Targeting phenylalanine assemblies as a prospective disease-modifying therapy for phenylketonuria.

Phenylketonuria is characterized by the accumulation of phenylalanine, resulting in severe cognitive and neurological disorders if not treated by a remarkably strict diet. There are two approved drugs today, yet both provide only a partial solution. We have previously demonstrated the formation of amyloid-like toxic assemblies by aggregation of phenylalanine, suggesting a new therapeutic target to be further pursued. Moreover, we showed that compounds that halt the formation of these assemblies also prevent their resulting toxicity. Here, we performed high-throughput screening, searching for compounds with inhibitory effects on phenylalanine aggregation. Morin hydrate, one of the most promising hits revealed during the screen, was chosen to be tested in vivo using a phenylketonuria mouse model. Morin hydrate significantly improved cognitive and motor function with a reduction in the number of phenylalanine brain deposits. Moreover, while phenylalanine levels remained high, we observed a recovery in dopaminergic, adrenergic, and neuronal markers. To conclude, the ability of Morin hydrate to halt phenylalanine aggregation without reducing phenylalanine levels implies the toxic role of the phenylalanine assemblies in phenylketonuria and opens new avenues for disease-modifying treatment.

Allosteric inhibitors targeting the calmodulin-PIP2 interface of SK4 K+ channels for atrial fibrillation treatment.

The Ca2+-activated SK4 K+ channel is gated by Ca2+-calmodulin (CaM) and is expressed in immune cells, brain, and heart. A cryoelectron microscopy (cryo-EM) structure of the human SK4 K+ channel recently revealed four CaM molecules per channel tetramer, where the apo CaM C-lobe and the holo CaM N-lobe interact with the proximal carboxyl terminus and the linker S4-S5, respectively, to gate the channel. Here, we show that phosphatidylinositol 4-5 bisphosphate (PIP2) potently activates SK4 channels by docking to the boundary of the CaM-binding domain. An allosteric blocker, BA6b9, was designed to act to the CaM-PIP2-binding domain, a previously untargeted region of SK4 channels, at the interface of the proximal carboxyl terminus and the linker S4-S5. Site-directed mutagenesis, molecular docking, and patch-clamp electrophysiology indicate that BA6b9 inhibits SK4 channels by interacting with two specific residues, Arg191 and His192 in the linker S4-S5, not conserved in SK1-SK3 subunits, thereby conferring selectivity and preventing the Ca2+-CaM N-lobe from properly interacting with the channel linker region. Immunohistochemistry of the SK4 channel protein in rat hearts showed a widespread expression in the sarcolemma of atrial myocytes, with a sarcomeric striated Z-band pattern, and a weaker occurrence in the ventricle but a marked incidence at the intercalated discs. BA6b9 significantly prolonged atrial and atrioventricular effective refractory periods in rat isolated hearts and reduced atrial fibrillation induction ex vivo. Our work suggests that inhibition of SK4 K+ channels by targeting drugs to the CaM-PIP2-binding domain provides a promising anti-arrhythmic therapy.

The contribution of individual residues of an aggregative hexapeptide derived from the human γD-crystallin to its amyloidogenicity.

Human γD-crystallin protein is abundant in the lens and is essential for preserving lens transparency. With age the protein may lose its native structure resulting in the formation of cataract. We recently reported an aggregative peptide, 41Gly-Cys-Trp-Met-Leu-Tyr46 from the human γD-crystallin, termed GDC6, exhibiting amyloidogenic properties in vitro. Here, we aimed to determine the contribution of each residue of the GDC6 to its amyloidogenicity. Molecular dynamic (MD) simulations revealed that the residues Trp, Leu, and Tyr played an important role in the amyloidogenicity of GDC6 by facilitating inter-peptide main-chain hydrogen bonds, and π-π interactions. MD predictions were further validated using single-, double- and triple-alanine-substituted GDC6 peptides in which their amyloidogenic propensity was individually evaluated using complementary biophysical techniques including Thioflavin T assay, turbidity assay, CD spectroscopy, and TEM imaging. Results revealed that the substitution of Trp, Leu, and Tyr together by Ala completely abolished aggregation of GDC6 in vitro, highlighting their importance in the amyloidogenicity of GDC6.

Chemical Chaperones Modulate the Formation of Metabolite Assemblies.

The formation of amyloid-like structures by metabolites is associated with several inborn errors of metabolism (IEMs). These structures display most of the biological, chemical and physical properties of protein amyloids. However, the molecular interactions underlying the assembly remain elusive, and so far, no modulating therapeutic agents are available for clinical use. Chemical chaperones are known to inhibit protein and peptide amyloid formation and stabilize misfolded enzymes. Here, we provide an in-depth characterization of the inhibitory effect of osmolytes and hydrophobic chemical chaperones on metabolite assemblies, thus extending their functional repertoire. We applied a combined in vivo-in vitro-in silico approach and show their ability to inhibit metabolite amyloid-induced toxicity and reduce cellular amyloid content in yeast. We further used various biophysical techniques demonstrating direct inhibition of adenine self-assembly and alteration of fibril morphology by chemical chaperones. Using a scaffold-based approach, we analyzed the physiochemical properties of various dimethyl sulfoxide derivatives and their role in inhibiting metabolite self-assembly. Lastly, we employed whole-atom molecular dynamics simulations to elucidate the role of hydrogen bonds in osmolyte inhibition. Our results imply a dual mode of action of chemical chaperones as IEMs therapeutics, that could be implemented in the rational design of novel lead-like molecules.

Alleviation of a polyglucosan storage disorder by enhancement of autophagic glycogen catabolism.

This work employs adult polyglucosan body disease (APBD) models to explore the efficacy and mechanism of action of the polyglucosan-reducing compound 144DG11. APBD is a glycogen storage disorder (GSD) caused by glycogen branching enzyme (GBE) deficiency causing accumulation of poorly branched glycogen inclusions called polyglucosans. 144DG11 improved survival and motor parameters in a GBE knockin (Gbeys/ys ) APBD mouse model. 144DG11 reduced polyglucosan and glycogen in brain, liver, heart, and peripheral nerve. Indirect calorimetry experiments revealed that 144DG11 increases carbohydrate burn at the expense of fat burn, suggesting metabolic mobilization of pathogenic polyglucosan. At the cellular level, 144DG11 increased glycolytic, mitochondrial, and total ATP production. The molecular target of 144DG11 is the lysosomal membrane protein LAMP1, whose interaction with the compound, similar to LAMP1 knockdown, enhanced autolysosomal degradation of glycogen and lysosomal acidification. 144DG11 also enhanced mitochondrial activity and modulated lysosomal features as revealed by bioenergetic, image-based phenotyping and proteomics analyses. As an effective lysosomal targeting therapy in a GSD model, 144DG11 could be developed into a safe and efficacious glycogen and lysosomal storage disease therapy.

Inhibition of tau amyloid formation and disruption of its preformed fibrils by Naphthoquinone-Dopamine hybrid.

Misfolding and aggregation of tau protein, into pathological amyloids, are hallmarks of a group of neurodegenerative diseases collectively termed tauopathies and their modulation may be therapeutically valuable. Herein, we describe the synthesis and characterization of a dopamine-based hybrid molecule, naphthoquinone-dopamine (NQDA). Using thioflavin S assay, CD, transmission electron microscopy, dynamic light scattering, Congo Red birefringence, and large unilamellar vesicle leakage assays, we demonstrated its efficacy in inhibiting the in vitro aggregation of key tau-derived amyloidogenic fragments, PHF6 (VQIVYK) and PHF6* (VQIINK), prime drivers of aggregation of full-length tau in disease pathology. Isothermal titration calorimetry analysis revealed that the interaction between NQDA and PHF6 is spontaneous and has significant binding efficiency driven by both entropic and enthalpic processes. Furthermore, NQDA efficiently disassembled preformed fibrils of PHF6 and PHF6* into nontoxic species. Molecular dynamic simulations supported the in vitro results and provided a plausible mode of binding of NQDA with PHF6 fibril. NQDA was also capable of inhibiting the aggregation of full-length tau protein and disrupting its preformed fibrils in vitro in a dose-dependent manner. In a comparative study, the IC50 value (50% inhibition of fibril formation) of NQDA in inhibiting the aggregation of PHF6 (25 µm) was ~ 17 µm, which is lower than for other bona fide amyloid inhibitors, naphthoquinone-tryptophan, rosmarinic acid, epigallocatechin gallate, ~ 21, ~ 77, or ~ 19 µm, respectively. Comparable superiority of NQDA was observed for inhibition of PHF6*. These findings suggest that NQDA can be a useful scaffold for designing new therapeutics for Alzheimer's disease and other tauopathies.

Inhibition of amyloid fibrillation of γD-crystallin model peptide by the cochineal Carmine.

γD-crystallin is among the most abundant γ-crystallins in the human eye lens which are essential for preserving its transparency. Aging, and environmental changes, cause crystallins to lose their native soluble structure and aggregate, resulting in the formation of cataract. Current treatment of cataract is surgical removal which is costly. Pharmaceutical therapeutics of cataract is an unmet need. We report a screen for small molecules capable of inhibiting aggregation of human γD-crystallin. Using a highly amyloidogenic hexapeptide model 41GCWMLY46 derived from the full-length protein, we screened a library of 68 anthraquinone molecules using ThT fluorescence assay. A leading hit, the cochineal Carmine, effectively reduced aggregation of the model GDC6 peptide in dose dependent manner. Similar effect was observed toward aggregation of the full-length γD-crystallin. Transmission electron microscopy, intrinsic Tryptophan fluorescence and ANS fluorescence assays corroborated these results. Insights obtained from molecular docking suggested that Carmine interaction with monomeric GDC6 involved hydrogen bonding with Ace group, Cys, Met residues and hydrophobic contact with Trp residue. Carmine was non-toxic toward retinal cells in culture. It also reduced ex vivo the turbidity of human extracted cataract material. Collectively, our results indicate that Carmine could be used for developing new therapeutics to treat cataract.

TOR Complex 2- independent mutations in the regulatory PIF pocket of Gad8AKT1/SGK1 define separate branches of the stress response mechanisms in fission yeast.

The Target of rapamycin (TOR) protein kinase forms part of TOR complex 1 (TORC1) and TOR complex 2 (TORC2), two multi-subunit protein complexes that regulate growth, proliferation, survival and developmental processes by phosphorylation and activation of AGC-family kinases. In the fission yeast, Schizosaccharomyces pombe, TORC2 and its target, the AGC kinase Gad8 (an orthologue of human AKT or SGK1) are required for viability under stress conditions and for developmental processes in response to starvation cues. In this study, we describe the isolation of gad8 mutant alleles that bypass the requirement for TORC2 and reveal a separation of function of TORC2 and Gad8 under stress conditions. In particular, osmotic and nutritional stress responses appear to form a separate branch from genotoxic stress responses downstream of TORC2-Gad8. Interestingly, TORC2-independent mutations map into the regulatory PIF pocket of Gad8, a highly conserved motif in AGC kinases that regulates substrate binding in PDK1 (phosphoinositide dependent kinase-1) and kinase activity in several AGC kinases. Gad8 activation is thought to require a two-step mechanism, in which phosphorylation by TORC2 allows further phosphorylation and activation by Ksg1 (an orthologue of PDK1). We focus on the Gad8-K263C mutation and demonstrate that it renders the Gad8 kinase activity independent of TORC2 in vitro and independent of the phosphorylation sites of TORC2 in vivo. Molecular dynamics simulations of Gad8-K263C revealed abnormal high flexibility at T387, the phosphorylation site for Ksg1, suggesting a mechanism for the TORC2-independent Gad8 activity. Significantly, the K263 residue is highly conserved in the family of AGC-kinases, which may suggest a general way of keeping their activity in check when acting downstream of TOR complexes.

Structural basis of heterotetrameric assembly and disease mutations in the human cis-prenyltransferase complex.

The human cis-prenyltransferase (hcis-PT) is an enzymatic complex essential for protein N-glycosylation. Synthesizing the precursor of the glycosyl carrier dolichol-phosphate, mutations in hcis-PT cause severe human diseases. Here, we reveal that hcis-PT exhibits a heterotetrameric assembly in solution, consisting of two catalytic dehydrodolichyl diphosphate synthase (DHDDS) and inactive Nogo-B receptor (NgBR) heterodimers. Importantly, the 2.3 Å crystal structure reveals that the tetramer assembles via the DHDDS C-termini as a dimer-of-heterodimers. Moreover, the distal C-terminus of NgBR transverses across the interface with DHDDS, directly participating in active-site formation and the functional coupling between the subunits. Finally, we explored the functional consequences of disease mutations clustered around the active-site, and in combination with molecular dynamics simulations, we propose a mechanism for hcis-PT dysfunction in retinitis pigmentosa. Together, our structure of the hcis-PT complex unveils the dolichol synthesis mechanism and its perturbation in disease.

A novel specific PERK activator reduces toxicity and extends survival in Huntington's disease models.

One of the pathways of the unfolded protein response, initiated by PKR-like endoplasmic reticulum kinase (PERK), is key to neuronal homeostasis in neurodegenerative diseases. PERK pathway activation is usually accomplished by inhibiting eIF2α-P dephosphorylation, after its phosphorylation by PERK. Less tried is an approach involving direct PERK activation without compromising long-term recovery of eIF2α function by dephosphorylation. Here we show major improvement in cellular (STHdhQ111/111) and mouse (R6/2) Huntington's disease (HD) models using a potent small molecule PERK activator that we developed, MK-28. MK-28 showed PERK selectivity in vitro on a 391-kinase panel and rescued cells (but not PERK-/- cells) from ER stress-induced apoptosis. Cells were also rescued by the commercial PERK activator CCT020312 but MK-28 was significantly more potent. Computational docking suggested MK-28 interaction with the PERK activation loop. MK-28 exhibited remarkable pharmacokinetic properties and high BBB penetration in mice. Transient subcutaneous delivery of MK-28 significantly improved motor and executive functions and delayed death onset in R6/2 mice, showing no toxicity. Therefore, PERK activation can treat a most aggressive HD model, suggesting a possible approach for HD therapy and worth exploring for other neurodegenerative disorders.

Chemical Modifications Reduce Auditory Cell Damage Induced by Aminoglycoside Antibiotics.

Although aminoglycoside antibiotics are effective against Gram-negative infections, these drugs often cause irreversible hearing damage. Binding to the decoding site of the eukaryotic ribosomes appears to result in ototoxicity, but there is evidence that other effects are involved. Here, we show how chemical modifications of apramycin and geneticin, considered among the least and most toxic aminoglycosides, respectively, reduce auditory cell damage. Using molecular dynamics simulations, we studied how modified aminoglycosides influence the essential freedom of movement of the decoding site of the ribosome, the region targeted by aminoglycosides. By determining the ratio of a protein translated in mitochondria to that of a protein translated in the cytoplasm, we showed that aminoglycosides can paradoxically elevate rather than reduce protein levels. We showed that certain aminoglycosides induce rapid plasma membrane permeabilization and that this nonribosomal effect can also be reduced through chemical modifications. The results presented suggest a new paradigm for the development of safer aminoglycoside antibiotics.

Purpurin modulates Tau-derived VQIVYK fibrillization and ameliorates Alzheimer's disease-like symptoms in animal model.

Neurofibrillary tangles of the Tau protein and plaques of the amyloid ß peptide are hallmarks of Alzheimer's disease (AD), which is characterized by the conversion of monomeric proteins/peptides into misfolded ß-sheet rich fibrils. Halting the fibrillation process and disrupting the existing aggregates are key challenges for AD drug development. Previously, we performed in vitro high-throughput screening for the identification of potent inhibitors of Tau aggregation using a proxy model, a highly aggregation-prone hexapeptide fragment 306VQIVYK311 (termed PHF6) derived from Tau. Here we have characterized a hit molecule from that screen as a modulator of Tau aggregation using in vitro, in silico, and in vivo techniques. This molecule, an anthraquinone derivative named Purpurin, inhibited ~ 50% of PHF6 fibrillization in vitro at equimolar concentration and disassembled pre-formed PHF6 fibrils. In silico studies showed that Purpurin interacted with key residues of PHF6, which are responsible for maintaining its ß-sheets conformation. Isothermal titration calorimetry and surface plasmon resonance experiments with PHF6 and full-length Tau (FL-Tau), respectively, indicated that Purpurin interacted with PHF6 predominantly via hydrophobic contacts and displayed a dose-dependent complexation with FL-Tau. Purpurin was non-toxic when fed to Drosophila and it significantly ameliorated the AD-related neurotoxic symptoms of transgenic flies expressing WT-FL human Tau (hTau) plausibly by inhibiting Tau accumulation and reducing Tau phosphorylation. Purpurin also reduced hTau accumulation in cell culture overexpressing hTau. Importantly, Purpurin efficiently crossed an in vitro human blood-brain barrier model. Our findings suggest that Purpurin could be a potential lead molecule for AD therapeutics.

Mechanisms of Metabolite Amyloid Formation: Computational Studies for Drug Design against Metabolic Disorders.

Ordered self-organization of polypeptides into fibrillar assemblies has been associated with a number of pathological conditions linked to degenerative diseases. Recent experimental observations have demonstrated that even small-molecule metabolites can aggregate into supramolecular arrangements with structural and functional properties reminiscent of peptide-based amyloids. The molecular determinants of such mechanisms, however, are not clear yet. Herein, we examine the process of formation of ordered aggregates by adenine in aqueous solution by molecular dynamics simulations. We also investigate the effects of an inhibiting polyphenol, namely, epigallocatechin gallate (EGCG), on this mechanism. We show that, while adenine alone is able to form extended amyloid-like oligomers, EGCG interferes with the supramolecular organization process. Interestingly, acetylsalicylic acid is shown not to interfere with ordered aggregation, consistent with experiments. The results of these mechanistic studies indicate the main pharmacophoric determinants that a drug-like inhibitor should possess to effectively interfere with metabolite amyloid formation.

Fibril formation and therapeutic targeting of amyloid-like structures in a yeast model of adenine accumulation.

The extension of the amyloid hypothesis to include non-protein metabolite assemblies invokes a paradigm for the pathology of inborn error of metabolism disorders. However, a direct demonstration of the assembly of metabolite amyloid-like structures has so far been provided only in vitro. Here, we established an in vivo model of adenine self-assembly in yeast, in which toxicity is associated with intracellular accumulation of the metabolite. Using a strain blocked in the enzymatic pathway downstream to adenine, we observed a non-linear dose-dependent growth inhibition. Both the staining with an indicative amyloid dye and anti-adenine assemblies antibodies demonstrated the accumulation of adenine amyloid-like structures, which were eliminated by lowering the supplied adenine levels. Treatment with a polyphenol inhibitor reduced the occurrence of amyloid-like structures while not affecting the dramatic increase in intracellular adenine concentration, resulting in inhibition of cytotoxicity, further supporting the notion that toxicity is triggered by adenine assemblies.

Integrating in vitro and in silico approaches to evaluate the "dual functionality" of palmatine chloride in inhibiting and disassembling Tau-derived VQIVYK peptide fibrils.

BACKGROUND: Alzheimer's disease (AD) is the most common neurodegenerative disorder which is characterized by the deposits of intra-cellular tau protein and extra-cellular amyloid-ß (Aß) peptides in the human brain. Understanding the mechanism of protein aggregation and finding compounds that are capable of inhibiting its aggregation is considered to be highly important for disease therapy. METHODS: We used an in vitro High-Throughput Screening for the identification of potent inhibitors of tau aggregation using a proxy model; a highly aggregation-prone hexapeptide fragment 306VQIVYK311 derived from tau. Using ThS fluorescence assay we screened a library of 2401 FDA approved, bio-active and natural compounds in attempt to find molecules which can efficiently modulate tau aggregation. RESULTS: Among the screened compounds, palmatine chloride (PC) alkaloid was able to dramatically reduce the aggregation propensity of PHF6 at sub-molar concentrations. PC was also able to disassemble preformed aggregates of PHF6 and reduce the amyloid content in a dose-dependent manner. Insights obtained from MD simulation showed that PC interacted with the key residues of PHF6 responsible for ß-sheet formation, which could likely be the mechanism of inhibition and disassembly. Furthermore, PC could effectively inhibit the aggregation of full-length tau and disassemble preformed aggregates. CONCLUSIONS: We found that PC possesses "dual functionality" towards PHF6 and full-length tau, i.e. inhibit their aggregation and disassemble pre-formed fibrils. GENERAL SIGNIFICANCE: The "dual functionality" of PC is valuable as a disease modifying strategy for AD, and other tauopathies, by inhibiting their progress and reducing the effect of fibrils already present in the brain.

Real-Time Imaging of the Azole Class of Antifungal Drugs in Live Candida Cells.

Azoles are the most commonly used class of antifungal drugs, yet where they localize within fungal cells and how they are imported remain poorly understood. Azole antifungals target lanosterol 14α-demethylase, a cytochrome P450, encoded by ERG11 in Candida albicans, the most prevalent fungal pathogen. We report the synthesis of fluorescent probes that permit visualization of antifungal azoles within live cells. Probe 1 is a dansyl dye-conjugated azole, and probe 2 is a Cy5-conjugated azole. Docking computations indicated that each of the probes can occupy the active site of the target cytochrome P450. Like the azole drug fluconazole, probe 1 is not effective against a mutant that lacks the target cytochrome P450. In contrast, the azole drug ketoconazole and probe 2 retained some antifungal activity against mutants lacking the target cytochrome P450, implying that both act against more than one target. Both fluorescent azole probes colocalized with the mitochondria, as determined by fluorescence microscopy with MitoTracker dye. Thus, these fluorescent probes are useful molecular tools that can lead to detailed information about the activity and localization of the important azole class of antifungal drugs.

Momentum Distribution as a Fingerprint of Quantum Delocalization in Enzymatic Reactions: Open-Chain Path-Integral Simulations of Model Systems and the Hydride Transfer in Dihydrofolate Reductase.

The inclusion of nuclear quantum effects such as zero-point energy and tunneling is of great importance in studying condensed phase chemical reactions involving the transfer of protons, hydrogen atoms, and hydride ions. In the current work, we derive an efficient quantum simulation approach for the computation of the momentum distribution in condensed phase chemical reactions. The method is based on a quantum-classical approach wherein quantum and classical simulations are performed separately. The classical simulations use standard sampling techniques, whereas the quantum simulations employ an open polymer chain path integral formulation which is computed using an efficient Monte Carlo staging algorithm. The approach is validated by applying it to a one-dimensional harmonic oscillator and symmetric double-well potential. Subsequently, the method is applied to the dihydrofolate reductase (DHFR) catalyzed reduction of 7,8-dihydrofolate by nicotinamide adenine dinucleotide phosphate hydride (NADPH) to yield S-5,6,7,8-tetrahydrofolate and NADP(+). The key chemical step in the catalytic cycle of DHFR involves a stereospecific hydride transfer. In order to estimate the amount of quantum delocalization, we compute the position and momentum distributions for the transferring hydride ion in the reactant state (RS) and transition state (TS) using a recently developed hybrid semiempirical quantum mechanics-molecular mechanics potential energy surface. Additionally, we examine the effect of compression of the donor-acceptor distance (DAD) in the TS on the momentum distribution. The present results suggest differential quantum delocalization in the RS and TS, as well as reduced tunneling upon DAD compression.

Hybrid Quantum and Classical Simulations of the Formate Dehydrogenase Catalyzed Hydride Transfer Reaction on an Accurate Semiempirical Potential Energy Surface.

Formate dehydrogenase (FDH) catalyzes the oxidation of formic acid to carbon dioxide using nicotinamide adenine dinucleotide (NAD(+)) as a cofactor. In the current work we present extensive benchmark calculations for several model reactions in the gas phase that are relevant to the FDH catalyzed hydride transfer. To this end we employ G4MP2 and CBS-QB3 ab initio calculations as well as density functional theory methods. Using these results we develop a specific reaction parameter (SRP) Hamiltonian based on the semiempirical AM1 method. The SRP semiempirical Hamiltonian is subsequently used in hybrid quantum mechanics/molecular mechanics simulations of the FDH catalyzed reaction in Pseudomonas sp. 101 (PseFDH). The classical potential of mean force (PMF) is computed as a function of structural progress coordinates during the course of the hydride transfer reaction: The antisymmetric reactive stretch, the donor-acceptor distance, and an orbital rehybridization coordinate. The quantum PMF is computed using a centroid Feynman path-integral (PI) approach. Subsequently, kinetic isotope effects are computed using a mass-perturbation based PI method. Finally, the antisymmetric stretch vibrational frequency is computed for an azide ion in FDH and in aqueous solution.

Path-Integral Calculations of Nuclear Quantum Effects in Model Systems, Small Molecules, and Enzymes via Gradient-Based Forward Corrector Algorithms.

A practical approach to treat nuclear quantum mechanical (QM) effects in simulations of condensed phases, such as enzymes, is via Feynman path integral (PI) formulations. Typically, the standard primitive approximation (PA) is employed in enzymatic PI simulations. Nonetheless, these PI simulations are computationally demanding due to the large number of discretizations, or beads, required to obtain converged results. The efficiency of PI simulations may be greatly improved if higher order factorizations of the density matrix operator are employed. Herein, we compare the results of model calculations obtained employing the standard PA, the improved operator of Takahashi and Imada (TI), and several gradient-based forward corrector algorithms due to Chin (CH). The quantum partition function is computed for the harmonic oscillator, Morse, symmetric, and asymmetric double well potentials. These potentials are simple models for nuclear quantum effects, such as zero-point energy and tunneling. It is shown that a unique set of CH parameters may be employed for a variety of systems. Additionally, the nuclear QM effects of a water molecule, treated with density functional theory, are computed. Finally, we derive a practical perturbation expression for efficient computation of isotope effects in chemical systems using the staging algorithm. This new isotope effect approach is tested in conjunction with the PA, TI, and CH methods to compute the equilibrium isotope effect in the Schiff base-oxyanion keto-enol tautomerism in the cofactor pyridoxal-5'-phosphate in the enzyme alanine racemase. The study of the different factorization methods reveals that the higher-order actions converge substantially faster than the PA approach, at a moderate computational cost.

Global uniform semiclassical approximation for Clebsch-Gordan coefficients.

Semiclassical integral representations, analogous to initial value expressions for the propagator, are presented for the Clebsch-Gordan angular momentum coupling coefficients. Two forms (L and R types) of the approximation are presented. For each form, new non-Gaussian expressions, which are specifically adapted to the nature of angular momentum variables, are proposed in place of the familiar Gaussian coherent state functions. With these non-Gaussian kernels, it is found that the present treatments are capable of accuracy similar to that obtained from a uniform Airy approximation. Although the present semiclassical approximations involve only real-valued angle variables, associated with sets of angular momenta that are related by ordinary, real, classical transformations, the treatments produce accurate results not only for classically allowed choices of quantum numbers but also for very strongly classically forbidden values.