Gustavo Martínez-Mekler

The study of inter-beat intervals (IBI) and systolic blood pressure (SBP) fluctuations is of public health importance. Here we obtain insights about their underlying dynamics by means of an innovative study of the distribution of their rank-ordered registers, provided by fits to the Discrete Generalized Beta Distribution (DGBD), for healthy subjects and patients with end-stage renal disease (ESRD), under an active standing maneuver. SBP and IBI non-invasive time series were recorded during supine position followed by active standing for nine ESRD patients and eighteen age-matched healthy subjects. Once the data were rank ordered, the three parameter DGBD function was fitted through the Levenberg–Marquardt non-linear algorithm. Taking into consideration the statistical interpretations of the parameters, the quantitative exploration of their dependence with regard to the cases examined and changes in body position provided new insights: (i) Evidence for the presence of regulatory mechanisms that preserve the tail symmetry of the IBI distributions in healthy subjects, which are not evident in ESRD patients; (ii) The identification of a more pronounced weight of low-magnitude fluctuations at active standing in the SBP time series, manifested as a broader statistical dispersion of blood pressure values; (iii) A quantitative determination of a more undermined SBP regulation in ESRD. Overall, a better understanding of the statistical behavior of IBI and SBP time series is achieved by means of the DGBD function. Through the variation of its parameters, the DGBD approach has the potential to become a marker for assessing or even predicting the impairment of cardiovascular control mechanisms.

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. Mathematical modeling emerges as a potent tool to study sperm physiology, providing a framework to integrate experimental results and capture functional dynamics considering biochemical, biophysical, and cellular elements. Depending on research objectives, different modeling strategies, broadly categorized into continuous and discrete approaches, reveal valuable insights into cell function. These models allow the exploration of hypotheses regarding molecules, conditions, and pathways, whenever they become challenging to evaluate experimentally. This review presents an overview of current theoretical and experimental efforts to understand sperm motility regulation, capacitation, and the acrosome reaction. We discuss the strengths and weaknesses of different modeling strategies and highlight key findings and unresolved questions. Notable discoveries include the importance of specific ion channels, the role of intracellular molecular heterogeneity in capacitation and the acrosome reaction, and the impact of pH changes on acrosomal exocytosis. Ultimately, this review underscores the crucial importance of mathematical frameworks in advancing our understanding of sperm physiology and guiding future experimental investigations.

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. Our J-index data analysis shows that both Greenland and Antarctica climatic fluctuations possess deterministic traits and suggests the presence of an underlying nonlinear dynamics. Furthermore, in both regions, it reveals the simultaneous occurrence of an important global event known as the “Pelukian transgression.” For Antarctica, it also detects the marine isotopic stage 11. Additionally, our calculation of the time series Hurst exponents and our detrended fluctuation analysis show the presence of long-range persistent correlations for Antarctica and anti-persistent correlations for Greenland. For the latter case, our fractal dimension determinations are indicative of a more complex climatic dynamics in Greenland with respect to Antarctica. Our results are encouraging for further development of climate variability deterministic models for these regions.

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.

This paper explores theoretically the formation of a system of cities in which ports affect the spatial location and the size of cities. We use a complex systems and economic geography approach to generate 2D cellular automata to simulate the formation of the landscape of urban agglomerations based on different configurations of port locations. The dynamics of the model shows the emergence of the classical city-size distributions in which the number of ports and their layout affects the growth rate and location of the city-size values. Our findings showed that the two port-city configuration give rise to cities at a long distance from a small number of ports. The size of the cities shows a positive correlations with their distance to ports. A four port-city configuration showed that if the number of ports increases, lower city-sizes are attained and their population displays a negative correlations with their distance to ports. For a lateral configuration with a significantly increase in the number of ports, mainly homogeneous city-size distributions are favored with a slight long-distance size correlation. Therefore, our theoretical model shows a high internal consistency between the theory and assumptions used for describing reliable scenarios in the relationship of ports and urban systems.

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.

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.

The acrosome reaction (AR) is an exocytotic process essential for mammalian fertilization. It involves diverse biochemical and physiological changes 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 in physiological conditions is not well understood. Also, the dependence of the proportion of sperm capable of undergoing AR on the biochemical heterogeneity within a sperm population has not been studied. Here we present a discrete mathematical model for the human sperm AR, based on the biophysical and biochemical 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 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 physiological inducer of AR. Most importantly, we show that the proportion of sperm undergoing AR is directly related to the detailed structure of the population biochemical heterogeneity.

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. Author summary: Fertilization is one of the fundamental processes for the preservation of life. In mammals, sperm undergo a complex process during their passage through the female tract known as capacitation, which enables them for fertilization. At the present time, it is accepted from experimental observation, though not understood, that only a fraction of the sperm is capacitated. In this work, by means of a network mathematical model for regulatory sperm intracellular signaling processes involved in mice capacitation, we find that the variability in the distribution of the number of ion transporters intervenes in the regulation of the capacitation fraction. Experimental verification of this suggestion could open a line of research geared to the regulation of the degree of heterogeneity in the number of ion transporters as a fertility control. The model also uncovers, through in silico overactivation and loss of function of network nodes, synergetic traits which again call for experimental verification.