The participation of the DNA-coding protons1 in genetic stability2,3 is an essential topic in molecular biology. Recent experiments investigating the collective dynamics of the microscopic components in human blood4,5,6 and plant cells7 have provided the entropy, spectral signature, and Lyapunov exponent of a dynamic system from a univariate time series near the organism's optimum life temperature. It was observed that an increase/decrease in the inverse temperature above/below the critical value causes the appearance of phase transitions in a system8. Here, we show that thermal excitation in a living cell system occurs in this dissipative environment9,10 as a collective molecular response11, dynamic H+-H+ quasi-particle formation12. A non-equilibrium phase transition and a condensate phase were obtained at ~ 36oC, which was interpreted as an H+-H+ quasi-particle decay into two separate H+ ions of the opposite momenta and spins at critical temperature and magnetic field. Based on the empirical results, we reconsidered the canonical and tautomeric mutations within the quantum physics (open systems) two-fluid model13,14. It was found that the concentration ratio between the canonical and tautomeric base pairs differs at and beyond criticality, respectively. The deviation of a cell (ion) system from a specific temperature, at which entropy has a minimum15 and critical pH occurs16, could be a source of the point mutations that lead to tautomerization.
Although much theoretical effort and experimentation have been devoted to its study, the dynamics of living systems remain a mystery. In a series of recent works, however, researchers have observed the collective dynamics11 of the microscopic components in a non-equilibrium phase transition in human blood5,6 and pollen tube cells of living plants4,7. These living systems can exhibit the non-classical correlation pattern that is typical of quantum systems under certain thermal conditions. Hence, the question arises about the physical nature of this collective dynamic of its ionic environment. Here, we show that the thermal excitation in a living cell system occurs in this dissipative environment9 as a collective molecular response (quasi-particles formation), which is also present in higher plants17. A coherent polarization wave occurs as spike-like peaks, which produce a long-range correlation among the electrical dipoles11 and a superfluid or super-diffusive behavior. Under a slow temperature change, the bifurcation point on the current-voltage characteristic appears at the critical temperature Tc = 36.6 oC, thus showing the cumulative dynamics in two branches at the magnetic field B > Bc = 350 mT. These two branches disappear once again when a constant magnetic field of more than 500 mT is applied. Amazingly, not only is this critical temperature molecularly encoded by the cellular system of interacting ions, but it is also the individually variable temperature of homeostasis5,6 as well as of germination and optimum growth4,7 for humans and plants, respectively.
Recently, it was found2 that proton transfer through quantum tunneling might play a more critical role in DNA mutation than has hitherto been suggested, even at room temperature. This observation and a quantum calculation of the excitation energy transfer coupling between all of the pairs of chlorophylls that are performed for photosystem II in light-harvesting complexes18 confirmed the expectations3 of the role of quantum mechanics in specific (fine-tuning) processes in biology, even at room temperature.
In this work, we consider the participation of the protons in living blood in near homeostatic conditions. Recent experiments, in which we investigated the dynamic ion properties of human blood, provided a time series of an electromotive force (EMF) near an (individually variable) organism's optimum life temperature. Consequently, this data yielded magnitudes such as entropy, power spectral density, and the maximum Lyapunov exponent of a dynamic system from a univariate time series. Here, the EMF (voltage, U) and electric current (I) were measured in noninvasive experiments, whereas inferences are made only on those raw data that are not affected by the information theory methods. We confirmed a non-equilibrium phase transition and a condensate phase at a critical temperature. The latter was interpreted as the H+-H+ (a dynamic "Cooper pair" in the momentum space) quasi-particle decay into two separate H+ ions of the opposite momenta (moving forward and backward in time) and spins at the bifurcation temperature and critical magnetic field.
Bose-Einstein condensation (BEC) is the macroscopic accumulation of particles in the ground state at low temperatures and high density. It consists in creating a collective quantum state that is composed of identical particles. For a long time, the only physical systems in which the BEC effect was observed were superfluid systems and superconductors19. Research on living biological cells at temperatures close to living temperatures has shown the possibility of a dynamic (i.e., derived from a time series) equivalent of the superfluid phenomenon in the vicinity of a non-equilibrium phase transition5,6 (see also Ref. 16). The time series (a series of numbers), which was examined with dynamic metrics, showed a significant change in its character in the area of the phase transition and beyond it. It enabled, among others, the temperature of the non-equilibrium phase transition to be determined, which in the case of an isolated human blood sample was approximately 36.6 degrees Celsius (individually variable); molecular coding supports this characteristic temperature in the system of the examined blood cells. A similar finding concerned plant cell systems (pollen tubes), but there were two characteristic temperatures: germination and optimum growth4,7. However, the molecular mechanism behind this phenomenon is unknown.
While previous studies have used some global variables such as time-series entropy and the dominant Lyapunov exponent as a function of system temperature, in this article, we show the usual current vs. voltage (I-V) waveforms that were generated by the system being studied. This strategy enabled the measurements to be presented without the accompanying number-crunching calculations and, thus, without the preliminary interpretation of data using complex numerical algorithms5,6. Nevertheless, we suggest that the system being studied is the dynamic counterpart of the Bose system in living matter (dynamic 2H+ quasi-particle condensate formation occur) and that the system condenses in this non-equilibrium phase transition, thereby revealing the correlated collective dynamics at criticality. Moreover, we also attempted to interpret our results within the context of bound fermions similar to those presented in Figs. 1–2 in Ref. 20 or Fig. 2 in Ref. 21.
In what follows, we use a two-fluid model, such as the one used in superfluidity, but for single protons (the effective mass of the charge carriers is of the order of 2 × 103 me, i.e., proton mass)5 and the pairs of protons coexisting at the critical temperature and critical pH. In terms of the motion of elementary excitations, Landau's interpretation13 of the two-fluid model of liquid helium can be extended to provide the basis for a two-fluid model for superconductivity22. We also took the Slocombe et al.2 result on proton tunneling in the proton exchange between the nucleotide base pairs in DNA at room temperature as a given. Moreover, the low energy quantum tunneling of Cooper pairs as bosonic particles23 can explain our experiments in which a zero bias peak was observed, which is in agreement with the profound minimum in the dynamic entropy15. Therefore, we hypothesized whether the ratio of the single protons (changing the level of the chemical potential, and hence, the pH of a system) to the paired protons (do not participate in pH-level) in the condensate might be responsible for the normal (canonical) and abnormal (tautomeric) mutations. [According to the definition, pH = pH(µH+(T),T) is considered to be a function of the chemical potential of the H+ (hydronium) ions (µH+), as well as an implicit and explicit function of temperature].
Finally, in this context, we considered the problem of the canonical and tautomeric mutagenesis. This issue remains unresolved, although it is a central problem of genetics as well as an essential subject of molecular biology. However, a change of perspective or deepening of the level is usually required in order to find the appropriate solution; in other words, a metalanguage is required. Here, we provide a qualitative solution that is based on the open quantum systems approach. Our proposal is falsifiable and can be verified by researchers.