# State-dependent dynamic communication networks in a pentameric ligand-gated ion channel

Bogdan Lev, Samuel Murail, Igor Vorobyov, Marc Baaden, Toby Allen

► To cite this version:

Bogdan Lev, Samuel Murail, Igor Vorobyov, Marc Baaden, Toby Allen. State-dependent dynamic communication networks in a pentameric ligand-gated ion channel. Journal of Physical Chemistry B, 2025, 129 (37), pp.9333-9356. 10.1021/acs.jpcb.5c03991. hal-05412186

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# State-dependent dynamic communication networks in a pentameric ligand-gated ion channel

Bogdan Lev¹, Samuel Murail²†, Igor Vorobyov³,⁴, Marc Baaden² & Toby W. Allen¹*

¹School of Science, RMIT University, Melbourne, Australia; ²Laboratoire de Biochimie Théorique, CNRS, UPR9080, Univ Paris Diderot, Sorbonne Paris, France, ³Department of Physiology and Membrane Biology, University of California Davis, Davis, CA, USA, ⁴Department of Pharmacology, University of California Davis, Davis, CA, USA

## ABSTRACT

Pentameric ligand-gated ion channels control synaptic neurotransmission via an allosteric mechanism, whereby agonist binding induces global protein conformational changes that open an ion-conducting pore. For the proton-activated bacterial (Gloeobacter) ligand-gated ion channel (GLIC), there exist high-resolution structures available in multiple conformational states. We used a library of atomistic molecular dynamics (MD) simulations to study conformational changes and to perform dynamic network analysis to elucidate the communication pathways underlying the gating process. We describe state- and pH-dependent communication between the agonist-binding extracellular domain (ECD) and the ion-conducting trans-membrane domain (TMD), revealing variation in pathways associated with conformational changes. We identify five main signal pathway families that connect the TMD and ECD via intra- and inter-subunit communication. These pathway families implicate the Cys loop, the $β_1-β_2$ loop and loop F in the ECD, along with the pre-M1 covalent connection and the M2-M3 loop in the TMD, each of which has previously been suggested to be important for gating. The $β_1-β_2$ loop and the loop F pathway families exhibit stark dependence on functional state, in contrast to the more constant Cys-loop and pre-M1 pathway families, suggesting that the channel may communicate differently during its transitions between open, closed and intermediate states of its activity cycle. We interpret the state-dependence in terms of the conformational changes that affect ECD-TMD alignment and, in particular, the breakage of the D32-R192 salt bridge, which is crucial in regulating the communication pathway. These communication networks are expected to be conserved within the super-family of pentameric ligand-gated channels, with potential applications in improved anesthetics, neuromodulatory drugs, anti-parasitics, and pesticides.

**KEYWORDS** Pentameric ligand-gated ion channel, Ion channel gating, Molecular Dynamics, Correlation Network Analysis, Allosteric modulation, pH activation

<footnote>† Current address: Université Paris Cité, BFA, CNRS UMR 8251, INSERM ERL U1133, Paris, France.</footnote>

<footnote>* Corresponding author: Prof. Toby W. Allen, School of Science, RMIT University, GPO Box 2476, Melbourne, Vic, 3001, Australia. Phone: +61-3-9925-0439. Email: toby.allen@rmit.edu.au.</footnote>
INTRODUCTION

Pentameric ligand-gated ion channels (pLGICs) facilitate signal conduction across neuron synapses by translating chemical into electric signals through the selective transport of ions across the cell membrane. This is achieved in pLGICs by the binding of a ligand in the extracellular domain (ECD; see Fig.1) causing allosteric conformational change (1) that is communicated via the TMD-ECD “gating interface” to open an ion-conducting pore located within the transmembrane domain (TMD). While the physiology and pharmacology of pLGICs have been extensively studied over several decades (2), it is more recently that experimentally determined structures have emerged for a number of prokaryotic and eukaryotic members of the family (3-15), allowing for molecular level insight into pLGIC function. Describing the signal transduction linking ligand-binding to ion conduction is essential for defining pLGIC function. Interruption in signaling pathways by mutations might lead to the channel's partial or complete loss of function associated with various genetic disorders, such as Alzheimer's, Parkinson's and epilepsy(16). pLGICs are also targets for many drugs and general anesthetics, which may influence signaling in ways that need to be defined.

There have been several high-resolution structures of pLGICs solved with X-ray crystallography and cryogenic electron microscopy (cryo-EM). The pentameric ligand-gated ion channel from *Erwinia chrysanthemi* (ELIC) (8), 5-hydroxytryptamine receptor (5-HT₃) (13), β₃ GABA<sub>A</sub> receptor (GABA<sub>A</sub>R) (14) and α₄β₂ nicotinic acetylcholine receptor (nAChR) (11) channel structures have been solved, providing valuable comparison between family members. Both open (O) and closed (C) states of the glutamate-gated chloride channel (GluCl) are available (4, 9), yet the large antiparasitic drug ivermectin was used to trap this channel in its active O form (4), likely impacting the structural changes associated with gating. The α₁-glycine receptor's (GlyR) O and C forms have been solved with cryo-EM (10, 12), also in the presence of ivermectin or the inhibitor strychnine. In contrast, high-resolution structures of bacterial (*Gloeobacter*) ligand-gated ion channel (GLIC) are available in O (6, 15) and C (5) forms, differing only by the presence of the agonist (protons). GLIC has also been solved in proposed intermediate locally-closed (LC) (3, 17, 18) states, with one substate (LC2) suggested to correspond to a “pre-active” conformation (19). Overall, this set of conformational states permits molecular-level studies to describe channel activity within one member of the pLGIC family.

pLGICs are pentamers that consist of five homologous subunits, with each subunit comprised of an ECD and a TMD, as illustrated in Fig.1 for GLIC. Each subunit of the ECD is made of an N-terminal β-sheet sandwich, while each subunit of the TMD consists of four transmembrane helices, M1, M2, M3 and M4, arranged around an ion-conducting pore. Ligands are known to bind between ECD subunits with a number of conserved segments, involving A–C loops from the principal or *n*th subunit and D–G loops from the complementary (*n*-1)th subunit (20). Perturbation due to ligand binding is communicated through the ECD-TMD (“gating”) interface to the ion-conducting pore formed by the five M2 helices within the TMD. In GLIC, deprotonation at multiple possible sites within the ECD (21) triggers a transition from maximally open at pH 4.6 to fully closed at pH 7, with a pH of half-maximal activation (pH₅₀) of ~5.3 (5), as illustrated in Fig.2a. Residues E26, E35, E67, E69, E75, E82 and E177 in the ECD (Fig.1), as well as E243 and H277 in the TMD (not shown), have been theorized to act as proton-sensing sites, based on pKₐ estimates, mutagenesis, and crystallographic data (15, 22-24). In particular, E26 and E35 (on the lower part of the β sandwich; Fig.1) reside close to the ECD-TMD interface and are thus maybe more likely to be involved in pH-gating (24). Moreover, E26, E35 and E75 are located on the interface between
two adjacent subunits, and each of these residues has been predicted experimentally to change protonation state between C and O states, along with E177 in loop C (25). Of particular interest is residue E35, which has been shown experimentally to be a key proton sensing site; with mutations E35A and E35Q exhibiting clear gain of function, in contrast to other residues which either had little change of function or left the channel non-functional (25).

<figure><img src="image_2.png" /><figcaption>**Figure 1.** **GLIC channel's molecular architecture.** The GLIC simulation system is shown, with all but one protein subunit grayed out. The four transmembrane helices within a subunit of the TMD (M1-M4) and structural elements at the TMD-ECD interface (β₁-β₂ loop (green), Loop F (orange), Cys loop (red) and M2-M3 loop (yellow-green)) have been labelled. Likely ECD protonation sites within the ECD (E35, E82, E26, E75, E177, E67 and E69) and the location of the constriction within the pore (F238) are indicated with yellow residue labels. Lipid molecules are shown in wireframe representation with C atoms in cyan, O – red, N – blue, P – orange, and H atoms not shown. Na⁺ and Cl⁻ ions are shown as yellow and cyan spheres, and water oxygens as red dots.</figcaption></figure>

Adjustments in ECD structure, resulting from changes in the protonation states of these residues, are expected to promote a state transition, as illustrated in Fig.2a. Conformational changes have been inferred from high-resolution structures of GLIC in O, LC and C states (3, 5, 6, 15), as summarized in Fig.2b-d. The O state of GLIC was crystallized with open TMD
pore and compact ECD, as opposed to the C state with closed TMD pore and significantly expanded and dynamic ECD. The change from O to C state includes both spreading and twisting of the ECD (Fig.2b), influencing inter-subunit packing and interactions at the ECD-TMD interface (Fig.2c; discussed further below) that propagates into the TMD to open or close the pore (Fig.2d). Despite the appearance of concurrent changes in ECD and TMD in these structures, the LC state was crystallized with the closed pore but O-like ECD features (3), implying decoupling of ECD and TMD changes. This is supported by functional ECD-TMD chimeras that suggest these domains may act as largely independent modules (21, 26, 27), but which rely on some conserved communication mechanism that transmits changes within the ECD structure to the TMD to alter its ion conducting state. There exist several conserved features that may facilitate interactions at the ECD-TMD interface. To start with, there is a covalent bond that links pre-M1 (attached to the $β_{10}$ strand/loop C in the ECD) to the M1 helix in the TMD (Fig.1). Other features, including the M2-M3 loop, $β_1-β_2$ loop, Cys loop (loop 7) and loop F are all conserved among the pLGIC family and come into contact at the ECD-TMD interface (Fig.1), with many residues on these flexible loops having been shown to be essential for GLIC gating (3, 17, 18, 25, 28).

The ways in which signals from the ECD transmit to the TMD are expected to vary as the structure of the protein changes. The different functional states of the protein feature altered positions and orientations of the M2 helix, M2-M3 loop and the $β_1-β_2$ loop, possibly affecting ECD-TMD signal transduction. Moreover, solution of the crystallographic C state has revealed a significant tangential twisting of the ECD, compared to O and LC states (indicated in Fig.2b), which alters the association of these residues at the gating interface (Fig.2c). Furthermore, there is splaying of the lower part of the β sandwich, which constitutes each ECD subunit, leading to the breaking of the D32-R192 salt bridge on the $β_1-β_2$ loop. This loop is known to be important across the pLGIC family (9, 10, 17, 29), with mutation of D32 leading to loss of function (17). This feature, directly adjacent to the TMD, undergoes a discrete change during the gating process (Fig.2c) that has been shown to affect the TMD's state (24). Breaking of the D32-R192 salt bridge likely causes changes that alter inter-domain signal transduction via pre-M1, or through a network of specific interactions involving the $β_1-β_2$ and M2-M3 loops (24) on which D32 and R192 are located, as indicated in Fig.2c. Thus, several key structural features have been implicated in ECD-TMD signal transduction that may be affected by the protein conformational state.

Experimental studies have been used to model the communication pathways in pLGICs using a range of methods, including site-directed mutagenesis and electrophysiology (e.g. (25, 30)), fluorescence-quenching (19, 31) and structural biology (e.g. (32-34)). On the other hand, computational studies to model the allosteric communication in pLGICs have mainly focused on normal mode analysis, elastic network models or coarse-grained methods to predict transition pathways (5, 35). Atomistic molecular dynamics (MD) on relatively short time scales can be informative when looking at quaternary and tertiary changes in the different domains of pLGICs (36, 37), while simulations on longer timescale (microseconds) can offer insight to gating changes that follow binding or removal of agonists or inhibitors (29, 38-40). Simulations on these time scales, being short compared to the timescales of activation itself, can, however, lead to anecdotal evidence of the gating mechanism. Direct modelling of the gating process can be better achieved with enhanced sampling approaches (e.g.(24, 41)). For example, Lindahl and co-workers have used time-lagged independent component analysis to capture kinetically-relevant motions from a library of multi-microsecond simulations for use in the construction of a Markov State Model of gating (41). Another approach is to instead undertake a guided search for the optimal pathways between O and C states with a fully-atomistic string method
(24, 42, 43). Such a method has been carried out within a conformational space defined by a set of protein collective variables (CVs) derived from X-ray crystallography (5). These simulations revealed pH-dependent conformational changes, while identifying what are the important CVs that can be used as a space in which to analyze the propagation and cooperativity of changes involved in channel gating (24). The important CVs include ECD spreading and/or twist (Fig.2a), expansion of the ECD subunit β sandwich (β expansion; Fig.2b), and pore-lining M2 helix movements (e.g. M2-M1(-) distance; Fig.2c), with sample free energy projection maps shown in Fig.S3.

<figure><img src="image_3.png" /><figcaption>**Figure 2.** GLIC conformational changes. **a)** Thermodynamic cycle of GLIC gating transitions (arrow sizes are an indication only). **b-d)** Conformational state-defining variables are indicated with arrows (e.g., ECD twist, β expansion, M2-M1(-) distance). In (b), the ECD is shown with blue surface and the TMD as ribbons. In (c), the Cys loop is shown as red strand, β₁-β₂ loop in ECD (containing E32) as green ribbon, F loop as brown strand, M2-M3 loop in TMD (containing L246 and K248) as green strand, pre-M1 (containing R192) as yellow strand, M1 helix as yellow ribbon, M2 helix as cyan ribbon, M3 helix as pink ribbon, and M4 helix as grey ribbon. Subunits other than the front subunit are semi-transparent. In (d), M2 pore-lining helices are shown as a semi-transparent cyan surface, with M2 and M1(-) helices on one pair of subunits shown as solid surfaces.</figcaption></figure>
Several key interactions at the gating ECD-TMD interface have also been inferred (Fig.2c), but they do not immediately tell us what is the network of interactions that communicate a protonation event in the ECD with a change in the pore-lining helices within the TMD. Communication of molecular movements across the protein can, however, be examined using correlation network analysis of microsecond-long protein dynamics (44-47). Such methods have been used to examine voltage-gated channels, for instance, uncovering the pathways by which voltage-sensing helix movements transmit to pore-lining helices (48). This approach allows one to obtain an ensemble of signaling pathways that connect different points of interest spanning disparate regions of the protein, such as protonation sites in the ECD and a constriction site in the TMD's ion conducting pore. Importantly, given a library of multi-microsecond MD simulations from multiple starting states, the approach allows for the examination of state-dependence of inter-domain communication, explaining which residues transmit conformational change from ECD to TMD that may be responsible for channel opening and closing, as well as the transition to gating intermediates. Uncovering this state and pH dependence of interdomain communication is important for understanding allosteric pH-gating in pLGICs.

# METHODS

## Molecular Dynamics

Given the expanse of multi-microsecond simulations needed to explore state-dependent cooperative motions in multiple membrane-protein systems, we have incorporated disparate models using different computers, programs and force fields. Systems were simulated using one of three different software/forcefield combinations, referred to as (i) A-GMX, (ii) C36-GMX and (iii) C27-Anton. Model (i) used Gromacs 4.5 software (49) with Amber 03 (50) force fields for protein and ions, and the Berger force field for DOPC lipids (51) (abbreviated as A-GMX). Model (ii) used Gromacs 4.5 software (49) with CHARMM C36 protein force field (52) with C36 force field for lipids (53) (abbreviated as C36-GMX). Model (iii) used Anton (54) software with C27+CMAP force field for protein (55, 56) with C36 force field for POPC lipids (53) (abbreviated as C27-Anton). The TIP3P water model (57) was used in all the simulations. Simulation times varied and were dictated by observations of conformational change and available resources on different platforms, with each providing sampling on microsecond or longer timescales (see Table S1 for a list of simulations). In total, there is ~41 µs of sampling included in this study.

The protein structures used in simulations represented one of three starting states: open (O) Protein Data Bank (PDB) ID 4HFI (6); locally closed (LC) PDB ID: 3TLT (3); and closed (C) PDB ID 4NPQ (5). Standard protein ionization states were used at high pH, by default, although with variations between different simulations (involving Asp 86, Asp 88, His 127 or His 277; see Table S2). At pH 4.7, protonation states were based on different $pK_a$ prediction methods (24) and involved protonation of glutamates 26, 35, 67, 69, 75, 82, 177, 243, aspartates 86, 88 and/or histidines 127 and 277, as shown in Table S2. Given the uncertainty in $pK_a$ prediction methods (22), performing simulations with varied protonated states allows for inspection of their impacts on protein structure; notably H127 at high pH. We note that, although H235 has previously been suggested to stabilize the O state in short MD simulation (58), this residue, in the middle of the TMD, was found in our independent tests (not shown) to corrupt the structure of the TMD, as reported previously (24), and was thus set to be neutral in all our simulations. All GLIC structures were inserted into dipalmitoylphosphatidylcholine (DOPC) lipid bilayer solvated with 100 mM NaCl aqueous solution (Gromacs simulations) or palmitoyloleoylphosphatidylcholine (POPC) lipid bilayer solvated with 300 mM NaCl aqueous
solution (Anton simulations) with numbers of positively and negatively charged ions selected to neutralize any existent charge from the protein. All systems contained around 30,000 water molecules and 150,000 atoms. An example of such a system is shown in Fig.1.

For simulations using Gromacs 4.5 (49), all bonds were constrained using the LINCS algorithm allowing a time step of 2.5 fs. Particle mesh Ewald electrostatics was used with a 10 Å cutoff for non-bonded interactions and neighbor lists updated every 10 steps. Three baths (protein, water and ion, membrane) were coupled to a temperature of 310 K using the Bussi velocity rescaling thermostat with a time constant of $τ_T = 0.1$ ps. The *xy* dimensions were scaled isotropically with a Berendsen weak barostat and the *z* dimension independently to reference pressures of 1 bar, $τ_p = 1$ ps and compressibility of $4.5 \times 10^{-5}$ bar⁻¹. The systems were minimized for 10,000 steps with steepest descent, followed by MD simulation for 1-3.7 µs each (see Table S1).

Anton (59) simulations were built with CHARMM (60), equilibrated for 4-6 ns using NAMD 2.13 (61), prior to production simulation. The *NPT* ensemble was imposed by using a Langevin piston (62, 63) in NAMD (Martyna-Tobias-Klein barostat on Anton (64)) to maintain a pressure of 1 atm, and a Nosé-Hoover thermostat (65, 66) to maintain a temperature of 310 K. The Gaussian Split Ewald (GSE) method (17) was used for electrostatics. All simulation parameters including non-bonded cutoffs were optimized using default parameter optimization (54). A typical non-bonded cutoff was ~14 Å, and value of cutoff for non-bonded lookup table was 0.5 Å more than the cutoff. The time step was 2.0 fs for bonded and near non-bonded interactions and 6.0 fs for far non-bonded interactions using the RESPA algorithm (16). The M-SHAKE algorithm (67) was using for bonds involving hydrogens. Anton MD simulations were run for up to 7 µs each (see Table S1).

## Collective variable analysis

One can trace conformational changes by following the evolution of a set of CVs. The set used here includes $β$ expansion, M2-M1(-) distance and ECD twist. $β$ expansion is defined as the distance between $C_α$ centre of mass (COM) for residues 30-34 to $C_α$ COM for residues 190-194. M2-M1(-) distance (with (-) indicating a preceding subunit) is defined as the distance between M1 ($C_α$ COM for residues 200-204, subunit *n*-1) and M2 ($C_α$ COM for residues 241-245, subunit *n*). Change in the overall ECD structure can be examined either via its spreading or twisting, but ECD twist is chosen here because it better discriminates between O, LC and C states (whereas LC and O have similar ECD spread) (24). ECD twist is defined as the dihedral angle involving $C_α$ COMs of subunit ECD – full ECD – full TMD – subunit TMD.

Projections of the protein structure's evolution in the two-dimensional space of selected CVs have been visualized on existing free energy maps (24), shown in Fig.S3 with projected crystallographic O (6, 15), LC (3) and C (5) states indicated. These maps reveal how protonation causes structural changes in the ECD (spread and twist), propagating to the TMD (M2-M1(-) distance) via the ECD-TMD interface ($β$ expansion). Marked on Fig.S1 (horizontal dashed lines) are the values of the CVs corresponding to: the crystallographic O state, with an open pore (shorter M2-M1(-) distance), low ECD twist, and formed salt bridge (small D32-R192 distance, $β$ expansion); C state with longer M2-M1(-) distance, high ECD twist, and longer D32-R192 distance; and LC state with the closed pore but O-like ECD attributes.

Values of collective variables were collected for each subunit of the protein over the duration of the simulation in fixed intervals that depend on the simulation length. Intervals have been
chosen to limit the number of points to 100 per subunit per simulation. This has been done to not overcrowd maps on which these sets are being projected. Five sets of points in CV space (one set per each subunit) are projected onto a single map representing the same CV space. Each simulation is shown on a separate map.

## Dynamic network analysis

Trajectories of protein dynamics from unbiased MD simulations can be interpreted via measures of correlation in motion between parts of the system by using sampling within a single state or during a change in conformational state. An example of such analysis that reveals pathways of communication (information transfer) within the system is Correlation Network Analysis (44-47). Information about the system's intercommunication comes from analysis of Dynamic Correlation Networks. To analyze dynamic correlation networks, we follow a similar protocol to that described previously (47).

A network is defined as a collection of nodes that are interconnected (via edges) according to some prescribed rules defined by a set of attributes assigned to nodes and/or edges. We assign nodes to be represented by a set of alpha carbons ($C_α$), for each amino acid in a protein. The edges between pairs of nodes are assigned if the distance between atoms representing the nodes is within a cut-off distance (4.5Å) for at least 75% of an MD trajectory (47). The edge length “distance” $d_{ij}$ is a dimensionless quantity defined via pairwise correlations ($C_{ij}$) as (68)

$$d_{ij} = -\log(|C_{ij}|),$$

where

$$C_{ij} = \frac{\Delta\vec{r}_i(t) \cdot \Delta\vec{r}_j(t)}{((\Delta\vec{r}_i(t))^2)(\Delta\vec{r}_j(t))^2)^{1/2}},$$

$\Delta\vec{r}_i(t) = \vec{r}_i(t) - \langle\vec{r}_i(t)\rangle$, and $\vec{r}_i(t)$ is the position vector of the $i^{th}$ node (47). Correlation coefficients were calculated from an MD trajectory (with frames saved every 2.4 ns) using the program Carma (69). We define the optimal (shortest) available path as one that has the shortest correlation distance, defined as a sum of $d_{ij}$ between two nodes, representing residues of interest. While the absolute correlation distances may be hard to gauge directly, they offer a way of quantifying the correlated motions of residues along different paths in relative terms. Moreover, this measure captures the impacts of both the physical path length and the strength of coupling between residues along that path. The values therefore offer a means for capturing and comparing the strength of signals passing along disparate communication pathways and across simulations under different conditions and functional states.

Dynamic network analysis has been carried out to extract the shortest possible communication pathways (shortest correlation distances) between residues of interest, likely associated with conformational changes related to gating. We aim to demonstrate the ways that information can be transmitted from protonation sites in the ECD to the ion-conducting pore in the TMD. We examine communication between all putative protonation sites in the ECD believed to be instrumental for triggering gating to the TMD pore (Fig.1), but focus on residue E35 for our main illustrations, because of its proven role in GLIC gating (25). As a result of ECD deprotonation, the TMD pore experiences a narrowing at high pH, closely associated with TMD M2 helix movement away from the M1 helix in the adjacent [complementary or (-)] subunit (24) (Fig.2c). This constriction is centered around M2 residue F238 (referred to as F14' in pLGIC numbering), which is considered the terminal for interdomain communication in this study.
We have chosen the known 7 protonation sites E26, E35, E67, E69, E75, E82 and E177 (all in the ECD) to assess how they are connected with residue F238 (F14') in the constriction region of the pore-lining M2 helix. Because GLIC is a pentamer, there are 5 distinct intra-/inter-subunit possibilities to connect two given residues. There is a set of residues within the same subunit that can be connected, and there are paths that connect residues on two direct neighbors ($n^{th}$ and ($n+1$)$^{th}$ or $n^{th}$ and ($n-1$)$^{th}$ subunits, see Fig.1). Adjacent subunits interact directly with each other and, therefore, may facilitate signal transduction. The remaining two possibilities connect residues that are located on subunits that are not direct neighbors ($n^{th}$ and ($n+2$)$^{th}$ or $n^{th}$ and ($n-2$)$^{th}$). These pathways would need to include intermediate subunits and are unlikely to have shorter correlation. We omit these types of pathways in our analysis. We identified 2820 individual optimal pathways, for 28 sets (one per simulation) of 5 paths (one per subunit) for 21 pairs of end points (due to having 7 identified ECD protonation sites, we have 7 pairs within the same subunit, 7 pairs for $n$ to $n-1$ adjacent (complementary or $-$) subunit communication and 7 pairs for $n$ to $n+1$ (the remaining neighbor or $(+)$ subunit communication), where it was possible to construct a correlation network.

We grouped pathways according to the particular secondary structure feature at which communication occurs between TMD and ECD. In addition to the direct covalent link between the ECD and TMD via pre-M1, ECD and TMD are in contact via interactions that involve the highly conserved Cys loop, $\beta_1-\beta_2$ loop, loop F on the ECD and the M2-M3 loop, with adjacent M2 and M3 helix residues, on the TMD. The list of pathway families is given in Table 1.

Simulations have been grouped into sets based on pH, original conformational state of the protein, or force field used. Within a given set, the “prevalence” of a pathway is the probability that a specific pathway of communication exists as the optimal pathway and is reported as the percentage of the total number of optimal pathways within that set. However, being prevalent (an optimal pathway seen often) does not necessarily mean that a pathway is the most correlated of all pathways seen. Average and minimum (optimal) correlation distances have been measured within a set that includes input from analysis involving 7 terminal pairs (one for each protonation site) using multiple simulations. Information on the relative prevalence as well as minimal and average lengths of optimal paths from specific families have been used to judge how relevant the family is to the interdomain communication. For example, if two optimum pathways have similar prevalence, the one with the shorter average pathway length may likely play a greater role in signal transduction. Table 1 reports average prevalence using the set of 7 ECD termini / protonation sites, based on the observation of similar observed pathways for a given family, irrespective of the starting residue (terminal). However, correlation length depends on the choice of terminal residues, due to both their physical distance (and the number of nodes the signal needs to travel), as well as the strength of those interactions, such that minimum correlation length values may differ greatly from average values that include all possible terminal pairs. Table S3 decomposes analysis into each individual ECD starting residue, allowing for the fact that some termini may favor different pathways depending on their location.

To visualize these statistical representations of the most likely pathways of communication, sets of optimal paths have been combined into a network. Weights were assigned to all nodes and edges according to the number of times they occurred in the set. To generate a visual representation of the optimal paths, the Fruchterman-Reingold force-directed algorithm (70) to position nodes has been used within the Dynamical Network Analysis tool in VMD program (68). While nodes are considered to have the same repulsion component, the attraction
component was assigned based on an edge's weight, the prevalence with which the edge occurs in the set. Such a procedure allows one to focus on the most likely path of communication between two nodes (70, 71).

## RESULTS

### Conformational state sampling

A range of MD simulations of the full GLIC protein embedded in lipid membranes (e.g. Fig. 1) has been carried out to allow for studies of the effect of conformational state and pH on inter-domain communication. This includes three starting conformational states (O, LC or C) two pH values (low 4.6 and high 7.0) and two different force fields (CHARMM and AMBER), as described in Methods.

Before analyzing communication pathways, we need to establish the extent of sampling of the different conformations and their interconversions within the library of MD simulations. We have selected several subunit-averaged CVs, including ECD twist, $\beta$-expansion and M2-M1(-) distance as being indicative of changes in ECD, gating interface and TMD structures, respectively (24). The O state should possess an open pore (short M2-M1(-) distance because the M2 helix is held away from the pore axis), mostly formed salt bridge (i.e. small D32-R192 distance representing $\beta$ expansion) and low ECD twist, while the C state should exhibit longer M2-M1(-) distance (M2 helix toward the channel axis), longer D32-R192 distance and high ECD twist values. A state with C-like TMD and O-like ECD attributes is indicative of the LC intermediate state. By examining 2-D projections as a function of two of these CVs in Fig. 3 (sample simulations) and Fig. S4-6 (all simulations), we can observe changes in the conformations of the ECD, the gating interface and/or the TMD. Changes in CV values from the current set of simulations, when overlaid on free energy surfaces (original free energy maps from (24) are shown in Fig. S3; with O, LC and C states marked), one can interpret conformational changes in terms of the extents and cooperativity of CV changes for the protein.

Fig. 3 includes 2-D projections for an illustrative sample set of simulations that has been chosen to highlight the longest available sets of simulations and to cover samples from all force fields simulated; although we note that variability is seen in the full set in Figs. S4-6, as discussed in the Supporting Text. The matching time series for individual CVs are shown in Fig. S1 for this sample set, and in Fig. S2 for the complete set. The selected samples include: A-GMX simulations from the O state (3.7 µs at pH 4.6 and 3.4 µs at pH 7); C36-GMX simulations that originated in the C state (1 µs each at pH 4.6 and pH 7); and C27-Anton simulations starting in the LC state (2.4 µs at pH 4.6 and 7 µs at pH 7; truncated to 4 µs, with full range in Fig. S2).

The first CV projection we consider is one that captures overall changes in both the ECD and TMD. This can be represented by pore closure, reflected in the M2-M1(-) distance, and ECD change, illustrated either using ECD spread (as done in Ref. (24)) or by ECD twist. The second projection we consider is designed to capture changes in the TMD and how they relate to changes at the gating interface, illustrated by D32-R192 salt bridge breaking (D32-R192 distance). Samples are shown in Fig. 3, with point color representing separate subunits and brightness indicating time (brighter being earlier in time and darker later in time; although this can be hard to resolve in some cases). The left-hand graphs show M2-M1(-) distance vs ECD-twist, while the right-hand graphs show M2-M1(-) distance vs D32-R192 distance.
<figure><img src="image_4.png" /><figcaption>**Figure 3.** Projections of key structural variable dynamics onto free energy surfaces show subunit-based two-dimensional projections of key variable dynamics superimposed to corresponding free energy surfaces (from (24)) for sample simulations (see Fig.S4-6 for all simulations). They are shown for: A-GMX simulations of the O state (pH 4.6 – panel e, and pH 7 - panel f); C27-Anton simulations of the LC state (pH 4.6 - panel c, pH 7 - panel d); and C36-GMX simulations of the C state (pH 4.6 - panel a, pH 7 - panel b). Crystallographic values are included in panel (a) for clarity (large green, red and blue circles), but can also be seen in Fig.S1. Red, blue, green, orange and purple colors correspond to different subunits with lighter and darker shades corresponding to the start and end of the simulations, respectively.</figcaption></figure>

*Open state simulations:* Figs.3a and 3b show systems that originated in the O state at pH 4.6 and pH 7, respectively. The system at low pH (Fig.3a) remains in the free energy minimum that corresponds to the crystallographic O state, maintaining low M2-M1(−) distance, low ECD twist values and a largely uninterrupted salt bridge between D32 and R192. At high pH (Fig.3b) a noticeable drift towards LC and C states is observed. High pH triggers partial or complete closure of the pore (vertical movement on each graph), as well as changes in the ECD (horizontal movements), with wide-ranging ECD twist and induced change in the D32-R192
salt bridge, consistent with its propensity to be broken at high pH (5). Despite including more
than 3.5 µs, with each of these simulations showing propagation towards the LC and C states,
according to the underlying free energy surface, a change in conformational state (from
occupying predominantly the O state minimum to the LC or C state minima) appears
incomplete in this timeframe, but the trends and observed differences between the two pH
conditions appear significant.

*Locally-closed intermediate state simulations:* Fig.3c and d show sample results for simulations that commenced in the intermediate LC state at low and high pH, respectively. In this case, the protein maintained a closed pore over the duration of the simulations, signified by high M2-M1(-) distance values. At low pH (Fig.3c) the M2-M1(-) distance fluctuates within only a narrow range, indicative of a locked-in closed pore within the TMD, although this range is seen to expand at high pH (Fig.3d).

Simulations that started in the LC state exhibit a dynamic ECD, as is evident by the lateral spread of points in Fig.3c and d (left panels). At low pH (Fig.3c, left), O-state-like, lower values of ECD twist have been observed, although still with a wide range. Surprisingly, the range sampled extends further left than the free energy map would suggest possible, suggesting the previous string method simulations (that connected O and C states) may not have fully explored the LC intermediate state, as a result of connecting defined O and C states without any bias towards the LC state. In contrast, at high pH, the twist range increased significantly, spanning the full range available, with an obvious shift in the distribution to the right (larger C state-like twist values), as expected.

Also suggestive of the dynamics of the ECD in the LC state are the wider ranges of D32-R192 salt bridge distance values in Fig.3c (right), compared to the O state simulations (Fig.3a, right), made possible by the breadth of the free energy surface in the upper parts of the map, with the existence of LC and C state-like minima. Moreover, the effect of increasing the pH (Fig.3d, right) is to further increase D32-R192 dynamics, exploring the full range of the underlying free energy map obtained in previous string method simulations. Overall, the LC simulations reveal good sampling of LC and C state-like states, with LC to C transitions most evident at high pH.

*Closed state simulations:* Figs.3e and f are examples of simulations that began in the C state at pH 4.6 and pH 7, respectively. The protein maintained high M2-M1(-) distance values, consistent with a closed/non-conducting pore. However, the ECD was highly dynamic, with wide-ranging ECD twist and D32-R192 distance distributions, reflecting the underlying free energy maps. Increased pH (Fig.3f) is associated with increased range of ECD twist angles and D32-R192 distances, extending towards generally larger numbers, indicating higher propensity for a twisted and spread ECD with a broken E32-R192 salt bridge.

*Summary of state sampling:* Because GLIC is pH gated, increase in pH should instigate closure of the channel, with ECD spread being the driver, accompanied by ECD twist (24). We observed for low pH (Figs.3a,c and e for O, LC and C simulations, respectively) that ECD twist (left-hand graphs) remained in a range consistent with crystallographic and previous string MD simulation values for the O and LC states, while for high pH we observed ECD-twist pushing towards higher values, characteristic of the C state. Moreover, in LC- and C-state simulations, the crucial gating interface (illustrated with D32-R192 distance in Fig.3; right-hand graphs) became dynamic upon protonation, covering values associated with all states at higher pH (panels d and f), expanding to the map's edge. This observation illustrates the dynamic and conformationally diverse nature of the ECD at high pH. The increased pH-induced changes
likely predispose the channel for its conformational gating transition, which may occur on
longer timescales. As a consequence, indications of state changes have been seen due to pH
change, yet these conformational changes may not be fully captured in the library of multi-µs
simulations. Many simulations diffused between states, but few did so in a reproducible
manner, and many did not fully transition. This was expected and a reason why enhanced
sampling methods have been previously used to capture channel gating transitions. Here we do
not aim to fully capture gating transitions but instead seek to explore protein dynamics from
within the conformational states.

The Supporting Text describes the variability among the full set of models used to simulate GLIC in its O, LC and C states, with time series of CVs shown in Fig.S2 and 2D CV maps in Figs.S4, S5 and S6, respectively. Overall, there were similar outcomes regardless of force field, but with variability among all simulations (including those with the same force field). Simulations at low and high pH starting in the O state (Fig.S4) demonstrated broad sampling of the CV space, with indications of partial conversion of states for high pH. All simulations initially with open pores experienced dewetting, even at pH 4.6, with only the Amber (A-GMX) force field experiencing rewetting during the simulation time. The Anton C27 O-state simulations showed more transitions to LC and C states than C36 or Amber force fields, spending more time away from the original O state. The set of LC-state simulations (Fig.S5) maintained an LC-like state at low pH, while at high pH the models observed ECD twist and D32-R192 salt bridge distance changes, but with consistently closed pores. A larger range of ECD variables was seen with Anton C27 (lower ECD twist at pH 4.6 and higher ECD twist at pH 7) compared to C36-GMX LC-state simulations. All C-state systems (Fig.S6) exhibited a dynamic ECD, where high pH was associated with increased ECD twist and D32-R192 salt bridge expansion, with large M2-M1(⁻) distance maintained in all simulations, consistent with a C state with a non-conducting pore. Further details on the variability of sampling is discussed within the Supporting Text. We therefore have ~41 µs of sampling of concerted protein fluctuations within and between O, C and LC states, which we now analyze for inter-domain communication and explore effects of pH and conformational state in the simulations.

## Description of the major communication pathways

Correlation network analysis has been performed to measure the correlation of molecular fluctuations between 7 protonation sites (E26, E35, E67, E69, E75, E82 and E177) in the ECD and the constriction site in the TMD pore's M2 helices at F238 (F14'). The shortest pathways (for same-subunit or inter-subunit communication) were grouped into five major families according to common secondary structure features at which communication occurs between the TMD and ECD. Of the five families, three (Cys loop, $β_1-β_2$ loop and pre-M1/M1), predominantly facilitate TMD - ECD communication within the same subunit, although these same pathways also exist for inter-subunit communication, traversing to adjacent subunits before or after passing the gating interface. Inter-subunit communication is additionally facilitated by Loop F – M2-M3 loop(+) and pre-M1 – M2-M3 loop(+) pathways involving loop F (with superscript "+" representing the (n+1)th subunit). These 5 pathway families together comprise ~99% of all communication.

We show, in Fig.4, a comparison of pathways for each of the 5 dominant families. Within each panel we show the shortest pathways for the 7 different ECD starting residues studied. Given overall conservation of pathways across different starting points in the ECD, we will illustrate families based on one starting point only in Figs.5-9. For same-subunit communication (Fig.4a-c and Figs.5-7), we have chosen the E35 starting residue for main illustrations, because E35 has been identified as a key pH-sensing binding site (25), and because of the proximity of E35
to the gating interface (residing on the $β_1-β_2$ loop), this choice corresponds to the shortest/more correlated pathway (discussed below). However, for inter-subunit communication (Fig.4d and e and Figs.8-9), the proximity of E26 to the ECD-TMD crossing point makes it the shortest path (see discussion below) and more logical choice for illustration.

While the pathway through the body of the ECD to the gating interface does depend on the terminal residue chosen, to some degree, the paths follow the same interacting or bonded residues to cross between the ECD and TMD. In fact, examination shows little or no variation in the path across the gating interface for any of the pathway families in Fig.4b-e. For Fig.4a (Cys-loop pathway family), however, we notice that for termini high in the ECD (E67, E69, E75 and E177), the paths generally traverse strands $β_7$ (orange path) or $β_{10}$ (purple path) to the left before transmitting to the TMD. But regardless of the originating residue, transmission to the TMD may occur through M2 or M3 before approaching the M2 constriction site. These two possible gating interface transmission mechanisms (Cys loop to M2 or M3) are clearly reflected in the analysis of the possible pathways for the E35 terminal alone. Thus, by focusing on one ECD terminal site only for main illustrations, no ECD-TMD communication paths are neglected. We begin by introducing the main pathways between the ECD E35 (or E26) and the TMD F238 pore constriction. We then return to describe how prevalent the families are, how correlated they are, and discuss their state- and pH-dependence in the following sections.

**Cys-loop family:** The shortest pathways connecting E35 to F238 within the same subunit that belong to the Cys-loop pathway family are shown in Fig.5a. This family consists of pathways that cross domains involving Cys-loop communication with M2 or M3 helices (or the M2-M3 loop), with key residues described below. Fig.5b depicts the network representation of optimal paths for E35 to F238 intra-subunit communications that belong to the Cys-loop pathway family, based on analysis of the full library of simulations. Residues are shown as color-filled circles connected by edges, with thickness representing the number of occurrences within the library. Generally, the path involves communication from $β_1-β_2$ loop (E35) to Cys loop (L114 and F116) and then across the interface to the M3 helix (T253) and then to the M2 helix (H235).

The most significant communication between the $β_1-β_2$ loop and Cys loop has been determined to be between residues E35 ($β_1-β_2$ loop) and L114 (Cys loop) followed by F116 (Cys loop), as shown in Fig 5b, inset i. The underlying interaction is between the carboxyl oxygen of E35 and the amide hydrogen of L114. L114 and F116 are covalently bonded via D115 (Cys loop). The backbone carbonyl of F116 occasionally is seen to form a favorable H-bond with the side chain hydroxyl group of T253 on the M3 helix (Fig.5b.ii), with less likely connections to the M2-M3 loop and M2 helix, interacting with P247 or L246 (Fig.6b.iii). Following the M3 helix, the communication pathway crosses over to M2 at I259 that is interacting with H235, involving interactions of the imidazole ring of histidine and the isoleucine backbone (Fig 5b.iv).

**$β_1-β_2$-loop family:** The $β_1-β_2$-loop pathway family is defined as one that involves $β_1-β_2$ loop communication directly with the M2 helix or M2-M3 loop near the M2 helix. The shortest pathways that belong to the $β_1-β_2$-loop family, based on 7 starting residues, are shown in Fig.4b, revealing little to no variation in TMD – ECD communication. The route of communication follows the inner side of the $β$ sandwich to the $β_1-β_2$ loop, jumping to the M2 helix or M2-M3 loop near the M2 helix, as illustrated for starting point E35 in Fig.6a.

The graphical network representation for the $β_1-β_2$ loop family of pathways connecting E35 and F238 within the same subunit is shown in Fig.6b. Generally, the path involves communication from the $β_1-β_2$ loop (K33 and E35) across the interface to the M2 helix and
M2-M3 loop (L246, T244 and N245) and then follows M2 to the end point (F238). It is worth noting that residues within M2, such as V242, are involved in this pathway most of the time (around 2/3 of all pathways in the $β_1-β_2$ loop family) but are not involved in ECD-TMD communication directly. Communication across the gating interface involves connecting K33 of the $β_1-β_2$ loop to the TMD via multiple interactions with the M2-M3 loop, as indicated in Fig.6b, insets i-iii. In particular, the K33 ζ-ammonium hydrogen is interchangeably interacting with carbonyl oxygens of L246, T244 and N245 (M2 and M2-M3 loop), as shown in Fig.6b.i, while the carbonyl oxygen of D32 is forming a hydrogen bond with the P247(M2) pyrrolidine ring (Fig.6b.ii), in simulations started in the O state. For C-state simulation at pH 4.6, $n^{th}$ to $(n+1)^{th}$ subunit communication sometimes directly connects E35 on the $β_1-β_2$ loop to Y251 on M2 via hydrogen bonding between the carboxyl oxygen of glutamate and the terminal hydroxyl group of the tyrosine aromatic ring, such as shown in Fig.6b.iii. This situation is an exception that is only applicable to C-state simulation at pH 4.6 involving $n^{th}$ to $(n+1)^{th}$ subunit communication (the only situation where this pathway becomes important for the C state; see Table 1). Although Y251 has not been identified as a major player in the correlation network analysis, it is positioned right next to residues involved in the pathway shown in Fig.6a,b.

<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /></figure>
**Figure 4. Summary of pathway families with varying starting terminal residue.** The shortest pathways of communication between the ECD and TMD that belong to five major pathway families are shown for each terminal residue pair: a) Cys loop; b) β₁-β₂ loop; c) pre-M1 - M1; d) F-loop - M2-M3-loop(+); and e) pre-M1 - M2-M3 loop(+) pathway family. Key structural elements that come into contact at the TMD-ECD interface are indicated. The β₁-β₂ loop is shown in light green, β₁ and β₂ strands are green-blue, Cys loop is red, loop F is brown, M1 is yellow, M2 is light blue, M2-M3 loop is yellow-green, M3 is pink and M4 is white. All other protein is grey. All but one subunit is semi-transparent. Pathways are shown for 7 terminal pairs originating at E26 (yellow), E35 (red), E67 (black), E69 (blue), E75 (orange), E82 (pink) or E177 (magenta) finishing at F238.

<figure><img src="image_10.png" /></figure>

**Figure 5. The Cys loop pathway family.** Example from the Cys loop family of communication connecting E35 and F238 of the same subunit. a) Pathways shown in blue are projected on the GLIC structure, with coloring as in Fig.4. Edge size represents probability with which a particular edge occurs in the set of paths shown. b) Graphical network representation of pathways from panel (a) using the same colors to mark nodes, although β₁ and β₂ strands are green and blue. Thickness of edges represents probability of occurrence. Insets i-iv show important interactions involved in communication between distinct structural features at the ECD-TMD interface only: i) between E35, L114 and F116; ii) F116 interacting with T253; iii) F116 interacting with L246 and P247; and iv) I259 interacting with H235. H atoms are not shown.
<figure><img src="image_11.png" /><figcaption>**Figure 6. The β₁-β₂ loop pathway family.** Example from the β₁-β₂ loop pathway family of communication pathways connecting E35 and F238 of the same subunit. a) Pathways in blue are projected on the GLIC structure, with coloring as in the previous figures. b) Graphical network representation of pathways from panel (a). Insets i and ii show important interactions involved in communication at the ECD-TMD interface: i) example interaction of K33 with T244, N245 and L246; ii) example interaction between D32 and P247; and iii) E35 and Y251.</figcaption></figure>

*pre-M1/M1 family:* The pre-M1/M1 pathway family involves TMD - ECD communication between pre-M1 and M1 via covalent bonding. The shortest pathways (one for each terminal pair) that belong to the pre-M1/M1 pathway family are shown in Fig.4c, again with little variation observed as a function of terminal residue. Again, while the pathway through the ECD to the interface (pre-M1 in this case) may depend on the terminal residue chosen, the paths then follow the same covalently bonded residues to the M2 helix, via the M1 helix.

The set of shortest pathways from the pre-M1/M1 pathway family connecting E35 to F238 on the same subunit are shown in Fig.7a. Fig.7b contains a network representation of the pre-M1/M1 pathway family for E35 to F238 communication within the same subunit. Generally, the pathways involve communication from β₁-β₂ loop (E35) to Cys loop (L114) then following Cys loop (F116 and Y119) and communicating to the pre-M1/M1 helix (R192, Y197, I201). The network is reinforced by another route involving direct β₁-β₂ loop (D32) communication via the salt bridge with pre-M1 (R192), after which pre-M1 is followed across the interface, finally connecting the M1 helix (I201) with the M2 helix (F238).
<figure><img src="image_12.png" /><figcaption>**Figure 7.** The pre-M1/M1 pathway family. Example from the pre-M1/M1 family of communication pathways connecting E35 and F238 of the same subunit. a) Pathways in blue are projected on the GLIC structure, with coloring as in the previous figures. b) Graphical network representation from panel (a). Insets i-iv show important interactions involved in communication at the ECD-TMD interface: i) example interaction with the D32-R192 salt bridge formed; ii) example of interactions between L30, W160 and R192; iii) example of network of interactions between L114, L116 and Y119 of the Cys loop and R192, Y197 and I201 of pre-M1 and the M1 helix; iv) example of I201 interaction with F238.</figcaption></figure>

Communication in this family involves E35-L114 interaction (as seen for the Cys-loop family above), along with the critical D32($\beta_1$-$\beta_2$ loop)-R192(pre-M1) salt bridge, shown on Fig.7b.i. Less prominent communication involving another $\beta_1$-$\beta_2$ loop residue (L30) and residue next to loop F (W160 in $\beta_9$) is D32-L30-W160-D192 shown in Fig.7b.ii. This is likely an alternative communication pathway that arises because of the breaking of the D32-R192 salt bridge, which occurs at high pH (Figs. 2c and 3b), as well as in C and LC states (Fig 3c-f). Transitions from the Cys loop to pre-M1 and the M1 helix occur at multiple points including R192 and multiple hydrophobic and aromatic side chains (L114, L116, Y119, Y197 and I201; Fig.7b.iii) and are associated with a network of interactions between two closely positioned structural elements. The pathway between M1 and M2 helices is then facilitated via interaction between two hydrophobic residues I201 and F238 (Fig7b.iv).

*Inter-subunit loop F - M2-M3 loop(+) and pre-M1 - M2-M3 loop(+) families:* Another two pathway families have been identified (Fig.4d and e), almost exclusively for inter-subunit ($n^{th}$ to ($n+1)^{th}$) communication (and only for the O state). These inter-subunit families feature significant loop F involvement, as well as adjacent residues, such as W160 ($\beta_9$). We define the loop F - M2-M3 loop(+) family, where communication is facilitated by interactions between loop F and the M2-M3 loop of the ($n+1)^{th}$ subunit, while the pre-M1 - M2-M3 loop(+) pathway family involves a signal that moves from loop F to pre-M1 before following to the M2-M3 loop of the ($n+1)^{th}$ subunit (see Fig.4d and e). In both cases, the pathways cross the ECD to TMD interface and the $n^{th}$ to ($n+1)^{th}$ subunit boundary simultaneously. Again, the comparison of different starting residues in Fig.4d/e reveals limited variability for ECD-TMD crossing, based on the choice of terminal. However, in this case we choose E26-F238 instead of E35-F238, because it has the shorter pathway length for both families (discussed below). For inter-
subunit (n^th^ to (n+1)^th^) communication, E26 is positioned closer than E35 to the features facilitating the crossing.

Family members connecting β₁ residue E26 and M2 residue F238(+) on the (n+1)th subunit are shown in Fig.8a and Fig.9a for the Loop F – M2-M3 loop(+) and pre-M1 – M2-M3 loop(+) families, respectively. Both, Loop F – M2-M3 loop(+) and pre-M1-M2 – M3 loop(+) pathways feature significant loop F involvement and residues directly near loop F, such as, W160. This communication is facilitated by interactions between loop F and M2-M3 loop of (n+1)th subunit. It mainly employs hydrogen bonding between the backbone amide hydrogen of G159 on loop F and the backbone carbonyl oxygen of K248(+) (M2-M3 loop of (n+1)th subunit), interacting preferentially in the O state (Fig.8b.i). In the C state, the preferred communication is via the backbone carbonyl oxygen of tryptophan W160 (residue next to loop F) forming a hydrogen bond with the hydroxyl hydrogen of tyrosine Y251(+) on the M2-M3 loop of the adjacent subunit (Fig.8b.ii). These interactions are specific to the O state, with pore closure and ECD twist likely to cause misalignment in other states (state dependence discussed below).

The pre-M1 – M2-M3 loop(+) pathways of inter-subunit communication employ pre-M1 to connect to loop F to the M2-M3 loop. Communication between pre-M1 and the M2-M3 loop is interchangeably facilitated by glutamine Q193 terminal amide interaction with the backbone carbonyl of lysine K248(+) (Fig.9b.i), as well as the carboxamide oxygen of glutamine Q193 and hydroxyl hydrogen of tyrosine Y251 on the adjacent subunit, shown in Fig.9b.ii.

*Rare pathway families:* Besides the five major pathway families, there are three (Loop F, Loop F – M2-M3 loop(-) and Cys-loop – M4(+) pathway types that are rarely occurring and usually not well correlated. The Loop F pathway family is essentially a sub-family within the loop F - M2-M3 loop(+) family, with the only difference being *n*^th^ to (n-1)^th^ subunit jump further up in the ECD prior to the *n*^th^ to (n+1)^th^ subunit change, as shown in Fig.9a. Although this is a rare pathway (nonexistent within the error), it can exhibit strong communication, as shall be discussed below. The Loop F – M2-M3 loop(-) pathway has only been observed once, with communication occurring via loop F to the M2-M3 loop from the (n-1)^th^ subunit. The Cys loop – M4(+) pathway family communicates via the Cys loop to the M4 helix of the (n+1)^th^ adjacent subunit interaction. These pathways are not expected to contribute significantly to ECD-TMD communication and will not be discussed further.
<figure><img src="image_13.png" /><figcaption>**Figure 8.** The F loop - M2-M3 loop<sup>(+)</sup> pathway family. Example from the F loop - M2-M3 loop<sup>(+)</sup> pathway family of communication pathways connecting E26 and F238 of the next, (n+1)th subunit. a) Pathways in blue are projected on the GLIC structure, with coloring as in the previous figures. b) Graphical network representation of pathways. Insets i and ii show interactions involved in communication at the ECD-TMD interface: i) interaction of T158, G159 and W160 (mostly loop F) with K248 and Y251 of M2-M3 loop of adjacent subunit, representative for pH 4.6; ii) representative for pH 7.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>**Figure 9.** The pre-M1 – M2-M3 loop<sup>(+)</sup> pathway family. Example from the pre-M1 – M2-M3 loop<sup>(+)</sup> pathway family of communication pathways connecting E26 and F238 of the next (n+1)th subunit. a) Pathways in blue are projected on the GLIC structure, with coloring as in the previous figures. b) Graphical network representation. Insets i and ii show important interactions involved in communication at the ECD-TMD interface: i) interaction of Q193 (pre-M1) with K248 and Y251 of the M2-M3 loop of the adjacent subunit, representative for pH 4.6; ii) representative for pH 7.</figcaption></figure>
## Correlation measures for the different pathway families

The five major families, including the three Cys loop, $β_1-β_2$ loop and pre-M1/M1 that operate either within or between subunits, as well as the inter-subunit Loop F – M2-M3-loop$^{(+)}$ and pre-M1 – M2-M3-loop$^{(+)}$ families, exhibit differing prevalence and extents of correlation. Here we first describe the overall measures of prevalence and correlation and then will subsequently break this down into state and pH dependence in the following section.

*Overall prevalence of pathway families:* Table 1 lists the prevalence of each pathway family for the different intra- and inter-subunit paths at different pH for each conformational state. The breakdown into prevalence by pH and state will be discussed in detail below, but here we focus on overall prevalence (right hand column). Table S3 provides a decomposition of prevalence based on data for individual ECD termini, showing that particular termini favor different pathways to some extent based on their location in the ECD.

The Cys-loop pathway family is most prevalent of all families, accounting for 58±8% of all ECD-TMD communications (Table 1g, right). It accounts for up to 71±15% of all the pathways for the case of E35-F238 same-subunit communication (Table S3), with generally similar numbers for inter-subunit communication. This family also has consistent contributions regardless of the starting ECD residue chosen (Table S3). This highlights the significant role played by the Cys loop in the gating of Cys-loop receptors.

The $β_1-β_2$-loop pathway family is frequently occurring, with average prevalence across all simulations of 15±7% (Table 1g, right), being similar for all ECD termini, but is slightly elevated for E35, which exists on the $β_1-β_2$ loop itself (Table S3). However, occurrence of this pathway is strongly dependent on the conformational state and pH, varying from as low as 0% (non-existent) to as high as 39±4% (detailed below).

The pre-M1/M1 family is prevalent in all simulations, accounting for 24±8% of all pathways (Table 1g, right), with some dependence on state and pH (described below). It occurs irrespective of the starting terminal in the ECD (Table S3), but is reduced (from a level of 30-38% down to 9-16%, based on same-subunit communication) for terminal residues that prefer connection with the rear-facing β-sheet (bonded to the $β_1-β_2$ loop) in Fig.1, and in particular it is diminished for E35 and E82 (Table S2).

The other two main families, loop F – M2-M3 loop$^{(+)}$ and pre-M1 – M2-M3 loop$^{(+)}$ families contribute only ~4% overall (Table 1g, right). These families only act via inter-subunit ($n^{th}$ to ($n+1$)$^{th}$) communication, where they account for 9-12% of pathways in total (Table 1e,f). Because of their involvement of loop F, the prevalence depends on the chosen ECD terminal (Table S3), disfavored (or nearly eliminated) for E35 (on the $β_1-β_2$ loop), in particular.

*Comparing correlation lengths across intra- and inter-subunit pathways:* While prevalence is a useful measure to observe how often a pathway is seen to provide optimal communication between the ECD and TMD for a particular intra- or inter-subunit mode, we turn to measures of correlation length as a way of comparing the strength of communication across different modes. Correlation length is a measure of the sum of ‘correlation distances’ over all edges that make up the path, with shorter distances telling us that there exists stronger correlation in the atomic motions along that path. Table 2 lists the minimal and average correlation lengths of each pathway family for the different intra- and inter-subunit paths at different pH for each conformational state. While dependence on pH and state will be discussed below, here we
focus on overall minima and averages (right hand column). In Table S4 we provide a decomposition based on individual ECD termini, with data sorted according to minimal and average correlation length for individual termini in Tables S5 and S6, respectively. We also provide sorted overall correlation length minima and averages (including data for all termini) in the right columns of those tables. We note, however, that when summarizing data for all termini, wide-ranging values of correlation length from disparate terminal residues lead to large numbers with large variance. We have also summarized the overall minimum and average correlation lengths (including data for all termini) in Figure 10.

<table><caption>**Table 1.** State-dependent and overall prevalence of pathways (rare pathways excluded). Pathway families are shown along with their relative prevalence (in %) and absolute number of occurrences # (in parentheses), as a function of pH and initial conformational state of the system (Open – O, Locally Closed – LC, or Closed - C). Average prevalence for all states and total number of occurrences (times reported as optimal pathway) are presented in the right column, and for all modes of communication in panel g. Pathway families are shown for: intra-subunit communication at pH 4.6 (a) and pH 7 (b); Inter *n*<sup>th</sup> to (*n*-1)<sup>th</sup> subunit communication at pH 4.6 (c) and pH 7 (d); Inter *n*<sup>th</sup> to (*n*-1)<sup>th</sup> subunit communication at pH 4.6 (e) and pH 7 (f). Uncertainties were computed as the standard error of means using all available relevant trajectories (if path only existed in a single trajectory, error is omitted). Not included in the table are rare pathways that contribute small prevalence that is within error of 0%. This includes same-subunit Loop F pathways contributing 1±2% (1 occurrence) and 2±2% (5 occurrences) at pH 4.6 and pH 7, respectively, and 1±1% (1 occurrence) for loop F *n*<sup>th</sup> to (*n*-</caption><thead><tr><th>Prevalence</th><th>O<br/>%(#)</th><th>LC<br/>%(#)</th><th>C<br/>%(#)</th><th>All states<br/>%(#)</th></tr></thead><tbody><tr><td colspan="5"><strong>a) Same subunit communication at pH 4.6</strong></td></tr><tr><td>Cys loop</td><td>47±2(66)</td><td>61±17(43)</td><td>74±9(25)</td><td>55±7(134)</td></tr><tr><td>β<sub>1</sub>-β<sub>2</sub> loop</td><td>39±4(54)</td><td>0</td><td>6±9(2)</td><td>23±4(56)</td></tr><tr><td>Pre-M1/M1</td><td>14±4(19)</td><td>39±17(27)</td><td>21±15(7)</td><td>22±9(53)</td></tr><tr><td colspan="5"><strong>b) Same subunit communication at pH 7</strong></td></tr><tr><td>Cys loop</td><td>48±3(100)</td><td>40±11(28)</td><td>63±12(264)</td><td>57±9(392)</td></tr><tr><td>β<sub>1</sub>-β<sub>2</sub> loop</td><td>31±5(66)</td><td>10±8(7)</td><td>3±3(11)</td><td>12±4(84)</td></tr><tr><td>Pre-M1/M1</td><td>19±6(39)</td><td>50±17(35)</td><td>34±14(142)</td><td>31±12(216)</td></tr><tr><td colspan="5"><strong>c) n<sup>th</sup> to (n-1)<sup>th</sup> subunit communication at pH 4.6</strong></td></tr><tr><td>Cys loop</td><td>60±7(84)</td><td>91±6(64)</td><td>56±17(19)</td><td>69±8(167)</td></tr><tr><td>β<sub>1</sub>-β<sub>2</sub> loop</td><td>27±6(38)</td><td>0</td><td>38±16(13)</td><td>21±6(51)</td></tr><tr><td>Pre-M1/M1</td><td>12±3(17)</td><td>9±6(6)</td><td>6±10(2)</td><td>10±5(25)</td></tr><tr><td colspan="5"><strong>d) n<sup>th</sup> to (n-1)<sup>th</sup> subunit communication at pH 7</strong></td></tr><tr><td>Cys loop</td><td>56±4(117)</td><td>47±7(33)</td><td>81±4(337)</td><td>70±4(487)</td></tr><tr><td>β<sub>1</sub>-β<sub>2</sub> loop</td><td>34±5(71)</td><td>29±10(20)</td><td>3.1±0.6(13)</td><td>15±3(104)</td></tr><tr><td>Pre-M1/M1</td><td>9±3(19)</td><td>24±12(17)</td><td>16±4(67)</td><td>15±4(103)</td></tr><tr><td colspan="5"><strong>e) n<sup>th</sup> to (n+1)<sup>th</sup> subunit communication at pH 4.6</strong></td></tr><tr><td>Cys loop</td><td>35±7(49)</td><td>61±15(43)</td><td>82±7(28)</td><td>49±9(120)</td></tr><tr><td>β<sub>1</sub>-β<sub>2</sub> loop</td><td>27±7(37)</td><td>11±4(8)</td><td>6±9(2)</td><td>19±6(47)</td></tr><tr><td>Pre-M1/M1</td><td>22±9(31)</td><td>27±16(19)</td><td>12±10(4)</td><td>22±11(54)</td></tr><tr><td>Loop F - M2-M3 loop<sup>(+)</sup></td><td>12±7(17)</td><td>0</td><td>0</td><td>7±4(17)</td></tr><tr><td>pre-M1 - M2-M3 loop<sup>(+)</sup></td><td>4±3(5)</td><td>0</td><td>0</td><td>2±2(5)</td></tr><tr><td colspan="5"><strong>f) n<sup>th</sup> to (n+1)<sup>th</sup> subunit communication at pH 7</strong></td></tr><tr><td>Cys loop</td><td>26±6(54)</td><td>34±12(24)</td><td>58±14(241)</td><td>46±11(319)</td></tr><tr><td>β<sub>1</sub>-β<sub>2</sub> loop</td><td>29±8(60)</td><td>13±10(9)</td><td>1.4±1.9(6)</td><td>11±4(75)</td></tr><tr><td>Pre-M1/M1</td><td>26±8(55)</td><td>51±17(36)</td><td>30±13(127)</td><td>31±12(218)</td></tr><tr><td>Loop F - M2-M3 loop<sup>(+)</sup></td><td>12±3(25)</td><td>1±4(1)</td><td>9±6(39)</td><td>9±5(65)</td></tr><tr><td>pre-M1 - M2-M3 loop<sup>(+)</sup></td><td>6±3(13)</td><td>0</td><td>1±1(5)</td><td>3±2(18)</td></tr><tr><td colspan="5"><strong>g) All communication at any pH</strong></td></tr><tr><td>Cys loop</td><td>45±4(470)</td><td>56±8(235)</td><td>68±10(914)</td><td>58±8(1619)</td></tr><tr><td>β<sub>1</sub>-β<sub>2</sub> loop</td><td>31±14(326)</td><td>11±5(44)</td><td>4±2(47)</td><td>15±7(417)</td></tr><tr><td>Pre-M1/M1</td><td>17±5(180)</td><td>33±11(140)</td><td>26±10(349)</td><td>24±8(669)</td></tr><tr><td>Loop F - M2-M3 loop<sup>(+)</sup></td><td>4±2(42)</td><td>0.2±1.0(1)</td><td>3±2(39)</td><td>3±2(82)</td></tr><tr><td>pre-M1 - M2-M3 loop<sup>(+)</sup></td><td>1.7±1.0(18)</td><td>0(0)</td><td>0.4±0.4(5)</td><td>0.8±0.5(23)</td></tr></tbody></table>
1)th subunit communication at pH 7, as well as the Cys loop-M4(+) pathway contributing 1±2% (3 occurrences) for nth to (n+1)th subunit communication at pH 7.

<table><caption>**Table 2.** State-dependent and overall correlation lengths of pathways (rare pathways excluded). Pathway families are shown along with their minimum and average (in parentheses) dimensionless total correlation distances as a function of pH and initial conformational state of the system. The minimum overall correlation distance of 88 is for the β₁-β₂ loop family (bold). See Table 1 for details. Uncertainties were computed as standard error of means using all available trajectories (if path only existed in a single trajectory, error is omitted). Not included are the same low-prevalence pathways omitted in Table 1. This includes same-subunit Loop F values of 434 (single value) at pH 4.6; 248 minimum (314±43 average) based on 5 occurrences at pH 7, and 457 (single value) for nth to (n-1)th subunit communication at pH 7, as well as Cys loop-M4(+) for nth to (n+1)th subunit communication at pH 7 with 277 minimum (362±75 average) based on 3 occurrences.</caption><thead><tr><th>Correlation length</th><th>O</th><th>LC</th><th>C</th><th>All states</th></tr><tr><th>Dominant pathways</th><th>Min (Ave)</th><th>Min (Ave)</th><th>Min (Ave)</th><th>Min (Ave)</th></tr></thead><tbody><tr><td colspan="5"><strong>a) Same subunit communication at pH 4.6</strong></td></tr><tr><td>Cys loop</td><td>161 (356±65)</td><td>239 (410±86)</td><td>170 (354±61)</td><td>161 (373±72)</td></tr><tr><td>β₁-β₂ loop</td><td>144 (313±70)</td><td>-</td><td>208 (260±52)</td><td>144 (287±50)</td></tr><tr><td>Pre-M1/M1</td><td>293 (438±83)</td><td>286 (449±64)</td><td>281 (395±119)</td><td>281 (427±92)</td></tr><tr><td colspan="5"><strong>b) Same subunit communication at pH 7</strong></td></tr><tr><td>Cys loop</td><td>152 (303±53)</td><td>162 (340±66)</td><td>170 (339±52)</td><td>152 (327±57)</td></tr><tr><td>β₁-β₂ loop</td><td>88 (302±73)</td><td>168 (350±138)</td><td>171 (321±60)</td><td>88 (324±97)</td></tr><tr><td>Pre-M1/M1</td><td>174 (369±55)</td><td>168 (323±73)</td><td>200 (357±60)</td><td>168 (350±63)</td></tr><tr><td colspan="5"><strong>c) n<sup>th</sup> to (n-1)<sup>th</sup> subunit communication at pH 4.6</strong></td></tr><tr><td>Cys loop</td><td>225 (396±62)</td><td>240 (458±86)</td><td>234 (391±91)</td><td>225 (415±81)</td></tr><tr><td>β₁-β₂ loop</td><td>234 (409±73)</td><td>-</td><td>247 (368±50)</td><td>234 (389±51)</td></tr><tr><td>Pre-M1/M1</td><td>259 (495±92)</td><td>352 (454±93)</td><td>292 (380±88)</td><td>259 (443±91)</td></tr><tr><td colspan="5"><strong>d) n<sup>th</sup> to (n-1)<sup>th</sup> subunit communication at pH 7</strong></td></tr><tr><td>Cys loop</td><td>161 (371±54)</td><td>161 (369±87)</td><td>200 (370±53)</td><td>161 (370±67)</td></tr><tr><td>β₁-β₂ loop</td><td>188 (389±72)</td><td>228 (397±86)</td><td>219 (391±62)</td><td>188 (392±74)</td></tr><tr><td>Pre-M1/M1</td><td>219 (427±84)</td><td>205 (295±39)</td><td>236 (404±48)</td><td>205 (375±60)</td></tr><tr><td colspan="5"><strong>e) n<sup>th</sup> to (n+1)<sup>th</sup> subunit communication at pH 4.6</strong></td></tr><tr><td>Cys loop</td><td>233 (400±42)</td><td>303 (474±77)</td><td>228 (410±67)</td><td>228 (428±64)</td></tr><tr><td>β₁-β₂ loop</td><td>231 (367±62)</td><td>351 (476±86)</td><td>274 (326±52)</td><td>231 (390±68)</td></tr><tr><td>Pre-M1/M1</td><td>257 (467±84)</td><td>393 (547±73)</td><td>351 (392±31)</td><td>257 (469±67)</td></tr><tr><td>Loop F - M2-M3 loop<sup>(+)</sup></td><td>280 (437±60)</td><td>-</td><td>-</td><td>280 (437±60)</td></tr><tr><td>pre-M1 - M2-M3 loop<sup>(+)</sup></td><td>324 (430±87)</td><td>-</td><td>-</td><td>324 (430±87)</td></tr><tr><td colspan="5"><strong>f) n<sup>th</sup> to (n+1)<sup>th</sup> subunit communication at pH 7</strong></td></tr><tr><td>Cys loop</td><td>275 (394±48)</td><td>199 (402±71)</td><td>219 (397)</td><td>199 (398±49)</td></tr><tr><td>β₁-β₂ loop</td><td>158 (365±60)</td><td>239 (416±140)</td><td>239 (397)</td><td>158 (393±88)</td></tr><tr><td>Pre-M1/M1</td><td>224 (396±48)</td><td>231 (361±75)</td><td>256 (422)</td><td>224 (393±51)</td></tr><tr><td>Loop F - M2-M3 loop<sup>(+)</sup></td><td>162 (328±73)</td><td>566 (566)</td><td>258 (389)</td><td>162 (428±42)</td></tr><tr><td>pre-M1 - M2-M3 loop<sup>(+)</sup></td><td>294 (404±64)</td><td>-</td><td>373 (411)</td><td>294 (408±64)</td></tr><tr><td colspan="5"><strong>g) All communication at any pH</strong></td></tr><tr><td>Cys loop</td><td>152 (370±55)</td><td>162 (409±79)</td><td>170 (377±60)</td><td>152 (385±65)</td></tr><tr><td>β₁-β₂ loop</td><td>88 (358±69)</td><td>168 (410±94)</td><td>171 (344±51)</td><td>88 (370±73)</td></tr><tr><td>Pre-M1/M1</td><td>188 (432±76)</td><td>168 (405±71)</td><td>200 (392±69)</td><td>168 (410±72)</td></tr><tr><td>Loop F - M2-M3 loop<sup>(+)</sup></td><td>162 (383±67)</td><td>566 (566)</td><td>258 (389)</td><td>162 (446±67)</td></tr><tr><td>pre-M1 - M2-M3 loop<sup>(+)</sup></td><td>294 (417±76)</td><td>-</td><td>373 (411)</td><td>248 (414±76)</td></tr></tbody></table>

The β₁-β₂-loop family provides the strongest connections between the ECD and the TMD based on minimal correlation length (Table S5, column 2 and rightmost column, and Fig.10, left-most point). It achieves a minimal correlation length of 88 for same-subunit E35-F238 communication (for O state at pH 7). It can be seen in Table S5 that for all termini in the ECD except E75 and E177, the shortest minimal path length occurs through the β₁-β₂ loop. For E75 and E177 this is replaced by the pre-M1/M1 pathway (described below), likely because these
two termini reside on or near loop F and loop C, which are connected to pre-M1 via $β_{10}$ and $β_9$ strands on the front-facing sheet of the β sandwich (Fig.1), whereas the other residues must have more direct connections with the rear-facing sheet connected to the $β_1-β_2$ loop.

While the Cys-loop family is overall the most prevalent, it exhibits the second shortest minimal length, being nearly twice as long as that seen for the $β_1-β_2$-loop family (Table S5 columns 2 and 8, and Fig.10, two left-most points), i.e. minimal correlation length of 152 for Cys-loop same-subunit E35-F238 communication (which occurred in the O state at pH 7; see Table 2), compared to the $β_1-β_2$-loop value of 88. Based on average lengths (for terminal E35 only, or for all residues; Table S6, columns 2 and 8), the measures are closer but still favoring the $β_1-β_2$-loop paths over the Cys loop (see also solid line in Fig.10). This same general preference for $β_1-β_2$-loop over Cys-loop pathways is seen when these results are broken down according to all 7 different starting points in Tables S4, S5 and S6. The Cys-loop pathway is clearly favored for starting residue E35, as well as to a lesser extent E26 and E82, obtaining lower minimal correlation lengths (Table S4), because of their closer proximity to that loop. Relative to other pathways, however, it is ranked second for E35 and E177, based on minimal length (Table S5).

<figure><img src="image_15.png" /><figcaption>**Figure 10. Correlation lengths of communication.** Average correlation length based on all simulations and all ECD termini, sorted from lowest to highest, is plotted as circles with solid lines, with minimal values plotted as crosses connected by dashed lines (rare pathways included). See Tables S6 and S6 for full data and errors.</figcaption></figure>

The pre-M1/M1 family provides a slightly longer minimal correlation length than the Cys-loop family, being 168 (occurring for same-subunit communication in the LC state at pH 7; Table S5). According to Table S5 (columns 2 and 8), this family does not come close to the lowest minimal length. However, analysis if each terminal in Table S5 shows it achieves the shortest lengths for termini E177, E75, communicating directly or via loop F to pre-M1. Based on average correlation lengths, this family is the third lowest (Table S6; Fig.10), albeit within the errors of the value seen for the Cys loop family.

The pathway family, loop F-M2-M3 loop$^{(+)}$ typically has longer average correlation lengths because they involve inter-subunit ($n^{th}$ to $(n+1)^{th}$) communication with connection between adjacent subunits, typically causing longer correlation distances compared to same-subunit pathways. Yet, loop F-M2-M3 loop$^{(+)}$ still ranks 4$^{th}$ or 5$^{th}$ based on minimal length in Table
S5 (and Fig.10), and for termini E26 and E82 is even ranked 2^nd^ and 3^rd^, respectively, because of the proximity or connection to loop F. For pre-M1 – M2-M3 loop(+) (that involves loop F) we observe much longer average and minimal lengths in Tables S5 and S6, though lowered somewhat with E26 and E82 termini), suggesting a smaller role is played by this family. It is because of the shorter lengths for the E26-F238 terminal pair for loop F-type inter-subunit communication that we chose to highlight this choice in Figs.8 and 9.

The above measures suggest the dominant communication between ECD and TMD is achieved
by the β₁-β₂ loop, the Cys loop and pre-M1/M1, but with relative contributions that will depend
on the conformational state and pH, as we now detail.

State- and pH-dependence for the dominant pathways

The mechanism by which structural change in the ECD is transferred to the TMD depends on
the functional state, owing to the conformational changes (in particular at the ECD-TMD gating
interface), as well as the pH, owing to the effect of protonation states on interactions within
and between ECD subunits. How the percentage of pathways that belong to a specific family
depends on the conformational state and pH is summarized in Table 1, while the effect of state
and pH on correlation length is summarized in Table 2.

Overall, correlation lengths of pathways reach lower numbers (i.e. more correlated) at pH 7. This might be associated with increased protein conformational dynamics observed in pH 7 simulations (Fig.3), consistent with the structural diversity reported in that state (6, 15), which increases the extent of movements in the equation for pairwise correlations (Cᵢⱼ). It may be also due to the substantial increase in ECD net charge at high pH (by 35e), causing stronger interactions. Moreover, the lowest correlation distance values are observed in simulations that originated in the O state, likely because of the relationship between the ECD and TMD in that conformation; in particular, the maintenance of a tight lower β sandwich with formed D32-R192 salt bridge, and the positioning of the M2-M3 loop adjacent to the ECD. Below we detail the state and pH dependence of each of the main families.

*Sustained communication via the Cys-loop family:* These pathways, shown in Figs.4a and 5a,b, generally communicate via Cys loop interaction with the M3 helix, and are dominant (or equally dominant, within errors) for all intra- and inter-subunit communication pathways, with consistently high prevalence (Table 1). Overall, the Cys loop plays a prominent role in ECD-TMD communication, regardless of functional state and pH, consistent with its defining role for the Cys-loop receptor family (72, 73). We have, however, recorded somewhat higher Cys loop involvement when in the C state, perhaps due to a closer alignment of the Cys loop and M3, suggesting that the Cys-loop family may play an even greater role in channel opening. The Cys-loop family also maintains low minimum and average correlation lengths, regardless of conformational state or pH (although is considerably less correlated than the *β*₁-*β*₂-loop family, described below). This suggests that the Cys loop plays an important role in channel activity, contributing substantially to conformational changes between all states at all pH.

*Strongly state-dependent β₁-β₂-loop family:* This family (Fig.4b and Fig.6a,b) is commonly the second most prevalent family within each set, with frequency as high as 39±4% for intra-subunit communication in simulations that originated in the O state at low pH (Table 1a), where it attains the shortest correlation distance of all simulations (88 for E35-F238 communication; Tables 1 and S4). The ability to have such strong correlation can be attributed to the direct β₁-β₂ loop interaction with the M2 helix (Fig.4b), rather than indirect interaction via another
feature (e.g. Cys loop – M3), but this is only possible if the conformational state of the protein
allows it. We observe that, in contrast, same-subunit communication via the β₁-β₂ loop is
substantially diminished in LC and C state simulations; even being eliminated for LC
simulations at pH 4.6.

For inter-subunit communication, the contributions from the β₁-β₂ loop remain strong in the O state, but it is a mixed bag in the LC and C states (Table 1). In the LC state, communication is strong for nᵗʰ to (n-1)ᵗʰ subunit communication at pH 7, but is otherwise weak and even eliminated for nᵗʰ to (n-1)ᵗʰ subunit communication at pH 4.6. In the C state, communication via this loop is strong for nᵗʰ to (n-1)ᵗʰ communication at pH 4.6, but is otherwise weak. This state-dependence of inter-subunit communication is likely due to changes in alignment between K33 (β₁-β₂ loop) and T244, N245, L246 and K248 (M2-M3 loop).

Thus, whereas the Cys loop family plays a role regardless of conformational state, there is clear
competition for communication via the β₁-β₂-loop and Cys-loop families in the O state. How
do we compare their contributions? The shortest correlation length of 88 belongs to the β₁-β₂-
loop pathway family, for an intra-subunit path that connects E35 and F238 during simulation
of the O state at pH 7. Mean correlation lengths (average over all 7 termini and 5 subunits) for
β₁-β₂-loop and Cys-loop families (Table S4) are, however, similar for the O state (same to
within errors); noting the large standard deviations due to the inclusion of disparate paths with
wide-spanning terminal pairs. We thus conclude that Cys loop and β₁-β₂ loop communication
are both important in the O state, but that deprotonation at site E35 when in the O state is likely
to give the strongest gating signal to the TMD pore via the β₁-β₂ loop.

*pre-M1/M1 family is important when other communication is diminished:* The pre-M1/M1 family (Fig.7) exists as a significant contributor to ECD-TMD communication, regardless of conformational state or pH. This maintenance of communication via pre-M1/M1 can be attributed to the fact that this is a covalently linked pathway between the ECD and TMD that cannot be severed by a conformational change. These pathways have similar prevalence to the β₁-β₂-loop family overall but may compete with (or even exceed) that family when in the LC or C state, where interaction with the β₁-β₂ loop is diminished. Table 1g shows that overall (including all modes of communication at any pH), pre-M1/M1 prevalence jumps up from 17±5% in the O state to 33±11% and 26±10% in the LC and C states, concomitant with a decrease in β₁-β₂ loop involvement from 31±14% down to 11±5% and 4±2%, respectively.

The pre-M1/M1 family therefore plays a relatively larger role within the LC and C states when
the β₁-β₂-loop family of pathways has been interrupted. Surprisingly, pre-M1/M1
communication is even the dominant mode of transfer at pH 7 for intra-subunit communication
in the LC state (Table 1b), suggesting interruption of not only β₁-β₂ loop but also Cys loop
interaction with the TMD in that case. For inter-subunit communication, with the exception of
nᵗʰ to (n-1)ᵗʰ communication (where the Cys loop dominates), pre-M1/M1 communication also
plays an important role, most strikingly for nᵗʰ to (n+1)ᵗʰ subunit communication at high pH in
the LC state. In terms of correlation length, the pre-M1/M1 family ranks only sixth by minimal
correlation length of 168 (Table S5, rightmost column) and fourth for mean correlation length
(although often within the errors; column 4). However, these ranks vary depending on the
starting residue (Table S5/S6), where it can be seen that for some termini (notably E75 and
E177), the pre-M1/M1 family actually exhibits the strongest ECD-TMD communication.
*Loop F contributes via inter-subunit communication predominantly in the open state:* Inter-subunit $n^{th}$ to (n+1)th pathways, Loop F – M2-M3 loop$^{(+)}$ and pre-M1 – M2-M3 loop$^{(+)}$ are present to varying degrees depending on state and pH. At pH 4.6, they together comprise 18±6% of $n^{th}$ to (n+1)th communication for O state simulations and are completely absent for LC and C states (Table 1e). At pH 7 (Table 1f) there remains strong contributions for the O state, near elimination for LC but we see a substantial 10±7% contribution for the C state. The loop F – M2-M3 loop$^{(+)}$ family itself contributes 12±3% for O-state simulations, regardless of pH (Table 1e,f) and 9±6% in C-state simulations at pH 7 (Table 1f), but this is reduced dramatically to just 1±4% in LC simulations. This demonstrates state- and pH-dependence, and in particular loss of communication for the LC form, potentially due to misalignment of ECD and TMD that positions the loop F differently relative to the adjacent subunit. Given elongated inter-subunit pathways, elevated correlation lengths might be expected. However, we note that the Loop F – M2-M3-loop$^{(+)}$ family achieves a minimal correlation length of just 162 (O state pH 7), comparable to the main intra-subunit paths in Table S5, and it is even the second shortest path observed for the E26 terminal, because of its proximity. This strong communication in the O state at high pH, suggests that this inter-subunit pathway may be involved in the closing of the channel, alongside the main three families.

DISCUSSION AND CONCLUSION

We have studied extensive unbiased all-atom MD simulations at two pH and three starting conformational states, with a combined simulation time of ~41 µs, to elucidate the communication networks responsible for allosteric gating of GLIC, a prototypical pLGIC. To survey the sampling of conformational changes, we selected a set of collective variables that account for ECD structural changes associated with ligand binding, expansion of the lower β sandwich related to changes at the ECD-TMD gating interface, and TMD M2 helix movements, linked to pore opening and closing. The variability in protein structure observed within this library of simulations was sufficient to explore correlated movements across the protein and to identify pH- and state-dependent networks that shed light on allosteric gating. Despite the set of simulations being somewhat heterogeneous, with different numbers, lengths and force fields, with some potential to bias the exploration of certain conformational changes, they represent a library of MD simulations predominantly in their starting states with partial state interconversions, sufficient to examine the prevalence and strength of communication for different possible modes of inter-domain communication in state and pH-dependent ways.

Using dynamic network analysis, we identified five dominant signal pathway families that facilitate ~99% of all information transfer between the TMD and ECD domains via intra- and inter-subunit communication. While we broke down the pathways according to the different possible protonation sites in the ECD, it was evident that we have a consensus pathway for each family, with little branching away from a common path connecting ECD sites and the TMD M2 residue F238, representing a key constriction point in the pore. Each of the 7 protonation sites could be relevant to GLIC gating, although more distant sites generally have longer correlation lengths than sites such as E35 near the gating interface, owing to their geometrical distance. The strong correlation seen for E35 to the pore is consistent with the experimental finding that mutations of this residue strongly affect gating (25), which is why it was highlighted in this study. However, the general preservation of communication pathways from ECD to TMD irrespective of the protonation site suggests that allosteric communication seen within the GLIC channel may be conserved among the pLGIC family.
The Cys-loop pathway family, which crosses domains via Cys loop interaction with M2 or M3 helices, or the M2-M3 loop, was shown to be present across all the simulations, independent of pH or conformational state of origin. The fact that this pathway family is well conserved across all simulations, is one of most prevalent and has some of the shortest pathways across the library, suggests that it plays an important role in the function of the protein, and possibly for other pLGICs (74). This may potentially explain its conservation across the Cys-loop superfamily to preserve a common allosteric mechanism. The lack of variability results from sustained interactions between the Cys loop and the TMD, despite rearrangements in M2-M3 and Cys loop structural features, suggesting it is likely to play that role in all state changes within the channel's activity cycle. Fig. 11 summarizes the results for state- and pH-dependent pathway prevalence (for same-subunit communication only), where we can see an abundance of Cys loop involvement, independent of functional state or pH, as is illustrated with a thick red arrow in each state (right panels). This is also evident for inter-subunit communication (Fig. S7). While clearly showing persistent contributions of the Cys loop, the figure does however suggest an overall trend where the Cys loop contribution systematically increases from the O to the LC and C states, likely owing to better alignment of the Cys loop and the M2-M3 loop (which moves upon gating) in the C state.

Important residues along the Cys-loop pathway have been summarized in Table 3 (first row). Any residue that appears in the dominant path (thickest lines) of Fig. 5 is included, with residues in bold being ones identified as providing key interactions. We have identified residues on the Cys loop (L114 and F116 and their neighbors) as interacting with the $β_1-β_2$ loop (E35), crossing to the M3 helix (T253; via interaction of the F116 carbonyl with the T253 side chain hydroxyl group), and then to the M2 helix at I259, which interacts with M2's H235 (involving interaction with its imidazole ring), with possible involvement of M2-M3's P247 and L246. Experimentally, several of these residues have been shown to be important for function, with M2-M3's P247 and L246 being essential for gating in all pLGICs (5), and the Cys loop's F116 being the binding partner for L246 in the channel's O state (with L246 binding to F238 in the C state) (5, 24). The simulations do, however, also implicate the side chain of T253 as an important contributor. Note also that residue H235 also appears in the main pathways of other families, explaining why it is an important residue functionally, with its mutation having been shown to promote channel closure (58), and protonation of this residue leads to corruption of TMD structure (24).

The $β_1-β_2$ loop is known to be essential to gating (e.g. (17)) and has been shown here to provide the strongest of all communication pathways (see Fig. 10), with particular importance in the O state. The $β_1-β_2$ loop pathway family, defined by communication with the M2 helix or M2-M3 loop, exhibits prevalence and correlation lengths that are strongly dependent on pH and conformational state. This pathway provided the shortest (most correlated) of all pathways observed (Fig. 10) and was the second most represented in simulations that started in the O state but was essentially eliminated in other states. This is evident in Fig. 11 (intra-subunit case) with diminished prevalence or even absence in the LC and C states; indicated with thin dashed green arrow in the right panels for the $β_1-β_2$ loop path. This significant role for the $β_1-β_2$ loop in the O state is represented by a thick green arrow (right panel of Fig. 11a) that competes with the Cys-loop family in prevalence, but with enhanced correlation (Fig. 10), making it the dominant mode of ECD-TMD information transfer in the O state.
<figure><img src="image_16.png" /><figcaption>**Figure 11.** pH-dependence of communication. Summary of pathway prevalence in each of the O (a), LC (b) and C (c) states for intra-subunit (n^th^ to n^th^ subunit) communication only (see Fig.S7 for inter-subunit communication). For each state prevalence is broken down into pH 4.6 (left) and pH 7 (right). Right panels are illustrations of the ECD-TMD communication within each state, with arrow thickness approximately representing prevalence (not accounting for pH dependence, for clarity).</figcaption></figure>

Communication via the β₁-β₂ loop does, however, depend on the ability of the β₁-β₂ loop to form an interaction with the top of the M2 helix or M2-M3 loop. The O-state simulations (where the β₁-β₂ loop pathway is prominent) have a strong preference for the D32-R192 salt bridge to be formed (Fig.2). Loss of prevalence for this pathway was observed in the LC and C states (where D32-R192 tends to be broken), especially for intra-subunit communication (although, for inter-subunit communication, the β₁-β₂ loop pathway can still be observed within the C and LC states). These observations suggest that communication via β₁-β₂-loop pathways requires a specific arrangement of the ECD and TMD, affecting interactions between the β₁-β₂ loop and M2-M3 loop. Additionally, significant changes in prevalence of the β₁-β₂-loop family with pH and conformational state suggest disruption in communication due to breaking of the D32-R192 salt bridge. This communication, involving a critical part of the gating interface that undergoes a discrete change during channel closure, emphasizes the role of the D32-R192 salt bridge.
<table><caption>**Table 3. Important residues for each of the pathway families.** Residues seen to be involved in interactions along the most strongly correlated pathways are listed. Residues in bold have been identified as participating in key interactions along these paths. Residues have been grouped according to the structural features in which they belong, with their residue ranges specified. Note that pre-M1 is defined as residues ~192-194 here, but residue 192 may be considered to lie on strand β<sub>10</sub>.</caption><thead><tr><th>Residues involved<br>most correlated<br>pathways</th><th>β<sub>1</sub>-β<sub>2</sub><br>loop<br>(31-35)</th><th>Cys<br>loop<br>(112-<br>122)</th><th>loop F<br>(143-<br>162)</th><th>Pre-M1<br>(~192-<br>194)</th><th>M1<br>(195-<br>217)</th><th>M2<br>(222-<br>245)</th><th>M2-M3<br>loop<br>(246-<br>253)</th><th>M3<br>(254-<br>281)</th></tr></thead><tbody><tr><td rowspan="2">Cys loop family</td><td>D32</td><td>L114</td><td></td><td></td><td></td><td>H235</td><td>L246</td><td>G256</td></tr><tr><td>E35</td><td>F116</td><td></td><td></td><td></td><td>F238<br>V242</td><td>P247<br>T253</td><td>A257<br>I259</td></tr><tr><td rowspan="4">β<sub>1</sub>-β<sub>2</sub> loop family</td><td>D32</td><td></td><td></td><td></td><td></td><td>F238<br>I240</td><td>L246</td><td></td></tr><tr><td>K33</td><td></td><td></td><td></td><td></td><td>V242</td><td>P247</td><td></td></tr><tr><td>E35</td><td></td><td></td><td></td><td></td><td>T244<br>N245</td><td>Y251</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="3">Pre-M1/M1 family</td><td>L30</td><td>L114</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>D32</td><td>F116</td><td>W160</td><td>R192</td><td>Y197</td><td></td><td></td><td></td></tr><tr><td>E35</td><td>Y119</td><td></td><td>Y194</td><td>I201</td><td>F238</td><td></td><td></td></tr><tr><td rowspan="4">Loop F - M2-M3 loop<sup>(+)</sup><br>family</td><td>Y28</td><td></td><td>F156<br>L157</td><td></td><td></td><td>H235</td><td>L246</td><td></td></tr><tr><td>E26</td><td></td><td>T158<br>G159</td><td></td><td>Q193</td><td>F238<br>V242</td><td>K248<br>Y251</td><td>A257<br>I259</td></tr><tr><td></td><td></td><td>W160</td><td></td><td></td><td></td><td>T253</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="4">pre-M1 - M2-M3<br>loop<sup>(+)</sup> family</td><td>E26</td><td></td><td>G159</td><td></td><td></td><td>H235</td><td>L246</td><td></td></tr><tr><td>Y28</td><td></td><td>W160</td><td></td><td>Q193</td><td>F238<br>V242</td><td>K248<br>P250</td><td>A257<br>F260</td></tr><tr><td>L30</td><td></td><td></td><td></td><td></td><td></td><td>Y251<br>M252</td><td>I262</td></tr></tbody></table>

Key interactions within the β₁-β₂-loop family (Table 3, second row) include residues K33 and E35 on the β₁-β₂ loop, which interact with M2 and M2-M3 loop residues V242, L246, T244 and N245 within the same subunit, with particular involvement of the K33 side chain ammonium group. This β₁-β₂-loop communication is almost eliminated when in the LC and C states (Fig.11). The breakage of same-subunit communication when leaving the O state can be understood from the splaying of the lower β sandwich causing movement of D32 and K33, along with movement of the M2-M3 loop, such that the main pathways of communication from K33 to L246, T244 and N245 or from D32 to P247 (Fig.6b) are lost. Some level of communication still exists, however, via inter-subunit communication (Fig.S7, left and right), although these modes of communication are nowhere near as well correlated (Fig.10), and depend on the pH for the C state. In this case, communication relies on E35 connection to Y251 on M2.

Mutation of D32 is known to cause loss of function (17). These results also suggest mutation of K33 or P247 would affect gating. In the C state, communication also connects E35 on the β₁-β₂ loop to Y251 on M2, involving the carboxylate side chain of E35 and the tyrosine side chain hydroxyl. It has been experimentally shown in mutagenesis studies (3), that double mutants that combine, interchangeably, mutation of K33 with those of T244, N245 and L246 (3), as well as single P247 (17) and Y251 (18) mutants, cause loss of function. These residues have been implicated in β₁-β₂ loop pathways here, suggesting important roles.

One may envisage channel closure as involving displacements in the ECD, caused by changes in ligand binding (or deprotonation), originating at or propagating to the β₁-β₂ loop structural element at the gating interface. Although communication may continue to the pore itself, along the direct and strongly-correlated pathway described, it may also lead to D32-R192 salt bridge
breakage, which has been suggested to act as a switch, communicating to the M2 bundle due to changed interactions between the ECD's $β_1-β_2$ and TMD's M2-M3 loops, driving constriction and dewetting of the pore through a domino-like collapse of the five M2 helices (24). We note, however, the existence of additional inter-subunit communication modes, despite reduced prevalence and correlation strength, may suggest correlation of TMD subunit gating motions, with M2 collapse events not occurring in a purely sequential (domino) nature.

The pre-M1/M1 pathway family involves TMD-ECD communication between pre-M1 (base of the $β_{10}$ strand) in the ECD and the M1 helix in the TMD via covalent bonding (as opposed to non-bonded interactions across domains) and remains in action, regardless of pH and the functional state (Fig.11). This pathway family has elevated prevalence in simulations at high pH, with the shortest correlation distance found for the LC state. This is, however, mainly because other communication has been disfavored due to changes at the gating interface arising from ECD-TMD twist and D32-R192 breakage. Overall, the pre-M1/M1 pathways have longer minimal and average correlation lengths than the preceding pathways. However, for particular ECD termini (notably E75, E177 and E26), it may exhibit shorter correlation lengths due to better association with pre-M1 than other gating interface structural features.

The pre-M1/M1 pathway family involves communication from the $β_1-β_2$ loop (E35) to Cys loop (L114), then following Cys loop (F116 and Y119) and communicating to the pre-M1/M1 helix (R192, Y197, I201); see Table 3 (third row). Alternatively, the path involves direct $β_1-β_2$ loop (D32) communication via the salt bridge with pre-M1 (R192), after which pre-M1 is followed across the interface, finally connecting the M1 helix (I201) with the M2 helix (F238). Communication in this family involves E35-L114 interaction (as seen in the Cys-loop family above), along with the D32($β_1-β_2$ loop)-R192(pre-M1) salt bridge. As mentioned previously, mutation of D32 leads to loss of function (17), and R192 is part of a triplet of residues that are critical for pLGIC gating (17, 75). Mutation of Q193 in pre-M1 also leads to partial loss of function (25). Less prominent communication involving another $β_1-β_2$ loop residue (L30) and residue next to loop F (W160 in $β_9$) is D32-L30-W160-R192. The pathway between M1 and M2 helices is then facilitated via interaction between two hydrophobic residues I201 and F238, which would be expected to be susceptible to experimental mutation, as previously suggested by the double I201/E243 mutation that causes complete loss of function (25). Interestingly, the involvement of Y197 (seen in ~25% of all pathways), as well as I201, coincides with a known site of anesthetic binding (76).

There are two additional inter-subunit-only pathway families involving loop F. These pathways facilitate information transfer via interactions between loop F and the M2-M3 loop of the $(n+1)^{th}$ subunit (named loop F – M2-M3 loop$^{(+)}$ and pre-M1-M2 – M3 loop$^{(+)}$). Combined, these pathways have significant prevalence for $n^{th}$ to $(n+1)^{th}$ subunit communication (Fig.S7), despite having longer correlation lengths. The loop F – M2-M3 loop$^{(+)}$ pathway family dominates this communication, but displays significant pH and conformational state dependence, suggesting that this pathway may play a role in the transition between O to C states.

The inter-subunit loop F families feature residues (Table 3, bottom two rows) on or adjacent to loop F, such as, G159 and W160 and K248$^{(+)}$ (M2-M3 loop of $(n+1)^{th}$ subunit). Alternatively, pathways may involve communication between pre-M1 and the M2-M3 loop facilitated by Q193 and lysine K248$^{(+)}$ or Y251 on the adjacent subunit. It has been shown experimentally (28) that large loop F movement occurs during activation of the GLIC channel. Mutagenesis studies have identified residues Q193 (25), E243 (3, 25), P247 (17), T249 (18), Y251 and K248
(18) as key players involved in ECD-TMD interaction, with mutation leading to loss of function. In particular, we have observed involvement of Y251 hydroxyl and Q193 carboxamide, consistent with their mutations leading to partial and complete loss of function, respectively.

The protein segments and residues involved in these five major pathway families show overlap with existing models for ECD-TMD communication in pLGICs. Mutagenesis has been used to examine the effects on the equilibrium of coexisting functional states of the GLIC channel. By examining mutations that affect the equilibrium of O and LC forms at low pH, Hu et al (25) were able to infer residues that may promote TMD pore closure, from which they proposed interaction networks, involving the Cys loop, β₁-β₂ loop, pre-M1, loop F and the M2-M3 loop, which may enable a path from protonation site E35 in the ECD down to H235 in the TMD. This work identified networks of interactions that control the interconversion of O and C pore states, providing valuable residue-based data to validate any proposed communication pathways. We note, however, that Hu et al (25) suggested a different loop F network to what we describe here. They implicated E35 transmitting to nearby loop F residues, involving a Y197-K248-E243-N239-H235 network. They suggested rearrangement of nearby β₁-β₂ loop and pre-M1's R192, tightening the salt bridge triad R192-D122-D32, as well as influencing another triad involving Y197 (pre-M1), Y119 (Cys loop) and the M2-M3 loop (K248), before propagating from the M2-M3 loop to the M2 helix's H235 residue (25). Regardless, both studies suggest that inter-subunit communication via loop F may play an important role in gating.

Mutagenesis has also been used to infer the sequence of events leading to nicotinic acetylcholine receptor (nAChR) channel opening (77, 78). Auerbach and co-workers proposed a “conformational wave” of communication based on φ analysis (35, 79, 80). The pathways involved the structural features β₁-β₂ loop and pre-M1, in common with our findings. Computationally, Tang and co-workers (81) used a Markovian transition model based on a coarse-grained representation of GLIC to investigate how a perturbation (mutation at a ligand binding/protonation site) was transmitted through a protein network over time. The authors identified multiple networks including paths via pre-M1 and the β₁-β₂ loop, and subsequent coupling to M2 helices.

Overall, our analysis includes many of the same features thought previously to control gating but placed within the context of five dominant communication pathway families. The Cys-loop family of pathways is well preserved between states and corresponds to a feature that is conserved between channels in the family. The β₁-β₂ loop family is important for state-dependence owing to the binary-switch nature of that feature, while the pre-M1 family appears to exist as a form of “backup pathway”, when others are diminished due to the conformational state affecting ECD-TMD alignment. This suggestion of the existence of multiple redundant pathways is consistent with the findings of mutagenesis that suggest conservation of channel gating occurs regardless of the sequence at the gating interface, instead relying on the complementary shapes of the ECD and TMD at that interface (30).

In summary, we set out to understand signal propagation in a member of the pLGIC family, the pH-activated GLIC channel. We discovered conformational state- and pH-sensitive means for communication between the channel's ECD and TMD, governing allosteric structural changes. We studied correlated movements across the protein and identified five main pathway families that are important for TMD-ECD communication related to channel gating. We showed that β₁-β₂ loop and loop F pathway families exhibit stark dependence on the GLIC
functional state, in contrast to the more constant Cys-loop and pre-M1 pathway families,
suggesting that the protein may communicate differently between the proton-sensing ECD and
the ion-conducting TMD during its transitions between the O, C and intermediate (LC) states
of its activity cycle. Identification of these state- and ligand-dependent communication
pathways is an important step in understanding channel activity, as well as the mechanisms of
pLGIC dysfunction and pharmacological regulation. Interruption in identified signaling
pathways may lead to a partial or complete loss of function associated with a range of inherited
or acquired disorders and may play a prominent and yet unidentified role in the actions of
neuromodulatory drugs and general anesthetics, worthy of further investigation.

SUPPORTING INFORMATION

The supporting document includes:

- Descriptions of collective variable time series and conformational sampling across the library of simulations.

- Seven supporting figures showing: collective variable timeseries and their projections onto free energy surfaces; histograms of state-and pH-dependent communication.

- Six supporting tables: full library of simulations; protonation states used; prevalence, minimal and average path lengths as a function of ECD terminal residue; sorted path lengths as a function of ECD terminal residue.

ACKNOWLEDGEMENTS

The authors thank Prof. Marc Delarue for his feedback on the manuscript. We acknowledge support from Erik Lindahl who provided computational resources for some GROMACS simulations performed by S.M.. We are grateful for support from the Australian Research Council (DP210102405 and DP2201035501; T.W.A.), National Health and Medical Research Council (APP1104259 & APP1141974; T.W.A.), National Computational Initiative (dd7; T.W.A.), LIEF HPC-GPGPU Facility (LE170100200; T.W.A.), Anton supercomputer / Pittsburgh Supercomputing Center (through NIH Grant R01GM116961), and the Medical Advances Without Animals Trust. We thank the National Institutes of Health (NHLBI grant R01HL174001; I.V.) and the French National Agency for Research for funding (Grant ANR-2010-BLAN-1534, LABEX DYNAMO ANR- LABX-011, EQUIPEX CACSICE ANR-11- EQPX-0008; M.B.). Some molecular simulations were performed using HPC computing resources from GENCI-/TGCC/ CINES/IDRIS (Grant 2011-072292 to MD). M.B. thanks Sesame Ile-de-France.

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