Fig 1.
A) Connectivity between neurons in the same column follows the canonical circuit. Arrows indicate directed connections between layers. Neurons are never connected to themselves. B) Connectivity diagram between different cortical columns and thalamocortical cells in the core (TC) or matrix (TCa). C) Exponential decay of connection probability with distance between columns. Previously reported inter-parcel dMRI connectivity [31] shows an exponential relation with fiber distance. Column-wise connection probability is obtained by applying the dMRI exponential function to inter-column fiber distances (synthesized from their corresponding geodesic distances) and then adding the residual inter-parcel dMRI connectivity, estimated by regressing out the exponential trend (see Diffusion MRI guided connection probability for details). D) Estimated myelination index [34, 35] throughout the cortex. A hierarchical index inversely proportional to this myelination index is assigned to each of the 180 cortical parcels designated in the HCP-MMP atlas [33]. E) Excitatory corticocortical connections belong to one of 6 classes based on the myelination-derived hierarchical index of the pre- and post-synaptic neurons: within the same column, within the same parcel, weakly or strongly feedforward (from lower to higher hierarchical index) and weakly or strongly feedback (from higher to lower hierarchical index). Based on experimental reports on connectivity, weights are scaled according to the connection type by the factor shown in the matrices (see Hierarchically guided laminar connectivity for details). F) Parcel-wise connectivity as previously reported [31]. Fpt stands for “fraction of probabilistic tractography” and represents the log10 probability of connection resulting from fractionally scaling raw streamline counts (detailed in [31]). G) Generated model connectivity, which retains the parcel-wise structure from data in panel F (Pearson’s correlation r = 0.81, p < 0.0001). Fpt in the model is computed as the log10 of the ratio of the number of connections from parcel A into parcel B to the total number of connections that either originate at A or terminate at B, excluding within-parcel connections.
Fig 2.
Baseline model activity in awake and sleep states.
A) Wake state. a.1) Membrane voltages of all neurons from layer 2 over 5 seconds of simulation; a.2) Layer average voltage over time, simulating LFP; a.3) Activity of two representative neurons from layer 2, both showing irregular tonic firing; a.4) Voltage histogram of all neurons over the whole simulation time, note approximately -60mV peak representing baseline membrane voltage; a.5) Power spectral density (PSD) of the average voltage revealed a distinct 1/f phenomenon typical for in-vivo recordings. B) Slow-wave dynamics. b.1) Membrane voltages of all neurons (excluding medial wall) from layer 2 over 30 seconds of simulation, revealed synchronized bands of activity during Up states; b.2) Average voltage of all cortical layers (dashed black line) and layer 2 neurons (solid blue line, excluding medial wall) over time, with nearly identical behavior. Red triangles above and below the trace mark global Up and Down states, respectively, from layer 2 (coincident with global Up and Down states from the average of layers); a.3) Activity of two representative neurons from layer 2, both showing synchronized transitions between Up and Down states; a.4) Voltage histogram of all neurons over the whole simulation time, revealed the characteristic bi-modal distribution caused by Up and Down state alternations during SWS. Dashed vertical lines labeled V− and V+ indicate the voltage thresholds used to detect Down states and Up states, respectively; b.5) Distribution of the Up state onsets and offsets for all neurons over the whole simulation time. Narrow histograms indicate highly synchronous initiation and termination of the Up states. C) Zoom into the first Up state from panel b.1, with neurons sorted from earliest to latest onset time, and a single cell voltage from panel b.2, showing the transition from Down to Up state, steady firing during the Up state, and transition to Down state. D) Latency map, calculated as the onset delay of each neuron with respect to the earliest onset, for each Up state in panel b.2 (see Onset/offset detection in Methods for details). The percent of active neurons during each Up state is shown below the corresponding latency map. Up states involve nearly every neuron in the cortex within 300ms from its initiation time.
Fig 3.
Effect of connection density on SO dynamics.
A) Example target cortical column (yellow) with all columns connected to it through any layer (green) for different connection densities. Density is reduced by decreasing P, which denotes the probability of preserving a connection from the original dMRI-based connectivity. With P = 1 all connections are preserved, while for P = 0.5, P = 0.3 and P = 0.1 each connection is preserved with a 50%, 30% or 10% probability, respectively. B) Percent of the original number of connections retained for different values of P. C) Distribution of connection distances, or lengths, for different values of P. Red horizontal lines indicate medians, bottom and top box edges indicate the 25th and 75th percentiles, respectively, whiskers extend to the most extreme data points not considered outliers, and outliers are plotted individually using the ‘+’ marker symbol. Note, connection density is reduced uniformly across all lengths. D-E) Individual analysis of SO dynamics for different values of P. Subpanels as in Fig 2. F) Summary of the effect of reducing connection density on the global SO frequency and amplitude as well as the standard deviation of the onset/offset delays (i.e. the width of the onset/offset histograms in d.5 / e.5).
Fig 4.
Effect of connection range on SO dynamics.
A) Example target column (yellow) with all its connected columns (green). The blue area indicates the connection range for the corresponding radius R. No connections are made in the black region outside the radius. R = 226mm encompasses all the original dMRI-derived connections. B) Percent of the original number of connections preserved for different values of R. C) Distance distribution for different values of R, with inset zooming into radii below 10mm. R imposes a maximum connection length and truncates the distance distribution accordingly. Red horizontal lines indicate medians, bottom and top box edges indicate the 25th and 75th percentiles, respectively, whiskers extend to the most extreme data points not considered outliers, and outliers are plotted individually using the ‘+’ marker symbol. D-E) SO analysis for R = 5mm and R = 2.5mm. Subpanels as in Fig 2. F) Summary of the effect of reducing connection density on the global SO frequency and amplitude as well as the standard deviation of the onset/offset delays (i.e. the width of the onset/offset histograms in d.5 / e.5).
Fig 5.
Local SO for small connection radius (R = 2.5mm).
A) Ten cortical areas with a 5mm radius, that were used to calculate local dynamics. B) Average membrane voltage of layer II neurons, as in Fig 4e.2. C-E) For each region in (A), subpanels show (C) the single-cell voltage for two neurons in the area, (D) the local field potential (LFP) for the 5mm area, and (E) heatmap of individual voltages of all neurons in the area. Note that even within these very small regions, there are still subgroups of independently synchronized neurons. F) Latency map, calculated as the onset delay of each neuron with respect to the earliest onset, for each Up state identified in Fig 4e.2. Note that even the most global of slow waves has very low participation, around 35%, and can be seen to consist of many extremely small initiation sites that generally do not spread.
Fig 6.
Effect of cortical excitatory synaptic strength on the network dynamics.
A) Reduction of all cortical connections by 3x. B) Reduction of only connections longer than 10 mm by 5x. All subpanels as in Fig 2. C) Summary of changes in frequency, amplitude, speed, participation, and onset/offset distribution spread when all connections are reduced as shown in (A). Increasing all weights shows little effect while decreasing all weights shows decreased amplitude and participation, with increases in onset/offset distributions (decreases in synchrony). The frequency of slow waves also becomes more variable. Note, Increasing all weights 5x results in the ablation of slow waves due to constant Up state, i.e., SO characteristics cannot be meaningfully quantified. D) Summary of changes in SO characteristics when only long-range connections are reduced as shown in (B). Across all plots, 5 mm is seen to be an inflection point (or “elbow”) where network activity changes.
Fig 7.
Mixed global (Type I) and local (Type II) Slow Waves: Connections greater than 10mm reduced 5-fold.
A) Ten cortical areas with a 5mm radius, that were used to calculate local dynamics. B) Average membrane voltage of layer II neurons. C-E) For each region in (A), subpanels show (C) the single-cell voltage for two neurons in the area, (D) the local field potential (LFP) for the 5mm area, and (E) heatmap of individual voltages of all neurons in the area. This demonstrates that while there is some alignment, up states are not strongly global. F) Latency map, calculated as the onset delay of each neuron with respect to the earliest onset, for each Up state. Note, that while some Up states are global (characteristic examples are marked by blue lines), others are comprised of several independent but coinciding local events (examples are marked by yellow lines).
Fig 8.
Quantification of Global vs Local Slow Waves.
The labels show the radius and factor of strength reduction in each model—e.g., 5/4 indicates a model where connections longer than 5 mm are reduced by a factor of 4. A) For each model, the Regularity of each parcel is calculated; the mean and variance of these distributions predict the overall network behavior, with global models showing high Regularity and local models showing low Regularity. The group of models in the middle of the distribution, boxed in orange, represents Mixed states. B) Mean Regularity is plotted against the Intact Score (total percent of synaptic strength relative to the global base model). Note that the total level of synaptic strength is itself predictive of network behavior—the same mixed models fall in the orange box in the middle of the distribution. C) Example traces of 10 random parcels in representative Global, Mixed, and Local models show different levels of synchrony across the brain.
Fig 9.
Functional Connectivity and Coherence Analysis of Experimental v.s. Model data.
Coherence analysis was performed on all data sets according to the procedure described in Coherence analysis. A) The parcel-to-parcel coherence matrices are first averaged in the slow wave frequency band and scaled by parcel-to-parcel distances to determine functional connectivity via percent of connected parcels and number of communities (determined by Louvain community detection). B) Full (unaveraged, unscaled) coherence matrices are then fitted with an exponential function to determine the full shape of the coherence landscape across distance and frequency. The resultant first (0.5 Hz) Lambda and mean Alpha in the slow wave frequency range (<2 Hz) are taken to describe the shape of the coherence landscape, and plotted in (B). (A.1 and B.1) show zoom-ins of each respective plot; the labels show the radius and factor of strength reduction—e.g., 10/5 indicates a model where connections longer than 10 mm are reduced by a factor of 5. This shows that the models with primarily mixed slow waves are the closest fit to experimental results across all 4 metrics. Full 3D coherence plots across distance and frequency are shown for the experimental data (C), the 10mm / 5 model (D), and the global slow wave base model (E), showing that the global slow wave model has a fundamentally different shape (lacking a dependence of coherence on distance) and much higher levels of coherence at low frequencies.
Table 1.
Summary of results for each network manipulation.
Decreasing connection density resulted in decreased slow wave frequency, amplitude, synchrony, and spread, but slow waves remained global. Decreasing connection radius resulted in decreased slow wave amplitude, speed, participation, and spread. Increasing delays resulted in effects are seen only for manipulations far past biological plausibility, as indicated with a single down arrow for frequency, amplitude, and participation. Decreases in synaptic strength caused reduced amplitude, synchrony, frequency and participation. Finally, decreasing the strength of only long-range connections resulted in traveling local slow waves with decreased amplitude, speed, and synchrony.
Table 2.
Map-based model parameter definitions and values.
Parameters γ and δ may take one of the two values shown (see text). Parameters were initially set to the values in [30] and then fine tuned to maintain biologically reasonable spiking behavior in the current larger-scale network. Sub-index X stands for “AMPA” or “GABA”. For all parameters regarding synapses, the PY and IN columns denote the post-synaptic neuron.
Table 3.
Parameter definitions and values for conductance-based models are based on previous modeling of single-cell dynamics [23, 36, 93, 94].
Table 4.
Parameter changes between sleep and wake stages.