scholarly journals Fast–slow variable dissection with two slow variables related to calcium concentrations: a case study to bursting in a neural pacemaker model

2021 ◽  
Author(s):  
Yuye Li ◽  
Huaguang Gu ◽  
Yanbing Jia ◽  
Kaihua Ma
Keyword(s):  
Slow Variable ◽  
Slow Variables

Fast–Slow Variable Dissection with Two Slow Variables: A Case Study on Bifurcations Underlying Bursting for Seizure and Spreading Depression

2021 ◽  
Vol 31 (06) ◽  
pp. 2150096
Author(s):  
Kaihua Ma ◽  
Huaguang Gu ◽  
Zhiguo Zhao
Keyword(s):  
Hopf Bifurcation ◽  
Spreading Depression ◽  
Slow Variable ◽  
Multiple Time Scales ◽  
Extracellular Potassium ◽  
Fast Subsystem ◽  
Depolarization Block ◽  
Bifurcation Points ◽  
Slow Variables ◽  
Dissection Method

The identification of nonlinear dynamics of bursting patterns related to multiple time scales and pathology of brain tissues is still an open problem. In the present paper, representative cases of bursting related to seizure (SZ) and spreading depression (SD) simulated in a theoretical model are analyzed. When the fast–slow variable dissection method with only one slow variable (extracellular potassium concentration, [Formula: see text]) taken as the bifurcation parameter of the fast subsystem is used, the mismatch between bifurcation points of the fast subsystem and the beginning and ending phases of burst appears. To overcome this problem, both slow variables [Formula: see text] and [Formula: see text] (intracellular sodium concentration) are regarded as bifurcation parameters of the fast subsystem, which exhibits three codimension-2 bifurcation points and multiple codimension-1 bifurcation curves containing the saddle-node bifurcation on an invariant cycle (SNIC), the supercritical Hopf bifurcation (the border between spiking and the depolarization block), and the saddle homoclinic (HC) bifurcation. The bursting patterns for SD are related to the Hopf bifurcation and the depolarization block while for SZ to SNIC. Furthermore, at the intersection points between the bursting trajectory and the bifurcation curves in plane ([Formula: see text], [Formula: see text]), the initial or termination phases of burst match the SNIC or HC point well or the Hopf point to a certain extent due to the slow passage effect, showing that the fast–slow variable dissection method with suitable process is still effective to analyze bursting activities. The results present the complex bifurcations underlying the bursting patterns and a proper performing process for the fast–slow variable dissection with two slow variables, which are helpful for modulation to bursting patterns related to brain disfunction.

A kinetic analysis of coupled (or auxiliary) enzyme reactions

2018 ◽  
Author(s):  
Justin Eilertsen ◽  
Santiago Schnell
Keyword(s):  
Enzyme Assay ◽  
Slow Variable ◽  
Indicator Reaction ◽  
Single Substrate ◽  
Complex Sequences ◽  
Catalyzed Reactions ◽  
Enzyme Catalyzed Reactions ◽  
Coupled Reaction ◽  
Single Enzyme

<div>As a case study, we consider a coupled (or auxiliary) enzyme assay of two reactions obeying the Michaelis-Menten mechanism. The coupled reaction consists of a single-substrate, single-enzyme non-observable reaction followed by another single-substrate, single-enzyme observable reaction (indicator reaction). In this assay, the product of the non-observable reaction is the substrate of the indicator reaction. A mathematical analysis of the reaction kinetics is performed, and it is found that after an initial fast transient, the coupled reaction is described by a pair of interacting Michaelis-Menten equations. Moreover, we show that when the indicator reaction is slow, the quasi-steady-state dynamics are governed by two fast variables and two slow variables, and when the indicator reaction is fast, the dynamics are governed by three fast variables and one slow variable. Timescales that approximate the respective lengths of the indicator and non-observable reactions, as well as conditions for the validity of the Michaelis-Menten equations are derived. The theory can be extended to deal with more complex sequences of enzyme catalyzed reactions.</div>

scholarly journals A kinetic analysis of coupled (or auxiliary) enzyme reactions

2018 ◽  
Author(s):  
Justin Eilertsen ◽  
Santiago Schnell
Keyword(s):  
Enzyme Assay ◽  
Slow Variable ◽  
Indicator Reaction ◽  
Single Substrate ◽  
Complex Sequences ◽  
Catalyzed Reactions ◽  
Enzyme Catalyzed Reactions ◽  
Coupled Reaction ◽  
Single Enzyme

<div>As a case study, we consider a coupled (or auxiliary) enzyme assay of two reactions obeying the Michaelis-Menten mechanism. The coupled reaction consists of a single-substrate, single-enzyme non-observable reaction followed by another single-substrate, single-enzyme observable reaction (indicator reaction). In this assay, the product of the non-observable reaction is the substrate of the indicator reaction. A mathematical analysis of the reaction kinetics is performed, and it is found that after an initial fast transient, the coupled reaction is described by a pair of interacting Michaelis-Menten equations. Moreover, we show that when the indicator reaction is slow, the quasi-steady-state dynamics are governed by two fast variables and two slow variables, and when the indicator reaction is fast, the dynamics are governed by three fast variables and one slow variable. Timescales that approximate the respective lengths of the indicator and non-observable reactions, as well as conditions for the validity of the Michaelis-Menten equations are derived. The theory can be extended to deal with more complex sequences of enzyme catalyzed reactions.</div>

scholarly journals Fast-slow Variable Dissection with Two Slow Variables Related to Calcium Concentrations: A Case Study to Bursting in a Neural Pacemaker Model

2021 ◽  
Author(s):  
Yuye Li ◽  
Huaguang Gu ◽  
Yanbing Jia ◽  
Kaihua Ma
Keyword(s):  
Bifurcation Point ◽  
Slow Variable ◽  
Quiescent State ◽  
Bifurcation Curve ◽  
Fast Subsystem ◽  
Saddle Node Bifurcation ◽  
Initiation Point ◽  
Saddle Node ◽  
Pathological Pain ◽  
Slow Variables

Abstract Neuronal bursting is an electrophysiological behavior participating in physiological or pathological functions and a complex nonlinear alternating between burst and quiescent state modulated by slow variables. Identification of dynamics of bursting modulated by two slow variables is still an open problem. In the present paper, a novel fast-slow variable dissection method with two slow variables is proposed to analyze the complex bursting in a 4-dimensional neuronal model to describe bursting associated with pathological pain. The lumenal (Clum) and intracellular (Cin) calcium concentrations are the slowest variables respectively in the quiescent state and burst duration. Questions encountered when the traditional method with one low variable is used. When Clum is taken as slow variable, the burst is successfully identified to terminate near the saddle-homoclinic bifurcation point of the fast subsystem and begin not from the saddle-node bifurcation. With Cin chosen as slow variable, Clum value of initiation point is far from the saddle-node bifurcation point, due to Clum not contained in the equation of membrane potential. To overcome this problem, both Cin and Clum are regarded as slow variables, the two-dimensional fast subsystem exhibits a saddle-node bifurcation point, which is extended to a saddle-node bifurcation curve by introducing Clum dimension. Then, the initial point of burst is successfully identified to be near the saddle-node bifurcation curve. The results present a feasible method for fast-slow variable dissection and deep understanding to the complex bursting behavior with two slow variables, which is helpful for the modulation to pathological pain.

The Genesis and Internal Dynamics of El Salvador's People's Revolutionary Army, 1970–1976

2014 ◽  
Vol 38 (01) ◽  
pp. 102-129
Author(s):  
ALBERTO MARTÍN ÁLVAREZ ◽  
EUDALD CORTINA ORERO
Keyword(s):  
Latin America ◽  
El Salvador ◽  
Early Years ◽  
Left Wing ◽  
Internal Dynamics ◽  
Internal Coherence ◽  
The 1960S

AbstractUsing interviews with former militants and previously unpublished documents, this article traces the genesis and internal dynamics of the Ejército Revolucionario del Pueblo (People's Revolutionary Army, ERP) in El Salvador during the early years of its existence (1970–6). This period was marked by the inability of the ERP to maintain internal coherence or any consensus on revolutionary strategy, which led to a series of splits and internal fights over control of the organisation. The evidence marshalled in this case study sheds new light on the origins of the armed Salvadorean Left and thus contributes to a wider understanding of the processes of formation and internal dynamics of armed left-wing groups that emerged from the 1960s onwards in Latin America.

Culture and the plasticity of perception

2020 ◽  
Vol 43 ◽  
Author(s):  
Michael Lifshitz ◽  
T. M. Luhrmann
Keyword(s):  
Cultural Context ◽  
Sensory Experience ◽  
Cultural Learning ◽  
The World

Abstract Culture shapes our basic sensory experience of the world. This is particularly striking in the study of religion and psychosis, where we and others have shown that cultural context determines both the structure and content of hallucination-like events. The cultural shaping of hallucinations may provide a rich case-study for linking cultural learning with emerging prediction-based models of perception.

Dual systems for all: Higher-order, role-based relational reasoning as a uniquely derived feature of human cognition

2019 ◽  
Vol 42 ◽  
Author(s):  
Daniel J. Povinelli ◽  
Gabrielle C. Glorioso ◽  
Shannon L. Kuznar ◽  
Mateja Pavlic
Keyword(s):  
Temporal Reasoning ◽  
Higher Order ◽  
Important Case ◽  
Human Cognition ◽  
Relational Reasoning ◽  
Dual Systems ◽  
First Order ◽  
Reasoning System ◽  
Role Based

Abstract Hoerl and McCormack demonstrate that although animals possess a sophisticated temporal updating system, there is no evidence that they also possess a temporal reasoning system. This important case study is directly related to the broader claim that although animals are manifestly capable of first-order (perceptually-based) relational reasoning, they lack the capacity for higher-order, role-based relational reasoning. We argue this distinction applies to all domains of cognition.

Sociocultural memory development research drives new directions in gadgetry science

2019 ◽  
Vol 42 ◽  
Author(s):  
Penny Van Bergen ◽  
John Sutton
Keyword(s):  
Episodic Memory ◽  
Autobiographical Memory ◽  
Developmental Psychology ◽  
Cross Cultural ◽  
Memory Development ◽  
Development Research ◽  
Cultural Research ◽  
New Directions ◽  
Cross Cultural Research

Abstract Sociocultural developmental psychology can drive new directions in gadgetry science. We use autobiographical memory, a compound capacity incorporating episodic memory, as a case study. Autobiographical memory emerges late in development, supported by interactions with parents. Intervention research highlights the causal influence of these interactions, whereas cross-cultural research demonstrates culturally determined diversity. Different patterns of inheritance are discussed.

Construction of plastic contact deformation maps on ceramics: a case study on aluminum nitride

1996 ◽  
Vol 54 ◽  
pp. 636-637
Author(s):  
D. L. Callahan
Keyword(s):  
Plastic Deformation ◽  
Aluminum Nitride ◽  
Mechanical Response ◽  
Three Dimensional ◽  
Bright Field Image ◽  
Perfectly Plastic ◽  
Contrast Analysis ◽  
Deformation Patterns

Modern polishing, precision machining and microindentation techniques allow the processing and mechanical characterization of ceramics at nanometric scales and within entirely plastic deformation regimes. The mechanical response of most ceramics to such highly constrained contact is not predictable from macroscopic properties and the microstructural deformation patterns have proven difficult to characterize by the application of any individual technique. In this study, TEM techniques of contrast analysis and CBED are combined with stereographic analysis to construct a three-dimensional microstructure deformation map of the surface of a perfectly plastic microindentation on macroscopically brittle aluminum nitride.The bright field image in Figure 1 shows a lg Vickers microindentation contained within a single AlN grain far from any boundaries. High densities of dislocations are evident, particularly near facet edges but are not individually resolvable. The prominent bend contours also indicate the severity of plastic deformation. Figure 2 is a selected area diffraction pattern covering the entire indentation area.

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