Predicting nonspecific ion binding using DelPhi

HIT-2: Implementing machine learning algorithms to treat bound ions in biomolecules

Electrostatic features are fundamental to protein functions and protein-protein interactions. Studying highly charged biomolecules is challenging given the heterogeneous distribution of the ionic cloud around such biomolecules. Here we report a new computational method, Hybridizing Ions Treatment-2 (HIT-2), which is used to model biomolecule-bound ions using the implicit solvation model. By modeling ions, HIT-2 allows the user to calculate important electrostatic features of the biomolecules. HIT-2 applies an efficient algorithm to calculate the position of bound ions from molecular dynamics simulations. Modeling parameters were optimized by machine learning methods from thousands of datasets. The optimized parameters produced results with errors lower than 0.2 Å. The testing results on bound Ca²⁺ and Zn²⁺ in NAMD simulations also proved that HIT-2 can effectively identify bound ion types, numbers, and positions. Also, multiple tests performed on HIT-2 suggest the method can handle biomolecules that undergo remarkable conformational changes. HIT-2 can significantly improve electrostatic calculations for many problems in computational biophysics.

Computational Study of the pH-Dependent Ionic Environment around β-Lactoglobulin

Ions are involved in multiple biological processes and may exist bound to biomolecules or may be associated with their surface. Although the presence of ions in nucleic acids has traditionally gained more interest, ion-protein interactions, often with a marked dependency on pH, are beginning to gather attention. Here we present a detailed analysis on the binding and distribution of ions around β-lactoglobulin using a constant-pH MD (CpHMD) method, at a pH range 3-8, and compare it with the more traditional Poisson-Boltzmann (PB) model and the existing experimental data. Most analyses used ion concentration maps built around the protein, obtained from either the CpHMD simulations or PB calculations. The requirements of approximate charge neutrality and ionic strength equal to bulk, imposed on the MD box, imply that the absolute value of the ion excess should be half the protein charge, which is in agreement with experimental observation on other proteins ( Proc. Natl. Acad. Sci. U.S.A. 2021, 118, e2015879118) and lends support to this protocol. In addition, the protein total charge (including territorially bound ions) estimated with MD is in excellent agreement with electrophoretic measurements. Overall, the CpHMD simulations show good agreement with the nonlinear form of the PB (NLPB) model but not with its linear form, which involves a theoretical inconsistency in the calculation of the concentration maps. In several analyses, the observed pH-dependent trends for the counterions and co-ions are those generally expected, and the ion concentration maps correctly converge to the bulk ionic strength as one moves away from the protein. Despite the overall similarity, the CpHMD and NLPB approaches show some discrepancies when analyzed in more detail, which may be related to an apparent overestimation of counterion excess and underestimation of co-ion exclusion by the NLPB model, particularly at short distances from the protein.

A reinforcement learning approach for protein-ligand binding pose prediction

Protein ligand docking is an indispensable tool for computational prediction of protein functions and screening drug candidates. Despite significant progress over the past two decades, it is still a challenging problem, characterized by the still limited understanding of the energetics between proteins and ligands, and the vast conformational space that has to be searched to find a satisfactory solution. In this project, we developed a novel reinforcement learning (RL) approach, the asynchronous advantage actor-critic model (A3C), to address the protein ligand docking problem. The overall framework consists of two models. During the search process, the agent takes an action selected by the actor model based on the current location. The critic model then evaluates this action and predict the distance between the current location and true binding site. Experimental results showed that in both single- and multi-atom cases, our model improves binding site prediction substantially compared to a naïve model. For the single-atom ligand, copper ion (Cu²⁺), the model predicted binding sites have a median root-mean-square-deviation (RMSD) of 2.39 Å to the true binding sites when starting from random starting locations. For the multi-atom ligand, sulfate ion (SO₄^2-), the predicted binding sites have a median RMSD of 3.82 Å to the true binding sites. The ligand-specific models built in this study can be used in solvent mapping studies and the RL framework can be readily scaled up to larger and more diverse sets of ligands.

A Newton-like iterative method implemented in the DelPhi for solving the nonlinear Poisson-Boltzmann equation

DelPhi is a popular scientific program which numerically solves the Poisson-Boltzmann equation (PBE) for electrostatic potentials and energies of biomolecules immersed in water via finite difference method. It is well known for its accuracy, reliability, flexibility, and efficiency. In this work, a new edition of DelPhi that uses a novel Newton-like method to solve the nonlinear PBE, in addition to the already implemented Successive Over Relaxation (SOR) algorithm, is introduced. Our tests on various examples have shown that this new method is superior to the SOR method in terms of stability when solving the nonlinear PBE, being able to converge even for problems involving very strong nonlinearity.

Ab-initio binding of barnase–barstar with DelPhiForce steered Molecular Dynamics (DFMD) approach

Receptor–ligand interactions are involved in various biological processes, therefore understanding the binding mechanism and ability to predict the binding mode are essential for many biological investigations. While many computational methods exist to predict the 3D structure of the corresponding complex provided the knowledge of the monomers, here we use the newly developed DelPhiForce steered Molecular Dynamics (DFMD) approach to model the binding of barstar to barnase to demonstrate that first-principles methods are also capable of modeling the binding. Essential component of DFMD approach is enhancing the role of long-range electrostatic interactions to provide guiding force of the monomers toward their correct binding orientation and position. Thus, it is demonstrated that the DFMD can successfully dock barstar to barnase even if the initial positions and orientations of both are completely different from the correct ones. Thus, the electrostatics provides orientational guidance along with pulling force to deliver the ligand in close proximity to the receptor.

Model for Counterion Binding and Charge Reversal on Protein Surfaces

The structural stability and solubility of proteins in liquid therapeutic formulations is important, especially since new generations of therapeutics are designed for efficacy before consideration of stability. We introduce an electrostatic binding model to measure the net charge of proteins with bound ions in solution. The electrostatic potential on a protein surface is used to separately group together acidic and basic amino acids into patches, which are then iteratively bound with oppositely charged counterions. This model is aimed toward formulation chemists for initial screening of a range of conditions prior to lab-work. Computed results compare well with experimental zeta potential measurements from the literature covering a range of solution conditions. Importantly, the binding model reproduces the charge reversal phenomenon that is observed with polyvalent ion binding to proteins and its dependence on ion charge and concentration. Intriguingly, protein sequence can be used to give similarly good agreement with experiment as protein structure, interpreted as resulting from the close proximity of charged side chains on a protein surface. Further, application of the model to human proteins suggests that polyanion binding and overcharging, including charge reversal for cationic proteins, is a general feature. These results add to evidence that addition of polyanions to protein formulations could be a general mechanism for modulating solution stability.

DelPhi Suite: New Developments and Review of Functionalities

Electrostatic potential, energies, and forces affect virtually any process in molecular biology, however, computing these quantities is a difficult task due to irregularly shaped macromolecules and the presence of water. Here, we report a new edition of the popular software package DelPhi along with describing its functionalities. The new DelPhi is a C++ object-oriented package supporting various levels of multiprocessing and memory distribution. It is demonstrated that multiprocessing results in significant improvement of computational time. Furthermore, for computations requiring large grid size (large macromolecular assemblages), the approach of memory distribution is shown to reduce the requirement of RAM and thus permitting large-scale modeling to be done on Linux clusters with moderate architecture. The new release comes with new features, whose functionalities and applications are described as well. © 2019 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc.

DelPhiPKa: Including salt in the calculations and enabling polar residues to titrate

DelPhiPKa is a widely used and unique approach to compute pK_a 's of ionizable groups that does not require molecular surface to be defined. Instead, it uses smooth Gaussian-based dielectric function to treat computational space via Poisson-Boltzmann equation (PBE). Here, we report an expansion of DelPhiPKa functionality to enable inclusion of salt in the modeling protocol. The method considers the salt mobile ions in solvent phase without defining solute-solvent boundary. Instead, the ions are penalized to enter solute interior via a desolvation penalty term in the Boltzmann factor in the framework of PBE. Hence, the concentration of ions near the protein is balanced by the desolvation penalty and electrostatic interactions. The study reveals that correlation between experimental and calculated pK_a 's is improved significantly by taking into consideration the presence of salt. Furthermore, it is demonstrated that DelphiPKa reproduces the salt sensitivity of experimentally measured pK_a 's. Another new development of DelPhiPKa allows for computing the pK_a 's of polar residues such as cysteine, serine, threonine and tyrosine. With this regard, DelPhiPKa is benchmarked against experimentally measured cysteine and tyrosine pK_a 's and for cysteine it is shown to outperform other existing methods (DelPhiPKa RMSD of 1.73 vs RMSD between 2.40 and 4.72 obtained by other existing pK_a prediction methods).

Explicit ions/implicit water generalized Born model for nucleic acids

The ion atmosphere around highly charged nucleic acid molecules plays a significant role in their dynamics, structure, and interactions. Here we utilized the implicit solvent framework to develop a model for the explicit treatment of ions interacting with nucleic acid molecules. The proposed explicit ions/implicit water model is based on a significantly modified generalized Born (GB) model and utilizes a non-standard approach to define the solute/solvent dielectric boundary. Specifically, the model includes modifications to the GB interaction terms for the case of multiple interacting solutes-disconnected dielectric boundary around the solute-ion or ion-ion pairs. A fully analytical description of all energy components for charge-charge interactions is provided. The effectiveness of the approach is demonstrated by calculating the potential of mean force for Na⁺-Cl^- ion pair and by carrying out a set of Monte Carlo (MC) simulations of mono- and trivalent ions interacting with DNA and RNA duplexes. The monovalent (Na⁺) and trivalent (CoHex³⁺) counterion distributions predicted by the model are in close quantitative agreement with all-atom explicit water molecular dynamics simulations used as reference. Expressed in the units of energy, the maximum deviations of local ion concentrations from the reference are within k _B T. The proposed explicit ions/implicit water GB model is able to resolve subtle features and differences of CoHex distributions around DNA and RNA duplexes. These features include preferential CoHex binding inside the major groove of the RNA duplex, in contrast to CoHex biding at the "external" surface of the sugar-phosphate backbone of the DNA duplex; these differences in the counterion binding patters were earlier shown to be responsible for the observed drastic differences in condensation propensities between short DNA and RNA duplexes. MC simulations of CoHex ions interacting with the homopolymeric poly(dA·dT) DNA duplex with modified (de-methylated) and native thymine bases are used to explore the physics behind CoHex-thymine interactions. The simulations suggest that the ion desolvation penalty due to proximity to the low dielectric volume of the methyl group can contribute significantly to CoHex-thymine interactions. Compared to the steric repulsion between the ion and the methyl group, the desolvation penalty interaction has a longer range and may be important to consider in the context of methylation effects on DNA condensation.

Treating ion distribution with Gaussian-based smooth dielectric function in DelPhi

The standard treatment of ions in the framework of the Poisson-Boltzmann equation relies on molecular surfaces, which are commonly constructed along with the Stern layer. The molecular surface determines where ions can be present. In the Gaussian-based smooth dielectric function in DelPhi, smooth boundaries between the solute and solvent take the place of molecular surface. Therefore, this invokes the question of how to model mobile ions in the water phase without a definite solute-solvent boundary. This article reports a natural extension of the Gaussian-based smooth dielectric function approach that treats mobile ions via Boltzmann distribution with an added desolvation penalty. Thus, ion concentration near macromolecules is governed by the local electrostatic potential and the desolvation penalty (from being partially desolvated). The approach is tested against the experimental salt dependence of binding free energy on 7 protein-protein complexes and 12 DNA-protein complexes, resulting in Pearson correlations of 0.95 and 0.88, respectively. © 2017 Wiley Periodicals, Inc.

DelPhiForce, a tool for electrostatic force calculations: Applications to macromolecular binding

Long-range electrostatic forces play an important role in molecular biology, particularly in macromolecular interactions. However, calculating the electrostatic forces for irregularly shaped molecules immersed in water is a difficult task. Here, we report a new tool, DelPhiForce, which is a tool in the DelPhi package that calculates and visualizes the electrostatic forces in biomolecular systems. In parallel, the DelPhi algorithm for modeling electrostatic potential at user-defined positions has been enhanced to include triquadratic and tricubic interpolation methods. The tricubic interpolation method has been tested against analytical solutions and it has been demonstrated that the corresponding errors are negligibly small at resolution 4 grids/Å. The DelPhiForce is further applied in the study of forces acting between partners of three protein-protein complexes. It has been demonstrated that electrostatic forces play a dual role by steering binding partners (so that the partners recognize their native interfaces) and exerting an electrostatic torque (if the mutual orientations of the partners are not native-like). The output of DelPhiForce is in a format that VMD can read and visualize, and provides additional options for analysis of protein-protein binding. DelPhiForce is available for download from the DelPhi webpage at http://compbio.clemson.edu/downloadDir/delphiforce.tar.gz © 2017 Wiley Periodicals, Inc.

A New DelPhi Feature for Modeling Electrostatic Potential around Proteins: Role of Bound Ions and Implications for Zeta-Potential

A new feature of the popular software DelPhi is developed and reported, allowing for computing the surface averaged electrostatic potential (SAEP) of macromolecules. The user is given the option to specify the distance from the van der Waals surface where the electrostatic potential will be outputted. In conjunction with DelPhiPKa and the BION server, the user can adjust the charges of titratable groups according to specific pH values, and add explicit ions bound to the macromolecular surface. This approach is applied to a set of four proteins with "experimentally" delivered zeta (ζ)-potentials at different pH values and salt concentrations. It has been demonstrated that the protocol is capable of predicting ζ-potentials in the case of proteins with relatively large net charges. This protocol has been less successful for proteins with low net charges. The work demonstrates that in the case of proteins with large net charges, the electrostatic potential should be collected at distances about 4 Å away from the vdW surface and explicit ions should be added at a binding energy cutoff larger than 1-2kT, in order to accurately predict ζ-potentials. The low salt conditions substantiate this effect of ions on SAEP.

Computational investigation of proton transfer, pKa shifts and pH-optimum of protein-DNA and protein-RNA complexes

Protein-nucleic acid interactions play a crucial role in many biological processes. This work investigates the changes of pKa values and protonation states of ionizable groups (including nucleic acid bases) that may occur at protein-nucleic acid binding. Taking advantage of the recently developed pKa calculation tool DelphiPka, we utilize the large protein-nucleic acid interaction database (NPIDB database) to model pKa shifts caused by binding. It has been found that the protein's interfacial basic residues experience favorable electrostatic interactions while the protein acidic residues undergo proton uptake to reduce the energy cost upon the binding. This is in contrast with observations made for protein-protein complexes. In terms of DNA/RNA, both base groups and phosphate groups of nucleotides are found to participate in binding. Some DNA/RNA bases undergo pKa shifts at complex formation, with the binding process tending to suppress charged states of nucleic acid bases. In addition, a weak correlation is found between the pH-optimum of protein-DNA/RNA binding free energy and the pH-optimum of protein folding free energy. Overall, the pH-dependence of protein-nucleic acid binding is not predicted to be as significant as that of protein-protein association. Proteins 2017; 85:282-295. © 2016 Wiley Periodicals, Inc.

In vivo effects of metal ions on conformation and mechanical performance of silkworm silks

BACKGROUND

The mechanism of silk fiber formation is of particular interest. Although in vitro evidence has shown that metal ions affect conformational transitions of silks, the in vivo effects of metal ions on silk conformations and mechanical performance are still unclear.

METHODS

This study explored the effects of metal ions on silk conformations and mechanical properties of silk fibers by adding K⁺ and Cu²⁺ into the silk fibroin solutions or injecting them into the silkworms. Aimed by CD analysis, FTIR analysis, and mechanical testing, the conformational and mechanical changes of the silks were estimated. By using BION Web Server, the interactions of K⁺ and N-terminal of silk fibroin were also simulated.

RESULTS

We presented that K⁺ and Cu²⁺ induced the conformational transitions of silk fibroin by forming β-sheet structures. Moreover, the mechanical parameters of silk fibers, such as strength, toughness and Young's modulus, were also improved after K⁺ or Cu²⁺ injection. Using BION Web Server, we found that potassium ions may have strong electrostatic interactions with the negatively charged residues.

CONCLUSION

We suggest that K⁺ and Cu²⁺ play crucial roles in the conformation and mechanical performances of silks and they are involved in the silk fiber formation in vivo.

GENERAL SIGNIFICANCE

Our results are helpful for clarifying the mechanism of silk fiber formation, and provide insights for modifying the mechanical properties of silk fibers.

Statistical investigation of surface bound ions and further development of BION server to include pH and salt dependence

Ions are engaged in multiple biological processes in cells. By binding to the macromolecules or being mobile in the solvent, they maintain the integrity of the structure of macromolecules; participate in their enzymatic activity; or screen electrostatic interactions. While experimental methods are not always able to assign the exact location of ions, computational methods are in demand. Although the majority of computational methods are successful in predicting the position of ions buried inside macromolecules, they are less effective in deciphering positions of surface bound ions. Here, we propose the new BION algorithm (http://compbio.clemson.edu/bion_server_ph/) that predicts the location of the surface bound ions. It is more efficient and accurate compared to the previous version since it uses more advanced clustering algorithm in combination with pairing rules. In addition, the BION webserver allows specifying the pH and the salt concentration in predicting ions positions.

Modulation of Self-Assembly Process of Fibroin: An Insight for Regulating the Conformation of Silk Biomaterials

Controlling the mechanism of self-assembly in proteins has emerged as a potent tool for various biomedical applications. Silk fibroin self-assembly consists of gradual conformational transition from random coil to β-sheet structure. In this work we elucidated the intermediate secondary conformation in the presence of Ca(2+) ions during fibroin self-assembly. The interaction of fibroin and calcium ions resulted in a predominantly α-helical intermediate conformation, which was maintained to certain extent even in the final conformation as illustrated by circular dichroism and attenuated total reflectance-Fourier transform infrared spectroscopy. Further, to elucidate the mechanism behind this interaction molecular modeling of the N-terminal region of fibroin with Ca(2+) ions was performed. Negatively charged glutamate and aspartate amino acids play a key role in the electrostatic interaction with positively charged calcium ions. Therefore, insights about modulation of self-assembly mechanism of fibroin could potentially be utilized to develop silk-based biomaterials consisting of the desired secondary conformation.

On the energy components governing molecular recognition in the framework of continuum approaches

Molecular recognition is a process that brings together several biological macromolecules to form a complex and one of the most important characteristics of the process is the binding free energy. Various approaches exist to model the binding free energy, provided the knowledge of the 3D structures of bound and unbound molecules. Among them, continuum approaches are quite appealing due to their computational efficiency while at the same time providing predictions with reasonable accuracy. Here we review recent developments in the field emphasizing on the importance of adopting adequate description of physical processes taking place upon the binding. In particular, we focus on the efforts aiming at capturing some of the atomistic details of the binding phenomena into the continuum framework. When possible, the energy components are reviewed independently of each other. However, it is pointed out that rigorous approaches should consider all energy contributions on the same footage. The two major schemes for utilizing the individual energy components to predict binding affinity are outlined as well.

Features of CPB: a Poisson-Boltzmann solver that uses an adaptive Cartesian grid

The capabilities of an adaptive Cartesian grid (ACG)-based Poisson-Boltzmann (PB) solver (CPB) are demonstrated. CPB solves various PB equations with an ACG, built from a hierarchical octree decomposition of the computational domain. This procedure decreases the number of points required, thereby reducing computational demands. Inside the molecule, CPB solves for the reaction-field component (ϕrf ) of the electrostatic potential (ϕ), eliminating the charge-induced singularities in ϕ. CPB can also use a least-squares reconstruction method to improve estimates of ϕ at the molecular surface. All surfaces, which include solvent excluded, Gaussians, and others, are created analytically, eliminating errors associated with triangulated surfaces. These features allow CPB to produce detailed surface maps of ϕ and compute polar solvation and binding free energies for large biomolecular assemblies, such as ribosomes and viruses, with reduced computational demands compared to other Poisson-Boltzmann equation solvers. The reader is referred to http://www.continuum-dynamics.com/solution-mm.html for how to obtain the CPB software.

Chronic Beryllium Disease: revealing the role of beryllium ion and small peptides binding to HLA-DP2

Chronic Beryllium (Be) Disease (CBD) is a granulomatous disorder that predominantly affects the lung. The CBD is caused by Be exposure of individuals carrying the HLA-DP2 protein of the major histocompatibility complex class II (MHCII). While the involvement of Be in the development of CBD is obvious and the binding site and the sequence of Be and peptide binding were recently experimentally revealed [1], the interplay between induced conformational changes and the changes of the peptide binding affinity in presence of Be were not investigated. Here we carry out in silico modeling and predict the Be binding to be within the acidic pocket (Glu26, Glu68 and Glu69) present on the HLA-DP2 protein in accordance with the experimental work [1]. In addition, the modeling indicates that the Be ion binds to the HLA-DP2 before the corresponding peptide is able to bind to it. Further analysis of the MD generated trajectories reveals that in the presence of the Be ion in the binding pocket of HLA-DP2, all the different types of peptides induce very similar conformational changes, but their binding affinities are quite different. Since these conformational changes are distinctly different from the changes caused by peptides normally found in the cell in the absence of Be, it can be speculated that CBD can be caused by any peptide in presence of Be ion. However, the affinities of peptides for Be loaded HLA-DP2 were found to depend of their amino acid composition and the peptides carrying acidic group at positions 4 and 7 are among the strongest binders. Thus, it is proposed that CBD is caused by the exposure of Be of an individual carrying the HLA-DP2*0201 allele and that the binding of Be to HLA-DP2 protein alters the conformational and ionization properties of HLA-DP2 such that the binding of a peptide triggers a wrong signaling cascade.

Ion binding to biological macromolecules

Biological macromolecules carry out their functions in water and in the presence of ions. The ions can bind to the macromolecules either specifically or non-specifically, or can simply to be a part of the water phase providing physiological gradient across various membranes. This review outlines the differences between specific and non-specific ion binding in terms of the function and stability of the corresponding macromolecules. Furthermore, the experimental techniques to identify ion positions and computational methods to predict ion binding are reviewed and their advantages compared. It is indicated that specifically bound ions are relatively easier to be revealed while non-specifically associated ions are difficult to predict. In addition, the binding and the residential time of non-specifically bound ions are very much sensitive to the environmental factors in the cells, specifically to the local pH and ion concentration. Since these characteristics differ among the cellular compartments, the non-specific ion binding must be investigated with respect to the sub-cellular localization of the corresponding macromolecule.

Structural and antigenic features of the synthetic SF23 peptide corresponding to the receptor binding fragment of diphtheria toxin

The SF23 peptide corresponding to the receptor binding fragment of diphtheria toxin (residues 508-530) has been synthesized. This fragment forming a protruding beta hairpin has been chosen because it is the less mutable B-cell epitope. Affine chromatography and ELISA show that antibodies from the sera of persons infected by toxigenic Corynebacterium diphtheriae and those immunized by diphtheria toxoid are able to bind the synthetic SF23 peptide. There are antibodies recognizing the SF23 peptide in the serum of horses hyperimmunized with diphtheria toxoid. Analysis of circular dichroism spectra show formation of beta hairpin by the peptide. Taken together, the results showed that the structure of the less mutable epitope of C. diphtheriae toxin was reproduced by the short SF23 peptide. Since antibodies against that epitope should block its interactions with cellular receptor (heparin-binding epidermal growth factor), the SF23 peptide can be considered as a promising candidate for synthetic vaccine development. Fluorescence quenching studies showed the existence of chloride and phosphate binding sites on the SF23 molecule. Phosphate containing adjuvants (aluminum hydroxyphosphate or aluminum hydroxyphosphate sulfate) are recommended to increase the SF23 immunogenic properties.

BION web server: predicting non-specifically bound surface ions

MOTIVATION

Ions are essential component of the cell and frequently are found bound to various macromolecules, in particular to proteins. A binding of an ion to a protein greatly affects protein's biophysical characteristics and needs to be taken into account in any modeling approach. However, ion's bounded positions cannot be easily revealed experimentally, especially if they are loosely bound to macromolecular surface.

RESULTS

Here, we report a web server, the BION web server, which addresses the demand for tools of predicting surface bound ions, for which specific interactions are not crucial; thus, they are difficult to predict. The BION is easy to use web server that requires only coordinate file to be inputted, and the user is provided with various, but easy to navigate, options. The coordinate file with predicted bound ions is displayed on the output and is available for download.