Computational Model of In Vivo Corneal Pharmacokinetics and Pharmacodynamics of Topically Administered Ophthalmic Drug Products.

INTRODUCTION: Although the eye is directly accessible on the surface of the human body, drug delivery can be extremely challenging due to the presence of multiple protective barriers in eye tissues. Researchers have developed complex formulation strategies to overcome these barriers to ophthalmic drug delivery. Current development strategies rely heavily on in vitro experiments and animal testing to predict human pharmacokinetics (PK) and pharmacodynamics (PD). OBJECTIVE: The primary objective of the study was to develop a high-fidelity PK/PD model of the anterior eye for topical application of ophthalmic drug products. METHODS: Here, we present a physiologically-based in silico approach to predicting PK and PD in rabbits after topical administration of ophthalmic products. A first-principles based approach was used to describe timolol dissolution, transport, and distribution, including consideration of ionized transport, following topical instillation of a timolol suspension. RESULTS: Using literature transport and response parameters, the computational model described well the concentration-time and response-time profiles in rabbit. Comparison of validated rabbit model results and extrapolated human model results demonstrate observable differences in the distribution of timolol at multiple time points. CONCLUSION: This modeling framework provides a tool for model-based prediction of PK in eye tissues and PD after topical ophthalmic drug administration to the eyes.

Clinical Ocular Exposure Extrapolation for Ophthalmic Solutions Using PBPK Modeling and Simulation.

BACKGROUND: The development of generic ophthalmic drug products is challenging due to the complexity of the ocular system, and a lack of sensitive testing to evaluate the interplay of physiology with ophthalmic formulations. While measurements of drug concentration at the site of action in humans are typically sparse, these measurements are more easily obtained in rabbits. The purpose of this study is to demonstrate the utility of an ocular physiologically based pharmacokinetic (PBPK) model for translation of ocular exposure from rabbit to human. METHOD: The Ocular Compartmental Absorption and Transit (OCAT™) model within GastroPlus® v9.8.2 was used to build PBPK models for levofloxacin (Lev), moxifloxacin (Mox), and gatifloxacin (Gat) ophthalmic solutions. in the rabbit eye. The models were subsequently used to predict Lev, Mox, and Gat exposure after ocular solution administrations in humans. Drug-specific parameters were used as fitted and validated in the rabbit OCAT model. The physiological parameters were scaled to match human ocular physiology. RESULTS: OCAT model simulations for rabbit well described the observed concentrations in the eye compartments following Lev, Mox, and Gat solution administrations of different doses and various administration schedules. The clinical ocular exposure following ocular administration of Lev, Mox, and Gat solutions at different doses and various administration schedules was well predicted. CONCLUSION: Even though additional case studies for different types of active pharmaceutical ingredients (APIs) and formulations will be needed, the current study represents an important step in the validation of the extrapolation method to predict human ocular exposure for ophthalmic drug products using PBPK models.

Ocular Physiologically Based Pharmacokinetic Modeling for Ointment Formulations.

PURPOSE: The purpose of this study is to show how the Ocular Compartmental Absorption & Transit (OCAT™) model in GastroPlus® can be used to characterize ocular drug pharmacokinetic performance in rabbits for ointment formulations. METHODS: A newly OCAT™ model developed for fluorometholone, as well as a previously verified model for dexamethasone, were used to characterize the aqueous humor (AH) concentration following the administration of multiple ointment formulations to rabbit. The model uses the following parameters: application surface area (SA), a fitted application time, and the fitted Higuchi release constant to characterize the rate of passage of the active pharmaceutical ingredient from the ointment formulations into the tears in vivo. RESULTS: Parameter sensitivity analysis was performed to understand the impact of ointment formulation changes on ocular exposure. While application time was found to have a significant impact on the time of maximal concentration in AH, both the application SA and the Higuchi release constant significantly influenced both the maximum concentration and the ocular exposure. CONCLUSIONS: This initial model for ointment ophthalmic formulations is a first step to better understand the interplay between physiological factors and ophthalmic formulation physicochemical properties and their impact on in vivo ocular drug pharmacokinetic performance in rabbits.

A single-site multipole model for liquid water.

Accurate and efficient empirical potential energy models that describe the atomistic interactions between water molecules in the liquid phase are essential for computer simulations of many problems in physics, chemistry, and biology, especially when long length or time scales are important. However, while models with non-polarizable partial charges at four or five sites in a water molecule give remarkably good values for certain properties, deficiencies have been noted in other properties and increasing the number of sites decreases computational efficiency. An alternate approach is to utilize a multipole expansion of the electrostatic potential due to the molecular charge distribution, which is exact outside the charge distribution in the limits of infinite distances or infinite orders of multipoles while partial charges are a qualitative representation of electron density as point charges. Here, a single-site multipole model of water is presented, which is as fast computationally as three-site models but is also more accurate than four- and five-site models. The dipole, quadrupole, and octupole moments are from quantum mechanical-molecular mechanical calculations so that they account for the average polarization in the liquid phase, and represent both the in-plane and out-of-plane electrostatic potentials of a water molecule in the liquid phase. This model gives accurate thermodynamic, dynamic, and dielectric properties at 298 K and 1 atm, as well as good temperature and pressure dependence of these properties.

Hydrophobic hydration and the anomalous partial molar volumes in ethanol-water mixtures.

The anomalous behavior in the partial molar volumes of ethanol-water mixtures at low concentrations of ethanol is studied using molecular dynamics simulations. Previous work indicates that the striking minimum in the partial molar volume of ethanol VE as a function of ethanol mole fraction XE is determined mainly by water-water interactions. These results were based on simulations that used one water model for the solute-water interactions but two different water models for the water-water interactions. This is confirmed here by using two more water models for the water-water interactions. Furthermore, the previous work indicates that the initial decrease is caused by association of the hydration shells of the hydrocarbon tails, and the minimum occurs at the concentration where all of the hydration shells are touching each other. Thus, the characteristics of the hydration of the tail that cause the decrease and the features of the water models that reproduce this type of hydration are also examined here. The results show that a single-site multipole water model with a charge distribution that mimics the large quadrupole and the p-orbital type electron density out of the molecular plane has "brittle" hydration with hydrogen bonds that break as the tails touch, which reproduces the deep minimum. However, water models with more typical site representations with partial charges lead to flexible hydration that tends to stay intact, which produces a shallow minimum. Thus, brittle hydration may play an essential role in hydrophobic association in water.

The molecular charge distribution, the hydration shell, and the unique properties of liquid water.

The most essential features of a water molecule that give rise to its unique properties are examined using computer simulations of different water models. The charge distribution of a water molecule characterized by molecular multipoles is quantitatively linked to the liquid properties of water via order parameters for the degree (S(2)) and symmetry (ΔS(2)) of the tetrahedral arrangement of the nearest neighbors, or "hydration shell." ΔS(2) also appears to determine the long-range tetrahedral network and interfacial structure. From the correlations, some models are shown to be unable to reproduce certain properties due to the limitations of the model itself rather than the parameterization, which indicates that they are lacking essential molecular features. Moreover, since these properties depend not only on S(2) but also on ΔS(2), the long-range structure in these models may be incorrect. Based on the molecular features found in the models that are best able to reproduce liquid properties, the most essential features of a water molecule in liquid water appear to be a charge distribution with a large dipole, a large quadrupole, and negative charge out of the molecular plane, as well as a symmetrically ordered tetrahedral hydration shell that results from this charge distribution. The implications for modeling water are also discussed.

Clinical Ocular Exposure Extrapolation for a Complex Ophthalmic Suspension Using Physiologically Based Pharmacokinetic Modeling and Simulation.

The development of generic ophthalmic drug products with complex formulations is challenging due to the complexity of the ocular system and a lack of sensitive testing to evaluate the interplay of its physiology with ophthalmic drugs. New methods are needed to facilitate the development of ophthalmic generic drug products. Ocular physiologically based pharmacokinetic (O-PBPK) models can provide insight into drug partitioning in eye tissues that are usually not accessible and/or are challenging to sample in humans. This study aims to demonstrate the utility of an ocular PBPK model to predict human exposure following the administration of ophthalmic suspension. Besifloxacin (Bes) suspension is presented as a case study. The O-PBPK model for Bes ophthalmic suspension (Besivance® 0.6%) accounts for nasolacrimal drainage, suspended particle dissolution in the tears, ocular absorption, and distribution in the rabbit eye. A topical controlled release formulation was used to integrate the effect of Durasite® on Bes ocular retention. The model was subsequently used to predict Bes exposure after its topical administration in humans. Drug-specific parameters were used as validated for rabbits. The physiological parameters were adjusted to match human ocular physiology. Simulated human ocular pharmacokinetic profiles were compared with the observed ocular tissue concentration data to assess the OCAT models' ability to predict human ocular exposure. The O-PBPK model simulations adequately described the observed concentrations in the eye tissues following the topical administration of Bes suspension in rabbits. After adjustment of physiological parameters to represent the human eye, the extrapolation of clinical ocular exposure following a single ocular administration of Bes suspension was successful.

Use of physiologically-based pharmacokinetic modeling to understand the effect of omeprazole administration on the pharmacokinetics of oral extended-release nifedipine.

Proton pump inhibitors (PPIs) can affect the release of drugs from their dosage forms in vivo by elevating the gastric pH. Our recent clinical study has demonstrated that drug-drug interactions (DDIs) exist between a PPI, omeprazole, and nifedipine extended-release formulations, where systemic exposure of nifedipine was increased in subjects after multiple-dose pretreatment of omeprazole. However, the mechanism of the observed DDIs between omeprazole and nifedipine has not been well-understood, as the DDI may also be mediated through CYP3A4 enzyme inhibition in addition to the elevated gastric pH caused by omeprazole. This study used physiologically-based pharmacokinetic (PBPK) modeling and simulations to investigate the underlying mechanism of these complex DDIs. A formulation exhibiting differences in in vitro dissolution across physiological pH range and another formulation where pH does not impact dissolution appreciably (e.g., an osmotic pump) were chosen to characterize the potential impact of pH. The PBPK models incorporated two-stage in vitro release profiles via US Pharmacopeia 2 apparatus. PBPK simulations suggest that the elevated gastric pH following multiple-dose administration of omeprazole has a minimal effect on nifedipine pharmacokinetics (PKs), whereas CYP3A4-mediated DDI is likely the main driver to the observed change of nifedipine PKs in the presence of omeprazole. Compared to the osmotic formulation, the slightly increased exposure of nifedipine can be accounted for by the enhanced drug release in the pH-dependent formulation. The reported model-based approach may be useful in DDI risk assessments, product formulation designs, and bioequivalence evaluations.

Effects of microcomplexity on hydrophobic hydration in amphiphiles.

Hydrophobic hydration is critical in biology as well as many industrial processes. Here, computer simulations of ethanol/water mixtures show that a three-stage mechanism of dehydration of ethanol explains the anomalous concentration dependence of the thermodynamic partial molar volumes, as well as recent data from neutron diffraction and Raman scattering. Moreover, the simulations show that the breakdown of hydrophobic hydration shells, whose structure is determined by the unique molecular properties of water, is caused by the microcomplexity of the environment and may be representative of early events in protein folding and structure stabilization in aqueous solutions.

Vagus Nerve Stimulation Prevents Endothelial Necroptosis to Alleviate Blood-Spinal Cord Barrier Disruption After Spinal Cord Injury.

Vagus nerve stimulation (VNS) is a promising neuromodulation technique, which has been demonstrated to promote functional recovery after spinal cord injury (SCI) in our previous study. But the underlying mechanism remains to be explored. Using a compressed SCI model, our present study first demonstrated that activated microglia produce abundant tumor necrosis factor-α (TNF-α) to induce endothelial necroptosis via receptor-interacting protein kinase 1 (RIP1)/RIP3/mixed lineage kinase domain-like protein (MLKL) pathway, thus destroying the blood-spinal cord barrier (BSCB) after SCI. While both TNF-α specifical antibody (infliximab) and necroptosis inhibitor (necrostatin-1) alleviate BSCB disruption. Then our study found that VNS significantly inhibits microglia-derived TNF-α production and reduces expression of p-RIP3 and p-MLKL in endothelial cells. As expected, further results indicated that VNS mitigates the BSCB disruption, thus reducing inflammatory cells infiltration and neural damage. Finally, both electrophysiological evaluation and locomotor test demonstrated that VNS promotes motor function recovery after SCI. In conclusion, our data demonstrated VNS restricts microglia-derived TNF-α to prevent RIP1/RIP3/MLKL mediated endothelial necroptosis, thus alleviating the decisive pathophysiological BSCB disruption to reduce neuroinflammation and neural damage, which ultimately promotes motor function recovery after SCI. Therefore, these results further elaborate that VNS might be a promising therapeutic strategy for SCI. Vagus nerve stimulation prevents microglia-derived TNF-α induced endothelial necroptosis to alleviate blood-spinal cord barrier disruption after spinal cord injury.

Transcranial direct current stimulation regulates phenotypic transformation of microglia to relieve neuropathic pain induced by spinal cord injury.

Objective: Neuropathic pain is a common complication after spinal cord injury (SCI). Transcranial direct current stimulation (tDCS) has been confirmed to be effective in relieving neuropathic pain in patients with SCI. The aim of this study is to investigate the effect of tDCS on neuropathic pain induced by SCI and its underlying mechanism. Materials and methods: The SCI model was induced by a clip-compression injury and tDCS stimulation was performed for two courses (5 days/each). The motor function was evaluated by Basso-Beattie-Bresnahan (BBB) score, and the thermal withdrawal threshold was evaluated by the thermal radiation method. The effects of tDCS on the cerebral cortex, thalamus, midbrain, and medulla were detected by the enzyme-linked immunosorbent assay (ELISA) and immunofluorescence. Results: The results showed that SCI reduced the thermal withdrawal threshold and increased the concentration of inflammatory cytokines in the cortex, thalamus, midbrain, and medulla, including the tumor necrosis factor-α (TNF-α), interleukin-1ß (IL-1ß), and interleukin-6 (IL-6). In addition, the activation of microglia and the proportion of M1 phenotypic polarization increased significantly in the ventral posterolateral (VPL), ventral tegmental (VTA), and periaqueductal gray (PAG) regions after SCI. After tDCS treatment, the thermal withdrawal threshold and motor function of SCI rats were significantly improved compared to the vehicle group. Meanwhile, tDCS effectively reduced the concentration of pro-inflammatory cytokines in the cortex, thalamus, midbrain, and medulla and increased the concentration of anti-inflammatory cytokines interleukin-10 (IL-10) in the thalamus. In addition, tDCS reduced the proportion of the M1 phenotype of microglia in VPL, VTA, and PAG regions and increase the proportion of the M2 phenotype. Conclusion: The results suggest that tDCS can effectively relieve SCI-induced neuropathic pain. Its mechanism may be related to regulating the inflammatory and anti-inflammatory cytokines in corresponding brain regions via promoting the phenotypic transformation of microglia.

Effect of Omeprazole Administration on the Pharmacokinetics of Oral Extended-Release Nifedipine in Healthy Subjects.

Oral extended-release (ER) dosage forms have been used to sustain blood drug levels, reduce adverse events, and improve patient compliance. We investigated potential effects of comedication on pharmacokinetic exposure of nifedipine ER products with different formulation designs and manufacturing processes. A clinical study compared a generic version of nifedipine ER tablet with pH-dependent dissolution behavior with an osmotic pump product with pH independent drug release under fasting condition. In this study, two nifedipine tablet products were tested with or without short-term omeprazole comedication in healthy subjects. Seven-day administration of omeprazole before nifedipine dosing significantly increased the gastric pH, and subsequently increased the geometric least square (LS) means of area under the concentration-time curve from time zero to the last measurable timepoint (AUC0-t ) and maximum plasma concentration (Cmax ) of nifedipine to 132.6% (90% confidence interval (CI): 120.6-145.7%) and 112.8% (90% CI: 100.8-126.3%) for pH-dependent ER tablets, and 120.6% (90% CI: 109.7-132.5%) and 122.5% (90% CI: 113.7-131.9%) for the pH-independent ER tablets, respectively. Similar extent of increase in AUC0-t and Cmax was confirmed in the subpopulations whose gastric pH was ≥ 4 or ≤ 3 in subjects with or without omeprazole administration. Given that similar increases in drug exposures were observed for both pH-dependent and pH-independent nifedipine formulations and the geometric LS mean ratios were between 112% and 133% with and without short-term omeprazole comedication, the gastric pH may have limited effects on omeprazole-induced nifedipine PK changes on the tested formulations. The inhibition of cytochrome P450 3A4 activity may play a significant role causing nifedipine exposure changes for both formulations, which would warrant additional assessment.

Mechanistic modeling of ophthalmic, nasal, injectable, and implant generic drug products: A workshop summary report.

For approval, a proposed generic drug product must demonstrate it is bioequivalent (BE) to the reference listed drug product. For locally acting drug products, conventional BE approaches may not be feasible because measurements in local tissues at the sites of action are often impractical, unethical, or cost-prohibitive. Mechanistic modeling approaches, such as physiologically-based pharmacokinetic (PBPK) modeling, may integrate information from drug product properties and human physiology to predict drug concentrations in these local tissues. This may allow clinical relevance determination of critical drug product attributes for BE assessment during the development of generic drug products. In this regard, the Office of Generic Drugs of the US Food and Drug Administration has recently established scientific research programs to accelerate the development and assessment of generic products by utilizing model-integrated alternative BE approaches. This report summarizes the presentations and panel discussion from a public workshop that provided research updates and information on the current state of the use of PBPK modeling approaches to support generic product development for ophthalmic, injectable, nasal, and implant drug products.

Regulatory utility of mechanistic modeling to support alternative bioequivalence approaches: A workshop overview.

On September 30 and October 1, 2021, the US Food and Drug Administration (FDA) and the Center for Research on Complex Generics cosponsored a live virtual workshop titled "Regulatory Utility of Mechanistic Modeling to Support Alternative Bioequivalence Approaches." The overall aims of the workshop included (i) engaging the generic drug industry and other involved stakeholders regarding how mechanistic modeling and simulation can support their product development and regulatory submissions; (ii) sharing the current state of mechanistic modeling for bioequivalence (BE) assessment through case studies; (iii) establishing a consensus on best practices for using mechanistic modeling approaches, such as physiologically based pharmacokinetic modeling and computational fluid dynamics modeling, for BE assessment; and (iv) introducing the concept of a Model Master File to improve model sharing between model developers, industry, and the FDA. More than 1500 people registered for the workshop. Based on a postworkshop survey, the majority of participants reported that their fundamental scientific understanding of mechanistic models was enhanced, there was greater consensus on model validation and verification, and regulatory expectations for mechanistic modeling submitted in abbreviated new drug applications were clarified by the workshop.

Topical pharmacokinetics of brinzolamide suspensions in rabbits and variability analysis for sample size and design considerations.

Identifying critical attributes for complex locally acting ophthalmic formulations and establishing in vitro-in vivo correlations can facilitate selection of appropriate thresholds for formulation changes that reflect lack of impact on in vivo performance. In this study the marketed antiglaucoma product Azopt® (1% brinzolamide suspension) and five other brinzolamide formulations varying in particle size distributions and apparent viscosities were topically administered in rabbits, and their ocular pharmacokinetics was determined in multiple ocular tissues. Statistical evaluation with ANOVA showed no significant differences between the formulations in the peak drug concentration (Cmax) in the aqueous humor and iris-ciliary body. As a post-hoc analysis, the within animal and total variability was determined for Cmax in the aqueous humor and iris-ciliary body. Based on the observed variability, we investigated the sample size needed for two types of study designs to observe statistically significant differences in Cmax. For the sample size calculations, assuming both 25% and 50% true differences in Cmax between two formulations, two study designs were compared: paired-eye dosing design (one formulation in one eye and another formulation in the other eye of the same animal at the same time) versus parallel-group design. The number of rabbits needed in the paired-eye dosing design are much lower than in the parallel-group design. For example, when the true difference in aqueous humor Cmax is 25%, nine rabbits are required in the paired-eye design versus seventy rabbits (35 per treatment) in the parallel-group design to observe a statistically significant difference with a power of 80%. Therefore, the proposed paired-eye dosing design is a viable option for the design of pharmacokinetic studies comparing ophthalmic products to determine the impact of formulation differences.

Effective treatment for massive neonatal catheter-related right atrial thrombosis.

Catheter-related thrombosis is a common complication caused by central venous catheters. Although right atrial thrombosis is uncommon, it may lead to life-threatening situations. Here, we report 2 cases of neonates with massive catheter-related right atrial thrombosis after congenital heart disease surgery. During therapeutic management, we attempted different treatments but failed to clear the mass. Finally, we found thrombectomy to be the most effective method for treating massive catheter-related right atrial thrombosis with favourable results.

Vagus Nerve Stimulation Reduces Neuroinflammation Through Microglia Polarization Regulation to Improve Functional Recovery After Spinal Cord Injury.

Background: Spinal cord injury (SCI) is a devastating disease that lacks effective treatment. Interestingly, recent studies indicated that vagus nerve stimulation (VNS), neuromodulation that is widely used in a variety of central nervous system (CNS) diseases, improved motor function recovery after SCI. But the exact underlying mechanism of how VNS ameliorates SCI is unclear. This study aimed to confirm the efficacy and further explore the potential therapeutic mechanism of VNS in SCI. Method: A T10 spinal cord compression model was established in adult female Sprague-Dawley rats. Then the stimulation electrode was placed in the left cervical vagus nerve (forming Sham-VNS, VNS, and VNS-MLA groups). Basso-Beattie-Bresnahan (BBB) behavioral scores and Motor evoked potentials (MEPs) analysis were used to detect motor function. A combination of histological and molecular methods was used to clarify the relevant mechanism. Results: Compared with the Sham-VNS group, the VNS group exhibited better functional recovery, reduced scar formation (both glial and fibrotic scars), tissue damage, and dark neurons, but these beneficial effects of VNS were diminished after alpha 7 nicotinic acetylcholine receptor (α7nAchR) blockade. Specifically, VNS inhibited the pro-inflammatory factors TNF-α, IL-1ß, and IL-6 and increased the expression of the anti-inflammatory factors IL-10. Furthermore, we found that VNS promotes the shift of M1-polarized Iba-1+/CD86+ microglia to M2-polarized Iba-1+/CD206+ microglia via upregulating α7nAchR to alleviate neuroinflammation after SCI. Conclusion: Our results demonstrated that VNS promotes microglial M2 polarization through upregulating α7nAChR to reduce neuroinflammation, thus improving motor function recovery after SCI. These findings indicate VNS might be a promising neuromodulation strategy for SCI.

Analgesic Effects of Repetitive Transcranial Magnetic Stimulation in Patients With Advanced Non-Small-Cell Lung Cancer: A Randomized, Sham-Controlled, Pilot Study.

Objective: Current pharmacological intervention for the cancer-related pain is still limited. The aim of this study was to explore whether repetitive transcranial magnetic stimulation (rTMS) could be an effective adjuvant therapy to reduce pain in patients with advanced non-small cell lung cancer (NSCLC). Methods: This was a randomized, sham-controlled study. A total of 41 advanced NSCLC patients with uncontrolled pain (score≥4 on pain intensity assessed with an 11-point numeric rating scale) were randomized to receive active (10 Hz, 2000 stimuli) (n = 20) or sham rTMS (n = 20) for 3 weeks. Pain was the primary outcome and was assessed with the Numeric Rating Scale (NRS). Secondary outcomes were oral morphine equivalent (OME) daily dose, quality of life (WHO Quality of Life-BREF), and psychological distress (the Hospital Depression and Anxiety Scale). All outcomes were measured at baseline, 3 days, 1 week, 2 weeks, and 3 weeks. Results: The pain intensity in both groups decreased gradually from day 3 and decreased to the lowest at the week 3, with a decrease rate of 41.09% in the rTMS group and 23.23% in the sham group. The NRS score of the rTMS group was significantly lower than that of the sham group on the week 2 (p < 0.001, Cohen's d =1.135) and week 3 (p=0.017, Cohen's d = -0.822). The OME daily dose, physiology and psychology domains of WHOQOL-BREF scores, as well as the HAM-A and HAM-D scores all were significantly improved at week 3 in rTMS group. Conclusion: Advanced NSCL patients with cancer pain treated with rTMS showed better greater pain relief, lower dosage of opioid, and better mood states and quality of life. rTMS is expected to be a new effective adjuvant therapy for cancer pain in advanced NSCLC patients.

Dynamics of the [4Fe-4S] cluster in Pyrococcus furiosus D14C ferredoxin via nuclear resonance vibrational and resonance Raman spectroscopies, force field simulations, and density functional theory calculations.

We have used (57)Fe nuclear resonance vibrational spectroscopy (NRVS) to study oxidized and reduced forms of the [4Fe-4S] cluster in the D14C variant ferredoxin from Pyrococcus furiosus (Pf D14C Fd). To assist the normal-mode assignments, we conducted NRVS with D14C ferredoxin samples with (36)S substituted into the [4Fe-4S] cluster bridging sulfide positions, and a model compound without ligand side chains, (Ph(4)P)(2)[Fe(4)S(4)Cl(4)]. Several distinct regions of NRVS intensity are identified, ranging from "protein" and torsional modes below 100 cm(-1), through bending and breathing modes near 150 cm(-1), to strong bands from Fe-S stretching modes between 250 and ∼400 cm(-1). The oxidized ferredoxin samples were also investigated by resonance Raman (RR) spectroscopy. We found good agreement between NRVS and RR frequencies, but because of different selection rules, the intensities vary dramatically between the two types of spectra. The (57)Fe partial vibrational densities of states for the oxidized samples were interpreted by normal-mode analysis with optimization of Urey-Bradley force fields for local models of the [4Fe-4S] clusters. Full protein model calculations were also conducted using a supplemented CHARMM force field, and these calculations revealed low-frequency modes that may be relevant to electron transfer with Pf Fd partners. Density functional theory (DFT) calculations complemented these empirical analyses, and DFT was used to estimate the reorganization energy associated with the [Fe(4)S(4)](2+/+) redox cycle. Overall, the NRVS technique demonstrates great promise for the observation and quantitative interpretation of the dynamical properties of Fe-S proteins.

The large quadrupole of water molecules.

Many quantum mechanical calculations indicate water molecules in the gas and liquid phase have much larger quadrupole moments than any of the common site models of water for computer simulations. Here, comparisons of multipoles from quantum mechanical∕molecular mechanical (QM∕MM) calculations at the MP2∕aug-cc-pVQZ level on a B3LYP∕aug-cc-pVQZ level geometry of a waterlike cluster and from various site models show that the increased square planar quadrupole can be attributed to the p-orbital character perpendicular to the molecular plane of the highest occupied molecular orbital as well as a slight shift of negative charge toward the hydrogens. The common site models do not account for the p-orbital type electron density and fitting partial charges of TIP4P- or TIP5P-type models to the QM∕MM dipole and quadrupole give unreasonable higher moments. Furthermore, six partial charge sites are necessary to account reasonably for the large quadrupole, and polarizable site models will not remedy the problem unless they account for the p-orbital in the gas phase since the QM calculations show it is present there too. On the other hand, multipole models by definition can use the correct multipoles and the electrostatic potential from the QM∕MM multipoles is much closer than that from the site models to the potential from the QM∕MM electron density. Finally, Monte Carlo simulations show that increasing the quadrupole in the soft-sticky dipole-quadrupole-octupole multipole model gives radial distribution functions that are in good agreement with experiment.