Introduction

Quantum activity within biological systems and the applications of information theorytherein have drawn much recent attention1,2,3,4,5. Examples ofsystems that exploit such phenomenon are: quantum coherence and entanglement inphotosynthetic complexes6,7,8,9,10,11,12,13,14,15, quantummutations16,17, information theory and thermodynamics ofcancers18,19,the avian magnetic compass20,21,22,23, tunneling behavior in the antioxidant breakdown of catechols present in greentea24, enzymatic action25, olfaction26,and genetic coding27. G Protein-Coupled Receptors (GPCR) are the targetfor the greatest portion of modern therapeutic small molecule medications28. Predictability of pharmacological efficacy and potency for new drugs prior to acomplex total synthesis can be aided by in silico methods such as pharmacophoremodeling, or the construction of homology models. Protein/agonist binding theory hasbeen described through variants of the Lock and Key model, originally proposed byFischer29 and the extensions thereof30. Although thistheory has provided insights into free energy changes associated with the formation ofthe activated protein/agonist complex, it has not manifested sufficient capacity for theprediction ligand potency due to a lack of knowledge concerning the mechanism by whichthe agonist activates the complex. Growth in the computational power of modern machines,as well as developments within the field of computational chemistry and molecularmodeling, has afforded reconnaissance and scouting methods in the field of drug design.Additionally methods such as QM/MM have been used in studies of protein folding andgeneration of the protein-agonist activated complex. Furthering our ability to predictinformation regarding the viability of molecules as drugs is greatly important.

Early models attempting to account for predictability of agonist classification beyondmere shape were those of odorant binding31,32; these works proposed avibrational theory of receptor activation. Vibrational theories were eventuallydisregarded for reasons that include a lack of conceived mechanism and the inability ofthe protein (which undertakes thermally driven random walks in their conformation) todetect the continuum of thermally-activated, classical vibrations of the odorant. Arecently suggested theory for olfactory activation consists of a physical mechanismclosely resembling Inelastic Electron Tunneling Spectroscopy (IETS)26,33,34. The plausibility of time scales associated with this processwas verified to be consistent with relevant biological time-scales through Marcustheory35. Electron tunneling rates for the olfaction system have beencalculated and support the theory36. Furthermore, eigenvalue spectralanalysis of odorant molecules has shown a high correlation between the vibrations andodorant classification37.

We focus on an initial examination of the viability of the vibrational theory of proteinactivation in cases involving protein-agonist binding within the central nervous systemvia application of IETS theory as a predictor of potency as defined within38. Activation of the 5-HT1A and 5-HT2Areceptors is implicated as being associated with human hallucinogenic responses39,40,41. We utilize a model of inelastic electron tunneling to describethe protein/agonist complex in a manner that will utilize the vibrational frequencies ofthe bound agonist to facilitate electron transfer within the activation site of theprotein/agonist complex. The prerequisite agonist information was collected throughmolecular quantum mechanics calculations utilizing density function theory as well asnormal mode analysis and natural bonding order methods; necessary were the harmonicdisplacements, frequencies and partial charges of each constituent atom. In Section II,we will first present a qualitative discussion of the relationship between the tunnelingmodel and the protein-agonist complex. Section III will discuss the tunneling featuresof several 5-HT1A and 5-HT2A agonists and how thesecorrelate with the potency of these molecules taken from previousstudies42. We conclude with a proposed set of molecules that could beemployed in experimental validation of the vibrational theory’s applicabilityin the central nervous system and present the expected results in accordance with thisproposed mechanism.

Mapping the model into the biological system

Application of the IETS model for the agonists protein environment requires mappingseveral aspects of the IETS methodology into the biological system. The two-plateapparatus of the tunneling junction herein represent the walls of the receptor site;more explicitly, under electron transfer, the valance and conductance bandsassociated with each side of the junction are mapped to specific HOMOs and LUMOs ofparticular residues comprising the walls of the receptor. This dictates that energytransition detectable by the protein should be the energy difference betweenelectronic levels of residue side-chains or any bound cofactors, such as a metalion. This alteration of IETS also localizes the source of tunneling electrons to asingle residue side-chain; the implication is that electrons are not capable ofdistributed tunneling through the molecule in the manner of a doped analyte within ajunction. This lack of a spatial distribution of electron trajectories suggests thatthe act of tunneling is localized to regions of the agonist molecule along theclassical trajectory of the tunneling electron between the site of the electrondonor and the site of the electron acceptor. This implies that not all localoscillators associated with a specific mode may fully contribute to the currentenhancement due to the fall-off of the charge-dipole coupling between the tunnelingelectron and the local atomic oscillators.

Secondly, unlike the typical experimental IETS procedure, the analyte is notdeposited upon a surface, being encapsulated by the active site. There is noexternally applied potential within the receptor site which would have allowed forthe scanning of energies; yet, it has been suggested that an ionic cofactor, likelya calcium ion, could provide this driving field. The implication of this is that thereceptor is set to test the vibrational-assisted enhancement to the electrontunneling rate at a specific energy, opposed to scanning a range of energies. Theelectrostatic interactions which govern docking orientation would be a means oforienting the endogenous agonists in such a way that the tunneling junction isappropriately aligned for maximized electron transfer across the atoms responsiblefor the inelastic contribution. Non-endogenous agonists would align with residues ina manner which may place energetically appropriate vibrational modes of the agonistin proximity of the tunneling vector specific to this protein, thus allowing for theactivation of the receptor.

Results

Generation of tunneling spectra was completed through the procedure described byTurin26,43 and outlined within the SupplementaryMaterial. This procedure is an adaptation of earlier inelastic tunnelingliterature44,45 and similarly uses arbitrary units (a.u.)for the tunneling intensity. Our spectral procedure was validated by comparison ofthe spectra of the formate ion, which is prevalent throughout experimental andtheoretical literature in IETS43. These a.u. are proportionalto the conductance enhancement, as well as representative of an enhancement to themagnitude of electrostatic charge-dipole interaction an electron experiences duringtunneling. Necessary information for implementing the calculations - outlined in theSupplementary Material - was collected through quantumchemical calculations. Computations were performed using Density Functional Theoryat the 6-311G basis-level, utilizing the B3LYP functional which serves well fororganic hydrocarbons; in contrast to similar previous works26,43.Expanded pseudopotential correlation consistent 5-zeta basis was used for largeatoms where necessary46. DFT was employed both due to its highaccuracy in transition dipole frequencies and due to a desire to avoid encroachingerrors associated with dissimilarities between analyte and parameter molecules insemi-empirical methods. Initial applications of Hartree-Fock theory displayed thecharacteristic 0.8 factor shift to the vibrational frequencies, which is less thandesirable for ease of interpretation of the vibrational spectra. Vibrationalcalculations utilize reduced modal displacements, μ; proportionalto the Cartesian displacement through the modal center-of-mass factor, .This factor arises due to use ofcenter-of-mass coordinates within the classical theory after application of theharmonic approximation during calculations of the normal modes. Natural bond ordercalculations were performed to yield the partial charges, qiattributed to each atom constituting the agonist. Scaled Kronecker delta functionsare plotted at the on-resonance absorbance frequency of the mode; these functionswere convolved with Gaussian functions possessing a conservative FWHM of25 cm−1, representing a very narrow thermaldistribution. The spectral width was introduced to allow for peak additions, while25 cm−1 was selected to avoid overestimations of peak breadth.

Assessment of vibrational bands from the 5-HT2A agonists whichcould facilitate the inelastic transfer of electrons within the protein environmentis of primary import. Agonists of a particular protein would share a single spectralfeature associated with the inelastic transfer, as the same amino acid side-chainswould be responsible for the electron donation and acceptance for a specificprotein. Tunneling spectrum of several selected 5-HT2A agonistshave been generated. LSD, was selected as it possesses a high potency as well asactivity at this particular serotonin receptor within the cortical interneurons47. DOI (2,5-dimethoxy-4-Iodo-amphetamine) was selected due to its highselective for the 2A-subtype receptor48. The remaining selectedmolecules are members of the 2C-X (4-X-2,5-dimethoxyphenethylamine) class ofpsychedelic phenethylamines. All compounds selected are known hallucinogens49,50,51 some first characterized by Alexander Shulgin in thecompendia works PiHKAL and TiHKAL52,53.

Figure 1 shows the tunneling spectra of select agonists (abovethe axis). The selection of candidate peaks, possibly responsible for facilitatinginelastic transfer, was performed using the Spectral Similarity Index (SI), similarto that used for comparison of mass spectra54. The SI was taken overthe entire spectral region and repeated for a scan of the local regions with anoverlapping step of 500 cm−1 with a width of1000 cm−1. The SI is given by:

Figure 1
figure 1

The tunneling spectrum of several known 5-HT2A agonists aswell as the square of the tunneling PDF reflected below the energy axes; thesquare is used to highlight major spectral aspects.

The Spectral Similarity Index of each plot is given in the Supplemental Materials over several ranges and regions, notingthat these similarity indices allude to good spectral agreement with thereference spectrum, LSD. More detailed information is provided within theSupplemental Material.

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Where, within the above equation, N is the normalization constant (thenumerator performed for spectra b and a = b); bi isthe value of the spectra being analyzed at discrete location i while ais a reference spectra. Being the most potent agonist, LSD was selected as thereference spectra for our SI calculations. The SIs, both global and local scans,associated with each of the tunneling spectra can be found within a table providedin the Supplementary Material. To highlight major aspects of thetunneling PDF, we squared the function, exaggerating aspects which exhibit largetunneling amplitudes within the spectra (Figure 1 reflectedbelow energy axis). The only broadly shared spectral aspects were those at1500 cm−1. For a more thorough discussionof the spectral aspects, isotopic effects at functional groups and density of statesfor these systems, please see the provided SupplementaryMaterials.

The integral of the tunneling probability density was taken around the 1500± 35 cm−1 region and compared toknown EC50 data for compounds shown to be agonists of the 5-HT2Areceptor. The EC50 used within this paper is taken from Parrish et al42 who determined the elevated levels of phosphoinositides associated with theactivation of the 5-HT2A receptors of the human A20 cell lineemployed within the experiement across a collection of compounds from thephenethylamine (PEA, or 2C-X) and phenylisopropylamine (PIA, or DOX) classes. Thedetection procedure was replicated from Kurrasch-Orbaugh et al.55.The selection of data used for our comparison is provided within our Supplemental Material. Data was selected from a single source, helping toassure uniformity in both collection and determination, while selecting andcomparing members of specific families of molecules (i.e. PIA/PEAs) helps tominimize drastic changes in their docking configurations which may affect potency.The similarities granted by selecting compounds from families may not allow forsubstantive prediction in the relative potency, beyond docking affinities; this canbe seen by noting that two PIAs, DOI and DOB, have similar docking affinities at the5-HT2A receptor56, while possessing greatdifferences in their potency57.

The effective concentrations of several phenethylamines were taken from42 and compared to the local integrals of the tunneling PDF. Thiscomparison exposes a possible correlation to the inverse of the EC50 data, taken tobe representative of the potency for each species at the receptor. Results for the1500 cm−1 region are shown in Figures 2 and 3 for the DOX class and 2C-Xclass molecules computed, respectively. Figures 2a and 3a give the tunneling spectra for each molecule, Fig. 2b and 3b compare the integral values to theknown EC50s.

Figure 2
figure 2

(a) The tunneling spectra of several DOX class agonists as well as theirmolecular structures. (b) The inverse of the median effective concentration forthe DOX class agonists plotted against the tunneling probability within theregion at 1500 ± 35 cm−1. Thetrend of tunneling intensity follows roughly the trend of theagonist’s potency at the 5-HT2A receptor.

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Figure 3
figure 3

(a) The tunneling spectra of several 2C-X class agonists as well as theirmolecular structures. (b) The inverse of the median effective concentration forthe 2C-X class agonists plotted against the tunneling probability within theregion at 1500 ± 35 cm−1. Thetrend of tunneling intensity follows roughly the trend of theagonist’s potency at the 5-HT2A receptor.

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As inelastic tunneling facilitated by a charge-dipole interaction is a highly localprocess where the interaction potential falls-off as r−3for non-parallel displacements. Modes not local to the electron donor/acceptor siteswill not maximally contribute to the electron transfer, which is proposed to beresponsible for protein activation. Particular modes in 2C-T-2 and in Aleph-2 residewithin the thioether (roughly 5 angstrom from the ring system); due to thenon-locality of these oscillators, tunneling probability should be examined afterhaving removed their contributions from the spectra. Figures2a and 3a present the tunneling spectrum of 2C-T-2and Aleph-2 disregarding these contributions. After correction for non-localmotions, the integrals are in good qualitative agreement with the inverse EC50. Thispreliminary information supports a possible quantum mechanical origin for theactivation of sensory proteins. We shall propose a possible experimental validationof the theory within the following section.

Proposed Experiment

Early findings suggest that both the lake whitefish and the American cockroach canidentify isotopologues of amino acids and pheromones, respectively58,59. Recent experiments have shown that the common fruit flypresents both naive bias to and a potential for trained aversion towards theisotopologues of acetophenone60 and reposte61. Recentworks featuring human subjects have shown that naive participants are incapable ofdiscerning between deuterated acetophenone62; a second study63 presented evidence which suggests human capability at discerningdeuterated variants of musk odorants. Other works have attempted to identify thecharacteristic vibrations associated with particular odors64, yethave not explicitly considered an electron tunneling mechanism. In this spirit, wepropose an experimental procedure for testing this new iteration of the vibrationaltheory of protein activation in vivo.

DAM-57 (N,N-dimethyllysergamide) is an ergot derivative with a mild hallucinogeneffect associated with activity at the 5-HT2A receptor. As itactivates the same receptor, the above discussed candidate peak should and does,appear in the tunneling spectrum of DAM-57. By using isotopologues of a singlecompound, we may minimize any differences which may lead to alterations in eitherdocking geometry or affinity for the activation site. It, however, should be notedthat binding isotope effects and kinetic isotope effects can cause differences inthe potency of compounds, but this effect rarely outstrips 10%65.

Using 1500 cm−1 as a central point, andrecalling the applied FWHM, the modes contributing to inelastic transfer are thoseat 1500 ± 35 cm−1. Modes within thatrange have motions associated with (in order of contribution): stretching of theamide methyl hydrogen; stretching of the phenyl and indole hydrogens; and bending ofthe methyl hydrogen of the tertiary amine.

Deuteration of the three phenyl hydrogens (DAM-57-i) yields a marginal attenuation inintensity near 1500 cm−1 and small change intunneling probability. DAM-57-ii displays a reduction in the3700 cm−1 region, N-H stretch, shiftingweight to 2700 cm−1. Deuteration of the indoleamine results in almost no character change near the active region. Pro-deuterationof a single amide methyl (DAM-57-iii) significantly decreases the tunnelingintensity in the 1500 cm−1 region. Continueddeuteration of the amide system (DAM-57-vi), reduces this peak to roughly one-halfthe pro-protium intensity. DAM-57-vi and DAM-57-v, moiety co-deuteration scenarios,present very small alterations of the peak intensity when compared to DAM-57-iii andDAM-57-vi, respectively.

Within the tunneling model, deuteration of the amide side chains should dampen theactivity of the molecule at the 5-HT2A receptor through a relativereduction in potency. This conclusion is supported by the relative activity betweenDAM-57 and LSD. The flexible ethyl amide of LSD has been found to be essential toits high activity39,40,66,67 and that the methyl analogue(DAM-57) is far less potent; the tunneling probability at the1500 cm−1 region of DAM-57 isdepleted when compared to that of LSD. Following this, a prediction that furtherdepletion of the tunneling probability within this region should continue todiminish the potency at the receptor may be entertained. The intensity of thetunneling spectrum of DAM-57-iv is roughly a third the pro-protium and theprobability density of tunneling is roughly tenthed this implies a possible extremeloss of potency associated with deuteration of the amide side-chains.

Figure 4
figure 4

The tunneling spectrum of several deuterium-isotopologues of DAM-57.

Yellow highlights have been given to the energy region which is assumed to bethe active energy region for inelastic tunneling transfer. Specificdeuterations deplete the tunneling probability within this region and mayeffectively eliminate the agonism of the molecule within the5-HT2A receptor.

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Conclusions

Herein we describe the agonist-protein system by an electron tunneling junctioncoupled to a field of oscillating dipoles, representative of the constituent atomsof the agonist. The oscillator field provides a secondary path for electron transferbetween the donor and acceptor states of the junction. This secondary inelastic pathfacilitates the transfer if and only if the electron can donate a quantum of energyto the oscillator field. Using this method we examined classes of agonists for the5-HT2A receptor and found that all agonist, to varyingdegrees, are capable of facilitating electron transfer within the same energyregion. The degree to which this tunneling is facilitated correlates roughly to thepotency of the agonist within our test cases. We examined the tunnelingcharacteristics of isotopologues of these agonists and predict that it may bepossible to modulate or quench their agonist properties though the isotope exchangeof specific atoms. Also included is a proposed experimental path to test the modeldescribed herein. We conclude that this mechanism is a candidate for the activationstep for some transmembrane proteins and its examination may allow for betterprediction of candidate drug molecules and the possible ability to control agonismof molecules.