Distinguish protein decoys by Using a scoring function based on a new AMBER force field, short molecular dynamics simulations, and the generalized born solvent model

Molecular Dynamics Simulations for Rationalizing Polymer Bioconjugation Strategies: Challenges, Recent Developments, and Future Opportunities

The covalent modification of proteins with polymers is a well-established method for improving the pharmacokinetic properties of therapeutically valuable biologics. The conjugated polymer chains of the resulting hybrid represent highly flexible macromolecular structures. As the dynamics of such systems remain rather elusive for established experimental techniques from the field of protein structure elucidation, molecular dynamics simulations have proven as a valuable tool for studying such conjugates at an atomistic level, thereby complementing experimental studies. With a focus on new developments, this review aims to provide researchers from the polymer bioconjugation field with a concise and up to date overview of such approaches. After introducing basic principles of molecular dynamics simulations, as well as methods for and potential pitfalls in modeling bioconjugates, the review illustrates how these computational techniques have contributed to the understanding of bioconjugates and bioconjugation strategies in the recent past and how they may lead to a more rational design of novel bioconjugates in the future.

Application of Ligand- and Structure-Based Prediction Models for the Design of Alkylhydrazide-Based HDAC3 Inhibitors as Novel Anti-Cancer Compounds

Histone deacetylases (HDAC) represent promising epigenetic targets for several diseases including different cancer types. The HDAC inhibitors approved to date are pan-HDAC inhibitors and most show a poor selectivity profile, side effects, and in particular hydroxamic-acid-based inhibitors lack good pharmacokinetic profiles. Therefore, the development of isoform-selective non-hydroxamic acid HDAC inhibitors is a highly regarded field in medicinal chemistry. In this study, we analyzed different ligand-based and structure-based drug design techniques to predict the binding mode and inhibitory activity of recently developed alkylhydrazide HDAC inhibitors. Alkylhydrazides have recently attracted more attention as they have shown promising effects in various cancer cell lines. In this work, pharmacophore models and atom-based quantitative structure-activity relationship (QSAR) models were generated and evaluated. The binding mode of the studied compounds was determined using molecular docking as well as molecular dynamics simulations and compared with known crystal structures. Calculated free energies of binding were also considered to generate QSAR models. The created models show a good explanation of in vitro data and were used to develop novel HDAC3 inhibitors.

Benchmarking biomolecular force field-based Zn2+ for mono- and bimetallic ligand binding sites

Zn²⁺ is one of the most versatile biologically available metal ions, but accurate modeling of Zn²⁺ -containing metalloproteins at the biomolecular force field level can be challenging. Since most Zn²⁺ models are parameterized in bulk solvent, in-depth knowledge about their performance in a protein environment is limited. Thus, we systematically investigate here the behavior of non-polarizable Zn²⁺ models for their ability to reproduce experimentally determined metal coordination and ligand binding in metalloproteins. The benchmarking is performed in challenging environments, including mono- (carbonic anhydrase II) and bimetallic (metallo-β-lactamase VIM-2) ligand binding sites. We identify key differences in the performance between the Zn²⁺ models with regard to the preferred ligating atoms (charged/non-charged), attraction of water molecules, and the preferred coordination geometry. Based on these results, we suggest suitable simulation conditions for varying Zn²⁺ site geometries that could guide the further development of biomolecular Zn²⁺ models.

Mechanistic Modeling of Lys745 Sulfonylation in EGFR C797S Reveals Chemical Determinants for Inhibitor Activity and Discriminates Reversible from Irreversible Agents

Targeted covalent inhibitors hold promise for drug discovery, particularly for kinases. Targeting the catalytic lysine of epidermal growth factor receptor (EGFR) has attracted attention as a new strategy to overcome resistance due to the emergence of C797S mutation. Sulfonyl fluoride derivatives able to inhibit EGFR^{L858R/T790M/C797S} by sulfonylation of Lys745 have been reported. However, atomistic details of this process are still poorly understood. Here, we describe the mechanism of inhibition of an innovative class of compounds that covalently engage the catalytic lysine of EGFR, through a sulfur(VI) fluoride exchange (SuFEx) process, with the help of hybrid quantum mechanics/molecular mechanics (QM/MM) and path collective variables (PCVs) approaches. Our simulations identify the chemical determinants accounting for the irreversible activity of agents targeting Lys745 and provide hints for the further optimization of sulfonyl fluoride agents.

Quantum computing in pharma: A multilayer embedding approach for near future applications

Quantum computers are special purpose machines that are expected to be particularly useful in simulating strongly correlated chemical systems. The quantum computer excels at treating a moderate number of orbitals within an active space in a fully quantum mechanical manner. We present a quantum phase estimation calculation on F₂ in a (2,2) active space on Rigetti's Aspen-11 QPU. While this is a promising start, it also underlines the need for carefully selecting the orbital spaces treated by the quantum computer. In this work, a scheme for selecting such an active space automatically is described and simulated results obtained using both the quantum phase estimation (QPE) and variational quantum eigensolver (VQE) algorithms are presented and combined with a subtractive method to enable accurate description of the environment. The active occupied space is selected from orbitals localized on the chemically relevant fragment of the molecule, while the corresponding virtual space is chosen based on the magnitude of interactions with the occupied space calculated from perturbation theory. This protocol is then applied to two chemical systems of pharmaceutical relevance: the enzyme [Fe] hydrogenase and the photosenzitizer temoporfin. While the sizes of the active spaces currently amenable to a quantum computational treatment are not enough to demonstrate quantum advantage, the procedure outlined here is applicable to any active space size, including those that are outside the reach of classical computation.

Protein 3D Hydration: A Case of Bovine Pancreatic Trypsin Inhibitor

Characterization of the hydrated state of a protein is crucial for understanding its structural stability and function. In the present study, we have investigated the 3D hydration structure of the protein BPTI (bovine pancreatic trypsin inhibitor) by molecular dynamics (MD) and the integral equation method in the three-dimensional reference interaction site model (3D-RISM) approach. Both methods have found a well-defined hydration layer around the protein and revealed the localization of BPTI buried water molecules corresponding to the X-ray crystallography data. Moreover, under 3D-RISM calculations, the obtained positions of waters bound firmly to the BPTI sites are in reasonable agreement with the experimental results mentioned above for the BPTI crystal form. The analysis of the 3D hydration structure (thickness of hydration shell and hydration numbers) was performed for the entire protein and its polar and non-polar parts using various cut-off distances taken from the literature as well as by a straightforward procedure proposed here for determining the thickness of the hydration layer. Using the thickness of the hydration shell from this procedure allows for calculating the total hydration number of biomolecules properly under both methods. Following this approach, we have obtained the thickness of the BPTI hydration layer of 3.6 Å with 369 water molecules in the case of MD simulation and 3.9 Å with 333 water molecules in the case of the 3D-RISM approach. The above procedure was also applied for a more detailed description of the BPTI hydration structure near the polar charged and uncharged radicals as well as non-polar radicals. The results presented for the BPTI as an example bring new knowledge to the understanding of protein hydration.

Docking, Binding Free Energy Calculations and In Vitro Characterization of Pyrazine Linked 2-Aminobenzamides as Novel Class I Histone Deacetylase (HDAC) Inhibitors

Class I histone deacetylases, HDAC1, HDAC2, and HDAC3, represent potential targets for cancer treatment. However, the development of isoform-selective drugs for these enzymes remains challenging due to their high sequence and structural similarity. In the current study, we applied a computational approach to predict the selectivity profile of developed inhibitors. Molecular docking followed by MD simulation and calculation of binding free energy was performed for a dataset of 2-aminobenzamides comprising 30 previously developed inhibitors. For each HDAC isoform, a significant correlation was found between the binding free energy values and in vitro inhibitory activities. The predictive accuracy and reliability of the best preforming models were assessed on an external test set of newly designed and synthesized inhibitors. The developed binding free-energy models are cost-effective methods and help to reduce the time required to prioritize compounds for further studies.

NMR and MD Analysis of the Bonding Interaction of Vancomycin with Muramyl Pentapeptide

The article describes an NMR spectroscopy study of interactions between vancomycin and a muramyl pentapeptide in two complexes: vancomycin and a native muramyl pentapeptide ended with D-alanine (MPP-D-Ala), and vancomycin and a modified muramyl pentapeptide ended with D-serine (MPP-D-Ser). The measurements were made in a 9:1 mixture of H₂O and D₂O. The obtained results confirmed the presence of hydrogen bonds previously described in the literature. At the same time, thanks to the pentapeptide model used, we were able to prove the presence of two more hydrogen bonds formed by the side chain amino group of L-lysine and oxygen atoms from the vancomycin carboxyl and amide groups. This type of interaction has not been described before. The existence of these hydrogen bonds was confirmed by the ¹H NMR and molecular modeling. The formation of these bonds incurs additional through-space interactions, visible in the NOESY spectrum, between the protons of the L-lysine amino group and a vancomycin-facing hydrogen atom in the benzylic position. The presence of such interactions was also confirmed by molecular dynamics trajectory analysis.

Cofactor-free ActVA-Orf6 monooxygenase catalysis via proton-coupled electron transfer: A QM/MM study

Uncovering the comprehensive catalytic mechanism for the activation of triplet O2 through metal-free and cofactor-free oxidases and oxygenases remains one of the most challenging questions in the area of enzymatic...

Model Setup and Procedures for Prediction of Enzyme Reaction Kinetics with QM-Only and QM:MM Approaches

The enzyme-catalyzed reactions are traditionally studied with experimental kinetic assays. The modern theoretical modeling techniques provide a complementary way to investigate these catalytic reactions. Experimental assay frequently does not allow an unequivocal answer to the factors controlling the reaction mechanism. On the other hand, the theoretical experiments provide a precise understanding of the molecular-level steps involved in catalytic reactions. However, modeling requires at least structural data on the enzyme and reactant, and the complexity of the enzyme systems can still be a challenge.In this chapter, we are going to describe how to apply theoretical modeling methods, such as MD simulation, QM-only cluster models of enzyme active site, or QM:MM multiscale modeling to study enzyme kinetics and even to predict kinetic isotope effect (KIE). We present a full protocol that starts from the PDB structure of the enzyme, through MD simulation of enzyme: substrate complex and statistical analysis of MD trajectory, selection of a model of the active site, and study of reaction pathways. We show how theoretical predictions basing on QM-only cluster models, QM:MM model, or multiple QM:MM models derived from QM:MM:MD simulations can be correlated with experimental kinetic results. Finally, we show how one can calculate intrinsic KIE associated with an individual molecular step.

FSATOOL 2.0: An integrated molecular dynamics simulation and trajectory data analysis program

Molecular dynamics simulation is important in the computational study of the biomolecules. In this paper, we upgrade our previous FSATOOL to version 2.0. It is no longer a plugin as before. Besides the existed enhanced sampling and Markov state model analysis module, FSATOOL 2.0 has three new features now. First, it contains a molecular dynamics simulation engine on both CPU and GPU device. The engine works with an embedded enhanced sampling module. Second, it can do the free energy calculation by various practical methods, including the weighted histogram analysis method and Gaussian mixture model. Third, it has many subroutines to process the trajectory data, such as principal component analysis, time-structure based independent component analysis, contact analysis, and Φ-value analysis. Most importantly, all these calculations are integrated into one package. The trajectory data format is compatible with all the modules. With a proper input parameter file, users can do the molecular dynamics simulation and data analysis work by only a few simplified commands. The capabilities and theoretical backgrounds of FSATOOL 2.0 are introduced in the paper.

Use of the Molecular Dynamics Method to Investigate the Stability of α-α-Corner Structural Motifs in Proteins

This study investigated the stability of structural motifs via molecular dynamics, using α-α-corners as an example. A molecular dynamics experiment was performed on a sample of α-α-corners selected by the authors from the PDB database. For the first time during a molecular dynamics experiment, we investigated the characteristics of structural motifs by describing their geometry, including the interplanar distance, area of polygon of the helices projections intersection, and torsion angles between axes of helices in helical pairs. The torsion angles for the constriction amino acids in the equilibrium portion of the molecular dynamics trajectory were analyzed. Using the molecular dynamics method, α-α-corners were found to be autonomous structures that are stable in aquatic environments.

Binding Free Energy (BFE) Calculations and Quantitative Structure-Activity Relationship (QSAR) Analysis of Schistosoma mansoni Histone Deacetylase 8 (smHDAC8) Inhibitors

Histone-modifying proteins have been identified as promising targets to treat several diseases including cancer and parasitic ailments. In silico methods have been incorporated within a variety of drug discovery programs to facilitate the identification and development of novel lead compounds. In this study, we explore the binding modes of a series of benzhydroxamates derivatives developed as histone deacetylase inhibitors of Schistosoma mansoni histone deacetylase (smHDAC) using molecular docking and binding free energy (BFE) calculations. The developed docking protocol was able to correctly reproduce the experimentally established binding modes of resolved smHDAC8–inhibitor complexes. However, as has been reported in former studies, the obtained docking scores weakly correlate with the experimentally determined activity of the studied inhibitors. Thus, the obtained docking poses were refined and rescored using the Amber software. From the computed protein–inhibitor BFE, different quantitative structure–activity relationship (QSAR) models could be developed and validated using several cross-validation techniques. Some of the generated QSAR models with good correlation could explain up to ~73% variance in activity within the studied training set molecules. The best performing models were subsequently tested on an external test set of newly designed and synthesized analogs. In vitro testing showed a good correlation between the predicted and experimentally observed IC₅₀ values. Thus, the generated models can be considered as interesting tools for the identification of novel smHDAC8 inhibitors.

Molecular dynamics simulation studies on the specific regulation of PTPN18 to the HER2 phospho-peptides

The specific regulation of PTPN18 protein to three HER2 phospho-peptides has been studied by molecular dynamics simulations and free energy calculations. The results revealed that the three HER2 phospho-peptides binding to the PTPN18 catalytic domain is energetically favorable due to substrate specificity of PTPN18, and moreover, the PTPN18 protein have significantly higher affinity to pY1248 peptide (-45.22 kcal/mol) than that of pY1112 (-25.3 kcal/mol) and pY1196 (-31.86 kcal/mol) peptides. Further, the binding of HER2 phospho-peptides to PTPN18 have also caused the closure of WPD-loop with the decrease of the centroid distances between the P-loop and the WPD loop. The WPD-loop closure of PTPN18 relates directly to the new hydrogen bond and hydrophobic interaction formations between the residues Tyr62, Asp64, Val65, Ala231, Arg235, and Ala273 in PTPN18 and Tyr(PO3) in the HER2 phospho-peptides, which suggests that these key residues would contribute to the specific regulation of PTPN18 to the substrates. The correlation analysis revealed the allosteric communication networks from the pY binding loop to the WPD loop through the structural change and the residue interactions in PTPN18. These results will be helpful to understand the specific regulation through the allosteric communication network in the PTPN18 catalytic domain.

Functional roles of the hexamer structure of C-phycocyanin revealed by calculation of absorption wavelength

Cyanophyta-phycocyanin (C-PC) is the main constituent of the rod of phycobilisome (PBS), which is a highly ordered and large peripheral light-harvesting protein complex present on the cytoplasmic side of the thylakoid membrane in cyanobacteria and red algae. The C-PC monomer comprises two chains, α- and β-subunits, and aggregates to form ring-shaped trimers (αβ)3 with rotational symmetry. The ring-shaped trimer (αβ)3 is a structural block unit (SBU) that forms the rod of PBS. Two (αβ)3 SBUs are arranged in a face-to-face manner to form an (αβ)6 -hexamer. In this study, the electronic states of three phycocyanobilins, α84, β84, and β155 in C-phycocyanin, constituting the rod of the PBS, were calculated for both the trimer and hexamer models by considering the effect of the electrostatic field of protein moieties and water molecules. For the hexamer, the absorption wavelengths of α84, β84, and β155 were similar to those obtained experimentally; however, for the trimer, only the absorption wavelength of β155 shifted toward a shorter-wavelength. The nature of the hexamer structure as a hierarchical structure is revealed by considering the calculated absorption wavelength and energy transfer.

Comparative structural and mechanistic studies of 4-hydroxy-tetrahydrodipicolinate reductases from Mycobacterium tuberculosis and Vibrio vulnificus

BACKGROUND

The products of the lysine biosynthesis pathway, meso-diaminopimelate and lysine, are essential for bacterial survival. This paper focuses on the structural and mechanistic characterization of 4-hydroxy-tetrahydrodipicolinate reductase (DapB), which is one of the enzymes from the lysine biosynthesis pathway. DapB catalyzes the conversion of (2S, 4S)-4-hydroxy-2,3,4,5-tetrahydrodipicolinate (HTPA) to 2,3,4,5-tetrahydrodipicolinate in an NADH/NADPH dependent reaction. Genes coding for DapBs were identified as essential for many pathogenic bacteria, and therefore DapB is an interesting new target for the development of antibiotics.

METHODS

We have combined experimental and computational approaches to provide novel insights into mechanism of the DapB catalyzed reaction.

RESULTS

Structures of DapBs originating from Mycobacterium tuberculosis and Vibrio vulnificus in complexes with NAD⁺, NADP⁺, as well as with inhibitors, were determined and described. The structures determined by us, as well as currently available structures of DapBs from other bacterial species, were compared and used to elucidate a mechanism of reaction catalyzed by this group of enzymes. Several different computational methods were used to provide a detailed description of a plausible reaction mechanism.

CONCLUSIONS

This is the first report presenting the detailed mechanism of reaction catalyzed by DapB.

GENERAL SIGNIFICANCE

Structural data in combination with information on the reaction mechanism provide a background for development of DapB inhibitors, including transition-state analogues.

MDMS: Software Facilitating Performing Molecular Dynamics Simulations

Molecular Dynamics Made Simple (MDMS) is software that facilitates performing molecular dynamics (MD) simulations of solvated protein/protein-ligand complexes with Amber, one of the most popular MD codes. It guides users through the whole process of running MD starting with choosing a protein structure, preparing the model, parametrization of the system, establishing parameters for controlling MD, and finally running simulations. By accommodating every step required for running MD, this software ensures that the simulations performed by a user will provide as realistic insight as it is possible. Its sequential structure and a text-based interface ensure ease of use, while the flexibility required for complex cases is still preserved. MDMS also provides a very time-efficient and streamlined method to start MD simulations, which makes it a feasible tool for both novices and experienced computational chemists. © 2019 Wiley Periodicals, Inc.

Unraveling the Unbinding Pathways of Products Formed in Catalytic Reactions Involved in SIRT1-3: A Random Acceleration Molecular Dynamics Simulation Study

Sirtuins are a family of nicotinamide adenine dinucleotide (NAD⁺)-dependent enzymes, which undergo robust deacetylase activity, resulting in the production of nicotinamide. It is well known that nicotinamide, which is one of the products, can also act as an inhibitor for further deacetylation process by forming NAD⁺ again. Hence, the removal of nicotinamide from sirtuins is a demanding process, and the mechanistic understanding of the process remains elusive. In this investigation, we have made an attempt to unravel the unbinding pathways of nicotinamide from SIRT1, SIRT2, and SIRT3 (SIRT1-3) using Random Acceleration Molecular Dynamics (RAMD) Simulations, and we have successfully identified various unbinding channels. The selectivity of the egression channel is determined by using a thorough analysis of the frequency of egression trajectories. Similarly, various inhibitors have been docked with the active sites of SIRT1-3, and their egression pathways have been investigated to understand whether they follow the same egression pathway as that of nicotinamide. The residues that are responsible for the unbinding pathways have been determined from the analysis of RAMD trajectories. From these results, it is clear that phenylalanine and histidine residues play major roles in the egression of inhibitors. Additionally, the key residues Leu, Pro, Met, Phe, Tyr, and Ile are found to control the release by acting as gateway residues. The role of these residues from different egression channels has been studied by carrying out mutations with alanine residue. This is the first report on sirtuins, which demonstrates the novel unbinding pathways for nicotinamide/inhibitors. This work provides new insights for developing more promising SIRT1-3 inhibitors.

Design of l-Lysine-Based Organogelators and Their Applications in Drug Release Processes

This work reports on the synthesis of three new l-lysine-based organogelators bis(N²-alkanoyl-N⁶-l-lysyl ethylester)oxalylamides, where alkanoyls are lauroyl, myristoyl, and palmitoyl. The gels of these gelators were prepared with high yields in eco-friendly solvents commonly used in cosmetics such as ethyl and isopropyl esters of lauric and myristic acids, liquid paraffin, 1-decanol, and 1,2-propanediol. Fourier transform infrared measurements revealed the involvement of intermolecular hydrogen bonds in the gelation. Scanning electron microscopy images of xerogels indicated different morphologic patterns with regard to the alkanoyl chain length and the solvent employed in their preparation. The gel formation was supported by rheological measurements. Three gels prepared in liquid paraffin were loaded with naproxen (Npx) with a quite high loading capacity (up to 166.6% as percentage of gelator) without gel disruption. The release of Npx from the gel matrix into the buffered solution at physiologic pH was evaluated using UV-vis spectroscopy. The results revealed that the release rate of Npx from the organogels significantly retarded with increasing organogelator concentration, whereas it enhanced with increasing Npx concentration. The rate was also found to be pH-dependent; the lower the pH, the lower the rate. Furthermore, molecular dynamic calculations performed on the octamer of myristoyl-bearing gelator (N ² M/N ⁶ Lys) in 1,2-propanediol provided useful information regarding the structural properties of the gels, which may be of interest to interpret the structure of the gel matrix. Altogether, this work provided valuable outcomes, which may be relevant to the pharmaceutical industry. It may be suggested that l-lysine-based gels have potentials in the delivery of nonsteroidal anti-inflammatory drug molecules. Besides, the release of the drug can be fine-tuned by the correct choice of gelator-solvent combination.

In silico and in vitro identification of candidate SIRT1 activators from Indonesian medicinal plants compounds database

Sirtuin 1 (SIRT1) is a class III family of protein histone deacetylases involved in NAD⁺-dependent deacetylation reactions. It has been suggested that SIRT1 activators may have a protective role against type 2 diabetes, the aging process, and inflammation. This study aimed to explore and identify medicinal plant compounds from Indonesian Herbal Database (HerbalDB) that might potentially become a candidate for SIRT1 activators through a combination of in silico and in vitro methods. Two pharmacophore models were developed using co-crystalized ligands that allosterically bind with SIRT1 similar to the putative ligands used by SIRT1 activators. Then, these were used for the virtual screening of HerbalDB. The identified compounds were subjected to molecular docking and 50 ns molecular dynamics simulation. Molecular dynamics simulation was analyzed using MM-GB(PB)SA methods. The compounds identified by these methods were tested in an in vitro study using a SIRT-Glo™ luminescence assay. Virtual screening using structure-based pharmacophores predicted that mulberrin as the best candidate SIRT1 activator. Virtual screening using ligand-based pharmacophores predicted that gartanin, quinidine, and quinine to be the best candidates as SIRT1 activators. The molecular docking studies showed the important residues involved were Ile223 and Ile227 at the allosteric region. The MM-GB(PB)SA calculations confirmed that mulberrin, gartanin, quinidine, quinine showed activity at allosteric region and their EC₅₀ in vitro values are 2.10; 1.79; 1.71; 1.14 μM, respectively. Based on in silico and in vitro study results, mulberin, gartanin, quinidine, and quinine had good activity as SIRT1 activators.

Computational structural enzymology methodologies for the study and engineering of fatty acid synthases, polyketide synthases and nonribosomal peptide synthetases

Various computational methodologies can be applied to enzymological studies on enzymes in the fatty acid, polyketide, and non-ribosomal peptide biosynthetic pathways. These multi-domain complexes are called fatty acid synthases, polyketide synthases, and non-ribosomal peptide synthetases. These mega-synthases biosynthesize chemically diverse and complex bioactive molecules, with the intermediates being chauffeured between catalytic partners via a carrier protein. Recent efforts have been made to engineer these systems to expand their product diversity. A major stumbling block is our poor understanding of the transient protein-protein and protein-substrate interactions between the carrier protein and its many catalytic partner domains and product intermediates. The innate reactivity of pathway intermediates in two major classes of polyketide synthases has frustrated our mechanistic understanding of these interactions during the biosynthesis of these natural products, ultimately impeding the engineering of these systems for the generation of engineered natural products. Computational techniques described in this chapter can aid data interpretation or used to generate testable models of these experimentally intractable transient interactions, thereby providing insight into key interactions that are difficult to capture otherwise, with the potential to expand the diversity in these systems.

Importance of Incorporating Protein Flexibility in Molecule Modeling: A Theoretical Study on Type I1/2 NIK Inhibitors

NF-κB inducing kinase (NIK), which is considered as the central component of the non-canonical NF-κB pathway, has been proved to be an important target for the regulation of the immune system. In the past few years, NIK inhibitors with various scaffolds have been successively reported, among which type I^1/2 inhibitors that can not only bind in the ATP-binding pocket at the DFG-in state but also extend into an additional back pocket, make up the largest proportion of the NIK inhibitors, and are worthy of more attention. In this study, an integration protocol that combines molecule docking, MD simulations, ensemble docking, MM/GB(PB)SA binding free energy calculations, and decomposition was employed to understand the binding mechanism of 21 tricyclic type I^1/2 NIK inhibitors. It is found that the docking accuracy is largely dependent on the selection of docking protocols as well as the crystal structures. The predictions given by the ensemble docking based on multiple receptor conformations (MRCs) and the MM/GB(PB)SA calculations based on MD simulations showed higher linear correlations with the experimental data than those given by conventional rigid receptor docking (RRD) methods (Glide, GOLD, and Autodock Vina), highlighting the importance of incorporating protein flexibility in predicting protein–ligand interactions. Further analysis based on MM/GBSA demonstrates that the hydrophobic interactions play the most essential role in the ligand binding to NIK, and the polar interactions also make an important contribution to the NIK-ligand recognition. A deeper comparison of several pairs of representative derivatives reveals that the hydrophobic interactions are vitally important in the structural optimization of analogs as well. Besides, the H-bond interactions with some key residues and the large desolvation effect in the back pocket devote to the affinity distinction. It is expected that our study could provide valuable insights into the design of novel and potent type I^1/2 NIK inhibitors.

How graphene affects the misfolding of human prion protein: A combined experimental and molecular dynamics simulation study

As the broad application of graphene in the biomedical field, it is urgent and important to evaluate how the graphene affects the structure and function of the proteins in our body, especially the amyloid-related proteins. Prion protein, as a typical amyloid protein, it misfolding and aggregation will lead to serious prion diseases. To explore if graphene promotes or inhibits the formation of amyloid, here, we combined the experimental and molecular dynamics (MD) simulation methods to study the influence of graphene on the globular domain of prion protein (PrP_117-231). The results from fluorescence quenching and circular dichroism spectrum showed that the addition of graphene changed the secondary structure of prion protein largely, mainly reflecting in the reduced α-helix structure and the increased coil structure, indicating graphene may strengthen the misfolding inclination of prion. To further uncover the mechanism of conformational change of prion under the induction of graphene, the all-atoms MD simulations in explicit solvent were performed. Our simulations suggest that prion protein can be quickly and tightly adsorbed onto graphene together with the weak conformational rearrangement and may reorient when approaching the surface. The Van der Waals' force drive the adsorption process. In the induction of graphene, H1 and S2-H2 loop regions of prion become unstable and prion begins to misfold partially. Our work shows that graphene can induce the misfolding of prion protein and may cause the potential risk to biosystems.

Molecular dynamics and free energy studies on the Drosophila melanogaster and Leptinotarsa decemlineata ecdysone receptor complexed with agonists: Mechanism for binding and selectivity

The ecdysone receptor is a nuclear hormone receptor that plays a pivotal role in the insect metamorphosis and development. To address the molecular mechanisms of binding and selectivity, the interactions of two typical agonists Ponasterone A and 20-Hydroxyecdysone with Drosophila melanogaster (DME) and Leptinotarsa decemlineata ecdysone (LDE) receptors were investigated by homology modeling, molecular docking, molecular dynamic simulation, and thermodynamic analysis. We discover that 1) the L5-loop, L11-loop, and H12 helix for DME, L7-loop, and L11-loop for LDE are more flexible, which affect the global dynamics of the ligand-binding pocket, thus facilitating the ligand recognition of ecdysone receptor; 2) several key residues (Thr55/Thr37, Phe109/Phe91, Arg95/Arg77, Arg99/Arg81, Phe108/Leu90, and Ala110/Val92) are responsible for the binding of the proteins; 3) the binding-free energy is mainly contributed by the van der Waals forces as well as the electrostatic interactions of ligand and receptor; 4) the computed binding-free energy difference between DME-C1 and LDE-C1 is -4.65 kcal/mol, explains that C1 can form many more interactions with the DME; 5) residues Phe108/Leu90 and Ala110/Val92 have relatively position and orientation difference in the two receptors, accounting most likely for the ligand selectivity of ecdysone receptor from different orders of insects. This study underscores the expectation that different insect pests should be able to discriminate among compounds from different as yet undiscovered compounds, and the results firstly show a structural and functional relay between the agonists and receptors (DME and LDE), which can provide an avenue for the development of target-specific insecticides. Communicated by Ramaswamy H. Sarma.

Structural Studies of the 3',3'-cGAMP Riboswitch Induced by Cognate and Noncognate Ligands Using Molecular Dynamics Simulation

Riboswtich RNAs can control gene expression through the structural change induced by the corresponding small-molecule ligands. Molecular dynamics simulations and free energy calculations on the aptamer domain of the 3′,3′-cGAMP riboswitch in the ligand-free, cognate-bound and noncognate-bound states were performed to investigate the structural features of the 3′,3′-cGAMP riboswitch induced by the 3′,3′-cGAMP ligand and the specificity of ligand recognition. The results revealed that the aptamer of the 3′,3′-cGAMP riboswitch in the ligand-free state has a smaller binding pocket and a relatively compact structure versus that in the 3′,3′-cGAMP-bound state. The binding of the 3′,3′-cGAMP molecule to the 3′,3′-cGAMP riboswitch induces the rotation of P1 helix through the allosteric communication from the binding sites pocket containing the J1/2, J1/3 and J2/3 junction to the P1 helix. Simultaneously, these simulations also revealed that the preferential binding of the 3′,3′-cGAMP riboswitch to its cognate ligand, 3′,3′-cGAMP, over its noncognate ligand, c-di-GMP and c-di-AMP. The J1/2 junction in the 3′,3′-cGAMP riboswitch contributing to the specificity of ligand recognition have also been found.

Computer-aided design, synthesis and biological characterization of novel inhibitors for PKMYT1

In the current work, we applied computational methods to analyze the membrane-associated inhibitory kinase PKMYT1 and small molecule inhibitors. PKMYT1 regulates the cell cycle at G2/M transition and phosphorylates Thr14 and Tyr15 in the Cdk1-cyclin B complex. A combination of in silico and in vitro screening was applied to identify novel PKMYT1 inhibitors. The computational approach combined structural analysis, molecular docking, binding free energy calculations, and quantitative structure-activity relationship (QSAR) models. In addition, a computational fragment growing approach was applied to a set of previously identified diaminopyrimidines. Based on the derived computational models, several derivatives were synthesized and tested in vitro on PKMYT1. Novel inhibitors active in the sub-micromolar range were identified which provide the basis for further characterization of PKMYT1 as putative target for cancer therapy.

Molecular dynamics simulation on the allosteric analysis of the c-di-GMP class I riboswitch induced by ligand binding

Riboswitches are RNA molecules that regulate gene expression using conformation change, affected by binding of small molecule ligands. Although a number of ligand-bound aptamer complex structures have been solved, it is important to know ligand-free conformations of the aptamers in order to understand the mechanism of specific binding by ligands. In this paper, we use dynamics simulations on a series of models to characterize the ligand-free and ligand-bound aptamer domain of the c-di-GMP class I (GEMM-I) riboswitch. The results revealed that the ligand-free aptamer has a stable state with a folded P2 and P3 helix, an unfolded P1 helix and open binding pocket. The first Mg ions binding to the aptamer is structurally favorable for the successive c-di-GMP binding. The P1 helix forms when c-di-GMP is successive bound. Three key junctions J1/2, J2/3 and J1/3 in the GEMM-I riboswitch contributing to the formation of P1 helix have been found. The binding of the c-di-GMP ligand to the GEMM-I riboswitch induces the riboswitch's regulation through the direct allosteric communication network in GEMM-I riboswitch from the c-di-GMP binding sites in the J1/2 and J1/3 junctions to the P1 helix, the indirect ones from those in the J2/3 and P2 communicating to P1 helix via the J1/2 and J1/3 media.

Accuracy Comparison of Generalized Born Models in the Calculation of Electrostatic Binding Free Energies

The need for accurate yet efficient representation of the aqueous environment in biomolecular modeling has led to the development of a variety of generalized Born (GB) implicit solvent models. While many studies have focused on the accuracy of available GB models in predicting solvation free energies, a systematic assessment of the quality of these models in binding free energy calculations, crucial for rational drug design, has not been undertaken. Here, we evaluate the accuracies of eight common GB flavors (GB-HCT, GB-OBC, GB-neck2, GBNSR6, GBSW, GBMV1, GBMV2, and GBMV3), available in major molecular dynamics packages, in predicting the electrostatic binding free energies ( ΔΔ G_el) for a diverse set of 60 biomolecular complexes belonging to four main classes: protein-protein, protein-drug, RNA-peptide, and small complexes. The GB flavors are examined in terms of their ability to reproduce the results from the Poisson-Boltzmann (PB) model, commonly used as accuracy reference in this context. We show that the agreement with the PB of ΔΔ G_el estimates varies widely between different GB models and also across different types of biomolecular complexes, with R² correlations ranging from 0.3772 to 0.9986. A surface-based "R6" GB model recently implemented in AMBER shows the closest overall agreement with reference PB ( R² = 0.9949, RMSD = 8.75 kcal/mol). The RNA-peptide and protein-drug complex sets appear to be most challenging for all but one model, as indicated by the large deviations from the PB in ΔΔ G_el. Small neutral complexes present the least challenge for most of the GB models tested. The quantitative demonstration of the strengths and weaknesses of the GB models across the diverse complex types provided here can be used as a guide for practical computations and future development efforts.

Validation of molecular force field parameters for peptides including isomerized amino acids

Recently, stereoinversions and isomerizations of amino acid residues in the proteins of living beings have been observed. Because isomerized amino acids cause structural changes and denaturation of proteins, isomerizations of amino acid residues are suspected to cause age-related diseases. In this study, AMBER molecular force field parameters were tested by using computationally generated nonapeptides and tripeptides including stereoinverted and/or isomerized amino acid residues. Energy calculations by using density functional theory were also performed for comparison. Although the force field parameters were developed by parameter fitting for l-α-amino acids, the accuracy of the computational results for d-amino acids and β-amino acids was comparable to those for l-α-amino acids. The conformational energies for tripeptides calculated by using density functional theory were reproduced more accurately than those for nonapeptides calculated by using the molecular mechanical force field. The evaluations were performed for the ff99SB, ff03, ff12SB, and the latest ff14SB force field parameters.

Mechanistic Insights into the Reaction of Chlorination of Tryptophan Catalyzed by Tryptophan 7-Halogenase

Tryptophan 7-halogenase catalyzes chlorination of free tryptophan to 7-chlorotryptophan, which is the first step in the antibiotic pyrrolnitrin biosynthesis. Many biologically and pharmaceutically active natural products contain chlorine and thus, an understanding of the mechanism of its introduction into organic molecules is important. Whilst enzyme-catalyzed chlorination is accomplished with ease, it remains a difficult task for the chemists. Therefore, utilizing enzymes in the synthesis of chlorinated organic compounds is important, and providing atomistic mechanistic insights about the reaction mechanism of tryptophan 7-halogenase is vital and timely. In this work, we examined a mechanism for the reaction of tryptophan chlorination, performed by tryptophan 7-halogenase, by calculating potential energy and free energy surfaces using two different Combined Quantum Mechanical/Molecular Mechanical (QM/MM) methods both employing Density Functional Theory (DFT) for the QM region. Both computational strategies agree on the nature of the rate-limiting step and provided close results for the reaction barriers of the two reaction steps. The calculations for both the potential energy and the free energy profiles showed very similar geometric features and hydrogen bonding interactions for the characterized stationary points.

New insights into human farnesyl pyrophosphate synthase inhibition by second-generation bisphosphonate drugs

Pamidronate, alendronate, APHBP and neridronate are a group of drugs, known as second-generation bisphosphonates (2G-BPs), commonly used in the treatment of bone-resorption disorders, and recently their use has been related to some collateral side effects. The therapeutic activity of 2G-BPs is related to the inhibition of the human Farnesyl Pyrophosphate Synthase (hFPPS). Available inhibitory activity values show that 2G-BPs act time-dependently, showing big differences in their initial inhibitory activities but similar final IC₅₀ values. However, there is a lack of information explaining this similar final inhibitory potency. Although different residues have been identified in the stabilization of the R₂ side chain of 2G-BPs into the active site, similar free binding energies were obtained that highlighted a similar stability of the ternary complexes, which in turns justified the similar IC₅₀ values reported. Free binding energy calculations also demonstrated that the union of 2G-BPs to the active site were 38 to 54 kcal mol^-1 energetically more favourable than the union of the natural substrate, which is the basis of the inhibition potency of the hFPPS activity.

Computational protein structure refinement: Almost there, yet still so far to go

Protein structures are essential in modern biology yet experimental methods are far from being able to catch up with the rapid increase in available genomic data. Computational protein structure prediction methods aim to fill the gap while the role of protein structure refinement is to take approximate initial template-based models and bring them closer to the true native structure. Current methods for computational structure refinement rely on molecular dynamics simulations, related sampling methods, or iterative structure optimization protocols. The best methods are able to achieve moderate degrees of refinement but consistent refinement that can reach near-experimental accuracy remains elusive. Key issues revolve around the accuracy of the energy function, the inability to reliably rank multiple models, and the use of restraints that keep sampling close to the native state but also limit the degree of possible refinement. A different aspect is the question of what exactly the target of high-resolution refinement should be as experimental structures are affected by experimental conditions and different biological questions require varying levels of accuracy. While improvement of the global protein structure is a difficult problem, high-resolution refinement methods that improves local structural quality such as favorable stereochemistry and the avoidance of atomic clashes are much more successful.

Improving the accuracy of high-throughput protein-protein affinity prediction may require better training data

Background

One goal of structural biology is to understand how a protein’s 3-dimensional conformation determines its capacity to interact with potential ligands. In the case of small chemical ligands, deconstructing a static protein-ligand complex into its constituent atom-atom interactions is typically sufficient to rapidly predict ligand affinity with high accuracy (>70% correlation between predicted and experimentally-determined affinity), a fact that is exploited to support structure-based drug design. We recently found that protein-DNA/RNA affinity can also be predicted with high accuracy using extensions of existing techniques, but protein-protein affinity could not be predicted with >60% correlation, even when the protein-protein complex was available.

Methods

X-ray and NMR structures of protein-protein complexes, their associated binding affinities and experimental conditions were obtained from different binding affinity and structural databases. Statistical models were implemented using a generalized linear model framework, including the experimental conditions as new model features. We evaluated the potential for new features to improve affinity prediction models by calculating the Pearson correlation between predicted and experimental binding affinities on the training and test data after model fitting and after cross-validation. Differences in accuracy were assessed using two-sample t test and nonparametric Mann–Whitney U test.

Results

Here we evaluate a range of potential factors that may interfere with accurate protein-protein affinity prediction. We find that X-ray crystal resolution has the strongest single effect on protein-protein affinity prediction. Limiting our analyses to only high-resolution complexes (≤2.5 Å) increased the correlation between predicted and experimental affinity from 54 to 68% (p = 4.32x10⁻³). In addition, incorporating information on the experimental conditions under which affinities were measured (pH, temperature and binding assay) had significant effects on prediction accuracy. We also highlight a number of potential errors in large structure-affinity databases, which could affect both model training and accuracy assessment.

Conclusions

The results suggest that the accuracy of statistical models for protein-protein affinity prediction may be limited by the information present in databases used to train new models. Improving our capacity to integrate large-scale structural and functional information may be required to substantively advance our understanding of the general principles by which a protein’s structure determines its function.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-017-1533-z) contains supplementary material, which is available to authorized users.

Nonketotic hyperglycinemia: Functional assessment of missense variants in GLDC to understand phenotypes of the disease

The rapid analysis of genomic data is providing effective mutational confirmation in patients with clinical and biochemical hallmarks of a specific disease. This is the case for nonketotic hyperglycinemia (NKH), a Mendelian disorder causing seizures in neonates and early-infants, primarily due to mutations in the GLDC gene. However, understanding the impact of missense variants identified in this gene is a major challenge for the application of genomics into clinical practice. Herein, a comprehensive functional and structural analysis of 19 GLDC missense variants identified in a cohort of 26 NKH patients was performed. Mutant cDNA constructs were expressed in COS7 cells followed by enzymatic assays and Western blot analysis of the GCS P-protein to assess the residual activity and mutant protein stability. Structural analysis, based on molecular modeling of the 3D structure of GCS P-protein, was also performed. We identify hypomorphic variants that produce attenuated phenotypes with improved prognosis of the disease. Structural analysis allows us to interpret the effects of mutations on protein stability and catalytic activity, providing molecular evidence for clinical outcome and disease severity. Moreover, we identify an important number of mutants whose loss-of-functionality is associated with instability and, thus, are potential targets for rescue using folding therapeutic approaches.

Multi-step virtual screening to develop selective DYRK1A inhibitors

Developing selective inhibitors for a particular kinase remains a major challenge in kinase-targeted drug discovery. Here we performed a multi-step virtual screening for dual-specificity tyrosine-phosphorylation-regulated kinase 1A (DYRK1A) inhibitors by focusing on the selectivity for DYRK1A over cyclin-dependent kinase 5 (CDK5). To examine the key factors contributing to the selectivity, we constructed logistic regression models to discriminate between actives and inactives for DYRK1A and CDK5, respectively, using residue-based binding free energies. The residue-based parameters were calculated by molecular mechanics-generalized Born surface area (MM-GBSA) decomposition methods for kinase-ligand complexes modeled by computer ligand docking. Based on the findings from the logistic regression models, we built a three-dimensional (3D) pharmacophore model and chose filter criteria for the multi-step virtual screening. The virtual hit compounds obtained from the screening were assessed for their inhibitory activities against DYRK1A and CDK5 by in vitro assay. Our screening identified two novel selective DYRK1A inhibitors with IC50 values of several μM for DYRK1A and >100μM for CDK5, which can be further optimized to develop more potent selective DYRK1A inhibitors.

Influence of Secondary-Structure Folding on the Mutually Exclusive Folding Process of GL5/I27 Protein: Evidence from Molecular Dynamics Simulations

Mutually exclusive folding proteins are a class of multidomain proteins in which the host domain remains folded while the guest domain is unfolded, and both domains achieve exchange of their folding status by a mutual exclusive folding (MEF) process. We carried out conventional and targeted molecular dynamics simulations for the mutually exclusive folding protein of GL5/I27 to address the MEF transition mechanisms. We constructed two starting models and two targeted models, i.e., the starting models GL5/I27-S and GL5/I27-ST in which the first model involves the host domain GL5 and the secondary-structure unfolded guest domain I27-S, while the second model involves the host domain GL5 and the secondary/tertiary-structure extending guest domain I27-ST, and the target models GL5-S/I27 and GL5-ST/I27 in which GL5-S and GL5-ST represent the secondary-structure unfolding and the secondary/tertiary-structure extending, respectively. We investigated four MEF transition processes from both starting models to both target models. Based on structural changes and the variations of the radius of gyration (R_g) and the fractions of native contacts (Q), the formation of the secondary structure of the I27-guest domain induces significant extending of the GL5-host domain; but the primary shrinking of the tertiary structure of the I27-guest domain causes insignificant extending of the GL5-host domain during the processes. The results indicate that only formation of the secondary structure in the I27-guest domain provides the main driving force for the mutually exclusive folding/unfolding between the I27-guest and GL5-host domains. A special structure as an intermediate with both host and guest domains being folded at the same time was found, which was suggested by the experiment. The analysis of hydrogen bonds and correlation motions supported the studied transition mechanism with the dynamical "tug-of-war" phenomenon.

Improved Accuracy in RNA-Protein Rigid Body Docking by Incorporating Force Field for Molecular Dynamics Simulation into the Scoring Function

RNA-protein interactions play fundamental roles in many biological processes. To understand these interactions, it is necessary to know the three-dimensional structures of RNA-protein complexes. However, determining the tertiary structure of these complexes is often difficult, suggesting that an accurate rigid body docking for RNA-protein complexes is needed. In general, the rigid body docking process is divided into two steps: generating candidate structures from the individual RNA and protein structures and then narrowing down the candidates. In this study, we focus on the former problem to improve the prediction accuracy in RNA-protein docking. Our method is based on the integration of physicochemical information about RNA into ZDOCK, which is known as one of the most successful computer programs for protein-protein docking. Because recent studies showed the current force field for molecular dynamics simulation of protein and nucleic acids is quite accurate, we modeled the physicochemical information about RNA by force fields such as AMBER and CHARMM. A comprehensive benchmark of RNA-protein docking, using three recently developed data sets, reveals the remarkable prediction accuracy of the proposed method compared with existing programs for docking: the highest success rate is 34.7% for the predicted structure of the RNA-protein complex with the best score and 79.2% for 3,600 predicted ones. Three full atomistic force fields for RNA (AMBER94, AMBER99, and CHARMM22) produced almost the same accurate result, which showed current force fields for nucleic acids are quite accurate. In addition, we found that the electrostatic interaction and the representation of shape complementary between protein and RNA plays the important roles for accurate prediction of the native structures of RNA-protein complexes.

Molecular dynamics simulations on the conformational transitions from the GA 98 (GA 88) to GB 98 (GB 88) proteins

We performed conventional and targeted molecular dynamics simulations to address the dynamic transition mechanisms of the conformational transitions from the G_A 98 protein with only 1 mutation of Leu45Tyr to G_B 98 and from the G_A 88 protein with 7 mutations of Gly24Ala, Ile25Thr, Ile30Phe, Ile33Tyr, Leu45Tyr, Ile49Thr, and Leu50Lys to G_B 88. The results show that the conformational transition mechanism from the mutated 3α G_A 98 (G_A 88) state to the α+4β G_B 98 (G_B 88) state via several intermediate conformations involves the bending of loops at the N and C termini firstly, the unfolding of αA and αC, then the traversing of αB, and the formation of the 4β layer with the conversion of the hydrophobic core. The bending of loops at the N and C termini and the formation of the crucial transition conformation with the full unfolded structure are key factors in their transition processes. The communication of the interaction network, the bending directions of loops, and the traversing site of αB in the transition of G_A 98 to G_B 98 are markedly different from those in G_A 88 to G_B 88 because of the different mutated residues. The analysis of the correlations and the calculated mass center distances between some segments further supported their conformational transition mechanisms. These results could help people to better understand the Paracelsus challenge. Copyright © 2016 John Wiley & Sons, Ltd.

Study on the Application of the Combination of TMD Simulation and Umbrella Sampling in PMF Calculation for Molecular Conformational Transitions

Free energy calculations of the potential of mean force (PMF) based on the combination of targeted molecular dynamics (TMD) simulations and umbrella samplings as a function of physical coordinates have been applied to explore the detailed pathways and the corresponding free energy profiles for the conformational transition processes of the butane molecule and the 35-residue villin headpiece subdomain (HP35). The accurate PMF profiles for describing the dihedral rotation of butane under both coordinates of dihedral rotation and root mean square deviation (RMSD) variation were obtained based on the different umbrella samplings from the same TMD simulations. The initial structures for the umbrella samplings can be conveniently selected from the TMD trajectories. For the application of this computational method in the unfolding process of the HP35 protein, the PMF calculation along with the coordinate of the radius of gyration (R_g) presents the gradual increase of free energies by about 1 kcal/mol with the energy fluctuations. The feature of conformational transition for the unfolding process of the HP35 protein shows that the spherical structure extends and the middle α-helix unfolds firstly, followed by the unfolding of other α-helices. The computational method for the PMF calculations based on the combination of TMD simulations and umbrella samplings provided a valuable strategy in investigating detailed conformational transition pathways for other allosteric processes.

Investigations of the CLOCK and BMAL1 Proteins Binding to DNA: A Molecular Dynamics Simulation Study

The circadian locomotor output cycles kaput (CLOCK), and brain and muscle ARNT-like 1 (BMAL1) proteins are important transcriptional factors of the endogenous circadian clock. The CLOCK and BMAL1 proteins can regulate the transcription-translation activities of the clock-related genes through the DNA binding. The hetero-/homo-dimerization and DNA combination of the CLOCK and BMAL1 proteins play a key role in the positive and negative transcriptional feedback processes. In the present work, we constructed a series of binary and ternary models for the bHLH/bHLH-PAS domains of the CLOCK and BMAL1 proteins, and the DNA molecule, and carried out molecular dynamics simulations, free energy calculations and conformational analysis to explore the interaction properties of the CLOCK and BMAL1 proteins with DNA. The results show that the bHLH domains of CLOCK and BMAL1 can favorably form the heterodimer of the bHLH domains of CLOCK and BMAL1 and the homodimer of the bHLH domains of BMAL1. And both dimers could respectively bind to DNA at its H1-H1 interface. The DNA bindings of the H1 helices in the hetero- and homo-bHLH dimers present the rectangular and diagonal binding modes, respectively. Due to the function of the α-helical forceps in these dimers, the tight gripping of the H1 helices to the major groove of DNA would cause the decrease of interactions at the H1-H2 interfaces in the CLOCK and BMAL1 proteins. The additional PAS domains in the CLOCK and BMAL1 proteins affect insignificantly the interactions of the CLOCK and BMAL1 proteins with the DNA molecule due to the flexible and long loop linkers located at the middle of the PAS and bHLH domains. The present work theoretically explains the interaction mechanisms of the bHLH domains of the CLOCK and BMAL1 proteins with DNA.