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The pre-Bötzinger complex, which is located at a ventrolateral medulla of human and mammal, is considered to be the center for the generation of respiratory rhythms. In a normal state, the respiratory rhythm is uniform and orderly. Otherwise, the respiratory rhythm will change to a pathological state. Therefore, the monitoring of respiratory rhythm is of great significance in monitoring the health. In this paper, according to a two-coupled model of pre-Bötzinger complex with calcium ion current, we investigate the generation and transition mechanism of anti-phase bursting synchronization by using phase-plane analysis, bifurcation and fast-slow decomposition. It is found that the pre-Bötzinger complex model can exhibit mixed bursting when calcium ion concentration is at steady state, which indicates that the oscillation of calcium is not a necessary condition for the generation of mixed bursting. This is quite different from the results obtained in previous studies, indicating that the mixed bursting is caused by the periodic fluctuations of calcium. The methods used in this paper can provide a new idea for investigating the dynamics of mixed bursting, and it can also be applied to the study of other neuronal systems on a multiple time scale.
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Keywords:
- pre-Bötzinger complex/
- mixed bursting/
- bifurcation/
- fast-slow analysis
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] -
$[{{\rm{IP}} _3}]$的取值/
(μmol·L–1)${\rm{SNIC}}$ ${\rm{Hopf}}$ 稳定极限环所在
区域${L_{{\rm{I}}{{\rm{P}}_3}}}$$1 $ $0.2789$ $20.8584$ $[0.2789, 20.8584]$ $1.05$ $0.2239$ $19.3199$ $[0.2239, 19.3199]$ $1.1 $ $0.1842$ $17.6358$ $[0.1842, 17.6358]$ $1.2$ $0.1317$ $13.9694$ $[0.1317, 13.9694]$ 
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参数 参数值 参数 参数值 参数 参数值 ${C_{\rm{m}}}$ $ 21 \; {\rm{ {\text{μ} } F} }$ ${g_{{\rm{Na}}}}$ $28 \; {\rm{nS}}$ ${L_{{\rm{I}}{{\rm{P}}_3}}}$ ${\rm{varied, } } \;{\rm{PL} } \cdot { {\rm{s} }^{ - 1} }$ ${E_{{\rm{Na}}}}$ $50 \; {\rm{mV}}$ ${g_{\rm{K}}}$ $11.2 \; {\rm{nS}}$ ${P_{{\rm{I}}{{\rm{P}}_3}}}$ $31000 \; {\rm{PL}} \cdot {{\rm{s}}^{ - 1}}$ ${E_{\rm{K}}}$ $ - 85 \; {\rm{mV}}$ ${g_{{\rm{Nap}}}}$ $15 \; {\rm{nS}}$ ${K_{\rm{l}}}$ 1.0 μmol/L ${E_{\rm{L}}}$ $ - 58 \; {\rm{mV}}$ ${g_{ {\rm{tonic \text- e} } } }$ $0.4 \; {\rm{nS}}$ ${K_{\rm{a}}}$ 0.4 μmol/L ${E_{ {\rm{syn \text- e} } } }$ $0 \; {\rm{mV}}$ ${g_{{\rm{CAN}}}}$ $0.7 \; {\rm{nS}}$ ${V_{{\rm{SERCA}}}}$ $400 \; {\rm{aMol}} \cdot {{\rm{S}}^{ - 1}}$ ${\theta _m}$ $ - 34 \; {\rm{mV}}$ ${g_{ {\rm{syn \text- e} } } }$ $9 \; {\rm{nS}}$ ${E_{{\rm{SERCA}}}}$ 0.2 μmol/L ${\theta _n}$ $ - 29 \; {\rm{mV}}$ ${g_{\rm{L}}}$ $11.2 \; {\rm{nS}}$ $A$ $0.001 \; {({\rm{ {\text{μ} } mol} }/{\rm{L)} }^{ - 1} } \cdot {\rm{m} }{ {\rm{s} }^{ - 1} }$ ${\theta _{mp}}$ $ - 40\; {\rm{mV}}$ ${\sigma _{\rm{s}}}$ $ - 5 \; {\rm{mV}}$ ${K_{{\rm{d}}}}$ 0.4 μmol/L ${\theta _h}$ $ - 48 \; {\rm{mV}}$ ${\sigma _n}$ $ - 4 \;{\rm{mV}}$ ${K_{{\rm{CAN}}}}$ 0.74 μmol/L ${\alpha _{\rm{s}}}$ 0.2 ms-1 ${\sigma _{mp}}$ $ - 6 \; {\rm{mV}}$ ${n_{{\rm{CAN}}}}$ $0.97$ ${\bar \tau _{\rm{s}}}$ 5 ms ${\sigma _h}$ $5 \; {\rm{mV}}$ $[{\rm{I}}{{\rm{P}}_3}]$ varied, μmol/L ${\bar \tau _h}/\varepsilon $ 10000 ms ${\theta _s}$ $ - 10 \; {\rm{mV}}$ ${[{\rm{Ca}}]_{{\rm{Tot}}}}$ 1.25 μmol/L ${\bar \tau _n}$ 10 ms ${\sigma _m}$ $ - 5 \; {\rm{mV}}$ ${f_m}$ $0.000025 \; {\rm{P}}{{\rm{L}}^{ - 1}}$ $\sigma $ $0.185$ DownLoad:
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[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33]
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