A Class Of Complex Bifurcation Sequence Of Experiments And Mathematical Model Simulation

Neurons can encode information using both the frequency of discharge sequences and the neural firing patterns. The rhythms of neural discharges are often different under different physiological parameters. The rhythms present changes of the qualitative nature of the firing patterns with the changes of the input signals and other physiological parameters, which is called bifurcation in nonlinear dynamics. Large-scale changes in physiological parameters will lead a series of bifurcation which exhibit special bifurcation scenario. Using bifurcation theories, identification of the rules of the bifurcation scenarios exhibited in the neural firing rhythms can contribute to understand how the firing patterns transit between different rhythm patterns when the physiological parameters changed, and how neurons encode information under the changes of physiological parameters using the rhythm pattern transition regularity. The simulation of the mathematic neuronal models which include a fast subsystem and a slow subsystem, predicts a bifurcation scenario of the neural firing patterns that experience period-adding bifurcation, present crisis, then via inverse period-doubling bifurcation to period 1 spiking. But it has not been verified in the experiments. Previous research reported a part of this type of bifurcation scenario corresponding to the period-adding bifurcation scenario without chaos, however, the other part of the bifurcation scenario from crisis to period 1 spiking was not observed.In this work, the bifurcation scenarios are recorded in the experimental neural pacemaker under different parameters. The bifurcation scenarios that period-adding bifurcation with stochastic rhythms, present crisis, then via inverse period-doubling bifurcation to period 1 spiking are observed when [Ca2+]。decreased,or[K+]。increased,or adjusting two parameters respectively, and simulated by mathematical model. Meanwhile, some new bifurcation scenarios are observed in the experiment. This study provide experimental evidence for theoretical anticipation, and provide basis for understanding the neural coding.The main results are as follows:1.Various bifurcation scenarios including the bifurcation scenario as mentioned above and the new bifurcation scenarios, are observed when [Ca2+]。decreased,or[K+]o increased,or adjusting two parameters respectively. When applying the antagonist of the large conductance calcium-activated potassium channel, the small conductance calcium-activated potassium channel, or the agonist of the intracellular calcium stores, the bifurcation scenarios above are not observed. 2.The bifurcation scenario of period adding bifurcation scenarios with stochastic bursting from period 1 bursting to high order bursting firstly, then to spiking pattern via crisis was discovered in experimental neural pacemaker when [Ca2+]。decreased gradually. The quiescence of the bursting pattern disappeared, the firing pattern changed into chaotic and periodic spiking patterns when crisis was generated. And after the crisis, the track of the neural firing to period 1 spiking can go through inverse period doubling bifurcation, as well as from chaos to period 1 spiking directly. The bifurcation scenario of period adding bifurcation scenarios with stochastic bursting from period 1 bursting to high order bursting firstly, and then to spiking pattern via crisis are regulated under different parameters, and also observed when [K+]o increased, or adjusting two parameters of [4-AP]。and [Ca2+]。3.The bifurcation scenario observed in the experiment was simulated realistically by adjusting the relevant parameters in stochastic Chay model. The experimental results proved the previous theoretical anticipation in the deterministic mathematical model, were simulated in the stochastic theoretical model which simulated the behavior in real neural system. The mathematic simulation results demonstrated the rhythm transfer from chaotic spiking to period 1 spiking directly, submerged period 2 spiking, when noise intensity is stronger, but it didn't submerge period 2 spiking when noise intensity is weaker. These suggest the appearance of period 2 spiking has relation to the noise intensity of neural inner system.4. The new bifurcation scenarios were observed when [K+]o increased, or changing two parameters of the neural pacemaker that keeping [4-AP]。in different levels and decreasing [Ca2+]。One type of the bifurcation scenarios is from period 1 bursting to period 2 bursting via period adding bifurcation with stochastic bursting, then via inverse period adding bifurcation to period 1 spiking. The other is from period 1 bursting to period 2 bursting via period adding bifurcation with stochastic bursting, via period doubling bifurcation to period 4 bursting, then via inverse period doubling bifurcation to period 2 spiking, and via inverse period adding bifurcation to period 1 spiking.Based on the previous studies, the new discoveries of this research are as follows:the bifurcation scenario which procedure from period adding bifurcation scenarios with stochastic bursting from period 1 bursting to high order bursting firstly, and then to spiking pattern via crisis was discovered in the experimental neural pacemaker when parameters changed. The experimental results proved the previous theoretical anticipation in the deterministic mathematical model, were simulated in the stochastic theoretical model which simulated the behavior in real neural system. The simulative results revealed a kind of transformational regulation of neural firing patterns. And two new bifurcation scenarios were observed in experimental neural pacemaker. The results above provide the basis for us to understanding neural firing rhythms transformational regulation, and are helpful to cognize neural coding and its mechanism.