Rapid thalamocortical network switching mediated by cortical synchronization underlies propofol-induced EEG signatures: a biophysical model

Propofol-mediated unconsciousness elicits strong alpha/low-beta and slow oscillations in the electroencephalogram (EEG) of patients. As anesthetic dose increases, the EEG signal changes in ways that give clues to the level of unconsciousness; the network mechanisms of these changes are only partially understood. Here, we construct a biophysical thalamocortical network involving brainstem influences that reproduces transitions in dynamics seen in the EEG involving the evolution of the power and frequency of alpha/low beta and slow rhythm, as well as their interactions. Our model suggests propofol engages thalamic spindle and cortical sleep mechanisms to elicit persistent alpha/low-beta and slow rhythms, respectively. The thalamocortical network fluctuates between two mutually exclusive states on the timescale of seconds. One state is characterized by continuous alpha/low-beta frequency spiking in thalamus (C-state), while in the other, thalamic alpha spiking is interrupted by periods of co-occurring thalamic and cortical silence (I-state). In the I-state, alpha co-localizes to the peak of the slow; in the C-state, there is a variable relationship between an alpha/beta rhythm and the slow oscillation. The C-state predominates near loss of consciousness; with increasing dose, the proportion of time spent in the I-state increases, recapitulating EEG phenomenology. Cortical synchrony drives the switch to the I-state by changing the nature of the thalamocortical feedback. Brainstem influence on the strength of thalamocortical feedback mediates the amount of cortical synchrony. Our model implicates loss of low-beta, cortical synchrony, and coordinated thalamocortical silent periods as contributing to the unconscious state. New & Noteworthy GABAergic anesthetics induce alpha/low-beta and slow oscillations in the EEG, which interact in dose-dependent ways. We construct a thalamocortical model to investigate how these interdependent oscillations change with propofol dose. We find two dynamic states of thalamocortical coordination, which change on the timescale of seconds and dose-dependently mirror known changes in EEG. Thalamocortical feedback determines the oscillatory coupling and power seen in each state, and this is primarily driven by cortical synchrony and brainstem neuromodulation.

continuous alpha/low-beta frequency spiking in thalamus (C-state), while in the other, thalamic 47 alpha spiking is interrupted by periods of co-occurring thalamic and cortical silence (I-state). In 48 the I-state, alpha co-localizes to the peak of the slow; in the C-state, there is a variable 49 relationship between an alpha/beta rhythm and the slow oscillation. The C-state predominates 50 near loss of consciousness; with increasing dose, the proportion of time spent in the I-state 51 increases, recapitulating EEG phenomenology. Cortical synchrony drives the switch to the I-state 52 by changing the nature of the thalamocortical feedback. Brainstem influence on the strength of 53 thalamocortical feedback mediates the amount of cortical synchrony. Our model implicates loss 54 of low-beta, cortical synchrony, and coordinated thalamocortical silent periods as contributing to 55 the unconscious state. 56 57 New & Noteworthy: 58 GABAergic anesthetics induce alpha/low-beta and slow oscillations in the EEG, which interact 59 in dose-dependent ways. We construct a thalamocortical model to investigate how these 60 interdependent oscillations change with propofol dose. We find two dynamic states of 61 thalamocortical coordination, which change on the timescale of seconds and dose-dependently 62 mirror known changes in EEG. Thalamocortical feedback determines the oscillatory coupling 63 and power seen in each state, and this is primarily driven by cortical synchrony and brainstem 64 neuromodulation. 65 66 Introduction: 67 Unconsciousness mediated by GABAergic anesthetics, such as propofol and sevoflurane, is char-68 acterized by a presence of alpha/low-beta (8-20 Hz) and slow oscillations (0.5-2.0 Hz) in the 69 electroencephalogram (EEG) ( lighted two states they called "peak-max" and "trough-max". These are two states in which the 77 slow and alpha rhythms are coupled by phase-amplitude coupling (PAC). In the peak-max, the 78 amplitude of the alpha rhythm is maximal during the peak of the slow rhythm; in trough-max, 79 the maximal alpha amplitude appears in the trough of the slow. The trough-max state appears 80 close to the loss of consciousness (LOC), whereas the peak-max state occurs with deeper levels 81 of propofol. However, during most of the time spent under propofol, the EEG does not reflect 82 either of these states. This is shown in Fig. 1. 83 84 Anesthetics act on their molecular targets, and it is then through network mechanisms that they 93 alter brain rhythms ( In this paper, we use 8-12 Hz as the range for alpha rather than the 8-14 Hz range used in 108 (Purdon et al. 2013; Mukamel et al. 2014). We note that 8-12 Hz is the standard range for alpha 109 in the cognitive literature (Van Diepen, Foxe, and Mazaheri 2019; Foster and Awh 2019). In the 110 current paper, we aim to relate the propofol-induced rhythms to loss of cognitive function; and 111 thus, we make a distinction between alpha (8-12 Hz) and low-beta (13-20 Hz). 112 113 We show that the dynamics on small space and time scales are highly complex: on each slow 114 cycle, there is one of two network states, which can change after some indeterminate number of 115 slow cycles. One of those states is called the "C-state" and is characterized by a continuous ("C") 116 alpha/low-beta oscillations in thalamus; the other state is called "I-state" in which there is 117 thalamic spiking at an alpha frequency interrupted ("I") by a time period within a slow 118 oscillation cycle in which there is no thalamic activity. The I-state is highly related to what has 119 been called peak-max, since the alpha activity is co-localized with the peak of the slow 120 oscillation. The interaction of alpha, low-beta, and slow during the C-state is more variable than 121 in the I-state, and the alpha portion includes what has previously been called "trough-max". We 122 show that the statistics of these states are dose-dependent, with higher doses of propofol 123 corresponding to a larger percentage of the I-state. A significant finding of the work is that the 124 statistics of the two states are strongly influenced by the synchrony of the cortical cells. Thus, the 125 depth of anesthesia corresponds to the statistics of the I-states and C-states. Unconsciousness is 126 associated with a prevalence of the I-state and thus a higher degree of cortical synchronization. 127 Such increased synchronization has been reported experimentally (Gutiérrez et al. 2022). See the 128 Discussion for more details. 129 130 Systemic administration of GABAergic anesthetics effects all structures in the brain, and the 131 influence of these drugs on the brainstem can alter neuromodulatory systems (Moody et al. 132 2021). Our simulations show that when feedback from thalamus to cortex is potentiated because 133 of these alterations, the synchronization of cortex is facilitated, and makes the switch to the I-134 state more probable. Endogenous noise in the system facilitates switching back to the C-state. 135 Our work suggests that cortical synchronization due to potentiated thalamic feedback resulting 136 from neuromodulatory alterations are key in understanding the mechanism of GABAergic 137 anesthetics mediated unconsciousness. The loss of beta with increasing dose also has 138 implications for loss of long-distance communication needed for consciousness. 139 140 Results

142
Model of propofol acts on cortical, thalamic and brainstem biophysics. 143 We develop a model consisting of interacting thalamic and cortical circuits (see Methods  (Fig. 1). Among the spectral 147 features that we investigate with our modeling are: (a) increased co-localization of the alpha with 148 the peak of slow as dose is increased (Fig. 1A), (b) increased amplitude of the slow oscillation 149 with increasing propofol dose (Fig. 1A), (c) increased low-beta power near loss of consciousness 150 (LOC) and return of consciousness (ROC) (Fig. 1A,B), and (d) decreased mean frequency of 151 alpha and decreased alpha power with higher doses (Fig. 1B). We show below that each of these 152 features reflects properties of the model suggestive of mechanisms of loss of consciousness. 153 154 We model the cortical circuit using 100 pyramidal cells (PY) and 20 cortical interneurons (IN)  155 from ; Benita et al. 2012) ( Fig. 2A). The pyramidal cells are modeled with 156 two compartments: the soma (PYso) and the dendrite (PYdr). The thalamic circuit is modeled as 157 in , except with 20 thalamocortical cells (TC) and 20 thalamic reticular 158 neurons (TRN). Our model currents are conductance-based with Hodgkin-Huxley dynamics. 159 Details of the currents used in each neuron type, network connectivity, and all other aspects of 160 the model can be found in the Methods and Appendix.

175
We modeled the addition of propofol as five changes from wake-like conditions. The first is an 176 increase in the maximal conductance and the inhibition time constant of the GABA receptors, 177 which are known to be produced by propofol ( The "wake-like" condition without propofol produces a "depolarized relay state" (Destexhe et al. 198 1996) in thalamus as shown in Fig. 2B With propofol, the thalamocortical network produces prominent slow and alpha/low-beta 207 oscillations that are visible in the raster plots (Fig. 1C). Here we show with a blow-up of Fig. 1C  208 that the alpha/low-beta oscillation is visible in the thalamic TC cell spiking. The network 209 dynamics can change in time in a way that will be examined in detail below. We find that the 210 model cortex alone can generate slow oscillations and thus thalamic involvement is not needed 211 (Fig. 2D). With propofol, an alpha oscillation arises in thalamus from the potentiation of GABA-212 A and the decrease in H-current, as shown in our previous work, which simulates thalamus in the 213 absence of cortex. A description of the alpha generating mechanism is in )in 214 the section entitled "Propofol induces sustained alpha via changing the balance of 215 excitation/inhibition." This alpha uses the interaction between TC and TRN and engages 216 thalamic spindling mechanisms. In our previous work, we did not include thalamocortical 217 feedback; our current work shows that the thalamic alpha oscillations persist in the presence of 218 thalamic feedback (Fig. 2C). 219 220 Our model EEG shows strong slow and alpha/low-beta oscillations (Fig. 2E). The alpha/low-beta 221 oscillations are more evident (Fig. 2E, top) in the first and last 10 seconds of the simulation in 222 Fig. 2C than during the middle 10 seconds (Fig. 2E, bottom). A spectrogram of the model EEG 223 from the simulation in Fig. 2C, shows a continuous slow oscillation and a prominent higher 224 frequency oscillation that switches between alpha/low-beta (8-20 Hz) and a lower average 225 frequency alpha (~ 8 Hz) (Fig. 2F). 226 227 Propofol induces rapid switching between two distinct thalamocortical network states. 228 With propofol, the network switches between two mutually exclusive network states on a rapid 229 timescale (seconds) both on the single cell level and the population level (Fig. 2C, 3A-F), each of  230  which can span over multiple cycles of the slow oscillation. The main difference between these  231 states is the periodic cessation of spiking in the thalamus in one state but not the other; when this 232 happens, the cortex and thalamus are simultaneously silent (Fig. 3A, D). The thalamic silence 233 occurs because the thalamus enters a silent depolarized state, which stops the thalamus from 234 spiking and thus thalamic input to cortex is lost. We call this network state the "I-state" (short for 235 "interrupt"). In contrast, in the other network state, there are no thalamic silent periods because 236 spiking from thalamus in continuous. Thus, we refer to this network state as the "C-state" (short 237 for "continuous"). during the C-state the fast thalamic frequencies range from 8-20 Hz and thus spans the 254 alpha/low-beta range (Fig. 3F,I). These two network states correspond to different interactions 255 between the slow and the alpha or alpha/low-beta in the EEG. In the I-state, there is always high 256 amplitude alpha associated with the peak (or rising phase) of the slow oscillations (Fig. 3G); the 257 trough of the slow oscillations corresponds to the simultaneous silent periods in thalamus and 258 cortex (Fig. 3G). In contrast, the C-state has a variable relationship between alpha/low-beta and 259 slow (Fig. 3I). The thalamic spiking persists continuously throughout the slow oscillation cycles 260 with some variation in the relationship of the alpha/low-beta amplitude to the phase of the slow. 261 In particular, the alpha and low-beta tend to couple at different phases of the slow oscillation 262 during the C-state. Our simulations suggest that one possible coupling during the C-state is a 263 transient coupling of alpha to the trough of the slow oscillation as seen on some slow cycles in 264 Fig. 3I, as well as in experimental literature (Purdon et al. 2013;Mukamel et al. 2014). When 265 this occurs, the low-beta couples to a different phase of the slow oscillation (Fig. 3I). Note that, 266 in the C-state, the slow oscillation has lower amplitude than in the I-state (compare Fig. 3G  The type of corticothalamic feedback dictates the spectral coupling observed during the different 302 states. In the C-state, the alpha often occurs near the trough of the slow wave, while the low-beta 303 occurs more towards the peak of the slow wave. This phenomenon stems from the influence of 304 cortical spiking on the excitation level of the thalamus: when cortical spiking is low, as in the 305 trough of the slow wave, the thalamus is more hyperpolarized and thus has a lower frequency of 306 spiking (alpha spiking). In contrast, when the cortical spiking is higher, as in the peak of the slow 307 wave, the thalamus is more depolarized and thus the thalamic spiking is at beta. The positive 308 feedback from thalamus to cortex engages the activity-dependent K(Na)-current with the thala-309 mus giving less excitation (alpha) to cortex when the cortical activity is low and more excitation 310 (low-beta) when the cortical excitation is high. Note that this accounts for increasing frequency 311 of the K(Na)-mediated slow oscillations between the wake-like state (~ 0.2 Hz) and the C-state 312 (1 Hz) (Fig. 2B, C). In contrast, when the network is in its homeostatic feedback regime (I-state), 313 cortical synchrony leads to thalamic silence, which in turn leads to a profound loss of cortical 314 spiking. This simultaneous loss of thalamic and cortical spiking is reflected in a large slow wave 315 trough with no alpha coupling. The thalamus responds to the loss of cortical input by hyperpolar-316 izing into its spindling regime and again spiking, now at predominately alpha, which depolarizes 317 the cortex into its active phase. The diminished cortical K(Na), which decreased during the corti-318 cal inactive phase, additionally primes the cortex to spike more synchronously in response to the 319 thalamic input. The more synchronous spiking during the cortical active phase is reflected in the 320 EEG as a higher amplitude peak in the slow wave. The alpha spiking in the thalamus is coupled 321 to the peak of the slow wave since this is the only phase at which the thalamus is active. 322 323 Summarizing the connection between cortical synchronization and thalamic state, we find that 324 under propofol the thalamocortical network can abruptly switch between two dynamic networks 325 states governed by the level of synchronization in the cortex. The spectral features of the EEG 326 during these two states are the results of a switch in thalamic feedback dynamics: positive feed-327 back during the C-state and homeostatic feedback during the I-state. In particular, we find that 328 during the state of positive corticothalamic feedback (C-state), the amplitude and duration of the 329 slow oscillation is controlled by the kinetics of the activity-dependent K(Na) current in the cor-330 tex, whereas during the state of homeostatic corticothalamic feedback (I-state), the amplitude and 331 duration of the slow oscillation is influenced by the thalamic feedback. The larger amplitude 332 slow waves during the I-state are a consequence of engaging the homeostatic thalamocortical 333 feedback, while the low amplitude slow waves during the C-state result primarily from cortical 334 K(Na) dynamics. 335 336 To verify the relationship between the cortical synchronization and the thalamocortical state, we 337 tested whether we could change the thalamocortical state by introducing artificial cortical 338 synchronization or de-synchronization. We applied 100 milliseconds of either a synchronizing or 339 desynchronizing input to cortex during a period when the system was in a C-state. Artificial 340 synchronization of cortex switched the thalamocortical network to an I-state, whereas with 341 artificial the thalamocortical network remained in the C-state ( Fig. 4A-E). These results support 342 cortical synchronization as a driver of C-state to I-state transitions. When cortical synchronizing 343 or de-synchronizing inputs were applied to the network when the system was in an I-state, we 344 found that de-synchronizing inputs induced a transition to the C-state, whereas the network 345 remained in the I-state in response to synchronizing inputs (Fig. 5)

362
Scoring was done by visual inspection, where each simulation was marked as "All" if >95% of simulation time 363 after the Synchronizing Input exhibited I-state; analogously, each simulation was otherwise marked as "Most" 364 = 95%-50%, "Half" = ~50%, "Some" = 50%-10%, or "None" = <10%. The bar chart is the summation of all In the previous section, we showed that cortical synchronization is a key driver of C-state to I-392 state transitions in corticothalamic circuits. Here we propose the physiological mechanism by 393 which increased cortical synchronization occurs as propofol dose is increased. 394 395 We model increasing propofol dose by progressively decreasing ACh neuromodulation on 396 corticothalamic circuits (see Methods): we increased maximal AMPA synaptic strength between 397 cortical pyramidal cells (ḡ AMPA:PY→PY ) and from TC cells to cortical pyramidal cells 398 (ḡ AMPA:TC→PY ), which strengthens feedback from thalamus to cortex. As propofol dose is 399 increased in our model, the amount of time spent in the C-state progressively decreases and is 400 replaced by more time spent in the I-state (

409
To determine whether the change to more I-states relies primary on TC→PY or PY→PY 410 synapses, we looked at the incidence of I-states when changing one of these synapses at a time. 411 We found that the dose-dependent increased time spent in the I-state is primarily due to 412 increasing the TC→PY AMPA synapse (

422
That the C-state to I-state switch requires thalamocortical feedback is supported by the finding 423 that in the absence of TC feedback, the thalamocortical networks remain in the C-state (Fig. 6). It 424 also shows that the cortical synchronization caused by the K(Na)-production of the slow wave 425 does not produce sufficient cortical synchrony to induce the C-state to I-state transition. In 426 contrast, we showed in the last section that the switch from the I-state to the C-state is facilitated 427 by cortical desynchronization. This can occur physiologically under propofol due to cortical 428 noise (Fig. 3).

436
The increasing time spent in the I-state with higher doses of propofol accounts for several dose-437 related EEG findings including: (1) less low-beta because this frequency is predominately in the 438 C-state, (2) more lower frequency alpha because the alpha in the I-state has a lower average 439 frequency than the alpha in the C-state (see Fig. 4B), (3) decreased alpha power because alpha is 440 only present for a short period on the peak of the slow wave in the I-state, (4) loss of trough-max 441 because trough-max is seen only in the C-state and only occasionally in that state, (5) increased 442 peak-max due to thalamic alpha spiking occurring only during the peak of the slow wave in the 443 I-state, (6) increased slow wave amplitude/power due to the I-state having larger amplitude slow 444 oscillations as a result of increased cortical synchronization and its coordinated cortico-thalamic 445 silent states. 446 447 Discussion 448 Overview and Clinical Implications 449 The anesthetic propofol produces oscillatory signatures on the electroencephalogram (EEG): 450 prominent alpha/low-beta oscillations (8-20 Hz), slow oscillations (0.5-2.0 Hz), and increased 451 co-localization of the alpha to the peak of the slow with increasing effect site concentration 452 (Mukamel et al. 2014). Here we use computational models to examine the role of brainstem, 453 thalamus, and cortex in producing these oscillations and shaping the interactions between them. 454 Specifically, our results help to understand the biophysical origin of the rhythms and the role of 455 the rhythms in producing loss of consciousness. 456 457 One surprising finding in our simulations is that the thalamocortical network switches at the 458 timescale of seconds between two dynamic states characterized by continuous alpha/low-beta in 459 thalamus (C-state) or by transient interruption of the thalamic alpha (I-state). In the latter, the 460 alpha is co-localized to the peak of the slow rhythm ("peak-max"), whereas in the former, there 461 need not be consistent co-localization. we find that, during the C-state, the thalamus does not hyperpolarize enough to completely stop 536 thalamic spiking during the cortical active phase; rather, the thalamus produces alpha/low-beta 537 throughout all phases of the slow oscillation. As a result of this, alpha/low-beta is more 538 prominent, and thus will show higher power, during low-dose time periods, which the C-state is 539 more prevalent in (see (3) The addition of thalamocortical feedback allows changes in cortical synchronization with 541 increase in dose: continuous alpha/low-beta in thalamus results from less cortical 542 synchronization, and hence the slow waves that appear in cortical EEG have a significantly 543 lower amplitude and greater variability (Fig. 1B,C; Fig. 3  changing GABAergic effects), we predict that a smaller dose of physostigmine may produce less 625 I-state and more C-state and thus, may lead to more EEG low-beta, higher frequency alpha, 626 increased alpha power, less peak-max, and lower slow wave amplitude. 627 628 Propofol, slow oscillations, and sleep 629 Our work suggests that propofol utilizes not only thalamic spindling mechanisms (Soplata et al. Our model is relatively small considering its significant complexity: there are a total of 160 677 neurons among multiple types in both cortex and thalamus. Larger models may sometimes 678 display behavior that is not captured in smaller ones because of the degree of heterogeneity that 679 is possible. Delineating such behavior is beyond the scope of this work. Also, not included in our 680 model is complexity associated with the multiple layers of the cortex and the multiple kinds of 681 nuclei in the thalamus. The use of Hodgkin-Huxley modeling in this study is justified when 682 examining the effects of anesthetic drugs such as propofol, which work to change the kinetics of 683 synaptic receptors and the conductances of intrinsic membrane currents that interact to sculpt the 684 network behavior (Brown, Purdon, and Van Dort 2011). As such, the size and complexity of the 685 model is driven by the questions asked. We found that simpler models, both in cellular 686 components and neuron numbers, were not sufficient to replicate the spectrum of propofol-687 induced EEG changes explored in this paper and understand their mechanisms. As to further 688 detail, our philosophy is to look for a minimal model, however complex, that will reproduce the 689 interactions propofol tend to express different proportions of these two network states on a small spatial 700 scale. Our results also suggest that, under propofol, different local cortical networks may, on a 701 fast timescale, switch between the I-state and the C-state even while a regional EEG signal 702 predominantly shows a single type of dose-dependent PAC. By introducing region-specific 703 heterogeneity to cortex (e.g., sensory and higher-order) and thalamus (e.g., core and matrix), 704 future simulations may be able to investigate the significant spatiotemporal changes between 705 low-and high-dose propofol. "Anteriorization" is a well-known phenomenon in which propofol 706 administration initially leads to the loss of awake, occipital alpha and an increase in frontal alpha 707 (Tinker, Sharbrough, and Michenfelder 1977;Cimenser et al. 2011;Vijayan et al. 2013). This 708 frontal alpha is at its strongest and most persistent state during low-dose propofol, before 709 spreading to become region-nonspecific during high-dose propofol ( 2017) and may modulate higher frequencies more in frontal regions during high-dose (Stephen et  714 al. 2020). We note that our current modeling captures many of these results for frontal cortex: (1) 715 alpha is strongest and most persistent during low-dose propofol; (2), alpha decreases in power 716 with increasing dose; (3) slow power is greater during high dose than low-dose propofol. 717 718 In the future, modeling multiple cortices will allow us to probe why holding propofol at a low-719 dose results in trough-max coupling that is most prevalent in frontal cortex (Mukamel et al. 720 2014), why there is stronger frontal slow modulation at higher doses (Stephen et al. 2020), and 721 why there is increased thalamocortical alpha coherence in this region (Flores et al. 2017). 722 Modeling multiple cortices will also allow us to explore coherence, phase ( This state is associated with low-beta (as well as alpha) oscillations in the thalamus. As discussed 762 above, beta oscillations have been documented to be highly involved in long-distance 763 coordination in the brain (Siegel, Donner, and Engel 2012). Thus, the loss of this beta could 764 contribute to the higher degree of unconsciousness associated with higher doses. 765 766 One unintuitive finding suggested by our model was that TC neurons may be depolarized into 767 "relay mode" during I-state and could potentially relay sensory information during this window, 768 even during deep anesthesia. In our simulations, strong corticothalamic excitation after 769 synchronized active cortical states increased the membrane potential of TC cells during the I-770 state, as shown in Fig. 3A,D. This increase was enough to interrupt the intrinsic alpha bursts of 771 the thalamus, but if this occurs at the same time as strong sensory input spikes, the TC cells may 772 be depolarized enough to briefly relay sensory spiking information up to the cortex. Recently, 773 even in humans under low-dose propofol anesthesia, auditory stimuli resulted in wake-like 774 cortical neural activity in primary auditory cortex but not higher-order cortex (Krom et al. 2020). 775 This suggests that some thalamic sensory relay may still occur under propofol anesthesia, even if 776 changes to cross-cortical communication prevent its higher-order processing. Furthermore, in our 777 simulations, the I-state may occur during individual slow cycles of both low-and high-dose 778 propofol projections to go to 100 PY cells. Ultimately, this results in each PY cell receiving connections 841 from 4 TC synapses, resulting in each synapse being normalized to 1/4th of the total maximum 842 conductance. If the total maximum conductances of PY→PY and TC→PY are equal (see next  843 paragraph), then each connection from a single source TC cell to a single target PY cell will have 844 a larger maximal synaptic conductance than each single PY to PY connection, but there will be 845 fewer TC to PY connections. 846 847 Except for the simulations done for Table 2, the total maximal conductances of our intracortical 848 PY→PY and thalamocortical TC→PY AMPA synapses were kept equal to each other and 849 changed simultaneously. We assumed that the ratio between these two maximal synaptic 850 conductances could be held to be equal due to prior thalamocortical models using the same 851 (Ching et al. 2010) or similar (Krishnan et al. 2016) (0.020:0.024) ratios. Additionally, by using 852 equal values for these conductances, we could model the effects of propofol decreasing ACh on 853 each of these synapse types in identical ways (see Table 1). We could then compare the effects 854 on the system of treating these conductances heterogeneously (see Table 2) to understand their 855 relative contribution to the case where they are set identically. 856 857 The total maximal conductances used for the PY→PY and TC→PY AMPA synapses ranged 858 from 0.002 mS/cm 2 to 0.012 mS/cm 2 . These values change in response to the concentration of 859 ACh present, but the relationship between concentration and proportion of change in 860 conductance is not clear, so we were required to explore a range of values; for the relationship of 861 ACh to these conductances, see the subsection "Propofol effects" below. We initially based our 862 intracortical and thalamocortical total maximal conductances on the default value used for 863 PY→PY AMPA total maximal conductance in the original cortical SWO model paper (Compte 864 et al. anesthesia (see the aforementioned subsection below). We did simulate higher values such as 869 0.0154 mS/cm 2 as in the original paper, but these were not significantly different than the I-state 870 shown in the paper, and continued the trend shown in the Tables of a dominance of I-state.  871  872  Model Inputs  873  874 For all simulations, in order to model background activity, excitatory Poisson spiketrains were 875 input into all PY, TC, and TRN cells. These spiketrains had a firing rate of 40 Hz and were 876 convolved with an exponential with a decay time of 2 milliseconds. The total maximal 877 conductance of these virtual synapses were always held equal to that of the total maximal 878 conductance of PY→PY and TC→PY AMPA synapses, except for the simulations in Table 2 scarce, but the increase may be as high as +300% (see Figure 8 F of (Favero, Varghese, and 935 Castro-Alamancos 2012)). We therefore focused our synaptic changes on a wide range of 936 decreases from 0.0154 mS/cm 2 , the derived value of the low-ACh sleep state used in the cortical 937 SWO model of . 938 939 For the K(Na)-current maximal conductance ḡ K(Na) , we only used two values: 0.10 mS/cm 2 in 940 our wake-like simulation (similar to the tonic, wake-like state of Figure 14 of the original paper 941 , or 1.33 mS/cm 2 for all anesthetic states. We specifically chose to not make 942 small changes to ḡ K(Na) between anesthetic states because it has impacts on the frequency of the 943 SWO produced, which the original paper investigates.  1 General Notes Units of maximal conductances and currents for all equations below are in mS cm 2 and µA cm 2 , respectively, based on the original formulation of [Hodgkin and Huxley, 1952]. Capacitance C m for all cells was 1 µF cm 2 . Thalamic circuitry is based on [Destexhe et al., 1993], , and [Ching et al., 2010] and is mostly identical to . Cortical circuitry is based on a from-scratch implementation of ] and [Benita et al., 2012]. Thalamocortical and corticothalamic synaptic equations were derived from the same AMPAergic synapse equations as in . Occasionally, multiplication dots will be used (·) to help legibility. All simulations were run for 30 seconds of simulation time (unless otherwise indicated) and solved using Euler integration, with a time resolution (dt) of 0.01 ms. 2.3 (K(Ca)) Slow Calcium-activated K Channel

(NaP) Persistent Na Channel
Parameters and Functions:

(KS) Non-inactivating K Channel
Parameters: State Variable Equations: m, h

(T) T-type Calcium Channel
Parameters:

(H) Hyperpolarization-activated Cation Channel
Note: This is the more complex  formulation of the H-current, not that of [Destexhe et al., 1993]. O U is the proportion of unlocked channels, O L is the proportion of locked-open channels, and P 1 is the proportion of utilized substrate for channel locking.
[Cai]crit ) n Ca (1 − P 1 ) − k 2 P 1 -[Ca] i is a state variable determined by the T-current.

Direct Compartmental Connections
Each PYdr compartment has a special connection to and from a single PYso compartment called I COM , meant to simulate voltage fluctuations between the axo-soma and dendrite of a single cell. Note that these conductances are not exact inverses of each other due to the difference in size between the two compartments. These two currents are calculated using the following: g COM |P Y so→P Y dr = 5 mS cm 2 7.2 (K(Na) Intercompartmental Naactivated K Channel Additionally, there is a special and very important current, I K(N a) , which requires information on the state of the Na present in directly-connected PYso and PYdr compartments. This changes depending on ACh dose. Practically speaking, this can be modeled somewhat easily by programming it as if it is a synaptic current. The equations follow: The electrical current equations for each class of synapse (AM P A, AM P A D , N M DA, GABA A , and GABA B ) were the same within their class, with the sole exception of different connections having different maximal conductances. All conductances of individual synapses were divided by a normalizing factor of how many connections each target cell received. Note that AM P A D is referred to as AM P A in the main manuscript; its different name is only relevant here for explaining that it contains depression mechanisms in the implementation.
Note that P M multiplies bothḡ GABA A and τ GABA A .

Synaptic connectivity and conductances
See the Methods section for general description of connectivity. For the "nearest neighbors" connection algorithm, see the code file "models/netconNearestNeighbors.m". Additionally, incoming synapse maximal conductances are divided by a Normalization Factor (NF). This NF ensures that the total maximal conductance for a particular synaptic type into a target cell is balanced across the number of incoming cell synapses. NF is defined as: Where N source and N target are the number of cells in the source and target populations, respectively.
The following table lists all synaptic connection radii and synaptic maximal conductances (before NF has been applied). P Y so → P Y dr synaptic connections only connect to 2·radius target cells so as not to synapse onto their corresponding compartment. All maximal conductances are giving in units of

Propofol Effects
For the "wakelike" non-propofol state, see the Methods. For the anesthetic simulations, the following parameters were set. Note that PM or "Propofol Multiplier" multiplies both g GABA A and τ GABA A .

Reproducibility and Code
All simulations were run using the MATLAB-based DynaSim software package  on the "dev" branch, using MATLAB 2021a. The individual mechanism files for use with DynaSim are available online , and so are all the runscripts needed to reproduce simulations of the paper [Soplata, 2023b].