Neurons at rest can exhibit diverse firing activities patterns in response to various external deterministic and random stimuli, especially additional currents. In this paper, neuronal firing patterns from bursting to...Neurons at rest can exhibit diverse firing activities patterns in response to various external deterministic and random stimuli, especially additional currents. In this paper, neuronal firing patterns from bursting to spiking, induced by additional direct and stochastic currents, are explored in rest states corresponding to two values of the parameter VK in the Chay neuron system. Three cases are considered by numerical simulation and fast/slow dynamic analysis, in which only the direct current or the stochastic current exists, or the direct and stochastic currents coexist. Meanwhile, several important bursting patterns in neuronal experiments, such as the period-1 ＂circle/homoclinic＂ bursting and the integer multiple ＂fold/homoclinic＂ bursting with onc spike per burst, as well as the transition from integer multiple bursting to period-1 ＂circle/homoclinic＂ bursting and that from stochastic ＂Hopf/homoclinic＂ bursting to ＂Hopf/homoclinic＂ bursting, are investigated in detail.展开更多
A mathematical model proposed by Grubelnk et al. [Biophys. Chem. 94 （2001） 59] is employed to study the physiological role of mitochondria and the cytosolic proteins in generating complex Ca^2＋ oscillations, lntrac...A mathematical model proposed by Grubelnk et al. [Biophys. Chem. 94 （2001） 59] is employed to study the physiological role of mitochondria and the cytosolic proteins in generating complex Ca^2＋ oscillations, lntracellulax bursting calcium oscillations of point-point, point-cycle and two-folded limit cycle types are observed and explanations are given based on the fast/slow dynamical analysis, especially for point-cycle and two-folded limit cycle types, which have not been reported before. Furthermore, synchronization of coupled bursters of Ca^2＋ oscillations via gap junctions and the effect of bursting types on synchronization of coupled cells are studied. It is argued that bursting oscillations of point-point type may be superior to achieve synchronization than that of point cycle type.展开更多
Some new elements are introduced into a mathematical model of intracellular calcium oscillations, which make it particularly suitable for the study of bifurcation. In addition to generating regular oscillations, such ...Some new elements are introduced into a mathematical model of intracellular calcium oscillations, which make it particularly suitable for the study of bifurcation. In addition to generating regular oscillations, such a modified model can be used to reproduce the burst discharges similar to those recorded in experiments and to describe two new types of oscillatory phenomena. By means of a fast/slow dynamical analysis, we explore the bifurcation and transition mechanisms associated with two types of bursters due to changes in the interaction of two slow variables with different timescales.展开更多
The contribution of this work is the modification of a mathematical model for bursting Ca2＋ oscillations by introducing the proportion of receptors not inactivated by Ca2＋ as a new variable. Generation mechanisms of...The contribution of this work is the modification of a mathematical model for bursting Ca2＋ oscillations by introducing the proportion of receptors not inactivated by Ca2＋ as a new variable. Generation mechanisms of different oscillatory patterns in this modified model are investigated and classified, based on fast/slow dynamical analysis. It is shown that periodic oscillations appear around the original chaotic regions. Moreover, two new types of oscillatory phenomena are observed at the sustaining region. The results may be instructive for understanding the difference between direct observation of dynamical behavior in real cells and theoretical explanations under a variety of stimulus conditions.展开更多
基金Project supported by the National Natural Science Foundation of China （Grant Nos 10432010 and 10526002）.Acknowledgement The bifurcation diagrams in this paper are obtained by means of the package C0NTENT.
文摘Neurons at rest can exhibit diverse firing activities patterns in response to various external deterministic and random stimuli, especially additional currents. In this paper, neuronal firing patterns from bursting to spiking, induced by additional direct and stochastic currents, are explored in rest states corresponding to two values of the parameter VK in the Chay neuron system. Three cases are considered by numerical simulation and fast/slow dynamic analysis, in which only the direct current or the stochastic current exists, or the direct and stochastic currents coexist. Meanwhile, several important bursting patterns in neuronal experiments, such as the period-1 ＂circle/homoclinic＂ bursting and the integer multiple ＂fold/homoclinic＂ bursting with onc spike per burst, as well as the transition from integer multiple bursting to period-1 ＂circle/homoclinic＂ bursting and that from stochastic ＂Hopf/homoclinic＂ bursting to ＂Hopf/homoclinic＂ bursting, are investigated in detail.
基金Supported by the National Natural Science Foundation of China under Grant Nos 10872014 and 10702002.
文摘A mathematical model proposed by Grubelnk et al. [Biophys. Chem. 94 （2001） 59] is employed to study the physiological role of mitochondria and the cytosolic proteins in generating complex Ca^2＋ oscillations, lntracellulax bursting calcium oscillations of point-point, point-cycle and two-folded limit cycle types are observed and explanations are given based on the fast/slow dynamical analysis, especially for point-cycle and two-folded limit cycle types, which have not been reported before. Furthermore, synchronization of coupled bursters of Ca^2＋ oscillations via gap junctions and the effect of bursting types on synchronization of coupled cells are studied. It is argued that bursting oscillations of point-point type may be superior to achieve synchronization than that of point cycle type.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11372017,11572084 and 11472061the Natural Science Foundation for the Higher Education Institutions of Anhui Province under Grant No KJ2016SD54+1 种基金the Fundamental Research Funds for the Central Universitiesthe Distinguished Young Professor Program of Donghua University under Grant No 16D210404
文摘Some new elements are introduced into a mathematical model of intracellular calcium oscillations, which make it particularly suitable for the study of bifurcation. In addition to generating regular oscillations, such a modified model can be used to reproduce the burst discharges similar to those recorded in experiments and to describe two new types of oscillatory phenomena. By means of a fast/slow dynamical analysis, we explore the bifurcation and transition mechanisms associated with two types of bursters due to changes in the interaction of two slow variables with different timescales.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11202083 and 11372017
文摘The contribution of this work is the modification of a mathematical model for bursting Ca2＋ oscillations by introducing the proportion of receptors not inactivated by Ca2＋ as a new variable. Generation mechanisms of different oscillatory patterns in this modified model are investigated and classified, based on fast/slow dynamical analysis. It is shown that periodic oscillations appear around the original chaotic regions. Moreover, two new types of oscillatory phenomena are observed at the sustaining region. The results may be instructive for understanding the difference between direct observation of dynamical behavior in real cells and theoretical explanations under a variety of stimulus conditions.
