Biomedical subjects

Piotr Cieplak

Publications and source records attributed to Piotr Cieplak.

10 recordsLinked to original sources

PubMed2025

CaXML: Chemistry-informed machine learning explains mutual changes between protein conformations and calcium ions in calcium-binding proteins using structural and topological features.

Proteins' flexibility is a feature in communicating changes in cell signaling instigated by binding with secondary messengers, such as calcium ions, associated with the coordination of muscle contraction, neurotransmitter release, and gene expression. When binding with the disordered parts of a protein, calcium ions must balance their charge states with the shape of calcium-binding proteins and their versatile pool of partners depending on the circumstances they transmit. Accurately determining the ionic charges of those ions is essential for understanding their role in such processes. However, it is unclear whether the limited experimental data available can be effectively used to train models to accurately predict the charges of calcium-binding protein variants. Here, we developed a chemistry-informed, machine-learning algorithm that implements a game theoretic approach to explain the output of a machine-learning model without the prerequisite of an excessively large database for high-performance prediction of atomic charges. We used the ab initio electronic structure data representing calcium ions and the structures of the disordered segments of calcium-binding peptides with surrounding water molecules to train several explainable models. Network theory was used to extract the topological features of atomic interactions in the structurally complex data dictated by the coordination chemistry of a calcium ion, a potent indicator of its charge state in protein. Our design created a computational tool of CaXML, which provided a framework of explainable machine learning model to annotate ionic charges of calcium ions in calcium-binding proteins in response to the chemical changes in an environment. Our framework will provide new insights into protein design for engineering functionality based on the limited size of scientific data in a genome space.

Machine Learning↗

PubMed2006

New-generation amber united-atom force field.

We have developed a new-generation Amber united-atom force field for simulations involving highly demanding conformational sampling such as protein folding and protein-protein binding. In the new united-atom force field, all hydrogens on aliphatic carbons in all amino acids are united with carbons except those on Calpha. Our choice of explicit representation of all protein backbone atoms aims at minimizing perturbation to protein backbone conformational distributions and to simplify development of backbone torsion terms. Tests with dipeptides and solvated proteins show that our goal is achieved quite successfully. The new united-atom force field uses the same new RESP charging scheme based on B3LYP/cc-pVTZ//HF/6-31g** quantum mechanical calculations in the PCM continuum solvent as that in the Duan et al. force field. van der Waals parameters are empirically refitted starting from published values with respect to experimental solvation free energies of amino acid side-chain analogues. The suitability of mixing new point charges and van der Waals parameters with existing Amber covalent terms is tested on alanine dipeptide and is found to be reasonable. Parameters for all new torsion terms are refitted based on the new point charges and the van der Waals parameters. Molecular dynamics simulations of three small globular proteins in the explicit TIP3P solvent are performed to test the overall stability and accuracy of the new united-atom force field. Good agreements between the united-atom force field and the Duan et al. all-atom force field for both backbone and side-chain conformations are observed. In addition, the per-step efficiency of the new united-atom force field is demonstrated for simulations in the implicit generalized Born solvent. A speedup around two is observed over the Duan et al. all-atom force field for the three tested small proteins. Finally, the efficiency gain of the new united-atom force field in conformational sampling is further demonstrated with a well-known toy protein folding system, an 18 residue polyalanine in distance-dependent dielectric. The new united-atom force field is at least a factor of 200 more efficient than the Duan et al. all-atom force field for ab initio folding of the tested peptide.

Models, Molecular↗

PubMed2006

Strike a balance: optimization of backbone torsion parameters of AMBER polarizable force field for simulations of proteins and peptides.

Based on the AMBER polarizable model (ff02), we have re-optimized the parameters related to the main-chain (Phi, Psi) torsion angles by fitting to the Boltzmann-weighted average quantum mechanical (QM) energies of the important regions (i.e., beta, P(II), alpha(R), and alpha(L) regions). Following the naming convention of the AMBER force field series, this release will be called ff02pol.rl The force field has been assessed both by energetic comparison against the QM data and by the replica exchange molecular dynamics simulations of short alanine peptides in water. For Ace-Ala-Nme, the simulated populations in the beta, P(II) and alpha(R) regions were approximately 30, 43, and 26%, respectively. For Ace-(Ala)(7)-Nme, the populations in these three regions were approximately 24, 49, and 26%. Both were in qualitative agreement with the NMR and CD experimental conclusions. In comparison with the previous force field, ff02pol.rl demonstrated good balance among these three important regions. The optimized torsion parameters, together with those in ff02, allow us to carry out simulations on proteins and peptides with the consideration of polarization.

Computer Simulation↗

PubMed2006

Molecular basis for the Cu2+ binding-induced destabilization of beta2-microglobulin revealed by molecular dynamics simulation.

According to experimental data, binding of the Cu(2+) ions destabilizes the native state of beta2-microglobulin (beta2m). The partial unfolding of the protein was generally considered an early step toward fibril formation in dialysis-related amyloidosis. Recent NMR studies have suggested that the destabilization of the protein might be achieved through increased flexibility upon Cu(2+) binding. However, the molecular mechanism of destabilization due to Cu(2+), its role in amyloid formation, and the relative contributions of different potential copper-binding sites remain unclear. To elucidate the effect of ion ligation at atomic detail, a series of molecular dynamics simulations were carried out on apo- and Cu(2+)-beta2m systems in explicit aqueous solutions, with varying numbers of bound ions. Simulations at elevated temperatures (360 K) provide detailed pictures for the process of Cu(2+)-binding-induced destabilization of the native structure at the nanosecond timescale, which are in agreement with experiments. Conformational transitions toward partially unfolded states were observed in protein solutions containing bound copper ions at His-31 and His-51, which is marked by an increase in the protein vibrational entropy, with TDeltaS(vibr) ranging from 30 to 69 kcal/mol. The binding of Cu(2+) perturbs the secondary structure and the hydrogen bonding pattern disrupts the native hydrophobic contacts in the neighboring segments, which include the beta-strand D2 and part of the beta-strand E, B, and C and results in greater exposure of the D-E loop and the B-C loop to the water environment. Analysis of the MD trajectories suggests that the changes in the hydrophobic environment near the copper-binding sites lower the barrier of conformational transition and stabilize the more disordered conformation. The results also indicate that the binding of Cu(2+) at His-13 has little effect on the conformational stability, whereas the copper-binding site His-31, and to a lesser extent His-51, are primarily responsible for the observed changes in the protein conformation and dynamics.

Cations, Divalent↗

PubMed2005

5,10-Methylene-5,6,7,8-tetrahydrofolate conformational transitions upon binding to thymidylate synthase: molecular mechanics and continuum solvent studies.

We applied the molecular mechanics Poisson-Boltzmann surface area (MM-PBSA) approach to evaluate relative stability of the extended (flat) and C-shaped (bent) solution conformational forms of the 5,10-methylene-5,6,7,8-tetrahydrofolate (mTHF) molecule in aqueous solution. Calculations indicated that both forms have similar free energies in aqueous solution but detailed energy components are different. The bent solution form has lower intramolecular electrostatic and van der Waals interaction energies. The flat form has more favorable solvation free energy and lower contribution from the bond, angle and torsion angle molecular mechanical internal energies. We exploit these results and combine them with known crystallographic data to provide a model for the progressive binding of the mTHF molecule, a natural cofactor of thymidylate synthase (TS), to the complex forming in the TS-catalyzed reaction. We propose that at the time of initial weak binding in the open enzyme the cofactor molecule remains in a close balance between the flat and bent solution conformations, with neither form clearly favored. Later, thymidylate synthase undergoes conformational change leading to the closure of the active site and the mTHF molecule is withdrawn from the solvent. That effect shifts the thermodynamic equilibrium of the mTHF molecule toward the bent solution form. At the same time, burying the cofactor molecule in the closed active site produces numerous contacts between mTHF and protein that render change in the shape of the mTHF molecule. As a result, the bent solution conformer is converted to more strained L-shaped bent enzyme conformer of the mTHF molecule. The strain in the bent enzyme conformation allows for the tight binding of the cofactor molecule to the productive ternary complex that forms in the closed active site, and facilitates the protonation of the imidazolidine N10 atom, which promotes further reaction.

Hydrogen Bonding↗

PubMed2003

A point-charge force field for molecular mechanics simulations of proteins based on condensed-phase quantum mechanical calculations.

Molecular mechanics models have been applied extensively to study the dynamics of proteins and nucleic acids. Here we report the development of a third-generation point-charge all-atom force field for proteins. Following the earlier approach of Cornell et al., the charge set was obtained by fitting to the electrostatic potentials of dipeptides calculated using B3LYP/cc-pVTZ//HF/6-31G** quantum mechanical methods. The main-chain torsion parameters were obtained by fitting to the energy profiles of Ace-Ala-Nme and Ace-Gly-Nme di-peptides calculated using MP2/cc-pVTZ//HF/6-31G** quantum mechanical methods. All other parameters were taken from the existing AMBER data base. The major departure from previous force fields is that all quantum mechanical calculations were done in the condensed phase with continuum solvent models and an effective dielectric constant of epsilon = 4. We anticipate that this force field parameter set will address certain critical short comings of previous force fields in condensed-phase simulations of proteins. Initial tests on peptides demonstrated a high-degree of similarity between the calculated and the statistically measured Ramanchandran maps for both Ace-Gly-Nme and Ace-Ala-Nme di-peptides. Some highlights of our results include (1) well-preserved balance between the extended and helical region distributions, and (2) favorable type-II poly-proline helical region in agreement with recent experiments. Backward compatibility between the new and Cornell et al. charge sets, as judged by overall agreement between dipole moments, allows a smooth transition to the new force field in the area of ligand-binding calculations. Test simulations on a large set of proteins are also discussed.

Algorithms↗

PubMed2003

Relative free energies of binding to thymidylate synthase of 2- and/or 4-thio and/or 5-fluoro analogues of dUMP.

Free energy perturbation calculations have been applied to evaluate the relative free energies of binding of 2'-deoxyuridine-5'-monophosphate (dUMP) and its 2- and/or 4-thio and/or 5-fluoro analogues to the wild-type E. coli thymidylate synthase (ecTS). The results accurately reproduce experimentally measured differences in the free energy of binding of dUMP versus 5-fluoro-dUMP to thymidylate synthase. They indicate that preferred binding of dUMP compared to 5-fluoro-dUMP in the binary complex is equally related to (i) more favorable electrostatic interactions of the dUMP molecule in the enzyme active site, and (ii) its less favorable solvation in the aqueous solution. The relative free energies of binding in the binary complex show moderate and qualitatively indistinguishable discrimination among the studied fluorinated and non-fluorinated 2- and/or 4-thio analogues of dUMP. The binding free energies of monothio analogues of dUMP and 5-fluoro-dUMP correspond quite well with experimentally measured activities of these nucleotides in the thymidylate synthase reaction. On the other hand, the binding free energies of both dithio analogues, 2,4-dithio-dUMP and 2,4-dithio-FdUMP, show lack of such correlation. The latter suggests that very low activities of the dithio analogues of dUMP and 5-fluoro-dUMP may relate more to the covalent reaction of these nucleotides within the ternary complex with TS and 5,10-methylenetetrahydrofolate, than to their pre-covalent binding. We speculate that a lack of substrate activity of 2,4-dithio-dUMP is related to the high aromaticity of its pyrimidine ring that prevents the Michael addition of the active site cysteine thiol to the pyrimidine C6 atom. A stronger affinity of the fluorinated analogues of dUMP to thymidylate synthase, compared to the non-fluorinated congeners, results from the fluorine substituent producing a local strain in the C6 region in the pyrimidine ring, thus sensitizing C6 to the Michael addition of the cysteine thiol.

Binding Sites↗

PubMed2002

Molecular dynamics and free energy analyses of cathepsin D-inhibitor interactions: insight into structure-based ligand design.

In this study, we compare the calculated and experimental binding free energies for a combinatorial library of inhibitors of cathepsin D (CatD), an aspartyl protease. Using a molecular dynamics (MD)-based, continuum solvent method (MM-PBSA), we are able to reproduce the experimental binding affinity for a set of seven inhibitors with an average error of ca. 1 kcal/mol and a correlation coefficient of 0.98. By comparing the dynamical conformations of the inhibitors complexed with CatD with the initial conformations generated by CombiBuild (University of California, San Francisco, CA, 1995), we have found that the docking conformation observed in an X-ray structure of one peptide inhibitor bound to CatD (Proc. Natl. Acad. Sci. U.S.A. 1993, 90, 6796-6800) is in good agreement with our MD simulation. However, the DOCK scoring function, based on intermolecular van der Waals and electrostatics, using a distance-dependent dielectric constant (J. Comput. Chem. 1992, 13, 505-524), poorly reproduces the trend of experimental binding affinity for these inhibitors. Finally, the use of PROFEC (J. Comput.-Aided Mol. Des. 1998, 12, 215-227) analysis allowed us to identify two possible substitutions to improve the binding of one of the better inhibitors to CatD. This study offers hope that current methods of estimating the free energy of binding are accurate enough to be used in a multistep virtual screening protocol.

Algorithms↗

PubMed2002

Theoretical calculation of the coiled-coil stability in water in the context of its possible use as a molecular rack.

The coiled-coil stability and rigidity may be of importance for molecular electronics (electronically bistable molecules). The coiled-coil binding free energy has been calculated using molecular dynamics (MD). The energy has been computed as a difference of the appropriate free energies; derived for the coiled-coil and isolated alpha-helices separately. All MD simulations have been performed using an explicit model of the solvent, whereas the continuum solvent approach has been applied to analyze the MD trajectories. The computed stability of the coiled-coil is of the order of -87 kcal/mol, i.e., about -1.2 kcal/mol per amino acid residue, and arises mainly from the electrostatic interactions and hydrophobic effect. The entropy term has been roughly estimated to be of the order of -22 kcal/mol. This assures that coiled-coil polypeptides may be used as a stable molecular scaffolding.

Amino Acid Sequence↗

PubMed1996

Elucidating the Origin of Conformational Energy Differences in Substituted 1,3-Dioxanes: A Combined Theoretical and Experimental Study.

13C NMR spectroscopy, ab initio quantum mechanics, and molecular mechanics have been used to investigate the trans-4-(trifluoromethyl)-2,2,6-trimethyl-1,3-dioxane chair/twist-boat equilibrium. The molecular mechanics calculations were based upon the MM3 and AMBER force fields. A 6-31G basis set was used for the ab initio calculations, and MP2 correlation corrections were applied. Both the ab initio and AMBER molecular mechanics calculations are consistent with the (13)C NMR chemical shift differences for the trans-4-(trifluoromethyl)-2,2,6-trimethyl-1,3-dioxane conformers. The predicted chair to twist-boat equilibrium suggested by the MM3 calculations is not consistent with the experimental data. These results support the suggestion by Howard et al. (Howard, A. E.; Cieplak, P.; Kollman, P. A. J. Comput.Chem. 1995, 16, 243-261) on the critical role of electrostatic interactions in determining the chair/twist-boat equilibrium.

Journal Article↗