Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

We present an improved and extended version of our coarse grained lipid model. The new version, coined the MARTINI force field, is parametrized in a systematic way, based on the reproduction of partitioning free energies between polar and apolar phases of a large number of chemical compounds. To reproduce the free energies of these chemical building blocks, the number of possible interaction levels of the coarse-grained sites has increased compared to those of the previous model. Application of the new model to lipid bilayers shows an improved behavior in terms of the stress profile across the bilayer and the tendency to form pores. An extension of the force field now also allows the simulation of planar (ring) compounds, including sterols. Application to a bilayer/cholesterol system at various concentrations shows the typical cholesterol condensation effect similar to that observed in all atom representations.

/pdf/the-martini-force-field-coarse-grained-model-for-3l11ncr3fg.pdf

The MARTINI force field : Coarse grained model for biomolecular simulations

N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

https://iopscience.iop.org/article/10.1088/0031-9112/34/4/040/pdf

Stochastic Processes in Physics and Chemistry

Brownian motors: noisy transport far from equilibrium

Intermolecular And Surface Forces

We use a simple and efficient computer model to investigate the physical properties of bilayer membranes. The amphiphilic molecules are modeled as short rigid trimers with finite range pair interactions between them. The pair potentials have been designed to mimic the hydrophobic interactions, and to allow the simulation of the membranes without the embedding solvent as if the membrane is in vacuum. We find that upon decreasing the area density of the molecules the membrane undergoes a solid–fluid phase transition, where in the fluid phase the molecules can diffuse within the membrane plane. The surface tension and the bending modulus of the fluid membranes are extracted from the analysis of the spectrum of thermal undulations. At low area densities we observe the formation of pores in the membrane through which molecules can diffuse from one layer to the other. The appearance of the pores is explained using a simple model relating it to the area dependence of the free energy.

“Water-free” computer model for fluid bilayer membranes

We present a revision to the well known Stormer–Verlet algorithm for simulating second order differential equations. The revision addresses the inclusion of linear friction with associated stochastic noise, and we analytically demonstrate that the new algorithm correctly reproduces diffusive behaviour of a particle in a flat potential. For a harmonic oscillator, our algorithm provides the exact Boltzmann distribution for any value of damping, frequency and time step for both underdamped and overdamped behaviour within the usual stability limit of the Verlet algorithm. Given the structure and simplicity of the method, we conclude that this approach can trivially be adapted for contemporary applications, including molecular dynamics with extensions such as molecular constraints.

A simple and effective Verlet-type algorithm for simulating Langevin dynamics

We present a revision to the well known Stormer-Verlet algorithm for simulating second order differential equations. The revision addresses the inclusion of linear friction with associated stochastic noise, and we analytically demonstrate that the new algorithm correctly reproduces diffusive behavior of a particle in a flat potential. For a harmonic oscillator, our algorithm provides the exact Boltzmann distribution for any value of damping, frequency, and time step for both underdamped and over damped behavior within the usual the stability limit of the Verlet algorithm. Given the structure and simplicity of the method we conclude this approach can trivially be adapted for contemporary applications, including molecular dynamics with extensions such as molecular constraints.

We compare Monte Carlo simulations of knotted and unknotted polymers whose ends are connected to two parallel walls. The force f exerted on the polymer is measured as a function of the separation R between the walls. For unknotted polymers of several monomer numbers N, the product fNν is a simple function of R/Nν, where ν 0.59. By contrast, knotted polymers exhibit strong finite-size effects which can be interpreted in terms of a new length scale related to the size of the knot. Based on this interpretation, we conclude that the number of monomers forming the knot scales as Nt, with t = 0.4 ± 0.1.

Pulling knotted polymers

http://www.bgu.ac.il/%7Eofarago/cpc-gjf.pdf

Oded Farago

Papers

“Water-free” computer model for fluid bilayer membranes

A simple and effective Verlet-type algorithm for simulating Langevin dynamics

A simple and effective Verlet-type algorithm for simulating Langevin dynamics

Pulling knotted polymers

Application of the G-JF discrete-time thermostat for fast and accurate molecular simulations