Constraint methods for determining pathways and free energy of activated processes

Activated processes from chemical reactions up to conformational transitions of large biomolecules are hampered by barriers which are overcome only by the input of some free energy of activation. Hence, the characteristic and rate-determining barrier regions are not sufficiently sampled by usual simulation techniques. Constraints on a reaction coordinate r have turned out to be a suitable means to explore difficult pathways without changing potential function, energy or temperature. For a dense sequence of values of r, the corresponding sequence of simulations provides a pathway for the process. As only one coordinate among thousands is fixed during each simulation, the pathway essentially reflects the system's internal dynamics. From mean forces the free energy profile can be calculated to obtain reaction rates and insight in the reaction mechanism. In the last decade, theoretical tools and computing capacity have been developed to a degree where simulations give impressive qualitative insight in the processes at quantitative agreement with experiments. Here, we give an introduction to reaction pathways and coordinates, and develop the theory of free energy as the potential of mean force. We clarify the connection between mean force and constraint force which is the central quantity evaluated, and discuss the mass metric tensor correction. Well-behaved coordinates without tensor correction are considered. We discuss the theoretical background and practical implementation on the example of the reaction coordinate of targeted molecular dynamics simulation. Finally, we compare applications of constraint methods and other techniques developed for the same purpose, and discuss the limits of the approach

Allosteric effects in cyclophilin mutants may be explained by changes in nano-microsecond time scale motions

The relationship between molecular motion and catalysis in enzymes is debated. Here, simulations of cyclophilin A and three catalytically-impaired mutants reveal a nanosecond-scale interconversion between active and inactive conformations, orders of magnitude faster than previously suggested

Mechanism of Action of Cyclophilin A Explored by Metadynamics Simulations

Trans/cis prolyl isomerisation is involved in several biological processes, including the development of numerous diseases. In the HIV-1 capsid protein (CA), such a process takes place in the uncoating and recruitment of the virion and is catalyzed by cyclophilin A (CypA). Here, we use metadynamics simulations to investigate the isomerization of CA's model substrate HAGPIA in water and in its target protein CypA. Our results allow us to propose a novel mechanistic hypothesis, which is finally consistent with all of the available molecular biology data

Convergence of Free Energy Profile of Coumarin in Lipid Bilayer

Atomistic molecular dynamics (MD) simulations of druglike molecules embedded in lipid bilayers are of considerable interest as models for drug penetration and positioning in biological membranes. Here we analyze partitioning of coumarin in dioleoylphosphatidylcholine (DOPC) bilayer, based on both multiple, unbiased 3 μs MD simulations (total length) and free energy profiles along the bilayer normal calculated by biased MD simulations (∼7 μs in total). The convergences in time of free energy profiles calculated by both umbrella sampling and z-constraint techniques are thoroughly analyzed. Two sets of starting structures are also considered, one from unbiased MD simulation and the other from “pulling” coumarin along the bilayer normal. The structures obtained by pulling simulation contain water defects on the lipid bilayer surface, while those acquired from unbiased simulation have no membrane defects. The free energy profiles converge more rapidly when starting frames from unbiased simulations are used. In addition, z-constraint simulation leads to more rapid convergence than umbrella sampling, due to quicker relaxation of membrane defects. Furthermore, we show that the choice of RESP, PRODRG, or Mulliken charges considerably affects the resulting free energy profile of our model drug along the bilayer normal. We recommend using z-constraint biased MD simulations based on starting geometries acquired from unbiased MD simulations for efficient calculation of convergent free energy profiles of druglike molecules along bilayer normals. The calculation of free energy profile should start with an unbiased simulation, though the polar molecules might need a slow pulling afterward. Results obtained with the recommended simulation protocol agree well with available experimental data for two coumarin derivatives

Insuffisance rénale chronique et érythropoïétines (une stratégie marketing de leadership)

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