Date Published: March 7, 2016
Publisher: Public Library of Science
Author(s): Vahid Salari, Felix Scholkmann, Istvan Bokkon, Farhad Shahbazi, Jack Tuszynski, Steven Barnes.
For several decades the physical mechanism underlying discrete dark noise of photoreceptors in the eye has remained highly controversial and poorly understood. It is known that the Arrhenius equation, which is based on the Boltzmann distribution for thermal activation, can model only a part (e.g. half of the activation energy) of the retinal dark noise experimentally observed for vertebrate rod and cone pigments. Using the Hinshelwood distribution instead of the Boltzmann distribution in the Arrhenius equation has been proposed as a solution to the problem. Here, we show that the using the Hinshelwood distribution does not solve the problem completely. As the discrete components of noise are indistinguishable in shape and duration from those produced by real photon induced photo-isomerization, the retinal discrete dark noise is most likely due to ‘internal photons’ inside cells and not due to thermal activation of visual pigments. Indeed, all living cells exhibit spontaneous ultraweak photon emission (UPE), mainly in the optical wavelength range, i.e., 350–700 nm. We show here that the retinal discrete dark noise has a similar rate as UPE and therefore dark noise is most likely due to spontaneous cellular UPE and not due to thermal activation.
Photoreceptor cells have two components of the dark noise: a continuously low amplitude component (≈ 0.2 pA) and a spontaneous discrete component (≈ 1 pA) . For half a century, the mechanism underlying discrete dark noise of photoreceptors in the eye has remained highly controversial and poorly understood . The main question is: Why is there spiking activity of photoreceptors when there is no photon absorbed by it ? This spiking reduces the sensitivity of vision and is referred as a false signal .
It has to be noted that the application of the Hinshelwood distribution to model one molecule, fH=e-Ea,HkBT∑1m1(m-1)!(Ea,HkBT)m-1 where kB is the Boltzmann constant, is only valid in the classical limit where the thermal energy scale is much larger than the energy level spacing (ϵ) of the quadratic modes of the molecule (i.e. kBT ≫ ϵ). Hence, assuming room temperature at which the thermal energy is about 25 meV, there must exist many modes with much less energies than this value. However, the opposite is true since the resonance Raman excitation of rhodopsin reveals that the Raman lines corresponds to several tens of modes with energies varying from 98–1655 cm−1 (corresponding to ∼ 10–200 meV, respectively) which are in order or larger than the scale of the thermal energy [10–12]. Moreover, Luo et al obtained 45 modes that have equal energy values, kBT (“each vibrational mode of the molecule contributing a nominal energy of kBT”)  in which the 45 modes all are activated and each energy mode has exactly the same energy as the thermal energy. As a conclusion, the equipartition theorem  cannot be applied for these modes; hence the application of the Hinshelwood distribution to model the dark noise of photoreceptors is questionable.
Even if we agree that the Hinshelwood distribution is applicable for photoreceptors then the methodology and the obtained results by Luo et al can be questioned. The rate of change of the term ln k with temperature, ∂ ln k/∂T according to the ‘conventional Arrhenius’ model (i.e. Eq 1) is 
It is claimed that the ratio of rate constants equals to the ratio of their distribution functions , i.e.
Conventional understanding of the human and animal visuals systems holds that the external light signal is transformed into a neural electrical signal by the retina, and then enters into the central nervous system through the optic nerve and produces visual perception. Recent studies have found that UPE may explain some aspects of special visual phenomena [25, 26]. There are two groups of light emissions from biological systems: induced and spontaneous [27, 28]. In the induced light emission there should be an external excitation such as electric filed, light, heat, ultrasound, etc. But the spontaneous light emission does not need any external excitation and it is produced spontaneously due to biochemical reactions in the cells. The spontaneous light is classified into three subgroups: (1) blackbody radiation, (2) bioluminescence and (2) ultraweak photon emission (UPE) [27–29](See Fig 4).
In this paper we have tried to answer to this question that why there is spiking activity of photoreceptors when there is no external photon absorbed by it? We have considered two possible mechanisms for these false alarms in the eye: (1) thermal energy and (2) spontaneous UPE (or biophotons). In the first case, the Arrhenius equation based on the Boltzmann distribution gives the activation energies of discrete dark noise at a level which is around half the energy for activation in vertebrate rod and cone pigments. Thus, there is a serious inconsistency between the apparent energy barriers of thermal events compared with those found in the photon-driven process. Recently, Luo et al.  claimed that they have solved this problem by using the Hinshelwood distribution instead the Boltzmann distribution in the Arrhenius equation to give the correct amount of activation energy. Their approach was also supported by Gozem et al.  by proposing a molecular mechanism for thermal activation. In this paper, we have shown that a careful reanalysis of the methodology and results based on the Hinshelwood distribution puts these claims in doubt. We briefly explain the main problems toward the thermal activation approach as follow: