The Arg/Lys NH3 energy amplifier

Wilson P. Ralston. (1/27/2022)

This is the amplification by NH3 inversion resonance developed in my 2005 book "Electron-gated ion channels: With Amplification by NH3 Inversion Resonance". The amplification is created by inverting NH3 sites attached to carbon at the end of the long (6-7Å) arginine or lysine amino acid side chains. Proof for C-NH3 inversion is provided by the recorded microwave spectrum in the 11-20 GHz range (Fig. 3, BFP microwave spectra and in 2005 book Fig. 10-2.).
The C-NH3 amplifiers make biological life possible by reducing the Boltzmann thermal noise (kT) by 23-24 fold. This reduction equals the C-NH3 amplifier gain.
The 2nd law of thermodynamics with Boltzmann's entropy equation (1872) imposes a detection limit on chemical and biological signaling systems including ion channels, but a C-NH3 amplifier using quantum-mechanical electron transitions reduce noise temperature and entropy by an amount given by the amplifier's gain (hE). Electron tunneling between Arg/Lys inverting C-NH3 groups provide a low-noise world for ion channels. The low noise increases the dynamic range for signaling (Fig. 3-2.D) making possible sodium and calcium oscillators (Fig. 8-5. 2005 book). The essential physics is the quantum-mechanical amplifying system (Fig. 2-1.). It reduces noise temperature down to 13K. The reduced noise increases sensitivity to small changes in an electric field or a potential v across two adjacent tunneling sites by hw or by the factor hE for energy.
The 2nd law of thermodynamics is violated by the noise reduction, because it reduces entropy. Entropy reduction is the key that makes our world possible; ion channels require entropy reduction to function. A mathematical proof for noise and entropy reduction is developed in Ch. 3 of Electron-gated ion channels (2005). The proof concludes with Eq. 3.23 and Eq. 3.24 showing that energy, entropy and noise are reduced by amplification hw. Fig. 3-2.A. shows a curve of amplification hw increasing to 23.3 with displacement energy and noise decreasing until the noise temperature is 13K.
The energy range extends from 1.6 meV (13K) to 37.3 meV (310K) and then (with hE=1) from 37.3 to 83 meV. The dynamic range is 23.5×83/37.3= 52. The energy allocation is shown in Fig. 3-2. D. Energy values are from Fig. 2-1. A.
The inversion resonance peak near 16.5 GHz in the recorded BFP microwave spectra results from infrared vibrations in potential energy v2 (Fig. 2-1. A). The C-NH3 v2 has a center resonance at 670 cm-1. This is the NH3 gas phase 950 cm-1 peak scaled down by 0.705 due to Multiphase C-NH3 bonding (Fig. 2-1. C). Converting the v2 vibration to energy gives E1 = 83.1 meV (Fig. 2-1. A).

Fig.3-2. Amplification energy allocation
The curves in Fig. 3-2. A. to C. are for electron tunneling between two adjacent arginine sites. They are analyzed in Sect. 3-5 (2005 book).
In Fig. 3-2. D there are two regions of energy gain; an amplifying region where energy, entropy and noise decrease (hwEd), and a non-amplifying region (EA). The sum of the two energies gives the peak energy E1 for electron tunneling. Fig. 3-2. D. shows the energy allocation based on the ammonia C-NH3 amplifier energies (Fig. 2-1 A & B).

Fig.2-1. The ammonia amplifier

Fig. 2-1. The C-NH3 amplifier system. Amplification and resonances are generated by inversion vibrations in potential energy of v2. The C-NH3 v2 has a center resonance at 670 cm-1. This is the NH3 gas phase 950 cm-1 infrared peak scaled down by 0.705 due to arginine or lysine C-NH3 and its 2/3 binding energy. For ion channels the Fig. 2-1. potential energy curve has a amplification energy bandwidth window given by ΔE1+ΔE0 and amplification energy gain: hE=(ΔE1+E0)/2ΔE0) =23.3. Amplifier energy gain is defined by the quantum transitions between ΔE1 and ΔE0. Additional gain EA (Fig. 3-2. D) increases the amplitude of energy pulses for electron tunneling.

  Fig.2-1D ground state energy

The above analysis is similar to Fig. 9-2. of The Feynman Lectures on Physics Vol. III., except this only considers the ground state energy. The above Eqs. 2.2 and 2.3 were used to plot curves for Fig. 2.1.D. The blue curves with exponent n =0 are like Fig. 9-2. The red curves are for n =2. They have amplification hE determined by the quantum transitions between ΔE1 and ΔE0.

Fig.4-6 amplification window

Key early history of NH3 inversion
The inversion of NH3 in the gas phase has been extensively studied since the first theoretical model was described by Dennison and Uhlenbeck (1932) Phys. Rev., 41, 213. The NH3 spectrum was recorded by Cleeton and Williams (1934) Phys. Rev. 45, 234. It had a single broad peak; the peak was broad due to collisions with air molecules. The technology rapidly advanced and by the 1940's the hyperfine structure of ammonia at reduced gas pressure was analyzed using absorption spectroscopy.