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polymer physics amphiphilic systems rod-like colloids reaction rates
alpha-synuclein clathrin

Reaction Rates

The isomerization reaction of calix[4]arene (see picture) involves the rotation of one phenol group around the two methyl "hinges" by which it is connected to two neighbouring phenol groups. This process takes about a picosecond, and hence lies well within the timescale of molecular dynamics simulations. But these isomerizations are rare events, they occur just once every ~10 millisecond, which makes it impossible to calculate the equilibrium constant and reaction rate by conventional molecular dynamics simulations. A calix[4]arene in the partial cone (paco) conformation

reactive flux method

By combining simulations with statistical mechanics, it nevertheless proves possible to study reactions within the ~100 nanosecond timescale of molecular dynamics. The central idea in the reactive flux method is to express the rate as the product of i) the probability for a molecule in the reactant state to reach the transition state, and ii) the probability of this activated molecule to proceed to the product state. The former is calculated by free energy techniques, like umbrella sampling or the constraint methods developed in our group [1-3]. The second probability follows from relaxation runs starting at the transition state.

solvent effects

The calculated rates of 36 and 264 per second for calix[4]arenes in chloroform and benzene, respectively, are in good agreement with NMR measurements [4]. The isomerisation of p-tert-butyl-calix[4]arene, in which the hydrogens opposite the hydroxyl groups have been replaced by C(CH3)3, is considerably more complicated. With these bulky side groups, the calix acquires four 'doors' surrounding a central 'cargo bay'. A solvent molecule or a 'payload' arrested in this cavity will drastically change the conformational behaviour [5].

The free energy methods used here are a recurring theme in the research of the computational biophysics group. They are also intensively used in our study of pores in lipid membranes.

selected publications

1 The calculation of free energy differences by constrained molecular dynamics simulations
W.K. den Otter and W.J.Briels
J. Chem. Phys. 109, 4139 (1998)
2 Thermodynamic integration of the free energy along a reaction coordinate in Cartesian coordinates
W.K. den Otter
J. Chem. Phys. 112, 7283 (2000)
3 Free energy from molecular dynamics with multiple constraints
W.K. den Otter and W.J. Briels
Mol. Phys. 98, 773 (2000)
4 Solvent effect on the isomerization rate of calix(4)arene studied by molecular dynamics simulations
W.K. den Otter and W.J.Briels
J. Am. Chem. Soc. 120, 13167 (1998)
5 Impact of the solvent on the conformational isomerism of calix[4]arenes: a study based on continuum solvation models
C. Aleman, W.K. den Otter, T.V. Tolpekina and W.J. Briels
J. Org. Chem. 69, 951 (2004)