Inferred network from prefrontal cortex activity of rats unveils cell assemblies
Inferred network from prefrontal cortex activity of rats unveils cell assemblies
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从大鼠前额叶皮层活动推断的网络揭示了细胞组装
作者：
G. Tavoni;U. Ferrari;F. Battaglia;S. Cocco;R. Monasson
我们分析了大鼠在三个不同阶段的前额叶皮层活动的记录：当动物面临一个任务，其中一个规则必须学习，并在之前和之后的睡眠阶段。我们推断伊辛模型（其特征在于二进制变量和本地字段和耦合参数）从记录的尖峰频率和神经元之间的成对相关性。我们已经展示了如何使用推断的模型来深化对记录的分析，揭示了高度协调的神经元组（细胞集合体）的存在，即一起激活并同步抑制其他特定神经元活动的神经元。
为了识别共激活组，我们发现了神经元（稳定状态）配置的对数似然的最大值，定义为相对于活跃神经元的所有场和耦合的总和，在能量景观上执行上升动力学。当模型从被分仓到10 ms时间仓中的活动推断时，唯一稳定的状态是具有所有沉默神经元的状态。通过向模型中添加外部输入并缓慢增加其值，从尖峰频率较高的神经元开始，出现越来越多活跃神经元的稳定状态（见图1A），1A）。值得注意的是，图1A 1A中的曲线显示了在特定输入强度值处的大跳跃，对应于强互连神经元的共激活，这些神经元不一定具有高平均活性。这些高度同步的神经元已经从清醒和睡眠时期的模型中发现（见图1B），并且在不同阶段之间部分共享。
图1
作为输入强度和时间仓的函数的神经元的共激活。A：处于稳定状态的活跃神经元数量A（H）与外部输入H。伊辛模型的参数（场和耦合）是从迷宫的活动中推断出来的。
我们研究了外部输入参数的含义，发现它携带了我们观察神经元之间相关性的时间尺度上的信息，即时间仓宽度。事实上，图1A、1A的两条曲线是指从分仓到两个不同时间仓（10 ms和30 ms）的神经元活动推断的模型，通过在输入强度中应用log（30 ms/10 ms）的平移而重叠。在Δt = 30 ms时，对于小输入强度H~1出现第一个共激活组的事实意味着该组可能在30 ms时间尺度内被共激活。
从我们的模型中提取的激活和抑制组中发现的神经元对应于从记录的活动中获得的Pearson相关矩阵的两个主要特征向量中的大条目。特别地，第一分量在两个激活的组上具有大的和正的条目，并且第二分量在第一组上显示负的条目，并且在第二组上显示正的条目，这意味着这些组可以一起激活或不一起激活。此外，一个组的激活引起另一个组的抑制，该另一个组在第一和第二分量上也具有大的条目，但具有相反的符号。因此，成分的符号以复杂的方式反映了不同组之间的激活-抑制关系。
We analyzed recordings of prefrontal cortex activity of a rat in three different phases: while the animal faces a task in which a rule has to be learned and during the previous and subsequent sleep phases. We inferred an Ising model (characterized by binary variables and local fields and couplings as parameters) from the recorded spiking frequencies and pairwise correlations between neurons. We have shown how the inferred model can be used to deepen the analysis of the recordings, unveiling the presence of highly coordinated groups of neurons (cell assemblies), that is neurons that are activated together and synchronously inhibit the activity of other specific neurons.
To identify the coactivated groups, we found the maxima of the log-likelihood of a configuration of neurons (stable states), defined as the sum of all the fields and couplings relative to the active neurons, performing an ascent dynamics on the energy landscape. When the model is inferred from the activity binned into 10 ms time bins, the only stable state is the one with all silent neurons. By adding an external input into the model and slowly increasing its value, stable states with more and more active neurons appear (see Figure Figure1A),1A), starting from the neurons with higher spiking frequency. Remarkably, the curves in Figure Figure1A1A show large jumps at specific values of the input strength, corresponding to the co-activation of strongly interconnected neurons, which not necessarily have high average activity. These highly synchronized neurons have been found from the models of both the awake and sleep epochs (see Figure Figure1B),1B), and are partially shared between different phases.
Figure 1
Co-activation of neurons as a function of the input strength and of the time bin. A: Number of active neurons A(H) in the stable states vs external input H. Parameters (fields and couplings) of the Ising model were inferred from the activity of the Maze ...
We investigated the meaning of the external input parameter, discovering that it carries information on the time scale at which we observe correlations between neurons, namely the time bin width. In fact, the two curves of Figure Figure1A,1A, which refer to the model inferred from the neuronal activity binned into two different time bins (10 ms and 30 ms), overlap by applying a translation of log(30 ms/10 ms) in the input strength. The fact that at Δt = 30 ms the first co-activated group appears for a small input strength H~1 means that the group is likely to be co-activated in a 30 ms time scale.
Neurons found in activated and inhibited groups extracted from our model correspond to large entries in the two principal eigenvectors of the Pearson correlation matrix obtained from the recorded activity. In particular the 1st component has large and positive entries on both activated groups, and the 2nd component shows negative entries on the 1st group, and positive ones on the 2nd group which entails that the groups can activate together or not. Moreover the activation of a group causes the inhibition of another group, which has also large entries on the 1st and 2nd components but with opposite signs. The sign of the components therefore refects in an intricate manner the activation-inhibition relationships between different groups.