We build on our earlier quantum wavepacket study of hydrogen transfer in the biological enzyme, soybean lipoxygenase-1, by using von Neumann quantum measurement theory to gain qualitative insights into the transfer event. We treat the enzyme active site as a measurement device which acts on the tunneling hydrogen nucleus via the potential it exerts at each configuration. A series of changing active site geometries during the tunneling process effects a sequential projection of the initial, reactant state onto the final, product state. We study this process using several different kinds of von Neumann measurements and show how a discrete sequence of such measurements not only progressively increases the projection of the hydrogen nuclear wavepacket onto the product side but also favors proton over deuteron transfer. Several qualitative features of the hydrogen tunneling problem found in wavepacket dynamics studies are also recovered here. These include the shift in the "transition state" towards the reactant as a result of nuclear quantization, greater participation of excited states in the case of deuterium, and presence of critical points along the reaction coordinate that facilitate hydrogen and deuterium transfer and coincide with surface crossings. To further "tailor" the dynamics, we construct a perturbation to the sequence of measurements, that is a perturbation to the dynamical sequence of active site geometry evolution, which leads us to insight on the existence of sensitive regions of the reaction profile where subtle changes to the dynamics of the active site can have an effect on the hydrogen and deuterium transfer process.
We build on our earlier quantum wavepacket study of hydrogen transfer in the biological enzyme, soybean lipoxygenase-1, by using von Neumann quantum measurement theory to gain qualitative insights into the transfer event. We treat the enzyme active site as a measurement device which acts on the tunneling hydrogen nucleus via the potential it exerts at each configuration. A series of changing active site geometries during the tunneling process effects a sequential projection of the initial, reactant state onto the final, product state. We study this process using several different kinds of von Neumann measurements and show how a discrete sequence of such measurements not only progressively increases the projection of the hydrogen nuclear wavepacket onto the product side but also favors proton over deuteron transfer. Several qualitative features of the hydrogen tunneling problem found in wavepacket dynamics studies are also recovered here. These include the shift in the "transition state" towards the reactant as a result of nuclear quantization, greater participation of excited states in the case of deuterium, and presence of critical points along the reaction coordinate that facilitate hydrogen and deuterium transfer and coincide with surface crossings. To further "tailor" the dynamics, we construct a perturbation to the sequence of measurements, that is a perturbation to the dynamical sequence of active site geometry evolution, which leads us to insight on the existence of sensitive regions of the reaction profile where subtle changes to the dynamics of the active site can have an effect on the hydrogen and deuterium transfer process.
Abstract The role of proton tunnelling in biological catalysis is investigated here within the frameworks of quantum information theory and thermodynamics. We consider the quantum correlations generated through two hydrogen bonds between a substrate and a prototypical enzyme that first catalyses the tautomerization of the substrate to move on to a subsequent catalysis, and discuss how the enzyme can derive its catalytic potency from these correlations. In particular, we show that classical changes induced in the binding site of the enzyme spreads the quantum correlations among all of the four hydrogen-bonded atoms thanks to the directionality of hydrogen bonds. If the enzyme rapidly returns to its initial state after the binding stage, the substrate ends in a new transition state corresponding to a quantum superposition. Open quantum system dynamics can then naturally drive the reaction in the forward direction from the major tautomeric form to the minor tautomeric form without needing any additional catalytic activity. We find that in this scenario the enzyme lowers the activation energy so much that there is no energy barrier left in the tautomerization, even if the quantum correlations quickly decay.
A method of molecular dynamics with quantum corrections, practical for studies of large molecular systems, is reviewed. The approach is based on the Bohmian formulation of the time-dependent Schrödinger equation in which a wavefunction is represented by an ensemble of interdependent trajectories. The quantum effects come from the quantum potential acting on trajectories on par with the usual classical potential. The quantum potential is determined from the evolving nuclear wavefunction, i.e. from the quantum trajectory (QT) ensemble itself. For practical and conceptual reasons the quantum potential and corresponding quantum nuclear effect are computed only for the selected light nuclei. For studies of reactive chemical processes, the classical potential is computed on-the-fly using the density functional tight binding method of electronic structure. A massively parallel implementation, based on the message passing interface allows for efficient simulations of ensembles of thousands of trajectories describing systems of up to 200 atoms. As a biochemical application, the approximate QT approach is used to model the tunnelling-dominated proton transfer in soybean-lipoxygenase-1. A materials science application is represented by a study of the nuclear quantum effect on adsorption of hydrogen and deuterium on a C37H15 molecule, which is a model ‘flake’ of graphene.
A study published on bioRxiv demonstrated that quantum tunneling plays a key role in in vitro hydrolytic enzyme reactions by analyzing kinetic isotope effects (KIE) through deuterium substitution. The involvement of the quantum tunneling effect was confirmed through temperature dependence experiments in major biochemical reactions such as SIRT3-mediated deacetylation, I-SceI-mediated DNA cleavage, and caspase-3-mediated protein cleavage. By observing that DNA homologous recombinational (HR) repair in living cells is almost completely inhibited in a deuterium environment that lowers the probability of quantum tunneling, it was demonstrated that quantum effects dominate cell survival itself. [Quantum Biology Society] Behind life phenomena lies a strange quantum world that cannot be explained by classical mechanics. A prime example is quantum tunneling, where particles pass through reaction energy barriers as if by magic. While it has been known that quantum tunneling contributes to speeding up some enzyme reactions inside proteins , there has been a lack of concrete empirical evidence as to whether this is an essential physical requirement directly linked to actual cell survival. Recently, a groundbreaking study was published showing that if the quantum tunneling effect is inhibited, the cell's life support system itself completely halts. The paper titled "Cell viability is dominated by quantum effects," published on the preprint repository bioRxiv, strongly supports this. A multi-institutional joint research team, including Takeshi Yasuda from the National Institutes for Quantum and Radiological Sciences and Technology (QST) and Kobe University in Japan, led this innovative research. ■ The Link Between Enzyme Hydrolysis and Quantum Tunneling The research team utilized deuterium, an isotope of hydrogen, to track how quantum tunneling is involved in enzymatic chemical reactions. In a heavy deuterium environment, the probability of quantum tunneling is significantly lower compared to light hydrogen, and the research team precisely measured the resulting kinetic isotope effects (KIE) and their temperature dependence. Experimental results proved that the quantum tunneling effect is deeply involved in in vitro hydrolysis reactions essential for cellular metabolism, such as SIRT3-mediated deacetylation, I-SceI-mediated DNA cleavage, and caspase-3-mediated protein cleavage, as evidenced by the disappearance of the isotope effect above specific temperatures. ■ A Halted DNA Repair System Furthermore, the research team directly investigated the impact of the quantum characteristics of these enzyme reactions on living cells. When human cells were exposed to a deuterium-substituted (D₂O) medium environment that artificially lowered the probability of quantum tunneling, it was observed that DNA homologous recombinational (HR) repair, one of the core survival mechanisms of cells, was almost completely inhibited. This means that the most important biochemical repair process protecting and maintaining the genetic information of organisms undergoes a chain reaction of several enzymes and cannot function normally without quantum tunneling phenomena. ■ Quantum Effects Dominating Cell Viability This study empirically demonstrates that core biochemical reactions in living organisms do not simply rely on thermodynamic energy but are fundamentally indebted to quantum mechanical tunneling phenomena. The discovery that numerous hydrolysis and repair reactions performed by enzymes within cells are ultimately strictly dominated by quantum effects serves as crucial evidence that rewrites life phenomena from a purely quantum physics perspective. https://www.biorxiv.org/content/10.1101/2023.07.18.549596v1
This paper proposes an alternative interpretation of quantum tunneling within the framework of TIMED THEORY.Rather than treating tunneling as a particle’s penetration through an energy barrier, we argue thattunneling is the ability of a particle to exist without leaving an observable record in regions where observation conditions are fundamentally unstable. We define such regions as the jari-michi (gravel road): domains in which the coordinate and time axes fail to stabilize long enough to form persistent measurement records.Within this framework, particle mass and de Broglie wavelength determine observability, which in turn governs whether a particle can enter and traverse these regions. Using published kinetic isotope effect (KIE) data from enzyme-catalyzed reactions — where hydrogen exhibits strong tunneling contributions while deuterium does not — we show that these experimental results are naturally explained by an observability-based mechanism rather than by wavefunction decay alone. This work does not reject the mathematical formalism of standard quantum mechanics.Instead, it reinterprets the physical mechanism underlying tunneling, reframing it as observational evasion rather than barrier penetration.The proposed framework offers new insight into why hydrogen occupies a unique tunneling “sweet spot” under ambient conditions and clarifies the minimal physical requirements for observation to occur. 本稿は、量子トンネリングを「粒子がエネルギー障壁を貫通する現象」とみなす標準的解釈に対し、トンネリングとは観測条件が不安定な領域において、粒子が観測記録を残さずに存在できる性質であるという代替的枠組みを、TIMED THEORYに基づいて提示する。 本研究では、座標軸および時間軸が安定した観測足場を形成できない領域を「砂利道(jari-michi)」として定義し、質量・ド・ブロイ波長・観測可能性の関係が、トンネリング現象をどのように制御しているかを示す。 特に、酵素触媒反応における速度論的同位体効果(Kinetic Isotope Effect, KIE)の公開データ——水素は効率的にトンネリングするが、重水素は著しく抑制される——が、本枠組みにより自然に説明できることを論証する。 本稿は、標準量子力学の数学的記述を否定するものではない。しかし、トンネリングを「透過」ではなく「観測回避」として再定義することで、水素が室温条件において特異的なトンネリング粒子となる理由、および観測事象が成立する物理的最小条件について、新たな解釈可能性を与える。
Tunneling is a supreme quantum effect. Every introductory text [1] on quantum mechanics gives the paradigm example of a particle tunneling through a one-dimensional potential barrier despite having a total energy less than the barrier height. Indeed, the reader typically works through a number of exercises, all involving one-dimensional potential barriers of one form or another modeling several key physical phenomena ranging from atom transfer reactions to the decay of α-particles [2]. However, one seldom encounters coupled multidimenisonal tunneling in such texts since an analytical solution of the Schro¨dinger equation in such cases is not possible. Interestingly, the richness and complexity of the tunneling phenomenon manifest themselves in full glory in the case of multidimensional systems [3]. Thus, for instance, the usual one-dimensional expectation of increasing tunneling splittings as one approaches the barrier top from below is not necessarily true as soon as one couples another bound degree of freedom to the tunneling coordinate. In the context of molecular reaction dynamics, multidimensional tunneling can result in strong mode-specificity and fluctuations in the reaction rates [4]. In fact, a proper description of tunneling of electrons and hydrogen atoms is absolutely essential [5,6] even in molecular systems as large as enzymes and proteins. Although one usually assumes tunneling effects to be significant in molecules involving light atom transfers, it is worth pointing out that neglecting the tunneling of even a heavy atom like carbon is the difference between a reaction occurring or not occurring. In particular, one can underestimate rates by nearly hundred orders of magnitude [7]. Interestingly, and perhaps paradoxically, several penetrating insights into the nature and mechanism of multidimensional barrier tunneling have been obtained from a phase-space perspective [8,9]. The contributions by Creagh, Shudo and Ikeda, and Takahashi in the present volume provide a detailed account of the latest advances in the phasespace-based understanding of multidimensional barrier tunneling.
The hydrogen spectrum is explored as a sensitive probe of a massive object being in a superposition of two distinct locations. Here I solve the simpler but instructive semiclassical problem of the proton hopping stochastically between two sites but forbidden to be anywhere else, analogous to the superposition over two locations. Although the model is semiclassical, it captures symmetry properties and the structure of the energy spectrum that one would expect in a fully quantum treatment. The hydrogen atom is a well-understood system whose spectroscopy reaches exceptional precision, and its semiclassical description displays symmetry with respect to two fixed locations. I develop a classical model for an electron and a proton, with the proton stochastically hopping between two fixed sites; and describe its classical dynamics mathematically via a one-particle effective Hamiltonian. For this Hamiltonian I identify a set of invariance properties that are characteristic of heteronuclear diatomic molecules and are not as extensive as the SO(4) symmetries present in the traditional models of the hydrogen atom. I connect the classical description of the proton-hopping model with the two-fixed-centre problem with time-dependent charges. I find that there is a lower limit to the hopping distance of the proton below which state-of-the-art measurements cannot resolve the spectral signature predicted; and also an upper limit above which approximation methods are not applicable. I gain meaningful insight into the mechanisms that shape the quantum dynamics of proton tunnelling in hydrogen by analyzing the classical counterpart, leveraging the shared symmetries between quantum and classical analogous systems. My results predict an observable spectral shift in the ground-state energy when the proton is delocalized over two sites separated by a distance large enough to be considered macroscopically distinct. With this research, I support the idea that proton tunnelling inside the hydrogen atom is worth exploring as a probe for a delocalized massive object.