Thalamocortical network connectivity controls spatiotemporal dynamics of cortical and thalamic traveling waves

Propagation of neural activity in spatially structured neuronal networks has been observed in awake, anesthetized and sleeping brains. However, it remains unclear how traveling waves are coordinated temporally across recurrently connected brain structures, and how network connectivity affects spatiotemporal neural activity. Here we develop a computational model of a two-dimensional thalamocortical network that enables us to investigate traveling wave characteristics in space-time. We show that thalamocortical and intracortical network connectivity, excitation/inhibition balance, thalamocortical/corticothalamic delay can independently or jointly change the spatiotemporal patterns (radial, planar and rotating waves) and characteristics (speed, direction and frequency) of cortical and thalamic traveling waves. Simulations of our model further predict that increased thalamic inhibition induces slower cortical wave frequency, and enhanced cortical excitation increases cortical wave speed and oscillation frequencies. Overall, the model study provides not only theoretical insight into the basis for spatiotemporal wave patterns, but also experimental predictions that potentially control these dynamics. Author Summary Cognition or sensorimotor control requires the coordination of neural activity across widespread brain circuits. Propagating waves of oscillatory neural activities have been observed at both macroscopic and mesoscopic levels, with various frequencies, spatial coverage, and modalities. However, a complete understanding how thalamocortical traveling waves are originated and temporally coordinated in the thalamus and cortex are still unclear. Furthermore, it remains unknown how the network connectivity, excitation/inhibition balance, thalamocortical or corticothalamic delay determine the spatiotemporal wave patterns and characteristics of cortical and thalamic traveling waves. Here we develop a computational model of a two-dimensional thalamocortical network to investigate the thalamic and neocortical traveling wave characteristics in space-time, which allows us to quantitatively assess the impact of thalamocortical network properties on the formation and maintenance of complex traveling wave patterns. Our computational model provides strong theoretical insight into the basis of spatiotemporal wave propagation, as well as experimental predictions that control these wave dynamics.

6 136 and thalamus at 10%; higher RE-CX connectivity would cause the cortical wave to dominate the thalamic 137 wave, or cause the thalamic lurching (staggered activity in time) to vanish quickly (Video S3 and Fig. S2).
138 Together, these results suggest that by closing the loop, the thalamocortical model may produce rich 139 oscillations with random traveling wave patterns, as well as distinct traveling wave speed between the 140 cortex and thalamus.

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142 Low intracortical connectivity necessitates clustered cortical neurons to yield traveling waves 143 144 In order to sustain wave propagation, or equivalently, to maintain sufficient wave propagation area in time, 145 we found that a high percentage of intracortical connectivity was necessary. In the neocortex, we assumed 146 that the overall intracortical connectivity was 25-36%, with 4:1 ratio of exc-to-inh neurons. In our cortex-147 alone structure (i.e., without the thalamus) with 25% intracortical connectivity, we found that it was difficult 148 to sustain spontaneous cortical wave propagation. The cortical wave area increased proportionally with the 149 intracortical connectivity (Fig. 2a). When the intracortical connectivity was below 25%, the cortical wave 150 structure lost continuity and reduced to isolated dot patterns. When the thalamus was included in the 151 closed loop, a punctate wave band was observed in the cortex, completely in synchronization with the 152 thalamus (Fig. S2), thereby not enabling spontaneous cortical wave propagation.

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In cortical circuits, excitatory connections are not uniformly distributed, and exhibit clustering into 155 groups of highly connected neurons [23]. Therefore, for a fixed intracortical connectivity, it implies that the 156 connectivity is high within the clustered groups, and low outside the clustered groups. To investigate the 157 impact of connectivity topography, we modified the 2D arrangement of neurons from uniform connectivity 158 (Fig. 2b, left and middle panels) to clustered structure (Fig. 2b, right panel, with the same overall 159 connectivity as the middle panel). Within the clustered group, the intracortical connectivity was ~90%, while 160 maintaining the overall 25% connectivity. Our model simulations showed that the propagating waves were 161 prominent within the cluster, as opposed to the puncta patterns outside the cluster (Fig. 2c,d).

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10 243 in our simulations, a 1D space-time representation was insufficient to fully comprehend the underlying 244 spiral wave, and only the 2D traveling wave representation could convey the complete picture. Together, 245 the results suggest that based on the thalamocortical connectivity and transmission delays, one can 246 potentially predict the characteristics of the spatiotemporal patterns that may ensue as a result of 247 perturbations.

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First, we examined the impact of E/I imbalance in RE inhibition on the cortex. To help illustrate this 258 point, we assumed that the cortex contained 99% excitatory neurons. In a standard closed-loop condition, 259 we showed the 2D thalamic and cortical traveling wave dynamics (Fig. 5a, left), as well as their 1D 260 projections (Fig. 5a, right). The RE and TC competed to trigger the cortical wave activity. In the presence 261 of lower RE inhibition, TC excitation dominated, resulting in firing cortical neurons (Fig. 5a, red dots in 262 white circle). These dots ultimately propagated to form cortical waves (Video S1). However, with increased 263 RE inhibition, the effect of TC excitation decreased (due to a lack of firing within the white circle), resulting 264 in fewer cortical traveling waves, or lower frequency (Video S12). Comparing the number of striped firing 265 patterns in 1D projections (Fig. 5b vs. Fig. 5a), we observed a decrease in traveling wave frequency 266 induced by increased RE inhibition. When we switched the cortical setup from 99% excitatory neurons 267 back to the 4:1 exc-to-inh neuron ratio, we could still observe a similar effect (Fig. 5c). However, the 268 differences in cortical wave frequency became less prominent as the percentage of excitatory neurons was 269 decreased (Fig. 5d). This result may be ascribed to the fact that inhibitory neurons play a critical role for 11 270 the oscillatory frequency in the cortex. In contrast, the change in cortical wave speed was insignificant.
271 This insignificant wave speed change was consistent irrespective of the number of excitatory neurons.
272 Adding the effect of lateral RE inhibition to the three-layer model, may potentially alter the wave speed 273 along with frequency.

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Next, we examined the effect of imbalance in cortical excitation on traveling waves, by increasing 276 the excitatory weights in the cortex by two folds. As a result, we observed a dramatic change in traveling 277 wave patterns (Fig. 5e, Video S13), and a significant increase in both cortical wave frequency and wave 278 speed (Fig. 5f). In the case of 4:1 exc-to-inh neuron ratio and normal model operating conditions, the 279 excitable parameters were assumed such that the thalamus and cortex were synchronized at frequency.
280 However, as we increased the cortical excitation by using a two-fold larger excitatory synaptic weight, the 281 difference between the RE and CX frequencies became prominent (Fig. 5f). Together, the results suggest

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To illustrate this point, we conducted computer simulations by calibrating the phase offset between 295 adjacent neurons for varying noise levels at neuronal firing. The sources of external noise could be 296 ascribed to variability in synaptic noise, thermal or conductance noise, and contributions from the 12 297 modulatory input. We introduced an additional degree of randomness to the basal activity of each neuron 298 in the CX layer (Methods). The initiated wave pattern was gleaned from observing the thalamic activity, to 299 which no noise was added. We considered two points in the CX layer (red and blue dots, separated by 300 distance p). When the noise level was small (Fig. 6a), the propagating cortical wave was discernible 301 through the time-lapse images, and the phase shift was prominent (Fig. 6a, right panel). Increasing 302 distance p led to a greater phase lag. However, when we gradually increased the variance of random 303 noise in the cortical input (Fig. 6b,c), the phase shift decreased or even diminished. Nevertheless, the 304 thalamic traveling wave patterns were still preserved in the latter cases. Together, these results suggest 305 that cortical firing variability would impose challenges to observe the firing phase shift in cortical traveling 306 wave patterns, highlighting the major differences between in vivo and in vitro conditions.

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Transmission delay between adjacent neuronal connections can cause bifurcations resulting in 346 altered dynamics [18,24]. Our computer simulations have also confirmed that the thalamocortical delay can 347 not only alter spatiotemporal dynamics, but also produce a wide range of traveling wave patterns. The 348 delay parameter elicits a biphasic response, and an optimum delay exists for a particular neural field size 349 that can generate the maximum number and duration of wave patterns. As evidenced from literature 350 [34,35], the corticothalamic delay is more prominent compared to the thalamocortical delay. Throughout 14 351 our simulations, we have used a thalamocortical delay to produce traveling wave dynamics. However, as 352 we demonstrated in Fig. S3, an asymmetric corticothalamic delay also produced similar cortical traveling 353 wave alterations as the RE-CX connections were changed. In a closed-loop system, the exact location of 354 the delay along the neural pathway (feedforward vs. feedback) did not change the logic behind wave 355 pattern alterations, as the pattern formation theory necessitates only a long-range antagonist that is 356 delayed in time when compared to the local activity [36]. Therefore, with the presence of thalamocortical or 357 corticothalamic delay and the long-range inhibition, a diverse array of traveling wave patterns, including 358 planar, radial, rotating and stationary waves, could be produced from our proposed 2D thalamocortical 359 network. These results suggest that the wave patterns observed in cortical slices may emerge from 360 thalamocortical or intracortical connectivity and altered excitation-inhibition levels rather than purely 361 spontaneous activity. 366 and threshold (excitation-inhibition balance) [27]. Although most studies have considered a uniform 367 excitable medium for altering wave patterns, these parameters can be also altered through manipulating 368 interconnections in a layered system. As we have showed in the current study, the space-scale separation 369 simply amounts to lateral thalamic inhibition that spreads faster than the cortical activity. Similarly, time-370 scale separation can be equivalent to the corticothalamic delay between long-range connections. The 371 threshold of the system can easily be altered by changing the balance between excitatory and inhibitory 372 synaptic strengths. Therefore, through indirectly manipulating these system parameters, it is theoretically 373 possible to generate a wide range of complex spatiotemporal wave patterns [5,20].

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Through numerical simulations, large-scale computational models may provide insights into the 376 spatiotemporal dynamics of the thalamocortical network at a pathological brain state. The E/I imbalance is 377 an important factor that contributes to epilepsy and seizures [28]. Our results have suggested that in a 15 378 clustered cortical network, increasing the E/I ratio drastically increases traveling wave speed and overall 379 neuronal excitability, a phenomenon commonly observed in the pathological brain. For instance, traveling 380 waves have been observed during epileptic seizures [37-39], but a complete understanding of their origin 381 remains unclear. One potential mechanism of absence seizure (one kind of primary generalized seizures) 382 is thalamic dysfunction [40][41][42]. Another plausible mechanism of recurrent seizure is E/I imbalance induced 383 by stronger cortical excitation, which further causes the neuronal network to reach hyperexcitability [43].
384 Our computer simulations have suggested that the closed-loop thalamocortical system is important for 385 cortical wave propagation, and that the input of excitatory TC cells is necessary to maintain high oscillation 386 frequencies, and subduing TC input through RE inhibition can significantly reduce thalamocortical 387 oscillations. This is consistent with experimental results of a rat model that the thalamus is required to 388 maintain cortical seizure oscillations, and that optogenetic inhibition of TC cell activity disrupts seizure 389 oscillations [44]. Therefore, the dynamic properties of spatiotemporal traveling waves, such as the wave 390 speed, direction and duration, may provide a window to examine pathological brain functions.