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Palacio-Castañeda, Valentina, Simon Dumas, Philipp Albrecht, Thijmen J. Wijgers, Stéphanie Descroix, and Wouter P. R. Verdurmen. "A Hybrid In Silico and Tumor-on-a-Chip Approach to Model Targeted Protein Behavior in 3D Microenvironments." Cancers 13, no. 10 (May 18, 2021): 2461. http://dx.doi.org/10.3390/cancers13102461.
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To rationally improve targeted drug delivery to tumor cells, new methods combining in silico and physiologically relevant in vitro models are needed. This study combines mathematical modeling with 3D in vitro co-culture models to study the delivery of engineered proteins, called designed ankyrin repeat proteins (DARPins), in biomimetic tumor microenvironments containing fibroblasts and tumor cells overexpressing epithelial cell adhesion molecule (EpCAM) or human epithelial growth factor receptor (HER2). In multicellular tumor spheroids, we observed strong binding-site barriers in combination with low apparent diffusion coefficients of 1 µm2·s−1 and 2 µm2 ·s−1 for EpCAM- and HER2-binding DARPin, respectively. Contrasting this, in a tumor-on-a-chip model for investigating delivery in real-time, transport was characterized by hindered diffusion as a consequence of the lower local tumor cell density. Finally, simulations of the diffusion of an EpCAM-targeting DARPin fused to a fragment of Pseudomonas aeruginosa exotoxin A, which specifically kills tumor cells while leaving fibroblasts untouched, correctly predicted the need for concentrations of 10 nM or higher for extensive tumor cell killing on-chip, whereas in 2D models picomolar concentrations were sufficient. These results illustrate the power of combining in vitro models with mathematical modeling to study and predict the protein activity in complex 3D models.
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Middendorf, Thomas R., and Richard W. Aldrich. "Structural identifiability of equilibrium ligand-binding parameters." Journal of General Physiology 149, no. 1 (December 19, 2016): 105–19. http://dx.doi.org/10.1085/jgp.201611702.
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Understanding the interactions of proteins with their ligands requires knowledge of molecular properties, such as binding site affinities and the effects that binding at one site exerts on binding at other sites (cooperativity). These properties cannot be measured directly and are usually estimated by fitting binding data with models that contain these quantities as parameters. In this study, we present a general method for answering the critical question of whether these parameters are identifiable (i.e., whether their estimates are accurate and unique). In cases in which parameter estimates are not unique, our analysis provides insight into the fundamental causes of nonidentifiability. This approach can thus serve as a guide for the proper design and analysis of protein–ligand binding experiments. We show that the equilibrium total binding relation can be reduced to a conserved mathematical form for all models composed solely of bimolecular association reactions and to a related, conserved form for all models composed of arbitrary combinations of binding and conformational equilibria. This canonical mathematical structure implies a universal parameterization of the binding relation that is consistent with virtually any physically reasonable binding model, for proteins with any number of binding sites. Matrix algebraic methods are used to prove that these universal parameter sets are structurally identifiable (SI; i.e., identifiable under conditions of noiseless data). A general approach for assessing and understanding the factors governing practical identifiability (i.e., the identifiability under conditions of real, noisy data) of these SI parameter sets is presented in the companion paper by Middendorf and Aldrich (2017. J. Gen. Physiol. https://doi.org/10.1085/jgp.201611703).
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Premarathna, Galkande Iresha, and Leif Ellingson. "A mathematical representation of protein binding sites using structural dispersion of atoms from principal axes for classification of binding ligands." PLOS ONE 16, no. 4 (April 8, 2021): e0244905. http://dx.doi.org/10.1371/journal.pone.0244905.
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Many researchers have studied the relationship between the biological functions of proteins and the structures of both their overall backbones of amino acids and their binding sites. A large amount of the work has focused on summarizing structural features of binding sites as scalar quantities, which can result in a great deal of information loss since the structures are three-dimensional. Additionally, a common way of comparing binding sites is via aligning their atoms, which is a computationally intensive procedure that substantially limits the types of analysis and modeling that can be done. In this work, we develop a novel encoding of binding sites as covariance matrices of the distances of atoms to the principal axes of the structures. This representation is invariant to the chosen coordinate system for the atoms in the binding sites, which removes the need to align the sites to a common coordinate system, is computationally efficient, and permits the development of probability models. These can then be used to both better understand groups of binding sites that bind to the same ligand and perform classification for these ligand groups. We demonstrate the utility of our method for discrimination of binding ligand through classification studies with two benchmark datasets using nearest mean and polytomous logistic regression classifiers.
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Ruan, Shuxiang, and Gary D. Stormo. "Inherent limitations of probabilistic models for protein-DNA binding specificity." PLOS Computational Biology 13, no. 7 (July 7, 2017): e1005638. http://dx.doi.org/10.1371/journal.pcbi.1005638.
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Sedaghat, Ahmad R., Arthur Sherman, and Michael J. Quon. "A mathematical model of metabolic insulin signaling pathways." American Journal of Physiology-Endocrinology and Metabolism 283, no. 5 (November 1, 2002): E1084—E1101. http://dx.doi.org/10.1152/ajpendo.00571.2001.
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We develop a mathematical model that explicitly represents many of the known signaling components mediating translocation of the insulin-responsive glucose transporter GLUT4 to gain insight into the complexities of metabolic insulin signaling pathways. A novel mechanistic model of postreceptor events including phosphorylation of insulin receptor substrate-1, activation of phosphatidylinositol 3-kinase, and subsequent activation of downstream kinases Akt and protein kinase C-ζ is coupled with previously validated subsystem models of insulin receptor binding, receptor recycling, and GLUT4 translocation. A system of differential equations is defined by the structure of the model. Rate constants and model parameters are constrained by published experimental data. Model simulations of insulin dose-response experiments agree with published experimental data and also generate expected qualitative behaviors such as sequential signal amplification and increased sensitivity of downstream components. We examined the consequences of incorporating feedback pathways as well as representing pathological conditions, such as increased levels of protein tyrosine phosphatases, to illustrate the utility of our model for exploring molecular mechanisms. We conclude that mathematical modeling of signal transduction pathways is a useful approach for gaining insight into the complexities of metabolic insulin signaling.
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Kimchi, Ofer, Carl P. Goodrich, Alexis Courbet, Agnese I. Curatolo, Nicholas B. Woodall, David Baker, and Michael P. Brenner. "Self-assembly–based posttranslational protein oscillators." Science Advances 6, no. 51 (December 2020): eabc1939. http://dx.doi.org/10.1126/sciadv.abc1939.
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Recent advances in synthetic posttranslational protein circuits are substantially impacting the landscape of cellular engineering and offer several advantages compared to traditional gene circuits. However, engineering dynamic phenomena such as oscillations in protein-level circuits remains an outstanding challenge. Few examples of biological posttranslational oscillators are known, necessitating theoretical progress to determine realizable oscillators. We construct mathematical models for two posttranslational oscillators, using few components that interact only through reversible binding and phosphorylation/dephosphorylation reactions. Our designed oscillators rely on the self-assembly of two protein species into multimeric functional enzymes that respectively inhibit and enhance this self-assembly. We limit our analysis to within experimental constraints, finding (i) significant portions of the restricted parameter space yielding oscillations and (ii) that oscillation periods can be tuned by several orders of magnitude using recent advances in computational protein design. Our work paves the way for the rational design and realization of protein-based dynamic systems.
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Wang, Debby D., Haoran Xie, and Hong Yan. "Proteo-chemometrics interaction fingerprints of protein–ligand complexes predict binding affinity." Bioinformatics 37, no. 17 (February 27, 2021): 2570–79. http://dx.doi.org/10.1093/bioinformatics/btab132.
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Abstract Motivation Reliable predictive models of protein–ligand binding affinity are required in many areas of biomedical research. Accurate prediction based on current descriptors or molecular fingerprints (FPs) remains a challenge. We develop novel interaction FPs (IFPs) to encode protein–ligand interactions and use them to improve the prediction. Results Proteo-chemometrics IFPs (PrtCmm IFPs) formed by combining extended connectivity fingerprints (ECFPs) with the proteo-chemometrics concept. Combining PrtCmm IFPs with machine-learning models led to efficient scoring models, which were validated on the PDBbind v2019 core set and CSAR-HiQ sets. The PrtCmm IFP Score outperformed several other models in predicting protein–ligand binding affinities. Besides, conventional ECFPs were simplified to generate new IFPs, which provided consistent but faster predictions. The relationship between the base atom properties of ECFPs and the accuracy of predictions was also investigated. Availability PrtCmm IFP has been implemented in the IFP Score Toolkit on github (https://github.com/debbydanwang/IFPscore). Supplementary information Supplementary data are available at Bioinformatics online.
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Conradi Smith, Gregory Douglas. "Allostery in oligomeric receptor models." Mathematical Medicine and Biology: A Journal of the IMA 37, no. 3 (December 10, 2019): 313–33. http://dx.doi.org/10.1093/imammb/dqz016.
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Abstract We show how equilibrium binding curves of receptor homodimers can be expressed as rational polynomial functions of the equilibrium binding curves of the constituent monomers, without approximation and without assuming independence of receptor monomers. Using a distinguished spanning tree construction for reduced graph powers, the method properly accounts for thermodynamic constraints and allosteric interactions between receptor monomers (i.e. conformational coupling). The method is completely general; it begins with an arbitrary undirected graph representing the topology of a monomer state-transition diagram and ends with an algebraic expression for the equilibrium binding curve of a receptor oligomer composed of two or more identical and indistinguishable monomers. Several specific examples are analysed, including guanine nucleotide-binding protein-coupled receptor dimers and tetramers composed of multiple ‘ternary complex’ monomers.
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Jiang, Yao, Hui-Fang Liu, and Rong Liu. "Systematic comparison and prediction of the effects of missense mutations on protein-DNA and protein-RNA interactions." PLOS Computational Biology 17, no. 4 (April 19, 2021): e1008951. http://dx.doi.org/10.1371/journal.pcbi.1008951.
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The binding affinities of protein-nucleic acid interactions could be altered due to missense mutations occurring in DNA- or RNA-binding proteins, therefore resulting in various diseases. Unfortunately, a systematic comparison and prediction of the effects of mutations on protein-DNA and protein-RNA interactions (these two mutation classes are termed MPDs and MPRs, respectively) is still lacking. Here, we demonstrated that these two classes of mutations could generate similar or different tendencies for binding free energy changes in terms of the properties of mutated residues. We then developed regression algorithms separately for MPDs and MPRs by introducing novel geometric partition-based energy features and interface-based structural features. Through feature selection and ensemble learning, similar computational frameworks that integrated energy- and nonenergy-based models were established to estimate the binding affinity changes resulting from MPDs and MPRs, but the selected features for the final models were different and therefore reflected the specificity of these two mutation classes. Furthermore, the proposed methodology was extended to the identification of mutations that significantly decreased the binding affinities. Extensive validations indicated that our algorithm generally performed better than the state-of-the-art methods on both the regression and classification tasks. The webserver and software are freely available at http://liulab.hzau.edu.cn/PEMPNI and https://github.com/hzau-liulab/PEMPNI.
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Sohrabi-Jahromi, Salma, and Johannes Söding. "Thermodynamic modeling reveals widespread multivalent binding by RNA-binding proteins." Bioinformatics 37, Supplement_1 (July 1, 2021): i308—i316. http://dx.doi.org/10.1093/bioinformatics/btab300.
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Abstract Motivation Understanding how proteins recognize their RNA targets is essential to elucidate regulatory processes in the cell. Many RNA-binding proteins (RBPs) form complexes or have multiple domains that allow them to bind to RNA in a multivalent, cooperative manner. They can thereby achieve higher specificity and affinity than proteins with a single RNA-binding domain. However, current approaches to de novo discovery of RNA binding motifs do not take multivalent binding into account. Results We present Bipartite Motif Finder (BMF), which is based on a thermodynamic model of RBPs with two cooperatively binding RNA-binding domains. We show that bivalent binding is a common strategy among RBPs, yielding higher affinity and sequence specificity. We furthermore illustrate that the spatial geometry between the binding sites can be learned from bound RNA sequences. These discovered bipartite motifs are consistent with previously known motifs and binding behaviors. Our results demonstrate the importance of multivalent binding for RNA-binding proteins and highlight the value of bipartite motif models in representing the multivalency of protein-RNA interactions. Availability and implementation BMF source code is available at https://github.com/soedinglab/bipartite_motif_finder under a GPL license. The BMF web server is accessible at https://bmf.soedinglab.org. Supplementary information Supplementary data are available at Bioinformatics online.
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Freedman, Simon L., Cristian Suarez, Jonathan D. Winkelman, David R. Kovar, Gregory A. Voth, Aaron R. Dinner, and Glen M. Hocky. "Mechanical and kinetic factors drive sorting of F-actin cross-linkers on bundles." Proceedings of the National Academy of Sciences 116, no. 33 (July 25, 2019): 16192–97. http://dx.doi.org/10.1073/pnas.1820814116.
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In cells, actin-binding proteins (ABPs) sort to different regions to establish F-actin networks with diverse functions, including filopodia used for cell migration and contractile rings required for cell division. Recent experimental work uncovered a competition-based mechanism that may facilitate spatial localization of ABPs: binding of a short cross-linker protein to 2 actin filaments promotes the binding of other short cross-linkers and inhibits the binding of longer cross-linkers (and vice versa). We hypothesize this sorting arises because F-actin is semiflexible and cannot bend over short distances. We develop a mathematical theory and lattice models encompassing the most important physical parameters for this process and use coarse-grained simulations with explicit cross-linkers to characterize and test our predictions. Our theory and data predict an explicit dependence of cross-linker separation on bundle polymerization rate. We perform experiments that confirm this dependence, but with an unexpected cross-over in dominance of one cross-linker at high growth rates to the other at slow growth rates, and we investigate the origin of this cross-over with further simulations. The nonequilibrium mechanism that we describe can allow cells to organize molecular material to drive biological processes, and our results can guide the choice and design of cross-linkers for engineered protein-based materials.
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Cortes, Eliceo, José Mora, and Edgar Márquez. "Modelling the Anti-Methicillin-Resistant Staphylococcus Aureus (MRSA) Activity of Cannabinoids: A QSAR and Docking Study." Crystals 10, no. 8 (August 11, 2020): 692. http://dx.doi.org/10.3390/cryst10080692.
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Twenty-four cannabinoids active against MRSA SA1199B and XU212 were optimized at WB97XD/6-31G(d,p), and several molecular descriptors were obtained. Using a multiple linear regression method, several mathematical models with statistical significance were obtained. The robustness of the models was validated, employing the leave-one-out cross-validation and Y-scrambling methods. The entire data set was docked against penicillin-binding protein, iso-tyrosyl tRNA synthetase, and DNA gyrase. The most active cannabinoids had high affinity to penicillin-binding protein (PBP), whereas the least active compounds had low affinities for all of the targets. Among the cannabinoid compounds, Cannabinoid 2 was highlighted due to its suitable combination of both antimicrobial activity and higher scoring values against the selected target; therefore, its docking performance was compared to that of oxacillin, a commercial PBP inhibitor. The 2D figures reveal that both compounds hit the protein in the active site with a similar type of molecular interaction, where the hydroxyl groups in the aromatic ring of cannabinoids play a pivotal role in the biological activity. These results provide some evidence that the anti-Staphylococcus aureus activity of these cannabinoids may be related to the inhibition of the PBP protein; besides, the robustness of the models along with the docking and Quantitative Structure–Activity Relationship (QSAR) results allow the proposal of three new compounds; the predicted activity combined with the scoring values against PBP should encourage future synthesis and experimental testing.
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Déchaud, H., H. Lejeune, M. Garoscio-Cholet, R. Mallein, and M. Pugeat. "Radioimmunoassay of testosterone not bound to sex-steroid-binding protein in plasma." Clinical Chemistry 35, no. 8 (August 1, 1989): 1609–14. http://dx.doi.org/10.1093/clinchem/35.8.1609.
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Abstract To measure the concentration of testosterone (T) that is not bound to sex-steroid-binding protein (SBP) in plasma, we quantified by radioimmunoassay the T in the supernates of plasma samples after precipitation with 50%-saturated ammonium sulfate. The concentrations of non-SBP-bound T. directly measured with this assay, correlated significantly (P less than 0.001) with those deduced from measurement of the percentage of non-SBP-bound T determined with [3H]T as tracer or from mathematical models according to the law of mass action. It also correlated significantly with the ratio of T to SBP and with the concentration of nonbound T. As determined with this assay, the mean concentration of non-SBP-bound T in normal men was higher in young (4.67, SD 2.68 nmol/L; n = 30) than in older (greater than 40 years) subjects (2.48, SD 1.61 nmol/L; n = 35; P less than 0.001) and lower than normal in hyperthyroid (1.61, SD 0.91 nmol/L; P less than 0.01) or infertile men (3.28, SD 1.70 nmol/L; P less than 0.01). In women, non-SBP-bound T was higher in hirsute patients (0.24, SD 0.11 nmol/L; P less than 0.01) and was lower during pregnancy (0.09, SD 0.05 nmol/L; P less than 0.05) than in normal women during the follicular phase (0.16, SD 0.07 nmol/L). We conclude that this direct measurement of non-SBP-bound T in plasma is suitable for routine use and represents a reliable index of androgenicity in human pathology, particularly when alterations of the binding capacity of SBP modify the concentrations of total T.
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Yamada, Naomi, William K. M. Lai, Nina Farrell, B. Franklin Pugh, and Shaun Mahony. "Characterizing protein–DNA binding event subtypes in ChIP-exo data." Bioinformatics 35, no. 6 (August 28, 2018): 903–13. http://dx.doi.org/10.1093/bioinformatics/bty703.
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Abstract Motivation Regulatory proteins associate with the genome either by directly binding cognate DNA motifs or via protein–protein interactions with other regulators. Each recruitment mechanism may be associated with distinct motifs and may also result in distinct characteristic patterns in high-resolution protein–DNA binding assays. For example, the ChIP-exo protocol precisely characterizes protein–DNA crosslinking patterns by combining chromatin immunoprecipitation (ChIP) with 5′ → 3′ exonuclease digestion. Since different regulatory complexes will result in different protein–DNA crosslinking signatures, analysis of ChIP-exo tag enrichment patterns should enable detection of multiple protein–DNA binding modes for a given regulatory protein. However, current ChIP-exo analysis methods either treat all binding events as being of a uniform type or rely on motifs to cluster binding events into subtypes. Results To systematically detect multiple protein–DNA interaction modes in a single ChIP-exo experiment, we introduce the ChIP-exo mixture model (ChExMix). ChExMix probabilistically models the genomic locations and subtype memberships of binding events using both ChIP-exo tag distribution patterns and DNA motifs. We demonstrate that ChExMix achieves accurate detection and classification of binding event subtypes using in silico mixed ChIP-exo data. We further demonstrate the unique analysis abilities of ChExMix using a collection of ChIP-exo experiments that profile the binding of key transcription factors in MCF-7 cells. In these data, ChExMix identifies possible recruitment mechanisms of FoxA1 and ERα, thus demonstrating that ChExMix can effectively stratify ChIP-exo binding events into biologically meaningful subtypes. Availability and implementation ChExMix is available from https://github.com/seqcode/chexmix. Supplementary information Supplementary data are available at Bioinformatics online.
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Ahmed, Asad, Bhavika Mam, and Ramanathan Sowdhamini. "DEELIG: A Deep Learning Approach to Predict Protein-Ligand Binding Affinity." Bioinformatics and Biology Insights 15 (January 2021): 117793222110303. http://dx.doi.org/10.1177/11779322211030364.
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Protein-ligand binding prediction has extensive biological significance. Binding affinity helps in understanding the degree of protein-ligand interactions and is a useful measure in drug design. Protein-ligand docking using virtual screening and molecular dynamic simulations are required to predict the binding affinity of a ligand to its cognate receptor. Performing such analyses to cover the entire chemical space of small molecules requires intense computational power. Recent developments using deep learning have enabled us to make sense of massive amounts of complex data sets where the ability of the model to “learn” intrinsic patterns in a complex plane of data is the strength of the approach. Here, we have incorporated convolutional neural networks to find spatial relationships among data to help us predict affinity of binding of proteins in whole superfamilies toward a diverse set of ligands without the need of a docked pose or complex as user input. The models were trained and validated using a stringent methodology for feature extraction. Our model performs better in comparison to some existing methods used widely and is suitable for predictions on high-resolution protein crystal (⩽2.5 Å) and nonpeptide ligand as individual inputs. Our approach to network construction and training on protein-ligand data set prepared in-house has yielded significant insights. We have also tested DEELIG on few COVID-19 main protease-inhibitor complexes relevant to the current public health scenario. DEELIG-based predictions can be incorporated in existing databases including RSCB PDB, PDBMoad, and PDBbind in filling missing binding affinity data for protein-ligand complexes.
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Michelson, Seth. "Multidrug Resistance and Its Reversal: Mathenatical Models." Journal of Theoretical Medicine 1, no. 2 (1997): 103–15. http://dx.doi.org/10.1080/10273669708833011.
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Classic multidrug resistance (MDR) is a phenomenon by which cells nonspecifically extrude noxious agents from the cutoplasm before lethal concentrations buils up. Some chemotherapeutically treated tumors exhibit these same dynamics. In tumor systems, the most common mechanism of facilitating MDR is the upregulation of the P-glycoprotein pump. This protein forms a transmembrance channel, and agter binding the chemotherapeutic agent and 2ATP molecules, forces the noxius agent through the channel. Hydrolysis of ATP to ADP provides the energy component of this reaction. General mathematical models describing drug resistamce are reviewed in this article. One model describing the molecular function of the P-glycoprotein pump in MDR cell lines is developed and presented in detail. The pump is modeled as an energy-dependent facilitated diffusion process. A partial differential equation is linked to a pair of ordinary differential equations to form the core of the model. To describe MDR reversal, the model is extended by additing an inhibitor to the equation system. Equations for competitive, one-site non-competitive, and allosteric non-competitive inhibition are then derived. Numerical simulations have been run to describe P-glycoprotein dynamics both in the presence and absence of inhibition, and these results are briefly reviewed. The character of the pump and its response to inhibition are discussed within the comtext of the models.
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Erban, Radek. "From molecular dynamics to Brownian dynamics." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, no. 2167 (July 8, 2014): 20140036. http://dx.doi.org/10.1098/rspa.2014.0036.
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Three coarse-grained molecular dynamics (MD) models are investigated with the aim of developing and analysing multi-scale methods which use MD simulations in parts of the computational domain and (less detailed) Brownian dynamics (BD) simulations in the remainder of the domain. The first MD model is formulated in one spatial dimension. It is based on elastic collisions of heavy molecules (e.g. proteins) with light point particles (e.g. water molecules). Two three-dimensional MD models are then investigated. The obtained results are applied to a simplified model of protein binding to receptors on the cellular membrane. It is shown that modern BD simulators of intracellular processes can be used in the bulk and accurately coupled with a (more detailed) MD model of protein binding which is used close to the membrane.
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Garcea, Robert L. "Biologic Constraints on Modelling Virus Assembly." Computational and Mathematical Methods in Medicine 9, no. 3-4 (2008): 257–64. http://dx.doi.org/10.1080/17486700802168007.
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The mathematic modelling of icosahedral virus assembly has drawn increasing interest because of the symmetric geometry of the outer shell structures. Many models involve equilibrium expressions of subunit binding, with reversible subunit additions forming various intermediate structures. The underlying assumption is that a final lowest energy state drives the equilibrium toward assembly. In their simplest forms, these models have explained why high subunit protein concentrations and strong subunit association constants can result in kinetic traps forming off pathway partial and aberrant structures. However, the cell biology of virus assembly is exceedingly complex. The biochemistry and biology of polyoma and papillomavirus assembly described here illustrates many of these specific issues. Variables include the use of cellular ‘chaperone’ proteins as mediators of assembly fidelity, the coupling of assembly to encapsidation of a specific nucleic acid genome, the use of cellular structures as ‘workbenches’ upon which assembly occurs, and the underlying problem of making a capsid structure that is metastable and capable of rapid disassembly upon infection. Although formidable to model, incorporating these considerations could advance the relevance of mathematical models of virus assembly to the real world.
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Zhang, Linda Yu, Emilio Gallicchio, Richard A. Friesner, and Ronald M. Levy. "Solvent models for protein-ligand binding: Comparison of implicit solvent poisson and surface generalized born models with explicit solvent simulations." Journal of Computational Chemistry 22, no. 6 (2001): 591–607. http://dx.doi.org/10.1002/jcc.1031.
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Rasmusson, R. L., J. W. Clark, W. R. Giles, E. F. Shibata, and D. L. Campbell. "A mathematical model of a bullfrog cardiac pacemaker cell." American Journal of Physiology-Heart and Circulatory Physiology 259, no. 2 (August 1, 1990): H352—H369. http://dx.doi.org/10.1152/ajpheart.1990.259.2.h352.
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Previous models of cardiac cellular electrophysiology have been based largely on voltage-clamp measurements obtained from multicellular preparations and often combined data from different regions of the heart and a variety of species. We have developed a model of cardiac pacemaking based on a comprehensive set of voltage-clamp measurements obtained from single cells isolated from one specific tissue type, the bullfrog sinus venosus (SV). Consequently, sarcolemmal current densities and kinetics are not influenced by secondary phenomena associated with multicellular preparations, allowing us to realistically simulate processes thought to be important in pacemaking, including the Na(+)-K+ pump and Na(+)-Ca2+ exchanger. The membrane is surrounded extracellularly by a diffusion-limited space and intracellularly by a limited myoplasmic volume containing Ca2(+)-binding proteins (calmodulin, troponin). The model makes several predictions regarding mechanisms involved in pacing. 1) Primary pacemaking cannot be attributed to any single current but arises from both the lack of a background K+ current and a complex interaction between Ca2+, delayed-rectifier K+, and background leak currents. 2) Ca2+ current displays complex behavior and is important during repolarization. 3) Because of Ca2+ buffering by myoplasmic proteins, the Na(+)-Ca2+ exchanger current is small and has little influence on action potential repolarization but may modulate the maximum diastolic potential. 4) The Na(+)-K+ pump current does not play an active role in repolarization but is of sufficient size to modulate the rate of diastolic depolarization. 5) K+ accumulation and Ca2+ depletion may occur in the extracellular spaces but play no role in either the diastolic depolarization or repolarization of a single action potential. This model illustrates the importance of basing simulations on quantitative measurements of ionic currents in myocytes and of including both electrogenic transporter mechanisms and Ca2+ buffering by myoplasmic Ca2(+)-binding proteins.
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Cholewa-Waclaw, Justyna, Ruth Shah, Shaun Webb, Kashyap Chhatbar, Bernard Ramsahoye, Oliver Pusch, Miao Yu, Philip Greulich, Bartlomiej Waclaw, and Adrian P. Bird. "Quantitative modelling predicts the impact of DNA methylation on RNA polymerase II traffic." Proceedings of the National Academy of Sciences 116, no. 30 (July 9, 2019): 14995–5000. http://dx.doi.org/10.1073/pnas.1903549116.
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Patterns of gene expression are primarily determined by proteins that locally enhance or repress transcription. While many transcription factors target a restricted number of genes, others appear to modulate transcription levels globally. An example is MeCP2, an abundant methylated-DNA binding protein that is mutated in the neurological disorder Rett syndrome. Despite much research, the molecular mechanism by which MeCP2 regulates gene expression is not fully resolved. Here, we integrate quantitative, multidimensional experimental analysis and mathematical modeling to indicate that MeCP2 is a global transcriptional regulator whose binding to DNA creates “slow sites” in gene bodies. We hypothesize that waves of slowed-down RNA polymerase II formed behind these sites travel backward and indirectly affect initiation, reminiscent of defect-induced shockwaves in nonequilibrium physics transport models. This mechanism differs from conventional gene-regulation mechanisms, which often involve direct modulation of transcription initiation. Our findings point to a genome-wide function of DNA methylation that may account for the reversibility of Rett syndrome in mice. Moreover, our combined theoretical and experimental approach provides a general method for understanding how global gene-expression patterns are choreographed.
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Lai, Hien T. T., Do Minh Ha, Duc Manh Nguyen, and Toan T. Nguyen. "Homology modeling of mouse NLRP3 NACHT protein domain and molecular dynamics simulation of its ATP binding properties." International Journal of Modern Physics C 31, no. 03 (January 8, 2020): 2050036. http://dx.doi.org/10.1142/s0129183120500369.
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Gout is an extremely painful form of inflammatory arthritis, caused by the formation of monosodium urate (MSU) crystals in the joints. MSU crystals are one of the triggers for the activation of nucleotide-binding domain (NOD)-like receptor protein 3 (NLRP3) inflammasome (NACHT, LRR and PYD domains-containing protein), which in turn induces caspase-1 activation and a nonspecific immune responses that cause inflammation. Further structural studies and ligand designs are needed to block the interaction of NLRP3 with MSU or allow the interaction without activating caspase-1. This would facilitate the screening of new drugs for the treatment of gout. Using computational methods for homology modeling and molecular dynamics simulations, the structural model of mouse NLRP3 protein with its domains, three potential structural models were consistently constructed and tested to find the most stable structural model. Adenosine triphosphate (ATP) — an activator of NACHT (the central domain of mouse NLRP3 protein) — was docked and simulated. Ligand effects to activate as well as limit this protein were analyzed. This study provides insights to deeper understanding about gout development pathway via the NLRP3 protein.
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Zhang, Fuhao, Wenbo Shi, Jian Zhang, Min Zeng, Min Li, and Lukasz Kurgan. "PROBselect: accurate prediction of protein-binding residues from proteins sequences via dynamic predictor selection." Bioinformatics 36, Supplement_2 (December 2020): i735—i744. http://dx.doi.org/10.1093/bioinformatics/btaa806.
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Abstract Motivation Knowledge of protein-binding residues (PBRs) improves our understanding of protein−protein interactions, contributes to the prediction of protein functions and facilitates protein−protein docking calculations. While many sequence-based predictors of PBRs were published, they offer modest levels of predictive performance and most of them cross-predict residues that interact with other partners. One unexplored option to improve the predictive quality is to design consensus predictors that combine results produced by multiple methods. Results We empirically investigate predictive performance of a representative set of nine predictors of PBRs. We report substantial differences in predictive quality when these methods are used to predict individual proteins, which contrast with the dataset-level benchmarks that are currently used to assess and compare these methods. Our analysis provides new insights for the cross-prediction concern, dissects complementarity between predictors and demonstrates that predictive performance of the top methods depends on unique characteristics of the input protein sequence. Using these insights, we developed PROBselect, first-of-its-kind consensus predictor of PBRs. Our design is based on the dynamic predictor selection at the protein level, where the selection relies on regression-based models that accurately estimate predictive performance of selected predictors directly from the sequence. Empirical assessment using a low-similarity test dataset shows that PROBselect provides significantly improved predictive quality when compared with the current predictors and conventional consensuses that combine residue-level predictions. Moreover, PROBselect informs the users about the expected predictive quality for the prediction generated from a given input protein. Availability and implementation PROBselect is available at http://bioinformatics.csu.edu.cn/PROBselect/home/index. Supplementary information Supplementary data are available at Bioinformatics online.
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Trott, L., M. Hafezparast, and A. Madzvamuse. "A mathematical understanding of how cytoplasmic dynein walks on microtubules." Royal Society Open Science 5, no. 8 (August 2018): 171568. http://dx.doi.org/10.1098/rsos.171568.
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Cytoplasmic dynein 1 (hereafter referred to simply as dynein) is a dimeric motor protein that walks and transports intracellular cargos towards the minus end of microtubules. In this article, we formulate, based on physical principles, a mechanical model to describe the stepping behaviour of cytoplasmic dynein walking on microtubules from the cell membrane towards the nucleus. Unlike previous studies on physical models of this nature, we base our formulation on the whole structure of dynein to include the temporal dynamics of the individual subunits such as the cargo (for example, an endosome, vesicle or bead), two rings of six ATPase domains associated with diverse cellular activities (AAA+ rings) and the microtubule-binding domains which allow dynein to bind to microtubules. This mathematical framework allows us to examine experimental observations on dynein across a wide range of different species, as well as being able to make predictions on the temporal behaviour of the individual components of dynein not currently experimentally measured. Furthermore, we extend the model framework to include backward stepping, variable step size and dwelling. The power of our model is in its predictive nature; first it reflects recent experimental observations that dynein walks on microtubules using a weakly coordinated stepping pattern with predominantly not passing steps. Second, the model predicts that interhead coordination in the ATP cycle of cytoplasmic dynein is important in order to obtain the alternating stepping patterns and long run lengths seen in experiments.
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Romero-Durana, Miguel, Brian Jiménez-García, and Juan Fernández-Recio. "pyDockEneRes: per-residue decomposition of protein–protein docking energy." Bioinformatics 36, no. 7 (December 6, 2019): 2284–85. http://dx.doi.org/10.1093/bioinformatics/btz884.
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Abstract Motivation Protein–protein interactions are key to understand biological processes at the molecular level. As a complement to experimental characterization of protein interactions, computational docking methods have become useful tools for the structural and energetics modeling of protein–protein complexes. A key aspect of such algorithms is the use of scoring functions to evaluate the generated docking poses and try to identify the best models. When the scoring functions are based on energetic considerations, they can help not only to provide a reliable structural model for the complex, but also to describe energetic aspects of the interaction. This is the case of the scoring function used in pyDock, a combination of electrostatics, desolvation and van der Waals energy terms. Its correlation with experimental binding affinity values of protein–protein complexes was explored in the past, but the per-residue decomposition of the docking energy was never systematically analyzed. Results Here, we present pyDockEneRes (pyDock Energy per-Residue), a web server that provides pyDock docking energy partitioned at the residue level, giving a much more detailed description of the docking energy landscape. Additionally, pyDockEneRes computes the contribution to the docking energy of the side-chain atoms. This fast approach can be applied to characterize a complex structure in order to identify energetically relevant residues (hot-spots) and estimate binding affinity changes upon mutation to alanine. Availability and implementation The server does not require registration by the user and is freely accessible for academics at https://life.bsc.es/pid/pydockeneres. Supplementary information Supplementary data are available at Bioinformatics online.
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Shi, Wentao, Jeffrey M. Lemoine, Abd-El-Monsif A. Shawky, Manali Singha, Limeng Pu, Shuangyan Yang, J. Ramanujam, and Michal Brylinski. "BionoiNet: ligand-binding site classification with off-the-shelf deep neural network." Bioinformatics 36, no. 10 (February 13, 2020): 3077–83. http://dx.doi.org/10.1093/bioinformatics/btaa094.
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Abstract Motivation Fast and accurate classification of ligand-binding sites in proteins with respect to the class of binding molecules is invaluable not only to the automatic functional annotation of large datasets of protein structures but also to projects in protein evolution, protein engineering and drug development. Deep learning techniques, which have already been successfully applied to address challenging problems across various fields, are inherently suitable to classify ligand-binding pockets. Our goal is to demonstrate that off-the-shelf deep learning models can be employed with minimum development effort to recognize nucleotide- and heme-binding sites with a comparable accuracy to highly specialized, voxel-based methods. Results We developed BionoiNet, a new deep learning-based framework implementing a popular ResNet model for image classification. BionoiNet first transforms the molecular structures of ligand-binding sites to 2D Voronoi diagrams, which are then used as the input to a pretrained convolutional neural network classifier. The ResNet model generalizes well to unseen data achieving the accuracy of 85.6% for nucleotide- and 91.3% for heme-binding pockets. BionoiNet also computes significance scores of pocket atoms, called BionoiScores, to provide meaningful insights into their interactions with ligand molecules. BionoiNet is a lightweight alternative to computationally expensive 3D architectures. Availability and implementation BionoiNet is implemented in Python with the source code freely available at: https://github.com/CSBG-LSU/BionoiNet. Supplementary information Supplementary data are available at Bioinformatics online.
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Yan, Zichao, William L. Hamilton, and Mathieu Blanchette. "Graph neural representational learning of RNA secondary structures for predicting RNA-protein interactions." Bioinformatics 36, Supplement_1 (July 1, 2020): i276—i284. http://dx.doi.org/10.1093/bioinformatics/btaa456.
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Abstract Motivation RNA-protein interactions are key effectors of post-transcriptional regulation. Significant experimental and bioinformatics efforts have been expended on characterizing protein binding mechanisms on the molecular level, and on highlighting the sequence and structural traits of RNA that impact the binding specificity for different proteins. Yet our ability to predict these interactions in silico remains relatively poor. Results In this study, we introduce RPI-Net, a graph neural network approach for RNA-protein interaction prediction. RPI-Net learns and exploits a graph representation of RNA molecules, yielding significant performance gains over existing state-of-the-art approaches. We also introduce an approach to rectify an important type of sequence bias caused by the RNase T1 enzyme used in many CLIP-Seq experiments, and we show that correcting this bias is essential in order to learn meaningful predictors and properly evaluate their accuracy. Finally, we provide new approaches to interpret the trained models and extract simple, biologically interpretable representations of the learned sequence and structural motifs. Availability and implementation Source code can be accessed at https://www.github.com/HarveyYan/RNAonGraph. Supplementary information Supplementary data are available at Bioinformatics online.
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Zhang, Jian, Sina Ghadermarzi, and Lukasz Kurgan. "Prediction of protein-binding residues: dichotomy of sequence-based methods developed using structured complexes versus disordered proteins." Bioinformatics 36, no. 18 (June 17, 2020): 4729–38. http://dx.doi.org/10.1093/bioinformatics/btaa573.
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Abstract Motivation There are over 30 sequence-based predictors of the protein-binding residues (PBRs). They use either structure-annotated or disorder-annotated training datasets, potentially creating a dichotomy where the structure-/disorder-specific models may not be able to cross-over to accurately predict the other type. Moreover, the structure-trained predictors were shown to substantially cross-predict PBRs among residues that interact with non-protein partners (nucleic acids and small ligands). We address these issues by performing first-of-its-kind comparative study of a representative collection of disorder- and structure-trained predictors using a comprehensive benchmark set with the structure- and disorder-derived annotations of PBRs (to analyze the cross-over) and the protein-, nucleic acid- and small ligand-binding proteins (to study the cross-predictions). Results Three predictors provide accurate results: SCRIBER, ANCHOR and disoRDPbind. Some of the structure-trained methods make accurate predictions on the structure-annotated proteins. Similarly, the disorder-trained predictors predict well on the disorder-annotated proteins. However, the considered predictors generally fail to cross-over, with the exception of SCRIBER. Our study also reveals that virtually all methods substantially cross-predict PBRs, except for SCRIBER for the structure-annotated proteins and disoRDPbind for the disorder-annotated proteins. We formulate a novel hybrid predictor, hybridPBRpred, that combines results produced by disoRDPbind and SCRIBER to accurately predict disorder- and structure-annotated PBRs. HybridPBRpred generates accurate results that cross-over structure- and disorder-annotated proteins and produces relatively low amount of cross-predictions, offering an accurate alternative to predict PBRs. Availability and implementation HybridPBRpred webserver, benchmark dataset and supplementary information are available at http://biomine.cs.vcu.edu/servers/hybridPBRpred/. Supplementary information Supplementary data are available at Bioinformatics online.
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SACHSE, F. B., K. G. GLÄNZEL, and G. SEEMANN. "MODELING OF PROTEIN INTERACTIONS INVOLVED IN CARDIAC TENSION DEVELOPMENT." International Journal of Bifurcation and Chaos 13, no. 12 (December 2003): 3561–78. http://dx.doi.org/10.1142/s0218127403008855.
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Modeling of protein interactions responsible for cardiac tension development can enhance the understanding of physiological and pathophysiological phenomena of the heart. Principal components of muscular tension development are the proteins actin, myosin, troponin and tropomyosin. The tension is produced by cross-bridge cycling of actin and myosin using adenosine triphosphate as energy source. The cross-bridge cycling is initiated by binding of intracellular calcium to troponin, resulting in configuration changes of tropomyosin. In this work a hybrid model of protein interactions in cardiac tension development is derived on basis of recent measurements and descriptions on protein level. Dependencies on intracellular calcium concentration, sarcomere stretch and stretch velocity as well as cooperativity mechanisms are incorporated. The model quantifies the tension development by states associated to configurations of the involved proteins. The model enables in conjunction with electrophysiological models of cardiac myocytes the reconstruction of electro-mechanical phenomena. Numerical simulations with the hybrid model were performed, which illustrated the reconstruction of steady state and length switches experiments. The steady state experiments describe the force-cytosolic [ Ca 2+] relationship in intact rat cardiac trabeculae. The length switch experiments provide data on the redevelopment of force after sudden stretch in rabbit right ventricular papillary muscles. Results of the numerical simulations show quantitative agreement with experimental studies. The hybrid model of cardiac tension development offers interfaces to further models of cardiac electro-mechanics. The hybrid model can be coupled with models of cellular electrophysiology and passive mechanics of myocardium allowing the inclusion of mechano-electrical feedback mechanisms. The hybrid model can be applied to elucidate cooperativity mechanisms, pathophysiological changes and metabolism of tension development.
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Lu, Wei, Carlos Bueno, Nicholas P. Schafer, Joshua Moller, Shikai Jin, Xun Chen, Mingchen Chen, et al. "OpenAWSEM with Open3SPN2: A fast, flexible, and accessible framework for large-scale coarse-grained biomolecular simulations." PLOS Computational Biology 17, no. 2 (February 12, 2021): e1008308. http://dx.doi.org/10.1371/journal.pcbi.1008308.
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We present OpenAWSEM and Open3SPN2, new cross-compatible implementations of coarse-grained models for protein (AWSEM) and DNA (3SPN2) molecular dynamics simulations within the OpenMM framework. These new implementations retain the chemical accuracy and intrinsic efficiency of the original models while adding GPU acceleration and the ease of forcefield modification provided by OpenMM’s Custom Forces software framework. By utilizing GPUs, we achieve around a 30-fold speedup in protein and protein-DNA simulations over the existing LAMMPS-based implementations running on a single CPU core. We showcase the benefits of OpenMM’s Custom Forces framework by devising and implementing two new potentials that allow us to address important aspects of protein folding and structure prediction and by testing the ability of the combined OpenAWSEM and Open3SPN2 to model protein-DNA binding. The first potential is used to describe the changes in effective interactions that occur as a protein becomes partially buried in a membrane. We also introduced an interaction to describe proteins with multiple disulfide bonds. Using simple pairwise disulfide bonding terms results in unphysical clustering of cysteine residues, posing a problem when simulating the folding of proteins with many cysteines. We now can computationally reproduce Anfinsen’s early Nobel prize winning experiments by using OpenMM’s Custom Forces framework to introduce a multi-body disulfide bonding term that prevents unphysical clustering. Our protein-DNA simulations show that the binding landscape is funneled towards structures that are quite similar to those found using experiments. In summary, this paper provides a simulation tool for the molecular biophysics community that is both easy to use and sufficiently efficient to simulate large proteins and large protein-DNA systems that are central to many cellular processes. These codes should facilitate the interplay between molecular simulations and cellular studies, which have been hampered by the large mismatch between the time and length scales accessible to molecular simulations and those relevant to cell biology.
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Santana, Charles A., Sabrina de A. Silveira, João P. A. Moraes, Sandro C. Izidoro, Raquel C. de Melo-Minardi, António J. M. Ribeiro, Jonathan D. Tyzack, Neera Borkakoti, and Janet M. Thornton. "GRaSP: a graph-based residue neighborhood strategy to predict binding sites." Bioinformatics 36, Supplement_2 (December 2020): i726—i734. http://dx.doi.org/10.1093/bioinformatics/btaa805.
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Abstract Motivation The discovery of protein–ligand-binding sites is a major step for elucidating protein function and for investigating new functional roles. Detecting protein–ligand-binding sites experimentally is time-consuming and expensive. Thus, a variety of in silico methods to detect and predict binding sites was proposed as they can be scalable, fast and present low cost. Results We proposed Graph-based Residue neighborhood Strategy to Predict binding sites (GRaSP), a novel residue centric and scalable method to predict ligand-binding site residues. It is based on a supervised learning strategy that models the residue environment as a graph at the atomic level. Results show that GRaSP made compatible or superior predictions when compared with methods described in the literature. GRaSP outperformed six other residue-centric methods, including the one considered as state-of-the-art. Also, our method achieved better results than the method from CAMEO independent assessment. GRaSP ranked second when compared with five state-of-the-art pocket-centric methods, which we consider a significant result, as it was not devised to predict pockets. Finally, our method proved scalable as it took 10–20 s on average to predict the binding site for a protein complex whereas the state-of-the-art residue-centric method takes 2–5 h on average. Availability and implementation The source code and datasets are available at https://github.com/charles-abreu/GRaSP. Supplementary information Supplementary data are available at Bioinformatics online.
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Rubinstein, Boris Y., Henry H. Mattingly, Alexander M. Berezhkovskii, and Stanislav Y. Shvartsman. "Long-term dynamics of multisite phosphorylation." Molecular Biology of the Cell 27, no. 14 (July 15, 2016): 2331–40. http://dx.doi.org/10.1091/mbc.e16-03-0137.
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Multisite phosphorylation cycles are ubiquitous in cell regulation systems and are studied at multiple levels of complexity, from molecules to organisms, with the ultimate goal of establishing predictive understanding of the effects of genetic and pharmacological perturbations of protein phosphorylation in vivo. Achieving this goal is essentially impossible without mathematical models, which provide a systematic framework for exploring dynamic interactions of multiple network components. Most of the models studied to date do not discriminate between the distinct partially phosphorylated forms and focus on two limiting reaction regimes, distributive and processive, which differ in the number of enzyme–substrate binding events needed for complete phosphorylation or dephosphorylation. Here we use a minimal model of extracellular signal-related kinase regulation to explore the dynamics of a reaction network that includes all essential phosphorylation forms and arbitrary levels of reaction processivity. In addition to bistability, which has been studied extensively in distributive mechanisms, this network can generate periodic oscillations. Both bistability and oscillations can be realized at high levels of reaction processivity. Our work provides a general framework for systematic analysis of dynamics in multisite phosphorylation systems.
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Norris, Noele, Naomi M. Levine, Vicente I. Fernandez, and Roman Stocker. "Mechanistic model of nutrient uptake explains dichotomy between marine oligotrophic and copiotrophic bacteria." PLOS Computational Biology 17, no. 5 (May 19, 2021): e1009023. http://dx.doi.org/10.1371/journal.pcbi.1009023.
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Marine bacterial diversity is immense and believed to be driven in part by trade-offs in metabolic strategies. Here we consider heterotrophs that rely on organic carbon as an energy source and present a molecular-level model of cell metabolism that explains the dichotomy between copiotrophs—which dominate in carbon-rich environments—and oligotrophs—which dominate in carbon-poor environments—as the consequence of trade-offs between nutrient transport systems. While prototypical copiotrophs, like Vibrios, possess numerous phosphotransferase systems (PTS), prototypical oligotrophs, such as SAR11, lack PTS and rely on ATP-binding cassette (ABC) transporters, which use binding proteins. We develop models of both transport systems and use them in proteome allocation problems to predict the optimal nutrient uptake and metabolic strategy as a function of carbon availability. We derive a Michaelis–Menten approximation of ABC transport, analytically demonstrating how the half-saturation concentration is a function of binding protein abundance. We predict that oligotrophs can attain nanomolar half-saturation concentrations using binding proteins with only micromolar dissociation constants and while closely matching transport and metabolic capacities. However, our model predicts that this requires large periplasms and that the slow diffusion of the binding proteins limits uptake. Thus, binding proteins are critical for oligotrophic survival yet severely constrain growth rates. We propose that this trade-off fundamentally shaped the divergent evolution of oligotrophs and copiotrophs.
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Young, David J., Jun O. Liu, and Donald Small. "Combinatorial Approaches to Overcome Plasma Protein Inhibition of FLT3 Tyrosine Kinase Inhibitors." Blood 132, Supplement 1 (November 29, 2018): 1362. http://dx.doi.org/10.1182/blood-2018-99-118820.
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Abstract Background: The FMS-like tyrosine kinase 3 (FLT3) is the most frequently mutated gene in acute myeloid leukemia (AML) and also results in poor prognosis for adult and pediatric patients, and thus represents an attractive target for tyrosine kinase inhibitors (TKI). The activity of FLT3-targeted TKI is inhibited to varying extents by plasma protein binding. Staurosporine (STS)-derived TKI are inhibited almost exclusively by the plasma protein alpha-1 acid glycoprotein (AGP), an acute-phase reactant. We studied the impact of AGP binding on the other STS-derivatives and report the development of a novel method to overcome this binding. Methods: We assayed the impact of human AGP upon the activity of the STS-derived TKI (midostaurin, lestaurtinib, TTT-3002) against proliferation of the FLT3-ITD dependent cell line MOLM-14 and upon the parent compound (staurosporine) against the non-FLT3-dependent cell line HL-60. These experiments were repeated, co-incubating with drugs that competitively bind AGP to identify those that may restore TKI activity. Results: The TKI are inhibited in a linear AGP-dependent manner (fold change increase of IC50 per mg/dL AGP: midostaurin 3.00-fold, lestaurtinib 11.73-fold, TTT-3002 0.33-fold) across the range of AGP concentrations observed in human plasma. These results correspond to the drug-protein binding constants for the TKI: midostaurin 12.6 µM-1, lestaurtinib 49.2 µM-1, TTT-3002 1.41 µM-1, all validated by competitive fluorescence displacement of the AGP-binding dye, 1-anilino-8-naphthalenesulfonate. These results predict that in vivo IC50 values for these FLT3 TKI will be significantly higher than those measured under typical (10% FCS) in vitro culture conditions: midostaurin 4.7 µM, lestaurtinib 4.8 µM, TTT-3002 34 nM. By comparison, activity of the parent compound, staurosporine, against HL60 is completely inhibited by AGP. Assays using bovine plasma, serum or purified AGP do not demonstrate similar inhibition of FLT3 TKI. We are developing a murine model to overcome this experimental limitation. We have developed a mathematical model describing the interactions of AGP with FLT3 TKI using classical mass action relationships that match experimental results and furthermore describe the effects of competitive plasma protein binding by unrelated agents. These models predict that disinhibition of TKI may be achievable in vivo, and define the properties of such "rescue" agents. Mifepristone binds AGP (2-10 fold greater than STS-derived TKI) and has no independent effect upon FLT3-dependent cell growth. Co-treatment with mifepristone restores the IC50 of TTT-3002 from 12 nM with AGP to < 0.1 nM. Disinhibition is seen for lestaurtinib (IC50 shift reduced from >1000-fold to 50-fold) and midostaurin (300-fold reduced to 80-fold). This results in predicted in vivo IC50 that are clinically relevant, and serve as a proof-of-principle for this method. Using this principle we have screened a library of FDA-approved compounds for the ability to rescue TKI activity despite the presence of potentially inhibitory plasma proteins. This screen has identified 40 potential agents that may displace STS-derived TKI from AGP, and an additional 90 agents that may restore TKI activity through off-target effects. Several agents have already been validated in vitro, and found to decrease the IC50 of midostaurin and other TKI to clinically achievable ranges despite the presence of inhibiting proteins. Conclusions: The failure of FLT3 TKI in previous clinical trials has been linked to a lack of plasma drug activity. This work provides biochemical confirmation of this effect. Furthermore, these results indicate that this is a property of the class as a whole, including midostaurin. Indeed, for midostaurin, the predicted in vivo IC50 is higher than steady state levels suggesting that in clinical trials it likely acts through non-FLT3 mechanisms. Disinhibition of TKIs by mifepristone suggests a novel combinatorial approach restore TKI activity using unrelated compounds. We are currently examining other agents for similar synergy. By improving TKI potency in the face of inhibitory plasma protein binding, such combinations would be expected to improve their clinical efficacy by reducing the dosages necessary to thoroughly inhibit FLT3. Finally, this report provides a method for predicting at least one factor that affects the success or failure of FLT3 TKI in clinical trials. Disclosures No relevant conflicts of interest to declare.
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Mullins, R. Dyche, Walter F. Stafford, and Thomas D. Pollard. "Structure, Subunit Topology, and Actin-binding Activity of the Arp2/3 Complex from Acanthamoeba." Journal of Cell Biology 136, no. 2 (January 27, 1997): 331–43. http://dx.doi.org/10.1083/jcb.136.2.331.
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The Arp2/3 complex, first isolated from Acanthamoeba castellani by affinity chromatography on profilin, consists of seven polypeptides; two actinrelated proteins, Arp2 and Arp3; and five apparently novel proteins, p40, p35, p19, p18, and p14 (Machesky et al., 1994). The complex is homogeneous by hydrodynamic criteria with a Stokes' radius of 5.3 nm by gel filtration, sedimentation coefficient of 8.7 S, and molecular mass of 197 kD by analytical ultracentrifugation. The stoichiometry of the subunits is 1:1:1:1:1:1:1, indicating the purified complex contains one copy each of seven polypeptides. In electron micrographs, the complex has a bilobed or horseshoe shape with outer dimensions of ∼13 × 10 nm, and mathematical models of such a shape and size are consistent with the measured hydrodynamic properties. Chemical cross-linking with a battery of cross-linkers of different spacer arm lengths and chemical reactivities identify the following nearest neighbors within the complex: Arp2 and p40; Arp2 and p35; Arp3 and p35; Arp3 and either p18 or p19; and p19 and p14. By fluorescent antibody staining with anti-p40 and -p35, the complex is concentrated in the cortex of the ameba, especially in linear structures, possibly actin filament bundles, that lie perpendicular to the leading edge. Purified Arp2/3 complex binds actin filaments with a Kd of 2.3 μM and a stoichiometry of approximately one complex molecule per actin monomer. In electron micrographs of negatively stained samples, Arp2/3 complex decorates the sides of actin filaments. EDC/NHS cross-links actin to Arp3, p35, and a low molecular weight subunit, p19, p18, or p14. We propose structural and topological models for the Arp2/3 complex and suggest that affinity for actin filaments accounts for the localization of complex subunits to actinrich regions of Acanthamoeba.
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Tesei, Giulio, João M. Martins, Micha B. A. Kunze, Yong Wang, Ramon Crehuet, and Kresten Lindorff-Larsen. "DEER-PREdict: Software for efficient calculation of spin-labeling EPR and NMR data from conformational ensembles." PLOS Computational Biology 17, no. 1 (January 22, 2021): e1008551. http://dx.doi.org/10.1371/journal.pcbi.1008551.
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Owing to their plasticity, intrinsically disordered and multidomain proteins require descriptions based on multiple conformations, thus calling for techniques and analysis tools that are capable of dealing with conformational ensembles rather than a single protein structure. Here, we introduce DEER-PREdict, a software program to predict Double Electron-Electron Resonance distance distributions as well as Paramagnetic Relaxation Enhancement rates from ensembles of protein conformations. DEER-PREdict uses an established rotamer library approach to describe the paramagnetic probes which are bound covalently to the protein.DEER-PREdict has been designed to operate efficiently on large conformational ensembles, such as those generated by molecular dynamics simulation, to facilitate the validation or refinement of molecular models as well as the interpretation of experimental data. The performance and accuracy of the software is demonstrated with experimentally characterized protein systems: HIV-1 protease, T4 Lysozyme and Acyl-CoA-binding protein. DEER-PREdict is open source (GPLv3) and available at github.com/KULL-Centre/DEERpredict and as a Python PyPI package pypi.org/project/DEERPREdict.
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González, Janneth, Angela Gálvez, Ludis Morales, George E. Barreto, Francisco Capani, Omar Sierra, and Yolima Torres. "Integrative Approach for Computationally Inferring Interactions between the Alpha and Beta Subunits of the Calcium-Activated Potassium Channel (BK): A Docking Study." Bioinformatics and Biology Insights 7 (January 2013): BBI.S10077. http://dx.doi.org/10.4137/bbi.s10077.
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Three-dimensional models of the alpha- and beta-1 subunits of the calcium-activated potassium channel (BK) were predicted by threading modeling. A recursive approach comprising of sequence alignment and model building based on three templates was used to build these models, with the refinement of non-conserved regions carried out using threading techniques. The complex formed by the subunits was studied by means of docking techniques, using 3D models of the two subunits, and an approach based on rigid-body structures. Structural effects of the complex were analyzed with respect to hydrogen-bond interactions and binding-energy calculations. Potential interaction sites of the complex were determined by referencing a study of the difference accessible surface area (DASA) of the protein subunits in the complex.
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Vijayakrishnan, Swetha, Philip Callow, Margaret A. Nutley, Donna P. McGow, David Gilbert, Peter Kropholler, Alan Cooper, Olwyn Byron, and J. Gordon Lindsay. "Variation in the organization and subunit composition of the mammalian pyruvate dehydrogenase complex E2/E3BP core assembly." Biochemical Journal 437, no. 3 (July 13, 2011): 565–74. http://dx.doi.org/10.1042/bj20101784.
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Crucial to glucose homoeostasis in humans, the hPDC (human pyruvate dehydrogenase complex) is a massive molecular machine comprising multiple copies of three distinct enzymes (E1–E3) and an accessory subunit, E3BP (E3-binding protein). Its icosahedral E2/E3BP 60-meric ‘core’ provides the central structural and mechanistic framework ensuring favourable E1 and E3 positioning and enzyme co-operativity. Current core models indicate either a 48E2+12E3BP or a 40E2+20E3BP subunit composition. In the present study, we demonstrate clear differences in subunit content and organization between the recombinant hPDC core (rhPDC; 40E2+20E3BP), generated under defined conditions where E3BP is produced in excess, and its native bovine (48E2+12E3BP) counterpart. The results of the present study provide a rational basis for resolving apparent differences between previous models, both obtained using rhE2/E3BP core assemblies where no account was taken of relative E2 and E3BP expression levels. Mathematical modelling predicts that an ‘average’ 48E2+12E3BP core arrangement allows maximum flexibility in assembly, while providing the appropriate balance of bound E1 and E3 enzymes for optimal catalytic efficiency and regulatory fine-tuning. We also show that the rhE2/E3BP and bovine E2/E3BP cores bind E3s with a 2:1 stoichiometry, and propose that mammalian PDC comprises a heterogeneous population of assemblies incorporating a network of E3 (and possibly E1) cross-bridges above the core surface.
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Bicknell, Brendan A., and Geoffrey J. Goodhill. "Emergence of ion channel modal gating from independent subunit kinetics." Proceedings of the National Academy of Sciences 113, no. 36 (August 22, 2016): E5288—E5297. http://dx.doi.org/10.1073/pnas.1604090113.
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Many ion channels exhibit a slow stochastic switching between distinct modes of gating activity. This feature of channel behavior has pronounced implications for the dynamics of ionic currents and the signaling pathways that they regulate. A canonical example is the inositol 1,4,5-trisphosphate receptor (IP3R) channel, whose regulation of intracellular Ca2+ concentration is essential for numerous cellular processes. However, the underlying biophysical mechanisms that give rise to modal gating in this and most other channels remain unknown. Although ion channels are composed of protein subunits, previous mathematical models of modal gating are coarse grained at the level of whole-channel states, limiting further dialogue between theory and experiment. Here we propose an origin for modal gating, by modeling the kinetics of ligand binding and conformational change in the IP3R at the subunit level. We find good agreement with experimental data over a wide range of ligand concentrations, accounting for equilibrium channel properties, transient responses to changing ligand conditions, and modal gating statistics. We show how this can be understood within a simple analytical framework and confirm our results with stochastic simulations. The model assumes that channel subunits are independent, demonstrating that cooperative binding or concerted conformational changes are not required for modal gating. Moreover, the model embodies a generally applicable principle: If a timescale separation exists in the kinetics of individual subunits, then modal gating can arise as an emergent property of channel behavior.
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Bernard, Samuel, Branka Čajavec, Laurent Pujo-Menjouet, Michael C. Mackey, and Hanspeter Herzel. "Modelling transcriptional feedback loops: the role of Gro/TLE1 in Hes1 oscillations." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 364, no. 1842 (March 21, 2006): 1155–70. http://dx.doi.org/10.1098/rsta.2006.1761.
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The transcriptional repressor Hes1, a basic helix-loop-helix family protein, periodically changes its expression in the presomitic mesoderm. Its periodic pattern of expression is retained in a number of cultured murine cell lines. In this paper, we introduce an extended mathematical model for Hes1 oscillatory expression that includes regulation of Hes1 transcription by Drosophila Groucho (Gro) or its vertebrate counterpart, the transducine-like enhancer of split/Groucho-related gene product 1 (TLE1). Gro/TLE1 is a necessary corepressor required by a number of DNA-binding transcriptional repressors, including Hes1. Models of direct repression via Hes1 typically display an expression overshoot after transcription initiation which is not seen in the experimental data. However, numerical simulation and theoretical predictions of our model show that the cofactor Gro/TLE1 reduces the overshoot and is thus necessary for a rapid and finely tuned response of Hes1 to activation signals. Further, from detailed linear stability and numerical bifurcation analysis and simulations, we conclude that the cooperativity coefficient ( h ) for Hes1 self-repression should be large (i.e. h ≥4). Finally, we introduce the characteristic turnaround duration, and show that for our model the duration of the repression loop is between 40 and 60 min.
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Jha, Amrita, and Neeru Adlakha. "Two-dimensional finite element model to study unsteady state Ca2+ diffusion in neuron involving ER LEAK and SERCA." International Journal of Biomathematics 08, no. 01 (January 2015): 1550002. http://dx.doi.org/10.1142/s1793524515500023.
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In this paper, finite element approach using two-dimensional unsteady state problem has been developed to study radial and angular calcium diffusion problem in neurons. Calcium is responsible messenger for transmitting information in communication process between neurons. The most important Ca 2+ binding proteins for the dynamics of Ca 2+ is itself buffer and other physiological parameters are located in Ca 2+ stores. In this study, the model incorporates the physiological parameters like diffusion coefficient, receptors, exogenous buffers etc. Appropriate boundary conditions have been framed in view of the physiological conditions. Computer simulations in MATLAB 7.11 are employed to investigate mathematical models of reaction–diffusion equation, the details of the implementation can heavily affect the numerical solutions and, thus, the outcome simulated on Core(TM) i3 CPU M 330 @ 2.13 GHz processing speed and 3 GB memory.
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Kapla, Jon, Ismael Rodríguez-Espigares, Flavio Ballante, Jana Selent, and Jens Carlsson. "Can molecular dynamics simulations improve the structural accuracy and virtual screening performance of GPCR models?" PLOS Computational Biology 17, no. 5 (May 13, 2021): e1008936. http://dx.doi.org/10.1371/journal.pcbi.1008936.
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The determination of G protein-coupled receptor (GPCR) structures at atomic resolution has improved understanding of cellular signaling and will accelerate the development of new drug candidates. However, experimental structures still remain unavailable for a majority of the GPCR family. GPCR structures and their interactions with ligands can also be modelled computationally, but such predictions have limited accuracy. In this work, we explored if molecular dynamics (MD) simulations could be used to refine the accuracy of in silico models of receptor-ligand complexes that were submitted to a community-wide assessment of GPCR structure prediction (GPCR Dock). Two simulation protocols were used to refine 30 models of the D3 dopamine receptor (D3R) in complex with an antagonist. Close to 60 μs of simulation time was generated and the resulting MD refined models were compared to a D3R crystal structure. In the MD simulations, the receptor models generally drifted further away from the crystal structure conformation. However, MD refinement was able to improve the accuracy of the ligand binding mode. The best refinement protocol improved agreement with the experimentally observed ligand binding mode for a majority of the models. Receptor structures with improved virtual screening performance, which was assessed by molecular docking of ligands and decoys, could also be identified among the MD refined models. Application of weak restraints to the transmembrane helixes in the MD simulations further improved predictions of the ligand binding mode and second extracellular loop. These results provide guidelines for application of MD refinement in prediction of GPCR-ligand complexes and directions for further method development.
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Asif, Maor, and Yaron Orenstein. "DeepSELEX: inferring DNA-binding preferences from HT-SELEX data using multi-class CNNs." Bioinformatics 36, Supplement_2 (December 2020): i634—i642. http://dx.doi.org/10.1093/bioinformatics/btaa789.
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Abstract Motivation Transcription factor (TF) DNA-binding is a central mechanism in gene regulation. Biologists would like to know where and when these factors bind DNA. Hence, they require accurate DNA-binding models to enable binding prediction to any DNA sequence. Recent technological advancements measure the binding of a single TF to thousands of DNA sequences. One of the prevailing techniques, high-throughput SELEX, measures protein–DNA binding by high-throughput sequencing over several cycles of enrichment. Unfortunately, current computational methods to infer the binding preferences from high-throughput SELEX data do not exploit the richness of these data, and are under-using the most advanced computational technique, deep neural networks. Results To better characterize the binding preferences of TFs from these experimental data, we developed DeepSELEX, a new algorithm to infer intrinsic DNA-binding preferences using deep neural networks. DeepSELEX takes advantage of the richness of high-throughput sequencing data and learns the DNA-binding preferences by observing the changes in DNA sequences through the experimental cycles. DeepSELEX outperforms extant methods for the task of DNA-binding inference from high-throughput SELEX data in binding prediction in vitro and is on par with the state of the art in in vivo binding prediction. Analysis of model parameters reveals it learns biologically relevant features that shed light on TFs’ binding mechanism. Availability and implementation DeepSELEX is available through github.com/OrensteinLab/DeepSELEX/. Supplementary information Supplementary data are available at Bioinformatics online.
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Igashov, Ilia, Kliment Olechnovič, Maria Kadukova, Česlovas Venclovas, and Sergei Grudinin. "VoroCNN: deep convolutional neural network built on 3D Voronoi tessellation of protein structures." Bioinformatics 37, no. 16 (February 23, 2021): 2332–39. http://dx.doi.org/10.1093/bioinformatics/btab118.
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Abstract Motivation Effective use of evolutionary information has recently led to tremendous progress in computational prediction of three-dimensional (3D) structures of proteins and their complexes. Despite the progress, the accuracy of predicted structures tends to vary considerably from case to case. Since the utility of computational models depends on their accuracy, reliable estimates of deviation between predicted and native structures are of utmost importance. Results For the first time, we present a deep convolutional neural network (CNN) constructed on a Voronoi tessellation of 3D molecular structures. Despite the irregular data domain, our data representation allows us to efficiently introduce both convolution and pooling operations and train the network in an end-to-end fashion without precomputed descriptors. The resultant model, VoroCNN, predicts local qualities of 3D protein folds. The prediction results are competitive to state of the art and superior to the previous 3D CNN architectures built for the same task. We also discuss practical applications of VoroCNN, for example, in recognition of protein binding interfaces. Availability and implementation The model, data and evaluation tests are available at https://team.inria.fr/nano-d/software/vorocnn/. Supplementary information Supplementary data are available at Bioinformatics online.
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Brown, Aidan I., and Elena F. Koslover. "Design principles for the glycoprotein quality control pathway." PLOS Computational Biology 17, no. 2 (February 1, 2021): e1008654. http://dx.doi.org/10.1371/journal.pcbi.1008654.
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Newly-translated glycoproteins in the endoplasmic reticulum (ER) often undergo cycles of chaperone binding and release in order to assist in folding. Quality control is required to distinguish between proteins that have completed native folding, those that have yet to fold, and those that have misfolded. Using quantitative modeling, we explore how the design of the quality-control pathway modulates its efficiency. Our results show that an energy-consuming cyclic quality-control process, similar to the observed physiological system, outperforms alternative designs. The kinetic parameters that optimize the performance of this system drastically change with protein production levels, while remaining relatively insensitive to the protein folding rate. Adjusting only the degradation rate, while fixing other parameters, allows the pathway to adapt across a range of protein production levels, aligning with in vivo measurements that implicate the release of degradation-associated enzymes as a rapid-response system for perturbations in protein homeostasis. The quantitative models developed here elucidate design principles for effective glycoprotein quality control in the ER, improving our mechanistic understanding of a system crucial to maintaining cellular health.
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Chen, Peng, Tong Shen, Youzhi Zhang, and Bing Wang. "A Sequence-segment Neighbor Encoding Schema for Protein Hotspot Residue Prediction." Current Bioinformatics 15, no. 5 (October 14, 2020): 445–54. http://dx.doi.org/10.2174/1574893615666200106115421.
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Background: Hotspots are those residues that contribute major free energy of binding in protein-protein interactions. Protein functions are frequently dependent on hotspot residues. At present, hotspot residues are always identified by Alanine scanning mutagenesis technology, which is costly, time-consuming and laborious. Objective: Therefore, more accurate and efficient methods have to be developed to identify protein hotspot residues. Methods: This paper proposed a novel encoding schema of sequence-segment neighbors and constructed a random forest-based model to identify hotspots in protein interaction interfaces. Firstly, 10 amino acid physicochemical properties, 16 features related to the PI and DI, and 25 features related to ASA were extracted. Different from the previous residue encoding schemas, such as auto correlation descriptor or triplet combination information, this paper employed the influence of amino acids neighbors to hotspot residues and amino acids with a certain distance in sequence to the hotspot. Results: Moreover, the proposed model was compared with other hotspot prediction methods, including APIS, Robetta, FOLDEF, KFC, MINERVA models, etc. Conclusion: The experimental results showed that the proposed model can improve the prediction ability of protein hotspot residues on the same test set.
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Liu, Yang, Xia-hui Ouyang, Zhi-Xiong Xiao, Le Zhang, and Yang Cao. "A Review on the Methods of Peptide-MHC Binding Prediction." Current Bioinformatics 15, no. 8 (January 1, 2021): 878–88. http://dx.doi.org/10.2174/1574893615999200429122801.
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Background: T lymphocyte achieves an immune response by recognizing antigen peptides (also known as T cell epitopes) through major histocompatibility complex (MHC) molecules. The immunogenicity of T cell epitopes depends on their source and stability in combination with MHC molecules. The binding of the peptide to MHC is the most selective step, so predicting the binding affinity of the peptide to MHC is the principal step in predicting T cell epitopes. The identification of epitopes is of great significance in the research of vaccine design and T cell immune response. Objective: The traditional method for identifying epitopes is to synthesize and test the binding activity of peptide by experimental methods, which is not only time-consuming, but also expensive. In silico methods for predicting peptide-MHC binding emerge to pre-select candidate peptides for experimental testing, which greatly saves time and costs. By summarizing and analyzing these methods, we hope to have a better insight and provide guidance for future directions. Methods: Up to now, a number of methods have been developed to predict the binding ability of peptides to MHC based on various principles. Some of them employ matrix models or machine learning models based on the sequence characteristic embedded in peptides or MHC to predict the binding ability of peptides to MHC. Some others utilize the three-dimensional structural information of peptides or MHC, for example, by extracting three-dimensional structural information to construct a feature matrix or machine learning model, or directly using protein structure prediction, molecular docking to predict the binding mode of peptides and MHC. Results: Although the methods in predicting peptide-MHC binding based on the feature matrix or machine learning model can achieve high-throughput prediction, the accuracy of which depends heavily on the sequence characteristic of confirmed binding peptides. In addition, it cannot provide insights into the mechanism of antigen specificity. Therefore, such methods have certain limitations in practical applications. Methods in predicting peptide-MHC binding based on structural prediction or molecular docking are computationally intensive compared to the methods based on feature matrix or machine learning model and the challenge is how to predict a reliable structural model. Conclusion: This paper reviews the principles, advantages and disadvantages of the methods of peptide-MHC binding prediction and discussed the future directions to achieve more accurate predictions.
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Jiang, Hanlun, Fu Kit Sheong, Lizhe Zhu, Xin Gao, Julie Bernauer, and Xuhui Huang. "Markov State Models Reveal a Two-Step Mechanism of miRNA Loading into the Human Argonaute Protein: Selective Binding followed by Structural Re-arrangement." PLOS Computational Biology 11, no. 7 (July 16, 2015): e1004404. http://dx.doi.org/10.1371/journal.pcbi.1004404.
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Koide, Hiroki, Noriyuki Kodera, Shveta Bisht, Shoji Takada, and Tsuyoshi Terakawa. "Modeling of DNA binding to the condensin hinge domain using molecular dynamics simulations guided by atomic force microscopy." PLOS Computational Biology 17, no. 7 (July 30, 2021): e1009265. http://dx.doi.org/10.1371/journal.pcbi.1009265.
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The condensin protein complex compacts chromatin during mitosis using its DNA-loop extrusion activity. Previous studies proposed scrunching and loop-capture models as molecular mechanisms for the loop extrusion process, both of which assume the binding of double-strand (ds) DNA to the hinge domain formed at the interface of the condensin subunits Smc2 and Smc4. However, how the hinge domain contacts dsDNA has remained unknown. Here, we conducted atomic force microscopy imaging of the budding yeast condensin holo-complex and used this data as basis for coarse-grained molecular dynamics simulations to model the hinge structure in a transient open conformation. We then simulated the dsDNA binding to open and closed hinge conformations, predicting that dsDNA binds to the outside surface when closed and to the outside and inside surfaces when open. Our simulations also suggested that the hinge can close around dsDNA bound to the inside surface. Based on these simulation results, we speculate that the conformational change of the hinge domain might be essential for the dsDNA binding regulation and play roles in condensin-mediated DNA-loop extrusion.
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WANG, ZHI-XIANG, and YONG DUAN. "DIRECT INTERACTION ENERGY: A COMPUTATIONAL QUANTITY FOR PARAMETERIZATION OF CONDENSED-PHASE FORCE FIELDS AND ITS APPLICATION TO HYDROGEN BONDING." Journal of Theoretical and Computational Chemistry 04, spec01 (January 2005): 689–705. http://dx.doi.org/10.1142/s0219633605001726.
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Using N-Methylacetamide (NMA) dimer and NMA–water as model complexes, the solvent effect on the protein inter- N – H ⋯ O =C and intra- N – H ⋯ OH 2, and C = O ⋯ H 2 O hydrogen bonding have been studied by the polarizable continuum model (PCM) ab initio calculations in the four media (vacuum, ether, nitromethane and water). In contrast to the empirical approaches, we suggested using the direction interaction energies (DE) to consider the solvent polarization, which can be derived from PCM ab initio calculations. The DEs of the model compounds in solvents are larger than their in vacuo binding energies, which reflect the solvent polarization effect. As the solvents become increasingly polar, the binding free energies decrease while DEs increase. The increasing DE is consistent with the increasing hydrogen bond length. Considering the protein environment, the DEs of NMA-NMA dimer in ether, 9.14 and 9.41 kcal/mol for NMADI and NMADII, are recommended for the intra N – H ⋯ O =C hydrogen bonding. The DEs of NMA–water complex in water, -5.47 (NMAWI) and -5.41 kcal/mol (NMAWI'), -8.44 (NMAWII) and -8.68 kcal/mol (NMAWII'), respectively, are suggested for the inter- N – H ⋯ OH 2 and C – O ⋯ H 2 O hydrogen bonding of proteins. Using the same approach, we have also computed the DE of water dimer in liquid water. The computed DE of water dimer (-5.63 kcal/mol) is larger than the in vacuo water dimerization energy (-5.14 kcal/mol) and in reasonable agreement with the dimerization energies (ranging from –6.0 to 6.8 kcal/mol) of polarization-included empirical water models.