Neuroreceptor Activation by Vibration-Assisted Tunneling

G protein-coupled receptors (GPCRs) constitute a large family of receptor proteins that sense molecular signals on the exterior of a cell and activate signal transduction pathways within the cell. Modeling how an agonist activates such a receptor is fundamental for an understanding of a wide variety of physiological processes and it is of tremendous value for pharmacology and drug design. Inelastic electron tunneling spectroscopy (IETS) has been proposed as a model for the mechanism by which olfactory GPCRs are activated by a bound agonist. We apply this hyothesis to GPCRs within the mammalian nervous system using quantum chemical modeling. We found that non-endogenous agonists of the serotonin receptor share a particular IET spectral aspect both amongst each other and with the serotonin molecule: a peak whose intensity scales with the known agonist potencies. We propose an experiential validation of this model by utilizing lysergic acid dimethylamide (DAM-57), an ergot derivative, and its deuterated isotopologues; we also provide theoretical predictions for comparison to experiment. If validated our theory may provide new avenues for guided drug design and elevate methods of in silico potency/activity prediction.


I. TUNNELING THEORY
Inelastic Electron Tunneling Spectroscopy is a well-founded experimental method utilizing a simplistic laboratory set-up that can deliver the vibrational spectra of an analyte. The mechanism of action is semi-classical and not optical, particular selection rules are derivable with IETS 1 but in general this method allows for forbidden transitions, thus all vibrational modes are addressable 2 . The method is implemented by the application of a potential across a two-plate junction with a spatial separation between the plates. High energy electrons from the valence band of one plate will tunnel across the junction into the conduction band of the other. When the tunneling process occurs in the absence of analyte molecules, the process is elastic in nature and electron energy is maintained throughout the process, thus the electrons energy must be respective of the energy between the valence and conductance band.
FIG. 1: Cartoon displaying the competing processes during IETS where V is potential energy and F e is the Fermi Level. Path A is radiative 1,3 , requiring the tunneling electron to spontaneously lose energy to meet the energy of the conductive band.
Path B shows the electron losing energy via a non-radiative process; it is implicit that the energy lost is to a normal mode of a deposited molecule within the gapsuch is our case.
Depositing an analyte molecule onto the electron source plate, as the tunneling electrons enter the gap they may interact with the deposited analyte molecules; in doing so they are effectively given a springboard, shortening their tunneling path.
This interaction comes at a cost of energy; the electron will lose energy to the analyte molecule, where the amount of lost energy is equal to that of a vibrational mode of the molecule. This process may be seen in Figure 1. This method has been well described theoretically 4-6 and expanded to include such considerations as molecular orientation 7 and short-ranged higher harmonics 8 . Here we shall review the theoretical description of the elastic process a seen in 9,10 . It is a fair starting assumption that the wave function is oscillatory in the x-and y-directions and evanescent in the z-direction. In this manner the decay constant for such a function is spatially dependent and thus the function is anisotropic; the wave functions used were described through WKB theory and are provided here: From the above it should be noted that L is the dimension of the square plate. Z e is the partial charge associated with a molecular mode with displacement R, and d is the distance between the two plates.
We shall use the wave functions in Eq. 1 to attain the average value of the current for the system, via the current operator, M e . The elastic process yields: where q is the difference between k || and k || . The inelastic process for a single specified normal mode is governed by the following interaction potential: where all symbols retain their standard definitions, including r being the permittivity of the generic real media, r and R are made clear by Figure 2 and u is the vector representing the displacement of the atom within the molecule with partial charge Z e . This potential allows us to calculate the inelastic contributions in a manner similarly to the above: Where the integral in Equation 5 can be performed analytically for cases where the vector directions of u are either parallel or perpendicular to the plate surfaces. For u along the z direction (parallel to gap): and for u parallel to the plates: Where, in both the above, the quantity M 0 is given by: 5 The decay constants for each of ψ i and ψ f should conform with the statement: where E is the energy of the tunneling electron, E c is the energy of the conductive band and m is the mass of the electron (effective mass is typically used). The above yields two unique decay constants consistent with the difference in electron energies at the conduction band and during tunneling. With these two unique decay constants we must append a factor of to our matrix elements due to the difference in α's. Carrying this factor through we note there is a depletion of tunneling probability equivalent to: and finally placing this into an expression for the relative conductivities associated with the inelastic and elastic processes, ∆σ σe , and finally including a 2-D density of states representative of the plate surface areas: The above allows us to make the statement: as those quantities on the R.H.S. of Eq. 12 are the only quantities dependent on molecular characteristics and thus are featured in Eq. 13. As the elastic tunneling process occurs with or without the presence of the analyte molecules, the experimental observable is the ratio between the known elastic contribution, σ e = M 2 e , to the current at a given applied potential (found through a zeroing process with a non-deposited gap) and the deposited gap current at the same potential; this ratio quantity is denoted as ∆σ σe . Armed with the above, the IETS intensity for a given active mode j can be approximated by 6,11 : where the sum is over all atoms within the molecule, q i is the partial charge of atom i, and ∆x i,j is the Cartesian displacement of atom i in mode j.

II. DISCUSSION OF TUNNELING SPECTRAL ASPECTS
An examination of the edrogenous agonist 5-HT is given in Figure 3. The main spectral features are (quantities are in cm −1 ): the OH stretch at 3700; NH 2 bend at 1700; coherent ring motions appear at both 1500 and 1150; and indole bending at 530. For reasons discussed below, we will focus our discussion on tunneling in the 1500 cm −1 region. Working within Turins theory, this implies that these motions assist in the turnneling and that the tunneling source and sink are in proximity to these motions. Docking studies of homology modeled 5-HT 2A show that the moieties discussed above are local to F339, F340, S159 and L229 residues 12-15 , alluding that one of these residues may facilitate the tunneling process. The spectral indices are given for the overall spectrum and followed by regional  Table II In the next few sections we have selected DOC (2,5-dimethoxy-4-C-amphetamines) as a prototypical molecule for discussion, this selection was based on its fairly tractable number of modes, simple geometry, symmetry and similarities to other agonists. Energy regions associated with an assisted electron transfer would bene- procedure was applied to the total spectra, and several sections of 1000cm −1 which march with an overlaping pattern and shifted by 500cm −1 . The region of interest is also performed with a calculated SI for the region of 1500±100 cm−1 fit from a large density of vibrational states; implying a greater number of possible states to interact with in this energy range. Figure 4 shows both the IETS and scaled density of states for DOC; the spectral feature at 1500cm −1 exhibits an enhanced number of vibrational states.  In the main body of the paper we propose an isotopolgue series for DAM-57; the series is of variants are dueterated functional groups altering the character in the 1500cm −1 region. We verified that isotopologues of other atoms do not to alter tunneling character in this region. Figure 5 shows the isotope effects within several groups of the molecule. Fig. 5 a) shows the effects of replacing the oxygens with 18 O's, this results in little alteration near 1500cm −1 ; substitution of the halide has similar results, with differences appearing at much lower energies. Fig. 5 b) displays the effects of dueterating the hydrogens on the methoxys, this show a large attenuation of the tunneling intensity; finally, Fig. 5 c) shows the effect of selectively dueterating different functional groups.