Three applications of path integrals: equilibrium and kinetic isotope effects, and the temperature dependence of the rate constant of the [1,5] sigmatropic hydrogen shift in (Z)-1,3-pentadiene

Recent experiments have confirmed the importance of nuclear quantum effects even in large biomolecules at physiological temperature. Here we describe how the path integral formalism can be used to describe rigorously the nuclear quantum effects on equilibrium and kinetic properties of molecules. Specifically, we explain how path integrals can be employed to evaluate the equilibrium (EIE) and kinetic (KIE) isotope effects, and the temperature dependence of the rate constant. The methodology is applied to the [1,5] sigmatropic hydrogen shift in pentadiene. Both the KIE and the temperature dependence of the rate constant confirm the importance of tunneling and other nuclear quantum effects as well as of the anharmonicity of the potential energy surface. Moreover, previous results on the KIE were improved by using a combination of a high level electronic structure calculation within the harmonic approximation with a path integral anharmonicity correction using a lower level method.Comment: 9 pages, 4 figure

Implementing Fault-tolerant Entangling Gates on the Five-qubit Code and the Color Code

We compare two different implementations of fault-tolerant entangling gates on logical qubits. In one instance, a twelve-qubit trapped-ion quantum computer is used to implement a non-transversal logical CNOT gate between two five qubit codes. The operation is evaluated with varying degrees of fault tolerance, which are provided by including quantum error correction circuit primitives known as flagging and pieceable fault tolerance. In the second instance, a twenty-qubit trapped-ion quantum computer is used to implement a transversal logical CNOT gate on two [[7,1,3]] color codes. The two codes were implemented on different but similar devices, and in both instances, all of the quantum error correction primitives, including the determination of corrections via decoding, are implemented during runtime using a classical compute environment that is tightly integrated with the quantum processor. For different combinations of the primitives, logical state fidelity measurements are made after applying the gate to different input states, providing bounds on the process fidelity. We find the highest fidelity operations with the color code, with the fault-tolerant SPAM operation achieving fidelities of 0.99939(15) and 0.99959(13) when preparing eigenstates of the logical X and Z operators, which is higher than the average physical qubit SPAM fidelities of 0.9968(2) and 0.9970(1) for the physical X and Z bases, respectively. When combined with a logical transversal CNOT gate, we find the color code to perform the sequence--state preparation, CNOT, measure out--with an average fidelity bounded by [0.9957,0.9963]. The logical fidelity bounds are higher than the analogous physical-level fidelity bounds, which we find to be [0.9850,0.9903], reflecting multiple physical noise sources such as SPAM errors for two qubits, several single-qubit gates, a two-qubit gate and some amount of memory error

Age-Related Changes in the Daily Rhythm of Photoreceptor Functioning and Circuitry in a Melatonin-Proficient Mouse Strain

Retinal melatonin is involved in the modulation of many important retinal functions. Our previous studies have shown that the viability of photoreceptors and ganglion cells is reduced during aging in mice that lack melatonin receptor type 1. This demonstrates that melatonin signaling is important for the survival of retinal neurons. In the present study, we investigate the effects of aging on photoreceptor physiology and retinal organization in CH3-f+/+ mice, a melatonin proficient mouse strain. Our data indicate that the amplitude of the a and b waves of the scotopic and photopic electroretinogram decreases with age. Moreover, the daily rhythm in the amplitude of the a- and b- waves is lost during the aging process. Similarly, the scotopic threshold response is significantly affected by aging, but only when it is measured during the night. Interestingly, the changes observed in the ERGs are not paralleled by relevant changes in retinal morphological features, and administration of exogenous melatonin does not affect the ERGs in C3H-f+/+ at 12 months of age. This suggests that the responsiveness of the photoreceptors to exogenous melatonin is reduced during aging

The dissociation catastrophe in fluctuating-charge models and its implications for the concept of atomic electronegativity

We have recently developed the QTPIE (charge transfer with polarization current equilibration) fluctuating-charge model, a new model with correct dissociation behavior for nonequilibrium geometries. The correct asymptotics originally came at the price of representing the solution in terms of charge-transfer variables instead of atomic charges. However, we have found an exact reformulation of fluctuating-charge models in terms of atomic charges again, which is made possible by the symmetries of classical electrostatics. We show how this leads to the distinguishing between two types of atomic electronegativities in our model. While one is a intrinsic property of individual atoms, the other takes into account the local electrical surroundings. This suggests that this distinction could resolve some confusion surrounding the concept of electronegativity as to whether it is an intrinsic property of elements, or otherwise.Comment: 17 pages, prepared for "Proceedings of QSCP-XIII" in Prog. Theor. Chem. Phy

The Role for HNF-1β-Targeted Collectrin in Maintenance of Primary Cilia and Cell Polarity in Collecting Duct Cells

Collectrin, a homologue of angiotensin converting enzyme 2 (ACE2), is a type I transmembrane protein, and we originally reported its localization to the cytoplasm and apical membrane of collecting duct cells. Recently, two independent studies of targeted disruption of collectrin in mice resulted in severe and general defects in renal amino acid uptake. Collectrin has been reported to be under the transcriptional regulation by HNF-1α, which is exclusively expressed in proximal tubules and localized at the luminal side of brush border membranes. The deficiency of collectrin was associated with reduction of multiple amino acid transporters on luminal membranes. In the current study, we describe that collectrin is a target of HNF-1β and heavily expressed in the primary cilium of renal collecting duct cells. Collectrin is also localized in the vesicles near the peri-basal body region and binds to γ-actin-myosin II-A, SNARE, and polycystin-2-polaris complexes, and all of these are involved in intracellular and ciliary movement of vesicles and membrane proteins. Treatment of mIMCD3 cells with collectrin siRNA resulted in defective cilium formation, increased cell proliferation and apoptosis, and disappearance of polycystin-2 in the primary cilium. Suppression of collectrin mRNA in metanephric culture resulted in the formation of multiple longitudinal cysts in ureteric bud branches. Taken together, the cystic change and formation of defective cilium with the interference in the collectrin functions would suggest that it is necessary for recycling of the primary cilia-specific membrane proteins, the maintenance of the primary cilia and cell polarity of collecting duct cells. The transcriptional hierarchy between HNF-1β and PKD (polycystic kidney disease) genes expressed in the primary cilia of collecting duct cells has been suggested, and collectrin is one of such HNF-1β regulated genes

Effects of low power laser irradiation on bone healing in animals: a meta-analysis

<p>Abstract</p> <p>Purpose</p> <p>The meta-analysis was performed to identify animal research defining the effects of low power laser irradiation on biomechanical indicators of bone regeneration and the impact of dosage.</p> <p>Methods</p> <p>We searched five electronic databases (MEDLINE, EMBASE, PubMed, CINAHL, and Cochrane Database of Randomised Clinical Trials) for studies in the area of laser and bone healing published from 1966 to October 2008. Included studies had to investigate fracture healing in any animal model, using any type of low power laser irradiation, and use at least one quantitative biomechanical measures of bone strength. There were 880 abstracts related to the laser irradiation and bone issues (healing, surgery and assessment). Five studies met our inclusion criteria and were critically appraised by two raters independently using a structured tool designed for rating the quality of animal research studies. After full text review, two articles were deemed ineligible for meta-analysis because of the type of injury method and biomechanical variables used, leaving three studies for meta-analysis. Maximum bone tolerance force before the point of fracture during the biomechanical test, 4 weeks after bone deficiency was our main biomechanical bone properties for the Meta analysis.</p> <p>Results</p> <p>Studies indicate that low power laser irradiation can enhance biomechanical properties of bone during fracture healing in animal models. Maximum bone tolerance was statistically improved following low level laser irradiation (average random effect size 0.726, 95% CI 0.08 - 1.37, p 0.028). While conclusions are limited by the low number of studies, there is concordance across limited evidence that laser improves the strength of bone tissue during the healing process in animal models.</p