A Time-Dependent Quantum Approach to Allostery and a Comparison With Light-Harvesting in Photosynthetic Phenomenon

Abstract

The allosteric effect is one of the most important processes in regulating the function of proteins, and the elucidation of this phenomenon plays a significant role in understanding emergent behaviors in biological regulation. In this process, a perturbation, generated by a ligand in a part of the macromolecule (the allosteric site), moves along this system and reaches a specific (active) site, dozens of Ångströms away, with a great efficiency. The dynamics of this perturbation in the macromolecule can model precisely the allosteric process. In this article, we will be studying the general characteristics of allostery, using a time-dependent quantum approach to obtain rules that apply to this kind of process. Considering the perturbation as a wave that moves within the molecular system, we will characterize the allosteric process with three of the properties of this wave in the active site: (1) t a , the characteristic time for reaching that site, (2) A a , the amplitude of the wave in this site, and (3) B a , its corresponding spectral broadening. These three parameters, together with the process mechanism and the perturbation efficiency in the process, can describe the phenomenon. One of the main purposes of this paper is to link the parameters t a , A a , and B a and the perturbation efficiency to the characteristics of the system. There is another fundamental process for life that has some characteristics similar to allostery: the light-harvesting (LH) process in photosynthesis. Here, as in allostery, two distant macromolecular sites are involvedtwo sites dozens of Ångströms away. In both processes, it is particularly important that the perturbation is distributed efficiently without dissipating in the infinite degrees of freedom within the macromolecule. The importance of considering quantum effects in the LH process is well documented in literature, and the quantum coherences are experimentally proven by time-dependent spectroscopic techniques. Given the existing similarities between these two processes in macromolecules, in this work, we suggest using Quantum Mechanics (QM) to study allostery.

An intrinsic temporal dimension of DNA: the new concept of time-island

“…1. The first is that, since the base-pairs are weakly coupled, the propagation time of the perturbation increases and this time grows almost linearly as a function of the number of replicas present, as we have seen in Villani [62]. It would seem, therefore, that this system could be a good way to have a lengthening of the characteristic time of the process and to obtain times similar to the biological ones.…”

“…(a) When the number of equal islands, and therefore degenerate, becomes large (hundreds of time-islands), the amount of perturbation transferred slowly decreases, as we have seen in Villani [62] in the propagation of a perturbation between equal sites.…”

“…2. In reality, a second aspect must be considered: in addition to the time of arrival at the final site, the amount of perturbation that reaches this site is also important, as we have seen in Villani [62]. In this case, we have seen that, even if the chain is composed of all equal sites, its elongation would correspond to a reduction in the amount of perturbation that would arrive at the final site, a reduction which practically cancels the propagation of the perturbation and distributes it uniformly over the whole system.…”

“…We believe that the dynamics in the picosecond and nanosecond scale, however, could be related to specific groups of base-pairs. In a recent article on the allosteric effect in proteins [62], we highlighted that a set of nodes and ridges that describe and model a macromolecule determine channels along which a perturbation can move coherently, initially located in an area of the macromolecule. In that article, we also showed that the coherent movement of a perturbation in a macromolecule must be treated with Quantum Mechanics (QM).…”

“…In this work, we want to extend to DNA the temporal and quantum aspect of the movement of a perturbation in a macromolecule as developed in my previous work on the allosteric effect in proteins [62]. In particular, in this case, we have three specificities:…”