Crystal Polymorph Search in the NPT Ensemble via a Deposition/Sublimation Alchemical Path

The formulation of active pharmaceutical ingredients involves discovering stable crystal packing arrangements or polymorphs, each of which has distinct pharmaceutically relevant properties. Traditional experimental screening techniques utilizing various conditions are commonly supplemented with in silico crystal structure prediction (CSP) to inform the crystallization process and mitigate risk. Predictions are often based on advanced classical force fields or quantum mechanical calculations that model the crystal potential energy landscape but do not fully incorporate temperature, pressure, or solution conditions during the search procedure. This study proposes an innovative alchemical path that utilizes an advanced polarizable atomic multipole force field to predict crystal structures based on direct sampling of the NPT ensemble. The use of alchemical (i.e., nonphysical) intermediates, a novel Monte Carlo barostat, and an orthogonal space tempering bias combine to enhance the sampling efficiency of the deposition/sublimation phase transition. The proposed algorithm was applied to 2-((4-(2-(3,4-dichlorophenyl)ethyl)phenyl)amino)benzoic acid (Cambridge Crystallography Database Centre ID: XAFPAY) as a case study to showcase the algorithm. Each experimentally determined polymorph with one molecule in the asymmetric unit was successfully reproduced via approximately 1000 short 1 ns simulations per space group where each simulation was initiated from random rigid body coordinates and unit cell parameters. Utilizing two threads of a recent Intel CPU (a Xeon Gold 6330 CPU at 2.00 GHz), 1 ns of sampling using the polarizable AMOEBA force field can be acquired in 4 h (equating to more than 300 ns/day using all 112 threads/56 cores of a dual CPU node) within the Force Field X software (https://ffx.biochem.uiowa.edu). These results demonstrate a step forward in the rigorous use of the NPT ensemble during the CSP search process and open the door to future algorithms that incorporate solution conditions using continuum solvation methods.

Constant-pH Simulations with the Polarizable Atomic Multipole AMOEBA Force Field

Accurately predicting protein behavior across diverse pH environments remains a significant challenge in biomolecular simulations. Existing constant-pH molecular dynamics (CpHMD) algorithms are limited to fixed-charge force fields, hindering their application to biomolecular systems described by permanent atomic multipoles or induced dipoles. This work overcomes these limitations by introducing the first polarizable CpHMD algorithm in the context of the Atomic Multipole Optimized Energetics for Biomolecular Applications (AMOEBA) force field. Additionally, our implementation in the open-source Force Field X (FFX) software has the unique ability to handle titration state changes for crystalline systems including flexible support for all 230 space groups. The evaluation of constant-pH molecular dynamics (CpHMD) with the AMOEBA force field was performed on 11 crystalline peptide systems that span the titrating amino acids (Asp, Glu, His, Lys, and Cys). Titration states were correctly predicted for 15 out of the 16 amino acids present in the 11 systems, including for the coordination of Zn2+ by cysteines. The lone exception was for a HIS-ALA peptide where CpHMD predicted both neutral histidine tautomers to be equally populated, whereas the experimental model did not consider multiple conformers and diffraction data are unavailable for rerefinement. This work demonstrates the promise polarizable CpHMD simulations for pKa predictions, the study of biochemical mechanisms such as the catalytic triad of proteases, and for improved protein-ligand binding affinity accuracy in the context of pharmaceutical lead optimization.

Endothelial lipase variant T111I does not alter inhibition by angiopoietin-like proteins

High levels of HDL-C are correlated with a decreased risk of cardiovascular disease. HDL-C levels are modulated in part by the secreted phospholipase, endothelial lipase (EL), which hydrolyzes the phospholipids of HDL and decreases circulating HDL-C concentrations. A 584C/T polymorphism in LIPG, the gene which encodes EL, was first identified in individuals with increased HDL levels. This polymorphism results in a T111I point mutation the EL protein. The association between this variant, HDL levels, and the risk of coronary artery disease (CAD) in humans has been extensively studied, but the findings have been inconsistent. In this study, we took a biochemical approach, investigating how the T111I variant affected EL activity, structure, and stability. Moreover, we tested whether the T111I variant altered the inhibition of phospholipase activity by angiopoietin-like 3 (ANGPTL3) and angiopoietin-like 4 (ANGPTL4), two known EL inhibitors. We found that neither the stability nor enzymatic activity of EL was altered by the T111I variant. Moreover, we found no difference between wild-type and T111I EL in their ability to be inhibited by ANGPTL proteins. These data suggest that any effect this variant may have on HDL-C levels or cardiovascular disease are not mediated through alterations in these functions.

Germline landscape of RPA1, RPA2 and RPA3 variants in pediatric malignancies: identification of RPA1 as a novel cancer predisposition candidate gene

Replication Protein A (RPA) is single-strand DNA binding protein that plays a key role in the replication and repair of DNA. RPA is a heterotrimer made of 3 subunits - RPA1, RPA2, and RPA3. Germline pathogenic variants affecting RPA1 were recently described in patients with Telomere Biology Disorders (TBD), also known as dyskeratosis congenita or short telomere syndrome. Premature telomere shortening is a hallmark of TBD and results in bone marrow failure and predisposition to hematologic malignancies. Building on the finding that somatic mutations in RPA subunit genes occur in ~1% of cancers, we hypothesized that germline RPA alterations might be enriched in human cancers. Because germline RPA1 mutations are linked to early onset TBD with predisposition to myelodysplastic syndromes, we interrogated pediatric cancer cohorts to define the prevalence and spectrum of rare/novel and putative damaging germline RPA1, RPA2, and RPA3 variants. In this study of 5,993 children with cancer, 75 (1.25%) harbored heterozygous rare (non-cancer population allele frequency (AF) < 0.1%) variants in the RPA heterotrimer genes, of which 51 cases (0.85%) had ultra-rare (AF < 0.005%) or novel variants. Compared with Genome Aggregation Database (gnomAD) non-cancer controls, there was significant enrichment of ultra-rare and novel RPA1, but not RPA2 or RPA3, germline variants in our cohort (adjusted p-value < 0.05). Taken together, these findings suggest that germline putative damaging variants affecting RPA1 are found in excess in children with cancer, warranting further investigation into the functional role of these variants in oncogenesis.

GJA3 Genetic Variation and Autosomal Dominant Congenital Cataracts and Glaucoma Following Cataract Surgery

Importance

The p.Asp67Tyr genetic variant in the GJA3 gene is responsible for congenital cataracts in a family with a high incidence of glaucoma following cataract surgery.

Objective

To describe the clinical features of a family with a strong association between congenital cataracts and glaucoma following cataract surgery secondary to a genetic variant in the GJA3 gene (NM_021954.4:c.199G>T, p.Asp67Tyr).

Design, Setting, and Participants

This was a retrospective, observational, case series, genetic association study from the University of Iowa spanning 61 years. Examined were the ophthalmic records from 1961 through 2022 of the family members of a 4-generation pedigree with autosomal dominant congenital cataracts.

Main Outcomes and Measures

Frequency of glaucoma following cataract surgery and postoperative complications among family members with congenital cataract due to the p.Asp67Tyr GJA3 genetic variant.

Results

Medical records were available from 11 of 12 family members (7 male [63.6%]) with congenital cataract with a mean (SD) follow-up of 30 (21.7) years (range, 0.2-61 years). Eight of 9 patients with congenital cataracts developed glaucoma, and 8 of 8 patients who had cataract surgery at age 2 years or younger developed glaucoma following cataract surgery. The only family member with congenital cataracts who did not develop glaucoma had delayed cataract surgery until 12 and 21 years of age. Five of 11 family members (45.5%) had retinal detachments after cataract extraction and vitrectomy. No patients developed retinal detachments after prophylactic 360-degree endolaser.

Conclusions and Relevance

The GJA3 genetic variant, p.Asp67Tyr, was identified in a 4-generation congenital cataract pedigree from Iowa. This report suggests that patients with congenital cataract due to some GJA3 genetic variants may be at especially high risk for glaucoma following cataract surgery. Retinal detachments after cataract extraction in the first 2 years of life were also common in this family, and prophylactic retinal endolaser may be indicated at the time of surgery.

Endothelial Lipase Variant, T111I, Does Not Alter Inhibition by Angiopoietin-like Proteins

High levels of HDL-C are correlated with a decreased risk of cardiovascular disease. HDL-C levels are modulated in part by the secreted phospholipase, endothelial lipase (EL), which hydrolyzes the phospholipids of HDL and decreases circulating HDL-C concentrations. A 584C/T polymorphism in LIPG, the gene which encodes EL, was first identified in individuals with increased HDL levels. This polymorphism results in a T111I point mutation the EL protein. The association between this variant, HDL levels, and the risk of coronary artery disease (CAD) in humans has been extensively studied, but the findings have been inconsistent. In this study, we took a biochemical approach, investigating how the T111I variant affected EL activity, structure, and stability. Moreover, we tested whether the T111I variant altered the inhibition of phospholipase activity by angiopoietin-like 3 (ANGPTL3) and angiopoietin-like 4 (ANGPTL4), two known EL inhibitors. We found that neither the stability nor enzymatic activity of EL was altered by the T111I variant. Moreover, we found no difference between wild-type and T111I EL in their ability to be inhibited by ANGPTL proteins. These data suggest that any effect this variant may have on HDL-C levels or cardiovascular disease are not mediated through alterations in these functions.

A generalized Kirkwood implicit solvent for the polarizable AMOEBA protein model

Computational simulation of biomolecules can provide important insights into protein design, protein-ligand binding interactions, and ab initio biomolecular folding, among other applications. Accurate treatment of the solvent environment is essential in such applications, but the use of explicit solvents can add considerable cost. Implicit treatment of solvent effects using a dielectric continuum model is an attractive alternative to explicit solvation since it is able to describe solvation effects without the inclusion of solvent degrees of freedom. Previously, we described the development and parameterization of implicit solvent models for small molecules. Here, we extend the parameterization of the generalized Kirkwood (GK) implicit solvent model for use with biomolecules described by the AMOEBA force field via the addition of corrections to the calculation of effective radii that account for interstitial spaces that arise within biomolecules. These include element-specific pairwise descreening scale factors, a short-range neck contribution to describe the solvent-excluded space between pairs of nearby atoms, and finally tanh-based rescaling of the overall descreening integral. We then apply the AMOEBA/GK implicit solvent to a set of ten proteins and achieve an average coordinate root mean square deviation for the experimental structures of 2.0 Å across 500 ns simulations. Overall, the continued development of implicit solvent models will help facilitate the simulation of biomolecules on mechanistically relevant timescales.

Assessing variants of uncertain significance implicated in hearing loss using a comprehensive deafness proteome

Hearing loss is the leading sensory deficit, affecting ~ 5% of the population. It exhibits remarkable heterogeneity across 223 genes with 6328 pathogenic missense variants, making deafness-specific expertise a prerequisite for ascribing phenotypic consequences to genetic variants. Deafness-implicated variants are curated in the Deafness Variation Database (DVD) after classification by a genetic hearing loss expert panel and thorough informatics pipeline. However, seventy percent of the 128,167 missense variants in the DVD are "variants of uncertain significance" (VUS) due to insufficient evidence for classification. Here, we use the deep learning protein prediction algorithm, AlphaFold2, to curate structures for all DVD genes. We refine these structures with global optimization and the AMOEBA force field and use DDGun3D to predict folding free energy differences (∆∆GFold) for all DVD missense variants. We find that 5772 VUSs have a large, destabilizing ∆∆GFold that is consistent with pathogenic variants. When also filtered for CADD scores (> 25.7), we determine 3456 VUSs are likely pathogenic at a probability of 99.0%. Of the 224 genes in the DVD, 166 genes (74%) exhibit one or more missense variants predicted to cause a pathogenic change in protein folding stability. The VUSs prioritized here affect 119 patients (~ 3% of cases) sequenced by the OtoSCOPE targeted panel. Approximately half of these patients previously received an inconclusive report, and reclassification of these VUSs as pathogenic provides a new genetic diagnosis for six patients.

Progressive alignment of crystals: reproducible and efficient assessment of crystal structure similarity

During in silico crystal structure prediction of organic molecules, millions of candidate structures are often generated. These candidates must be compared to remove duplicates prior to further analysis (e.g. optimization with electronic structure methods) and ultimately compared with structures determined experimentally. The agreement of predicted and experimental structures forms the basis of evaluating the results from the Cambridge Crystallographic Data Centre (CCDC) blind assessment of crystal structure prediction, which further motivates the pursuit of rigorous alignments. Evaluating crystal structure packings using coordinate root-mean-square deviation (RMSD) for N molecules (or N asymmetric units) in a reproducible manner requires metrics to describe the shape of the compared molecular clusters to account for alternative approaches used to prioritize selection of molecules. Described here is a flexible algorithm called Progressive Alignment of Crystals (PAC) to evaluate crystal packing similarity using coordinate RMSD and introducing the radius of gyration (R _g) as a metric to quantify the shape of the superimposed clusters. It is shown that the absence of metrics to describe cluster shape adds ambiguity to the results of the CCDC blind assessments because it is not possible to determine whether the superposition algorithm has prioritized tightly packed molecular clusters (i.e. to minimize R _g) or prioritized reduced RMSD (i.e. via possibly elongated clusters with relatively larger R _g). For example, it is shown that when the PAC algorithm described here uses single linkage to prioritize molecules for inclusion in the superimposed clusters, the results are nearly identical to those calculated by the widely used program COMPACK. However, the lower R _g values obtained by the use of average linkage are favored for molecule prioritization because the resulting RMSDs more equally reflect the importance of packing along each dimension. It is shown that the PAC algorithm is faster than COMPACK when using a single process and its utility for biomolecular crystals is demonstrated. Finally, parallel scaling up to 64 processes in the open-source code Force Field X is presented.

In Silico and In Vivo Analysis of Amino Acid Substitutions That Cause Laminopathies

Mutations in the LMNA gene cause diseases called laminopathies. LMNA encodes lamins A and C, intermediate filaments with multiple roles at the nuclear envelope. LMNA mutations are frequently single base changes that cause diverse disease phenotypes affecting muscles, nerves, and fat. Disease-associated amino acid substitutions were mapped in silico onto three-dimensional structures of lamin A/C, revealing no apparent genotype–phenotype connections. In silico analyses revealed that seven of nine predicted partner protein binding pockets in the Ig-like fold domain correspond to sites of disease-associated amino acid substitutions. Different amino acid substitutions at the same position within lamin A/C cause distinct diseases, raising the question of whether the nature of the amino acid replacement or genetic background differences contribute to disease phenotypes. Substitutions at R249 in the rod domain cause muscular dystrophies with varying severity. To address this variability, we modeled R249Q and R249W in Drosophila Lamin C, an orthologue of LMNA. Larval body wall muscles expressing mutant Lamin C caused abnormal nuclear morphology and premature death. When expressed in indirect flight muscles, R249W caused a greater number of adults with wing posturing defects than R249Q, consistent with observations that R249W and R249Q cause distinct muscular dystrophies, with R249W more severe. In this case, the nature of the amino acid replacement appears to dictate muscle disease severity. Together, our findings illustrate the utility of Drosophila for predicting muscle disease severity and pathogenicity of variants of unknown significance.

Implicit Solvents for the Polarizable Atomic Multipole AMOEBA Force Field

Computational protein design, ab initio protein/RNA folding, and protein-ligand screening can be too computationally demanding for explicit treatment of solvent. For these applications, implicit solvent offers a compelling alternative, which we describe here for the polarizable atomic multipole AMOEBA force field based on three treatments of continuum electrostatics: numerical solutions to the nonlinear and linearized versions of the Poisson-Boltzmann equation (PBE), the domain-decomposition conductor-like screening model (ddCOSMO) approximation to the PBE, and the analytic generalized Kirkwood (GK) approximation. The continuum electrostatics models are combined with a nonpolar estimator based on novel cavitation and dispersion terms. Electrostatic model parameters are numerically optimized using a least-squares style target function based on a library of 103 small-molecule solvation free energy differences. Mean signed errors for the adaptive Poisson-Boltzmann solver (APBS), ddCOSMO, and GK models are 0.05, 0.00, and 0.00 kcal/mol, respectively, while the mean unsigned errors are 0.70, 0.63, and 0.58 kcal/mol, respectively. Validation of the electrostatic response of the resulting implicit solvents, which are available in the Tinker (or Tinker-HP), OpenMM, and Force Field X software packages, is based on comparisons to explicit solvent simulations for a series of proteins and nucleic acids. Overall, the emergence of performative implicit solvent models for polarizable force fields opens the door to their use for folding and design applications.

Nanophthalmos patient with a THR518MET mutation in MYRF, a case report

Background

Nanophthalmos has a significant genetic background and disease-causing mutations have been recently been reported in the myelin regulatory factor (MYRF) gene. We report clinical features in a patient with nanophthalmos and a Thr518Met MYRF mutation.

Case presentation

A three-year-old male was discovered to have nanophthalmos after first presenting to the emergency department for a frontal headache, eye pain, emesis, and lethargy. Imaging studies (CT and MRI) were negative except for increased posterior fossa cerebrospinal fluid. Subsequent examinations revealed nanophthalmos (short axial eye lengths 18.1 mm OD and 18.3 mm OS), microcornea, and a large crystalline lens. Peripheral chorioretinal pigment abnormalities were also observed. He experienced episodes of marked ocular hypertension (53 mmHg OD and 60 mmHg) likely due to intermittent angle closure precipitated by nanophthalmos. The ocular hypertension was responsive to topical medicines. Genetic analysis of known nanophthalmos genes MFRP and TMEM98 were negative, while a novel mutation, Thr518Met was detected in MYRF. The Thr518Met mutation was absent from 362 matched normal controls and was extremely rare in a large population database, allele frequency of 0.000024. The Thr518Met mutation altered a highly conserved amino acid in the MYRF protein and three of four algorithms suggested that this mutation is likely pathogenic. Finally, molecular modeling showed that the Thr518Met mutation is damaging to MYRF structure. Together these data suggest that the Thr518Met mutation causes nanophthalmos.

Conclusions

Nanophthalmos may present at an early age with features of angle closure glaucoma and a Thr518Met mutation in MYRF was detected in a patient with nanophthalmos. Prevalence data, homology data, mutation analysis data, and protein modeling data suggest that this variant is pathogenic and may expand the phenotypic range of syndromic nanophthalmos caused by MYRF mutations to include central nervous system abnormalities (increased posterior fossa cerebrospinal fluid).

Novel Intragenic PAX6 Deletion in a Pedigree with Aniridia, Morbid Obesity, and Diabetes

Purpose: Aniridia is a rare congenital eye disease, characterized by a constellation of symptoms including hypoplastic irides, foveal hypoplasia, early cataract, corneal stem cell deficiency, and glaucoma. Large chromosomal deletions spanning the PAX6 gene cause WAGR syndrome (Wilms tumor, aniridia, genitourinary anomalies, and intellectual disability [formerly called mental retardation]). We describe clinical and genetic studies of a three-generation pedigree with aniridia along with additional systemic conditions (morbid obesity, diabetes) suggesting the possibility of a contiguous-gene syndrome like WAGR.Methods: Clinical records were obtained and DNA was prepared from blood samples from three of the four patients and tested for mutations in the coding sequences of the PAX6 gene. The index patient also had cardiomyopathy and was tested for known cardiomyopathy genetic mutations using a next-generation DNA sequencing assay.Results: We discovered a novel intragenic PAX6 mutation, a 16 bp heterozygous deletion c.203delCCAGGGCAATCGGTGG, with Sanger sequencing that is the likely cause of autosomal dominant aniridia in this pedigree. This PAX6 deletion causes a frameshift in predicted protein translation and a subsequent premature termination, p.Pro68Leufs*6. The PAX6 deletion was detected in all three available family members with aniridia, the index patient, his mother, and his maternal aunt but was not observed in the Exome Aggregation Consortium (ExAC) database. Targeted sequencing of known cardiomyopathy genes in the index patient identified a second mutation, a 1.7 Mp deletion that spans the MYBPC3 gene.Conclusions: We report a pedigree with aniridia and other systemic abnormalities that were initially suspicious for a contiguous-gene syndrome like WAGR. However, genetic analysis of the pedigree revealed two independent genetic abnormalities on chromosome 11p: 1) a novel PAX6 mutation, and 2) a large chromosome deletion spanning MYBPC3, a known cardiomyopathy gene. It is unclear if morbid obesity and type II diabetes mellitus have a related genetic cause.

Structural Insights into Hearing Loss Genetics from Polarizable Protein Repacking

Hearing loss is associated with ∼8100 mutations in 152 genes, and within the coding regions of these genes are over 60,000 missense variants. The majority of these variants are classified as "variants of uncertain significance" to reflect our inability to ascribe a phenotypic effect to the observed amino acid change. A promising source of pathogenicity information is biophysical simulation, although input protein structures often contain defects because of limitations in experimental data and/or only distant homology to a template. Here, we combine the polarizable atomic multipole optimized energetics for biomolecular applications force field, many-body optimization theory, and graphical processing unit acceleration to repack all deafness-associated proteins and thereby improve average structure MolProbity score from 2.2 to 1.0. We then used these optimized wild-type models to create over 60,000 structures for missense variants in the Deafness Variation Database, which are being incorporated into the Deafness Variation Database to inform deafness pathogenicity prediction. Finally, this work demonstrates that advanced polarizable atomic multipole force fields are efficient enough to repack the entire human proteome.

Tinker 8: Software Tools for Molecular Design

The Tinker software, currently released as version 8, is a modular molecular mechanics and dynamics package written primarily in a standard, easily portable dialect of Fortran 95 with OpenMP extensions. It supports a wide variety of force fields, including polarizable models such as the Atomic Multipole Optimized Energetics for Biomolecular Applications (AMOEBA) force field. The package runs on Linux, macOS, and Windows systems. In addition to canonical Tinker, there are branches, Tinker-HP and Tinker-OpenMM, designed for use on message passing interface (MPI) parallel distributed memory supercomputers and state-of-the-art graphical processing units (GPUs), respectively. The Tinker suite also includes a tightly integrated Java-based graphical user interface called Force Field Explorer (FFE), which provides molecular visualization capabilities as well as the ability to launch and control Tinker calculations.

Genomic Landscape and Mutational Signatures of Deafness-Associated Genes

The classification of genetic variants represents a major challenge in the post-genome era by virtue of their extraordinary number and the complexities associated with ascribing a clinical impact, especially for disorders exhibiting exceptional phenotypic, genetic, and allelic heterogeneity. To address this challenge for hearing loss, we have developed the Deafness Variation Database (DVD), a comprehensive, open-access resource that integrates all available genetic, genomic, and clinical data together with expert curation to generate a single classification for each variant in 152 genes implicated in syndromic and non-syndromic deafness. We evaluate 876,139 variants and classify them as pathogenic or likely pathogenic (more than 8,100 variants), benign or likely benign (more than 172,000 variants), or of uncertain significance (more than 695,000 variants); 1,270 variants are re-categorized based on expert curation and in 300 instances, the change is of medical significance and impacts clinical care. We show that more than 96% of coding variants are rare and novel and that pathogenicity is driven by minor allele frequency thresholds, variant effect, and protein domain. The mutational landscape we define shows complex gene-specific variability, making an understanding of these nuances foundational for improved accuracy in variant interpretation in order to enhance clinical decision making and improve our understanding of deafness biology.

Tinker-HP: a massively parallel molecular dynamics package for multiscale simulations of large complex systems with advanced point dipole polarizable force fields

We present Tinker-HP, a massively MPI parallel package dedicated to classical molecular dynamics (MD) and to multiscale simulations, using advanced polarizable force fields (PFF) encompassing distributed multipoles electrostatics. Tinker-HP is an evolution of the popular Tinker package code that conserves its simplicity of use and its reference double precision implementation for CPUs. Grounded on interdisciplinary efforts with applied mathematics, Tinker-HP allows for long polarizable MD simulations on large systems up to millions of atoms. We detail in the paper the newly developed extension of massively parallel 3D spatial decomposition to point dipole polarizable models as well as their coupling to efficient Krylov iterative and non-iterative polarization solvers. The design of the code allows the use of various computer systems ranging from laboratory workstations to modern petascale supercomputers with thousands of cores. Tinker-HP proposes therefore the first high-performance scalable CPU computing environment for the development of next generation point dipole PFFs and for production simulations. Strategies linking Tinker-HP to Quantum Mechanics (QM) in the framework of multiscale polarizable self-consistent QM/MD simulations are also provided. The possibilities, performances and scalability of the software are demonstrated via benchmarks calculations using the polarizable AMOEBA force field on systems ranging from large water boxes of increasing size and ionic liquids to (very) large biosystems encompassing several proteins as well as the complete satellite tobacco mosaic virus and ribosome structures. For small systems, Tinker-HP appears to be competitive with the Tinker-OpenMM GPU implementation of Tinker. As the system size grows, Tinker-HP remains operational thanks to its access to distributed memory and takes advantage of its new algorithmic enabling for stable long timescale polarizable simulations. Overall, a several thousand-fold acceleration over a single-core computation is observed for the largest systems. The extension of the present CPU implementation of Tinker-HP to other computational platforms is discussed.

The Use of Variant Maps to Explore Domain-Specific Mutations of FGFR1

Here we describe the genotype-phenotype correlations of diseases caused by variants in Fibroblast Growth Factor Receptor 1 ( FGFR1) and report a novel, de novo variant in FGFR1 in an individual with multiple congenital anomalies. The proband presented with bilateral cleft lip and palate, malformed auricles, and bilateral ectrodactyly of his hands and feet at birth. He was later diagnosed with diabetes insipidus, spastic quadriplegia, developmental delay, agenesis of the corpus callosum, and enlargement of the third cerebral ventricle. We noted the substantial phenotypic overlap with individuals with Hartsfield syndrome, the rare combination of holoprosencephaly and ectrodactyly. Sequencing of FGFR1 identified a previously unreported de novo variant in exon 11 (p.Gly487Cys), which we modeled to determine its predicted effect on the protein structure. Although it was not predicted to significantly alter protein folding stability, it is possible this variant leads to the formation of nonnative intra- or intermolecular disulfide bonds. We then mapped this and other disease-associated variants to a 3-dimensional model of FGFR1 to assess which protein domains harbored the highest number of pathogenic changes. We observed the greatest number of variants within the domains involved in FGF binding and FGFR activation. To further explore the contribution of each variant to disease, we recorded the phenotype resulting from each FGFR1 variant to generate a series of phenotype-specific protein maps and compared our results to benign variants appearing in control databases. It is our hope that the use of phenotypic maps such as these will further the understanding of genetic disease in general and diseases caused by variation in FGFR1 specifically.

LADD syndrome with glaucoma is caused by a novel gene

PURPOSE

Lacrimo-auriculo-dento-digital (LADD) syndrome is an autosomal dominant disorder displaying variable expression of multiple congenital anomalies including hypoplasia or aplasia of the lacrimal and salivary systems causing abnormal tearing and dry mouth. Mutations in the FGF10, FGFR2, and FGFR3 genes were found to cause some cases of LADD syndrome in prior genetic studies. The goal of this study is to identify the genetic basis of a case of LADD syndrome with glaucoma and thin central corneal thickness (CCT).

METHODS

Whole exome sequencing was performed, and previously described disease-causing genes (FGF10, FGFR2, and FGFR3) were first evaluated for mutations. Fifty-eight additional prioritized candidate genes were identified by searching gene annotations for features of LADD syndrome. The potential pathogenicity of the identified mutations was assessed by determining their frequency in large public exome databases; through sequence analysis using the Blosum62 matrix, PolyPhen2, and SIFT algorithms; and through homology analyses. A structural analysis of the effects of the top candidate mutation in tumor protein 63 (TP63) was also conducted by superimposing the mutation over the solved crystal structure.

RESULTS

No mutations were detected in FGF10, FGFR2, or FGFR3. The LADD syndrome patient's exome data was searched for mutations in the 58 candidate genes and only one mutation was detected, an Arg343Trp mutation in the tumor protein 63 (TP63) gene. This TP63 mutation is absent from the gnomAD sequence database. Analysis of the Arg343Trp mutation with Blosum62, PolyPhen2, and SIFT all suggest it is pathogenic. This arginine residue is highly conserved in orthologous genes. Finally, crystal structure analysis showed that the Arg343Trp mutation causes a significant alteration in the structure of TP63's DNA binding domain.

CONCLUSIONS

We report a patient with no mutations in known LADD syndrome genes (FGF10, FGFR2, and FGFR3). Our analysis provides strong evidence that the Arg343Trp mutation in TP63 caused LADD syndrome in our patient and that TP63 is a fourth gene contributing to this condition. TP63 encodes a transcription factor involved in the development and differentiation of tissues affected by LADD syndrome. These data suggest that TP63 is a novel LADD syndrome gene and may also influence corneal thickness and risk for open-angle glaucoma.

Calculating binding free energies of host-guest systems using the AMOEBA polarizable force field

Molecular recognition is of paramount interest in many applications. Here we investigate a series of host-guest systems previously used in the SAMPL4 blind challenge by using molecular simulations and the AMOEBA polarizable force field. The free energy results computed by Bennett's acceptance ratio (BAR) method using the AMOEBA polarizable force field ranked favorably among the entries submitted to the SAMPL4 host-guest competition [Muddana, et al., J. Comput.-Aided Mol. Des., 2014, 28, 305-317]. In this work we conduct an in-depth analysis of the AMOEBA force field host-guest binding thermodynamics by using both BAR and the orthogonal space random walk (OSRW) methods. The binding entropy-enthalpy contributions are analyzed for each host-guest system. For systems of inordinate binding entropy-enthalpy values, we further examine the hydrogen bonding patterns and configurational entropy contribution. The binding mechanism of this series of host-guest systems varies from ligand to ligand, driven by enthalpy and/or entropy changes. Convergence of BAR and OSRW binding free energy methods is discussed. Ultimately, this work illustrates the value of molecular modelling and advanced force fields for the exploration and interpretation of binding thermodynamics.

Toward polarizable AMOEBA thermodynamics at fixed charge efficiency using a dual force field approach: application to organic crystals

First principles prediction of the structure, thermodynamics and solubility of organic molecular crystals, which play a central role in chemical, material, pharmaceutical and engineering sciences, challenges both potential energy functions and sampling methodologies. Here we calculate absolute crystal deposition thermodynamics using a novel dual force field approach whose goal is to maintain the accuracy of advanced multipole force fields (e.g. the polarizable AMOEBA model) while performing more than 95% of the sampling in an inexpensive fixed charge (FC) force field (e.g. OPLS-AA). Absolute crystal sublimation/deposition phase transition free energies were determined using an alchemical path that grows the crystalline state from a vapor reference state based on sampling with the OPLS-AA force field, followed by dual force field thermodynamic corrections to change between FC and AMOEBA resolutions at both end states (we denote the three step path as AMOEBA/FC). Importantly, whereas the phase transition requires on the order of 200 ns of sampling per compound, only 5 ns of sampling was needed for the dual force field thermodynamic corrections to reach a mean statistical uncertainty of 0.05 kcal mol-1. For five organic compounds, the mean unsigned error between direct use of AMOEBA and the AMOEBA/FC dual force field path was only 0.2 kcal mol-1 and not statistically significant. Compared to experimental deposition thermodynamics, the mean unsigned error for AMOEBA/FC (1.4 kcal mol-1) was more than a factor of two smaller than uncorrected OPLS-AA (3.2 kcal mol-1). Overall, the dual force field thermodynamic corrections reduced condensed phase sampling in the expensive force field by a factor of 40, and may prove useful for protein stability or binding thermodynamics in the future.

Hypomorphic mutations in TRNT1 cause retinitis pigmentosa with erythrocytic microcytosis

Retinitis pigmentosa (RP) is a highly heterogeneous group of disorders characterized by degeneration of the retinal photoreceptor cells and progressive loss of vision. While hundreds of mutations in more than 100 genes have been reported to cause RP, discovering the causative mutations in many patients remains a significant challenge. Exome sequencing in an individual affected with non-syndromic RP revealed two plausibly disease-causing variants in TRNT1, a gene encoding a nucleotidyltransferase critical for tRNA processing. A total of 727 additional unrelated individuals with molecularly uncharacterized RP were completely screened for TRNT1 coding sequence variants, and a second family was identified with two members who exhibited a phenotype that was remarkably similar to the index patient. Inactivating mutations in TRNT1 have been previously shown to cause a severe congenital syndrome of sideroblastic anemia, B-cell immunodeficiency, recurrent fevers and developmental delay (SIFD). Complete blood counts of all three of our patients revealed red blood cell microcytosis and anisocytosis with only mild anemia. Characterization of TRNT1 in patient-derived cell lines revealed reduced but detectable TRNT1 protein, consistent with partial function. Suppression of trnt1 expression in zebrafish recapitulated several features of the human SIFD syndrome, including anemia and sensory organ defects. When levels of trnt1 were titrated, visual dysfunction was found in the absence of other phenotypes. The visual defects in the trnt1-knockdown zebrafish were ameliorated by the addition of exogenous human TRNT1 RNA. Our findings indicate that hypomorphic TRNT1 mutations can cause a recessive disease that is almost entirely limited to the retina.

PDZD7 and hearing loss: More than just a modifier

Deafness is the most frequent sensory disorder. With over 90 genes and 110 loci causally implicated in non-syndromic hearing loss, it is phenotypically and genetically heterogeneous. Here, we investigate the genetic etiology of deafness in four families of Iranian origin segregating autosomal recessive non-syndromic hearing loss (ARNSHL). We used a combination of linkage analysis, homozygosity mapping, and a targeted genomic enrichment platform to simultaneously screen 90 known deafness-causing genes for pathogenic variants. Variant segregation was confirmed by Sanger sequencing. Linkage analysis and homozygosity mapping showed segregation with the DFNB57 locus on chromosome 10 in two families. Targeted genomic enrichment with massively parallel sequencing identified causal variants in PDZD7: a homozygous missense variant (p.Gly103Arg) in one family and compound heterozygosity for missense (p.Met285Arg) and nonsense (p.Tyr500Ter) variants in the second family. Screening of two additional families identified two more variants: (p.Gly228Arg) and (p.Gln526Ter). Variant segregation with the hearing loss phenotype was confirmed in all families by Sanger sequencing. The missense variants are predicted to be deleterious, and the two nonsense mutations produce null alleles. This report is the first to show that mutations in PDZD7 cause ARNSHL, a finding that offers addition insight into the USH2 interactome. We also describe a novel likely disease-causing mutation in CIB2 and illustrate the complexity associated with gene identification in diseases that exhibit large genetic and phenotypic heterogeneity.

Dead-End Elimination with a Polarizable Force Field Repacks PCNA Structures

A balance of van der Waals, electrostatic, and hydrophobic forces drive the folding and packing of protein side chains. Although such interactions between residues are often approximated as being pairwise additive, in reality, higher-order many-body contributions that depend on environment drive hydrophobic collapse and cooperative electrostatics. Beginning from dead-end elimination, we derive the first algorithm, to our knowledge, capable of deterministic global repacking of side chains compatible with many-body energy functions. The approach is applied to seven PCNA x-ray crystallographic data sets with resolutions 2.5-3.8 Å (mean 3.0 Å) using an open-source software. While PDB_REDO models average an Rfree value of 29.5% and MOLPROBITY score of 2.71 Å (77th percentile), dead-end elimination with the polarizable AMOEBA force field lowered Rfree by 2.8-26.7% and improved mean MOLPROBITY score to atomic resolution at 1.25 Å (100th percentile). For structural biology applications that depend on side-chain repacking, including x-ray refinement, homology modeling, and protein design, the accuracy limitations of pairwise additivity can now be eliminated via polarizable or quantum mechanical potentials.

High-Throughput Genetic Testing for Thrombotic Microangiopathies and C3 Glomerulopathies

The thrombotic microangiopathies (TMAs) and C3 glomerulopathies (C3Gs) include a spectrum of rare diseases such as atypical hemolytic uremic syndrome, thrombotic thrombocytopenic purpura, C3GN, and dense deposit disease, which share phenotypic similarities and underlying genetic commonalities. Variants in several genes contribute to the pathogenesis of these diseases, and identification of these variants may inform the diagnosis and treatment of affected patients. We have developed and validated a comprehensive genetic panel that screens all exons of all genes implicated in TMA and C3G. The closely integrated pipeline implemented includes targeted genomic enrichment, massively parallel sequencing, bioinformatic analysis, and a multidisciplinary conference to analyze identified variants in the context of each patient's specific phenotype. Herein, we present our 1-year experience with this panel, during which time we studied 193 patients. We identified 17 novel and 74 rare variants, which we classified as pathogenic (11), likely pathogenic (12), and of uncertain significance (68). Compared with controls, patients with C3G had a higher frequency of rare and novel variants in C3 convertase (C3 and CFB) and complement regulator (CFH, CFI, CFHR5, and CD46) genes (P<0.05). In contrast, patients with TMA had an increase in rare and novel variants only in complement regulator genes (P<0.01), a distinction consistent with differing sites of complement dysregulation in these two diseases. In summary, we were able to provide a positive genetic diagnosis in 43% and 41% of patients carrying the clinical diagnosis of C3G and TMA, respectively.

Biomolecular electrostatics and solvation: a computational perspective

An understanding of molecular interactions is essential for insight into biological systems at the molecular scale. Among the various components of molecular interactions, electrostatics are of special importance because of their long-range nature and their influence on polar or charged molecules, including water, aqueous ions, proteins, nucleic acids, carbohydrates, and membrane lipids. In particular, robust models of electrostatic interactions are essential for understanding the solvation properties of biomolecules and the effects of solvation upon biomolecular folding, binding, enzyme catalysis, and dynamics. Electrostatics, therefore, are of central importance to understanding biomolecular structure and modeling interactions within and among biological molecules. This review discusses the solvation of biomolecules with a computational biophysics view toward describing the phenomenon. While our main focus lies on the computational aspect of the models, we provide an overview of the basic elements of biomolecular solvation (e.g. solvent structure, polarization, ion binding, and non-polar behavior) in order to provide a background to understand the different types of solvation models.

Computational insights for the discovery of non-ATP competitive inhibitors of MAP kinases

Due to their role in cellular signaling mitogen activated protein (MAP) kinases represent targets of pharmaceutical interest. However, the majority of known MAP kinase inhibitors compete with cellular ATP and target an ATP binding pocket that is highly conserved in the 500 plus representatives of the human protein kinase family. Here we review progress toward the development of non-ATP competitive MAP kinase inhibitors for the extracellular signal regulated kinases (ERK1/2), the c-jun N-terminal kinases (JNK1/2/3) and the p38 MAPKs (α, β, γ, and δ). Special emphasis is placed on the role of computational methods in the drug discovery process for MAP kinases. Topics include recent advances in X-ray crystallography theory that improve the MAP kinase structures essential to structurebased drug discovery, the use of molecular dynamics to understand the conformational heterogeneity of the activation loop and inhibitors discovered by virtual screening. The impact of an advanced polarizable force field such as AMOEBA used in conjunction with sophisticated kinetic and thermodynamic simulation methods is also discussed.

The Structure, Thermodynamics and Solubility of Organic Crystals from Simulation with a Polarizable Force Field

An important unsolved problem in materials science is prediction of the thermodynamic stability of organic crystals and their solubility from first principles. Solubility can be defined as the saturating concentration of a molecule within a liquid solvent, where the physical picture is of solvated molecules in equilibrium with their solid phase. Despite the importance of solubility in determining the oral bioavailability of pharmaceuticals, prediction tools are currently limited to quantitative structure-property relationships that are fit to experimental solubility measurements. For the first time, we describe a consistent procedure for the prediction of the structure, thermodynamic stability and solubility of organic crystals from molecular dynamics simulations using the polarizable multipole AMOEBA force field. Our approach is based on a thermodynamic cycle that decomposes standard state solubility into the sum of solid-vapor sublimation and vapor-liquid solvation free energies [Formula: see text], which are computed via the orthogonal space random walk (OSRW) sampling strategy. Application to the n-alkylamides series from aeetamide through octanamide was selected due to the dependence of their solubility on both amide hydrogen bonding and the hydrophobic effect, which are each fundamental to protein structure and solubility. On average, the calculated absolute standard state solubility free energies are accurate to within 1.1 kcal/mol. The experimental trend of decreasing solubility as a function of n-alkylamide chain length is recapitulated by the increasing stability of the crystalline state and to a lesser degree by decreasing favorability of solvation (i.e. the hydrophobic effect). Our results suggest that coupling the polarizable AMOEBA force field with an orthogonal space based free energy algorithm, as implemented in the program Force Field X, is a consistent procedure for predicting the structure, thermodynamic stability and solubility of organic crystals.

A SURGICAL GUIDE TO ACCURATELY PLACE PINS OR NAILS WITHIN THE FEMORAL HEAD

The purpose of this study was to demonstrate the accuracy of a novel, surgically useful guide that could place a drill or pin within the femoral head. The radiolucent guide for attachment to the lateral femoral cortex was tested for reproducibility on cadaveric specimens simulating a surgical procedure. The guide allows selection of the three-degree freedom angle of insertion of a drill or pin via two circular channels allowing anterior–posterior or superior–inferior adjustment. The guide can accurately place a pin tip within 2.5–3.8 mm of a desired location. We conclude this guide could be used to accurately place a fibular graft in an osteonecrotic lesion, or place pins or nails during many different surgical procedures such as fractures or slipped capital femoral epiphysis.

Polarizable atomic multipole X-ray refinement: weighting schemes for macromolecular diffraction

In the past, weighting between the sum of chemical and data-based targets in macromolecular crystallographic refinement was based on comparing the gradients or Hessian diagonal terms of the two potential functions. Here, limitations of this scheme are demonstrated, especially in the context of a maximum-likelihood target that is inherently weighted by the model and data errors. In fact, the congruence between the maximum-likelihood target and a chemical potential based on polarizable atomic multipole electrostatics evaluated with Ewald summation has opened the door to a transferable static weight. An optimal static weight is derived from first principles and is demonstrated to be transferable across a broad range of data resolutions in the context of a recent implementation of X-ray crystallographic refinement using the polarizable AMOEBA force field and it is shown that the resulting models are balanced with respect to optimizing both R(free) and MolProbity scores. Conversely, the classical automatic weighting scheme is shown to lead to underfitting or overfitting of the data and poor model geometry. The benefits of this approach for low-resolution diffraction data, where the need for prior chemical information is of particular importance, are also highlighted. It is demonstrated that this method is transferable between low- and high-resolution maximum-likelihood-based crystallographic refinement, which proves for the first time that resolution-dependent parameterization of either the weight or the chemical potential is unnecessary.

Assessment of protein structure refinement in CASP9

We assess performance in the structure refinement category in CASP9. Two years after CASP8, the performance of the best groups has not improved. There are few groups that improve any of our assessment scores with statistical significance. Some predictors, however, are able to consistently improve the physicality of the models. Although we cannot identify any clear bottleneck in improving refinement, several points arise: (1) The refinement portion of CASP has too few targets to make many statistically meaningful conclusions. (2) Predictors are usually very conservative, limiting the possibility of large improvements in models. (3) No group is actually able to correctly rank their five submissions-indicating that potentially better models may be discarded. (4) Different sampling strategies work better for different refinement problems; there is no single strategy that works on all targets. In general, conservative strategies do better, while the greatest improvements come from more adventurous sampling-at the cost of consistency. Comparison with experimental data reveals aspects not captured by comparison to a single structure. In particular, we show that improvement in backbone geometry does not always mean better agreement with experimental data. Finally, we demonstrate that even given the current challenges facing refinement, the refined models are useful for solving the crystallographic phase problem through molecular replacement. Proteins 2011;. © 2011 Wiley-Liss, Inc.

Reintroducing electrostatics into macromolecular crystallographic refinement: application to neutron crystallography and DNA hydration

Most current crystallographic structure refinements augment the diffraction data with a priori information consisting of bond, angle, dihedral, planarity restraints, and atomic repulsion based on the Pauli exclusion principle. Yet, electrostatics and van der Waals attraction are physical forces that provide additional a priori information. Here, we assess the inclusion of electrostatics for the force field used for all-atom (including hydrogen) joint neutron/X-ray refinement. Two DNA and a protein crystal structure were refined against joint neutron/X-ray diffraction data sets using force fields without electrostatics or with electrostatics. Hydrogen-bond orientation/geometry favors the inclusion of electrostatics. Refinement of Z-DNA with electrostatics leads to a hypothesis for the entropic stabilization of Z-DNA that may partly explain the thermodynamics of converting the B form of DNA to its Z form. Thus, inclusion of electrostatics assists joint neutron/X-ray refinements, especially for placing and orienting hydrogen atoms.

Polarizable Atomic Multipole X-Ray Refinement: Particle Mesh Ewald Electrostatics for Macromolecular Crystals

Refinement of macromolecular models from X-ray crystallography experiments benefits from prior chemical knowledge at all resolutions. As the quality of the prior chemical knowledge from quantum or classical molecular physics improves, in principle so will resulting structural models. Due to limitations in computer performance and electrostatic algorithms, commonly used macromolecules X-ray crystallography refinement protocols have had limited support for rigorous molecular physics in the past. For example, electrostatics is often neglected in favor of nonbonded interactions based on a purely repulsive van der Waals potential. In this work we present advanced algorithms for desktop workstations that open the door to X-ray refinement of even the most challenging macromolecular data sets using state-of-the-art classical molecular physics. First we describe theory for particle mesh Ewald (PME) summation that consistently handles the symmetry of all 230 space groups, replicates of the unit cell such that the minimum image convention can be used with a real space cutoff of any size and the combination of space group symmetry with replicates. An implementation of symmetry accelerated PME for the polarizable atomic multipole optimized energetics for biomolecular applications (AMOEBA) force field is presented. Relative to a single CPU core performing calculations on a P1 unit cell, our AMOEBA engine called Force Field X (FFX) accelerates energy evaluations by more than a factor of 24 on an 8-core workstation with a Tesla GPU coprocessor for 30 structures that contain 240 000 atoms on average in the unit cell. The benefit of AMOEBA electrostatics evaluated with PME for macromolecular X-ray crystallography refinement is demonstrated via rerefinement of 10 crystallographic data sets that range in resolution from 1.7 to 4.5 Å. Beginning from structures obtained by local optimization without electrostatics, further optimization using AMOEBA with PME electrostatics improved agreement of the model with the data (Rfree was lowered by 0.5%), improved geometric features such as favorable (ϕ, ψ) backbone conformations, and lowered the average potential energy per residue by over 10 kcal/mol. Furthermore, the MolProbity structure validation tool indicates that the geometry of these rerefined structures is consistent with X-ray crystallographic data collected up to 2.2 Å, which is 0.9 Å better than the actual mean quality (3.1 Å). We conclude that polarizable AMOEBA-assisted X-ray refinement offers advantages to methods that neglect electrostatics and is now efficient enough for routine use.

Trypsin-ligand binding free energy calculation with AMOEBA

The binding free energies of several benzamidine -like inhibitors to trypsin were examined using a polarizable molecular mechanics potential. All the computed binding free energies are in good agreement with the experimental data. From free energy decomposition, electrostatic interaction was indicated to be the driving force for the binding. MD simulations show that the ligands form hydrogen bonds with trypsin and water molecules nearby in a competitive fashion. While the binding free energy is independent of the ligand dipole moment, it shows a strong correlation with the ligand molecular polarizability.

Current status of the AMOEBA polarizable force field

Molecular force fields have been approaching a generational transition over the past several years, moving away from well-established and well-tuned, but intrinsically limited, fixed point charge models toward more intricate and expensive polarizable models that should allow more accurate description of molecular properties. The recently introduced AMOEBA force field is a leading publicly available example of this next generation of theoretical model, but to date, it has only received relatively limited validation, which we address here. We show that the AMOEBA force field is in fact a significant improvement over fixed charge models for small molecule structural and thermodynamic observables in particular, although further fine-tuning is necessary to describe solvation free energies of drug-like small molecules, dynamical properties away from ambient conditions, and possible improvements in aromatic interactions. State of the art electronic structure calculations reveal generally very good agreement with AMOEBA for demanding problems such as relative conformational energies of the alanine tetrapeptide and isomers of water sulfate complexes. AMOEBA is shown to be especially successful on protein-ligand binding and computational X-ray crystallography where polarization and accurate electrostatics are critical.

Assessment of the protein-structure refinement category in CASP8

Here, we summarize the assessment of protein structure refinement in CASP8. Twenty-four groups refined a total of 12 target proteins. Averaging over all groups and all proteins, there was no net improvement over the original starting models. However, there are now some individual research groups who consistently do improve protein structures relative to a starting starting model. We compare various measures of quality assessment, including (i) standard backbone-based methods, (ii) new methods from the Richardson group, and (iii) ensemble-based methods for comparing experimental structures, such as NMR NOE violations and the suitability of the predicted models to serve as templates for molecular replacement. On the whole, there is a general correlation among various measures. However, there are interesting differences. Sometimes a structure that is in better agreement with the experimental data is judged to be slightly worse by GDT-TS. This suggests that for comparing protein structures that are already quite close to the native, it may be preferable to use ensemble-based experimentally derived measures of quality, in addition to single-structure-based methods such as GDT-TS.

Polarizable atomic multipole X-ray refinement: application to peptide crystals

Recent advances in computational chemistry have produced force fields based on a polarizable atomic multipole description of biomolecular electrostatics. In this work, the Atomic Multipole Optimized Energetics for Biomolecular Applications (AMOEBA) force field is applied to restrained refinement of molecular models against X-ray diffraction data from peptide crystals. A new formalism is also developed to compute anisotropic and aspherical structure factors using fast Fourier transformation (FFT) of Cartesian Gaussian multipoles. Relative to direct summation, the FFT approach can give a speedup of more than an order of magnitude for aspherical refinement of ultrahigh-resolution data sets. Use of a sublattice formalism makes the method highly parallelizable. Application of the Cartesian Gaussian multipole scattering model to a series of four peptide crystals using multipole coefficients from the AMOEBA force field demonstrates that AMOEBA systematically underestimates electron density at bond centers. For the trigonal and tetrahedral bonding geometries common in organic chemistry, an atomic multipole expansion through hexadecapole order is required to explain bond electron density. Alternatively, the addition of interatomic scattering (IAS) sites to the AMOEBA-based density captured bonding effects with fewer parameters. For a series of four peptide crystals, the AMOEBA-IAS model lowered R(free) by 20-40% relative to the original spherically symmetric scattering model.

Polarizable Atomic Multipole Solutes in a Generalized Kirkwood Continuum

The generalized Born (GB) model of continuum electrostatics is an analytic approximation to the Poisson equation useful for predicting the electrostatic component of the solvation free energy for solutes ranging in size from small organic molecules to large macromolecular complexes. This work presents a new continuum electrostatics model based on Kirkwood's analytic result for the electrostatic component of the solvation free energy for a solute with arbitrary charge distribution. Unlike GB, which is limited to monopoles, our generalized Kirkwood (GK) model can treat solute electrostatics represented by any combination of permanent and induced atomic multipole moments of arbitrary degree. Here we apply the GK model to the newly developed Atomic Multipole Optimized Energetics for Biomolecular Applications (AMOEBA) force field, which includes permanent atomic multipoles through the quadrupole and treats polarization via induced dipoles. A derivation of the GK gradient is presented, which enables energy minimization or molecular dynamics of an AMOEBA solute within a GK continuum. For a series of 55 proteins, GK electrostatic solvation free energies are compared to the Polarizable Multipole Poisson-Boltzmann (PMPB) model and yield a mean unsigned relative difference of 0.9%. Additionally, the reaction field of GK compares well to that of the PMPB model, as shown by a mean unsigned relative difference of 2.7% in predicting the total solvated dipole moment for each protein in this test set. The CPU time needed for GK relative to vacuum AMOEBA calculations is approximately a factor of 3, making it suitable for applications that require significant sampling of configuration space.

Polarizable atomic multipole solutes in a Poisson-Boltzmann continuum

Modeling the change in the electrostatics of organic molecules upon moving from vacuum into solvent, due to polarization, has long been an interesting problem. In vacuum, experimental values for the dipole moments and polarizabilities of small, rigid molecules are known to high accuracy; however, it has generally been difficult to determine these quantities for a polar molecule in water. A theoretical approach introduced by Onsager [J. Am. Chem. Soc. 58, 1486 (1936)] used vacuum properties of small molecules, including polarizability, dipole moment, and size, to predict experimentally known permittivities of neat liquids via the Poisson equation. Since this important advance in understanding the condensed phase, a large number of computational methods have been developed to study solutes embedded in a continuum via numerical solutions to the Poisson-Boltzmann equation. Only recently have the classical force fields used for studying biomolecules begun to include explicit polarization in their functional forms. Here the authors describe the theory underlying a newly developed polarizable multipole Poisson-Boltzmann (PMPB) continuum electrostatics model, which builds on the atomic multipole optimized energetics for biomolecular applications (AMOEBA) force field. As an application of the PMPB methodology, results are presented for several small folded proteins studied by molecular dynamics in explicit water as well as embedded in the PMPB continuum. The dipole moment of each protein increased on average by a factor of 1.27 in explicit AMOEBA water and 1.26 in continuum solvent. The essentially identical electrostatic response in both models suggests that PMPB electrostatics offers an efficient alternative to sampling explicit solvent molecules for a variety of interesting applications, including binding energies, conformational analysis, and pK(a) prediction. Introduction of 150 mM salt lowered the electrostatic solvation energy between 2 and 13 kcalmole, depending on the formal charge of the protein, but had only a small influence on dipole moments.

Assessing the accuracy of a prototype drill guide for fibular graft placement in femoral head necrosis

A prototype drill guide was developed to improve the accuracy of surgical placement of fibular grafts for the treatment of femoral head necrosis. To document performance, two tantalum beads, one placed on the lateral femoral shaft and the other embedded in the superior portion of the head, were used to define the desired graft tract in a series of seven surrogate femurs. Two orthogonal x-rays of the drill guide mounted on each surrogate femur were taken both before and after drilling. After stylus digitization of each x-ray pair, a computer program calculated the achieved accuracy of the drill. The mean of the absolute error between the desired versus obtained position of the drill tip was 3.68 mm (s.d. 1.24 mm), and the random component of the error was 1.98 mm (s.d. 0.89 mm).