Distribution of spiking and bursting in Rulkov’s neuron model

Large-scale brain simulations require the investigation of large networks of realistic neuron models, usually represented by sets of differential equations. Here we report a detailed fine-scale study of the dynamical response over extended parameter ranges of a computationally inexpensive model, the two-dimensional Rulkov map, which reproduces well the spiking and spiking-bursting activity of real biological neurons. In addition, we provide evidence of the existence of nested arithmetic progressions among periodic pulsing and bursting phases of Rulkov’s neuron. We find that specific remarkably complex nested sequences of periodic neural oscillations can be expressed as simple linear combinations of pairs of certain basal periodicities. Moreover, such nested progressions are robust and can be observed abundantly in diverse control parameter planes which are described in detail. We believe such findings to add significantly to the knowledge of Rulkov neuron dynamics and to be potentially helpful in large-scale simulations of the brain and other complex neuron networks.

Galvanotaxis of ciliates: Spatiotemporal dynamics of Coleps hirtus under electric fields

Galvanotaxis describes the functional response of organisms to electric fields. In ciliates, the electric field influences the electrophysiology and thus the cilia beat dynamics. This leads to a change of the swimming direction towards the cathode. The dynamical response to electric fields of Coleps hirtus has not been studied since the observations of Verworn in 1890 (1). While galvanotaxis has been studied in other cilitates, C. hirtus exhibit properties not found elsewhere, such as biomineralization-processes of alveolar plates with impact on the intracellular calcium regulation and a bimodal resting membrane potential, which leads unique electrophysiological driven bimodal swimming dynamics. Here, we statistically analyze the galvanotactic dynamics of C. hirtus by automated cell tracking routines. We found that the number of cells that show a galvanotactic response, increases with the increase of the applied electric field strength with a mean at about 2.1 V/cm. The spatiotemporal swimming dynamics change and lead to a statistical increase of linear elongated cell trajectories that point toward the cathode. Further, the increase of the electric fields decreases the mean velocity variance for electric fields larger than about 1.3 V/cm, while showing no significant change in the absolute velocity for any applied electric field. Fully functional galvanotactic responses were observed at a minimum extracellular calcium concentration of 20 μM. The results add important insights to the current understanding of cellular dynamics of ciliates and suggest that the currently accepted model lags the inclusion of the swimming dynamics and the complex calcium regulatory system of the cell. The results of this study do not only extend the fundamental understanding of C. hirtus dynamics, but also open possibilities for technical applications, such as biosensors or microrobots in the future.

Controlling Resonator Nonlinearities and Modes through Geometry Optimization

Controlling the nonlinearities of MEMS resonators is critical for their successful implementation in a wide range of sensing, signal conditioning, and filtering applications. Here, we utilize a passive technique based on geometry optimization to control the nonlinearities and the dynamical response of MEMS resonators. Also, we explored active technique i.e., tuning the axial stress of the resonator. To achieve this, we propose a new hybrid shape combining a straight and initially curved microbeam. The Galerkin method is employed to solve the beam equation and study the effect of the different design parameters on the ratios of the frequencies and the nonlinearities of the structure. We show by adequately selecting the parameters of the structure; we can realize systems with strong quadratic or cubic effective nonlinearities. Also, we investigate the resonator shape effect on symmetry breaking and study different linear coupling phenomena: crossing, veering, and mode hybridization. We demonstrate the possibility of tuning the frequencies of the different modes of vibrations to achieve commensurate ratios necessary for activating internal resonance. The proposed method is simple in principle, easy to fabricate, and offers a wide range of controllability on the sensor nonlinearities and response.

Scale sensitivity of the Gill circulation, Part II: Off-equatorial case

We investigate the steady dynamical response of the atmosphere on the equatorial β-plane to a steady, localized, mid-tropospheric heating source. Following Part I which investigates the case of an equatorial diabatic heating, we explore the sensitivity of the Gill circulation to the latitudinal location of the heating, together with the sensitivity to its horizontal scale. Again, we focus on characteristics of the response which would be particularly important if the circulation interacted with the hydrologic and energy cycles: overturning circulation and low-level wind. In the off-equatorial case, the intensity of the overturning circulation has the same limit as in the equatorial case for small horizontal extent of the diabatic heating, which is also the limit in the f-plane case. The decrease in this intensity with increasing horizontal scale of the diabatic heating is slightly faster in the off-equatorial case than in the equatorial case, which is due to the increase of rotational winds at the expense of divergent winds. The low-level westerly jet is more intense than in the equatorial case, with larger maximum wind and eastward mass transport that tend to infinity for small horizontal extent of the diabatic heating. In terms of spatial characteristics, this jet has a similar latitudinal extent as in the equatorial case but, unlike in the equatorial case, it extends further equatorward than poleward of the diabatic-heating center. It also extends further eastward than in the equatorial case.

Scale sensitivity of the Gill circulation, Part I: Equatorial case

We investigate the steady dynamical response of the atmosphere on the equatorial β-plane to a steady, localized, mid-tropospheric heating source at the equator. Expanding Gill (1980)’s seminal work, we vary the latitudinal and longitudinal scales of the diabatic heating pattern while keeping its total amount fixed. We focus on characteristics of the response which would be particularly important if the circulation interacted with the hydrologic and energy cycles: the overturning circulation and the low-level wind. In the limit of very small scale in either the longitudinal or latitudinal direction, the vertical energy transport balances the diabatic heating and this sets the intensity of the overturning circulation. In this limit, a fast low-level westerly jet is located around the center of diabatic heating. With increasing longitudinal or latitudinal scale of the diabatic heating, the intensity of the overturning circulation decreases and the low-level westerly jet decreases in maximum velocity and spatial extent relative to the spatial extent of this heating. The associated low-level eastward mass transport decreases only with increasing longitudinal scale. These results suggest that moisture-convergence feedbacks will favor small-scale equatorial convective disturbances while surface-heat-flux feedbacks would favor small-scale disturbances in mean westerlies and large-scale disturbances in mean easterlies. Part II investigates the case of off-equatorial heating.

EFFECT OF ARTERIOLAR DISTENSIBILITY ON THE LATERAL MIGRATION OF LIQUID-FILLED MICROPARTICLES FLOWING IN A HUMAN ARTERIOLE

A promising advance of bioengineering consists in the development of micro-nanoparticles as drug delivery vehicles injected intravenously or intraarterialy for targeted treatment. Proficient functioning of drug carries is conditioned by a reliable prediction of pharmacokinetics in human as well as their dynamical behavior once injected in blood stream. In this study, we aim to provide a reliable numerical prediction of dynamical behavior of microparticles in human arteriole focusing on the crucial mechanism of lateral migration. The dynamical response of the microparticle upon blood flow and arteriolar distensibility is investigated by varying main controlling parameters: viscosity ratio, confinement and capillary number. The influence of the hyperelastic arteriolar wall is highlighted through comparison with an infinitely rigid arteriolar wall. The hydrodynamic interaction in a microparticle train is examined. Fluid–structure interaction is solved by the Arbitrary Lagrangian–Eulerian method using the COMSOL Multiphysics software.

Morphodynamical cell-state description via live-cell imaging trajectory embedding

Time-lapse imaging provides powerful insight into the dynamical response of cells to perturbation, but the quantitative analysis of morphological changes over time is a challenge. Here, we exploit the concept of "morphodynamical trajectories" to analyze cellular behavior using morphological feature trajectory histories, rather than the common practice of examining morphological feature time courses in the space of single-timepoint (snapshot) morphological features. Our morphodynamical trajectory embedding analysis yielded quantitative and descriptive models of future time points based on the extended history information of MCF10A mammary epithelial cells treated with a panel of ligands. The trajectory analysis constructs a shared morphodynamical cell-state landscape, where the response of MCF10A cells induced by various extracellular signals is characterized by ligand-specific regulation of state transitions. Additionally, we show that including trajectories in single-cell morphological analysis enables (i) systematic characterization of cell state trajectories, and (ii) better separation of phenotypes and more descriptive models of ligand-induced differences as compared to snapshot-based analysis. This morphodynamical trajectory embedding is broadly applicable for the quantitative analysis of cell responses via live-cell imaging across many biological and biomedical applications.

Machinery Foundations Dynamical Analysis: A Case Study on Reciprocating Compressor Foundation

A faulty dynamical interaction between a machine and a foundation can lead to unexpected and dangerous failures, impacting human lives and the environment. Some machines, as reciprocating compressors, have a low rotation speed; this can lead to dangerous frequency for the foundation blocks. For this reason, a careful analysis shall be done during the design phase to avoid the range of the frequency of resonances and low vibration speeds. Designers can approach this problem by relying both on Analytical Theory and Finite Element Analysis. This article compares these methods by studying the dynamical response of different foundation geometries in a case study of a reciprocating compressor foundation. The applicability limits of Analytical theory are explored and an evaluation of the difference in the estimation of natural frequencies of the system using Analytical Theory and Finite Elements Analysis are made for different foundation geometries. The comparison shows similar results until the foundation geometry is rigid; reference geometries limits are provided so that designers can choose which of the methods better suits their type of analysis.

Mathematical Modelling of p53 Signalling during DNA Damage Response: A Survey

No gene has garnered more interest than p53 since its discovery over 40 years ago. In the last two decades, thanks to seminal work from Uri Alon and Ghalit Lahav, p53 has defined a truly synergistic topic in the field of mathematical biology, with a rich body of research connecting mathematic endeavour with experimental design and data. In this review we survey and distill the extensive literature of mathematical models of p53. Specifically, we focus on models which seek to reproduce the oscillatory dynamics of p53 in response to DNA damage. We review the standard modelling approaches used in the field categorising them into three types: time delay models, spatial models and coupled negative-positive feedback models, providing sample model equations and simulation results which show clear oscillatory dynamics. We discuss the interplay between mathematics and biology and show how one informs the other; the deep connections between the two disciplines has helped to develop our understanding of this complex gene and paint a picture of its dynamical response. Although yet more is to be elucidated, we offer the current state-of-the-art understanding of p53 response to DNA damage.