Emergence of molecular chirality due to chiral interactions in a biological environment

Abstract

We explore the interplay between tunneling process and chiral interactions in the discrimination of chiral states for an ensemble of molecules in a biological environment. Each molecule is described by an asymmetric double-well potential and the environment is modeled as a bath of harmonic oscillators. We carefully analyze different time-scales appearing in the resulting master equation at both weak-and strong-coupling limits. The corresponding results are accompanied by a set of coupled differential equations characterizing optical activity of the molecules. We show that, at the weak-coupling limit, chiral interactions prohibit the coherent racemization induced by decoherence effects and thus preserve the initial chiral state. At the strong-coupling limit, considering the memory effects of the environment, Markovian behavior is observed at long times.

Validity Examination of the Dissipative Quantum Model of Olfaction

“…The simplest model arises when the odorant is treated as a point dipole inside a uniform and spherical protein surrounded by a uniform polar solvent. For a Debye solvent and a protein with a static dielectric constant, the spectral density is Ohmic with Drude-form cut-off as refs 39 and 40 with and where b is the radius of the protein containing the odorant, Δ μ is the difference between the dipole moment of the odorant in the ground and excited states, is the dielectric constant of the protein environment, and are the static and high-frequency dielectric constants of the solvent, and λ D is the Debye relaxation frequency of the solvent. For an odorant in the aqueous environment, we have and .…”

“…For a molecule confined in the double-well potential, we have shown that if the chiral interactions induced by a condensed biological environment are strong enough they can suppress the tunneling process and freeze the molecule in its initial state (see Fig. 7 ) 40 , 47 .

Figure 7 The dynamics of the right-handed state of the open chiral molecule in the aqueous bath at fixed tunneling frequency ω x = 10 −3 for ω z = 10 −5 (blue), ω z = 10 −4 (orange) and ω z = 10 −3 (green).

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“…The most common biological environment is water. The parameters of an aqueous environment can be estimated as J 0 ≈ 1 and λ ≈ 10 12 Hz [38,39]. Odorant Analysis We examine the ET rates for different odorants in terms of their molecular parameters, ω x and ω z .…”

Perturbative treatment of quantum to classical transition in chiral molecules: dilute phase versus condensed phase

“…As Harris and Stodolsky demonstrated, the relevant dynamics of chiral states samples the velocity distribution of the gas molecules, which is strongly temperature-dependent [21,22]. Starting from a microscopic model of the collisions with the gas particles, we derive the spectral density (32) where X(t) is the interaction-picture position operator of the environmental particles. Note that for simplicity we drop all normalization factors expressed by 2π.…”

“…The position operator of the environmental particles can be expanded as [45] X = d 3 r a(r)ρ E (r) (33) where a(r) is the interaction function and ρE (r) is the difference between the gas density operator ρ E (r) and its time-averaged value, assumed to be the uniform gas density ρ. If we substitute (33) in (32), we have…”