Asymmetric signaling across the hierarchy of cytoarchitecture within the human connectome

Abstract

Cortical variations in cytoarchitecture form a sensory-fugal axis that shapes regional profiles of extrinsic connectivity and is thought to guide signal propagation and integration across the cortical hierarchy. While neuroimaging work has shown that this axis constrains local properties of the human connectome, it remains unclear whether it also shapes the asymmetric signaling that arises from higher-order topology. Here, we used network control theory to examine the amount of energy required to propagate dynamics across the sensory-fugal axis. Our results revealed an asymmetry in this energy, indicating that bottom-up transitions were easier to complete compared to top-down. Supporting analyses demonstrated that asymmetries were underpinned by a connectome topology that is wired to support efficient bottom-up signaling. Lastly, we found that asymmetries correlated with differences in communicability and intrinsic neuronal time scales and lessened throughout youth. Our results show that cortical variation in cytoarchitecture may guide the formation of macroscopic connectome topology.

Fig. 1.. Estimating trans-hierarchical signal propagation.

Using the Schaefer atlas, we sampled 20 nonoverlapping groups of regions (n = 10 per state) traversing up the S-F gradient of cytoarchitectonic similarity (4). These groups formed brain states spanning the cortical hierarchy. By definition, regions within each state had relatively similar profiles of cytoarchitecture. Accordingly, pairs of states separated by long hierarchical distances have different underlying cytoarchitecture. (A) An example pair of brain states (x_i, x_j) at different locations along the S-F axis. (B) For a given pair of states (x_i, x_j), we calculated the minimum control energy (E) required to complete the transition from x_i to x_j and from x_j to x_i. (C) Minimum control energy between all pairs of states was assembled into a transition energy matrix, T_E. Owing to the ordered nature of our brain states, transition energies were trivially grouped into bottom-up (transitions moving up the hierarchy; T_E, upper triangle) and top-down (transitions moving down the hierarchy; T_E, lower triangle). a.u., arbitrary units. (D) Given this grouping, we subtracted top-down energy from bottom-up energy to create an energy asymmetry matrix (T_EΔ). In the upper triangle of this asymmetry matrix, positive values represented state transitions where bottom-up energy was higher than top-down energy, whereas negative values represented the opposite. Note that, apart from the sign of the Δ value, T_EΔ is symmetric; hence, all analyses of asymmetries focused on the upper triangle of this matrix.

Fig. 2.. The topology of the structural connectome is sensitive to asymmetries between top-down and bottom-up signal propagation across the S-F axis of cytoarchitecture.

(A) Bottom-up energy was significantly lower than top-down energy (left), demonstrating that bottom-up state transitions were easier for our network control model to complete. One thousand bootstrapped resamples of the group-averaged connectome (see Materials and Methods) revealed that the 95% confidence interval (CI) of this asymmetry did not overlap 0. In addition, this mean asymmetry was larger than expected under a pair of null network models (right), including one that preserved the spatial embedding and the edge weight distribution of the network and another that preserved the spatial embedding and the strength distribution. (B) The distance along the cytoarchitectonic gradient separating the initial and target states was negatively correlated with energy asymmetries, demonstrating that high cytoarchitectonic dissimilarity between states was linked to greater negative energy asymmetries (left). This finding shows that when cytoarchitecture differs between brain states, bottom-up transitions required lower energy to complete compared to their top-down counterparts. The same bootstrap test described above revealed that the 95% CI of this correlation did not overlap 0. In addition, this correlation with hierarchy distance was larger than expected under the same pair of null network models described above (right). Together, these observations suggest that trans-hierarchical transition energy may be supported by the higher-order topology of the structural connectome.

Fig. 3.. Asymmetries in transition energy are explained by asymmetries in communicability.

We examined how our energy asymmetries correlated with asymmetries in diffusion efficiency, search information, and path transitivity. While diffusion efficiency and search information represent asymmetric communicability metrics, path transitivity is symmetric. Thus, we defined a modified version of path transitivity that was sensitive to asymmetries in the human connectome. (A) Path transitivity measures the occurrence of returning detours (i.e., triangles) along a given shortest path. Path transitivity is typically estimated along the entire length of the shortest path and is symmetric. (B) We modified path transitivity by estimating it separately for each segment of the shortest path starting from nodes located at either end. (C) Doing so allowed us to estimate a pair of cumulative path transitivity curves: one for each direction along the shortest path. These curves allowed us to probe whether returning detours were encountered sooner in one direction or the other, which we quantified by subtracting the curves and summing the differences. (D) Energy asymmetries correlated negatively with asymmetries in diffusion efficiency. Thus, lower bottom-up energy corresponds to higher bottom-up diffusion efficiency. (E) Energy asymmetries correlated positively with asymmetries in search information. Thus, lower bottom-up energy corresponds to lower bottom-up search information. (F) Energy asymmetries correlated positively with asymmetries in cumulative path transitivity. Thus, lower bottom-up energy corresponds to lower bottom-up path transitivity; in turn, returning detours are encountered sooner for top-down signaling.

Fig. 4.. Uncontrolled dynamics preferentially flow up the cortical gradient of cytoarchitecture.

(A) We simulated the spread of uncontrolled dynamics seeded from each of our cytoarchitectonic brain states and tracked the activity as it unfolded over time and spread throughout the cortex. For a given seed state, we quantified the Spearman rank correlation between the S-F axis of cytoarchitecture and the pattern of simulated activity at time t as well as the difference in correlations between adjacent time points. (B) Correlations between cytoarchitecture and simulated activity seeded from each brain state as a function of time. Negative correlations indicate that brain activity at time t was higher at the bottom of the hierarchy than at the top, while positive correlations indicate the opposite. States lower on the hierarchy tend to show negative correlations between the S-F axis and early activity propagation (blue arrow), while states higher on the hierarchy tend to show positive correlations (peach arrow). (C) Differences in correlations between neighboring time points as a function of time. These low-hierarchy negative correlations diminish more quickly (blue arrow), by becoming less negative, compared to the positive correlations in high-hierarchy states (peach arrow). Collectively, these results suggest that uncontrolled dynamics spread more readily across the S-F axis in the bottom-up direction than top-down.

Fig. 5.. Energy asymmetries correlate with differences between brain states’ intrinsic neuronal time scales.

(A) We used resting-state ECoG data to examine differences between brain states’ intrinsic neuronal time scales [as per methods described by Gao et al. (24)] between our cytoarchitectonic brain states. (B) Energy asymmetries between brain states were negatively correlated with differences between brain states’ intrinsic time scales. This result shows that state transitions where bottom-up energy is lower than top-down (negative energy asymmetry) are also characterized by a slowing of intrinsic time scales going from state i to state j and vice versa.

Fig. 6.. Optimized control weights track the cortical gradient of cytoarchitecture and maximize energy asymmetries.

(A) For each trans-hierarchical state transition, we adopted the following procedure to generate optimized control weights that minimized transition energy. First, for a given state transition, we calculated uniformly weighted transition energy; nodes of the system were provided the same degree of control over system dynamics. Note that the results for uniformly weighted transition energy have been reported in all figures before this one. Second, we reestimated the transition energy n times, each time providing one node with additional control over the system. This approach generated a vector of perturbed transition energies (purple vector). Third, we subtracted the uniformly weighted energy from each of the perturbed energies to generate a vector of perturbed energy delta values (blue vector), the magnitude of which encoded the regions’ importance to the state transition. Fourth, we reestimated transition energy one more time using the perturbed energy deltas as optimized control weights. (B) Correlations between optimized control weights for each state transition and the S-F axis. For each state transition, we estimated the Spearman rank correlation between the nodes’ optimized weights and their distance along the S-F axis from the initial and target state and retained whichever correlation was strongest (see Materials and Methods). BrainSMASH P values were corrected for multiple comparisons using the Benjamini-Hochberg FDR (59). Significance was determined as P_FDR < 0.05. We found that optimized weights correlated negatively with hierarchical distance, indicating that they decayed as a function of distance from the initial/target state. (C) Mean energy asymmetries (∣T_EΔ∣) for uniform (light gray) compared to optimized (dark gray) control weights under 1000 bootstraps (see Materials and Methods). Mean ∣T_EΔ| was larger for optimized control weights compared to uniform control weights. Thus, optimizing control weights maximized energy asymmetries.

Fig. 7.. Energy asymmetries in trans-hierarchical state transitions vary systematically over development.

We estimated correlations between age and trans-hierarchical transition energy in 793 individuals while controlling for sex, total brain volume, edge density, and in-scanner motion. (A) Correlations between age and transition energy for all state transitions. We observed widespread negative correlations between age and transition energy, suggesting that state transitions became easier to complete as individuals got older. (B) Correlation between age and participant-specific energy asymmetries averaged over bottom-up and top-down state transitions. We found a positive correlation between age and energy asymmetries, indicating that the energy asymmetries between bottom-up and top-down closed throughout youth. (C) Correlation between age effects for individual state transitions [from (A)] and the energy asymmetries derived from the group-averaged structural connectome (T_EΔ; see Fig. 2). We found that the age effects (Pearson’s r) were negatively correlated with T_EΔ, demonstrating that the strongest age effects were concentrated in the state transitions with the largest energy asymmetries. (D) Schematic illustration of a cross-validated regression model that was used to assess the out-of-sample prediction of participants’ age. (E) Results from the out-of-sample prediction of participants’ age. Energy asymmetries robustly predicted the participants’ age in out-of-sample testing when scored using the correlation between true and predicted y (top left), negative root mean square error (middle left), and negative MAE (bottom left). As both error metrics represent the original units of y, these results show that our model was able to predict age to within 2.64 to 3.18 years. Note that these prediction effects were replicated when using both a higher-resolution version of our parcellation that included 400 parcels [Schaefer 400; correlation(y_true, y_predicted) = 0.30; negative[RMSE] = −3.15; negative[MAE] = −2.60] and a 360-parcel multimodal parcellation developed in the Human Connectome Project [correlation(y_true, y_predicted) = 0.30; negative[RMSE] = −3.15; negative[MAE] = −2.61]. Together, these results show that asymmetries in trans-hierarchical signal propagation and neurodevelopment are intimately intertwined.