Using forest plots to interpret covariate effects in pharmacometric models.

The inclusion of covariates in pharmacometric models is important due to their ability to explain variability in drug exposure and response. Clear communication of the impact of covariates is needed to support informed decision making in clinical practice and in drug development. However, effectively conveying these effects to key stakeholders and decision makers can be challenging. Forest plots have been proposed to meet these communication needs. However, forest plots for the illustration of covariate effects in pharmacometrics are complex combinations of model predictions, uncertainty estimates, tabulated results, and reference lines and intervals. The purpose of this tutorial is to outline the aspects that influence the interpretation of forest plots, recommend best practices, and offer specific guidance for a clear and transparent communication of covariate effects.

Properties of the full random-effect modeling approach with missing covariate data.

During drug development, a key step is the identification of relevant covariates predicting between-subject variations in drug response. The full random effects model (FREM) is one of the full-covariate approaches used to identify relevant covariates in nonlinear mixed effects models. Here we explore the ability of FREM to handle missing (both missing completely at random (MCAR) and missing at random (MAR)) covariate data and compare it to the full fixed-effects model (FFEM) approach, applied either with complete case analysis or mean imputation. A global health dataset (20 421 children) was used to develop a FREM describing the changes of height for age Z-score (HAZ) over time. Simulated datasets (n = 1000) were generated with variable rates of missing (MCAR) covariate data (0%-90%) and different proportions of missing (MAR) data condition on either observed covariates or predicted HAZ. The three methods were used to re-estimate model and compared in terms of bias and precision which showed that FREM had only minor increases in bias and minor loss of precision at increasing percentages of missing (MCAR) covariate data and performed similarly in the MAR scenarios. Conversely, the FFEM approaches either collapsed at ≥ $$ \ge $$ 70% of missing (MCAR) covariate data (FFEM complete case analysis) or had large bias increases and loss of precision (FFEM with mean imputation). Our results suggest that FREM is an appropriate approach to covariate modeling for datasets with missing (MCAR and MAR) covariate data, such as in global health studies.

Medicines postpartum in Sweden and coverage in Janusmed Breastfeeding.

PURPOSE: The purpose of this article is (1) to investigate which medicines are prescribed and dispensed to women the first 6 months postpartum, (2) to identify medicines dispensed postpartum but not recommended during breastfeeding, and (3) to find medicines commonly dispensed postpartum, but not currently included in Janusmed Breastfeeding. METHODS: In this register-based cohort study covering births between January 2017 and August 2019, the Swedish Medical Birth Register (MBR), the Prescribed Drug Register, and Janusmed Breastfeeding were linked to identify medicines dispensed to women during the first 6 months postpartum, and how they are covered and classified in Janusmed Breastfeeding. RESULTS: During the first 6 months postpartum, 66% of women purchased at least one prescription medicine from the pharmacy. The most common medicines were contraceptive agents, analgesics, antibiotics, and glucocorticoids. A third of the 30 most commonly dispensed medicines have no information available about the safety of use in breastfeeding. The most dispensed medicines, where the database advises against use in breastfeeding, included several antitussive agents, a local anaesthetic, and several gestagens. The most commonly dispensed medicines not covered by the Janusmed Breastfeeding were medicines for dry eyes, for assisted reproduction, and HIV. CONCLUSION: Prescribed medicines compatible with breastfeeding are more common during the first 6 months postpartum than medicines not compatible with breastfeeding, but medicines which lack evidence for safety in breastfeeding are still commonly used.

3D analysis and grading of calcifications from ex vivo human meniscus.

OBJECTIVE: Meniscal calcifications are associated with the pathogenesis of knee osteoarthritis (OA). We propose a micro-computed tomography (µCT) based 3D analysis of meniscal calcifications ex vivo, including a new grading system. METHOD: Human medial and lateral menisci were obtained from 10 patients having total knee replacement for medial compartment OA and 10 deceased donors without knee OA (healthy references). The samples were fixed; one subsection was imaged with µCT, and the adjacent tissue was processed for histological evaluation. Calcifications were examined from the reconstructed 3D µCT images, and a new grading system was developed. To validate the grading system, meniscal calcification volumes (CVM) were quantitatively analyzed and compared between the calcification grades. Furthermore, we estimated the relationship between histopathological degeneration and the calcification severity. RESULTS: 3D µCT images depict calcifications in every sample, including diminutive calcifications that are not visible in histology. In the new grading system, starting from grade 2, each grade results in a CVM that is 20.3 times higher (95% CI 13.3-30.5) than in the previous grade. However, there was no apparent difference in CVM between grades 1 and 2. The calcification grades appear to increase with the increasing histopathological degeneration, although histopathological degeneration is also observed with small calcification grades. CONCLUSIONS: 3D µCT grading of meniscal calcifications is feasible. Interestingly, it seems that there are two patterns of degeneration in the menisci of our sample set: 1) with diminutive calcifications (calcification grades 1-2), and 2) with large to widespread calcifications (calcification grades 3-5).

Efficient and relevant stepwise covariate model building for pharmacometrics.

Covariate modeling is an important opportunity for pharmacometrics to influence decision making in drug development. The stepwise covariate model (SCM) building procedure is the most common method for covariate model development. Despite its advantages, the traditional SCM method is known to have long runtimes and the suboptimal ability to select relevant covariates, especially in more complex phase III settings. In this work, two alternative approaches are presented: SCM+, which introduces the "adaptive scope reduction" and changes to general estimation settings, and "stage-wise filtering," which groups covariates into categories based on their importance (mechanistic, structural, and exploratory). The three methods (SCM, SCM+, and SCM+ with stage-wise filtering) are applied to data from a simulated phase III population pharmacokinetic study and are compared in terms of efficiency and relevance. The two SCM+ methods were considerably more efficient than the traditional SCM: the number of function evaluations was reduced by 70% for SCM+ and by 76% for SCM+ with stage-wise filtering compared to SCM; the corresponding number of executed models was reduced by 44% for SCM+ and 70% for SCM+ with stage-wise filtering. In addition, among the three methods, SCM+ with stage-wise filtering selected the highest number of relevant covariates. Given the improved efficiency and ability to select relevant covariates shown in this work, the use of SCM+ and stage-wise filtering can greatly increase the efficiency of covariate modeling in drug development, which will ultimately facilitate more timely support for decision making.

Contact with psychiatric care prior to suicide: are there differences between migrants and the majority population in Sweden? A cohort study of 12 474 persons who died by suicide between 2006 and 2016.

AIMS: The aim of this study was to determine possible differences in psychiatric care contact and the type of contact in the year prior to suicide by migrant status and region of origin compared to Swedish persons. METHODS: A population-based open cohort design, using linked national registers, to study all individuals aged 20-64 years who died by suicide between 1 January 2006 and 31 December 2016 in Sweden (N = 12 474). The primary exposure was migrant status compared to the Swedish majority population in the following categories: non-refugee migrants, refugee migrants and children of migrants. The secondary exposure was region of origin in seven regions: Sweden, other Nordic countries, Europe, Sub-Saharan Africa, the Middle East and North Africa, Asia, the Americas and Oceania. The four outcomes were psychiatric in- and outpatient care, prescribed and purchased psychotropic medication and a variable composing the other variables, all measured the year before death. Logistic regression models adjusted for age, sex, income and marital status estimated the likelihood of psychiatric care utilisation by type of care within the year prior to death by migrant status and region of origin (individually and combined). RESULTS: Out of all who had died by suicide, 81% had had psychiatric care of any type in the year before death by suicide. Among refugees the prevalence of psychiatric care before death by suicide was 88%. Compared with the Swedish reference group, non-refugees and persons from Asia and Sub-Saharan Africa had a lower likelihood of utilising psychiatric care prior to suicide driven by a lower use of prescribed psychotropic medication. Persons from the Middle East and North Africa had a higher likelihood, driven by higher use of psychiatric outpatient care and prescribed psychotropic medication. Non-refugees' likelihood of utilising care before death by suicide was lower within the first 5 years of living in Sweden. CONCLUSION: A large share of those who die by suicide use psychiatric care the year before they die. Non-refugee migrants and persons from Asia and Sub-Saharan Africa have a lower likelihood of utilising psychiatric care prior to suicide compared to Swedish, whereas persons from the Middle East and North Africa have a higher likelihood. Health care and policy makers should consider both migrant status, region of origin and time in the new country for further suicide prevention efforts.

Population pharmacokinetic analysis of tepotinib, an oral MET kinase inhibitor, including data from the VISION study.

PURPOSE: Tepotinib is a highly selective, potent, mesenchymal-epithelial transition factor (MET) inhibitor, approved for the treatment of non-small cell lung cancer (NSCLC) harboring MET exon 14 skipping. Objectives of this population pharmacokinetic (PK) analysis were to evaluate the dose-exposure relationship of tepotinib and its major circulating metabolite, MSC2571109A, and to identify the intrinsic/extrinsic factors that are predictive of PK variability. METHODS: Data were included from 12 studies in patients with cancer and in healthy participants. A sequential modeling approach was used to analyze the parent and metabolite data, including covariate analyses. Potential associations between observed covariates and PK parameters were illustrated using bootstrap analysis-based forest plots. RESULTS: A two-compartment model with sequential zero- and first-order absorption, and a first-order elimination from the central compartment, best described the plasma PK of tepotinib in humans across the dose range of 30-1400 mg. The bioavailability of tepotinib was shown to be dose dependent, although bioavailability decreased primarily at doses above the therapeutic dose of 500 mg. The intrinsic factors of race, age, sex, body weight, mild/moderate hepatic impairment and mild/moderate renal impairment, along with the extrinsic factors of opioid analgesic and gefitinib intake, had no relevant effect on tepotinib PK. Tepotinib has a long effective half-life of ~ 32 h. CONCLUSIONS: Tepotinib shows dose proportionality up to at least the therapeutic dose, and time-independent clearance with a profile appropriate for once-daily dosing. None of the covariates identified had a clinically meaningful effect on tepotinib exposure or required dose adjustments.

A quantitative approach to the choice of number of samples for percentile estimation in bootstrap and visual predictive check analyses.

Understanding the uncertainty in parameter estimates or in derived secondary variables is important in all data analysis activities. In pharmacometrics, this is often done based on the standard errors from the variance-covariance matrix of the estimates. Confidence intervals derived in this way are by definition symmetrical, which may lead to implausible outcomes, and will require translation to generate uncertainties in derived variables. An often-used alternative is numerical percentile estimation by, for example, nonparametric bootstraps to circumvent these issues. Visual predictive checks (VPCs), which is a commonly used model diagnostic tool in pharmacometric analyses, also rely on the estimation of percentiles through numerical approaches. Given the cost in terms of run times and processing times for these methods, it is important to consider the trade-off between the number of bootstrap samples or simulated data sets in the VPCs, to the increase in precision related to a large number of bootstrap samples or simulated data sets. The objective with this tutorial is to provide a quantitative framework for assessing the precision in estimated percentile limits in bootstrap and visual predictive checks analyses to facilitate an informed choice of confidence interval width, number of bootstrap samples/simulated data sets, and required level of precision.

An introduction to the full random effects model.

The full random-effects model (FREM) is a method for determining covariate effects in mixed-effects models. Covariates are modeled as random variables, described by mean and variance. The method captures the covariate effects in estimated covariances between individual parameters and covariates. This approach is robust against issues that may cause reduced performance in methods based on estimating fixed effects (e.g., correlated covariates where the effects cannot be simultaneously identified in fixed-effects methods). FREM covariate parameterization and transformation of covariate data records can be used to alter the covariate-parameter relation. Four relations (linear, log-linear, exponential, and power) were implemented and shown to provide estimates equivalent to their fixed-effects counterparts. Comparisons between FREM and mathematically equivalent full fixed-effects models (FFEMs) were performed in original and simulated data, in the presence and absence of non-normally distributed and highly correlated covariates. These comparisons show that both FREM and FFEM perform well in the examined cases, with a slightly better estimation accuracy of parameter interindividual variability (IIV) in FREM. In addition, FREM offers the unique advantage of letting a single estimation simultaneously provide covariate effect coefficient estimates and IIV estimates for any subset of the examined covariates, including the effect of each covariate in isolation. Such subsets can be used to apply the model across data sources with different sets of available covariates, or to communicate covariate effects in a way that is not conditional on other covariates.

Conditional distribution modeling as an alternative method for covariates simulation: Comparison with joint multivariate normal and bootstrap techniques.

Clinical trial simulation (CTS) is a valuable tool in drug development. To obtain realistic scenarios, the subjects included in the CTS must be representative of the target population. Common ways of generating virtual subjects are based upon bootstrap (BS) procedures or multivariate normal distributions (MVNDs). Here, we investigated the performance of an alternative method based on conditional distributions (CDs). Covariate data from a hypertension drug development program were used. The methods were evaluated based on the original data set (internal evaluation) and on their ability to reproduce an older, unobserved population (extrapolation). Similar results were obtained in the internal evaluation for summary statistics, yet BS was able to preserve the correlation structure of the empirical distribution, which was not adequately reproduced by MVND; CD was in between BS and MVND. BS does not allow to extrapolate to an unobserved population. When the data set used to inform the extrapolation was well approximated by an MVND, the results from CD and MVND were comparable. However, improved extrapolation performance was observed for CD when deviations from normality assumptions occurred. If CTS is used to simulate within the observed distribution, BS is the preferred method. When extrapolating to new populations, a parametric method like CD/MVND is needed. In case the empirical multivariate distribution is characterized by linearly related covariates and unimodal marginal distributions, MVND can be used because of the simpler statistical framework and well-established use; however, if uncertainty about the MVND assumptions exists, CD will increase the confidence in the simulations compared to MVND.

A Physiologically-Based Pharmacokinetic Framework for Prediction of Drug Exposure in Malnourished Children.

Malnutrition in children is a global health problem, particularly in developing countries. The effects of an insufficient supply of nutrients on body composition and physiological functions may have implications for drug disposition and ultimately affect the clinical outcome in this vulnerable population. Physiologically-based pharmacokinetic (PBPK) modeling can be used to predict the effect of malnutrition as it links physiological changes to pharmacokinetic (PK) consequences. However, the absence of detailed information on body composition and the limited availability of controlled clinical trials in malnourished children complicates the establishment and evaluation of a generic PBPK model in this population. In this manuscript we describe the creation of physiologically-based bridge to a malnourished pediatric population, by combining information on (a) the differences in body composition between healthy and malnourished adults and (b) the differences in physiology between healthy adults and children. Model performance was confirmed using clinical reference data. This study presents a physiologically-based translational framework for prediction of drug disposition in malnourished children. The model is readily applicable for dose recommendation strategies to address the urgent medicinal needs of this vulnerable population.

Silica dust and sarcoidosis in Swedish construction workers.

BACKGROUND: The aetiology of sarcoidosis is not well established. In previous studies, smoking has been negatively associated with sarcoidosis and there are some indications of an association between exposure to silica dust and sarcoidosis. AIMS: To study the risk of sarcoidosis in relation to silica dust exposure. METHODS: A longitudinal cohort of construction workers linked with a registry of Swedish inpatient diagnoses. Workers were designated as exposed or unexposed to silica based on job titles in a job-exposure matrix. The relative risk (RR) was analysed with Poisson regression adjusting for age and smoking. RESULTS: We identified 371 cases of sarcoidosis among 297 917 male workers. There was an increased risk of sarcoidosis in the medium- to high-exposure group [RR 1.83 (95% confidence interval {CI} 1.14-2.95)]. A stratified analysis according to smoking showed that ever-smoking workers had an increased risk of sarcoidosis if highly exposed to silica dust [RR 2.44 (95% CI 1.37-4.33)] compared to non-exposed ever-smokers. The risk of non-smokers highly exposed to silica was not significantly increased [RR 1.07 (95% CI 0.72-1.58)] compared to non-exposed non-smokers. CONCLUSION: The study indicates an increased risk of developing sarcoidosis in ever-smoking men exposed to silica.

Oxidative stress and biomarker responses in the Atlantic halibut after long term exposure to elevated CO2 and a range of temperatures.

CO2 emissions from human activities are increasing, resulting in greater rates of change in the oceans, exceeding any other event in geological and historical records over the past 300 million years. Oceans are warming and pH levels are decreasing. Marine organisms will need to respond to multiple stressors and the potential consequences of global change-related effects in fish needs to be investigated. Fish are affected by many biotic and abiotic environmental variables, including temperature and CO2 fluctuations, and it is therefore critical to investigate how these variables may affect physiological and biochemical processes. We investigated the effects of elevated CO2 levels (pH of 8.0, which served as a control, or 7.6, which is predicted for the year 2100) combined with exposure to different temperatures (5, 10, 12, 14, 16, and 18 °C) in the Atlantic halibut (Hippoglossus hippoglossus) during a three month experiment. Since regulation of reactive oxygen species (ROS) is crucial for physiological processes the focus was on the antioxidant defense system and we assessed the effects on catalytic activities of antioxidant enzymes (SOD, CAT, GR, GST, GPx). In addition we also analyzed effects on cholinesterase enzymes (AChE and BChE), and CYP1A enzyme activities (EROD). The treatments resulted in oxidative stress, and damage was evident in the form of protein carbonyls which were consistently higher in the elevated CO2-treated fish at all temperatures. Analyses of antioxidant enzymes did not show the same results, suggesting that the exposure to elevated CO2 increased ROS formation but not defences. The antioxidant defense system was insufficient, and the resulting oxidative damage could impact physiological function of the halibut on a cellular level.

A PK/PD Analysis of Circulating Biomarkers and Their Relationship to Tumor Response in Atezolizumab-Treated non-small Cell Lung Cancer Patients.

To assess circulating biomarkers as predictors of antitumor response to atezolizumab (anti-programmed death-ligand 1 (PD-L1), Tecentriq) serum pharmacokinetic (PK) and 95 plasma biomarkers were analyzed in 88 patients with relapsed/refractory non-small cell lung cancer (NSCLC) receiving atezolizumab i.v. q3w (10-20 mg/kg) in the PCD4989g phase I clinical trial. Following exploratory analyses, two plasma biomarkers were chosen for further study and correlation with change in tumor size (the sum of the longest diameter) was assessed in a pharmacokinetic/pharmacodynamic (PK/PD) tumor modeling framework. When longitudinal kinetics of biomarkers and tumor size were modeled, tumor shrinkage was found to significantly correlate with area under the curve (AUC), baseline factors (metastatic sites, liver metastases, and smoking status), and relative change in interleukin (IL)-18 level from baseline at day 21 (RCFBIL -18,d21 ). Although AUC was a major predictor of tumor shrinkage, the effect was estimated to dissipate with an average half-life of 80 days, whereas RCFBIL -18,d21 seemed relevant to the duration of the response.

PharmTeX: a LaTeX-Based Open-Source Platform for Automated Reporting Workflow.

Every year, the pharmaceutical industry generates a large number of scientific reports related to drug research, development, and regulatory submissions. Many of these reports are created using text processing tools such as Microsoft Word. Given the large number of figures, tables, references, and other elements, this is often a tedious task involving hours of copying and pasting and substantial efforts in quality control (QC). In the present article, we present the LaTeX-based open-source reporting platform, PharmTeX, a community-based effort to make reporting simple, reproducible, and user-friendly. The PharmTeX creators put a substantial effort into simplifying the sometimes complex elements of LaTeX into user-friendly functions that rely on advanced LaTeX and Perl code running in the background. Using this setup makes LaTeX much more accessible for users with no prior LaTeX experience. A software collection was compiled for users not wanting to manually install the required software components. The PharmTeX templates allow for inclusion of tables directly from mathematical software output as well and figures from several formats. Code listings can be included directly from source. No previous experience and only a few hours of training are required to start writing reports using PharmTeX. PharmTeX significantly reduces the time required for creating a scientific report fully compliant with regulatory and industry expectations. QC is made much simpler, since there is a direct link between analysis output and report input. PharmTeX makes available to report authors the strengths of LaTeX document processing without the need for extensive training. Graphical Abstract ᅟ.

Cerebellar volume and cerebellocerebral structural covariance in schizophrenia: a multisite mega-analysis of 983 patients and 1349 healthy controls.

Although cerebellar involvement across a wide range of cognitive and neuropsychiatric phenotypes is increasingly being recognized, previous large-scale studies in schizophrenia (SZ) have primarily focused on supratentorial structures. Hence, the across-sample reproducibility, regional distribution, associations with cerebrocortical morphology and effect sizes of cerebellar relative to cerebral morphological differences in SZ are unknown. We addressed these questions in 983 patients with SZ spectrum disorders and 1349 healthy controls (HCs) from 14 international samples, using state-of-the-art image analysis pipelines optimized for both the cerebellum and the cerebrum. Results showed that total cerebellar grey matter volume was robustly reduced in SZ relative to HCs (Cohens's d=-0.35), with the strongest effects in cerebellar regions showing functional connectivity with frontoparietal cortices (d=-0.40). Effect sizes for cerebellar volumes were similar to the most consistently reported cerebral structural changes in SZ (e.g., hippocampus volume and frontotemporal cortical thickness), and were highly consistent across samples. Within groups, we further observed positive correlations between cerebellar volume and cerebral cortical thickness in frontotemporal regions (i.e., overlapping with areas that also showed reductions in SZ). This cerebellocerebral structural covariance was strongest in SZ, suggesting common underlying disease processes jointly affecting the cerebellum and the cerebrum. Finally, cerebellar volume reduction in SZ was highly consistent across the included age span (16-66 years) and present already in the youngest patients, a finding that is more consistent with neurodevelopmental than neurodegenerative etiology. Taken together, these novel findings establish the cerebellum as a key node in the distributed brain networks underlying SZ.

Prefrontal cortical thinning links to negative symptoms in schizophrenia via the ENIGMA consortium.

BACKGROUND: Our understanding of the complex relationship between schizophrenia symptomatology and etiological factors can be improved by studying brain-based correlates of schizophrenia. Research showed that impairments in value processing and executive functioning, which have been associated with prefrontal brain areas [particularly the medial orbitofrontal cortex (MOFC)], are linked to negative symptoms. Here we tested the hypothesis that MOFC thickness is associated with negative symptom severity. METHODS: This study included 1985 individuals with schizophrenia from 17 research groups around the world contributing to the ENIGMA Schizophrenia Working Group. Cortical thickness values were obtained from T1-weighted structural brain scans using FreeSurfer. A meta-analysis across sites was conducted over effect sizes from a model predicting cortical thickness by negative symptom score (harmonized Scale for the Assessment of Negative Symptoms or Positive and Negative Syndrome Scale scores). RESULTS: Meta-analytical results showed that left, but not right, MOFC thickness was significantly associated with negative symptom severity (ß std = -0.075; p = 0.019) after accounting for age, gender, and site. This effect remained significant (p = 0.036) in a model including overall illness severity. Covarying for duration of illness, age of onset, antipsychotic medication or handedness weakened the association of negative symptoms with left MOFC thickness. As part of a secondary analysis including 10 other prefrontal regions further associations in the left lateral orbitofrontal gyrus and pars opercularis emerged. CONCLUSIONS: Using an unusually large cohort and a meta-analytical approach, our findings point towards a link between prefrontal thinning and negative symptom severity in schizophrenia. This finding provides further insight into the relationship between structural brain abnormalities and negative symptoms in schizophrenia.

A health economic simulation model for the clinical management of osteoporosis.

The objective was to estimate the burden of osteoporosis in Sweden based on current clinical practice and the cost-effectiveness of improvements in the management of osteoporosis over the clinical management compared to current clinical practice. Results showed that better compliance to treatment guidelines is associated with better projected outcomes and cost-savings. INTRODUCTION: The purpose of this study is to estimate the burden of osteoporosis in Sweden based on current clinical practice and the cost-effectiveness of improvements in the management of osteoporosis over the clinical management compared to current clinical practice. METHODS: The analysis was carried out using a model that simulates the individual patients considered for pharmacological treatment during 1 year and their projected osteoporosis treatment pathway, quality-adjusted life years (QALYs) and costs over their remaining lifetime. All patients regardless of treatment or no treatment were simulated. Information on current management of osteoporosis in terms of patient characteristics and treatment patterns were derived from a Swedish osteoporosis research database based on national registers and patient records. Current (standard) clinical management was compared with alternative scenarios mirroring Swedish treatment guidelines. RESULTS: The national burden in terms of lost QALYs was estimated at 14,993 QALYs and the total economic cost at €776M. Scenario analyses showed that 382-3864 QALYs could be gained at a cost/QALY ranging from cost-saving to €31368, depending on the scenario. The margin of investment, i.e. the maximum amount that could be invested in the healthcare system to achieve these improvements up to the limit of the willingness to pay/QALY, was estimated at €199M on a population level (€3,634/patient). CONCLUSIONS: The analysis showed that better compliance to treatment guidelines is associated with better projected outcomes and cost-savings. From a cost-effectiveness perspective, there is also considerable room for investment to achieve these improvements in the management of osteoporosis.

Grid-Based Projector Augmented Wave (GPAW) Implementation of Quantum Mechanics/Molecular Mechanics (QM/MM) Electrostatic Embedding and Application to a Solvated Diplatinum Complex.

A multiscale density functional theory-quantum mechanics/molecular mechanics (DFT-QM/MM) scheme is presented, based on an efficient electrostatic coupling between the electronic density obtained from a grid-based projector augmented wave (GPAW) implementation of density functional theory and a classical potential energy function. The scheme is implemented in a general fashion and can be used with various choices for the descriptions of the QM or MM regions. Tests on H2O clusters, ranging from dimer to decamer show that no systematic energy errors are introduced by the coupling that exceeds the differences in the QM and MM descriptions. Over 1 ns of liquid water, Born-Oppenheimer QM/MM molecular dynamics (MD) are sampled combining 10 parallel simulations, showing consistent liquid water structure over the QM/MM border. The method is applied in extensive parallel MD simulations of an aqueous solution of the diplatinum [Pt2(P2O5H2)4]4- complex (PtPOP), spanning a total time period of roughly half a nanosecond. An average Pt-Pt distance deviating only 0.01 Å from experimental results, and a ground-state Pt-Pt oscillation frequency deviating by <2% from experimental results were obtained. The simulations highlight a remarkable harmonicity of the Pt-Pt oscillation, while also showing clear signs of Pt-H hydrogen bonding and directional coordination of water molecules along the Pt-Pt axis of the complex.