Article Figures & Data
Figures
- Figure 1.
Modeling framework overview. A, The closed-loop neurotoxicity model integrates a model of proteinopathy dynamics and a BNM to simulate neural activity, interacting in a closed-loop: proteinopathy affects neural activity and vice-versa. B, Scheme of the Jansen–Rit (JR) NMM with three interacting subpopulations where triangles represent synaptic contacts between subpopulations, boxes represent the sigmoidal transformation of voltage into firing rate, and colored hexagons represent the transformation of firing rate into voltage. C, Implementation timeline for the closed-loop model. First, a baseline simulation is gathered to get a baseline firing rate. Then, the closed-loop model simulation begins by integrating the proteinopathy with dt = 0.25 (years) and simulating the BNM to update hyperactivity damage (
- Figure 2.
Single-node in-silico experiment. The behavior of a single NMM was simulated varying parameter values. Four different experiments are presented in columns exploring different combinations of parameters. In rows, measures derived from the simulations: oscillatory frequency peak of the node, mean firing rate, absolute power, and the relative power in two frequency bands: α and θ. The red circle points out the default parameter values. A 2D representation of each parameter change is shown in Extended Data Figure 2-1. Sample time series for the different oscillatory regimes are shown in Extended Data Figure 2-2.
- Figure 3.
Evolution of the parameters, state variables, and neural activity outputs from the closed-loop neurotoxicity model. Results are averaged over regions included in eight categories including frontal, parietal, temporal, and cingulate regions. A, Concentration of toxic proteins over time during model execution. B, Damage variables that determine the impact of the proteinopathy over the neural activity (i.e., JR-BNM parameters). C, JR-BNM parameters change over time. D, Functional measures derived from the simulation of the BNM including spectral frequency peak and power, PLV, and firing rate. The latter is used in the calculation of q(ha). E, Damage variable q(ha) that determines the impact of hyperactivity on the production and propagation of toxic proteins. The average of the parameter changes shown in (C) are plotted over the single-node experiments’ heatmaps in Figure 3-1.
- Figure 4.
Functional measures from the closed-loop neurotoxicity model. Metrics averaged from the simulation shown in Figure 3. A, We extracted spectral frequency peak, relative band power, firing rate, and α FC from the simulation over 40 years of the neurotoxicity model. A quadratic relationship is found over time for all these metrics (i.e., measures increase early in time and decrease later). B, Temporal excerpts of the same simulation including 3D representations of the BNM with node size as degree, node color as firing rate (orange/red is a higher rate), and edge colors as PLV. Last row shows averaged normalized spectra for all the regions included in the model. FC evolution in other frequency bands is shown in Figure 4-1. Regional spectra at several time points are shown in Figure 4-2.
- Figure 5.
Parameter spaces for the limits of change of the JR-BNM parameter candidates. For each parameter candidate (rows) and limit value explored (heatmaps y-axis), one simulation of 40 years (heatmaps x-axis) is performed. For each simulation, four neural activity measures are extracted including averaged frequency peak, relative α power, firing rate, and FC (columns). When exploring a parameter candidate, all other parameters are kept fixed with their default values that are highlighted in red and included in Table 2. These default values were used in the simulations for Figures 3 and 4. Note how taking apart from zero the limits of change impact differently the resulting behavior of the model. Two additional parameter spaces were computed to define values for g and s (Fig. 5-1).
- Figure 6.
Parameter spaces for Cip isolating the effects of Aβ and hp-tau. First row shows the results of simulating the neurotoxicity model with different limits of change for Cip isolating the effects of Aβ on inhibition, while the second row shows the results of simulating the same parameter space isolating the effects of hp-tau on inhibition.
- Figure 7.
Dominance of Braak sequences per seeding strategy. A, The percentage of simulations per seeding mode in which different Braak sequences of hp-tau propagation were dominant. Fixed implied seeding a usual, Aβ random implied randomizing Aβ seeding and using the fixed version for hp-tau, vice-versa for tau random, and random implied randomizing both Aβ and hp-tau seeding. B, Samples of the most representative Braak sequences showing the normalized concentration of
- Figure 8.
Impact of Aβ and hp-tau seeding on the antero-posterior temporal differentiation for firing rate (top) and FC (PLV; bottom). The neurotoxicity model shows a rise and decay for several variables including firing rate and FC. We measured the time elapsed to that peak for anterior and posterior regions as a proxy to understand where the neurophysiological changes happened before. Samples of the temporal evolution for each seeding strategy and for both firing rate and FC are represented in Figure 8-1.
Tables
Parameter Value Unit Description He 3.25 mV Average excitatory synaptic gain Hi 22 mV Average inhibitory synaptic gain 10 ms Time constant of excitatory PSP 20 ms Time constant of inhibitory PSP Cpe 135 Average synaptic contacts: pyramidals to excitatory interneurons Cep 108 Average synaptic contacts: excitatory interneurons to pyramidals Cpi 33.75 Average synaptic contacts: pyramidals to inhibitory interneurons Cip 33.75 Average synaptic contacts: inhibitory interneurons to pyramidals e0 0.0025 ms−1 Half the maximum firing rate r 0.56 mV−1 Slope of the presynaptic function at v0 v0 6 mV Potential when half the maximum firing rate is achieved p 0.1085 ms−1 Mean of random Gaussian intrinsic noisy input σ 0.022 ms−1 Standard deviation of random Gaussian intrinsic noisy input g 25 Coupling factor for interregional communication s 20 m/s Conduction speed for interregional communication Parameter Value Unit Description prodAβ 3 M ·· · years−1 Production rate for Aβ clearAβ 3 Years−1 Clearance rate for Aβ transAβ 3 M−1 ·· · years−1 Transformation constant of Aβ into its toxic isoform clearÃβ 2.4 Years−1 Clearance rate for prodT 3 M ·· · years−1 Production rate for T clearT 3 Years−1 Clearance rate for T transT 3 M−1 ·· · years−1 Transformation of tau into its toxic isoform clearT̃ 2.55 Years−1 Clearance rate for syn 0.4 M−2 ·· ·years Synergistic effect between ρ 50 cm ·· · years−1 Effective diffusion constant 1 M−1 ·· · years−1 Damage rate for 1 M−1 ·· · years−1 Damage rate for 0.01 Damage rate for hyperactivity 0.8 Years−1 Constant for the effect of 0.4 Years−1 Constant for the effect of 1.8 Years−1 Constant for the effect of 1.8 Years−1 Constant for the effect of 0.05 Years−1 Constant for the effect of 3.65 Maximum value allowed for He parameter change 13.25 Minimum value allowed for Cip parameter change 28 Minimum value allowed for Cep parameter change 0.3 Maximum damage of 2 Maximum damage value for hyperactivity Note. Aβ and T stand for healthy amyloid-β and tau proteins while
Left frontal pole Right frontal pole Left rostral middle frontal Right rostral middle frontal Left caudal middle frontal Right caudal middle frontal Left superior frontal Right superior frontal Left lateral orbitofrontalAβ Right lateral orbitofrontalAβ Left medial orbitofrontalAβ Right medial orbitofrontalAβ Left insulaAβ; IV Right insulaAβ; IV Left caudal anterior cingulate Right caudal anterior cingulate Left rostral anterior cingulate Right rostral anterior cingulate Left posterior cingulateAβ; IV Right posterior cingulateAβ; IV Left isthmus cingulateAβ Right isthmus cingulateAβ Left superior parietal Right superior parietal Left inferior parietalIV Right inferior parietal Left precuneusAβ Right precuneusAβ Left inferior temporalIV Right inferior temporalIV Left parahippocampalIII Right parahippocampalIII Left hippocampusII Right hippocampusII Left thalamus Right thalamus Left amygdalaIII Right amygdalaIII Left entorhinal cortextau I; Right entorhinal cortextau I; Notes. Aβ and tau superscripts denote the regions used as seeding (Braak and Braak, 1991; Palmqvist et al., 2017). I, II, III, and IV superscripts denote the regions included in the Braak stages (Therriault et al., 2022).
Extended Data 1
Code developed in Python 3.9 to simulate and visualize the closed-loop neurotoxicity model. Download Extended Data 1, ZIP file.
Figure 2-1
2D representations of single node experiments varying only one parameter at a time (i.e., He, Cip, Cep, p). Dashed lines showing the default parameter value. Markers' colour scales are the same as in the heatmaps of Figure 2. Download Figure 2-1, TIF file.
Figure 2-2
Timeseries and spectra for three different regimes shown in Figure 2: slow limit cycle, fast limit cycle and fixed point state. Two traces from independent simulations are shown. Download Figure 2-2, TIF file.
Figure 3-1
Parameter trajectories of the simulated closed-loop model with default parameters on heatmaps from single node experiments. Trajectories are represented as curves with varying colours. The colour represents time: starting in red and ending with blue. Note that heatmaps are extracted from single-node simulations in which just two parameters are varied at a time, while the trajectories imply a 4-dimensional parameter change. Therefore, the underlying heatmaps should be interpreted just as an orientation of what might happen when changing parameters in one direction. Download Figure 3-1, TIF file.
Figure 4-1
Averaged FC (PLV) of the simulated closed-loop model with default parameters for different frequency bands: delta (2 - 4 Hz), theta (4 - 8 Hz) and alpha (8 - 12 Hz). Download Figure 4-1, TIF file.
Figure 4-2
Normalized spectra per region over time (yrs.). Note the transition of all spectra to more noisy states with lower frequency peaks. Download Figure 4-2, TIF file.
Figure 5-1
Parameter spaces to select working point. Selected parameters were g=25 and s=20 m/s (see red highlights). Note how the rising of g leads to a situation in which no FC rise is observed, similar to the reduction of s, due to high early FC levels. Also, lowering g leads to the prebifurcation regime of the JR NMMs, a situation in which the spectral frequency peak lowers towards the delta band. Download Figure 5-1, TIF file.
Figure 8-1
Samples of the evolution for firing rate (left column) and FC (i.e., PLV; right column) in the antero-posterior differentiation experiments. In rows, each of the four seeding implemented strategies. The effect on FC is limited to a temporal shift of the curves, however, the seeding affects the level of hyperactivity reached by the anterior or posterior regions. Download Figure 8-1, TIF file.
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