Microscopic Reversibility Research Articles

A PDZ tandem repeat folds and unfolds via different pathways

AbstractProtein folding and unfolding experiments are interpreted under the assumption of microscopic reversibility, that is, that at equilibrium one process is the reverse of the other. Single‐domain proteins illustrate the validity of such an interpretation, although reversibility does not necessarily hold under the different conditions typically used for folding and unfolding experiments. In fact, more complex proteins, which often exhibit irreversible unfolding, are generally considered not amenable to folding kinetics studies. Here, the X11 PDZ1‐PDZ2 tandem repeat allows us to reveal the different folding and unfolding pathways at play under different experimental conditions, thus reconciling the apparent contradiction between theory and experiment.

Photoexcited Palladium-Catalyzed Deracemization of Allenes.

The different enantiomers of specific chiral molecules frequently exhibit disparate biological, physiological, or pharmacological properties. Therefore, the efficient synthesis of single enantiomers is of particular importance not only to the pharmaceutical sector but also to other industrial sectors, such as agrochemical and fine chemical industries. Deracemization, a process during which a racemic mixture is converted into a nonracemic product with 100% atom economy and theoretical yield, is the most straightforward method to access enantioenriched molecules but a challenging task due to a decrease in entropy and microscopic reversibility. Axially chiral allenes bear a distinctive structure of two orthogonal cumulative π-systems and are acknowledged as synthetically versatile synthons in organic synthesis. The selective creation of axially chiral allenes with high optical purity under mild reaction conditions has always been a very popular and hot topic in organic synthesis but remains challenging. Herein, a photoexcited palladium-catalyzed deracemization of nonprefunctionalized disubstituted allenes is disclosed. This method provides an efficient and economical strategy to accommodate a broad scope of allenes with good enantioselectivities and yields (53 examples, up to 96% yield and 95% ee). The use of a suitable chiral palladium complex with visible light irradiation is an essential factor in achieving this transformation. A metal-to-ligand charge transfer mechanism was proposed based on control experiments and density functional theory calculations. Quantum mechanical studies implicate dual modes of asymmetric induction behind our new protocol: (1) sterically controlled stereoselective binding of one allene enantiomer under the ground-state and (2) facile, noncovalent interaction-driven excited-state isomerization toward the opposite enantiomer. The success of this newly established photochemical deracemization strategy should provide inspiration for expansion to other multisubstituted allenes and will open up a new mode for enantioselective excited-state palladium catalysis.

The irreversibility of microscopic motions

People have long had a problem: the equations of motion that reflect the laws of physics are invariant under time inversion, while there always are irreversible processes for gases composed of microscopic particles. This article solves the problem. The point is that we should distinguish between the concepts of the equation of motion and concrete motion. We also need to distinguish between the concepts of time-inverse motion and reverse motion. The former is anticlockwise, which is a fictional motion, while the latter is clockwise. For the single-particle motions in classical mechanics and in quantum mechanics, we present mathematical expressions for time-inversion motion and reverse motion, respectively. We demonstrate that single-particle motion is irreversible. The definition of the reversibility of two-particle collisions is given. According to the definition, the two-particle collision as a microscopic motion process is irreversible. Consequently, for a gas consisting of a large number of particles colliding with each other, its movement should be irreversible, unless the condition of detailed balance is met. We provide a physical explanation for detailed balance, which does not concern the meaning of microscopic reversibility. The detailed balance means that after a pair of reciprocal collisions occur, the distribution function of the particles remains unchanged. Therefore, microscopic two-particle collision events are irreversible, but the statistical average of a large number of collision events makes it possible for the macroscopic process of a gas to be reversible. Conclusively, we clarify the microscopic mechanism of the irreversible process of gases.

Evaluating Diazene to N2 Interconversion at Iron-Sulfur Complexes.

Biological N2 reduction occurs at sulfur-rich multiiron sites, and an interesting potential pathway is concerted double reduction/ protonation of bridging N2 through PCET. Here, we test the feasibility of using synthetic sulfur-supported diiron complexes to mimic this pathway. Oxidative proton transfer from μ-η1 : η1-diazene (HN=NH) is the microscopic reverse of the proposed N2 fixation pathway, revealing the energetics of the process. Previously, Sellmann assigned the purple metastable product from two-electron oxidation of [{Fe2+(PPr3)L1}2(μ-η1 : η1-N2H2)] (L1=tetradentate SSSS ligand) at -78 °C as [{Fe2+(PPr3)L1}2(μ-η1 : η1-N2)]2+, which would come from double PCET from diazene to sulfur atoms of the supporting ligands. Using resonance Raman, Mössbauer, NMR, and EPR spectroscopies in conjunction with DFT calculations, we show that the product is not an N2 complex. Instead, the data are most consistent with the spectroscopically observed species being the mononuclear iron(III) diazene complex [{Fe(PPr3)L1}(η2-N2H2)]+. Calculations indicate that the proposed double PCET has a barrier that is too high for proton transfer at the reaction temperature. Also, PCET from the bridging diazene is highly exergonic as a result of the high Fe3+/2+ redox potential, indicating that the reverse N2 protonation would be too endergonic to proceed. This system establishes the "ground rules" for designing reversible N2/N2H2 interconversion through PCET, such as tuning the redox potentials of the metal sites.

Late-Stage C–H Deuteration of Organic Compounds via Ligand-Enabled Palladium-Catalyzed Hydrogen Isotope Exchange

AbstractOver the past years our lab has established a research program towards the late-stage introduction of deuterium into organic molecules using Pd-catalyzed reversible C–H activation as a means to affect hydrogen isotope exchange. Through catalyst design, including the introduction of novel ligand scaffolds, as well as the use of strategically chosen optimization and screening approaches, e.g., exploiting microscopic reversibility by first optimizing de-deuteration processes or using a multi-substrate screening approach, our studies have resulted in a number of synthetically useful labelling protocols and are described herein from a personal perspective.1 Introduction2 β-C(sp3)–H Deuteration of Free Carboxylic Acids3 Nondirected C–H Deuteration of Arenes4 Nondirected C–H Deuteration of Heteroarenes5 Conclusion

A Comparison of β–Phenyl Elimination in Nickel and Palladium Alkyl Complexes: A Potentially Relevant Process in the Mizoroki–Heck Reaction

There is currently much interest in avoiding precious metals in catalysis. The development of nickel catalysts to replace palladium in the Mizoroki–Heck reaction is a relevant case in this line of research, since both elements share many chemical features. This contribution focuses on β–phenyl (β–Ph) elimination in alkyl—nickel complexes. This is the microscopic reverse of olefin insertion (or carbometallation), a fundamental step in the Heck cycle that is usually considered irreversible and selectivity-determining. However, the potential reversibility of carbometallation is generally concealed by the facile β–hydrogen (β–H) elimination that follows. Where β–hydrogen elimination is hindered, β–aryl elimination may ensue. We have previously shown that cationic 2–methyl–2–phenylpropyl (neophyl) palladium complexes supported by bidentate ligands experience β–Ph elimination, which can be seen as an example of olefin de-insertion. In this contribution, we report that β–Ph elimination can also occur in their nickel analogs, in which case fast hydrolyses of the resulting phenyl product can follow the reaction. We investigated the mechanism of these processes and compared their feasibility for nickel and palladium catalysts using DFT calculations. These results are relevant information for the design of nickel-based catalysts for the Heck reaction.

Proton Transfer via π-Interactions from Pyridine Provides a Facilitated Route for Transfer of CO2 in Its Complex with a Carbanion.

Aromatic π-interactions have been recognized as enhancing enzymatic catalytic processes, providing an efficient route to overcome entropic barriers. A nonenzymic analogue, a complex of protonated pyridine and a phenyl substituent in a thiamin conjugate, facilitates the departure of CO2 by protonation of a vicinal carbanion in a reactive complex. To evaluate the efficiency of the catalytic pathway from the π-associated proton donor, a system was assessed that produced measurable competition through the rates of formation of alternative products resulting from the same thiamin-derived carbanion. The barriers to competing pathways from the decarboxylation of p-(bromomethyl)-mandelylthiamin in the presence and absence of protonated pyridine were determined, establishing the efficiency of the vicinal proton transfer between π-associated species. The formation of the complex of CO2 and the co-formed carbanion also addresses the mechanism of the uncatalyzed exchange of 13CO2 into carboxyl groups discovered by Lundgren. Finally, microscopic reversibility implicates pyridine as a vicinal Brønsted base in thiamin-aldehyde adducts, producing carbanions that could incorporate dissolved CO2 into carboxyl groups.

Accelerating Kinetics with Time-Reversal Path Sampling.

In comparison to numerous enhanced sampling methods for equilibrium thermodynamics, accelerating simulations for kinetics and nonequilibrium statistics are relatively rare and less effective. Here, we derive a time-reversal path sampling (tRPS) method based on time reversibility to accelerate simulations for determining the transition rates between free-energy basins. It converts the difficult uphill path sampling into an easy downhill problem. This method is easy to implement, i.e., forward and backward shooting simulations with opposite initial velocities are conducted from random initial conformations within a transition-state region until they reach the basin minima, which are then assembled to give the distribution of transition paths efficiently. The effects of tRPS are demonstrated using a comparison with direct simulations of protein folding and unfolding, where tRPS is shown to give results consistent with direct simulations and increase the efficiency by up to five orders of magnitude. This approach is generally applicable to stochastic processes with microscopic reversibility, regardless of whether the variables are continuous or discrete.

Quantum coherence and the principle of microscopic reversibility

Quantum coherence and the principle of microscopic reversibility

Multiplicative enhancement of stereoenrichment by a single catalyst for deracemization of alcohols.

Stereochemical enrichment of a racemic mixture by deracemization must overcome unfavorable entropic effects as well as the principle of microscopic reversibility; recently, photochemical reaction pathways unveiled by the energetic input of light have led to innovations toward this end, most often by ablation of a stereogenic C(sp3)-H bond. We report a photochemically driven deracemization protocol in which a single chiral catalyst effects two mechanistically different steps, C-C bond cleavage and C-C bond formation, to achieve multiplicative enhancement of stereoinduction, which leads to high levels of stereoselectivity. Ligand-to-metal charge transfer excitation of a titanium catalyst coordinated by a chiral phosphoric acid or bisoxazoline efficiently enriches racemic alcohols that feature adjacent and fully substituted stereogenic centers to enantiomeric ratios up to 99:1. Mechanistic investigations support a pathway of sequential radical-mediated bond scission and bond formation through a common prochiral intermediate and reveal that, although the overall stereoenrichment is high, the selectivity in each individual step is moderate.

Thermally Activated Geometrical Regioselective E→Z Isomerization-Enabled Cascade Sequences of Conjugated Dienals: Experimental and DFT Studies.

The geometrical regioselective E→Z isomerization of a conjugated alkene under thermal activation pose a challenge due to microscopic reversibility. Herein we report that such reversibility issues can be circumvented by integrating E→Z isomerization with subsequent cyclization cascade, particularly in the absence of commonly employed light, acids, or metal-catalysts. Thus, linearly conjugated dienals in a mixture of toluene-alcohol (2 : 1) solvents or only with alcohol at 60-70 °C can be converted to γ-alkoxybutenolides in moderate to good yields. The intermediary 2Z,4E-isomer can be isolated, which includes the first example of isolating the regioselective isomerization product under thermal conditions. Density functional theory (DFT) studies have been employed to shed light on the feasibility of geometrical alkene isomerization and ensuing cascade sequences. It has been observed that the regioselective 2E,4E→2Z,4E isomerization of dienal is a thermodynamically facile (ΔG <0) process. Structural elucidation further reveals that the presence of a certain charge transfer and a non-covalent interaction may be the primary reasons for the enhanced stability of the 2Z,4E-isomer. The thermodynamic plausibility of the subsequent cascade reaction from the Z-isomer to the anticipated product in the presence of a polar protic solvent (here MeOH) is also explicated. Out of the two probable pathways, the "hemiacetal pathway" involving a relay proton transfer is kinetically more feasible due to the diminished activation barrier than the "conjugate addition pathway".

Improved temperature dependence of rate coefficients for rotational state-to-state transitions in H2O + H2O collisions

Aims. We present an improved database of temperature-dependent rate coefficients for rotational state-to-state transitions in H2O + H2O collisions. The database includes 231 transitions between the lower para-states of H2O and 210 transitions between its lower ortho-states (up to j = 7) and can be employed in cometary and planetary applications up to the temperature of 1000 K. Methods. We developed and applied a new general method that allows the generation of rate coefficients for excitation and quenching processes that automatically satisfy the principle of microscopic reversibility and also helps to cover the range of low collision energies by interpolation of cross sections between the process threshold and the computed data points. Results. We find that in the range of intermediate temperatures, 150 &lt; T &lt; 600 K, our new rate coefficients are in good agreement with those reported earlier, but for higher temperatures, 600 &lt; T &lt; 1000 K, the new revised temperature dependence is recommended. The low temperature range, 5 &lt; T &lt; 150 K, is now covered by the above-mentioned interpolation of cross sections down to the process threshold.

The rotating lepton model: Electron and positron catalysis of chemical and nuclear synthesis

The rotating lepton model: Electron and positron catalysis of chemical and nuclear synthesis Professor Emeritus Constantinos Vayenas from the University of Patras and PhD student Dionysios Tsousis from Stanford University discuss electron and positron catalysis in the CERN e+e- annihilation experiments via the Rotating Lepton Model. Electrons and positrons play a central role in heterogeneous catalysis and electrochemistry since they can interact directly via electrostatic interactions with molecular or ionic reactants, intermediates, and products. Electrochemistry’s entire science and technology is based on electrostatic electron – or positron-atom interactions. Here, they discuss the elementary particles, microscopic reversibility and the Rotating Lepton Model, Experimental validations of the Rotating Lepton Model, neutrino rest masses computation, and finally, structural information. In summary, the CERN positron-electron annihilation experiments shed new light on the interactions between neutrinos, positrons and electrons and confirm the mechanism of the Rotating Lepton Model by showing that the Z boson is a rotating positron-electron-neutrino (m3) (e+e– ν3) particle.

Dynamical and Probabilistic Approaches to Irreversibility

Boltzmann’s H-theorem is considered a great triumph of science. Though some modifications are necessary to adapt it to modern dynamical theories, it is well established that one of its main tenets remains widely accepted: the introduction of probability is a key element in achieving a transition from time-reversible, deterministic dynamical laws at the microscopic level to irreversible laws describing the approach to equilibrium of isolated macroscopic systems. Thus, it is somehow surprising that we still find instances where this subject is labeled as paradoxical and elusive. More remarkable is the fact that this often happens in texts that succeed in presenting Boltzmann’s ideas with clarity. In order to shed light on how probability allows us to go form microscopic reversibility to macroscopic irreversibility, we use numerical results from a two-dimensional lattice gas composed of distinguishable particles. We discuss the roles played by noise, coarse graining, and probability. The simplicity of our model might help the newcomer to this area in better grasping Boltzmann’s fundamental breakthrough.

The Reversibility Paradox: Role of the Velocity Reversal Step

The reversibility, or Loschmidt paradox, is a thought experiment in which microscopic reversibility is exploited to generate an apparently spontaneous trajectory in which entropy decreases, thus violating the Second Law of Thermodynamics (SLT). To achieve this, the system is allowed to evolve from a low-entropy to a high-entropy configuration, at which point all velocities of its molecules are reversed, thus producing the desired effect. In this paper we focus on the velocity reversal step. Implementing this step requires the measurement of velocities and positions, which must be stored in a memory. Even in the case of a reversible measurement, the erasure of the stored information, necessary to reset the measuring device to its original state, has an entropy cost that offsets the entropy decrease during the reverse evolution of the system. This cost is sufficient to explain why the described procedure does not violate the SLT.

(Invited) Hard Polymers: Irreversible Synthetic Routes to Ultra-Strong Two-Dimensional Polymers in Bulk

Polymers that extend covalently in two dimensions have attracted recent attention as a means of combining the mechanical strength and in-plane energy conduction of conventional two-dimensional (2D) materials with the low densities, synthetic processability, and organic composition of their one-dimensional counterparts. Efforts to date have proven successful in forms that do not allow full realization of these properties, such as polymerization at flat interfaces or fixation of monomers in immobilized lattices. A frequently employed synthetic approach is to introduce microscopic reversibility, at the cost of bond stability, to achieve 2D crystals after extensive error correction. Herein we demonstrate a synthetic route to 2D irreversible polycondensation directly in the solution phase, resulting in a covalently bonded 2D polymer that is chemically stable and highly processable. Further fabrication offers highly oriented, free-standing films which exhibit exceptional 2D elastic modulus and yield strength at 12.7 ± 3.8 GPa and 488 ± 57 MPa, respectively. The highly planar asymmetry of 2D molecules is evidenced by chemical atomic force microscopy, and molecular alignment in nanofilms is supported by a polarized photoluminescence centered at 580 and 680 nm from different dipole transitions. We have also made substantial progresses in the theory of 2D chain growth. We performed a chemical kinetic simulation study to understand 2D polymerization in homogeneous solution with irreversible chemical steps. We show that reaction sites for polymerization in 2D always scale unfavourably compared to 3D, growing as molecular weight to the 1/2 power versus 2/3 power for 3D. However, certain mechanisms can effectively suppress out-of-plane defect formation and subsequent 3D growth. We consider two such mechanisms, which we call bond-planarity and templated autocatalysis. In the first, although single bonds can easily rotate out-of-plane to render polymerization in 3D, some double-bond linkages prefer a planar configuration. In the second mechanism, stacked 2D plates may act as van der Waals templates for each other to enhance growth, which leads to an autocatalysis. When linkage reactions possess a 1000:1 selectivity (γ) for staying in plane versus rotating, solution-synthesized 2D polymers can have comparable size and yield with those synthesized from confined polymerization on a surface. Autocatalysis could achieve similar effects when self-templating accelerates 2D growth by a factor β of 106. A combined strategy relaxes the requirement of both mechanisms by over one order of magnitude. We map the dependence of molecular weight and yield for 2D polymer on the reaction parameters, allowing experimental results to be used to estimate β and γ. Our calculations show for the first time from theory, the feasibility of producing two-dimensional polymers from irreversible polymerization in solution. These new synthetic routes, now experimentally validated, provides exciting, new opportunities for 2D polymers in applications ranging from composite structures to barrier coating materials.

Thermodynamic Bound on the Asymmetry of Cross-Correlations.

The principle of microscopic reversibility says that, in equilibrium, two-time cross-correlations are symmetric under the exchange of observables. Thus, the asymmetry of cross-correlations is a fundamental, measurable, and often-used statistical signature of deviation from equilibrium. Here we find a simple and universal inequality that bounds the magnitude of asymmetry by the cycle affinity, i.e., the strength of thermodynamic driving. Our result applies to a large class of systems and all state observables, and it suggests a fundamental thermodynamic cost for various nonequilibrium functions quantified by the asymmetry. It also provides a powerful tool to infer affinity from measured cross-correlations, in a different and complementary way to the thermodynamic uncertainty relations. As an application, we prove a thermodynamic bound on the coherence of noisy oscillations, which was previously conjectured by Barato and Seifert [Phys. Rev. E 95, 062409 (2017)PRESCM2470-004510.1103/PhysRevE.95.062409]. We also derive a thermodynamic bound on directed information flow in a biochemical signal transduction model.

(356) Microsurgical Training in a High-volume Academic Infertility Practice. What we Learn from the Residents

Abstract Introduction Surgical education has been traditionally rooted in the apprenticeship model, where the experts teach the surgeons-in-training during real-time surgeries. With the advent of robotics, the emphasis on simulation and virtual reality training is upon us. Objective The goal of this study is to examine lessons learned from the first few years of our institution’s microsurgical training. Methods A structured resident male infertility microsurgical training program was devised and multiple attempts at implementing it were made. When resident lack of interest/ time availability as well as COVID pandemic factored in, adjustments were made. And the devised assessment was applied to real-time surgeries. A structured assessment of the trainee’s skills was used by the faculty surgeon at initiation of the training, and throughout. All aspects of the assessment were evaluated on the scale of 1-5, with 1 being the lowest and 5 the highest. (Table 1) According to the individual improvement, the difficulty of the skills and steps of the procedure were advanced accordingly. This evaluation was not communicated with the trainees in order to avoid their undue stress/ intimidation. Results A total of 78 microscopic vasectomy reversal surgeries were performed by one staff surgeon and four consecutive resident surgeons between January 2020 and May 2022. All residents were in their 2nd year of Urology training (PGY-2). On average, each of the trainees participated in 17 vasectomy reversals (13-21), with similar amount of surgical time spent (about 3-4 hrs/ case). At initiation of their training, each individual had similar basic and microscopic surgical skills, procedure knowledge, economy of motion and tissue/ instrument/ needle handling ability (scores of 2-3 out of 5). Two of the trainees displayed higher level of interest and better listening skills, which resulted in willingness to correct their errors and ultimately improve on their surgical techniques. The resident with initial poor skill set and poor interest/ listening skills did not progress to more advanced stages of training and was relegated to initial dissection/ exposure and placement of adventitial sutures. The resident with slightly better surgical skills but unwilling to make corrections to his technique, progressed to the next level of placing occasional luminal sutures. The remaining two residents displayed the most interest, involvement and receptiveness to the feedback. They both progressed to the final stages of the training, with one of them performing the entire operation as a primary surgeon, with the staff assisting. (Table 2). Conclusions While the structured residency microsurgical training program is of utmost importance, competing professional and personal interests of the resident-surgeons may affect its full execution. Careful observation of the trainees, their skills, ability to receive and process the feedback in combination with teaching faculty’s patience and flexibility are paramount to the safe and effective “real-life” training. When devising a surgical training program it is important to keep in mind that surgical residents prefer hands-on operating experiences. Disclosure No

Comparison of Endoscopic and Microscopic Reversal Stapedotomies: Our Clinical Experience in 87 Patients with Otosclerosis

Comparison of Endoscopic and Microscopic Reversal Stapedotomies: Our Clinical Experience in 87 Patients with Otosclerosis

Protodemetalation of (Bipyridyl)Ni(II)-Aryl Complexes Shows Evidence for Five-, Six-, and Seven-Membered Cyclic Pathways.

Protonation of C-M bonds and its microscopic reverse, metalation of C-H bonds, are fundamental steps in a variety of metal-catalyzed processes. As such, studies on protonation of C-M bonds can shed light on C-H activation. We present here studies on the rate of protodemetalation (PDM) of a suite of arylnickel(II) complexes with various acids that provide evidence for a concerted, cyclic transition state for the PDM of C-Ni bonds and demonstrate that five-, six-, and seven-membered transition states are particularly favorable. Our data show that while the rate of protodemetalation of arylnickel(II) complexes scales with acidity for many acids, several are faster than predicted by pKa. For example, while acetic acid and acetohydroxamic acid are much less acidic than HCl, they both protodemetalate arylnickel(II) complexes significantly faster than HCl. Our data also show how in the case of acetohydroxamic acid, a seven-membered cyclic transition state (CH3C(O)NHOH) can be more favorable than a six-membered transition state (CH3C(O)NHOH). Similarly, five-membered transition states, such as for pyrazole, are highly favorable as well. Comparison of transition state polarization (from density functional theory) compares these new nickel transition states to better-studied precious-metal systems and demonstrates how the base can change the polarization of the transition state giving rise to opposing electronic preferences. Collectively, these studies suggest several new avenues for study in C-H activation as well as approaches to accelerate or slow protodemetalation in nickel catalysis.