Quantitative analysis of the heterogeneous population of endocytic vesicles

2017 ◽  
Vol 15 (02) ◽  
pp. 1750008 ◽  
Author(s):  
Konstantin Kozlov ◽  
Vera Kosheverova ◽  
Rimma Kamentseva ◽  
Marianna Kharchenko ◽  
Alena Sokolkova ◽  
...  
Keyword(s):  
Dynamical Behavior ◽  
Growth Factor Receptor ◽  
Basins Of Attraction ◽  
Endocytic Vesicle ◽  
Biological Images ◽  
Segmentation Methods ◽  
Characteristic Features ◽  
Object Shapes ◽  
Opening And Closing ◽  
Endocytic Vesicles

The quantitative characterization of endocytic vesicles in images acquired with microscope is critically important for deciphering of endocytosis mechanisms. Image segmentation is the most important step of quantitative image analysis. In spite of availability of many segmentation methods, the accurate segmentation is challenging when the images are heterogeneous with respect to object shapes and signal intensities what is typical for images of endocytic vesicles. We present a Morphological reconstruction and Contrast mapping segmentation method (MrComas) for the segmentation of the endocytic vesicle population that copes with the heterogeneity in their shape and intensity. The method uses morphological opening and closing by reconstruction in the vicinity of local minima and maxima respectively thus creating the strong contrast between their basins of attraction. As a consequence, the intensity is flattened within the objects and their edges are enhanced. The method accurately recovered quantitative characteristics of synthetic images that preserve characteristic features of the endocytic vesicle population. In benchmarks and quantitative comparisons with two other popular segmentation methods, namely manual thresholding and Squash plugin, MrComas shows the best segmentation results on real biological images of EGFR (Epidermal Growth Factor Receptor) endocytosis. As a proof of feasibility, the method was applied to quantify the dynamical behavior of Early Endosomal Autoantigen 1 (EEA1)-positive endosome subpopulations during EGF-stimulated endocytosis.

scholarly journals A Characterization of the Dynamics of Schröder’s Method for Polynomials with Two Roots

2021 ◽  
Vol 5 (1) ◽  
pp. 25
Author(s):  
Víctor Galilea ◽  
José M. Gutiérrez
Keyword(s):  
Nonlinear Equations ◽  
Complex Plane ◽  
Iterative Process ◽  
Dynamical Behavior ◽  
Basins Of Attraction ◽  
Schröder’S Method

The purpose of this work is to give a first approach to the dynamical behavior of Schröder’s method, a well-known iterative process for solving nonlinear equations. In this context, we consider equations defined in the complex plane. By using topological conjugations, we characterize the basins of attraction of Schröder’s method applied to polynomials with two roots and different multiplicities. Actually, we show that these basins are half-planes or circles, depending on the multiplicities of the roots. We conclude our study with a graphical gallery that allow us to compare the basins of attraction of Newton’s and Schröder’s method applied to some given polynomials.

scholarly journals Bifurcation, chaotic and hysteresis phenomena of broadband tristable energy harvesters

2018 ◽  
Vol 241 ◽  
pp. 01025
Author(s):  
Shengxi Zhou ◽  
Junyi Cao ◽  
Grzegorz Litak
Keyword(s):  
Multiple Solutions ◽  
Nonlinear Effects ◽  
Basins Of Attraction ◽  
Voltage Response ◽  
Mechanical Resonator ◽  
Potential Wells ◽  
Energy Harvesters ◽  
Characteristic Features ◽  
Bifurcation Chaotic ◽  
Hysteresis Phenomena

We analyze energy harvesting using a mechanical resonator with three potential wells. Nonlinear effects are leading to frequency broadband voltage response via bifurcations, multiple solutions and dynamical hysteresis. We show the characteristic features of the obtained solutions. In particular, basins of attraction of solutions are discussed.

ON TWO-DIMENSIONAL DYNAMICAL SYSTEMS ASSOCIATED WITH MEMBRANE KINETICS UNDERLYING CARDIAC ARRHYTHMIAS

2009 ◽  
Vol 19 (05) ◽  
pp. 1709-1732 ◽  
Author(s):  
B. M. BAKER ◽  
M. E. KIDWELL ◽  
R. P. KLINE ◽  
I. POPOVICI
Keyword(s):  
Dynamical Behavior ◽  
Basins Of Attraction ◽  
Two Dimensional ◽  
Stimulus Period ◽  
Smooth Maps ◽  
Periodic Stimulation ◽  
Piecewise Smooth Maps ◽  
Dimensional Version ◽  
Bifurcation Law ◽  
The One

We study the orbits, stability and coexistence of orbits in the two-dimensional dynamical system introduced by Kline and Baker to model cardiac rhythmic response to periodic stimulation — as a function of (a) kinetic parameters (two amplitudes, two rate constants) and (b) stimulus period. The original paper focused mostly on the one-dimensional version of this model (one amplitude, one rate constant), whose orbits, stability properties, and bifurcations were analyzed via the theory of skew-tent (hence unimodal) maps; the principal family of orbits were so-called "n-escalators", with n a positive integer. The two-dimensional analog (motivated by experimental results) has led to the current study of continuous, piecewise smooth maps of a polygonal planar region into itself, whose dynamical behavior includes the coexistence of stable orbits. Our principal results show (1) how the amplitude parameters control which escalators can come into existence, (2) escalator bifurcation behavior as the stimulus period is lowered — leading to a "1/n bifurcation law", and (3) the existence of basins of attraction via the coexistence of three orbits (two of them stable, one unstable) at the first (largest stimulus period) bifurcation. We consider the latter result our most important, as it is conjectured to be connected with arrhythmia.

scholarly journals Two-Parameter Dynamics of An Autonomous Mechanical Governor System With Time Delay

2021 ◽  
Author(s):  
Shuning Deng ◽  
Jinchen Ji ◽  
Guilin Wen ◽  
Huidong Xu
Keyword(s):  
Time Delay ◽  
Dynamical Behavior ◽  
Evolutionary Process ◽  
Basins Of Attraction ◽  
Poincaré Section ◽  
Poincare Section ◽  
Interesting Phenomenon ◽  
Computing Technique ◽  
Intersection Points ◽  
Two Parameter

Abstract Understanding of dynamical behavior in the parameter-state space plays a vital role in the optimal design and motion control of mechanical governor systems. By combining the GPU parallel computing technique with two determinate indicators, namely, the Lyapunov exponents and Poincaré section, this paper presents a detailed study on the two-parameter dynamics of a mechanical governor system with different time delays. By identifying different system responses in two-parameter plane, it is shown that the complexity of evolutionary process can increase significantly with the increase of time delay. The path-following strategy and the time domain collocation method are used to explore the details of the evolutionary process. An interesting phenomenon is found in the dynamical behavior of the delayed governor system, which can cause the inconsistency between the number of intersection points of certain periodic response on Poincaré section and the actual period characteristic. For example, the commonly exhibited period-1 orbit may have two or more intersection points on the Poincaré section instead of one point. Furthermore, the variations of basins of attraction are also discussed in the plane of initial history conditions to demonstrate the observed multistability phenomena and chaotic transitions.

scholarly journals An optimal fourth-order family of modified Cauchy methods for finding solutions of nonlinear equations and their dynamical behavior

2019 ◽  
Vol 17 (1) ◽  
pp. 1567-1598
Author(s):  
Tianbao Liu ◽  
Xiwen Qin ◽  
Qiuyue Li
Keyword(s):  
Nonlinear Equations ◽  
Fourth Order ◽  
Dynamical Behavior ◽  
Basins Of Attraction ◽  
Second Derivative ◽  
Third Order ◽  
Numerical Tests ◽  
The Family ◽  
Theoretical Results ◽  
High Computational Efficiency

Abstract In this paper, we derive and analyze a new one-parameter family of modified Cauchy method free from second derivative for obtaining simple roots of nonlinear equations by using Padé approximant. The convergence analysis of the family is also considered, and the methods have convergence order three. Based on the family of third-order method, in order to increase the order of the convergence, a new optimal fourth-order family of modified Cauchy methods is obtained by using weight function. We also perform some numerical tests and the comparison with existing optimal fourth-order methods to show the high computational efficiency of the proposed scheme, which confirm our theoretical results. The basins of attraction of this optimal fourth-order family and existing fourth-order methods are presented and compared to illustrate some elements of the proposed family have equal or better stable behavior in many aspects. Furthermore, from the fractal graphics, with the increase of the value m of the series in iterative methods, the chaotic behaviors of the methods become more and more complex, which also reflected in some existing fourth-order methods.

scholarly journals Dynamical Tangles in Third-Order Oscillator with Single Jump Function

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Jiří Petržela ◽  
Tomas Gotthans ◽  
Milan Guzan
Keyword(s):  
Differential Equation ◽  
Vector Field ◽  
Nonlinear Oscillator ◽  
Invariant Manifolds ◽  
Order Differential Equation ◽  
Dynamical Behavior ◽  
Basins Of Attraction ◽  
Third Order ◽  
Newtonian Dynamics ◽  
Jump Function

This contribution brings a deep and detailed study of the dynamical behavior associated with nonlinear oscillator described by a single third-order differential equation with scalar jump nonlinearity. The relative primitive geometry of the vector field allows making an exhaustive numerical analysis of its possible solutions, visualizations of the invariant manifolds, and basins of attraction as well as proving the existence of chaotic motion by using the concept of both Shilnikov theorems. The aim of this paper is also to complete, carry out and link the previous works on simple Newtonian dynamics, and answer the question how individual types of the phenomenon evolve with time via understandable notes.

scholarly journals Optimal Fourth, Eighth and Sixteenth Order Methods by Using Divided Difference Techniques and Their Basins of Attraction and Its Application

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 322 ◽  
Author(s):  
Yanlin Tao ◽  
Kalyanasundaram Madhu
Keyword(s):  
Dynamical Behavior ◽  
Computational Cost ◽  
Basins Of Attraction ◽  
Order Method ◽  
Eighth Order ◽  
Projectile Motion ◽  
First Derivative ◽  
Iteration Functions ◽  
Optimal Launch Angle ◽  
Fourth Order Method

The principal objective of this work is to propose a fourth, eighth and sixteenth order scheme for solving a nonlinear equation. In terms of computational cost, per iteration, the fourth order method uses two evaluations of the function and one evaluation of the first derivative; the eighth order method uses three evaluations of the function and one evaluation of the first derivative; and sixteenth order method uses four evaluations of the function and one evaluation of the first derivative. So these all the methods have satisfied the Kung-Traub optimality conjecture. In addition, the theoretical convergence properties of our schemes are fully explored with the help of the main theorem that demonstrates the convergence order. The performance and effectiveness of our optimal iteration functions are compared with the existing competitors on some standard academic problems. The conjugacy maps of the presented method and other existing eighth order methods are discussed, and their basins of attraction are also given to demonstrate their dynamical behavior in the complex plane. We apply the new scheme to find the optimal launch angle in a projectile motion problem and Planck’s radiation law problem as an application.

scholarly journals Epidermal Growth Factor Receptor and Abl2 Kinase Regulate Distinct Steps of Human Papillomavirus 16 Endocytosis

2020 ◽  
Vol 94 (11) ◽  
Author(s):  
Carina Bannach ◽  
Pia Brinkert ◽  
Lena Kühling ◽  
Lilo Greune ◽  
M. Alexander Schmidt ◽  
...  
Keyword(s):  
Epidermal Growth Factor Receptor ◽  
Growth Factor ◽  
Epidermal Growth Factor ◽  
Growth Factor Receptor ◽  
Endocytic Pathway ◽  
Egfr Signaling ◽  
Endocytic Vesicle ◽  
Human Papillomavirus 16 ◽  
Epidermal Growth

ABSTRACT Human papillomavirus 16 (HPV16), the leading cause of cervical cancer, exploits a novel endocytic pathway during host cell entry. This mechanism shares many requirements with macropinocytosis but differs in the mode of vesicle formation. Previous work indicated a role of the epidermal growth factor receptor (EGFR) in HPV16 endocytosis. However, the functional outcome of EGFR signaling and its downstream targets during HPV16 uptake are not well characterized. Here, we analyzed the functional importance of signal transduction via EGFR and its downstream effectors for endocytosis of HPV16. Our findings indicate two phases of EGFR signaling as follows: a—likely dispensable—transient activation with or shortly after cell binding and signaling required throughout the process of asynchronous internalization of HPV16. Interestingly, EGFR inhibition interfered with virus internalization and strongly reduced the number of endocytic pits, suggesting a role for EGFR signaling in the induction of HPV16 endocytosis. Moreover, we identified the Src-related kinase Abl2 as a novel regulator of virus uptake. Inhibition of Abl2 resulted in an accumulation of misshaped endocytic pits, indicating Abl2’s importance for endocytic vesicle maturation. Since Abl2 rather than Src, a regulator of membrane ruffling during macropinocytosis, mediated downstream signaling of EGFR, we propose that the selective effector targeting downstream of EGFR determines whether HPV16 endocytosis or macropinocytosis is induced. IMPORTANCE Human papillomaviruses are small, nonenveloped DNA viruses that infect skin and mucosa. The so-called high-risk HPVs (e.g., HPV16, HPV18, HPV31) have transforming potential and are associated with various anogenital and oropharyngeal tumors. These viruses enter host cells by a novel endocytic pathway with unknown cellular function. To date, it is unclear how endocytic vesicle formation occurs mechanistically. Here, we addressed the role of epidermal growth factor receptor signaling, which has previously been implicated in HPV16 endocytosis and identified the kinase Abl2 as a novel regulator of virus uptake. Since other viruses, such as influenza A virus and lymphocytic choriomeningitis virus, possibly make use of related mechanisms, our findings shed light on fundamental strategies of virus entry and may in turn help to develop new host cell-targeted antiviral strategies.

scholarly journals Adenovirus RIDα regulates endosome maturation by mimicking GTP-Rab7

2007 ◽  
Vol 179 (5) ◽  
pp. 965-980 ◽  
Author(s):  
Ankur H. Shah ◽  
Nicholas L. Cianciola ◽  
Jeffrey L. Mills ◽  
Frank D. Sönnichsen ◽  
Cathleen Carlin
Keyword(s):  
Growth Factor Receptor ◽  
Dominant Negative ◽  
Receptor Internalization ◽  
Site Directed Mutagenesis ◽  
Oxysterol Binding Protein ◽  
Early Endosomes ◽  
Catalytically Active ◽  
Guanosine Triphosphatase ◽  
Endocytic Vesicles

The small guanosine triphosphatase Rab7 regulates late endocytic trafficking. Rab7-interacting lysosomal protein (RILP) and oxysterol-binding protein–related protein 1L (ORP1L) are guanosine triphosphate (GTP)–Rab7 effectors that instigate minus end–directed microtubule transport. We demonstrate that RILP and ORP1L both interact with the group C adenovirus protein known as receptor internalization and degradation α (RIDα), which was previously shown to clear the cell surface of several membrane proteins, including the epidermal growth factor receptor and Fas (Carlin, C.R., A.E. Tollefson, H.A. Brady, B.L. Hoffman, and W.S. Wold. 1989. Cell. 57:135–144; Shisler, J., C. Yang, B. Walter, C.F. Ware, and L.R. Gooding. 1997. J. Virol. 71:8299–8306). RIDα localizes to endocytic vesicles but is not homologous to Rab7 and is not catalytically active. We show that RIDα compensates for reduced Rab7 or dominant-negative (DN) Rab7(T22N) expression. In vitro, Cu2+ binding to RIDα residues His75 and His76 facilitates the RILP interaction. Site-directed mutagenesis of these His residues results in the loss of RIDα–RILP interaction and RIDα activity in cells. Additionally, expression of the RILP DN C-terminal region hinders RIDα activity during an acute adenovirus infection. We conclude that RIDα coordinates recruitment of these GTP-Rab7 effectors to compartments that would ordinarily be perceived as early endosomes, thereby promoting the degradation of selected cargo.

Dynamics of tracheal compression in the horned passalus beetle

2013 ◽  
Vol 304 (8) ◽  
pp. R621-R627 ◽  
Author(s):  
James S. Waters ◽  
Wah-Keat Lee ◽  
Mark W. Westneat ◽  
John J. Socha
Keyword(s):  
Dynamical Behavior ◽  
The Body ◽  
Reverse Direction ◽  
Effective Diameter ◽  
Contrast Imaging ◽  
Tracheal System ◽  
Tracheal Compression ◽  
Internal Mixing ◽  
Respiratory Gases ◽  
Opening And Closing

Rhythmic patterns of compression and reinflation of the thin-walled hollow tubes of the insect tracheal system have been observed in a number of insects. These movements may be important for facilitating the transport and exchange of respiratory gases, but observing and characterizing the dynamics of internal physiological systems within live insects can be challenging due to their size and exoskeleton. Using synchrotron X-ray phase-contrast imaging, we observed dynamical behavior in the tracheal system of the beetle, Odontotaenius disjunctus. Similar to observations of tracheal compression in other insects, specific regions of tracheae in the thorax of O. disjunctus exhibit rhythmic collapse and reinflation. During tracheal compression, the opposing sides of a tracheal tube converge, causing the effective diameter of the tube to decrease. However, a unique characteristic of tracheal compression in this species is that certain tracheae collapse and reinflate with a wavelike motion. In the dorsal cephalic tracheae, compression begins anteriorly and continues until the tube is uniformly flattened; reinflation takes place in the reverse direction, starting with the posterior end of the tube and continuing until the tube is fully reinflated. We report the detailed kinematics of this pattern as well as additional observations that show tracheal compression coordinated with spiracle opening and closing. These findings suggest that tracheal compression may function to drive flow within the body, facilitating internal mixing of respiratory gases and ventilation of distal regions of the tracheal system.

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