#### 3.1. Statistical Indicators of Oscillation

To study the changes of oscillation over time, we focused on the time series during conversion of oscillatory states. Here, we take the typical continuous spike oscillation for example, which featured a slow depolarization process at the beginning stage, followed by a rapid process of depolarization and repolarization under gap free mode of the current clamp. The ApEn values were calculated firstly, based on which the three statistical indicators MA, SDA, and CVA were calculated for each one minute (

Figure 1).

**Figure 1.**
Three ApEn indicators of two different oscillation transition processes. (**A**) two types of oscillation transition. Type 1 shows a stable and continuous spike potential in 0–10 min, and it started to decay after 10 min. Type 2 shows the transition period lasted for roughly 0–8 min, followed by stable and continuous spike potential; (**B**) the corresponding variation tendencies of the three ApEn indicators of transition type 1; (**C**) the corresponding variation tendencies of the three ApEn indexes of transition type 2.

**Figure 1.**
Three ApEn indicators of two different oscillation transition processes. (**A**) two types of oscillation transition. Type 1 shows a stable and continuous spike potential in 0–10 min, and it started to decay after 10 min. Type 2 shows the transition period lasted for roughly 0–8 min, followed by stable and continuous spike potential; (**B**) the corresponding variation tendencies of the three ApEn indicators of transition type 1; (**C**) the corresponding variation tendencies of the three ApEn indexes of transition type 2.

With the disappearance of neuron spike potential, the discharge activity is weakened, which is manifested by the decrease of spike amplitude and discharge frequency, as well as the increase of the MA and the drop of the CVA. In

Figure 1A, type1, from the stable and continuous spike stage to a transition period after 10 min, the MA rose from 0.1 to 0.4, the SDA also increased with mild fluctuation, and the CVA displayed an evident downtrend from 0.9 to 0.3 (

Figure 1B). During the transition from sparse spike pattern to continuous spike activity (

Figure 1A type 2), the MA decreased from 0.4 to below 0.1. When the neuron returned to a normal discharge state, the MA stayed at a relatively low level of 0.05. At the same time, the SDA dropped and leveled out at about 0.05. The CVA increased to a peak of 0.8 from 0.4, and fluctuated in a certain range afterwards.

#### 3.2. Clustering Results

We adopted 12 recordings of different neurons in SOG. As the oscillation status varied over time, we took three sections of each recording, each section lasted for 60 s, and obtained 36 types of waveforms as a result. The ApEn values of each oscillation were firstly obtained. From the tests of normality of 36 groups of ApEn data, it was found that the normality could not be well satisfied, with

p values of 11 groups were > 0.05 and 25 groups were < 0.05. To test the difference between the ApEn distribution levels of 36 kinds of oscillations, we performed the Kruskal-Wallis instead of the ANOVA test to examine the difference between 36 groups. The

p was < 0.01 (

Table 1). What is more, the differences between the waveforms selected from one recording are statistically significant, while the waveform after stimulation by dopamine has no statistical significance with

p > 0.01.

**Table 1.**
Result of Kruskal-Wallis test of 12 groups of recordings.

**Table 1.**
Result of Kruskal-Wallis test of 12 groups of recordings.
No. of Recordings | No. of Oscillations | No. of ApEn Values for every Oscillation | Kruskal–Wallis Test |
---|

1 | 1/2/3 | 60 | p < 0.01 |

2 | 4/5/6 | 60 | p = 0.182 |

3 | 7/8/9 | 60 | p < 0.01 |

4 | 10/11/12 | 60 | p < 0.01 |

5 | 13/14/15 | 60 | p < 0.01 |

6 | 16/17/18 | 60 | p < 0.01 |

7 | 19/20/21 | 60 | p < 0.01 |

8 | 22/23/24 | 60 | p < 0.01 |

9 | 25/26/27 | 60 | p < 0.01 |

10 | 28/29/30 | 60 | p < 0.01 |

11 | 31/32/33 | 60 | p < 0.01 |

12 | 34/35/36 | 60 | p < 0.01 |

Total | 36 | 2160 | p < 0.01 |

Putting the ApEn of the 36 waveforms together, two ApEn oscillation patterns were simply displayed: one features low and fixed complexity while the other fluctuates severely. The indicators of ApEn in different neurons are different from each other, the oscillations in the same neuron also differ (

Figure 2A,B). The MA and CVA were used as the variables to calculate the distances in the hierarchical clustering method.

**Figure 2.**
Clustering results of 36 kinds of signals. (**A**) the MA of 36 kinds of signals; (**B**) the CVA of 36 kinds of signals; (**C**) the scatter diagram, taking the MA as abscissas and CVA as ordinates. The five different markers represent five different clusters; (**D**) the dendrogram by hierarchical clustering, wherein the dashed line shows the threshold of 0.15.

**Figure 2.**
Clustering results of 36 kinds of signals. (**A**) the MA of 36 kinds of signals; (**B**) the CVA of 36 kinds of signals; (**C**) the scatter diagram, taking the MA as abscissas and CVA as ordinates. The five different markers represent five different clusters; (**D**) the dendrogram by hierarchical clustering, wherein the dashed line shows the threshold of 0.15.

The clustering result in

Figure 2D shows the differences between the oscillations; a longer horizontal line signifies a longer distance .The coefficient of cophenet is 0.84. Combining clustering results with the spike patterns, we took 0.15 as the threshold of the between-class distance, and these oscillation patterns were divided into five categories.

Figure 3A–G shows the clustering results and the corresponding original oscillations.

The first cluster has relatively low MA staying below 0.15 with CVA staying around 0.25.

Figure 3A shows a mixed oscillation pattern, consisting of large amplitude waves with small amplitude waves in between.

Figure 3B shows the activity of a neuron with a mixed pattern after being stimulated by dopamine (the next section will go into detail).

The second cluster had a discharge pattern with both low MA almost below 0.15 and CVA below 0.2, manifested as constant and regular signals with quasi-periodicity. Most oscillations belong to this pattern, and the peak values always stand between 10 and 20 mV. This is named the continuous spike pattern.

**Figure 3.**
Five clusters of the original oscillation patterns and the corresponding ApEn values. The columns in A-L signify original oscillation sequences, while the corresponding a-1 below illustrate change sequences of ApEn values. Cluster 1 contains two oscillation patterns. Cluster 2 contains the continuous spike pattern. Cluster 3 contains two oscillation patterns, which were referred to as the mixed oscillation pattern and spikelet pattern respectively. Cluster 4 contains one oscillation pattern mixed with bursting oscillation and long-term excitability. Cluster 5 contains the sparse spike pattern.

**Figure 3.**
Five clusters of the original oscillation patterns and the corresponding ApEn values. The columns in A-L signify original oscillation sequences, while the corresponding a-1 below illustrate change sequences of ApEn values. Cluster 1 contains two oscillation patterns. Cluster 2 contains the continuous spike pattern. Cluster 3 contains two oscillation patterns, which were referred to as the mixed oscillation pattern and spikelet pattern respectively. Cluster 4 contains one oscillation pattern mixed with bursting oscillation and long-term excitability. Cluster 5 contains the sparse spike pattern.

The third cluster featured with high MA (0.15–0.3) and CVA staying around 0.45. Two corresponding types of discharge were observed: the first is of mixed signals with lower MA, which is referred to as the mixed oscillation pattern; the second type which records continuous and dense signals with less and smaller spikelet rising on the oscillations is called the spikelet pattern. The spikelet pattern is composed of single wavelet amplitude which is generally less than 5 mV with duration of 100–500 ms.

The fourth cluster had a relatively low MA (0.05–0.15) and the CVA staying around 0.6. The number of oscillations belonging to this pattern ranks second. The corresponding discharge was mixed with bursting oscillation discharge and has long-term excitability during certain periods. The plateaus lasting from 1 to 10 s frequently emerges and the depolarization can reach −20 mV. This is what we called the bursting pattern, featuring long lasting depolarization discharge and stable spontaneous discharge.

The fifth cluster featured relatively low MA (0.05–0.15) and the high CVA staying around 0.8, which was quite high. The corresponding discharge signal was also consistent and regular, but compared with the second cluster, the frequency of action potentials was lower. This is sparse spike pattern.

#### 3.3. Transformation of Oscillation

By adding the dopamine to the external solution, the embedded component of mixed electric signals would be disturbed and single continuous depolarized discharge emerges (

Figure 4A,B). Distribution of power spectrum was calculated. Before the stimulation, the power spectrum of signals has no obvious peak values with most energy volume below 1 Hz (

Figure 4C). After stimulation of dopamine, oscillation is featured with sine-like oscillation with amplitude of 10 mV (

Figure 4B). As shown in

Figure 4D, the proportion of 2–5 HZ component has an increase.

**Figure 4.**
Changes of oscillation caused by dopamine. (**A**) oscillation signals of 2 min before stimulation by dopamine. There are at least two sorts of spike potentials. The average amplitude of large waves is about 20 mV. The small waves are about 8 mV which are formed by smaller waves with amplitudes of less than 4 mV; (**B**) oscillation signals of 2 min after stimulation by dopamine; (**C**) power spectrum of signals with most energy volume below 1 Hz before the stimulation. The abscissa and ordinate is Log-Log; (**D**) power spectrum of signals after the stimulation.

**Figure 4.**
Changes of oscillation caused by dopamine. (**A**) oscillation signals of 2 min before stimulation by dopamine. There are at least two sorts of spike potentials. The average amplitude of large waves is about 20 mV. The small waves are about 8 mV which are formed by smaller waves with amplitudes of less than 4 mV; (**B**) oscillation signals of 2 min after stimulation by dopamine; (**C**) power spectrum of signals with most energy volume below 1 Hz before the stimulation. The abscissa and ordinate is Log-Log; (**D**) power spectrum of signals after the stimulation.

Compared with the power spectrum results, the difference between the ApEn results of this alternation is more significant. The baseline of oscillation before stimulation is obvious higher (MA = 0.074) than that of oscillation after stimulation (MA = 0.015), regardless of changes of sample points or parameters in the calculation. Three statistical indicators of ApEn also show a significant difference (

Table 2). The ApEn values after stimulation keep quite stable and relatively low while the ApEn values before stimulation fluctuate, which indicates a quasi-periodic change of probability for occurrence of new information (

Figure 5D,E). Increasing sample points can reduce the MA while the SDA and CVA will increase. Increasing coefficient of r can reduce the MA and the SDA while CVA hardly changes.

**Figure 5.**
ApEn results under different calculation conditions. Dashed lines indicate corresponding indicators of oscillation of 2 min before the simulation. Solid lines indicate corresponding indicators of oscillation of 2 min after the simulation. Red lines with * indicate samples of 1000. Green lines indicate samples of 2000. With the increase of ApEn threshold r from 0.15 to 0.25, the MA and the SDA have a decreasing trend; the corresponding gaps between the two oscillations become narrower. With the increase of sample point number N from 1000 to 2000, the MA decreases while the SDA and the CVA increase; the gaps of the MA and CVA between the two oscillations become narrower while the gap of the SDA becomes wider.

**Figure 5.**
ApEn results under different calculation conditions. Dashed lines indicate corresponding indicators of oscillation of 2 min before the simulation. Solid lines indicate corresponding indicators of oscillation of 2 min after the simulation. Red lines with * indicate samples of 1000. Green lines indicate samples of 2000. With the increase of ApEn threshold r from 0.15 to 0.25, the MA and the SDA have a decreasing trend; the corresponding gaps between the two oscillations become narrower. With the increase of sample point number N from 1000 to 2000, the MA decreases while the SDA and the CVA increase; the gaps of the MA and CVA between the two oscillations become narrower while the gap of the SDA becomes wider.

**Table 2.**
Values of the three statistical indicators of six ApEn parameters groups.

**Table 2.**
Values of the three statistical indicators of six ApEn parameters groups.
Sample Points(N) | The Threshold Coefficient(r) | MA-before | MA-after | SDA-before | SDA-after | CVA-before | CVA-after |
---|

1000 | 0.15 | 0.302 | 0.057 | 0.100 | 0.035 | 0.332 | 0.616 |

1000 | 0.2 | 0.220 | 0.040 | 0.076 | 0.024 | 0.347 | 0.596 |

1000 | 0.25 | 0.169 | 0.031 | 0.060 | 0.018 | 0.355 | 0.564 |

2000 | 0.15 | 0.134 | 0.026 | 0.157 | 0.028 | 1.168 | 1.067 |

2000 | 0.2 | 0.097 | 0.019 | 0.114 | 0.020 | 1.178 | 1.064 |

2000 | 0.25 | 0.074 | 0.015 | 0.087 | 0.016 | 1.180 | 1.064 |

In fact, the simple sine-like oscillation status after the stimulation only lasted about 50 s with the ApEn values started to peak instead of remaining low. The complexity of the oscillation began to resume, indicating that the neuron ability of regulating oscillation also began to recover.

#### 3.4. The Location of Neurons with Certain Pattern

The projection in SOG is very similar with local interneurons (LNs) in AL [

36], with its trajectory area only located on the soma ipsilateral hemisphere of SOG (

Figure 6). The biocytin staining and confocal imaging methods were according to what we described before [

37]. Neurons’ morphology is visualized by imaris 8.0 (Bitplane). The filament toolbox is applied to highlight the axonal trace and trajectory. Electrophysiologically, spontaneous action potentials (SAPs) of LNs demonstrated a bursting pattern of sodium channel dependent spikes, and spikes no fewer than two were considered as a burst. SAPs of projection neurons demonstrated lower frequency with less and smaller spikelets rising on the oscillations. The bursting pattern is mainly in large neurons of the central portion of one side of SOG (

Figure 7).The mixed oscillation pattern is located in the bottom of the central partial small neurons (

Figure 6C).

**Figure 6.**
The neurons with cell bodies located in the edge region of SOG. The scale is 80 μm. Soma and projection region of the neurons are in the same side of SOG, and the coverage of neurons does not exceed the SOG zone itself.

**Figure 6.**
The neurons with cell bodies located in the edge region of SOG. The scale is 80 μm. Soma and projection region of the neurons are in the same side of SOG, and the coverage of neurons does not exceed the SOG zone itself.

**Figure 7.**
The neurons with cell bodies located in the central region of SOG. The scale is 50 μm. The projection range exceeded SOG area.

**Figure 7.**
The neurons with cell bodies located in the central region of SOG. The scale is 50 μm. The projection range exceeded SOG area.