Berendsen method

The Berendsen method utilizes weak coupling of an external tensorial... 

The force field parameters for simulation of amphiphilic fatty ollgoethers obtained from the quanmm mechanics calculations were tested by comparing a computed set of thermodynamic properties with available experimental data. In the current study the validity of the parameters was demonstrated with atomistic MD simulations of diethyl ether (M(CH3)) in gas and liquid phase and in aqueous solution. The gas phase was represented by one molecule M(CH3) in vacuum. The liquid was modeled with 144 molecules of diethyl ether randomly distributed in a cubic periodic box. The dimensions of the box were chosen to ensure mass density of the liquid close to the experimental value at the same temperature - 0.714g/cm. The solution comprised one M(CH3) molecule immersed in a sufficient amount of water. Both the liquid and the solution were simulated by placing the repeating units in periodic boundary conditions. All simulations were performed with the force field parm 99 [21] appended with the derived MM parameters for the ether fragment in NPT ensemble at 300 K and 1 atm for the periodic calculations. The Berendsen method [22] was applied for the temperature and pressure couplings. 

Berendsen, H.J.C., Mavri, J. Quantum dynamics simulation of a small quantum system embedded in a classical environment. In Quantum mechanical simulation methods for studying biological systems, D. Bicout and M. Field, eds. Springer, Berlin (1996) 157-179. 

Hayward, S., Kitao, A., Berendsen, H.J.C. Model-free methods to analyze domain motions in proteins from simulation A comparison of normal mode analysis and molecular dynamics simulation of lysozyme. Proteins 27 (1997) 425-437. 

The most commonly used method for applying constraints, particularly in molecula dynamics, is the SHAKE procedure of Ryckaert, Ciccotti and Berendsen [Ryckaert et a 1977]. In constraint dynamics the equations of motion are solved while simultaneous satisfying the imposed constraints. Constrained systems have been much studied in classics mechanics we shall illustrate the general principles using a simple system comprising a bo sliding down a frictionless slope in two dimensions (Figure 7.8). The box is constrained t remain on the slope and so the box s x and y coordinates must always satisfy the equatio of the slope (which we shall write as y = + c). If the slope were not present then the bo... 

An early application of the free energy perturbation method was the determination of t] tree energy required to create a cavity in a solvent. Postma, Berendsen and Haak determin the free energy to create a cavity (A = 1) in pure water (A = 0) using isothermal-isobai... 

The simplest method that keeps the temperature of a system constant during an MD simulation is to rescale the velocities at each time step by a factor of (To/T) -, where T is the current instantaneous temperature [defined in Eq. (24)] and Tq is the desired temperamre. This method is commonly used in the equilibration phase of many MD simulations and has also been suggested as a means of performing constant temperature molecular dynamics [22]. A further refinement of the velocity-rescaling approach was proposed by Berendsen et al. [24], who used velocity rescaling to couple the system to a heat bath at a temperature Tq. Since heat coupling has a characteristic relaxation time, each velocity V is scaled by a factor X, defined as... 

An algorithm for performing a constant-pressure molecular dynamics simulation that resolves some unphysical observations in the extended system (Andersen s) method and Berendsen s methods was developed by Feller et al. [29]. This approach replaces the deterministic equations of motion with the piston degree of freedom added to the Langevin equations of motion. This eliminates the unphysical fluctuation of the volume associated with the piston mass. In addition, Klein and coworkers [30] present an advanced constant-pressure method to overcome an unphysical dependence of the choice of lattice in generated trajectories. 

In an early work by Mertz and Pettitt, an open system was devised, in which an extended variable, representing the extent of protonation, was used to couple the system to a chemical potential reservoir [67], This method was demonstrated in the simulation of the acid-base reaction of acetic acid with water [67], Recently, PHMD methods based on continuous protonation states have been developed, in which a set of continuous titration coordinates, A, bound between 0 and 1, is propagated simultaneously with the conformational degrees of freedom in explicit or continuum solvent MD simulations. In the acidostat method developed by Borjesson and Hiinenberger for explicit solvent simulations [13], A. is relaxed towards the equilibrium value via a first-order coupling scheme in analogy to Berendsen s thermostat [10]. However, the theoretical basis for the equilibrium condition used in the derivation seems unclear [3], A test using the pKa calculation for several small amines did not yield HH titration behavior [13],... 

The compounds of the invention were evaluated as antipruritic agents by measuring their ability to inhibit hind leg scratching induced in rats using a known pruritogenic agent according to the method of Berendsen (1). 

Lijnzaad, P., Berendsen, H.J.C., and Argos, P. (1996). A method for detecting hydrophobic patches protein. Protein. Struct Fund. Genet. 26, 192-203. 

Constant Pressure MD. The conventional MD technique uses a fixed size for the simulation box, that is, the calculation is performed under constant volume conditions. Using methods developed by Parrinello and Rahman and by Berendsen and coworkers, it is now possible to undertake constant pressure simulations by allowing cell dimensions to vary dnring the simulation. Detailed discussions are given in Referenced . The most obvious field of application of this technique is to the study of phase transitions, and useful applications have been reported to the study of melting and glass formation as discussed below. 

In order to demonstate the power of the formalism described above we applied the scheme to a simple model system studied recently by Mavri and Berendsen with the DME method [17]. The model consists of a quantum oscillator with reduced mass p immersed in a bath of 79 argon atoms, which are treated classically. The Hamiltonian for this system takes the form... 

The Berendsen [82] and Gauss [83] thermostats are also among other methods used. The Berendsen thermostat [82] was developed starting from the Langevin formalism by eliminating the random forces and replacing the friction term with one that depends on the ratio of the desired temperature to current kinetic temperature of the system. The resulting equation of motion takes the same form as the Nose-Hoover equation with... 

The temperature may be adjusted by coupling the system to a thermal bath as described by Berendsen et al. In this method the atomic velocities are scaled (multiplied) by a factor... 

The temperature coupling method of Berendsen [57] is related to Langevin dynamics except that it does not use random forces and it applies a temperature dependent scale factor to the friction coefficient ... 

Computation was carried out using a leap-frog algorithm proposed by Fincham with a time step of 1 fs. The total run was 20 ns for the CH4 system and 14 ns for the Xe system. Temperature and pressure were kept constant at 298 K and 100 MPa, respectively, using a method proposed by Berendsen et al Details of the simulation method is given in Ref. 4. 

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