A sodium-dependent communication pathway across class A G-protein coupled receptors

G-protein-coupled receptors (GPCRs) are membrane proteins that transmit signals across the cell membrane by activating intracellular effector proteins in response to extracellular ligand interaction. A large majority of GPCRs are characterized by an evolutionarily conserved activation mechanism, involving the reorientation of helices and residue side chains, rearrangement of an internal hydrogen bonding network, and the expulsion of a sodium ion from an ionizable binding site in the transmembrane region. However, how sodium, internal water, and protein residues interplay to determine the overall receptor state remains elusive. Here, we employed information theory to trace signal transmission pathways through the receptors and identify their concerted response to sodium binding and protonation. Applying our methodology, ‘State Specific Information’, to all-atom molecular dynamics simulations of pharmaceutically important GPCRs, we discovered a conserved communication pathway that enabled the exchange of information between the sodium binding site and the distal G-protein binding region, connecting the most highly conserved ionizable residues in the receptors. Reorientation of internal water molecules was essential for the coupling of conformational state changes of protein residues along this pathway, which ultimately reconfigured the conformation of the G-protein binding site. The presence of sodium disconnected this pathway. By inhibiting protonation, sodium was found to serve as a master switch that determined the molecular state of GPCRs during the receptors’ transition to activation.

G-protein-coupled receptors (GPCRs) are membrane proteins that transmit signals across the cell membrane by activating intracellular effector proteins in response to extracellular ligand interaction. A large majority of GPCRs are characterized by an evolutionarily conserved activation mechanism, involving the reorientation of helices and residue side chains, rearrangement of an internal hydrogen bonding network, and the expulsion of a sodium ion from an ionizable binding site in the transmembrane region. However, how sodium, internal water, and protein residues interplay to determine the overall receptor state remains elusive. Here, we employed information theory to trace signal transmission pathways through the receptors and identify their concerted response to sodium binding and protonation. Applying our methodology, 'State Specific Information', to all-atom molecular dynamics simulations of pharmaceutically important GPCRs, we discovered a conserved communication pathway that enabled the exchange of information between the sodium binding site and the distal G-protein binding region, connecting the most highly conserved ionizable residues in the receptors. Reorientation of internal water molecules was essential for the coupling of conformational state changes of protein residues along this pathway, which ultimately reconfigured the conformation of the G-protein binding site. The presence of sodium disconnected this pathway. By inhibiting protonation, sodium was found to serve as a master switch that determined the molecular state of GPCRs during the receptors' transition to activation.
Correspondence: u.zachariae@dundee.ac.uk Introduction G-protein coupled receptors (GPCRs) form the largest superfamily of cell surface receptors with over 800 members that control a broad range of physiological processes. GPCRs span the plasma membrane of the cell from the extracellular to the intracellular face and act as signal transducers that enable transmembrane communication between the outside and inside of the cell. Ligand interaction on the extracellular domain induces conformational changes that expose binding sites on the intracellular face, initiating intracellular signalling by binding various effector proteins including heterotrimeric G-proteins and β-arrestins, each of which cause different physiological changes (1). As such, GPCRs form the main target for drug therapies, with over 30% of US food and drug administration (FDA) approved drugs targeting about 108 different GPCRs (2). Class A receptors comprise the vast majority of GPCRs with over 700 members. High-resolution crystal structures of inactive class A GPCRs resolve a sodium ion (Na + ) bound to a highly conserved, ionizable residue central to the transmem-brane (TM) domain (residue Asp 2.50 -Ballesteros-Weinstein numbering system). However, this ion is not present in active state crystal structures, implicating the ion in GPCR activation (3)(4)(5)(6)(7)(8). Computational studies show that the absence of sodium triggers protonation of Asp 2. 50 , and protons and ionizable networks are thought to be involved in GPCR signaling (4,(9)(10)(11)(12). In addition, the presence of a conserved network of internal water molecules connecting polar residues, including Asp 2. 50 , likely plays an important role in GPCR signal transduction (13). Through molecular dynamics simulations of a range of class A GPCRs, Venkatakrishnan et al. reveal the presence of well-defined water pockets that are conserved across both active and inactive states and further, state-dependent water sites (14). Upon activation, a significant re-positioning of the TM water-network seems to be coupled to the collapse of the (Na + ) binding pocket, although the functional significance of these waters is unclear (14)(15)(16). Various studies correlate GPCR activation with transitions between distinct rotameric conformations of evolutionarily conserved residues, termed microswitches. It is believed that these rotamer transitions underpin the large scale conformational changes that govern activation (1, 15,[17][18][19][20][21][22][23][24]. Many microswitches form distinct motifs, such as the CWxP motif at the ligand binding site, which is known to link directly to the sodium ion binding pocket (8). The conformation of the P-I-F motif is also strongly coupled to ligand binding (24). The NPxxY 7.53 motif is located proximal to the ion binding site and includes Tyr 7.53 , which opens and closes a transmembrane water channel according to simulation studies (10,16). In addition, the ionizable DRY motif at the intracellular face plays a key role in G-protein binding, and forms ionic locks that maintain the inactive receptor state (1, 21) (Fig. 1). These observations suggest that the ion binding site, water mediated interactions, and conserved residues are critical for G-protein signalling. However so far, the functional interaction of these components remains unknown (8,14,25). GPCR signal transduction is a process whereby information is sent, encoded, transmitted and received, in parallel with the tenets of an information system (26). Therefore, Na + , internal water, and microswitches can be seen to act as essential components of an information system. To resolve their role in enabling receptor movements leading to activation, we developed a methodology termed "State Specific Information" (SSI), which combines Shannon's mutual information (26,27) and McGill's interaction information (also called co-information) (28)(29)(30)(31). SSI quantifies how much information, specific to a certain residue or cofactor state, is shared between coupled transitions in these networks. Con- trasting correlation approaches that calculate mutual information using residue or atom covariance (4,30,(32)(33)(34)(35), SSI is closely aligned with the concept of microswitches by requiring residues to have at least two conformational states to exchange any information. Thereby, we extracted information from large-scale, persistent changes between interlinked residue states that can be traced back to a specific cause, such as the binding of Na + . In the case of water molecules, transferred information was calculated based on pocket occupancy as well as water orientation. We conducted all-atom molecular dynamics simulations initiated from three inactive-state, antagonist-bound class A GPCRs: the A 2A -adenosine receptor (A 2A AR), the µ-opioid receptor (µOR), and the δ-opioid receptor (δOR). For each receptor, we collected simulation data on 1.7 µs timescales performed in three different receptor states of the main ion binding residue: Asp 2.50 in a charged state with sodium bound (Na + /D -), Asp 2.50 in a charged state with sodium removed (0/D -), and Asp 2.50 in a protonated state without sodium (0/D n ). Receptor transitions caused by expelling sodium, and subsequently protonating Asp 2.50 , were represented by concatenating trajectory pairs. This way, each process corresponds to 1 bit of information (e.g. 'protonated or de-protonated') termed "information source". SSI for each information source was then calculated between 7875 residue and internal water pairs. Focusing on information transferred through residue side chain movements (35), we investigated the effects in the side chain dihedral angles of all Ballesteros-Weinstein positions common to all three receptors from the intracellular face to the base of the orthosteric pocket, including the CWxP motif, totaling 121 residues.
Our results revealed how sodium, Asp 2.50 -protonation, and internal water molecules are coupled to protein microswitch conformations, forming a long-range information transfer pathway between two highly conserved ionizable regions -Asp 2.50 and the DRY motif at the G-protein binding site. By determining receptor protonation, sodium was found to act as the master switch turning on and off communication with the G-protein binding interface at the intracellular side.

Results
Sodium unbinding and protonation at Asp 2.50 forms an information pathway to the intracellular DRY motif. Five water pockets, local to receptor regions of highly conserved motifs and residues, exhibited large probability densities for receptor-internal water molecules in all three receptor simulations ( Fig. 2A,C). Four of these water sites are conserved in class A GPCRs (14). To determine whether these five water sites acted as information transfer routes, they were investigated in addition to the 121 protein residues. Rather than affecting the entire protein, information specific to the ion binding state of Asp 2.50 (SSI) was shared between a small group of key microswitch and water site pairs, both for sodium and protonation (∼ 5% and 6%, respectively). Within this small number of affected microswitches, our analysis revealed long-range information transfer sent from the ion binding site to the P-I-F motif, the NPxxY motif, and the distal ionizable DRY motif involved in the G-protein binding interface (Fig. 2B). For example, the conformation of residue Arg 3.50 of the DR 3.50 Y motif, at a distance of ∼22 Å, was strongly impacted by Asp 2.50 -protonation (Fig. 2B). We found that internal water molecules acted as important players in transmitting information emerging from the ion binding site. The states of these water molecules were more indicative of the ion binding states of Asp 2.50 than the majority of the protein residues (Fig. 2B). These results suggest that water molecules are an integral part of the signal transmission mechanism, and that the internal waters therefore represent additional elements of an extended set of microswitches. Furthermore, Water 1 (Wat1) is known to form water-mediated interactions present in the inactive receptor state, while interactions with water 2 (Wat2) are correlated with the active receptor state (14). In parallel with this, protonation of Asp 2.50 decreased the occupancy of the Wat1 site by ∼25%, whereas the Wat2 water site showed an increased occupancy by ∼25% in this state. The magnitude of information exchanged within the three receptors after sodium expulsion and Asp 2.50 -protonation was projected onto the µOR crystal structure in Fig. 2C. For both causes, the SSI values revealed a pathway that included water and transmitted information between Asp 2.50 and the DRY motif by propagating conformational changes along helix 7 and across the receptor base. The tight connectivity of coupled transitions on this pathway ultimately allowed changes at Asp 2.50 to affect the conformation of the distal G-protein binding site. This way, it established coupling between ionizable residues at long range (Asp 2.50 , Asp 3.49 , and Arg 3.50 ), whose ability to change protonation state is recognized as a SSI is passed on from the information source to protein microswitches and internal water molecules. Shown are all significant SSI values in bits, shared between both information sources (sodium expulsion and Asp 2.50protonation: 1 bit each) and each microswitch. High SSI values reflect microswitches that have a highly specific conformational state preference for each of the Asp 2.50 ion binding states. Both information sources uniquely alter the presence and orientation of all five investigated internal water molecules (Wat1-Wat5) as well as having a long-range impact on the conformational state of the DRY motif. The significance threshold is depicted by a vertical red dashed line (0.05 bits), internal water and key residues and motifs are highlighted in red. (C) SSI values (bits) representing information flow of Asp 2.50 ion binding changes projected as colour-code (from white, 0 bits to yellow, 0.85 bits) onto the µOR crystal structure (pdb:4dkl). Key microswitches are shown as sticks, water molecules as spheres. Microswitches involved in SSI transfer form a pathway bridging the ion binding site and the DRY motif at the G-protein binding site. Information is transmitted as conformational changes along this pathway to the intracellular face.
hallmark of class A GPCR activation (13). Following protonation of Asp 2.50 , the conformational change at Arg 3.50 also impacted the conformation of residue 6.30 (the helix 6 ionic lock), and position 34.57 on intracellular loop 2 (ICL2), known to play a role in effector protein binding specificity and bias. Since SSI is symmetric, note that the identified information pathway could also serve to support information flow from the DRY motif toward the ion binding site, caused for instance by the intracellular binding of G-proteins or other effectors.
Asp 2.50 -protonation couples to water molecules for efficient information transfer. Two key motifs implied in receptor activation, NPxxY and DRY, shared SSI only upon Asp 2.50 -protonation (Figs. 2B and S1; for full SSI data see Supplementary Information). Unlike sodium expulsion, Asp 2.50 -protonation caused all residues of the NP 7.50 xxY motif, including Pro 7.50 , to undergo various degrees of conformational rearrangement. Structurally, Asp 2.50 -protonation promoted a conformational change to Pro 7.50 , and altered the conformation of the hydrophobic barrier created by Tyr 7.53 (10) (Fig. 3A). In addition, SSI indicated that protonation strongly impacted Wat1 and Wat2, both of which acted as primary microswitches for the transmission of information.
To study the functional role of the internal water network in greater detail, we employed interaction or co-information (co-SSI) (28)(29)(30)(31) to quantify the effect of intercalated water molecules Wat1-Wat5 on information transfer between the Asp 2.50 ion binding site and all microswitches. Positive co-SSI indicated that the coupling between each microswitch and the ion binding site was stabilised by their interaction with water molecules, amplifying their shared SSI. In accordance with the results from LeVine & Weinstein (30), negative co-information was interpreted as destabilisation of microswitch conformations, induced by interacting with water molecules, attenuating their shared information. As shown by co-SSI, the water network had a particularly pronounced effect on the information pathway upon Asp 2.50protonation (Fig. 3A,B). Specifically, co-SSI values demonstrated that the conformations of Wat1 and Wat2 adopted in the Asp 2.50 -protonated state substantially contributed to stabilising the conformational reorientation along the pathway to the G-protein binding site. The reorientation of Wat1, in particular, was responsible for the majority of SSI shared between the protonation site and the NPxxY and DRY motifs (Fig. 3B). This showed that rearrangement of Wat1 and Wat2 was essential for triggering conformational changes coupled to Asp 2.50protonation throughout the receptor, including the establishment of communication between the NPxxY and DRY motifs. The negative value of co-SSI between Pro 7.50 , Wat1, and Asp 2.50 -protonation as the information source, by contrast, implied that Wat1 destabilised the conformational state of Pro 7.50 upon Asp 2.50 -protonation, which may contribute to the kinking of helix 7 seen upon activation (for full co-SSI data see Supplementary Information).

Molecular mechanism of information transfer from the ion binding site.
To elucidate the molecular mechanism of information transfer propagating from the ion binding site, we analysed the nature of the conformational changes induced by Asp 2.50 -protonation across the receptors. In our simulations of both deprotonated states (Na + /Dand 0/D -), it was observed that near the ion binding site, the side chain oxygen of Asp 2.50 acted as a H-bond acceptor for Wat1, mediating a bond with Asn 1.50 and Tyr 7.53 , whose OH group pointed towards the Wat1 pocket in all three receptors (Fig. 3C). Asp 2.50 -protonation triggered substantial rearrangements in its neighborhood in all three receptor types. The altered Hbonding pattern induced a change to the rotamer state of Wat1, while simultaneously, Tyr 7.53 rotated its OH group away from the Wat1 pocket (Fig. 3C). Furthermore, the water bridge between Asp 2.50 and Tyr 7.53 was disrupted upon Asp 2.50 protonation. Thereby, Tyr 7.53 flipped into its downward state (a movement previously shown to correlate with opening a hydrophobic gate (10,16)) in the protonated A 2A AR and µOR. In the δOR the same transition was observed upon further protonation of Asp 3. 49 . This residue forms part of the D 3.49 RY motif and is coupled to Asp 2.50protonation by the information pathway.
Our co-SSI analysis indicated that reorientation of Wat1 was essential for allowing Tyr 7.53 to adopt a new conformation. The protonation-dependent downward movement of Tyr 7.53 ultimately triggered the conformational change of the DRY motif, as demonstrated by the SSI shared between these microswitches. In the µOR, this conformational rearrangement was an upward swing of Arg 3.50 into its active, Gprotein binding conformation (Fig. 3C). In addition, the interhydroxyl distance between Tyr 7.53 and Tyr 5.58 was reduced in the µOR and A 2A AR. In the µOR, Asp 2.50 -protonation was sufficient to decrease the Tyr 7.53 -Tyr 5.58 inter-hydroxyl distance to the distribution seen in the active state, when compared to data from a 1.7-µs simulation of the active crystal structure (pdb: 6ddf) (Fig. S3). We also found that the Gprotein binding cavity opened upon further protonation of Asp 3.49 in the δOR, as measured by the TM2-TM6 activation coordinate between Thr 2.39 -Cα and Ile 6.33 -Cα (Fig. S4), indicating a role of protonating conserved residues in activation.
Sodium restrains key microswitches to a single conformation. The sodium-bound form of class A GPCRs is associated with their inactive state (5,8,10,36). Around the sodium binding site, Asp 2.50 , Tyr 7.53 and Asn 1.50 (a 100% conserved residue in class A GPCRs), three residues known to form a hydrogen bonding triplet with Wat1, were restrained to highly ordered single conformations in all three sodium-bound receptors. This was reflected by their zero conformational state entropies (see Methods) (Fig. 4). The water-mediated locking of Tyr 7.53 in one conformation, which was fully released only upon Asp 2.50 -protonation (Fig. 3D), decoupled information exchange between Tyr 7.53 and the DRY motif.
Additionally, Pro 5.50 of the P 5.50 -I-F motif also showed zero entropy, i.e. confinement to a single conformation, for the sodium-bound state. As opposed to protonation, SSI also indicated that sodium exerted an influence on both I 3.40 and F 6.44 of this motif. This highlighted that sodium altered the conformation of the P-I-F motif, which is known to be strongly coupled to ligand binding (24), as F 6.44 directly interacts with W 6.48 , forming the base of the extracellular ligand binding pocket (37). By contrast, our entropy analysis revealed that all microswitches displayed fluctuations between various different conformational states in the sodiumfree (0/D -) simulations. In the protonated Asp 2.50 state, only Asn 1.50 was restrained to a single conformation in its vicinity.
In summary, we conclude that the sodium ion holds the receptor in the inactive state by restraining the key microswitches Asp 2.50 , Tyr 7.53 , Asn 1.50 , and Pro 5.50 to single conformations. As they are locked in specific states, these microswitches are unable to participate in information transfer, disconnecting the information transfer route across the receptors that emerges fully only upon Asp 2.50 protonation. Since sodium dissociation is strongly coupled to Asp 2.50 protonation (10), the sodium-Asp 2.50 pair forms a single interlinked switch, governing information flow in GPCRs.

Exemplar frames from molecular dynamics simulations of µOR, δOR and A2AAR
in the Na + /Dstate (left). The side chain conformational state entropy (right) of the sodium-bound conformations of Asp 2.50 , Asn 1.50 and Tyr 7.53 is decreased to zero in all three receptors, fixing each residue to a specific conformation. All three residues participate in hydrogen bonding with Wat1 in the sodium-bound state, which correlates with a maintained water bridge between Asp 2.50 and Tyr 7.53 in all three receptors.

Discussion
Ions play important roles in GPCR signal transduction, affecting both their signal bias (38) and receptor activation (4,8,10,36). In particular, a sodium ion bound to a highly conserved ionizable binding site (4,5,9,13,36) is known to play a key part in activating class A GPCRs. Signal transmission is further thought to be underpinned by a tightly connected network of polar residues and internal water molecules that extends across the receptors (14,18) and by the conformational changes of protein microswitches (1, 17,24). How these components interact to affect activation and signaling, however, has been unclear. Here, we applied information theory to µs-timescale simulations of three class A GPCRs to identify coupled transitions between these elements and examine their relation to receptor activation. Our results revealed that a long range information transfer pathway connects the most highly-conserved protonatable residues in class A GPCRs (Asp 2.50 , Arg 3.50 and Asp 3.49 ) from the extracellular ion binding site to the intracellular G-protein interface (Fig. 5). The connectivity was established by protonation of Asp 2.50 , triggered by the removal of a sodium ion that is known to bind to Asp 2.50 in the inactive receptor state (1, 8).
A network of ionizable residues extending through GPCRs is thought to be involved in GPCR signal transduction and may represent an evolutionary link to microbial rhodopsins (7,(10)(11)(12)(13). Our findings therefore suggest that the long-range information pathway we identified may couple the protonation states of the distal conserved Asp 2.50 and Arg 3.50 /Asp 3. 49 . In the sodium-independent, visual class A GPCR rhodopsin, two protonation switches are known to initiate activation. The first protonation event is associated with the lightinduced transition of the retinal Schiff base, central to the receptor similar to Asp 2.50 in non-visual receptors, while the additional protonation occurs at the D 3.49 RY motif (39,40). The coordinated action of such a conserved twin-protonation switch during activation of class A GPCRs would likely require a mechanism to relay protons, and exchange information about the states of the two distal sites. The information pathway we found between Asp 2.50 and D 3.49 is composed of polarizable water molecules and residues with conformations that couple to hydrogen bonding patterns at Asp 2.50 , and therefore well suited to underpin proton transfer. In many cases, ligand binding alone is thought to provide insufficient energy for receptors to transition between inactive and active conformations (7,36). However, GPCRs are able to harness energy from the membrane potential gradient, potentially through ion and proton transfer (7,10,12,41). Even in the presence of bound antagonists, we observed conformational rearrangements within highly conserved microswitches in the DRY and NPxxY motifs upon protonation of three receptors, which were reminiscent of the transition between inactive and active state crystal structures. This stochastic, ligand-independent sampling of active state conformations is in line with reports that suggest spontaneous Asp 2.50 -protonation and egress of the sodium ion may be linked to basal signalling (10), as well as the observation that active state structures exhibit no bound sodium (8). Our results suggest that sodium unbinding and protonation, potentially coordinated between multiple conserved protonatable sites, play a key role in the activation process of class A receptors. Two water molecules, structurally conserved across both active and inactive receptor states, are known to facilitate watermediated interactions that correlate with the inactive (water 1) and active (water 2) receptor states (14). We found that these two water molecules function as microswitches which couple to the ion binding states of Asp 2.50 . Both waters are essential for the transmission of information along a conserved pathway between the ion binding site and the DRY motif. Other water molecules play further important roles in connecting protein microswitch states over long ranges. By disabling protonation and tightly restraining the conformation of Asp 2.50 and neighboring residues, sodium stabilised the inactive state of the receptor and disconnected these information transfer pathways. Only a small fraction of class A GPCRs do not possess a sodium binding site in their transmembrane domain (for example the NK1 neurokinin receptor (8,42)), however they contain a similarly dense internal network of polar residues and water. Whereas Asp 2.50 is replaced by Glu, the DRY motif is still present in these receptors. A sodium-independent mechanism of switching protonation states and rearranging the polar network is conceivable in these cases. However, future studies will be necessary to confirm if the polar signal transmission and activation mechanism we find is conserved in the limited number of atypical class A GPCRs.

Materials and Methods.
Information Theory. The current consensus in the field is that slow modes in protein dynamics, for instance those of GPCR microswitches, have the greatest functional relevance, as they represent large scale changes between conformational states, rather than high frequency oscillations of the same conformational state (43). Therefore, in order to obtain mutual information between low frequency changes to microswitch rotamers, our methodology, State Specific Information (SSI), differs from traditional approaches that derive mutual information from atom or residue covariance during MD simulations (30,32,33,44). In SSI, residue side chains are required to have at least two conformational states to store any information, e.g. 'up' and 'down' in the simplest case. By looking at the state of one residue, we can infer about the state of another, forming the first element of an information pathway. Deriving mutual information from long-lived conformational states rather than residue fluctuations eliminates noise from co-varying residues that always occupy the same conformation, while highlighting residues that are conformationally linked. The analysis was divided into two pairwise combinations of the three ion binding states of Asp 2.50 , isolating the functional effect of removing sodium from that of protonating Asp 2.50 . Since we aimed to investigate the effect of sodium and protonation, isolated from any other ligand-induced ef-fects, the antagonist bound to the inactive receptor state was added to every simulation. In this way, we focused on residue (and water) configurational changes that can be traced back to a certain cause, as opposed to pure correlative measures. The pairwise combinations of simulations were concatenated to create one larger trajectory representing the change in state of Asp 2.50 : removal of sodium (sodium-bound Asp 2.50 [Na + /D -] + charged Asp 2.50 [0/D -]), and protonation of Asp 2.50 (charged Asp 2.50 [0/D -] + protonated Asp 2.50 [0/D n ]). Protonation is hypothesised to occur at the ion binding site during sodium removal and activation (10). The 'source information', which corresponded to the cause of the associated conformational changes, depended on the pairwise combination of simulations used, and represented the binary change made to the state of the ion binding site (i.e., 1 bit of information -sodium-bound to sodium-free; and sodiumbound or -free to protonated). The theoretical upper limit for all mutual and co-information values was therefore 1 bit. By assigning binary states to the two parts of the concatenated simulations representing the ion binding/protonation state, we were able to conclude whether sodium expulsion and protonation caused information to be shared between the ion binding site and any particular microswitch. For example, if information was shared between the states of the ion binding site and Asn 7.49 , causality can be inferred because the state of the ion binding site can alter Asn 7.49 , whereas the state of Asn 7.49 can not alter the ion binding site as it is constant throughout each simulation. The information transfer we resolve therefore only travels from the ion binding site, and not to the ion binding site, though in principle as SSI is symmetric then two-way transfer is possible.
We investigated all residues from the intracellular face to the base of the orthosteric pocket, including the CWxP motif. To focus on information pathways shared between all three receptors, residues whose Ballesteros-Weinstein positions were not common to all three receptors were omitted (for example in loops with differing lengths). Furthermore, we excluded Ballesteros-Weinstein positions that did not have variable side chain dihedral angles in the same position in all three receptors, resulting in a total of 121 investigated side chains. We then took the geometric mean of our results across all common Ballesteros-Weinstein positions. Residues whose configurations are dependent on the state of Asp 2.50 responded with distinct changes in their rotamer states. Additionally, by investigating the water occupancy and dynamics of a number of water sites conserved in both inactive and active state crystal structures, we quantified the influence of water on these communication pathways using co-information (also termed interaction information (30)), applied to residue states as co-SSI. There are different interpretations of negative co-information values in the literature (29)(30)(31). We adpoted the interpretation used by LeVine & Weinstein (30).
Residue side chain rotamer conformations were defined by in-house Gaussian style clustering to χ1 and χ2 dihedral angles, as seen in Fig. 6. A Hanning window function was used to smooth the probability density function to remove noise and locate the state maxima for each rotamer confor-mation. Guess parameters for Gaussian fitting were then obtained by locating the full-width at half-maximum from each maximum and Gaussian curve fitting was applied. The microswitch conformational state limits were defined as the Gaussian intersects. Each discretized distribution was additionally checked visually to ensure the fitting was accurate. , followed by the same Gaussian style clustering algorithm. When water was not found in a specific water pocket at a certain time point, that pocket was assigned an empty state. Water pockets must have had all three water atoms within the pocket as defined above to be considered occupied. Together, this allowed us to deduce the functional effect of each water pocket on the communication between microswitch pairs. The conformational state entropy was determined from H = − i p(i)log 2 p(i), where p(i) is the probability of state i occurring, and H is the entropy, which is also a measure of the maximum information a microswitch can store. A regular average was taken across all common Ballesteros-Weinstein positions in the three receptors to deduce the average entropy of a specific residue. To stay consistent with the definition of states used in the state specific information transfer, the microswitch state limits of the concatenated simulations were used to define the states for the individual simulations. This ensured that residues would show zero entropy if they occupied only one of the information transfer states, and not just a single Gaussian distribution that spanned two information states, thereby identifying the effect of a specific Asp 2.50 state on the information states of the microswitch. State Specific Information (SSI) between two residues X and Y was calculated using SSI(X, Y ) = H(X) + H(Y ) − H(X, Y ), where H(X, Y ) is the joint entropy (26), quantifying the entropy of the rotameric state of residues X and Y as one multivariate system. SSI is thereby a measure of the mutual information between discrete residue states. The co-information (or interaction information), co-SSI, was calculated using where SSI(X, Y |H 2 O) determines what magnitude of SSI, or mutual information, shared between X and Y is dependent on the state of a specific third component, often an intercalating water molecule (H 2 O) (28). We deemed SSI and co-SSI values of less than 0.05 bits insignificant on a 95% significance level.
Protein structure preparations. All crystal structures (µORpdb:4dkl, δOR -pdb:4n6h, A 2A AR -pdb:5olz) were obtained from GPCRdb (45), selecting the GPCRdb refined structure in which mutations are reversed to the canonical sequence and cleaved loops are re-modelled using MODELLER 9.18 to produce the final structure (46,47). All transmembrane crystalline waters and ligands were kept in the structure, removing all external waters and non-protein molecules. The proteins were truncated and capped with acetyl and methyl groups at corresponding N and C terminals using PyMOL (48). As the µOR crystal structure did not resolve a sodium ion in the pocket, the sodium-bound structure was obtained by aligning the δOR crystal structure and placing the sodium ion in an identical position. Asp 2.50 -charged protein structures were prepared by removing sodium from the crystal structure and ensuring no sodium ion re-associated during the course of the simulation. The third, protonated-Asp 2. 50 protein state was prepared in the molecular dynamics software GROMACS-5.1.1 (49). Ligand structures were taken from their respective protein pdb files, and parameterised for molecular dynamics simulations in GROMACS-5.1.1 using ACPYPE (50).
MD simulations. We modelled the protein, membrane, and ligand using the amber99sb-ildn forcefield (51) in GROMACS-5.1.1 with virtual sites to allow a time-step of 4 fs. The proteins were embedded in a pre-equilibrated SLipid POPC membrane (52) using InflateGRO (53). The proteinmembrane complexes were solvated with a neutral solution of TIP3P water molecules (54) containing NaCl at ∼150 mM concentration, with a box size of ∼128x134x125 Å 3 . The systems were equilibrated in both the NVT and NPT ensembles at 310 K for 3 ns, with a further 70 ns of production run simulation considered as additional NPT equilibration. Following equilibration, simulations were performed for 1.7 µs each at a constant temperature of 310 K and pressure of 1 bar, with the protein-ligand complex, membrane, and solution independently coupled to a temperature bath using a Nosé-Hoover thermostat with a time constant of 0.5 ps and a semi-isotropic Parrinello-Rahman barostat with a time constant of 5 ps (55). The trajectory of the δOR protonated at Asp 2.50 was obtained from a previous simulation study (41,56). All protein and lipid bond lengths were constrained with the LINCS algorithm (57), while water bond lengths were constrained using SETTLE (58).
Obtaining rotamer angles. Rotamer angles were determined every 240 ps using gmx_chi. The frame separation was chosen to be slightly smaller than the autocorrelation time of the conserved water dynamics with the fastest relaxation time (59). For µOR, water pockets were defined using MDAnalysis (60) as spheres of radius 4 Å centred on the geometric centres of (i) the tetrahedron formed by joining the C-α atoms of Asn 1.50 -Asp 2.50 -Asn 7.49 -Leu 2.46 ; (ii) the triangle formed by joining the C-α atoms of Asn 7.45 -Asn 7.49 -Ala 6.38 ; (iii) the triangle formed by joining the C-α atoms of Cys 6.47 -Pro 6.50 -Cys 7.37 ; and (iv,v) spheres of 5 Å radius centred on the geometric centres of the tetrahedron formed by joining the C-α atoms of Asn 2.45 -Thr 3.42 -Val 4.45 -Trp 4.50 , and the triangle Val 3.48 -Arg 34.57 -Ala 4.42 , respectively, as seen in Fig. 7. Similar positions were used for the δOR and A 2A AR, determined by centering the water probability density in the geometric centre of the selected C-α atoms.