Fourier phase index for extracting signatures of determinism and nonlinear features in time series.

Detecting determinism and nonlinear properties from empirical time series is highly nontrivial. Traditionally, nonlinear time series analysis is based on an error-prone phase space reconstruction that is only applicable for stationary, largely noise-free data from a low-dimensional system and requires the nontrivial adjustment of various parameters. We present a data-driven index based on Fourier phases that detects determinism at a well-defined significance level, without using Fourier transform surrogate data. It extracts nonlinear features, is robust to noise, provides time-frequency resolution by a double running window approach, and potentially distinguishes regular and chaotic dynamics. We test this method on data derived from dynamical models as well as on real-world data, namely, intracranial recordings of an epileptic patient and a series of density related variations of sediments of a paleolake in Tlaxcala, Mexico.

Opportune warning of COVID-19 in a Mexican health care worker cohort: Discrete beta distribution entropy of smartwatch physiological records.

We present a statistical study of heart rate, step cadence, and sleep stage registers of health care workers in the Hospital General de México "Dr. Eduardo Liceaga" (HGM), monitored continuously and non-invasively during the COVID-19 contingency from May to October 2020, using the Fitbit Charge 3® Smartwatch device. The HGM-COVID cohort consisted of 115 participants assigned to areas of COVID-19 exposure. We introduce a novel biomarker for an opportune signal for the likelihood of SARS-CoV-2 infection based on the Shannon Entropy of the Discrete Generalized Beta Distribution fit of rank ordered smartwatch registers. Our statistical test indicated infection for 94% of patients confirmed by positive polymer chain reaction (PCR+) test, 47% before the test, and 47% in coincidence. These results required innovative data preprocessing for the definition of a new biomarker index. The statistical method parameters are data-driven, confidence estimates were calibrated based on sensitivity tests using appropriately derived surrogate data as a benchmark. Our surrogate tests can also provide a benchmark for comparing results from other anomaly detection methods (ADMs). Biomarker comparison of the negative Immunoglobulin G Antibody (IgG-) subgroup with the PCR+ subgroup showed a statistically significant difference (p < 0.01, effect size = 1.44). The distribution of the uninfected population had a lower median and less dispersion than the PCR+ population. A retrospective study of our results confirmed that the biomarker index provides an early warning of the likelihood of COVID-19, even several days before the onset of symptoms or the PCR+ test request. The method can be calibrated for the analysis of different SARS-CoV-2 strains, the effect of vaccination, and previous infections. Furthermore, our biomarker screening could be implemented to provide general health profiles for other population sectors based on physiological signals from smartwatch wearable devices.

High Incidence Rate of SARS-CoV-2 Infection in Health Care Workers at a Dedicated COVID-19 Hospital: Experiences of the Pandemic from a Large Mexican Hospital.

Health care workers (HCW) are at high risk of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection. The incidence of SARS-CoV-2 infection in HCW has been examined in cross-sectional studies by quantitative polymerase chain reaction (qPCR) tests, which may lead to underestimating exact incidence rates. We thus investigated the incidence of SARS-CoV-2 infection in a group of HCW at a dedicated coronavirus disease 2019 (COVID-19) hospital in a six-month follow-up period. We conducted a prospective cohort study on 109 participants of both sexes working in areas of high, moderate, and low SARS-CoV-2 exposure. qPCR tests in nasopharyngeal swabs and anti-SARS-CoV-2 IgG serum antibodies were assessed at the beginning and six months later. Demographic, clinical, and laboratory parameters were analyzed according to IgG seropositivity by paired Student's T-test or the chi-square test. The incidence rate of SARS-CoV-2 infection was considerably high in our cohort of HCW (58%), among whom 67% were asymptomatic carriers. No baseline risk factors contributed to the infection rate, including the workplace. It is still necessary to increase hospital safety procedures to prevent virus transmissibility from HCW to relatives and non-COVID-19 patients during the upcoming waves of contagion.

Mathematical model reveals that heterogeneity in the number of ion transporters regulates the fraction of mouse sperm capacitation.

Capacitation is a complex maturation process mammalian sperm must undergo in the female genital tract to be able to fertilize an egg. This process involves, amongst others, physiological changes in flagellar beating pattern, membrane potential, intracellular ion concentrations and protein phosphorylation. Typically, in a capacitation medium, only a fraction of sperm achieve this state. The cause for this heterogeneous response is still not well understood and remains an open question. Here, one of our principal results is to develop a discrete regulatory network, with mostly deterministic dynamics in conjunction with some stochastic elements, for the main biochemical and biophysical processes involved in the early events of capacitation. The model criterion for capacitation requires the convergence of specific levels of a select set of nodes. Besides reproducing several experimental results and providing some insight on the network interrelations, the main contribution of the model is the suggestion that the degree of variability in the total amount and individual number of ion transporters among spermatozoa regulates the fraction of capacitated spermatozoa. This conclusion is consistent with recently reported experimental results. Based on this mathematical analysis, experimental clues are proposed for the control of capacitation levels. Furthermore, cooperative and interference traits that become apparent in the modelling among some components also call for future theoretical and experimental studies.

Discrete Dynamic Model of the Mammalian Sperm Acrosome Reaction: The Influence of Acrosomal pH and Physiological Heterogeneity.

The acrosome reaction (AR) is an exocytotic process essential for mammalian fertilization. It involves diverse physiological changes (biochemical, biophysical, and morphological) that culminate in the release of the acrosomal content to the extracellular medium as well as a reorganization of the plasma membrane (PM) that allows sperm to interact and fuse with the egg. In spite of many efforts, there are still important pending questions regarding the molecular mechanism regulating the AR. Particularly, the contribution of acrosomal alkalinization to AR triggering physiological conditions is not well understood. Also, the dependence of the proportion of sperm capable of undergoing AR on the physiological heterogeneity within a sperm population has not been studied. Here, we present a discrete mathematical model for the human sperm AR based on the physiological interactions among some of the main components of this complex exocytotic process. We show that this model can qualitatively reproduce diverse experimental results, and that it can be used to analyze how acrosomal pH (pH a ) and cell heterogeneity regulate AR. Our results confirm that a pH a increase can on its own trigger AR in a subpopulation of sperm, and furthermore, it indicates that this is a necessary step to trigger acrosomal exocytosis through progesterone, a known natural inducer of AR. Most importantly, we show that the proportion of sperm undergoing AR is directly related to the detailed structure of the population physiological heterogeneity.

Modular analysis of the control of flagellar Ca2+-spike trains produced by CatSper and CaV channels in sea urchin sperm.

Intracellular calcium ([Ca2+]i) is a basic and ubiquitous cellular signal controlling a wide variety of biological processes. A remarkable example is the steering of sea urchin spermatozoa towards the conspecific egg by a spatially and temporally orchestrated series of [Ca2+]i spikes. Although this process has been an experimental paradigm for reproduction and sperm chemotaxis studies, the composition and regulation of the signalling network underlying the cytosolic calcium fluctuations are hitherto not fully understood. Here, we used a differential equations model of the signalling network to assess which set of channels can explain the characteristic envelope and temporal organisation of the [Ca2+]i-spike trains. The signalling network comprises an initial membrane hyperpolarisation produced by an Upstream module triggered by the egg-released chemoattractant peptide, via receptor activation, cGMP synthesis and decay. Followed by downstream modules leading to intraflagellar pH (pHi), voltage and [Ca2+]i fluctuations. The Upstream module outputs were fitted to kinetic data on cGMP activity and early membrane potential changes measured in bulk cell populations. Two candidate modules featuring voltage-dependent Ca2+-channels link these outputs to the downstream dynamics and can independently explain the typical decaying envelope and the progressive spacing of the spikes. In the first module, [Ca2+]i-spike trains require the concerted action of a classical CaV-like channel and a potassium channel, BK (Slo1), whereas the second module relies on pHi-dependent CatSper dynamics articulated with voltage-dependent neutral sodium-proton exchanger (NHE). We analysed the dynamics of these two modules alone and in mixed scenarios. We show that the [Ca2+]i dynamics observed experimentally after sustained alkalinisation can be reproduced by a model featuring the CatSper and NHE module but not by those including the pH-independent CaV and BK module or proportionate mixed scenarios. We conclude in favour of the module containing CatSper and NHE and highlight experimentally testable predictions that would corroborate this conclusion.

Rank ordered beta distributions of nonlinear map symbolic dynamics families with a first-order transition between dynamical regimes.

Rank-ordered distributions have been a matter of intense study. Often Zipf type invariant scaling is invoked; however, in the last decade the ubiquity of a Discrete Generalized Beta Distribution, DGBD, with two scaling exponents has been established. This distribution incorporates deviations from the power law at the extremes. A proper understanding of the meaning of these exponents is still lacking. Here, using two families of unimodal maps on the [0,1] interval, we construct binary sequences via standard symbolic dynamics. In both cases, the tent map, which is at the convex-concave border of the mapping families, separates intermittent regimes from chaotic dynamics. We show that the frequencies of n-tuples of the generated symbolic sequences are remarkably well fitted by the DGBD. We argue that in the underlying dynamics an order-disorder competition takes place and that one of the exponents is related to multiple range correlations, while the other is sensitive to disorder. In our study, we implement thermodynamic formalisms with which we can readily calculate n-tuple frequencies, in some particular cases, analytically. We show that for the convex mappings there is a first-order thermodynamic phase transition, while concave mappings have smooth free energy densities. Within our DGBD study, the transition between these two regimes coincides with a zero value for both exponents; in this sense, they may even be considered as indicators of the transition. An analysis of the difference between the exponents reinforces the interpretation we have assigned to them. Furthermore, the two regimes can be identified by the sign of such a difference. We also show that divergences in the invariant densities are responsible for the first order phase transitions observed in a range of the rank-frequency distributions. Our findings give further support to previous studies based on expansion-modification algorithms, birth-death processes, and random variable subtraction dynamics.

Network model predicts that CatSper is the main Ca2+ channel in the regulation of sea urchin sperm motility.

Spermatozoa sea urchin swimming behaviour is regulated by small peptides from the egg outer envelope. Speract, such a peptide, after binding to its receptor in Strongylocentrotus purpuratus sperm flagella, triggers a signaling pathway that culminates with a train of intracellular calcium oscillations, correlated with changes in sperm swimming pattern. This pathway has been widely studied but not fully characterized. Recent work on Arbacia punctulata sea urchin spermatozoa has documented the presence of the Ca2+ CatSper channel in their flagella and its involvement in chemotaxis. However, if other calcium channels participate in chemotaxis remains unclear. Here, based on an experimentally-backed logical network model, we conclude that CatSper is fundamental in the S. purpuratus speract-activated sea urchin sperm signaling cascade, although other Ca2+ channels could still be relevant. We also present for the first time experimental corroboration of its active presence in S. purpuratus sperm flagella. We argue, prompted by in silico knock-out calculations, that CatSper is the main generator of calcium oscillations in the signaling pathway and that other calcium channels, if present, have a complementary role. The approach adopted here allows us to unveil processes, which are hard to detect exclusively by experimental procedures.

Multiple scaling behaviour and nonlinear traits in music scores.

We present a statistical analysis of music scores from different composers using detrended fluctuation analysis (DFA). We find different fluctuation profiles that correspond to distinct autocorrelation structures of the musical pieces. Further, we reveal evidence for the presence of nonlinear autocorrelations by estimating the DFA of the magnitude series, a result validated by a corresponding study of appropriate surrogate data. The amount and the character of nonlinear correlations vary from one composer to another. Finally, we performed a simple experiment in order to evaluate the pleasantness of the musical surrogate pieces in comparison with the original music and find that nonlinear correlations could play an important role in the aesthetic perception of a musical piece.

Irregular Liesegang-type patterns in gas phase revisited. I. Experimental setup, data processing, and test of the spacing law.

Since the early work on Liesegang rings in gels, they have been a reference point for the study of pattern formation in chemical physics. Here we present a variant of the Liesegang experiment in gas phase, where ammonia and hydrochloric acid react within a glass tube producing a precipitate, which deposits along the tube wall producing a spatial pattern. With this apparently simple experiment a wide range of rich phenomenon can be observed due to the presence of convective flows and irregular dynamics reminiscent of turbulent behavior, for which precise measurements are scarce. In this first part of our work, we describe in detail the experimental setup, the method of data acquisition, the image processing, and the procedure used to obtain an intensity profile, which is representative of the amount of precipitate deposited at the tube walls. Special attention is devoted to the techniques rendering a data series reliable for statistical studies and model building, which may contribute to a characterization and understanding of the pattern formation phenomenon under consideration. As a first step in this direction, based on our data, we are able to show that the observed band pattern follows, with slight deviations, the spacing law encountered in common Liesegang rings, despite that the experimental conditions are very different. A further statistical correlation analysis of the data constitutes Paper II of this research.

Irregular Liesegang-type patterns in gas phase revisited. II. Statistical correlation analysis.

We present a statistical analysis of Liesegang-type patterns formed in a gaseous HCl-NH3 system by ammonium chloride precipitation along glass tubes, as described in Paper I [J. C. Torres-Guzmán et al., J. Chem. Phys. 144, 174701 (2016)] of this work. We focus on the detection and characterization of short and long-range correlations within the non-stationary sequence of apparently irregular precipitation bands. To this end we applied several techniques to estimate spatial correlations stemming from different fields, namely, linear auto-correlation via the power spectral density, detrended fluctuation analysis (DFA), and methods developed in the context of random matrix theory (RMT). In particular RMT methods disclose well pronounced long-range correlations over at least 40 bands in terms of both, band positions and intensity values. By using a variant of the DFA we furnish proof of the nonlinear nature of the detected long-range correlations.

On the dynamics of Liesegang-type pattern formation in a gaseous system.

Liesegang pattern formations are widely spread in nature. In spite of a comparably simple experimental setup under laboratory conditions, a variety of spatio-temporal structures may arise. Presumably because of easier control of the experimental conditions, Liesegang pattern formation was mainly studied in gel systems during more than a century. Here we consider pattern formation in a gas phase, where beautiful but highly complex reaction-diffusion-convection dynamics are uncovered by means of a specific laser technique. A quantitative analysis reveals that two different, apparently independent processes, both highly correlated and synchronized across the extension of the reaction cloud, act on different time scales. Each of them imprints a different structure of salt precipitation at the tube walls.

In silico determination of the effect of multi-target drugs on calcium dynamics signaling network underlying sea urchin spermatozoa motility.

The motility of spermatozoa of both Lytechinus pictus and Strongylocentrotus purpuratus sea urchin species is modulated by the egg-derived decapeptide speract via an oscillatory [Ca2+]-dependent signaling pathway. Comprehension of this pathway is hence directly related to the understanding of regulated sperm swimming. Niflumic acid (NFA), a nonsteroidal anti-inflammatory drug alters several ion channels. Though unspecific, NFA profoundly affects how sea urchin sperm respond to speract, increasing the [Ca2+]i oscillation period, amplitude, peak and average level values of the responses in immobilized and swimming cells. A previous logical network model we developed for the [Ca2+] dynamics of speract signaling cascade in sea urchin sperm allows integrated dissection of individual and multiple actions of NFA. Among the channels affected by NFA are: hyperpolarization-activated and cyclic nucleotide gated Na+ channels (HCN), [Ca2+]-dependent Cl- channels (CaCC) and [Ca2+]-dependent K+ channels (CaKC), all present in the sea urchin genome. Here, using our model we investigated the effect of blocking in silico HCN and CaCC channels suggested by experiments. Regarding CaKC channels, arguments can be provided for either their blockage or activation by NFA. Our study yielded two scenarios compliant with experimental observations: i) under CaKC inhibition, this [Ca2+]-dependent K+ channel should be different from the Slo1 channel and ii) under activation of the CaKC channel, another [Ca2+] channel not considered previously in the network is required, such as the pH-dependent CatSper channel. Additionally, our findings predict cause-effect relations resulting from a selective inhibition of those channels. Knowledge of these relations may be of consequence for a variety of electrophysiological studies and have an impact on drug related investigations. Our study contributes to a better grasp of the network dynamics and suggests further experimental work.

Niflumic acid disrupts marine spermatozoan chemotaxis without impairing the spatiotemporal detection of chemoattractant gradients.

In many broadcast-spawning marine organisms, oocytes release chemicals that guide conspecific spermatozoa towards them through chemotaxis. In the sea urchin Lytechinus pictus, the chemoattractant peptide speract triggers a train of fluctuations of intracellular Ca(2+) concentration in the sperm flagella. Each transient Ca(2+) elevation leads to a momentary increase in flagellar bending asymmetry, known as a chemotactic turn. Furthermore, chemotaxis requires a precise spatiotemporal coordination between the Ca(2+)-dependent turns and the form of chemoattractant gradient. Spermatozoa that perform Ca(2+)-dependent turns while swimming down the chemoattractant gradient, and conversely suppress turning events while swimming up the gradient, successfully approach the center of the gradient. Previous experiments in Strongylocentrotus purpuratus sea urchin spermatozoa showed that niflumic acid (NFA), an inhibitor of several ion channels, drastically altered the speract-induced Ca(2+) fluctuations and swimming patterns. In this study, mathematical modeling of the speract-dependent Ca(2+) signaling pathway suggests that NFA, by potentially affecting hyperpolarization-activated and cyclic nucleotide-gated channels, Ca(2+)-regulated Cl(-) channels and/or Ca(2+)-regulated K(+) channels, may alter the temporal organization of Ca(2+) fluctuations, and therefore disrupt chemotaxis. We used a novel automated method for analyzing sperm behavior and we identified that NFA does indeed disrupt chemotactic responses of L. pictus spermatozoa, although the temporal coordination between the Ca(2+)-dependent turns and the form of chemoattractant gradient is unaltered. Instead, NFA disrupts sperm chemotaxis by altering the arc length traveled during each chemotactic turning event. This alteration in the chemotactic turn trajectory disorientates spermatozoa at the termination of the turning event. We conclude that NFA disrupts chemotaxis without affecting how the spermatozoa decode environmental cues.

Discrete dynamics model for the speract-activated Ca2+ signaling network relevant to sperm motility.

Understanding how spermatozoa approach the egg is a central biological issue. Recently a considerable amount of experimental evidence has accumulated on the relation between oscillations in intracellular calcium ion concentration ([Ca2+]i) in the sea urchin sperm flagellum, triggered by peptides secreted from the egg, and sperm motility. Determination of the structure and dynamics of the signaling pathway leading to these oscillations is a fundamental problem. However, a biochemically based formulation for the comprehension of the molecular mechanisms operating in the axoneme as a response to external stimulus is still lacking. Based on experiments on the S. purpuratus sea urchin spermatozoa, we propose a signaling network model where nodes are discrete variables corresponding to the pathway elements and the signal transmission takes place at discrete time intervals according to logical rules. The validity of this model is corroborated by reproducing previous empirically determined signaling features. Prompted by the model predictions we performed experiments which identified novel characteristics of the signaling pathway. We uncovered the role of a high voltage-activated Ca2+ channel as a regulator of the delay in the onset of fluctuations after activation of the signaling cascade. This delay time has recently been shown to be an important regulatory factor for sea urchin sperm reorientation. Another finding is the participation of a voltage-dependent calcium-activated K+ channel in the determination of the period of the [Ca2+]i fluctuations. Furthermore, by analyzing the spread of network perturbations we find that it operates in a dynamically critical regime. Our work demonstrates that a coarse-grained approach to the dynamics of the signaling pathway is capable of revealing regulatory sperm navigation elements and provides insight, in terms of criticality, on the concurrence of the high robustness and adaptability that the reproduction processes are predicted to have developed throughout evolution.

Universality of rank-ordering distributions in the arts and sciences.

Searching for generic behaviors has been one of the driving forces leading to a deep understanding and classification of diverse phenomena. Usually a starting point is the development of a phenomenology based on observations. Such is the case for power law distributions encountered in a wealth of situations coming from physics, geophysics, biology, lexicography as well as social and financial networks. This finding is however restricted to a range of values outside of which finite size corrections are often invoked. Here we uncover a universal behavior of the way in which elements of a system are distributed according to their rank with respect to a given property, valid for the full range of values, regardless of whether or not a power law has previously been suggested. We propose a two parameter functional form for these rank-ordered distributions that gives excellent fits to an impressive amount of very diverse phenomena, coming from the arts, social and natural sciences. It is a discrete version of a generalized beta distribution, given by f(r) = A(N+1-r)(b)/r(a), where r is the rank, N its maximum value, A the normalization constant and (a, b) two fitting exponents. Prompted by our genetic sequence observations we present a growth probabilistic model incorporating mutation-duplication features that generates data complying with this distribution. The competition between permanence and change appears to be a relevant, though not necessary feature. Additionally, our observations mainly of social phenomena suggest that a multifactorial quality resulting from the convergence of several heterogeneous underlying processes is an important feature. We also explore the significance of the distribution parameters and their classifying potential. The ubiquity of our findings suggests that there must be a fundamental underlying explanation, most probably of a statistical nature, such as an appropriate central limit theorem formulation.

Interaction of the IP3-Ca2+ and MAPK signaling systems in the Xenopus blastomere: a possible frequency encoding mechanism for the control of the Xbra gene expression.

The intense periodic calcium activity experimentally observed in the Xenopus embryo at the Mid Blastula Transition stage is closely related to the competence of the embryonic cells of the marginal zone to respond to the posterior-mesodermal inducting signals from the Fibroblast Growth Factor (FGF). In this work we do a stability analysis and study numerically an extension of a mathematical model previously introduced by us [Diaz, J., Baier, G., Martinez-Mekler, G., Pastor, N., 2002. Interaction of the IP(3)-Ca(2+) and the FGF-MAPK signaling pathways in the Xenopus laevis embryo: a qualitative approach to the mesodermal induction problem. Biophys. Chem. 97, 55-72] for the interaction of the Inositol 1,4,5-triphosphate-Calcium (IP(3)-Ca(2+)) and the Mitogen-Activated Protein Kinase (MAPK) signaling pathways at the Mid Blastula Transition stage or stage 8 of development. This allows us to consider the effect of the oscillatory calcium dynamics on the FGF input signal carried by the MAP kinase (ERK) into the nucleus. We find that this interaction of the pathways induces a limit cycle behavior for ERK with frequency-encoding characteristics. We believe that this periodic increase of the ERK levels in the nucleus is related to the ability of the cell to express posteriorizing mesodermal features induced by the FGF signal at stage 8.

Role of a spatial distribution of IP3 receptors in the Ca2+ dynamics of the Xenopus embryo at the mid-blastula transition stage.

Periodic calcium activity correlates temporally with the onset of gene expression in the embryo, suggesting a causal relation between these two events. Calcium transients are elicited by the action of fibroblast growth factor (FGF) through the activation of phospholipase C. In this work, we present a reaction-diffusion model that extends our previous results on the generation of calcium oscillations for a single and two coupled blastomere cells to a meridian of the Xenopus embryo at the mid-blastula transition. In the model, all cells are subject to the same amount of FGF and contain the same concentration of intracellular components, except for the amount of IP(3) receptors (IP3R). A bell-shaped distribution of IP3R produces the correct shape of the calcium transients experimentally observed in the Xenopus blastula at stage 8 (mid-blastula transition stage). The model is also capable of predicting period and amplitude values close to the experimental values. In our model, calcium transients induce spatially localized ERK periodic transients that could activate specific nuclear genes, allowing for the regional differentiation of the cells in the zone under the influence of the calcium signal.

Interaction of the IP(3)-Ca(2+) and the FGF-MAPK signaling pathways in the Xenopus laevis embryo: a qualitative approach to the mesodermal induction problem.

In this work we propose that the animal-vegetal gradient spatial distribution of the IP(3) receptors observed in the Xenopus embryo can effect a uniform FGF inducting input signal, allowing for different modes of transcription of the Xbra gene, producing the differentiation of the cells of the marginal zone. We analyze this hypothesis with a model for the interaction of the calcium signaling system with the MAPK cascade during the FGF mesodermal induction process, consisting of five non-linear coupled differential equations. A numerical treatment of a one- and two-cell system shows that the calcium flux between cells enhances the Raf activity levels, leading to oscillatory behavior. This qualitative result may be of consequence for the expression of the ventralizing characteristics of the FGF inducting signal.