Through the Channel and around the Channel:  Validating and Comparing Microscopic Approaches for the Evaluation of Free Energy Profiles for Ion Penetration through Ion Channels

Kato, Mitsunori; Warshel, Arieh

doi:10.1021/jp053208l

Cited by 44 publications

(81 citation statements)

References 51 publications

(78 reference statements)

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“…We view these PMFs Figure 5 and the calculated changes in the total reorganization energies (∆∆λ). The correlation coefficient (R 2 ) for the linear regression is 0.8062. as preliminary results due to the well-known convergence problems associated with evaluation of PMF for large displacements (51). Thus we consider the work function as the free energy needed to bring the donor acceptor distance from either the minimum or the point with lowest energy (in the range of up to 4 Å) to 3 Å.…”

Section: Resultsmentioning

confidence: 99%

“…In the case of charge-transfer reaction, the PMF that uses only the solute coordinates involves significant hysteresis (see ref 51) while approaches that emphasize the charging coordinates (by using a mapping potential that changes the solute charges) are more reliable. Furthermore, as emphasized in our previous studies (e.g., refs 49 and 50), the EVB approaches capture the contribution of nonequilibrium effects to the barrier.…”

Section: Methodsmentioning

confidence: 99%

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The Catalytic Effect of Dihydrofolate Reductase and Its Mutants Is Determined by Reorganization Energies

2007

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The effect of distant mutations on the catalytic reaction of dihydrofolate reductase (DHFR) is reexamined by empirical valence bond simulations. The simulations reproduce for the first time the changes in the observed rate constants (without the use of adjustable parameters for this purpose) and show that the changes in activation barriers are strongly correlated with the corresponding changes in the reorganization energy. The preorganization of the polar groups of enzymes is the key catalytic factor, and anticatalytic mutations destroy this preorganization. Some anticatalytic mutations in DHFR also increase the distance between the donor and acceptor, but this effect is not directly related to catalysis since the native enzyme and the uncatalyzed reaction in water have similar average donor-acceptor distances. Insight into the effect of a mutation is provided by constructing the relevant free energy surfaces in terms of the generalized solute-solvent coordinates. It is shown how the mutations change the reaction coordinate and the activation barrier, and it is clarified that the corresponding changes do not reflect dynamical effects. It is also pointed out that all reactions in a condensed phase involve correlated motions (both in enzymes and in solution) and that the change of such motions upon mutations is a result of the change in the shape of the multidimensional reaction path on the solute-solvent surface, rather than the reason for the change in rate constant. Thus, as far as catalysis is concerned, the change in the activation barrier is due to the change in the electrostatic preorganization energy.

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Section: Resultsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

The Catalytic Effect of Dihydrofolate Reductase and Its Mutants Is Determined by Reorganization Energies

2007

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“…Using m and the FEP/ US approach, we sort the system in two dimensions (X 1 ) R g ; X 2 ) rmsd) rather than in one dimension as in ref 38.…”

Section: Exploring the Changes In The Folding Landscapementioning

confidence: 99%

On the Relationship between Thermal Stability and Catalytic Power of Enzymes

et al. 2007

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The possible relationship between the thermal stability and the catalytic power of enzymes is of great current interest. In particular, it has been suggested that thermophilic or hyperthermophilic (Tm) enzymes have lower catalytic power at a given temperature than the corresponding mesophilic (Ms) enzymes, because the thermophilic enzymes are less flexible (assuming that flexibility and catalysis are directly correlated). These suggestions presume that the reduced dynamics of the thermophilic enzymes is the reason for their reduced catalytic power. The present paper takes the specific case of dihydrofolate reductase (DHFR) and explores the validity of the above argument by simulation approaches. It is found that the Tm enzymes have restricted motions in the direction of the folding coordinate, but this is not relevant to the chemical process, since the motions along the reaction coordinate are perpendicular to the folding motions. Moreover, it is shown that the rate of the chemical reaction is determined by the activation barrier and the corresponding reorganization energy, rather than by dynamics or flexibility in the ground state. In fact, as far as flexibility is concerned, we conclude that the displacement along the reaction coordinate is larger in the Tm enzyme than in the Ms enzyme and that the general trend in enzyme catalysis is that the best catalyst involves less motion during the reaction than the less optimal catalyst. The relationship between thermal stability and catalysis appears to reflect the fact that to obtain small electrostatic reorganization energy it is necessary to invest some folding energy in the overall preorganization process. Thus, the optimized catalysts are less stable. This trend is clearly observed in the DHFR case.

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“…However, the PMF approach does not quantify absolute solvation energies of ligand, which makes it difficult to detect potential problems in treatment of long-range effect and boundary conditions (7,8). A comparison of PMF and FEP in ion channel study indicated the former suffered more seriously from hysteresis (9). Alternatives to free-energy pathway calculations include linear response analysis (LRA) (10) and linear interaction energy (LIE) (11), where only the ligand-bound and unbound states are simulated.…”

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confidence: 99%

Calculation of protein–ligand binding free energy by using a polarizable potential

Jiao

Golubkov

Darden

et al. 2008

Proc. Natl. Acad. Sci. U.S.A.

237

264

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The binding of charged ligands benzamidine and diazamidine to trypsin was investigated by using a polarizable potential energy function and explicit-water molecular dynamics simulations. The binding free energies were computed from the difference between the free energies of decoupling the ligand from water and protein environments. Both the absolute and the relative free energies from the perturbation simulations agree with experimental measurements to within 0.5 kcal⅐mol ؊1 . Comparison of free-energy components sampled from different thermodynamic paths indicates that electrostatics is the main driving force behind benzamidine recognition of trypsin. The contribution of electronic polarization to binding appears to be crucial. By computing the free-energy contribution caused by the polarization between the ligand and its surroundings, we found that polarization has the opposite effect in dissimilar environments. Although polarization favors ligand solvation in water, it weakens the protein-ligand attraction by screening the electrostatic interaction between trypsin and benzamidine. We also examined the relative binding free energies of a benzamidine analog diazamidine to trypsin. The changes in free energy on benzamidine-diazamidine substitution were tens of kilocalories in both water and trypsin environments; however, the change in the total binding free energy is <2 kcal⅐mol ؊1 because of cancellation, consistent with the experimental results. Overall, our results suggest that the use of a polarizable force field, given adequate sampling, is capable of achieving chemical accuracy in molecular simulations of protein-ligand recognition.simulation ͉ molecular dynamics ͉ trypsin ͉ benzamidine ͉ force field S pecific recognition of ligands by proteins is at the core of many crucial biological functions and systems such as enzyme catalysis and intracellular signaling. Binding affinity characterizes the strength of such recognition. With the recent advancements in computing, prediction of the binding affinity based on physical principles of molecular interaction has come to the forefront of active research and has been the subject of regular reviews (1-5). All-atom molecular dynamics (MD) simulation with explicit solvent, coupled with efficient free-energy sampling algorithms, can potentially offer accurate prediction of binding free energies of ligands to proteins (5). Common free-energy simulation algorithms include the double-decoupling method (DDM) and potential of mean force approach (PMF). Free-energy perturbation (FEP), thermodynamic integration (TI), or umbrella sampling can be used to compute free-energy differences in either DDM or PMF. It has been argued that DDM is problematic for charged systems, because the binding free energy is computed as a small difference between two large solvation energies in water and in protein (6). However, the PMF approach does not quantify absolute solvation energies of ligand, which makes it difficult to detect potential problems in treatment of long-range effect and bou...

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Through the Channel and around the Channel: Validating and Comparing Microscopic Approaches for the Evaluation of Free Energy Profiles for Ion Penetration through Ion Channels

Cited by 44 publications

References 51 publications

The Catalytic Effect of Dihydrofolate Reductase and Its Mutants Is Determined by Reorganization Energies

The Catalytic Effect of Dihydrofolate Reductase and Its Mutants Is Determined by Reorganization Energies

On the Relationship between Thermal Stability and Catalytic Power of Enzymes

Calculation of protein–ligand binding free energy by using a polarizable potential

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