Reviewing mathematical models of sperm signaling networks.

Dave Garbers' work significantly contributed to our understanding of sperm's regulated motility, capacitation, and the acrosome reaction. These key sperm functions involve complex multistep signaling pathways engaging numerous finely orchestrated elements. Despite significant progress, many parameters and interactions among these elements remain elusive.

Nonlinear comparative analysis of Greenland and Antarctica ice cores data.

We analyze the temperature time series of the EPICA Dome C ice cores in Antarctica and of the Greenland project, Summit, with durations of 800 000 and 248 000 years, respectively, with a recent mathematical tool defined through the Fourier phases of the series, known as the J-index. This data driven index can differentiate between purely random dynamics and dynamics with a deterministic component. It is sensitive to nonlinear components and robust to the presence of noise.

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.

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.

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.

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.

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.

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.

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.

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.

Network model predicts that CatSper is the main Ca 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.

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.

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.

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.

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.

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.

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.

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.

Analytical approach to the time-dependent probability density function in tilted periodic potentials.

In this work we introduce a scheme for the calculation of an approximate closed expression for the time-dependent probability density function for overdamped particles in tilted periodic potentials. Our derivation is based on an ansatz for the solution of the corresponding Fokker-Planck equation and on a self-consistent cumulant calculation. The high accuracy of our expression for the time-dependent probability density function is exhibited by comparisons with Langevin dynamics simulations and exact analytic results for the drift and diffusion coefficients.

Occurrence and robustness of current reversals in overdamped deterministic ratchets under symmetric forcing.

We analyze the conditions for the existence of current reversals in overdamped deterministic tilting ratchets under symmetric forcing. To this end, we use and extend the formalism recently introduced in R. Salgado-García, M.

Synchronization phenomena for a pair of locally coupled chaotic electrochemical oscillators: a survey.

Chaotic synchronization of two locally coupled electrochemical oscillators is studied numerically. Both bidirectional and unidirectional couplings are considered. For both these coupling scenarios, varying the characteristics of the coupling terms (functional form and/or strength) reveals a wide variety of synchronization phenomena.

Deterministic ratchets, circle maps, and current reversals.

In this work we transform the deterministic dynamics of an overdamped tilting ratchet into a discrete dynamical map by looking stroboscopically at the continuous motion originally ruled by differential equations. We show that, for the simple and widely used case of periodic dichotomous driving forces, the resulting discrete map belongs to the class of circle homeomorphisms. This approach allows us to apply the well-known properties of such maps to derive the necessary and sufficient conditions that the ratchet potential must satisfy in order to have a vanishing current.

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.

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.

Parameter space reduction criteria to search for synchronization domains in coupled discrete systems.

Based on analytical considerations, we introduce criteria that enable us to encapsulate the parameter domains for which chaotic synchronization in linearly coupled map systems may be attained. Our aim is to provide means to readily determine parameter regions which preclude synchronization. This results in a significant reduction of parameter space that one needs to explore.