Figures and data
Construction of the cortical connectivity.
(a) Visualization of all neurons in the hemispherical dataset we use to build the cortical connectivity. The hemisphere contains about 1 million neurons in total, including about 300,000 cortical neurons. (b) Algorithm of building the connectome: i) First, we identify neuronal excitatory/inhibitory information based on the spatial transcriptomic data. ii) We then identify the voxelized position for all the neurons. iii) Based on the voxelized projection data, we calculate the number of connections between every pair of voxels (see Use of the voxelized connectivity data). iv) Connections are created randomly between the neurons in each pair of voxels. v) Repeat for all voxels in regions of interest. vi) Complete the connectivity. (c) The connectivity matrix shows the number of connections between different cortical regions(in log 10 scale). A full version of the connectivity matrix with annotated regions is shown in Figure 1—figure supplement 1. (d) Visualization of outgoing connections from sampled neurons in the primary visual cortex (VISp, left), primary auditory cortex (AUDp, middle), and the ventral anterior cingulate areas (ACAv, right).
Anterior-posterior macroscopic traveling waves emerge from Allen connectivity
(a) Top: The average intracellular voltage of all neurons; bottom: Raster plots for 40000 neurons, which are evenly sampled from different cortical regions. The red and blue dashed lines indicate the time windows that are visualized in (b-e). (b) Visualization of average intracellular voltage across different locations in the cortex during the time window indicated by the red dashed lines in (a). (c) Visualization of the macroscopic traveling wave by coloring the neurons based on the first time they fire during the same time window visualized in (b). (d-e) Same plot as (b-c), but they visualize a different time window of the same simulation, indicated by the blue dashed lines in (a). The direction of the traveling wave is opposite to the one shown in the previous figures. See Videos for the movie of the simulation.
Figure 2—figure supplement 1. Visualization of the macroscopic traveling waves at single-neuron resolution. (a-b) Visualization of the same
Top: schematics of Allen (a), local (b), and uniform connectivity (c); bottom: Visualization of outgoing connections from the same 50 randomly selected neurons in the primary visual cortex (VISp) for the three connectivity. Figure 3—figure supplement 1. Comparison of the three connectivity matrices: a Allen, b local and c uniform connectivity. For local connectivity, the diagonal terms represent the connections within the same region. And the off-diagonal terms exist because these regions are physically adjacent to each other.
Schematics of analyzing 3D spatiotemporal data using phase gradient.
(a) A single frame from a simulation with Allen connectivity, where neurons are colored based on their intracellular voltage. (b) The same frame as in (a), but with voltage data transformed into a generalized phase and interpolated onto a regular 3D grid. (c) Calculation of phase gradient field based on the phase field presented in (b). The arrows indicate the gradient directions at different locations. Please see Quantitative measurement of neuronal activity for details of the calculation presented in this figure.
Allen connectivity produces a higher level of macroscopic wave activity than local and uniform connectivity.
(a-c) Time sequences of three simulations with Allen (a), local (b) and uniform (c) connectivity under the same stimulus. Colors represent the generalized phase of each neuron, which is further normalized for each simulation between 0 and 1. (d) Phase gradient directionality (PGD) of the corresponding simulations with respect to time. The three time windows are chosen such that the maximum PGD is reached. Please see Video 2 for animation of the three simulations.
Different oscillations and spatiotemporal patterns emerge from the cortical network with different connectivity and coupling strength.
For each panel, the raster plot (top) shows the firing behavior of the population and the visualization (bottom) shows the intracellular voltage activity across the cortical surface during the period marked in red dashed lines on the corresponding raster plot. There are 9 panels in total, corresponding to three different connectivity and coupling strengths. Left to right: Allen, local and uniform connectivity; Top to bottom: weak (50% baseline), medium (baseline) and strong (150% baseline) coupling strength.
Macroscopic wave activity is strongly affected by the coupling strength of the network and the frequency of the oscillation.
(a-b) The average phase gradient directionality (PGD) calculated from simulations of different connectivity under different applied currents (a) or coupling strengths (b). The error bar represents the values from other simulations with different coupling strengths (a) or applied currents (b). (c) The average PGD calculated from simulations of different connectivity under different kinds of oscillations categorized by the dominant oscillation frequency (see Quantitative measurement of neuronal activity).
Connectivity matrix with detail region legend and degree distribution.
a The same connectivity matrix shown in Fig. 1c, but with detailed region legend. b The out and in-degree distribution of all neurons in log 2 scale.
jectome was later refined to a finer level using a statistical model introduced by Knox et al. (2018), where the strength of connections is provided on a voxel (100µm3) resolution. Because both neuronal (Zhuang-ABCA1) and the voxelized connectivity data are registered with the Allen Brain Atlas Common Coordinate Framework (ABA-CCF) Wang et al. (2020), we now introduce an algorithm that integrates the two datasets to construct a neuron-to-neuron connectivity.
Visualization of the macroscopic traveling waves at single-neuron resolution.
(a-b) Visualization of the same simulation presented in Fig. 2, but showing intracellular voltage at single-neuron resolution.
Comparison of the three connectivity matrices: a Allen, b local and c uniform connectivity. For local connectivity, the diagonal terms represent the connections within the same region. And the off-diagonal terms exist because these regions are physically adjacent to each other.
Detailed plots of phase gradient directionality (PGD) measured in simulations conducted in different conditions.
a-c The average PGD versus applied currents when the coupling is weak (15ns, a), medium (30ns, b), or strong (45ns, c). d-f The average PGD versus different coupling strengths when the applied current is weak (1.2nA, d), medium (1.5nA, e), or strong (1.8nA, f)
Spectrum analysis and correlation with phase gradient directionality (PGD):
(a-c) In each plot, the top panel shows the average voltage of all neurons versus time, and the bottom panel shows the power spectral density of the corresponding voltage trace. For all three plots, the simulations are conducted with an applied current of 0.9 nA and coupling strengths of 15 nS (a), 30 nS (b), and 45 nS (c). (d) Each point represents a simulation, where the x-axis represents the dominant frequency of the oscillation calculated from the spectral analysis, y-axis represents the phase gradient directionality (PGD) measured in the same simulation.
