Coupling finite and boundary element methods to solve the Poisson-Boltzmann equation for electrostatics in molecular solvation.

The Poisson-Boltzmann equation is widely used to model electrostatics in molecular systems. Available software packages solve it using finite difference, finite element, and boundary element methods, where the latter is attractive due to the accurate representation of the molecular surface and partial charges, and exact enforcement of the boundary conditions at infinity. However, the boundary element method is limited to linear equations and piecewise constant variations of the material properties. In this work, we present a scheme that couples finite and boundary elements for the linearised Poisson-Boltzmann equation, where the finite element method is applied in a confined solute region and the boundary element method in the external solvent region. As a proof-of-concept exercise, we use the simplest methods available: Johnson-Nédélec coupling with mass matrix and diagonal preconditioning, implemented using the Bempp-cl and FEniCSx libraries via their Python interfaces. We showcase our implementation by computing the polar component of the solvation free energy of a set of molecules using a constant and a Gaussian-varying permittivity. As validation, we compare against well-established finite difference solvers for an extensive binding energy data set, and with the finite difference code APBS (to 0.5%) for Gaussian permittivities. We also show scaling results from protein G B1 (955 atoms) up to immunoglobulin G (20,148 atoms). For small problems, the coupled method was efficient, outperforming a purely boundary integral approach. For Gaussian-varying permittivities, which are beyond the applicability of boundary elements alone, we were able to run medium to large-sized problems on a single workstation. The development of better preconditioning techniques and the use of distributed memory parallelism for larger systems remains an area for future work. We hope this work will serve as inspiration for future developments that consider space-varying field parameters, and mixed linear-nonlinear schemes for molecular electrostatics with implicit solvent models.

Escherichia coli DNA repair helicase Lhr is also a uracil-DNA glycosylase.

DNA glycosylases protect genetic fidelity during DNA replication by removing potentially mutagenic chemically damaged DNA bases. Bacterial Lhr proteins are well-characterized DNA repair helicases that are fused to additional 600-700 amino acids of unknown function, but with structural homology to SecB chaperones and AlkZ DNA glycosylases. Here, we identify that Escherichia coli Lhr is a uracil-DNA glycosylase (UDG) that depends on an active site aspartic acid residue. We show that the Lhr DNA helicase activity is functionally independent of the UDG activity, but that the helicase domains are required for fully active UDG activity. Consistent with UDG activity, deletion of lhr from the E. coli chromosome sensitized cells to oxidative stress that triggers cytosine deamination to uracil. The ability of Lhr to translocate single-stranded DNA and remove uracil bases suggests a surveillance role to seek and remove potentially mutagenic base changes during replication stress.

Advancing structural biology through breakthroughs in AI.

The past century has witnessed an exponential increase in our atomic-level understanding of molecular and cellular mechanisms from a structural perspective, with multiple landmark achievements contributing to the field. This, coupled with recent and continuing breakthroughs in artificial intelligence methods such as AlphaFold2, and enhanced computational power, is enabling our understanding of protein structure and function at unprecedented levels of accuracy and predictivity. Here, we describe some of the major recent advances across these fields, and describe, as these technologies coalesce, the potential to utilise our enhanced knowledge of intricate cellular and molecular systems to discover novel therapeutics to alleviate human suffering.

Accurate Boundary Integral Formulations for the Calculation of Electrostatic Forces with an Implicit-Solvent Model.

An accurate force calculation with the Poisson-Boltzmann equation is challenging, as it requires the electric field on the molecular surface. Here we present a calculation of the electric field on the solute-solvent interface that is exact for piecewise linear variations of the potential and analyze four different alternatives to compute the force using a boundary element method. We performed a verification exercise for two cases: the isolated and two interacting molecules. Our results suggest that the boundary element method outperforms the finite difference method, as the latter needs a much finer mesh than in solvation energy calculations to get acceptable accuracy in the force, whereas the same surface mesh as in a standard energy calculation is appropriate for the boundary element method. Among the four evaluated alternatives of force calculation, we saw that the most accurate one is based on the Maxwell stress tensor. However, for a realistic application, like the barnase-barstar complex, the approach based on variations of the energy functional, which is less accurate, gives equivalent results. This analysis is useful toward using the Poisson-Boltzmann equation for force calculations in applications where high accuracy is key, for example, to feed molecular dynamics models or to enable the study of the interaction between large molecular structures, like viruses adsorbed onto substrates.

Modeling of the Electrostatic Interaction and Catalytic Activity of [NiFe] Hydrogenases on a Planar Electrode.

Hydrogenases are a group of enzymes that have caught the interest of researchers in renewable energies, due to their ability to catalyze the redox reaction of hydrogen. The exploitation of hydrogenases in electrochemical devices requires their immobilization on the surface of suitable electrodes, such as graphite. The orientation of the enzyme on the electrode is important to ensure a good flux of electrons to the catalytic center, through an array of iron-sulfur clusters. Here we present a computational approach to determine the possible orientations of a [NiFe] hydrogenase (PDB 1e3d) on a planar electrode, as a function of pH, salinity, and electrode potential. The calculations are based on the solution of the linearized Poisson-Boltzmann equation, using the PyGBe software. The results reveal that electrostatic interactions do not truly immobilize the enzyme on the surface of the electrode, but there is instead a dynamic equilibrium between different orientations. Nonetheless, after averaging over all thermally accessible orientations, we find significant differences related to the solution's salinity and pH, while the effect of the electrode potential is relatively weak. We also combine models for the protein adsoption-desorption equilibria and for the electron transfer between the proteins and the electrode to arrive at a prediction of the electrode's activity as a function of the enzyme concentration.

Quantitative electrostatic force tomography for virus capsids in interaction with an approaching nanoscale probe.

Electrostatic interactions are crucial for the assembly, disassembly and stability of proteinaceous viral capsids. Moreover, at the molecular scale, elucidating the organization and structure of the capsid proteins in response to an approaching nanoprobe is a major challenge in biomacromolecular research. Here, we report on a generalized electrostatic model, based on the Poisson-Boltzmann equation, that quantifies the subnanometric electrostatic interactions between an AFM tip and a proteinaceous capsid from molecular snapshots. This allows us to describe the contributions of specific amino acids and atoms to the interaction force. We show validation results in terms of total electrostatic forces with previous semi-empirical generalized models at available length scales (d > 1 nm). Then, we studied the interaction of the Zika capsid with conical and spherical AFM tips in a tomography-type analysis to identify the most important residues and atoms, showing the localized nature of the interaction. This method can be employed for the interpretation of force microscopy experiments in fundamental virological characterization and in diverse nanomedicine applications, where specific regions of the protein cages are aimed to electrostatically interact with molecular sized functionalized inhibitors, or tailoring protein-cage functional properties for nucleic acid delivery.

Predicting the Orientation of Adsorbed Proteins Steered with Electric Fields Using a Simple Electrostatic Model.

Under the most common experimental conditions, the adsorption of proteins to solid surfaces is a spontaneous process that leads to a rather compact layer of randomly oriented molecules. However, controlling such orientation is critically important for the development of catalytic surfaces. In this regard, the use of electric fields is one of the most promising alternatives. Our work is motivated by experimental observations that show important differences in catalytic activity of a trypsin-covered surface, which depended on the applied potential during the adsorption. Even though adsorption results from the combination of several processes, we were able to determine that (under the selected conditions) mean-field electrostatics play a dominant role, determining the orientation and yielding a difference in catalytic activity. We simulated the electrostatic potential numerically, using an implicit-solvent model based on the linearized Poisson-Boltzmann equation. This was implemented in an extension of the code PyGBe that included an external electric field, and rendered the electrostatic component of the solvation free energy. Our model (extensions available at the Github repository) allowed estimating the overall affinity of the protein with the surface, and their most likely orientation as a function of the potential applied. Our results show that the active sites of trypsin are, on average, more exposed when the electric field is negative, which agrees with the experimental results of catalytic activity, and confirm the premise that electrostatic interactions can be used to control the orientation of adsorbed proteins.

Towards optimal boundary integral formulations of the Poisson-Boltzmann equation for molecular electrostatics.

The Poisson-Boltzmann equation offers an efficient way to study electrostatics in molecular settings. Its numerical solution with the boundary element method is widely used, as the complicated molecular surface is accurately represented by the mesh, and the point charges are accounted for explicitly. In fact, there are several well-known boundary integral formulations available in the literature. This work presents a generalized expression of the boundary integral representation of the implicit solvent model, giving rise to new forms to compute the electrostatic potential. Moreover, it proposes a strategy to build efficient preconditioners for any of the resulting systems, improving the convergence of the linear solver. We perform systematic benchmarking of a set of formulations and preconditioners, focusing on the time to solution, matrix conditioning, and eigenvalue spectrum. We see that the eigenvalue clustering is a good indicator of the matrix conditioning, and show that they can be easily manipulated by scaling the preconditioner. Our results suggest that the optimal choice is problem-size dependent, where a simpler direct formulation is the fastest for small molecules, but more involved second-kind equations are better for larger problems. We also present a fast Calderón preconditioner for first-kind formulations, which shows promising behavior for future analysis. This work sets the basis towards choosing the most convenient boundary integral formulation of the Poisson-Boltzmann equation for a given problem.

The HelQ human DNA repair helicase utilizes a PWI-like domain for DNA loading through interaction with RPA, triggering DNA unwinding by the HelQ helicase core.

Genome instability is a characteristic enabling factor for carcinogenesis. HelQ helicase is a component of human DNA maintenance systems that prevent or reverse genome instability arising during DNA replication. Here, we provide details of the molecular mechanisms that underpin HelQ function-its recruitment onto ssDNA through interaction with replication protein A (RPA), and subsequent translocation of HelQ along ssDNA. We describe for the first time a functional role for the non-catalytic N-terminal region of HelQ, by identifying and characterizing its PWI-like domain. We present evidence that this domain of HelQ mediates interaction with RPA that orchestrates loading of the helicase domains onto ssDNA. Once HelQ is loaded onto the ssDNA, ATP-Mg2+ binding in the catalytic site activates the helicase core and triggers translocation along ssDNA as a dimer. Furthermore, we identify HelQ-ssDNA interactions that are critical for the translocation mechanism. Our data are novel and detailed insights into the mechanisms of HelQ function relevant for understanding how human cells avoid genome instability provoking cancers, and also how cells can gain resistance to treatments that rely on DNA crosslinking agents.

A new chapter for a better Bioscience Reports.

As Bioscience Reports enters its fifth decade of continuous multidisciplinary life science publishing, here we present a timely overview of the journal. In addition to introducing ourselves and new Associate Editors for 2021, we reflect on the challenges the new Editorial Board has faced and overcome since we took over the editorial leadership in June of 2020, and detail some key strategies on how we plan to encourage more submissions and broader readership for a better and stronger journal in the coming years.

Crystal structure and molecular dynamics of human POLDIP2, a multifaceted adaptor protein in metabolism and genome stability.

Polymerase δ-interacting protein 2 (POLDIP2, PDIP38) is a multifaceted, "moonlighting" protein, involved in binding protein partners from many different cellular processes, including mitochondrial metabolism and DNA replication and repair. How POLDIP2 interacts with many different proteins is unknown. Towards this goal, we present the crystal structure of POLDIP2 to 2.8 Å, which exhibited a compact two-domain ß-strand-rich globular structure, confirmed by circular dichroism and small angle X-ray scattering approaches. POLDIP2 comprised canonical DUF525 and YccV domains, but with a conserved domain linker packed tightly, resulting in an "extended" YccV module. A central channel was observed, which we hypothesize could influence structural changes potentially mediated by redox conditions, following observation of a modified cysteine residue in the channel. Unstructured regions were rebuilt by ab initio modelling to generate a model of full-length POLDIP2. Molecular dynamics simulations revealed a highly dynamic N-terminal region tethered to the YccV-domain by an extended linker, potentially facilitating interactions with distal binding partners. Models of POLDIP2 complexed with two of its partners, PrimPol and PCNA, indicated that dynamic flexibility of the POLDIP2 N-terminus and loop regions likely mediate protein interactions.

Efficient mesh refinement for the Poisson-Boltzmann equation with boundary elements.

The Poisson-Boltzmann equation is a widely used model to study electrostatics in molecular solvation. Its numerical solution using a boundary integral formulation requires a mesh on the molecular surface only, yielding accurate representations of the solute, which is usually a complicated geometry. Here, we utilize adjoint-based analyses to form two goal-oriented error estimates that allow us to determine the contribution of each discretization element (panel) to the numerical error in the solvation free energy. This information is useful to identify high-error panels to then refine them adaptively to find optimal surface meshes. We present results for spheres and real molecular geometries, and see that elements with large error tend to be in regions where there is a high electrostatic potential. We also find that even though both estimates predict different total errors, they have similar performance as part of an adaptive mesh refinement scheme. Our test cases suggest that the adaptive mesh refinement scheme is very effective, as we are able to reduce the error one order of magnitude by increasing the mesh size less than 20% and come out to be more efficient than uniform refinement when computing error estimations. This result sets the basis toward efficient automatic mesh refinement schemes that produce optimal meshes for solvation energy calculations.

Mechanistic insights into Lhr helicase function in DNA repair.

The DNA helicase Large helicase-related (Lhr) is present throughout archaea, including in the Asgard and Nanoarchaea, and has homologues in bacteria and eukaryotes. It is thought to function in DNA repair but in a context that is not known. Our data show that archaeal Lhr preferentially targets DNA replication fork structures. In a genetic assay, expression of archaeal Lhr gave a phenotype identical to the replication-coupled DNA repair enzymes Hel308 and RecQ. Purified archaeal Lhr preferentially unwound model forked DNA substrates compared with DNA duplexes, flaps and Holliday junctions, and unwound them with directionality. Single-molecule FRET measurements showed that binding of Lhr to a DNA fork causes ATP-independent distortion and base-pair melting at, or close to, the fork branchpoint. ATP-dependent directional translocation of Lhr resulted in fork DNA unwinding through the 'parental' DNA strands. Interaction of Lhr with replication forks in vivo and in vitro suggests that it contributes to DNA repair at stalled or broken DNA replication.

The Controversial Roles of ADP-Ribosyl Hydrolases MACROD1, MACROD2 and TARG1 in Carcinogenesis.

Post-translational modifications (PTM) of proteins are crucial for fine-tuning a cell's response to both intracellular and extracellular cues. ADP-ribosylation is a PTM, which occurs in two flavours: modification of a target with multiple ADP-ribose moieties (poly(ADP-ribosyl)ation or PARylation) or with only one unit (MARylation), which are added by the different enzymes of the PARP family (also known as the ARTD family). PARylation has been relatively well-studied, particularly in the DNA damage response. This has resulted in the development of PARP inhibitors such as olaparib, which are increasingly employed in cancer chemotherapeutic approaches. Despite the fact that the majority of PARP enzymes catalyse MARylation, MARylation is not as well understood as PARylation. MARylation is a dynamic process: the enzymes reversing intracellular MARylation of acidic amino acids (MACROD1, MACROD2, and TARG1) were discovered in 2013. Since then, however, little information has been published about their physiological function. MACROD1, MACROD2, and TARG1 have a 'macrodomain' harbouring the catalytic site, but no other domains have been identified. Despite the lack of information regarding their cellular roles, there are a number of studies linking them to cancer. However, some of these publications oppose each other, some rely on poorly-characterised antibodies, or on aberrant localisation of overexpressed rather than native protein. In this review, we critically assess the available literature on a role for the hydrolases in cancer and find that, currently, there is limited evidence for a role for MACROD1, MACROD2, or TARG1 in tumorigenesis.

Free Energies of the Disassembly of Viral Capsids from a Multiscale Molecular Simulation Approach.

Molecular simulations of large biological systems, such as viral capsids, remains a challenging task in soft matter research. On one hand, coarse-grained (CG) models attempt to make the description of the entire viral capsid disassembly feasible. On the other hand, the permanent development of novel molecular dynamics (MD) simulation approaches, like enhanced sampling methods, attempt to overcome the large time scales required for such simulations. Those methods have a potential for delivering molecular structures and properties of biological systems. Nonetheless, exploring the process on how a viral capsid disassembles by all-atom MD simulations has been rarely attempted. Here, we propose a methodology to analyze the disassembly process of viral capsids from a free energy perspective, through an efficient combination of dynamics using coarse-grained models and Poisson-Boltzmann simulations. In particular, we look at the effect of pH and charge of the genetic material inside the capsid, and compute the free energy of a disassembly trajectory precalculated using CG simulations with the SIRAH force field. We used our multiscale approach on the Triatoma virus (TrV) as a test case, and find that even though an alkaline environment enhances the stability of the capsid, the resulting deprotonation of the genetic material generates a Coulomb-type electrostatic repulsion that triggers disassembly.

A Boundary-Integral Approach for the Poisson-Boltzmann Equation with Polarizable Force Fields.

Implicit-solvent models are widely used to study the electrostatics in dissolved biomolecules, which are parameterized using force fields. Standard force fields treat the charge distribution with point charges; however, other force fields have emerged which offer a more realistic description by considering polarizability. In this work, we present the implementation of the polarizable and multipolar force field atomic multipole optimized energetics for biomolecular applications (AMOEBA), in the boundary integral Poisson-Boltzmann solver PyGBe. Previous work from other researchers coupled AMOEBA with the finite-difference solver APBS, and found difficulties to effectively transfer the multipolar charge description to the mesh. A boundary integral formulation treats the charge distribution analytically, overlooking such limitations. This becomes particularly important in simulations that need high accuracy, for example, when the quantity of interest is the difference between solvation energies obtained from separate calculations, like happens for binding energy. We present verification and validation results of our software, compare it with the implementation on APBS, and assess the efficiency of AMOEBA and classical point-charge force fields in a Poisson-Boltzmann solver. We found that a boundary integral approach performs similarly to a volumetric method on CPU. Also, we present a GPU implementation of our solver. Moreover, with a boundary element method, the mesh density to correctly resolve the electrostatic potential is the same for standard point-charge and multipolar force fields. Finally, we saw that for binding energy calculations, a boundary integral approach presents more consistent results than a finite difference approximation for multipolar force fields. © 2019 Wiley Periodicals, Inc.

Computational nanoplasmonics in the quasistatic limit for biosensing applications.

The phenomenon of localized surface plasmon resonance (LSPR) provides high sensitivity in detecting biomolecules through shifts in resonance frequency when a target is present. Computational studies in this field have used the full Maxwell equations with simplified models of a sensor-analyte system, or they neglected the analyte altogether. In the long-wavelength limit, one can simplify the theory via an electrostatics approximation while adding geometrical detail in the sensor and analytes (at moderate computational cost). This work uses the latter approach, expanding the open-source PyGBe code to compute the extinction cross section of metallic nanoparticles in the presence of any target for sensing. The target molecule is represented by a surface mesh, based on its crystal structure. PyGBe is research software for continuum electrostatics, written in python with computationally expensive parts accelerated on GPU hardware, via PyCUDA. It is also accelerated algorithmically via a treecode that offers O(NlogN) computational complexity. These features allow PyGBe to handle problems with half a million boundary elements or more. In this work, we demonstrate the suitability of PyGBe, extended to compute LSPR response in the electrostatic limit, for biosensing applications. Using a model problem consisting of an isolated silver nanosphere in an electric field, our results show grid convergence as 1/N, and accurate computation of the extinction cross section as a function of wavelength (compared with an analytical solution). For a model of a sensor-analyte system, consisting of a spherical silver nanoparticle and a set of bovine serum albumin (BSA) proteins, our results again obtain grid convergence as 1/N (with respect to the Richardson extrapolated value). Computing the LSPR response as a function of wavelength in the presence of BSA proteins captures a redshift of 0.5 nm in the resonance frequency due to the presence of the analytes at 1-nm distance. The final result is a sensitivity study of the biosensor model, obtaining the shift in resonance frequency for various distances between the proteins and the nanoparticle. All results in this paper are fully reproducible, and we have deposited in archival data repositories all the materials needed to run the computations again and recreate the figures. PyGBe is open source under a permissive license and openly developed. Documentation is available at http://pygbe.github.io/pygbe/docs/.

MicroRNA Quantitation During Dendritic Cell Endocytosis Using Imaging Flow Cytometry: Key Factors and Requirements.

BACKGROUND/AIMS: MicroRNA (miRNA)-induced suppression of dendritic cells (DCs) has been implicated in many diseases. Therefore, accurate monitoring of miRNA endocytosis by DCs is important for understanding the role of miRNAs in many diseases. Recently, a method for measuring the co-localization of Argonaute 2 (AGO2)-associated miRNAs on laser-scanning confocal microscopy method was proposed to localize the miRNAs. But its definition was limited by the number of observed cells through its accuracy. METHODS: In this study, a method based on imaging flow cytometry was developed to localize miR-590-5p with fluorescent probes in DCs. miR-590-5p proven to play an important role in tumor immunity. This method enabled the quantification, visualization and localization of the fluorescence intensity in 30,000 individual cells. RESULTS: Using this method, the DCs with different endocytotic ability were distinguished. The behaviour of miR-590-5p during endocytosis under the stimulation of tumor antigen in DCs was observed, binding to its cognate target mRNA and degradation in DCs. CONCLUSION: This method based on imaging flow cytometry provide an additional method to study miRNA processing in DCs, which makes it a valuable addition to existing miRNA research techniques.

Archaeal DNA polymerases: new frontiers in DNA replication and repair.

Archaeal DNA polymerases have long been studied due to their superior properties for DNA amplification in the polymerase chain reaction and DNA sequencing technologies. However, a full comprehension of their functions, recruitment and regulation as part of the replisome during genome replication and DNA repair lags behind well-established bacterial and eukaryotic model systems. The archaea are evolutionarily very broad, but many studies in the major model systems of both Crenarchaeota and Euryarchaeota are starting to yield significant increases in understanding of the functions of DNA polymerases in the respective phyla. Recent advances in biochemical approaches and in archaeal genetic models allowing knockout and epitope tagging have led to significant increases in our understanding, including DNA polymerase roles in Okazaki fragment maturation on the lagging strand, towards reconstitution of the replisome itself. Furthermore, poorly characterised DNA polymerase paralogues are finding roles in DNA repair and CRISPR immunity. This review attempts to provide a current update on the roles of archaeal DNA polymerases in both DNA replication and repair, addressing significant questions that remain for this field.