Membrane Permeability Drives the Extreme Potency of Fentanyl

Abstract

Fentanyl is a leading cause of drug overdose deaths in the United States, yet the mechanism driving its extreme in vivo potency is poorly defined. Here we developed novel computational and experimental approaches to examine whether the membrane contributes to the in vivo potency of fentanyl. Using weighted-ensemble continuous constant pH molecular dynamics (WE-CpHMD) simulations, we estimated the permeability of ionized fentanyl to be approximately 10^–7 cm/s, about 100-fold higher than that of ionized morphine and several more orders of magnitude higher than those of ionized naloxone and isotonitazene. Simulations revealed that all opioids deprotonate when diffusing below the lipid headgroup region, with isotonitazene and naloxone deprotonating closer to the hydrophobic core. Mean first passage time calculation revealed fentanyl’s rapid kinetics for bidirectional membrane transport, suggesting that it partitions into and permeates the membrane while also redistributing back into solution from both the membrane core and intracellular compartment. Consistently, cell washout experiments making use of a BRET senor demonstrated that fentanyl, but not morphine, is retained by cells and can repartition into solution to reactivate the mu-opioid receptor. The IAM-HPLC measurement confirmed fentanyl’s superior phospholipophilicity. These findings support the hypothesis that membrane permeation is a major driver of fentanyl’s extreme analgesic potency, rapid onset, and short duration of action, revealing a fundamental mechanism underlying opioid toxicity, with implication for developing more effective countermeasures. WE-CpHMD provides a valuable tool for mechanistic elucidation of membrane permeation of ionizable molecules, which remains poorly understood.

Introduction

The opioid-related deaths in the United States have increased sharply over the past decade. A new height was reached in 2023, with over 80,000 overdose deaths, among which 90% involved fentanyl, which is an ultrapotent synthetic (UPS) opioid exhibiting distinct pharmacology compared to the natural opiate morphine (Figure A). Comparison of cryogenic electron microscopy (cryo-EM) structures of fentanyl- and morphine-bound μOR suggests that fentanyl’s increased potency may result from the additional interactions with the receptor, particularly between its phenylethyl group and a minor pocket in μOR. These unique receptor interactions may contribute to the ∼10-fold higher in vitro functional potency of fentanyl compared to morphine; however, they cannot explain the substantially greater analgesic potency of fentanyl, which is 50–400 times that of morphine.

1.

Chemical structures of fentanyl, morphine, isotonitazene, naloxone, and the simulation setup. A. Chemical structures and experimental solution pK _a values of fentanyl, isotonitazene (*approximated by that of dimethyltryptamine), morphine, and naloxone. B. A snapshot of fentanyl (cyan) approaching the model lipid bilayer composed of POPC (yellow), POPE (brown), and cholesterol (pink). Water molecules and lipid phosphorus atoms are represented by red dots and orange spheres, respectively.

A recent experiment using whole-cell patch-clamp electrophysiology and signaling assays found that fentanyl, but not morphine, can reactivate μOR after washout, implying membrane retention. This lends support to an alternative hypothesis: fentanyl partitions into the plasma membrane, forming a local “drug depot” that may enhance binding kinetics and/or enable lipid-mediated receptor access. The hypothesis is consistent with fentanyl’s large octanol–water partition coefficient, which is about 700 times that of morphine, as well as its significantly faster onset and short duration of action for users, suggesting more rapid penetration of the blood-brain barrier (BBB). In the same study, coarse-grained molecular dynamics (MD) simulations were conducted. The related potential of mean force (PMF) calculations indicated a larger barrier for fentanyl than morphine to reach the membrane center, whereas the unbiased coarse-grained MD showed that fentanyl in both neutral and charged forms can diffuse into the membrane core, while morphine only interacts with the lipid headgroups.

Intrigued by the unresolved questions surrounding fentanyl’s extreme potency and lipophilicity, we set out to investigate the membrane permeation properties of three μOR agonists (fentanyl, morphine, and isotonitazene) and the μOR antagonist and opioid reversal agent naloxone (Figure B) by developing a state-of-the-art molecular dynamics (MD) protocol and experiments. Contrasting fentanyl, isotonitazene is an ultrapotent synthetic opioid first detected around 2019 in the Midwest of the United States. Of note, isotonitazene is about 50 times more potent than fentanyl and a Schedule I substance. Isotonitazene has also raised significant concerns in Europe, contributing to a second wave of drug-related deaths in the UK. Fentanyl, morphine, and isotonitazene belong to distinct structural families (Figure A), yet they share similarly basic solution K _a’s of 8.2–8.7, − which result in about 10% neutral species at physiological pH 7.5. Naloxone shares a similar structure with morphine but has a somewhat lower pK _a of 7.9.

To allow direct simulation of membrane permeation processes of titratable molecules with full atomic detail, we integrated the GPU-accelerated particle-mesh Ewald continuous constant pH MD (CpHMD), , which captures proton-coupled conformational dynamics, with the weighted ensemble (WE) protocol, , which accelerates sampling of rare events such as drug permeation.

Traditional theoretical studies of passive membrane permeation by small molecules have relied on calculating free energy profiles along the membrane normal using umbrella sampling − or biased sampling protocols such as metadynamics. , In contrast, the WE CpHMD simulations provide an atomic-level description of how drugs interact with the membrane and permeate through it while undergoing protonation state changes, none of which can be captured by molecular descriptors. Of note, the opioids examined here are significantly larger than the molecules studied by the previous all-atom simulation studies. − Our simulations quantified the exceptional membrane permeability of fentanyl relative to other opioids, revealing an apparent drug depot effect. Consistent with this prediction, the experiments demonstrated that fentanyl but not morphine is retained in cells and can repartition back into solution to react with the receptor.

Results and Discussion

Fentanyl Permeates the Membrane Orders of Magnitude Faster than Other Opioids

The membrane permeation simulations at 1 bar, 300 K, and solution pH 7.5 were conducted for three opioid agonists (fentanyl, morphine, and isotonitazene) and one antagonist (naloxone) using the PME-CpHMD module in Amber24. In order to accelerate sampling of rare events (i.e., membrane permeation), the WE method implemented in WESTPA 2.0 was employed, with the progress coordinate defined as the opioid center of mass (COM) z-position relative to that of the membrane. The simulations were conducted under steady-state conditions and initiated with an opioid placed approximately 10 Å away from a fully solvated model lipid bilayer composed of palmitoyloleoylphosphatidylcholine (POPC), palmitoyloleoylphosphatidylethanolamine (POPE) and cholesterol in a 5:5:1 ratio, following the work of Sutcliffe et al. (Figure B, Methods, and SI Figure S1). All molecules primarily adopt the charged (protonated amine) state in solution (SI Figure S2). Two sets of simulations was conducted for each opioid. The second set used a modified WE protocol, where additional WE bins were added near the upper leaflet-water interface to further enhance sampling of the membrane permeation events. Due to this sampling enhancement, our discussion will focus on this second set of simulations, while the first set serves as validation and is included in the SI.

We define the membrane permeation process as the passage of a drug from the donor to acceptor solution regions through the lipid bilayer. Based on the probability flux, we estimated the mean first passage time (MFPT), which is the average time for the opioid to pass through the bilayer for the first time. The estimated MFPT of fentanyl is 10 s, while those of morphine, isotonitazene, and naloxone are orders of magnitude larger, at 9.8 × 10² s, 3.9× 10¹² s, and 1.8× 10³⁰ s, respectively (Table ). Note, the MFPT of naloxone could not be estimated in the first trial, as it did not permeate the lower leaflet within the simulation time (SI Figure S3). These data suggest that, in contrast to isotonitazene and naloxone, fentanyl and morphine (100 times slower than fentanyl) can permeate the membrane on physiologically relevant time scales. Surprisingly, naloxone’s MFPT is orders of magnitude larger than morphine’s despite their highly similar structures.

1. Simulation-Estimated Microscopic Permeability Coefficients and Mean-First Passage Times of Ionized Opioids and Experimental Chromatographic Hydrophobicity Indices .

	log(P m [cm s–1])	MFPT (s)	CHI
Fentanyl	–7.5 [−7.8, −7.4]	8.0 [6.1, 13.0]	41
Morphine	–9.8 [−10.1, −9.6]	1.3e3 [8.0e2, 3.0e3]	17
Isotonitazene	–17.6 [−17.9, −17.3]	8.6e10 [5.6e10, 1.9e11]	n/d
Naloxone	–36.9 [−37.0, −36.9]	1.9e30 [1.6e30, 2.4e30]	28

^alog P _m and MFPT are calculated using the probability flux from the final 50 iterations of the second trial of the WE-CpHMD simulations. The average values and 95% confidence intervals are given. Data from the first set of simulations are given in SI Table S1. CHI values are estimated from IAM experiments (isotonitazene not measured due to regulatory restriction).

Based on the probability flux and an effective reaction volume, we also estimated the membrane permeability coefficient P _m [cm s^–1] to compare with other drug molecules (Table ). Fentanyl has an estimated logP _m around −7.5, which is much lower than the experimental logP _m of water (−4) but only 1 order of magnitude lower than the small, neutral drug-like compounds zacopride, sotalol, and tacrine (between −5 and −6). In contrast, the estimated logP _m values of morphine and isotonitazene, −9.8 and −17.6, respectively, are comparable to the experimental logP _m of potassium ions (−14), , while the estimated logP _m of naloxone is −36.9, which is orders of magnitude lower than all the opioid agonists.

Notably, fentanyl, the primary opioid of interest, exhibits the smallest uncertainty in the estimated P _m value, which is orders of magnitude higher than the reference opioids. Morphine’s P _m is 2 orders of magnitude lower than fentanyl’s, a difference that is statistically significant (two-sided t test on the last 50 WE iterations from both trials gave a p-value of 0.0001). Although individual P _m values for morphine and isotonitazene vary by approximately 2 orders of magnitude between trials, likely reflecting limited sampling of rare permeation events, the 95% confidence intervals for their P _m values – and in fact between any two opioids studied this work – do not overlap, confirming statistical significance of the differences between them (Table and Table S1).

Membrane Permeability Is Enhanced by Early Deprotonation within the Membrane

To understand the distinct membrane permeation behavior of the four molecules, we examined several microscopic quantities as a function of the z-position of the amine nitrogen atom, including PMF, fraction of deprotonation, change in the local membrane thickness, number of the first-solvation-shell water molecules, number of hydrogen bonds (h-bonds) and hydrophobic contacts (Figure and ; SI Figure S6). The z-dependent PMF profiles display a maximum at the membrane center for all of the molecules studied (Figure A). Consistent with the trend in permeation rates, fentanyl exhibits the lowest barrier at 7.8 kcal/mol, followed by morphine at 14.2 kcal/mol, then isotonitazene at 25.0 kcal/mol, and finally naloxone with the highest barrier at 52.8 kcal/mol. To understand how these ionized molecules enter the hydrophobic membrane core, we examined the deprotonation profiles along z (Figure B). Fentanyl and morphine remain protonated when its amine is near the phosphate headgroups (z ≈ 20 Å) and become fully deprotonated when z reaches ≈10 Å, about 5 Å below the carbonyl groups of the lipids. Despite sharing a highly similar structure with morphine, the titration profile of naloxone is more similar to that of isotonitazene, with complete deprotonation taking place deeper into the hydrophobic core region, when z is below 7 Å. Comparing the titration and PMF profiles demonstrates that the ability of an ionized molecule to complete deprotonation in the membrane is correlated with its permeability.

2.

Membrane permeability is related to deprotonation of the titratable amine group. A. Potential of mean force (A) and deprotonation fraction (B) of the opioid as a function of the amine nitrogen z-position. The PMFs were obtained by converting the raw steady-state probability distributions to the equilibrium state and symmetrizing about z = 0 following ref using WESTPA 2.0. Data are taken from the final 100 iterations of the second set of WE-CpHMD simulations (see SI Figure S6 for the first set of simulations).

3.

Characterization of the opioid interactions within the membrane. All quantities are calculated as a function of the amine nitrogen z-position. A,B. Number of hydrophobic contacts (A) and h-bonds (B) between the opioid and lipid molecules. C. Average number of water molecules within 3.4 Å of any heavy atom of the opioid. D. Change in the membrane local thickness around the opioid. The local thickness is defined as the z distance between the centers of phosphorus atoms in the upper and lower leaflets with a 10-Å cylinder around the opioid COM. The average local thickness when the opioid COM is >30 Å from the membrane is used as a reference. Data for A-D are taken from the final 100 iterations of the second set of WE-CpHMD simulations. The first set of data are given in SI Figure S6. E. A trajectory snapshot shows that naloxone (brown) forms two h-bonds between its hydroxyl groups and the phosphate groups of two lipids, while its charged amine interacts with several water molecules.

Hydrophobicity and Diminished Hydrogen Bonding Capacity Drive the Rapid Permeation of Fentanyl

Given similar titration behavior, why does fentanyl permeate the membrane significantly more quickly than does morphine? Important clues are provided by the hydrophobic and h-bond interaction profiles along z (Figure A and B; SI Figure S6), which correlate with the titration profiles. Throughout the membrane permeation process, fentanyl forms the largest number of hydrophobic contacts in comparison to all other molecules, starting at about 10 and increasing to about 40 at z ≈ 10 Å, compared to 5–25 for morphine (Figure A). This corroborates its 700-fold higher P_ow relative to morphine. At the same time, fentanyl forms the least number of h-bonds with lipids, with an average occupancy of 0.5 at the level of the phosphate group and decreases to zero below z ≈ 10 Å. In contrast, the hydroxyl groups of morphine and naloxone are capable of forming h-bonds with the phosphate groups of two lipids at the membrane-water interface, and one h-bond persists until z approaches 5 Å (Figure B). Thus, we attribute morphine’s slower permeation kinetics compared to fentanyl to its h-bond donors (Table S4), which enable h-bonding with lipid headgroups.

Interactions between the Charged Amine and Water Slow down Permeation and Cause Local Membrane Distortion

Given similar structures and a similar number of hydrophobic and h-bonding contacts, the significantly slower permeation rate of naloxone relative to morphine is puzzling. In solution, the charged amine group of an opioid is stabilized through hydrogen bonding (h-bonding) with water. As the opioid partitions into the membrane, the number of water molecules surrounding the amine decreases (Figure C and SI Figure S6). A key difference between the hydration profiles of the opioids occurs at z ≈ 10 Å, where the amine groups of fentanyl and morphine become desolvated while isotonitazene and naloxone retain 3 and 4 water molecules, respectively (Figure C and SI Figure S6). The delayed dehydration of isotonitazene and especially naloxone results in delayed deprotonation (Figure B). A closer examination of the trajectory snapshots revealed persistent interactions between naloxone’s charged amine and water molecules until approaching the bilayer center (Figure E). Since these water molecules simultaneously interact with surrounding lipids (Figure E), local lipids are displaced downward, reducing the local membrane thickness. Interestingly, upon naloxone deprotonation, the membrane thickness recovers to normal values (Figure D). The relationship between the hydration of the charged amine of naloxone and membrane thinning is corroborated by the first set of WE-CpHMD simulations, where the membrane exhibits progressive thinning as naloxone moves toward the bilayer center while preserving interactions between its charged amine and two water molecules (SI Figure S6). Similarly, the delayed titration of isotonitazene is also correlated with persistent interactions with water (Figure C) and the resulting local membrane thinning (Figure D). This suggests that interaction between the charged amine and water molecules is another significant contributor to decreased permeation rates.

Fentanyl Inserts Vertically at the Membrane-Water Interface but Adopts Random Orientations within the Bilayer

To further understand the extraordinary membrane permeability of fentanyl, we analyzed its conformational dynamics during the permeation process. The orientation of fentanyl is defined using an angle formed between the membrane normal and a vector drawn from the amide nitrogen to the piperidine amine nitrogen (Figure A). In solution, fentanyl samples random orientations (Figure A–C and SI Figure S8); as it initiates the partitioning process at the bilayer-water interface (z ∼ 20 Å), a vertical orientation relative to the membrane (angle around 30° or 160°) is preferred, as demonstrated by the trajectory snapshots and the bimodal free energy profiles (Figure A,B,D and SI Figure S8). This vertical orientational preference may reflect the elongated molecular geometry of fentanyl, which exhibits greater compatibility with lipid organization than the globular ‘T-shaped’ structure of morphine or naloxone, thereby facilitating rapid membrane permeation. Note, while both sets of WE-CpHMD simulations favor vertical orientations for fentanyl, the second set shows a modest preference for the downward conformation, where the phenethyl group is oriented toward the membrane center (Figure A,B,D). Interestingly, once past the lipid headgroups, fentanyl is free to adopt other orientations, and in the middle of the bilayer, no orientational preference is observed (Figure B,E, SI Figure S8, Supplemental Movie 1). This freedom of orientation in the membrane core region is also observed for morphine, isotonitazene, and naloxone (Supplemental Movies 2, 3, and 4), which may be attributed to the absence of directional interactions with lipids (i.e., h-bonds as shown in Figure B).

4.

Fentanyl inserts vertically into the bilayer and adopts various orientations in the membrane. A. The orientational angle of fentanyl (left) as a function of the z-position of the center of mass is calculated for unique continuous trajectories of fentanyl (right) permeating through the lipid bilayer. Angles greater than 90° show the phenethyl group to be oriented downward. B. The potential of mean force along the orientation angle while fentanyl is in three different regions: extracellular (blue; defined by z-position between 31 and 35 Å), at the upper leaflet interface (orange; z-position between 18 and 22 Å), and in the middle of the membrane (green; z-position between −2 and 2 Å). C-E. Snapshots selected from the seven trajectories, showing insertion into the upper leaflet (C, phosphorus atoms in tan), passage through the center of the bilayer (D), and insertion into the lower leaflet (E, phosphorus atoms in brown). Fentanyl is colored based on the trajectory the snapshot originated, matching A.

Simulation Predicts an Apparent Drug Depot Effect for Fentanyl

We now turn our attention to the kinetic steps of the drug–membrane permeation process by defining three regions within the membrane: two hydrophilic regions corresponding to the upper and lower lipid headgroup regions, separated by a hydrophobic core at the membrane center. Note, the two hydrophilic regions are not distinguished because of the identical upper and lower leaflets (symmetric membrane). Permeation can therefore be divided into four steps (Figure ): from solution to the headgroup region (step A), from the headgroup to the core (step B), from the core to the headgroup (step C), and from the headgroup back to solution (step D). Owing to the membrane symmetry, steps C and D can be regarded as the reverse processes of steps B and A, respectively. We refer to A+B as the membrane partitioning step, whereas C+D is the solution repartitioning step.

5.

Four kinetic steps in the drug-membrane permeation process. For each opioid, the MFPTs of four steps are calculated. Step A: from solution (z > 20 Å) to upper lipid headgroup region (z = [15:20] Å); Step B: from upper lipid headgroup region to membrane core (z = [−10:10] Å); Step C: from membrane core to lower lipid headgroup region (z = [−15:–20] Å); Step D: from lower lipid headgroup region to solution (z < – 20 Å). Data are taken from the final 50 iterations of the second set of WE-CpHMD simulations.

Walkers in the WE simulations were labeled according to the region where the amine group last resided, and the MFPTs between labels were calculated. Each drug is capable of associating with the hydrophilic region (step A) with similar MFPT of less than a microsecond; however, the MFPT to move into the hydrophobic core (step B) is significantly longer and follows the same trend as the overall permeability (Table ): fentanyl < morphine < isotonitazene < naloxone (Figure ), although the difference between naloxone and isotonitazene is less pronounced. For all drugs, the longest MFPT corresponds to moving from the hydrophobic core to the hydrophilic region (step C), which is slightly longer than the MFPT from the hydrophilic region to solution (step D) and is comparable to the MFPT for the complete permeation process (Table ).

This analysis demonstrates that solution repartitioning constitutes the rate-limiting step of the membrane-drug permeation process. It also reveals that fentanyl’s exceptional permeability stems from its rapid transition between the hydrophilic and hydrophobic membrane regions. Therefore, fentanyl displays the fastest kinetics for both membrane partitioning and solution repartitioning. In other words, once reaching the hydrophobic core, fentanyl can exit back into solution rapidly, whereas this process for morphine is about 100 times slower and unlikely for naloxone and isotonitazene at physiological time scales (Figure ). This analysis predicts an apparent drug depot effect, in which fentanyl exhibits bidirectional membrane transport on physiological time scales: partitioning into and permeating the membrane, while also redistributing back into solution from both the membrane core and intracellular compartment.

Fentanyl Is Capable of Reactivating the Receptor after Washout and Even in Competition with Naloxone

To experimentally test the computational predictions, we developed a sensitive bioluminescence resonance energy transfer (BRET) protocol that harnesses the ability of the μOR to efficiently activate G_i G proteins upon binding of an opioid agonist. Note, experiments were not conducted for isotonitazene due to regulatory restriction on controlled substances. Cells expressing this BRET sensor were first stimulated with either 100 nM fentanyl or 1 μM morphine. Ten min later, either 100 nM naloxone or the empty vehicle was injected. After another 15 min, three washouts were performed consecutively; these washouts were intended to completely remove any opioid agonist or naloxone even if it is initially bound to the receptor. The cells were then monitored for an additional 20 min, after which a high concentration of 10 μM naloxone was applied.

As expected, naloxone injection caused a sharp decrease in BRET ratio for the fentanyl- or morphine-stimulated cells, indicating that the receptor is largely inactivated, whereas vehicle injection (control) produced no change in BRET ratio (Figure ). Remarkably, following three washouts, the BRET ratios of the cells treated with fentanyl/vehicle (yellow) and fentanyl/naloxone (light brown) increased sharply, demonstrating that fentanyl reactivated the G protein complex even in competition with naloxone (Figure ). In contrast, minimal reactivation was shown by cells treated with morphine/vehicle (dark brown) or morphine/naloxone (purple). These observations suggest that fentanyl is retained by the cell membrane to a substantially greater degree than morphine, resulting in μOR reactivation following washout.

6.

Fentanyl reactivated the μOR after washout even in competition with naloxone. Cells were first transfected with μOR and BRET G_i G protein activation sensor. After reading the BRET baseline, cells were stimulated with either 100 nM fentanyl or 1 μM morphine. Ten min later, 100 nM naloxone or vehicle was introduced, followed by three consecutive washouts. The baseline-corrected BRET ratios of cells stimulated with fentanyl/vehicle (yellow), fentanyl/naloxone (light brown), morphine/vehicle (dark brown), and morphine/naloxone (purple) were monitored for 20 min before finally introducing a high dose of 10 μM naloxone.

Note, fentanyl’s residence time at the receptor (about 3.8 min) , is longer than morphine (about 0.72 min); , however, both residence times are significantly shorter than the cell’s exposure time (about 15 min) to the opioid before washout in our experiment. Therefore, the observed receptor reactivation by fentanyl after washout cannot be attributed to the longer residence time of fentanyl relative to that of morphine.

Unlike Other Opioids, Fentanyl Repartitions into the Extracellular Solution after Cell Washout

To further test if cells can retain fentanyl, a separate experiment was conducted where nontransfected cells were exposed to a 10 μM concentration of fentanyl, morphine, DAMGO, or naloxone for 30 min. The supernatant was then extracted, either immediately (No Wash) or after a series of 3–5 washes (Wash 3, Wash 4, and Wash 5). Reporter cells described above were then exposed to this supernatant (or in the case of naloxone, stimulated with 100 nM DAMGO) and the measured BRET ratio indicative of receptor activation or deactivation (in the case of naloxone) was compared to a direct exposure to a 10 μM concentration of the corresponding opioid (Direct, Figure ).

7.

In contrast to morphine and naloxone, fentanyl repartitioned into the extracellular solution after cell washout. Untransfected cells were first incubated with a 10 μM concentration of vehicle (blue), fentanyl (red), DAMGO (green), morphine (purple), or naloxone (turquoise) for 30 min; the supernatant of the cells was recovered either immediately (No Wash) or after a series of 3 to 5 washes (Wash 3–5). The supernatant was then added to separate cells transfected with μOR and BRET G_i G protein activation sensor as in Figure . In the case of naloxone, the transfected cells were first stimulated with 100 nM DAMGO (maroon). For comparison, the stimulation and inhibition from a direct application of the 10 μM vehicle or opioid (Direct) was also measured.

As a control, the transition from No Wash to Direct conditions produced only a slight decrease in agonist- (fentanyl, DAMGO, or morphine)-induced receptor activation and antagonist- (naloxone)-induced receptor deactivation (Figure ). In contrast, three washes significantly reduced the response of both morphine- and naloxone-incubated cells compared with direct application, confirming the effect of opioid removal (Figure ). Specifically, after three washes receptor activation in morphine-incubated cells was reduced by about 80%, and that in naloxone-incubated cells was nearly restored to the level of DAMGO. In contrast, fentanyl-exposed cells showed only about 25% reduction in response after three washes, which persisted through the fourth wash. In contrast, after three washes of cells exposed to fentanyl, a response level was reduced by only about 25% relative to No wash, and the level remained after four washes (Figure ). A significant drop in fentanyl-induced activation similar to the level for morphine was only observed after the fifth wash. Receptor activation by the supernatant following three washes of fentanyl-exposed cells suggests that fentanyl is retained intracellularly and subsequently repartitions into the extracellular solution.

We asked if the differential effects of the supernatants incubated with fentanyl or morphine could be attributed to the 10-fold potency difference between them (SI Figure S10). In other words, if the washout was equally effective for both compounds, the resulting concentration reduction in the supernatant might still elicit a response from fentanyl but not morphine due to fentanyl’s higher potency. To test this hypothesis, we examined DAMGO, a ligand with potency comparable to fentanyl but does not permeate the membrane. If potency alone explained the sustained response, DAMGO should exhibit similar postwashout effects. This was however not the case. DAMGO-incubated cells showed less than 10% response after three washes, compared to 75% for fentanyl-incubated cells (Figure ). Thus, fentanyl’s higher potency does not explain the sustained effects following washout.

Fentanyl Exhibits Greater Retention in the Immobilized Artificial Membrane Compared to Morphine and Naloxone

Finally, to further test the membrane partition ability of the opioids, we conducted an experiment using Immobilized artificial membrane-high performance liquid chromatography (IAM-HPLC). The IAM column is comprised of POPC monolayers covalently attached to amino-propyl silica particles which are intended to mimic the in vivo interactions of drug molecules with phospholipids. , Due to the monolayer construct, the analyte only binds to the phospholipid surface and does not pass through the membrane, in contrast to the simulation or physiological conditions where a bilayer exists. Nonetheless, the retention of the analyte in the column relative to the mobile phase, which is known as the chromatographic hydrophobicity index (CHI), provides a more accurate estimate of drug-membrane affinity compared with the octanol–water partition coefficient. IAM-HPLC yielded a CHI value of 41 for fentanyl, which is significantly higher than that for morphine (17) or naloxone (28, Table ), indicating a higher affinity for phospholipids. This is consistent with fentanyl’s substantially higher simulated permeability and resistance to cell washout.

The higher CHI value of naloxone (28) relative to that of morphine (11) appears inconsistent with its slower MFPT reaching the membrane core estimated by simulations (Figure ). Note, the cellular washout data does not have the sensitivity to discriminate between naloxone and morphine. The apparent discrepancy between CHI values and MFPTs can be explained by differences in what is measured versus what is simulated. Our simulations only examined ionized opioids whereas in solution (finite concentration) neutral species also exist albeit in a smaller fraction. Neutral species have substantially higher membrane permeability than the corresponding ionized forms. It is possible that neutral naloxone has a higher lipophilicity than morphine. Also of note, the pK _a of naloxone is lower than morphine, resulting in a larger fraction of neutral species in solution at neutral pH under the experimental conditions. This is a topic for future investigation.

Concluding Discussion

WE-CpHMD enabled the first visualization of membrane permeation by realistically sized ionizable drug molecules at atomic resolution while simultaneously modeling the pH titration. The estimated P _m of fentanyl at pH 7.5 is on the order of 10^–7 cm/s, which is 1–2 orders of magnitude smaller than nicotine, estimated as 10^–6 cm/s at pH 7.4 and 10^–5 cm/s at pH 7.8. The difference between fentanyl and nicotine is justified, as nicotine is much smaller and has a similar pK _a value of 7.9. Note, similarly sized neutral drug-like compounds, zacopride, sotalol, and tacrine, have a similar permeability range of 10^–5–10^–6 cm/s. The simulation estimated P _m of morphine is roughly 2 orders of magnitude lower than fentanyl, which is consistent with the previous coarse-grained simulations showing that fentanyl but not morphine can diffuse into the membrane core region. Fentanyl’s higher P _m suggests that it crosses BBB more rapidly, likely contributing to the faster in vivo onset time relative to morphine. Our stepwise kinetic analysis suggests that the membrane effectively acts as a drug depot, whereby fentanyl rapidly partitions into and permeates the membrane, while also redistributing back into solution from both the membrane core and intracellular compartment. Consistent with this prediction, the BRET washout experiments demonstrated that cells retain fentanyl, which can repartition back into the solution and reactivate μOR.

While most drugs are at least partially ionized in solution at physiological pH, , the long-standing pH partition hypothesis posits that only the neutral form can traverse biological membranes. This hypothesis is supported by the pH-dependent permeability profiles of ionizable drugs. For example, nicotine (with solution pK _a of 7.9) displays increased P _m with increased pH, , corresponding to a greater fraction of the neutral form. Our results directly challenge the pH partition hypothesis by demonstrating that membrane permeation of ionized opioids occurs through a proton-coupled mechanism in which deprotonation events facilitate passive diffusion into the hydrophobic core. This mechanism is kinetically feasible because the time scale of deprotonation events, which is experimentally estimated at 1–10 μs based on k _off on the order 1–10 × 10⁵ s^–1, is orders of magnitude faster than that of membrane permeation events of most permeable drugs, which is estimated as 0.4 – 40 ms based on the effective permeability range of 10^–7 – 10^–5 cm/s at physiological pH , and a membrane thickness of 40 Å. Note that our study examined only ionized species; a complete understanding requires kinetic comparison between ionized and neutral species, which awaits future investigation.

To contextualize our findings, it is important to compare them with previous all-atom simulations of membrane permeation of ionizable drugs. Except for one study, all prior work utilized fixed-charge simulations and assumed that ionized drugs can permeate the membrane while maintaining the charge (for example, in refs , ). Both our simulations and the previous hybrid-solvent CpHMD based PMF calculations of propranolol partitioning into the membrane center demonstrate that ionizable drugs neutralize as they approach the hydrophobic membrane core. This is consistent with the experimental data and multisite λ-dynamics simulations showing that ionizable residues in membrane-inserted peptides undergo large pK _a shifts, which allow them to adopt the neutral state at physiological pH. The only exception is arginine, which maintains positive charge, inducing pore formation and membrane deformation; , consistent with this, our simulations demonstrated that naloxone and isotonitazene, which remain partially protonated until reaching the membrane core, induce localized hydration and membrane thinning. Of note, a difference between our results and the hybrid-solvent CpHMD umbrella sampling of propranolol is that our calculated PMFs exhibit barriers at the membrane center, consistent with both fixed-charge umbrella sampling studies , and the WE permeation simulations of neutral molecules.

The simulations presented here have several caveats. While the relative permeability ranking among the four molecules is robust, the uncertainty in P _m values for poorly permeable molecules is substantial due to insufficient sampling of barrier-crossing events which are extremely rare. Notably, in the first set of simulations for naloxone, no permeating event was observed. Additionally, although WE simulations are theoretically unbiased, the selection of progress variables and other protocol parameters can influence the estimated P _m values, as demonstrated previously. Another limitation concerns the accuracy of the force fields. Additive force fields such as CHARMM36 used in this work are known to overestimate the hydrophobicity of alkane environments such as the bilayer core, resulting in underestimated P _m values for polar molecules. For example, CHARMM36 underestimates water P _m in POPC bilayer by 1 order of magnitude. Given their ability to form h-bonds with lipids via h-bond donors, the permeabilities of morphine and naloxone, particularly the latter, are likely underestimated. Nonetheless, the rank order of permeabilities among the four opioids likely remains valid, as the differences between them are more than 2 orders of magnitude.

Another caveat is that our simulations did not consider finite concentrations. At physiological pH, neutral opioids exist at lower mole fractions but exhibit a much faster membrane permeability than the corresponding cationic species. As evidence, the octanol–water partition coefficient of neutral morphine is approximately 1000-fold higher than that of its cationic form. Our analysis revealed that the substantial reduction in permeation of isotonitazene and naloxone relative to morphine and fentanyl in their ionized forms stems from delayed titration; i.e., complete deprotonation occurs deeper within the membrane core. Therefore, the neutral forms of isotonitazene and naloxone may exhibit permeabilities more than 3 orders of magnitude higher than their charged counterparts, effectively dominating macroscopic permeability and BBB penetration. Quantitative elucidation of macroscopic permeabilities of ionizable drugs using CpHMD simulations is a direction of future research.

There are several caveats with the performed experiments. While IAM-HPLC retention measurement more closely mimics the phospholipid membrane compared to the octanol–water partition estimates, it relies on POPC monolayers, which differ from the lipid bilayers of cell membranes. The BRET washout experiments demonstrated that fentanyl is retained within cells and can repartition back to solution and reactivate the receptor, suggesting re-entry into the receptor’s orthosteric binding pocket from solution. However, given fentanyl’s high lipophilicity and cellular retention demonstrated by our experiments, we speculate that it may also access an alternative lipid-facing pocket within the receptor. Sutcliffe et al. investigated such a possibility through mutagenesis of a potential pocket at the TM6/TM7 interface predicted by the coarse-grained simulations, but these mutations did not alter fentanyl’s in vitro pharmacology.

In summary, the present work offers compelling evidence to support the notation that plasma membrane permeability is an important driver of fentanyl’s extreme analgesic potency, fast onset time, and short duration of action. An important question for future investigation is whether fentanyl can access the receptor through a lipid-mediated route, thereby delineating the mechanism of receptor reactivation. Understanding membrane-dependent pharmacology has implications for the design of new opioid antagonists. Recently, antagonists based on the fentanyl structure have been developed. Testing these antagonists in vitro and in vivo is a future direction of research toward mitigating the current opioid crisis. While regulatory restrictions prevented experimental investigation of isotonitazene, our simulations demonstrated that its ionized form does not partition into the membrane at biological time scales. While membrane permeation of neutral isotonitazene will be investigated in our future work, we speculate that isotonitazene’s potency is primarily driven by its high affinity for μOR, as reflected by a subnanomolar K _i value approximately 12-fold lower than that of fentanyl. Our recent simulation work suggests that the nitro-containing nitazenes (e.g., isotonitazene) occupy subpocket 2 formed by TM1, TM2, and TM7, in contrast to fentanyl and morphine which engage subpocket 1 located between TM2 and TM3. We speculate that this distinct binding mode of isotonitazene mightcontribute to its enhanced potency relative to fentanyl.

Materials and Methods

This section describes the methods, protocols, and analysis of weighted-ensemble continuous constant pH molecular dynamics (WE-CpHMD) simulations, bioluminescence resonance energy transfer (BRET) experiments, and an IAM chromatography experiment.

WE-CpHMD Simulations

We developed a protocol that integrates the GPU-accelerated all-atom particle mesh Ewald CpHMD , implemented in AMBER24 for titration simulations with the WE protocol implemented in WESTPA2.0 ,, for enhanced sampling.

CpHMD Parametrization

In the all-atom PME-CpHMD method, , each titratable site (either in a protein or a small molecule) is represented by a fictitious particle λ whose coordinate is bound between 0 (protonated) and 1 (deprotonated) through an internal variable θ, λ = sin ²(θ), which is propagated simultaneously with the atomic coordinates. The CpHMD simulations necessitate two types of parameters: the pK _a of the model titratable site in solution (i.e., model compound) and the potential mean force (PMF) function of λ for the model compound. For fentanyl, morphine, and naloxone, the model pK _a’s were 8.4, 8.2, and 7.9, respectively. As the pK _a of isotonitazene has not been experimentally determined, it was set to that of the structurally similar dimethytryptamine, 8.7. The parameters in the PMF functions were determined through thermodynamic integration (TI) simulations in water, as described below. More details are given in the original CpHMD development work , and a recent tutorial.

The opioids were represented by the CGenFF force field. , Water molecules were represented by the modified TIP3P model. , The force field parameters of sodium and chloride ions were taken from refs. , For both TI and solution titration simulations for validation of the solution pK _a values of the opioids, a solvated system was built by solvating the opioid using a water box with a distance of at least 15 Å between the nearest water oxygen and the heavy atom on the small molecule. Six sodium and 7 chloride ions were added to compensate for the net charge of 1 at pH 7.5 and reach an ionic strength of 0.15 M. During the CpHMD titration, the effect of net charge was accounted for using a uniform background charge (plasma) in the PME correction term for propagating atomic coordinates. ,, Each system was minimized for 5,000 steps, and then seven independent replicas were created by fixing θ _i (0.2, 0.4, 0.6, 0.7854, 1.0, 1.2, or 1.4). Each replica was heated to 300 K under constant volume over 50 ps with a 5 kcal/mol/Å restraint on the heavy opioid atoms, then restraints were gradually relaxed over 100 ps under constant pressure of 1 bar. Pressure was controlled using the Monte-carlo barostat while temperature was controlled at 300 K using Langevin dynamics with a collision frequency of 1 ps^–1. Long-range electrostatic interactions were calculated using the particle mesh Ewald (PME) method with a real-space cutoff of 12 Å and a 1 Å grid spacing for the reciprocal space calculations. Lennard-Jones energies and forces were smoothly switched off over the range of 10 to 12 Å. The mean force ⟨∂U/∂θ⟩ was then calculated over a 10 ns simulation for each θ; fitting the calculated mean force at a series of θ values to the partial derivative of the quadratic PMF function yields the two parameters in the PMF. Note that, in order to minimize fitting errors, fitting was done in the θ space and not the transformed λ. Following the TI simulations, titration simulations were performed to verify the experimental pK _a’s in solution are recapitulated by CpHMD simulations. Six separate 20 ns simulations were conducted at different pH conditions ranging from 7.0 to 9.5. To verify the parameters obtained from TI, the average deprotonation fraction over the final 10 ns of each simulation was measured then used to fit to the generalized Henderson-Hasselbach equation to obtain a calculated pK _a (SI Figure S4).

System Preparation for the WE-CpHMD Simulations

CHARMM-GUI was used to construct a bilayer comprising 66 lipids in a 5:5:1 ratio of POPC, POPE, and cholesterol, following the work of Sutcliffe et al. While this composition is similar to that of mammalian neural soma, it does not include 9% anionic lipids. While the choice may be imperfect, it would not affect the conclusions of the work; the rate-limiting membrane region that differentiates among the permeants is the hydrophobic core rather than the lipid headgroup region, and the model membrane is small (9% corresponds to 3 lipids on each leaflet). An opioid was then induced and placed 30 Å from the center of the bilayer. A water layer of 22.5 Å was added above and below the bilayer. The system was minimized for 5000 steps and then heated under constant volume to 300 K over 125 ps with restraints on lipid positions and dihedrals. These restraints were then gradually removed over 2.25 ns under a constant pressure of 1 bar, followed by a 50 ns simulation to equilibrate the membrane. All steps were done using Amber24. The CHARMM36 lipid force field was used. All other parameters and settings were identical to those described above for the solution CpHMD simulations of opioids.

The Weighted-Ensemble (WE) Protocol

WE simulations, , in brief, involve iteratively evolving a number of independent replicate systems called walkers. After each iteration, a progress coordinate (or several coordinates) is calculated and used to place each walker into predefined bins; within each occupied bin, walkers are either replicated or removed such that the number of walkers per bin meets a target value. By updating a statistical weight for each walker after each split (replication) or merge (removal), both equilibrium and kinetic information can be estimated.

The progress coordinate used was defined as the z-position of the center of mass of the opioid (excluding hydrogen atoms), with the center of the membrane (defined by the center of all phosphorus atoms of POPC and POPE lipids) as the origin. Initial bin boundaries were set based on the environment: when the opioid was in solvent (|z| > 20 Å) boundaries were set 5 Å apart, while when inside the membrane (− 20Å < z < 20Å) boundaries were set 0.5 Å apart (85 bins total). This was chosen as diffusion within the membrane is likely slower than in the solvent. The WE protocol allows for dynamic bin boundaries, thus bins were added as needed at the membrane-extracellular interface (i.e., 20 < z < 25) in order to sample permeation. A steady-state WE simulation was prepared, where a walker would be recycled if z > 55 Å (far above the upper membrane leaflet) or z < −25 Å (below the lower membrane leaflet) at the end of the iteration. This was done to ensure the opioid does not cross the periodic boundary and that membrane partitioning occurs in one direction.

The WE simulations were conducted using WESTPA 2.0 and Amber24. The target count for each bin was set to 4; each iteration involved simulating each walker for 100 ps at pH 7.5 using all-atom PME-CpHMD following settings in the same reference. WE simulations were conducted until both the calculated PMF along the progress coordinate and the effective permeability had converged. Equilibrium and kinetic analysis was performed through the WESTPA2.0 package, , while quantities such as hydrophobic contacts and membrane thickness were calculated using MDTraj. The rates of permeation and partitioning were analyzed by dividing the system into five regions based on the z-position of the amine from the bilayer center: donor solvent (z > 20 Å), lipid head groups of the upper leaflet (15 < z < 20 Å), hydrophobic core of the membrane (− 10 < z < 10), lipid head groups of the lower leaflet (−20 < z < −15), and acceptor solvent (z < −20 Å). The probability flux from donor solvent region to acceptor solvent region f _ex→in was calculated using the w_assign and w_direct tools in the WESTPA package, , and then was used to calculate the effective permeability and mean first passage time (MFPT) following Zhang et al.:

$$\begin{array}{ll}\hfill P_m& ={f_{ex\to in}}^{*}{l}_d\\ MFPT& =\frac{p_{ext}}{f_{ex\to in}}\end{array}$$ 1

In the above equations, l _d represents the depth of the effective reaction volume while p _ext represents the fraction of trajectories that most recently sampled the extracellular state versus the intracellular state. The effective reaction volume is the region where the surface of the membrane influences neighboring molecules; thus, events in bulk solvent (such as stirring) do not affect molecules in this region. Following Zhang et al., we set this to half of the height of the overall water buffer (l _d = 22.5 Å) in our analysis. Since the intracellular region was set as a recycle condition, there are no trajectories that sample the intracellular before sampling the extracellular; thus, p _ext = 1. Statistical significance was determined by conducting a two-sided student’s t test using the f _ex→in from each of the final 50 iterations.

Symmetry about z = 0 was enforced by first calculating the probability of each bin (obtained by w_pdist) and then combining symmetric probabilities. An example script used to calculate the number of waters, hydrogen bonds, hydrophobic contacts, and membrane thickness is deposited for public access (see Data Availability).

Bioluminescence Resonance Energy Transfer (BRET) Experiments

Materials

DMEM was from Sigma-Aldrich, FBS was from Sigma-Aldrich, PEI was from PolySciences Inc., poly-d-lysine was from Fisher Scientific, coelenterazine h was from NanoLight Technology (Prolume Ltd.), morphine was from Tocris, fentanyl was from Sigma-Aldrich, DAMGO was from Hello Bio, Naloxone was from Hello Bio and D-PBS was from Gibco.

Cell Culture and Transfection

Human embryonic kidney 293 T (HEK 293T) cells were cultured at 37 °C, 5% CO₂ in Dulbecco’s modified eagle medium (DMEM) supplemented with 10% (v/v) fetal bovine serum (FBS). For transfection, cells were plated in 10 cm Petridishes (3 × 106 cells per dish) and allowed to grow overnight in full media at 37 °C, 5% CO₂. 24h later, cells were transiently transfected, using a 1:6 total DNA to PEI ratio and the following DNA constructs: 2 μM of Gαi2, 1 μM of Gβ1-Venus(156–239), 1 μM of Gγ2-Venus(1–155), 1 μM of masGRK3ct-Rluc8 and 1 μM of MOR [SNAPmMOR]. DNA/PEI mixtures were added to the cells. Twenty-four post-transfection, cells were plated in Greiner poly-d-lysine-coated, white bottom 96-well plates (SLS) in full media.

BRET Measurements

On the day of the assay (48h post-transfection), cells were washed once with D-PBS (Lonza, SLS) and incubated in D-PBS for 30 min at 37 °C. The Rluc substrate coelenterazine h was added to each well (final concentration of 5 μM) and treated as specified below. BRET measurements (Venus and Rluc emission signals at 535 and 475 nm, respectively) were performed using a PHERAstar FSX microplate reader (BMG Labtech) at 37 °C. BRET ratio was calculated as the emission at 535 nm divided by the emission intensity at 475 nm signal and corrected for the vehicle BRET ratio signal.

Kinetic BRET Experiments

After a 5 min baseline read after the addition of coelenterazine h (final concentration of 5 μM), morphine (1 μM), fentanyl (100 nM) or vehicle were added, and the signal was read for 10 min. Then, 100 nM of naloxone or vehicle were injected to the wells. At this concentration, naloxone was demonstrated to partially reverse the G protein activation evoked by morphine (1 μM) and fentanyl (100 nM) to similar levels. The BRET signal was read for a further 15 min prior to 3 washouts of the cells with D-PBS, readdition of coelenterazine h (final concentration of 5 μM) in drug-free D-PBS and measurement of the BRET signal for a further 20 min until the final addition of 10 μM naloxone to fully reverse MOR induced G protein activation.

Ligand-Release BRET Sensor Experiments

Untransfected HEK293T cells were incubated with vehicle or 10 μM of fentanyl, morphine, or naloxone for 30 min at 37 °C. After incubation, the supernatant of the cells was recovered (no wash), cells washed five times with D-PBS and supernatants recovered (wash 1, 2,3,4, 5, respectively). 100 μL of these supernatants were then used to stimulate a plate containing cells transfected with μOR, and the G protein activation sensor constructs (Gαi2, Gβ1-Venus(156–239), Gγ2-Venus(1–155) and masGRK3ct-Rluc8). Direct application of vehicle or 10 μM fentanyl, DAMGO, morphine, or naloxone was used as a control. BRET signal was measured as above after 10 min incubation.

IAM Chromatography Experiment

Equipment and Methods

Immobilized artificial membrane-high performance liquid chromatography (IAM-HPLC) was performed using a conventional HPLC set up fitted with a IAM P.C DD2 column (30 × 4.6 mm, 10 μM, 300 Å) (Regis technologies Inc., Chicago, USA). The column was maintained at 30 °C with a flow rate of 1.5 mL/min and UV detection at 254 nm. The system consisted of a Shimadzu systems controller SCL-40, degassing unit DGU-405, solvent delivery module LC-40D XR, auto sampler SIL-40C XR, column oven CTO-40C and a photo diode array (PDA) detector SPD-M40 (Shimadzu, Kyoto, JPN). Solvent A contained ammonium acetate (50 mM) (Sigma-Aldrich, Gillingham, UK) in Milli-Q water at pH 7.4, and solvent B was acetonitrile (Thermo-Fisher Scientific, Loughborough, UK).

Method

0–85% over 4.75 min; 85% B for 2 min; 85–0% B over 0.5 min, then 0% B. All standards and samples were dissolved via dropwise addition of DMSO, before being diluted in water to 1 mM final concentration. Each sample was loaded in 10 μL injections and repeated in triplicate on 2 separate days. IAM calibration mixture (Bio Mimetic Chromatography Ltd., Stevenage, UK) composition: octanophenone, heptanophenone, hexanophenone, valerophenone, butyrophenone, propiophenone, acetophenone, acetanilide, paracetamol. Test mixture 1: propranolol, indomethacin, and colchicine; Test mixture 2: warfarin, carbamazepine, nicardipine. Samples: fentanyl, buprenorphine, naloxone, [d-Ala², N-MePhe⁴, Gly-ol]-enkephalin (DAMGO), morphine  all commercially available from standard suppliers.

Calibration Plot

The system was calibrated by introducing the IAM calibration mixture (10 μL) using method 1 and plotting the t _R of each component in the mixture against chromatographic hydrophobicity index (CHI (IAM)) values from the literature. Typical chromatograms, retention times (t _R ) and values of CHI (IAM) from the literature are shown in SI Figure S10. A calibration plot and equation for the line of best fit was generated in Microsoft Excel (version 16.88) and the Pearson correlation coefficient (r) was calculated to be >0.99, as summarized in graphical plot (SI Figure S11).

Column Performance and Suitability Test

Before samples were analyzed, an assessment of column performance was carried out daily by introducing Test mixtures 1 and 2 (SI Figure S12) using Method 1. The retention time of the components in each mixture were converted to CHI­(IAM) values using the calibration plot in (SI Figure S11). The column was deemed suitable for analysis if all measured CHI (IAM) values were within ±5 of their corresponding literature values. Examples of typical chromatograms are shown in SI Figure S12 and all data is summarized in SI Table S4.

Sample Testing

Samples were analyzed using method 1 and typical chromatograms are shown in SI Figure S13. Retention time was converted to CHI (IAM) values for each sample using the calibration plot (SI Figure S11).

All simulation inputs, configurations, and analysis scripts can be found at https://github.com/JanaShenLab/Fentanyl-insert.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/jacsau.5c01666.

• Continuous trajectory showing the membrane permeation process of fentanyl (movie 1) (MP4)

• Continuous trajectory showing the membrane permeation process of morphine (movie 2) (MP4)

• Continuous trajectory showing the membrane permeation process of isotonitazene (movie 3) (MP4)

• Continuous trajectory showing the membrane permeation process of naloxone (movie 4) (MP4)

• Supplemental tables and figures detailing simulation parameters, additional results from simulations, and IAM calibration/raw data (PDF)

J.C.: conducted simulations and analyzed data, wrote and revised the manuscript; G.J.F.: designed and performed IAM experiments and revised the manuscript; J.G.: performed BRET assays; S.N.M.: designed and performed IAM experiments and revised the manuscript; M.C., R.L.: designed the project, supervised experiments, wrote and revised the manuscript; L. Shi and L.S.: designed the project and revised the manuscript; J.S.: designed the project, analyzed the data, wrote and revised the manuscript.

Disclaimer: This article reflects the views of the authors and should not be construed to represent FDA’s views or policies. The mention of commercial products, their sources, or their use in connection with material reported herein is not to be construed as either an actual or implied endorsement of such products by the FDA. The contributions of the NIH author(s) are considered Works of the United States Government. The findings and conclusions presented in this paper are those of the author(s) and do not necessarily reflect the views of the NIH or the U.S. Department of Health and Human Services.

The authors declare no competing financial interest.