Yatsenko Dimitri, Josić Krešimir, Ecker Alexander S, Froudarakis Emmanouil, Cotton R James, Tolias Andreas S
Department of Neuroscience, Baylor College of Medicine, Houston, Texas, United States of America.
Department of Mathematics and Department of Biology and Biochemistry, University of Houston, Houston, Texas, United States of America.
PLoS Comput Biol. 2015 Mar 31;11(3):e1004083. doi: 10.1371/journal.pcbi.1004083. eCollection 2015 Mar.
Ambitious projects aim to record the activity of ever larger and denser neuronal populations in vivo. Correlations in neural activity measured in such recordings can reveal important aspects of neural circuit organization. However, estimating and interpreting large correlation matrices is statistically challenging. Estimation can be improved by regularization, i.e. by imposing a structure on the estimate. The amount of improvement depends on how closely the assumed structure represents dependencies in the data. Therefore, the selection of the most efficient correlation matrix estimator for a given neural circuit must be determined empirically. Importantly, the identity and structure of the most efficient estimator informs about the types of dominant dependencies governing the system. We sought statistically efficient estimators of neural correlation matrices in recordings from large, dense groups of cortical neurons. Using fast 3D random-access laser scanning microscopy of calcium signals, we recorded the activity of nearly every neuron in volumes 200 μm wide and 100 μm deep (150-350 cells) in mouse visual cortex. We hypothesized that in these densely sampled recordings, the correlation matrix should be best modeled as the combination of a sparse graph of pairwise partial correlations representing local interactions and a low-rank component representing common fluctuations and external inputs. Indeed, in cross-validation tests, the covariance matrix estimator with this structure consistently outperformed other regularized estimators. The sparse component of the estimate defined a graph of interactions. These interactions reflected the physical distances and orientation tuning properties of cells: The density of positive 'excitatory' interactions decreased rapidly with geometric distances and with differences in orientation preference whereas negative 'inhibitory' interactions were less selective. Because of its superior performance, this 'sparse+latent' estimator likely provides a more physiologically relevant representation of the functional connectivity in densely sampled recordings than the sample correlation matrix.
雄心勃勃的项目旨在记录体内越来越大且密度越来越高的神经元群体的活动。在此类记录中测量的神经活动相关性能够揭示神经回路组织的重要方面。然而，估计和解释大型相关矩阵在统计学上具有挑战性。通过正则化，即对估计值施加一种结构，可以改进估计。改进的程度取决于假定结构与数据中的依赖性的接近程度。因此，对于给定的神经回路，必须通过实验确定最有效的相关矩阵估计器的选择。重要的是，最有效估计器的特性和结构能够告知支配该系统的主要依赖性类型。我们在来自大型密集皮质神经元群体的记录中寻找神经相关矩阵的统计有效估计器。利用钙信号的快速三维随机存取激光扫描显微镜，我们记录了小鼠视觉皮层中宽200μm、深100μm（150 - 350个细胞）体积内几乎每个神经元的活动。我们假设，在这些密集采样的记录中，相关矩阵最好建模为表示局部相互作用的成对偏相关稀疏图与表示共同波动和外部输入的低秩分量的组合。事实上，在交叉验证测试中，具有这种结构的协方差矩阵估计器始终优于其他正则化估计器。估计值的稀疏分量定义了一个相互作用图。这些相互作用反映了细胞的物理距离和方向调谐特性：正向“兴奋性”相互作用的密度随着几何距离和方向偏好差异而迅速降低，而负向“抑制性”相互作用的选择性则较低。由于其卓越的性能，与样本相关矩阵相比，这种“稀疏 + 潜在”估计器可能为密集采样记录中的功能连接性提供更符合生理的表示。
