) and voice recordings from the Voice-Icar-Federico II database. Finally, with a second correlation operation from two of these ratio distributions (a reference one, the other from the voices) we introduce another quantity that we call sonance, measuring the “harmony” (rationality) of two voices sung together as a function of a pitch transposition.

We study the avalanche statistics observed in a minimal random growth model. The growth is governed by a reproduction rate obeying a probability distribution with finite mean a[over ¯] and variance v_{a}. These two control parameters determine if the avalanche size tends to a stationary distribution (finite scale statistics with finite mean and variance, or power-law tailed statistics with exponent ∈(1,3]), or instead to a nonstationary regime with log-normal statistics. Numerical results and their statistical analysis are presented for a uniformly distributed growth rate, which are corroborated and generalized by mathematical results. The latter show that the numerically observed avalanche regimes exist for a wide family of growth rate distributions, and they provide a precise definition of the boundaries between the three regimes.

The 2D wavelet transform modulus maxima (WTMM) method is used to perform a comparison of the spatial fluctuations of mammographic breast tissue from patients with invasive lobular carcinoma, those with invasive ductal carcinoma, and those with benign lesions. We follow a procedure developed and validated in a previous study, in which a sliding window protocol is used to analyze thousands of small subregions in a given mammogram. These subregions are categorized according to their Hurst exponent values (H): fatty tissue (H ≤ 0.45), dense tissue (H ≥ 0.55), and disrupted tissue potentially linked with tumor-associated loss of homeostasis (0.45 < H < 0.55). Following this categorization scheme, we compare the mammographic tissue composition of the breasts. First, we show that cancerous breasts are significantly different than breasts with a benign lesion (p-value ∼ 0.002). Second, the asymmetry between a patient's cancerous breast and its contralateral counterpart, when compared to the asymmetry from patients with benign lesions, is also statistically significant (p-value ∼ 0.006). And finally, we show that lobular and ductal cancerous breasts show similar levels of disruption and similar levels of asymmetry. This study demonstrates reproducibility of the WTMM sliding-window approach to help detect and characterize tumor-associated breast tissue disruption from standard mammography. It also shows promise to help with the detection lobular lesions that typically go undetected via standard screening mammography at a much higher rate than ductal lesions. Here both types are assessed similarly.

Actin is the major cytoskeletal protein of mammal cells that forms microfilaments organized into higher-order structures by a dynamic assembly-disassembly mechanism with cross-linkers. These networks provide the cells with mechanical support, and allow cells to change their shape, migrate, divide and develop a mechanical communication with their environment. The quick adaptation of these networks upon stretch or compression is important for cell survival in real situations. Using atomic force microscopy to poke living cells with sharp tips, we revealed that they respond to a local and quick shear through a cascade of random and abrupt ruptures of their cytoskeleton, suggesting that they behave as a quasi-rigid random network of intertwined filaments. Surprisingly, the distribution of the strength and the size of these rupture events did not follow power-law statistics but log-normal statistics, suggesting that the mechanics of living cells would not fit into self-organized critical systems. We propose a random Gilbert network to model a cell cytoskeleton, identifying the network nodes as the actin filaments, and its links as the actin cross-linkers. We study mainly two versions of avalanches. First, we do not include the fractional visco-elasticity of living cells, assuming that the ruptures are instantaneous, and we observe three avalanche regimes, 1) a regime where avalanches are rapidly interrupted, and their size follows a distribution decaying faster than a power-law; 2) an explosive regime with avalanches of large size where the whole network is damaged and 3) an intermediate regime where the avalanche distribution goes from a power-law, at the critical point, to a distribution containing both 1) and (ii). Then, we introduce a time varying breaking probability, to include the fractional visco-elasticity of living cells, and recover an approximated log-normal distribution of avalanche sizes, similar to those observed in experiments. Our simulations show that the log-normal statistics requires two simple ingredients: a random network without characteristic length scale, and a breaking rule capturing the broadly observed visco-elasticity of living cells. This work paves the way for future applications to large populations of non-linear individual elements (brain, heart, epidemics, … ) where similar log-normal statistics have also been observed.

The crosstalk between organs plays a crucial role in physiological processes. This coupling is a dynamical process, it must cope with a huge variety of rhythms with frequencies ranging from milliseconds to hours, days, seasons. The brain is a central hub for this crosstalk. During sleep, automatic rhythmic interrelations are enhanced and provide a direct insight into organ dysfunctions, however their origin remains a difficult issue, in particular in sleep disorders. In this study, we focus on EEG, ECG, and airflow recordings from polysomnography databases. Because these signals are non-stationary, non-linear, noisy, and span wide spectral ranges, a time-frequency analysis, based on wavelet transforms, is more appropriate to handle this complexity. We design a wavelet-based extraction method to identify the characteristic rhythms of these different signals, and their temporal variability. These new constructs are combined in pairs to compute their wavelet-based time-frequency complex coherence. These time-frequency coherence maps highlight the occurrence of a slowly modulated coherence pattern in the frequency range [0.01–0.06] Hz, which appears in both obstructive and central apnea. A preliminary exploration of a large database from the National Sleep Research Resource with respiration disorders, such as apnea provides some clues on its relation with autonomic cardio-respiratory coupling and brain rhythms. We also observe that during sleep apnea episodes (either obstructive or central), the cardiopulmonary coherence (in particular respiratory sinus-arrhythmia) in the frequency range [0.1–0.7] Hz strongly diminishes, suggesting a modification of this coupling. Finally, comparing time-averaged coherence with heart rate variability spectra in different apnea episodes, we discuss their common trait and their differences.

Ramp-cliff patterns visible in scalar turbulent time series have long been suspected to enhance the fine-scale intermittency of scalar fluctuations compared to longitudinal velocity fluctuations. Here, we use the wavelet transform modulus maxima method to perform a multifractal analysis of air temperature time series collected at a pine forest canopy top for different atmospheric stability regimes. We show that the multifractal spectra exhibit a phase transition as the signature of the presence of strong singularities corresponding to sharp temperature drops (respectively jumps) bordering the so-called ramp (respectively inverted ramp) cliff patterns commonly observed in unstable (respectively stable) atmospheric conditions and previously suspected to contaminate and possibly enhance the internal intermittency of (scalar) temperature fluctuations. Under unstable (respectively stable) atmospheric conditions, these 'cliff' singularities are indeed found to be hierarchically distributed on a 'Cantor-like' set surrounded by singularities of weaker strength typical of intermittent temperature fluctuations observed in homogeneous and isotropic turbulence. Under near-neutral conditions, no such a phase transition is observed in the temperature multifractal spectra, which is a strong indication that the statistical contribution of the 'cliffs' is not important enough to account for the stronger intermittency of temperature fluctuations when compared to corresponding longitudinal velocity fluctuations.

Nucleosome-depleted regions around which nucleosomes order following the "statistical" positioning scenario were recently shown to be encoded in the DNA sequence in human. This intrinsic nucleosomal ordering strongly correlates with oscillations in the local GC content as well as with the interspecies and intraspecies mutation profiles, revealing the existence of both positive and negative selection. In this letter, we show that these predicted nucleosome inhibitory energy barriers (NIEBs) with compacted neighboring nucleosomes are indeed ubiquitous to all vertebrates tested. These 1 kb-sized chromatin patterns are widely distributed along vertebrate chromosomes, overall covering more than a third of the genome. We have previously observed in human deviations from neutral evolution at these genome-wide distributed regions, which we interpreted as a possible indication of the selection of an open, accessible, and dynamic nucleosomal array to constitutively facilitate the epigenetic regulation of nuclear functions in a cell-type-specific manner. As a first, very appealing observation supporting this hypothesis, we report evidence of a strong association between NIEB borders and the poly(A) tails of Alu sequences in human. These results suggest that NIEBs provide adequate chromatin patterns favorable to the integration of Alu retrotransposons and, more generally to various transposable elements in the genomes of primates and other vertebrates.

In a companion paper (I. Multifractal analysis of clinical data), we used a wavelet-based multiscale analysis to reveal and quantify the multifractal intermittent nature of the cardiac impulse energy in the low frequency range ≲ 2Hz during atrial fibrillation (AF). It demarcated two distinct areas within the coronary sinus (CS) with regionally stable multifractal spectra likely corresponding to different anatomical substrates. The electrical activity also showed no sign of the kind of temporal correlations typical of cascading processes across scales, thereby indicating that the multifractal scaling is carried by variations in the large amplitude oscillations of the recorded bipolar electric potential. In the present study, to account for these observations, we explore the role of the kinetics of gap junction channels (GJCs), in dynamically creating a new kind of imbalance between depolarizing and repolarizing currents. We propose a one-dimensional (1D) spatial model of a denervated myocardium, where the coupling of cardiac cells fails to synchronize the network of cardiac cells because of abnormal transjunctional capacitive charging of GJCs. We show that this non-ohmic nonlinear conduction 1D modeling accounts quantitatively well for the "multifractal random noise" dynamics of the electrical activity experimentally recorded in the left atrial posterior wall area. We further demonstrate that the multifractal properties of the numerical impulse energy are robust to changes in the model parameters.

We report on a wavelet based space-scale decomposition method for analyzing the response of living muscle precursor cells (C2C12 myoblasts and myotubes) upon sharp indentation with an AFM cantilever and quantifying their aptitude to sustain such a local shear strain. Beyond global mechanical parameters which are currently used as markers of cell contractility, we emphasize the necessity of characterizing more closely the local fluctuations of the shear relaxation modulus as they carry important clues about the mechanisms of cytoskeleton strain release. Rupture events encountered during fixed velocity shear strain are interpreted as local disruptions of the actin cytoskeleton structures, the strongest (brittle) ones being produced by the tighter and stiffer stress fibers or actin agglomerates. These local strain induced failures are important characteristics of the resilience of these cells, and their aptitude to maintain their shape via a quick recovery from local strains. This study focuses on the perinuclear region because it can be considered as a master mechanical organizing center of these muscle precursor cells. Using this wavelet-based method, we combine the global and local approaches for a comparative analysis of the mechanical parameters of normal myoblasts, myotubes and myoblasts treated with actomyosin cytoskeleton disruptive agents (ATP depletion, blebbistatin).

The time-dependent rate I(t) of origin firing per length of unreplicated DNA presents a universal bell shape in eukaryotes that has been interpreted as the result of a complex time-evolving interaction between origins and limiting firing factors. Here we show that a normal diffusion of replication fork components towards localized potential replication origins (p-oris) can more simply account for the I(t) universal bell shape, as a consequence of a competition between the origin firing time and the time needed to replicate DNA separating two neighboring p-oris . We predict the I(t) maximal value to be the product of the replication fork speed with the squared p-ori density. We show that this relation is robustly observed in simulations and in experimental data for several eukaryotes. Our work underlines that fork-component recycling and potential origins localization are sufficient spatial ingredients to explain the universality of DNA replication kinetics.

The authors propose a wavelet-based decomposition of creep fluctuation signals recorded from living muscle precursor cells that revisit the traditional computation of their power spectrum from FFT-based decomposition. This decomposition offers a higher sensitivity for detecting the occurrence of fractional fluctuations and for quantitatively estimating the power-law exponent β of this spectrum as a signature of the scale-invariant rheology of living cells. This new method has also the unprecedented advantage of providing a test of the validity of the commonly assumed “monofractal” self-similar (as compared to “multifractal” intermittent) nature of these fluctuations and hence accrediting the use of a single rheological exponent α = β / 2. We report and discuss results obtained when applying this method to creep experiments performed with an AFM nanoindenter placed in contact with single myoblasts and myotubes, adherent on collagen coated coverslips, and in different culture conditions.

Under physiological and pathological conditions, cells experience large forces and deformations that often exceed the linear viscoelastic regime. Here we drive CD34(+) cells isolated from healthy and leukemic bone marrows in the highly nonlinear elasto-plastic regime, by poking their perinuclear region with a sharp AFM cantilever tip. We use the wavelet transform mathematical microscope to identify singular events in the force-indentation curves induced by local rupture events in the cytoskeleton (CSK). We distinguish two types of rupture events, brittle failures likely corresponding to irreversible ruptures in a stiff and highly cross-linked CSK and ductile failures resulting from dynamic cross-linker unbindings during plastic deformation without loss of CSK integrity. We propose a stochastic multiplicative cascade model of mechanical ruptures that reproduces quantitatively the experimental distributions of the energy released during these events, and provides some mathematical and mechanistic understanding of the robustness of the log-normal statistics observed in both brittle and ductile situations. We also show that brittle failures are relatively more prominent in leukemia than in healthy cells suggesting their greater fragility.

The time-dependent rate I(t) of origin firing per length of unreplicated DNA presents a universal bell shape in eukaryotes that has been interpreted as the result of a complex time-evolving interaction between origins and limiting firing factors. Here, we show that a normal diffusion of replication fork components towards localized potential replication origins (p-oris) can more simply account for the I(t) universal bell shape, as a consequence of a competition between the origin firing time and the time needed to replicate DNA separating two neighboring p-oris. We predict the I(t) maximal value to be the product of the replication fork speed with the squared p-ori density. We show that this relation is robustly observed in simulations and in experimental data for several eukaryotes. Our work underlines that fork-component recycling and potential origins localization are sufficient spatial ingredients to explain the universality of DNA replication kinetics.

The spatiotemporal program of metazoan DNA replication is regulated during development and altered in cancers. We have generated novel OK-seq, Repliseq and RNA-seq data to compare the DNA replication and gene expression programs of twelve cancer and non-cancer human cell types. Changes in replication fork directionality (RFD) determined by OK-seq are widespread but more frequent within GC-poor isochores and largely disconnected from transcription changes. Cancer cell RFD profiles cluster with non-cancer cells of similar developmental origin but not with different cancer types. Importantly, recurrent RFD changes are detected in specific tumour progression pathways. Using a model for establishment and early progression of chronic myeloid leukemia (CML), we identify 1027 replication initiation zones (IZs) that progressively change efficiency during long-term expression of the BCR-ABL1 oncogene, being twice more often downregulated than upregulated. Prolonged expression of BCR-ABL1 results in targeting of new IZs and accentuation of previous efficiency changes. Targeted IZs are predominantly located in GC-poor, late replicating gene deserts and frequently silenced in late CML. Prolonged expression of BCR-ABL1 results in massive deletion of GC-poor, late replicating DNA sequences enriched in origin silencing events. We conclude that BCR-ABL1 expression progressively affects replication and stability of GC-poor, late-replicating regions during CML progression.

We use a physical model of nucleosome formation based on sequence-dependent DNA bending properties to investigate the role of nucleosome positioning in the multiscale coding of nuclear functions. We show the existence in most eukaryotic organisms of nucleosome-inhibitory energy barriers (NIEBs) that condition the statistical positioning of neighboring nucleosomes. In Saccharomyces cerevisiae, most of the nucleosome-depleted regions (NDRs) observed in vivo at transcription start sites (TSS) and active DNA replication origins indeed correspond to sequence-dependent excluding energy barriers up to finite-range remodeling action of external factors including transcription factors and ATP-dependent chromatin remodelers. If similar sequence-driven NDR regulation of transcription and replication initiation is likely to operate in different yeast species and probably in Caenorhabditis elegans, the situation is quite different in mammals where a high nucleosome affinity (high local GC content) is programmed at regulatory sequences to intrinsically restrict access to regulatory information that will mostly be used in vivo in an epigenetically controlled cell-type-dependent manner. In human, 1.6 millions of NIEBs and flanking nucleosome ordering are observed both in vitro and in vivo as covering ~37.5% of the genome. Likely encoded in the local GC content, these 1-kb-sized regions of intrinsic nucleosome occupancy are equally found in GC-rich and GC-poor isochores, in early and late replicating regions, in intergenic and genic regions but not at gene promoters and replication initiation loci. The comparison of interspecies and intraspecies rates of divergence confirms the existence of some selection pressure to maintain an optimal GC content depletion in NDRs relative to the local bulk GC content. We propose that these widely distributed chromatin patterns have been selected in human, and more generally in mammals and other higher eukaryotes, to impair the condensation of the nucleosomal array into the 30 nm chromatin fiber, so as to facilitate the epigenetic regulation of nuclear functions in a multiscale cell-type-specific fashion.

Alteration of [Formula: see text] channel functions (channelopathies) has been encountered in various hereditary muscle diseases. [Formula: see text] channel mutations lead to aberrant excitability in skeletal muscle myotonia and paralysis. In general, these mutations disable inactivation of the [Formula: see text] channel, producing either repetitive action potential firing (myotonia) or electrical dormancy (flaccid paralysis) in skeletal muscles. These "sick-excitable" cell conditions were shown to correlate with a mechanical stretch-driven left shift of the conductance factors of the two gating mechanisms of a fraction of [Formula: see text] channels, which make them firing at inappropriate hyperpolarised (left-shifted) voltages. Here we elaborate on a variant of the Hodgkin-Huxley model that includes a stretch elasticity energy component in the activation and inactivation gate kinetic rates. We show that this model reproduces fairly well sick-excitable cell behaviour and can be used to predict the parameter domains where aberrant excitability or paralysis may occur. By allowing us to separate the incidences of activation and inactivation gate impairments in [Formula: see text] channel excitability, this model could be a strong asset for diagnosing the origin of excitable cell disorders.

For more than 50 years, resonant waveguides (RWGs) have offered highly sensitive label-free sensing platforms to monitor surface processes such as protein adsorption, affinity binding, monolayer to multilayer build-up, bacteria and more generally adherent or confined living mammalian cells and tissues. Symmetrical planar dielectric RWG sensitivity was improved by metal coating of at least one of their surfaces for surface plasmon resonance undertaking (SPRWG). However, RWG sensitivity was often obtained at the expense of spatial resolution and could not compete with other high resolution fluorescence microscopies. For years, RWGs have only rarely been combined with high-resolution microscopy. Only recently, the improvement of intensity and phase light modulation techniques and the availability of low-cost high numerical aperture lenses have drastically changed the devices and methodologies based on RWGs. We illustrate in this chapter how these different technical and methodological evolutions have offered new, versatile, and powerful imaging tools to the biological community.

Background: Structural interaction frequency matrices between all genome loci are now experimentally achievable thanks to high-throughput chromosome conformation capture technologies. This ensues a new methodological challenge for computational biology which consists in objectively extracting from these data the structural motifs characteristic of genome organisation.Results: We deployed the fast multi-scale community mining algorithm based on spectral graph wavelets to characterise the networks of intra-chromosomal interactions in human cell lines. We observed that there exist structural domains of all sizes up to chromosome length and demonstrated that the set of structural communities forms a hierarchy of chromosome segments. Hence, at all scales, chromosome folding predominantly involves interactions between neighbouring sites rather than the formation of links between distant loci.Conclusions: Multi-scale structural decomposition of human chromosomes provides an original framework to question structural organisation and its relationship to functional regulation across the scales. By construction the proposed methodology is independent of the precise assembly of the reference genome and is thus directly applicable to genomes whose assembly is not fully determined.

We report on a high-resolution metal-clad waveguide scanning microscopic method with a diffraction-limited resolution. This microscope can be operated in both TM and TE waveguide modes with radially and azimuthally polarized beams, respectively, and allows both refractive index and topography of dielectric objects to be evaluated at high resolution and sensitivity. We emphasize the performance of this microscopic method from calibrated 3D polymer microstructures with rectangular, disk, and ring shapes.