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Mugnai ML, Thirumalai D. Molecular Transfer Model for pH Effects on Intrinsically Disordered Proteins: Theory and Applications. J Chem Theory Comput 2021; 17:1944-1954. [PMID: 33566618 DOI: 10.1021/acs.jctc.0c01316] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We present a theoretical method to study how changes in pH shape the heterogeneous conformational ensemble explored by intrinsically disordered proteins (IDPs). The theory is developed in the context of coarse-grained models, which enable a fast, accurate, and extensive exploration of conformational space at a given protonation state. In order to account for pH effects, we generalize the molecular transfer model (MTM), in which conformations are re-weighted using the transfer free energy, which is the free energy necessary for bringing to equilibrium in a new environment a "frozen" conformation of the system. Using the semi-grand ensemble, we derive an exact expression of the transfer free energy, which amounts to the appropriate summation over all the protonation states. Because the exact result is computationally too demanding to be useful for large polyelectrolytes or IDPs, we introduce a mean-field (MF) approximation of the transfer free energy. Using a lattice model, we compare the exact and MF results for the transfer free energy and a variety of observables associated with the model IDP. We find that the precise location of the charged groups (the sequence), and not merely the net charge, determines the structural properties. We demonstrate that some of the limitations previously noted for MF theory in the context of globular proteins are mitigated when disordered polymers are studied. The excellent agreement between the exact and MF results poises us to use the method presented here as a computational tool to study the properties of IDPs and other biological systems as a function of pH.
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Affiliation(s)
- Mauro Lorenzo Mugnai
- Department of Chemistry, The University of Texas at Austin, Austin, Texas 78712, United States
| | - D Thirumalai
- Department of Chemistry, The University of Texas at Austin, Austin, Texas 78712, United States
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Michael E, Polydorides S, Simonson T, Archontis G. Hybrid MC/MD for protein design. J Chem Phys 2021; 153:054113. [PMID: 32770896 DOI: 10.1063/5.0013320] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023] Open
Abstract
Computational protein design relies on simulations of a protein structure, where selected amino acids can mutate randomly, and mutations are selected to enhance a target property, such as stability. Often, the protein backbone is held fixed and its degrees of freedom are modeled implicitly to reduce the complexity of the conformational space. We present a hybrid method where short molecular dynamics (MD) segments are used to explore conformations and alternate with Monte Carlo (MC) moves that apply mutations to side chains. The backbone is fully flexible during MD. As a test, we computed side chain acid/base constants or pKa's in five proteins. This problem can be considered a special case of protein design, with protonation/deprotonation playing the role of mutations. The solvent was modeled as a dielectric continuum. Due to cost, in each protein we allowed just one side chain position to change its protonation state and the other position to change its type or mutate. The pKa's were computed with a standard method that scans a range of pH values and with a new method that uses adaptive landscape flattening (ALF) to sample all protonation states in a single simulation. The hybrid method gave notably better accuracy than standard, fixed-backbone MC. ALF decreased the computational cost a factor of 13.
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Affiliation(s)
- Eleni Michael
- Department of Physics, University of Cyprus, P.O 20537, CY678 Nicosia, Cyprus
| | - Savvas Polydorides
- Department of Physics, University of Cyprus, P.O 20537, CY678 Nicosia, Cyprus
| | - Thomas Simonson
- Laboratoire de Biochimie (CNRS UMR7654), Ecole Polytechnique, Palaiseau, France
| | - Georgios Archontis
- Department of Physics, University of Cyprus, P.O 20537, CY678 Nicosia, Cyprus
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Mignon D, Druart K, Michael E, Opuu V, Polydorides S, Villa F, Gaillard T, Panel N, Archontis G, Simonson T. Physics-Based Computational Protein Design: An Update. J Phys Chem A 2020; 124:10637-10648. [DOI: 10.1021/acs.jpca.0c07605] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Affiliation(s)
- David Mignon
- Laboratoire de Biologie Structurale de la Cellule (CNRS UMR7654), Ecole Polytechnique, 91128 Palaiseau, France
| | - Karen Druart
- Laboratoire de Biologie Structurale de la Cellule (CNRS UMR7654), Ecole Polytechnique, 91128 Palaiseau, France
| | - Eleni Michael
- Department of Physics, University of Cyprus, PO20537, CY1678 Nicosia, Cyprus
| | - Vaitea Opuu
- Laboratoire de Biologie Structurale de la Cellule (CNRS UMR7654), Ecole Polytechnique, 91128 Palaiseau, France
| | - Savvas Polydorides
- Department of Physics, University of Cyprus, PO20537, CY1678 Nicosia, Cyprus
| | - Francesco Villa
- Laboratoire de Biologie Structurale de la Cellule (CNRS UMR7654), Ecole Polytechnique, 91128 Palaiseau, France
| | - Thomas Gaillard
- Laboratoire de Biologie Structurale de la Cellule (CNRS UMR7654), Ecole Polytechnique, 91128 Palaiseau, France
| | - Nicolas Panel
- Laboratoire de Biologie Structurale de la Cellule (CNRS UMR7654), Ecole Polytechnique, 91128 Palaiseau, France
| | - Georgios Archontis
- Department of Physics, University of Cyprus, PO20537, CY1678 Nicosia, Cyprus
| | - Thomas Simonson
- Laboratoire de Biologie Structurale de la Cellule (CNRS UMR7654), Ecole Polytechnique, 91128 Palaiseau, France
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Fossat MJ, Pappu RV. q-Canonical Monte Carlo Sampling for Modeling the Linkage between Charge Regulation and Conformational Equilibria of Peptides. J Phys Chem B 2019; 123:6952-6967. [PMID: 31362509 PMCID: PMC10785832 DOI: 10.1021/acs.jpcb.9b05206] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Abstract
The overall charge content and the patterning of charged residues have a profound impact on the conformational ensembles adopted by intrinsically disordered proteins. These parameters can be altered by charge regulation, which refers to the effects of post-translational modifications, pH-dependent changes to charge, and conformational fluctuations that modify the pKa values of ionizable residues. Although atomistic simulations have played a prominent role in uncovering the major sequence-ensemble relationships of IDPs, most simulations assume fixed charge states for ionizable residues. This may lead to erroneous estimates for conformational equilibria if they are linked to charge regulation. Here, we report the development of a new method we term q-canonical Monte Carlo sampling for modeling the linkage between charge regulation and conformational equilibria. The method, which is designed to be interoperable with the ABSINTH implicit solvation model, operates as follows: For a protein sequence with n ionizable residues, we start with all 2n charge microstates and use a criterion based on model compound pKa values to prune down to a subset of thermodynamically relevant charge microstates. This subset is then grouped into mesostates, where all microstates that belong to a mesostate have the same net charge. Conformational distributions, drawn from a canonical ensemble, are generated for each of the charge microstates that make up a mesostate using a method we designate as proton walk sampling. This method combines Metropolis Monte Carlo sampling in conformational space with an auxiliary Markov process that enables interconversions between charge microstates along a mesostate. Proton walk sampling helps identify the most likely charge microstate per mesostate. We then use thermodynamic integration aided by the multistate Bennett acceptance ratio method to estimate the free energies for converting between mesostates. These free energies are then combined with the per-microstate weights along each mesostate to estimate standard state free energies and pH-dependent free energies for all thermodynamically relevant charge microstates. The results provide quantitative estimates of the probabilities and preferred conformations associated with every thermodynamically accessible charge microstate. We showcase the application of q-canonical sampling using two model systems. The results establish the soundness of the method and the importance of charge regulation in systems characterized by conformational heterogeneity.
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Affiliation(s)
- Martin J. Fossat
- Department of Biomedical Engineering and Center for Science & Engineering of Living Systems (CSELS), Washington University in St. Louis, One Brookings Drive, Campus Box 1097, St. Louis, MO 63130
| | - Rohit V. Pappu
- Department of Biomedical Engineering and Center for Science & Engineering of Living Systems (CSELS), Washington University in St. Louis, One Brookings Drive, Campus Box 1097, St. Louis, MO 63130
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Sakipov SN, Flores-Canales JC, Kurnikova MG. A Hierarchical Approach to Predict Conformation-Dependent Histidine Protonation States in Stable and Flexible Proteins. J Phys Chem B 2019; 123:5024-5034. [PMID: 31095377 DOI: 10.1021/acs.jpcb.9b00656] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
Abstract
Solution acidity measured by pH is an important environmental factor that affects protein structure. It influences the protonation state of protein residues, which in turn may be coupled to protein conformational changes, unfolding, and ligand binding. It remains difficult to compute and measure the p Ka of individual residues, as well as to relate them to pH-dependent protein transitions. This paper presents a hierarchical approach to compute the p Ka of individual protonatable residues, specifically histidines, coupled with underlying structural changes of a protein. A fast and efficient free energy perturbation (FEP) algorithm has also been developed utilizing a fast implementation of standard molecular dynamics (MD) algorithms. Specifically, a CUDA version of the AMBER MD engine is used in this paper. Eight histidine p Ka's are computed in a diverse set of pH stable proteins to demonstrate the proposed approach's utility and assess the predictive quality of the AMBER FF99SB force field. A reference molecule is carefully selected and tested for convergence. A hierarchical approach is used to model p Ka's of the six histidine residues of the diphtheria toxin translocation domain (DTT), which exhibits a diverse ensemble of individual conformations and pH-dependent unfolding. The hierarchical approach consists of first sampling equilibrium conformational ensembles of a protein with protonated and neutral histidine residues via long equilibrium MD simulations (Flores-Canales, J. C.; et al. bioRxiv, 2019, 572040). A clustering method is then used to identify sampled protein conformations, and p Ka's of histidines in each protein conformation are computed. Finally, an ensemble averaging formalism is developed to compute weighted average histidine p Ka's. These can be compared with an apparent experimentally measured p Ka of the DTT protein and thus allows us to propose a mechanism of pH-dependent unfolding of the DTT protein.
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Affiliation(s)
- Serzhan N Sakipov
- Chemistry Department , Carnegie Mellon University , Pittsburgh , Pennsylvania 15213 , United States
| | - Jose C Flores-Canales
- Chemistry Department , Carnegie Mellon University , Pittsburgh , Pennsylvania 15213 , United States
| | - Maria G Kurnikova
- Chemistry Department , Carnegie Mellon University , Pittsburgh , Pennsylvania 15213 , United States
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Zänker H, Heine K, Weiss S, Brendler V, Husar R, Bernhard G, Gloe K, Henle T, Barkleit A. Strong Uranium(VI) Binding onto Bovine Milk Proteins, Selected Protein Sequences, and Model Peptides. Inorg Chem 2019; 58:4173-4189. [PMID: 30860361 DOI: 10.1021/acs.inorgchem.8b03231] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Abstract
Hexavalent uranium is ubiquitous in the environment. In view of the chemical and radiochemical toxicity of uranium(VI), a good knowledge of its possible interactions in the environment is crucial. The aim of this work was to identify typical binding and sorption characteristics of uranium(VI) with both the pure bovine milk protein β-casein and diverse related protein mixtures (caseins, whey proteins). For comparison, selected model peptides representing the amino acid sequence 13-16 of β-casein and dephosphorylated β-casein were also studied. Complexation studies using potentiometric titration and time-resolved laser-induced fluorescence spectroscopy revealed that the phosphoryl-containing proteins form uranium(VI) complexes of higher stability than the structure-analog phosphoryl-free proteins. That is in agreement with the sorption experiments showing a significantly higher affinity of caseins toward uranium(VI) in comparison to whey proteins. On the other hand, the total sorption capacity of caseins is lower than that of whey proteins. The discussed binding behavior of milk proteins to uranium(VI) might open up interesting perspectives for sustainable techniques of uranium(VI) removal from aqueous solutions. This was further demonstrated by batch experiments on the removal of uranium(VI) from mineral water samples.
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Affiliation(s)
- Harald Zänker
- Institute of Resource Ecology , Helmholtz-Zentrum Dresden-Rossendorf , Bautzner Landstraße 400 , 01328 Dresden , Germany
| | - Katja Heine
- Institute of Resource Ecology , Helmholtz-Zentrum Dresden-Rossendorf , Bautzner Landstraße 400 , 01328 Dresden , Germany.,Faculty of Chemistry and Food Chemistry , Technische Universität Dresden , 01062 Dresden , Germany
| | - Stephan Weiss
- Institute of Resource Ecology , Helmholtz-Zentrum Dresden-Rossendorf , Bautzner Landstraße 400 , 01328 Dresden , Germany
| | - Vinzenz Brendler
- Institute of Resource Ecology , Helmholtz-Zentrum Dresden-Rossendorf , Bautzner Landstraße 400 , 01328 Dresden , Germany
| | - Richard Husar
- Institute of Resource Ecology , Helmholtz-Zentrum Dresden-Rossendorf , Bautzner Landstraße 400 , 01328 Dresden , Germany
| | - Gert Bernhard
- Institute of Resource Ecology , Helmholtz-Zentrum Dresden-Rossendorf , Bautzner Landstraße 400 , 01328 Dresden , Germany
| | - Karsten Gloe
- Faculty of Chemistry and Food Chemistry , Technische Universität Dresden , 01062 Dresden , Germany
| | - Thomas Henle
- Faculty of Chemistry and Food Chemistry , Technische Universität Dresden , 01062 Dresden , Germany
| | - Astrid Barkleit
- Institute of Resource Ecology , Helmholtz-Zentrum Dresden-Rossendorf , Bautzner Landstraße 400 , 01328 Dresden , Germany
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