Highly efficient and exact method for parallelization of grid-based algorithms and its implementation in DelPhi

Calculation of electrostatic free energy for the nonlinear Poisson-Boltzmann model based on the dimensionless potential

The Poisson-Boltzmann (PB) equation governing the electrostatic potential with a unit is often transformed to a normalized form for a dimensionless potential in numerical studies. To calculate the electrostatic free energy (EFE) of biological interests, a unit conversion has to be conducted, because the existing PB energy functionals are all described in terms of the original potential. To bypass this conversion, this paper proposes energy functionals in terms of the dimensionless potential for the first time in the literature, so that the normalized PB equation can be directly derived by using the Euler-Lagrange variational analysis. Moreover, alternative energy forms have been rigorously derived to avoid approximating the gradient of singular functions in the electrostatic stress term. A systematic study has been carried out to examine the surface integrals involved in alternative energy forms and their dependence on finite domain size and mesh step size, which leads to a recommendation on the EFE forms for efficient computation of protein systems. The calculation of the EFE in the regularization formulation, which is an analytical approach for treating singular charge sources of the PB equation, has also been studied. The proposed energy forms have been validated by considering smooth dielectric settings, such as diffuse interface and super-Gaussian, for which the EFE of the nonlinear PB model is found to be significantly different from that of the linearized PB model. All proposed energy functionals and EFE forms are designed such that the dimensionless potential can be simply plugged in to compute the EFE in the unit of kcal/mol, and they can also be applied in the classical sharp interface PB model.

The pH Effects on SARS-CoV and SARS-CoV-2 Spike Proteins in the Process of Binding to hACE2

COVID-19 has been threatening human health since the late 2019, and has a significant impact on human health and economy. Understanding SARS-CoV-2 and other coronaviruses is important to develop effective treatments for COVID-19 and other coronavirus-caused diseases. In this work, we applied multi-scale computational approaches to study the electrostatic features of spike (S) proteins for SARS-CoV and SARS-CoV-2. From our results, we found that SARS-CoV and SARS-CoV-2 have similar charge distributions and electrostatic features when binding with the human angiotensin-converting enzyme 2 (hACE2). Energy pH-dependence calculations revealed that the complex structures of hACE2 and the S proteins of SARS-CoV/SARS-CoV-2 are stable at pH values ranging from 7.5 to 9. Three independent 100 ns molecular dynamics (MD) simulations were performed using NAMD to investigate the hydrogen bonds between S proteins RBD and hACE2 RBD. From MD simulations, we found that SARS-CoV-2 forms 19 pairs (average of three simulations) of hydrogen bonds with high occupancy (>50%) to hACE2, compared to 16 pairs between SARS-CoV and hACE2. Additionally, SARS-CoV viruses prefer sticking to the same hydrogen bond pairs, while SARS-CoV-2 tends to have a larger range of selections on hydrogen bonds acceptors. We also labelled key residues involved in forming the top five hydrogen bonds that were found in all three independent 100 ns simulations. This identification is important to potential drug designs for COVID-19 treatments. Our work will shed the light on current and future coronavirus-caused diseases.

Structure and dynamics of major histocompatibility class Ib molecule H2-M3 complexed with mitochondrial-derived peptides

Presentation of antigenic peptides to T-cell receptors is an essential step in the adaptive immune response. In the mouse the class Ib major histocompatibility complex molecule, H2-M3, presents bacterial- and mitochondrial-derived peptides to T-cell receptors on cytotoxic T cells. Four mitochondrial heptapeptides, differing only at residue 6, form complexes with H2-M3 which can be distinguished by T cells. No structures of relevant receptors are available. To investigate the structural basis for this distinction, crystal structures were determined and molecular dynamics simulations over one microsecond were done for each complex. In the crystal structures of the heptapeptide complexes with H2-M3, presented here, the side chains of the peptide residues at position 6 all point into the H2-M3 binding groove, and are thus inaccessible, so that the very similar structures do not suggest how recognition and initiation of responses by the T cells may occur. However, conformational differences, which could be crucial to T-cell discrimination, appear within one microsecond during molecular dynamics simulations of the four complexes. Specifically, the three C-terminal residues of peptide ligands with alanine or threonine at position 6 partially exit the binding groove; this does not occur in peptide ligands with isoleucine or valine at position 6. Structural changes associated with partial peptide exit from the binding groove, along with relevant peptide binding energetics and immunological results are discussed. Communicated by Ramaswamy H. Sarma.

The pH Effects on SARS-CoV and SARS-CoV-2 Spike Proteins in the Process of Binding to hACE2

COVID-19 has been threatening human health since the late 2019, which has significant impact on human health and economy. Understanding the SARS-CoV-2 and other coronaviruses is important to develop effective treatments for COVID-19 and other coronaviruses-caused diseases. In this work, we applied multi-scale computational approaches to study the electrostatic features of spike (S) proteins for SARS-CoV and SARS-CoV-2. From our results, we found thatSARS-CoV and SARS-CoV-2 have similar charge distributions and electrostatic features when binding with the human angiotensin-converting enzyme 2 (hACE2). The energy pH-dependence calculation srevealed that the complex structures of hACE2 and the S proteins of SARS-CoV/SARS-CoV-2 are stable at pH values ranging from 7.5 to 9. Molecular dynamics simulations were performed using NAMD to investigate the hydrogen bonds between S proteins and hACE2. From the MD simulations it was found that SARS-CoV-2 has four pairsof essential hydrogenbonds (high occupancy, >80%), while SARS-CoV has three pairs, which indicates the SARS-CoV-2 S protein has relatively more robust binding strategy than SARS-CoVS protein.Four key residues forming essential hydrogen bonds from SARS-CoV-2 are identified, which are potential drug targets for COVID-19 treatments. The findings in this study shed lights on the current and future treatments for COVID-19 and other coronaviruses-caused diseases.

Hybrid method for representing ions in implicit solvation calculations

Fast and accurate calculations of the electrostatic features of highly charged biomolecules such as DNA, RNA, and highly charged proteins are crucial and challenging tasks. Traditional implicit solvent methods calculate the electrostatic features quickly, but these methods are not able to balance the high net biomolecular charges effectively. Explicit solvent methods add unbalanced ions to neutralize the highly charged biomolecules in molecular dynamic simulations, which require more expensive computing resources. Here we report developing a novel method, Hybridizing Ions Treatment (HIT), which hybridizes the implicit solvent method with an explicit method to realistically calculate the electrostatic potential for highly charged biomolecules. HIT utilizes the ionic distribution from an explicit method to predict the bound ions. The bound ions are then added in the implicit solvent method to perform the electrostatic potential calculations. In this study, two training sets were developed to optimize parameters for HIT. The performance on the testing set demonstrates that HIT significantly improves the electrostatic calculations. Results on molecular motors myosin and kinesin reveal some mechanisms and explain some previous experimental findings. HIT can be widely used to study highly charged biomolecules, including DNA, RNA, molecular motors, and other highly charged biomolecules. The HIT package is available at http://compbio.utep.edu/static/downloads/download_hit.zip.

StructureMan: A Structure Manipulation Tool to Study Large Scale Biomolecular Interactions

Studying biomolecular interactions is a crucial but challenging task. Due to their large scales, many biomolecular interactions are difficult to be simulated via all atom models. An effective approach to investigate the biomolecular interactions is highly demanded in many areas. Here we introduce a Structure Manipulation (StructureMan) program to operate the structures when studying the large-scale biomolecular interactions. This novel StructureMan tool provides comprehensive operations which can be utilized to study the interactions in various large biological systems. Combining with electrostatic calculation programs such as DelPhi and DelPhiForce, StructureMan was implemented to reveal the detailed electrostatic features in two large biological examples, the viral capsid and molecular motor-microtubule complexes. Applications on these two examples revealed interesting binding mechanisms in the viral capsid and molecular motor. Such applications demonstrated that the StructureMan can be widely used when studying the biomolecular interactions in large scale biological problems. This novel tool provides an alternative approach to efficiently study the biomolecular interactions, especially for large scale biology systems. The StructureMan tool is available at our website: http://compbio.utep.edu/static/downloads/script-for-munipulation2.zip.

Spike Proteins of SARS-CoV and SARS-CoV-2 Utilize Different Mechanisms to Bind With Human ACE2

The ongoing outbreak of COVID-19 has been a serious threat to human health worldwide. The virus SARS-CoV-2 initiates its infection to the human body via the interaction of its spike (S) protein with the human Angiotensin-Converting Enzyme 2 (ACE2) of the host cells. Therefore, understanding the fundamental mechanisms of how SARS-CoV-2 S protein receptor binding domain (RBD) binds to ACE2 is highly demanded for developing treatments for COVID-19. Here we implemented multi-scale computational approaches to study the binding mechanisms of human ACE2 and S proteins of both SARS-CoV and SARS-CoV-2. Electrostatic features, including electrostatic potential, electric field lines, and electrostatic forces of SARS-CoV and SARS-CoV-2 were calculated and compared in detail. The results demonstrate that SARS-CoV and SARS-CoV-2 S proteins are both attractive to ACE2 by electrostatic forces even at different distances. However, the residues contributing to the electrostatic features are quite different due to the mutations between SARS-CoV S protein and SARS-CoV-2 S protein. Such differences are analyzed comprehensively. Compared to SARS-CoV, the SARS-CoV-2 binds with ACE2 using a more robust strategy: The electric field line related residues are distributed quite differently, which results in a more robust binding strategy of SARS-CoV-2. Also, SARS-CoV-2 has a higher electric field line density than that of SARS-CoV, which indicates stronger interaction between SARS-CoV-2 and ACE2, compared to that of SARS-CoV. Key residues involved in salt bridges and hydrogen bonds are identified in this study, which may help the future drug design against COVID-19.

Revealing the mechanism of SARS-CoV-2 spike protein binding with ACE2

A large population in the world has been infected by COVID-19. Understanding the mechanisms of Severe Acute Respiratory Syndrome CoronaVirus 2 (SARS-CoV-2) is important for the management and treatment of COVID-19. When it comes to the infection process, one of the most important proteins in SARS-CoV-2 is the spike (S) protein, which is able to bind to human Angiotensin-Converting Enzyme 2 (ACE2) and initializes the entry of the host cell. In this study, we implemented multiscale computational approaches to study the electrostatic features of the interfaces of the SARS-CoV-2 S protein receptor binding domain and ACE2. The simulations and analyses were performed on high-performance computing resources in the Texas Advanced Computing Center. Our study identified key residues on SARS-CoV-2, which can be used as targets for future drug design. The results shed light on future drug design and therapeutic targets for COVID-19.

Aggregation of M3 (E376D) variant of alpha1- antitrypsin

Alpha1-antitrypsin (α1AT) is an abundant serine-protease inhibitor in circulation. It has an important role in neutralizing the neutrophil elastase activity. Different pathogenic point mutations like Z(E342K)-α1AT have been implicated in the development of liver cirrhosis and Chronic Obstructive Pulmonary Disease (COPD), the latter being a cluster of progressive lung diseases including chronic bronchitis and emphysema. M3-α1AT (376Glu > Asp) is another variant of α1AT which so far is largely being considered as normal though increased frequency of the variant has been reported in many human diseases including COPD. We also observed increased frequency of M3-α1AT in COPD cases in Kashmiri population. The frequency of heterozygous (AC) genotype in cases and controls was 58.57% and 27.61% (odds-ratio 6.53 (2.27-15.21); p < 0.0001) respectively, while homozygous CC genotype was found to be 21.42% and 6.66% (odds-ratio 10.56 (3.63-18.64); p < 0.0001) respectively. Comparative in vitro investigations that include trypsin‒antitrypsin assay, Circular Dichroism spectroscopy and dynamic light scattering performed on wild-type (M-α1AT), M3-α1AT, and Z-α1AT proteins along with the molecular dynamics simulations revealed that M3-α1AT has properties similar to Z-α1AT capable of forming aggregates of varied size. Our maiden observations suggest that M3-α1AT may contribute to the pathogenesis of COPD and other disorders by mechanisms that warrant further investigations.

A computational model of ESAT-6 complex in membrane

One quarter of the world's population are infected by Mycobacterium tuberculosis (Mtb), which is a leading death-causing bacterial pathogen. Recent evidence has demonstrated that two virulence factors, ESAT-6 and CFP-10, play crucial roles in Mtb's cytosolic translocation. Many efforts have been made to study the ESAT-6 and CFP-10 proteins. Some studies have shown that ESAT-6 has an essential role in rupturing phagosome. However, the mechanisms of how ESAT-6 interacts with the membrane have not yet been fully understood. Recent studies indicate that the ESAT-6 disassociates with CFP-10 upon their interaction with phagosome membrane, forming a membrane-spanning pore. Based on these observations, as well as the available structure of ESAT-6, ESAT-6 is hypothesized to form an oligomer for membrane insertion as well as rupturing. Such an ESAT-6 oligomer may play a significant role in the tuberculosis infection. Therefore, deeper understanding of the oligomerization of ESAT-6 will establish new directions for tuberculosis treatment. However, the structure of the oligomer of ESAT-6 is not known. Here, we proposed a comprehensive approach to model the complex structures of ESAT-6 oligomer inside a membrane. Several computational tools, including MD simulation, symmetrical docking, MM/PBSA, are used to obtain and characterize such a complex structure. Results from our studies lead to a well-supported hypothesis of the ESAT-6 oligomerization as well as the identification of essential residues in stabilizing the ESAT-6 oligomer which provide useful insights for future drug design targeting tuberculosis. The approach in this research can also be used to model and study other cross-membrane complex structures.

An effective molecular blocker of ion channel of M2 protein as anti-influenza a drug

Design of a drug compound that can effectively bind to the M2 ion channel and block the diffusion of hydrogen ions (H⁺) through and inhibit influenza A virus replication is an important task. Known anti-influenza drugs amantadine and rimantadine have a weak effect on influenza A virus. A new class of positively charged, +2 e.u., molecules is proposed here to block diffusion of H⁺ ion through the M2 channel. Several drug candidates, derivatives of a lead compound (diazabicyclooctane), were proposed and investigated. Molecular dynamics of thermal fluctuations of M2 protein structure and ionization-conformation coupling of all the ionizable residues were simulated at physiological pH. The influence of the most probable mutations of key drug-binding amino acid residues in the M2 ion channel were investigated too. It is shown that the suggested new blocker has high binding affinity for the M2 channel. There are two in-channel binding sites of high affinity, the first one has H-bonds with two of four serine residues Ser-31A (B) or Ser-31C(D), and the second one has H-bonds with two of four histidine residues His-37A (B), or His-37C(D). The main advantage of the new drug molecule is the positive charge, +2 e.u., which creates a positive electrostatic potential barrier (in addition to a steric one) for a transfer of H⁺ ion through M2 channel and may serve as an effective anti-influenza A virus drug.Communicated by Ramaswamy H. Sarma.

The urokinase plasminogen activator binding to its receptor: a quantum biochemistry description within an in/homogeneous dielectric function framework with application to uPA–uPAR peptide inhibitors

DFT calculations using the MFCC fragment-based model considering a spatial-dependent dielectric function based on the Poisson–Boltzmann approximation were performed to describe the uPA–uPAR interactions.

Using computational approaches to study dengue virus capsid assembly

Dengue viral capsid plays a significant role in viral life cycle of dengue, especially in vial genome protection and virus-cell fusion. Revealing mechanisms of the viral capsid protein assembly may lead to the discovery of anti-viral drugs that inhibit the assembly of the viral capsid. The E and M-proteins are arranged into heterotetramers, which consists of two copies of E and M-protein. The heterotetramers are assembled into a highly ordered capsid. While many investigations of the interactions between E and M-proteins have been performed, there are very few studies on the interactions between the heterotetramers and their roles in capsid assembly. Utilizing a series of computational approaches, this study focuses on the assembly mechanism of the heterotetramers. Our electrostatic analyses lead to the identification of four binding modes between each two dengue heterotetramers that repeat periodically throughout the virus capsid. Among these four binding modes, heterotetramers in binding modes I, II and IV are attractive. But in the binding mode III the heterotetramers repel each other, making mode III a suitable target for drug design. Furthermore, MD simulations were performed following by salt bridges analysis. This study demonstrates that using computational approaches is a promising direction to study the dengue virus.

DFMD: Fast and Effective DelPhiForce Steered Molecular Dynamics Approach to Model Ligand Approach Toward a Receptor: Application to Spermine Synthase Enzyme

Here we report a novel approach, the DelPhiForce Molecular Dynamics (DFMD) method, for steered molecular dynamics simulations to model receptor-ligand association involving charged species. The main purpose of developing DFMD is to simulate ligand's trajectory toward the receptor and thus to predict the "entrance" of the binding pocket and conformational changes associated with the binding. We demonstrate that the DFMD is superior compared with molecular dynamics simulations applying standard cut-offs, provides correct binding forces, allows for modeling the ligand approach at long distances and thus guides the ligand toward the correct binding spot, and it is very fast (frequently the binding is completed in <1 ns). The DFMD is applied to model the binding of two ligands to a receptor (spermine synthase) and it is demonstrated that it guides the ligands toward the corresponding pockets despite of the initial ligand's position with respect to the receptor. Predicted conformational changes and the order of ligand binding are experimentally verified.

A super-Gaussian Poisson-Boltzmann model for electrostatic free energy calculation: smooth dielectric distribution for protein cavities and in both water and vacuum states

Calculations of electrostatic potential and solvation free energy of macromolecules are essential for understanding the mechanism of many biological processes. In the classical implicit solvent Poisson-Boltzmann (PB) model, the macromolecule and water are modeled as two-dielectric media with a sharp border. However, the dielectric property of interior cavities and ion-channels is difficult to model realistically in a two-dielectric setting. In fact, the detection of water molecules in a protein cavity remains to be an experimental challenge. This introduces an uncertainty, which affects the subsequent solvation free energy calculation. In order to compensate this uncertainty, a novel super-Gaussian dielectric PB model is introduced in this work, which devices an inhomogeneous dielectric distribution to represent the compactness of atoms and characterizes empty cavities via a gap dielectric value. Moreover, the minimal molecular surface level set function is adopted so that the dielectric profile remains to be smooth when the protein is transferred from water phase to vacuum. An important feature of this new model is that as the order of super-Gaussian function approaches the infinity, the dielectric distribution reduces to a piecewise constant of the two-dielectric model. Mathematically, an effective dielectric constant analysis is introduced in this work to benchmark the dielectric model and select optimal parameter values. Computationally, a pseudo-time alternative direction implicit (ADI) algorithm is utilized for solving the super-Gaussian PB equation, which is found to be unconditionally stable in a smooth dielectric setting. Solvation free energy calculation of a Kirkwood sphere and various proteins is carried out to validate the super-Gaussian model and ADI algorithm. One macromolecule with both water filled and empty cavities is employed to demonstrate how the cavity uncertainty in protein structure can be bypassed through dielectric modeling in biomolecular electrostatic analysis.

The Roles of Electrostatic Interactions in Capsid Assembly Mechanisms of Giant Viruses

In the last three decades, many giant DNA viruses have been discovered. Giant viruses present a unique and essential research frontier for studies of self-assembly and regulation of supramolecular assemblies. The question on how these giant DNA viruses assemble thousands of proteins so accurately to form their protein shells, the capsids, remains largely unanswered. Revealing the mechanisms of giant virus assembly will help to discover the mysteries of many self-assembly biology problems. Paramecium bursaria Chlorella virus-1 (PBCV-1) is one of the most intensively studied giant viruses. Here, we implemented a multi-scale approach to investigate the interactions among PBCV-1 capsid building units called capsomers. Three binding modes with different strengths are found between capsomers around the relatively flat area of the virion surface at the icosahedral 2-fold axis. Furthermore, a capsomer structure manipulation package is developed to simulate the capsid assembly process. Using these tools, binding forces among capsomers were investigated and binding funnels were observed that were consistent with the final assembled capsid. In addition, total binding free energies of each binding mode were calculated. The results helped to explain previous experimental observations. Results and tools generated in this work established an initial computational approach to answer current unresolved questions regarding giant virus assembly mechanisms. Results will pave the way for studying more complicated process in other biomolecular structures.

Robustness and Efficiency of Poisson-Boltzmann Modeling on Graphics Processing Units

Poisson-Boltzmann equation (PBE) based continuum electrostatics models have been widely used in modeling electrostatic interactions in biochemical processes, particularly in estimating protein-ligand binding affinities. Fast convergence of PBE solvers is crucial in binding affinity computations as numerous snapshots need to be processed. Efforts have been reported to develop PBE solvers on graphics processing units (GPUs) for efficient modeling of biomolecules, though only relatively simple successive over-relaxation and conjugate gradient methods were implemented. However, neither convergence nor scaling properties of the two methods are optimal for large biomolecules. On the other hand, geometric multigrid (MG) has been shown to be an optimal solver on CPUs, though no MG have been reported for biomolecular applications on GPUs. This is not a surprise as it is a more complex method and depends on simpler but limited iterative methods such as Gauss-Seidel in its core relaxation procedure. The robustness and efficiency of MG on GPUs are also unclear. Here we present an implementation and a thorough analysis of MG on GPUs. Our analysis shows that robustness is a more pronounced issue than efficiency for both MG and other tested solvers when the single precision is used for complex biomolecules. We further show how to balance robustness and efficiency utilizing MG's overall efficiency and conjugate gradient's robustness, pointing to a hybrid GPU solver with a good balance of efficiency and accuracy. The new PBE solver will significantly improve the computational throughput for a range of biomolecular applications on the GPU platforms.

A Continuum Poisson-Boltzmann Model for Membrane Channel Proteins

Membrane proteins constitute a large portion of the human proteome and perform a variety of important functions as membrane receptors, transport proteins, enzymes, signaling proteins, and more. Computational studies of membrane proteins are usually much more complicated than those of globular proteins. Here, we propose a new continuum model for Poisson-Boltzmann calculations of membrane channel proteins. Major improvements over the existing continuum slab model are as follows: (1) The location and thickness of the slab model are fine-tuned based on explicit-solvent MD simulations. (2) The highly different accessibilities in the membrane and water regions are addressed with a two-step, two-probe grid-labeling procedure. (3) The water pores/channels are automatically identified. The new continuum membrane model is optimized (by adjusting the membrane probe, as well as the slab thickness and center) to best reproduce the distributions of buried water molecules in the membrane region as sampled in explicit water simulations. Our optimization also shows that the widely adopted water probe of 1.4 Å for globular proteins is a very reasonable default value for membrane protein simulations. It gives the best compromise in reproducing the explicit water distributions in membrane channel proteins, at least in the water accessible pore/channel regions. Finally, we validate the new membrane model by carrying out binding affinity calculations for a potassium channel, and we observe good agreement with the experimental results.

Modeling Membrane Protein-Ligand Binding Interactions: The Human Purinergic Platelet Receptor

Membrane proteins, due to their roles as cell receptors and signaling mediators, make prime candidates for drug targets. The computational analysis of protein-ligand binding affinities has been widely employed as a tool in rational drug design efforts. Although efficient implicit solvent-based methods for modeling globular protein-ligand binding have been around for many years, the extension of such methods to membrane protein-ligand binding is still in its infancy. In this study, we extended the widely used Amber/MMPBSA method to model membrane protein-ligand systems, and we used it to analyze protein-ligand binding for the human purinergic platelet receptor (P2Y12R), a prominent drug target in the inhibition of platelet aggregation for the prevention of myocardial infarction and stroke. The binding affinities, computed by the Amber/MMPBSA method using standard parameters, correlate well with experiment. A detailed investigation of these parameters was conducted to assess their impact on the accuracy of the method. These analyses show the importance of properly treating the nonpolar solvation interactions and the electrostatic polarization in the binding of nucleotide agonists and non-nucleotide antagonists to P2Y12R. On the basis of the crystal structures and the experimental conditions in the binding assay, we further hypothesized that the nucleotide agonists lose their bound magnesium ion upon binding to P2Y12R, and our computational study supports this hypothesis. Ultimately, this work illustrates the value of computational analysis in the interpretation of experimental binding reactions.

Cytoplasmic dynein binding, run length, and velocity are guided by long-range electrostatic interactions

Dyneins are important molecular motors involved in many essential biological processes, including cargo transport along microtubules, mitosis, and in cilia. Dynein motility involves the coupling of microtubule binding and unbinding to a change in the configuration of the linker domain induced by ATP hydrolysis, which occur some 25 nm apart. This leaves the accuracy of dynein stepping relatively inaccurate and susceptible to thermal noise. Using multi-scale modeling with a computational focusing technique, we demonstrate that the microtubule forms an electrostatic funnel that guides the dynein's microtubule binding domain (MTBD) as it finally docks to the precise, keyed binding location on the microtubule. Furthermore, we demonstrate that electrostatic component of the MTBD's binding free energy is linearly correlated with the velocity and run length of dynein, and we use this linearity to predict the effect of mutating each glutamic and aspartic acid located in MTBD domain to alanine. Lastly, we show that the binding of dynein to the microtubule is associated with conformational changes involving several helices, and we localize flexible hinge points within the stalk helices. Taken all together, we demonstrate that long range electrostatic interactions bring a level of precision to an otherwise noisy dynein stepping process.

Continuum Electrostatics Approaches to Calculating pKas and Ems in Proteins

Proteins change their charge state through protonation and redox reactions as well as through binding charged ligands. The free energy of these reactions is dominated by solvation and electrostatic energies and modulated by protein conformational relaxation in response to the ionization state changes. Although computational methods for calculating these interactions can provide very powerful tools for predicting protein charge states, they include several critical approximations of which users should be aware. This chapter discusses the strengths, weaknesses, and approximations of popular computational methods for predicting charge states and understanding the underlying electrostatic interactions. The goal of this chapter is to inform users about applications and potential caveats of these methods as well as outline directions for future theoretical and computational research.

A combined MPI-CUDA parallel solution of linear and nonlinear Poisson-Boltzmann equation

The Poisson-Boltzmann equation models the electrostatic potential generated by fixed charges on a polarizable solute immersed in an ionic solution. This approach is often used in computational structural biology to estimate the electrostatic energetic component of the assembly of molecular biological systems. In the last decades, the amount of data concerning proteins and other biological macromolecules has remarkably increased. To fruitfully exploit these data, a huge computational power is needed as well as software tools capable of exploiting it. It is therefore necessary to move towards high performance computing and to develop proper parallel implementations of already existing and of novel algorithms. Nowadays, workstations can provide an amazing computational power: up to 10 TFLOPS on a single machine equipped with multiple CPUs and accelerators such as Intel Xeon Phi or GPU devices. The actual obstacle to the full exploitation of modern heterogeneous resources is efficient parallel coding and porting of software on such architectures. In this paper, we propose the implementation of a full Poisson-Boltzmann solver based on a finite-difference scheme using different and combined parallel schemes and in particular a mixed MPI-CUDA implementation. Results show great speedups when using the two schemes, achieving an 18.9x speedup using three GPUs.

Biological applications of classical electrostatics methods

Continuum electrostatics modeling of solvation based on the Poisson–Boltzmann (PB) equation has gained wide acceptance in biomolecular applications such as energetic analysis and structural visualization. Successful application of the PB solvent models requires careful calibration of the solvation parameters. Extensive testing and validation is also important to ensure accuracy in their applications. Limitation in the continuum modeling of solvation is also a known issue in certain biomolecular applications. Growing interest in membrane systems has further spurred developmental efforts to allow inclusion of membrane in the PB solvent models. Despite their past successes due to careful parameterization, algorithm development and parallel implementation, there is still much to be done to improve their transferability from the small molecular systems upon which they were developed and validated to complex macromolecular systems as advances in technology continue to push forward, providing ever greater computational resources to researchers to study more interesting biological systems of higher complexity.

On the Modeling of Polar Component of Solvation Energy using Smooth Gaussian-Based Dielectric Function

Traditional implicit methods for modeling electrostatics in biomolecules use a two-dielectric approach: a biomolecule is assigned low dielectric constant while the water phase is considered as a high dielectric constant medium. However, such an approach treats the biomolecule-water interface as a sharp dielectric border between two homogeneous dielectric media and does not account for inhomogeneous dielectric properties of the macromolecule as well. Recently we reported a new development, a smooth Gaussian-based dielectric function which treats the entire system, the solute and the water phase, as inhomogeneous dielectric medium (J Chem Theory Comput. 2013 Apr 9; 9(4): 2126-2136.). Here we examine various aspects of the modeling of polar solvation energy in such inhomogeneous systems in terms of the solute-water boundary and the inhomogeneity of the solute in the absence of water surrounding. The smooth Gaussian-based dielectric function is implemented in the DelPhi finite-difference program, and therefore the sensitivity of the results with respect to the grid parameters is investigated, and it is shown that the calculated polar solvation energy is almost grid independent. Furthermore, the results are compared with the standard two-media model and it is demonstrated that on average, the standard method overestimates the magnitude of the polar solvation energy by a factor 2.5. Lastly, the possibility of the solute to have local dielectric constant larger than of a bulk water is investigated in a benchmarking test against experimentally determined set of pKa's and it is speculated that side chain rearrangements could result in local dielectric constant larger than 80.

Continuous development of schemes for parallel computing of the electrostatics in biological systems: implementation in DelPhi

Due to the enormous importance of electrostatics in molecular biology, calculating the electrostatic potential and corresponding energies has become a standard computational approach for the study of biomolecules and nano-objects immersed in water and salt phase or other media. However, the electrostatics of large macromolecules and macromolecular complexes, including nano-objects, may not be obtainable via explicit methods and even the standard continuum electrostatics methods may not be applicable due to high computational time and memory requirements. Here, we report further development of the parallelization scheme reported in our previous work (Li, et al., J. Comput. Chem. 2012, 33, 1960) to include parallelization of the molecular surface and energy calculations components of the algorithm. The parallelization scheme utilizes different approaches such as space domain parallelization, algorithmic parallelization, multithreading, and task scheduling, depending on the quantity being calculated. This allows for efficient use of the computing resources of the corresponding computer cluster. The parallelization scheme is implemented in the popular software DelPhi and results in speedup of several folds. As a demonstration of the efficiency and capability of this methodology, the electrostatic potential, and electric field distributions are calculated for the bovine mitochondrial supercomplex illustrating their complex topology, which cannot be obtained by modeling the supercomplex components alone.

Progress in developing Poisson-Boltzmann equation solvers

This review outlines the recent progress made in developing more accurate and efficient solutions to model electrostatics in systems comprised of bio-macromolecules and nano-objects, the last one referring to objects that do not have biological function themselves but nowadays are frequently used in biophysical and medical approaches in conjunction with bio-macromolecules. The problem of modeling macromolecular electrostatics is reviewed from two different angles: as a mathematical task provided the specific definition of the system to be modeled and as a physical problem aiming to better capture the phenomena occurring in the real experiments. In addition, specific attention is paid to methods to extend the capabilities of the existing solvers to model large systems toward applications of calculations of the electrostatic potential and energies in molecular motors, mitochondria complex, photosynthetic machinery and systems involving large nano-objects.

On the Dielectric "Constant" of Proteins: Smooth Dielectric Function for Macromolecular Modeling and Its Implementation in DelPhi

Implicit methods for modeling protein electrostatics require dielectric properties of the system to be known, in particular, the value of the dielectric constant of protein. While numerous values of the internal protein dielectric constant were reported in the literature, still there is no consensus of what the optimal value is. Perhaps this is due to the fact that the protein dielectric constant is not a “constant” but is a complex function reflecting the properties of the protein’s structure and sequence. Here, we report an implementation of a Gaussian-based approach to deliver the dielectric constant distribution throughout the protein and surrounding water phase by utilizing the 3D structure of the corresponding macromolecule. In contrast to previous reports, we construct a smooth dielectric function throughout the space of the system to be modeled rather than just constructing a “Gaussian surface” or smoothing molecule–water boundary. Analysis on a large set of proteins shows that (a) the average dielectric constant inside the protein is relatively low, about 6–7, and reaches a value of about 20–30 at the protein’s surface, and (b) high average local dielectric constant values are associated with charged residues while low dielectric constant values are automatically assigned to the regions occupied by hydrophobic residues. In terms of energetics, a benchmarking test was carried out against the experimental pK_a’s of 89 residues in staphylococcal nuclease (SNase) and showed that it results in a much better RMSD (= 1.77 pK) than the corresponding calculations done with a homogeneous high dielectric constant with an optimal value of 10 (RMSD = 2.43 pK).

The structure of the ARE-binding domains of Hu antigen R (HuR) undergoes conformational changes during RNA binding

Human RNA-binding protein (HuR), a ubiquitously expressed member of the Hu protein family, plays an important role in mRNA degradation and has been implicated as a key post-transcriptional regulator. HuR contains three RNA-recognition motif (RRM) domains. The two N-terminal tandem RRM domains can selectively bind AU-rich elements (AREs), while the third RRM domain (RRM3) contributes to interactions with the poly-A tail of target mRNA and other ligands. Here, the X-ray structure of two methylated tandem RRM domains (RRM1/2) of HuR in their RNA-free form was solved at 2.9 Å resolution. The crystal structure of RRM1/2 complexed with target mRNA was also solved at 2.0 Å resolution; comparisons of the two structures show that HuR RRM1/2 undergoes conformational changes upon RNA binding. Fluorescence polarization assays (FPA) were used to study the protein-RNA interactions. Both the structure and the FPA analysis indicated that RRM1 is the primary ARE-binding domain in HuR and that the conformational changes induce subsequent contacts of the RNA substrate with the inter-domain linker and RRM2 which greatly improve the RNA-binding affinity of HuR.

Protein Nano-Object Integrator (ProNOI) for generating atomic style objects for molecular modeling

Background

With the progress of nanotechnology, one frequently has to model biological macromolecules simultaneously with nano-objects. However, the atomic structures of the nano objects are typically not available or they are solid state entities. Because of that, the researchers have to investigate such nano systems by generating models of the nano objects in a manner that the existing software be able to carry the simulations. In addition, it should allow generating composite objects with complex shape by combining basic geometrical figures and embedding biological macromolecules within the system.

Results

Here we report the Protein Nano-Object Integrator (ProNOI) which allows for generating atomic-style geometrical objects with user desired shape and dimensions. Unlimited number of objects can be created and combined with biological macromolecules in Protein Data Bank (PDB) format file. Once the objects are generated, the users can use sliders to manipulate their shape, dimension and absolute position. In addition, the software offers the option to charge the objects with either specified surface or volumetric charge density and to model them with user-desired dielectric constants. According to the user preference, the biological macromolecule atoms can be assigned charges and radii according to four different force fields: Amber, Charmm, OPLS and PARSE. The biological macromolecules and the atomic-style objects are exported as a position, charge and radius (PQR) file, or if a default dielectric constant distribution is not selected, it is exported as a position, charge, radius and epsilon (PQRE) file. As illustration of the capabilities of the ProNOI, we created a composite object in a shape of a robot, aptly named the Clemson Robot, whose parts are charged with various volumetric charge densities and holds the barnase-barstar protein complex in its hand.

Conclusions

The Protein Nano-Object Integrator (ProNOI) is a convenient tool for generating atomic-style nano shapes in conjunction with biological macromolecule(s). Charges and radii on the macromolecule atoms and the atoms in the shapes are assigned according to the user’s preferences allowing various scenarios of modeling. The default output file is in PQR (PQRE) format which is readable by almost any software available in biophysical field. It can be downloaded from: http://compbio.clemson.edu/downloadDir/ProNO_integrator.tar.gz