Ethene polarization and neuromolecular computing

required to close the channel pore the system is at the threshold value. Following cessation of ion movement and concomitant neutralization of membrane ethenes, the channel protein relaxes to the a-helix conformation which restores hydro- phobic matching Leuchtag, 1994. In this man- ner, microdomain dynamics regulate the duration of channel opening, a model consistent with in vitro experimental manipulation of ion channel activity by variations in concentration of unsatu- rated membrane lipids Vreugdenhil et al., 1996. We describe the above process in terms of biomolecular computing Wallace and Price, 1999, i.e. as a mechanism by which the frequency coding of classical neural networks is regulated by molecular minimum potential energy searches Conrad, 1992. Finally, we propose experiments involving Raman and fluorescence resonance en- ergy transfer FRET spectroscopy as a means of investigating the above features in a liposomal system.

2. Computational modeling of membrane ethene system stability and polarization

2 . 1 . Rationale Our primary objective was to construct a com- putational model of ethene polarization. We in- vestigated dipole and quadrupole moments, and polarizability in the adjacent double bonds of a monomer, dimer, and trimer. The electrical per- manent moments dipole, quadrupole represent derivatives of the energy E with respect to the applied electric field vector E a . Specifically, dipole moment is given as − dEdE a and quadrupole moment is given as 1 2 d 2 EdE a . Similarly, polariz- ability is given as − d 2 EdE a 2 and varies with the oscillation of an applied electric field Dykstra, 1997. This latter feature is consistent with the complex, interacting fields with time-dependent variation in strength that are encountered in actual membranes. The use of a polymer model stabilized by methylene linkages was justified by computational pragmatics. When ab initio meth- ods are applied to disconnected model compo- nents, radical changes in system geometry frequently result. We further wished to demon- strate that systematically increasing the number of aligned ethenes would produce a dramatic in- crease in the observed polarization. 2 . 2 . Method Calculations were performed on an ethene monomer, dimer, and trimer using Hyperchem v. 4.5 Hypercube Inc., 1995 and Gaussian 95 W Frisch et al., 1995. The latter two components were stabilized by methylene linkages Fig. 2. The 4-31G basis set was used to optimize all structures. Dipole and quadrupole moments and polarizability values were then calculated on the optimized system using the same basis set. 2 . 3 . Results Sensitivity of the aligned ethenes to an applied electric field was indicated by our analysis of dipole and quadrupole moments, and polarizabil- ity Table 1. Proceeding from the ethene monomer to the trimer, total dipole moment in- creases from 0.0000 to 0.6538 Debye. Examina- tion of the quadrupole moments reveals a consistent 5-fold increase in the axial moments i.e. xx, yy, zz from monomer to trimer. These cumulative increases suggest a progressive mobi- lization of p electrons. Pronounced fluctuation of the p electronic structure in the applied field is indicated by component increases in polarizability from monomer to trimer a xx from 7.672 to 93.644, a yy from 19.226 to 125.284, a zz from 30.875 to 91.345 J − 1 C 2 m 2 . These increases in turn produced an increase in mean polarizability Ža from 19.258 to 103.424 [where Ža = a xx + a yy + a zz 3]. Together these results indicate an overall increase in the stability of the aligned ethenes, as well as a pronounced increase in the mobilized electron polarizability.

3. Ethene polarization and neuromolecular computing

In our opinion, the polarization of neural-mem- brane ethenes is a fundamental structural feature Fig. 2. Structures of ethene model compounds used in ab initio calculations of dipole and quadrupole moments, and polarizability. of a biomolecular computing system Conrad, 1984, 1989, 1992; Wallace, 1996; Wallace and Price, 1999. Although these systems are believed to operate on quantum-mechanical QM princi- ples, it may actually be somewhat misleading al- though technically accurate to refer to them as ‘quantum computers’. The latter term, coined by Feynman 1982 originally referred to a device, which utilized quantum mechanics to simulate a QM system. More exactly, Feynman argued that the feature of linear superposition, in which the values of an observable e.g. spin, position, en- ergy exist simultaneously in many dimensional Hilbert space, could be the basis for massively parallel computations. Such parallelism, he ar- gued, would make it possible to solve the ordinar- ily intractable exponential problem i.e. of the form H D N = X N where H D is computational steps, N is problem size and X is a real number of describing a large QM system within a realistic polynomial time frame i.e. in the form H D N = N X Garey and Johnson, 1979. Based on Feynman’s model, a number of candidate sys- tems are currently being proposed Deutsch, 1985; Deutsch and Jozsa, 1992; Bennett, 1995; Lloyd, 1993. Almost all of these, however, are based on Turing-machine theory also widely utilized in MP neural-network modeling in which informa- tion is encoded as a binary system of 0 and 1 s. Accordingly, the models emphasize the experi- mental manipulation of two-valued QM systems e.g. the spin states of an electron , ¡ which are construed as a superposition of 1 and 0, respectively. Unlike these devices, however, the biomolecular computers that may exist in living systems, following 3.5 billion years of cellular evolution, utilize superposition of many-valued QM observables e.g. position interacting in an ensemble search for a minimum local energy value. The difference is important because the molecular search process is under thermodynamic constraints, which permit open-system mapping from classical input to QM state changes to threshold value to classical output Conrad, 1989; Wallace et al., 1998. In this regard, biomolecular computers based on ensemble molecular searches are conceptually distinctive even from recent ar- tificial approaches that superficially resemble them such as nuclear magnetic manipulation of molecular nuclei in a liquid Gershenfeld and Chuang, 1997. The distinction raises the ques- tion; which features of the neural membrane would exemplify open-system mapping? We sug- gest that the following model identifies the key architectural elements. We begin with a picture of a membrane region in which the constituent molecules are in the liquid phase. Contrary to the earlier models Singer and Nicolson, 1972; Churchland and Se- jnowski, 1992 this phase is not entirely ‘pattern- less’. Lateral movements of molecules within the region do indeed occur Alfsen, 1989; Zachowski, 1993 but are thermodynamically constrained by lipid-protein hydrophobic matching Sperotto and Mouritsen, 1993; Lehtonen et al., 1996; Lehtonen and Kinnunen, 1997; Killian, 1998. Moreover, the cholesterol molecule induces close interaction between membrane phospholipids, and especially between the hydrocarbon ethenes Hyslop et al., 1990; Raffy and Teissie´, 1999. This dynamic equilibrium is disturbed by external inputs. Two physical forms of inputs are neurotransmitter binding with an ion-channel receptor, and an electromagnetic field applied at or above a threshold level to an ion-channel-associated polypeptide voltage sensor Catterall, 1988; Jan and Jan, 1989; Stuhmer et al., 1989; Hall, 1992. Response to the external input is instantiated as protein conformational change from the a-helix to random coil open channel followed by a mini- mum local potential energy search of lipid and protein molecules comprising the microdomain lipid selectivity Mouritsen and Bloom, 1993; Horvath et al., 1995; Mouritsen, 1998; Sabra and Mouritsen, 1998. Given the probabilistic struc- ture of the lipid and protein molecular hypersur- faces, successive instances of the ensemble search will utilize different pathways and will lose or recruit lipids from neighboring microdomains. Thus changes in interactions and elements exist within the system. The search process term- inates at threshold value; i.e. when the difference Table 1 Calculated moments and polarizabilities of ethene model compounds a Dipole moment Debye Ethene X = 0.0000 Y = 0.0000 Z = 0.0000 Total = 0.0000 Ethene dimer X = −0.0001 Y = −0.5306 Z = 0.0794 Total = 0.5365 X = 0.0005 Y = −0.6531 Ethene trimer Z = −0.0306 Total = 0.6538 Quadrupole moment Debye-A , XX = −15.1785 YY = −12.1966 Ethene ZZ = −11.9487 Ethene dimer XX = −48.4728 YY = −43.6183 ZZ = −42.6662 Ethene trimer XX = −75.6495 YY = −67.8488 ZZ = −67.3202 Polarizability J − 1 C 2 m 2 Ethene a xx = 7.672 a yy = 19.226 a zz = 30.875 Ža = 19.258 a xx = 54.029 a yy = 84.076 a zz = 62.289 Ža = 66.798 Ethene dimer a xx = 93.644 a yy = 125.284 a zz = 91.345 Ža = 103.424 Ethene trimer a Geometries of model compounds were optimized using the 4-31G basis set. Polarizabilities were obtained by performing frequency calculations on geometry optimized structures using the same basis set. The mean polarizability, Ža = a xx +a yy +a zz 3. E c − E m =d MIN see Section 1. A candidate phys- ical mechanism for d MIN is the specific potential energy difference between the membrane mi- crodomain and the ion-channel protein required to thermodynamically constrain the protein to the lower-potential-energy a -helix conformation closed state. In this manner, the duration of the channel open state, and thus, neuron spike fre- quency macroscopic output are directly regu- lated by the molecular-ensemble search. Clearly, the search could be prolonged or varied by spa- tial-temporal variation in ion-channel gatings fol- lowing the initial perturbation input. The implications of the latter property will be dis- cussed in Section 4.

4. Potential experiments