Parallel Utility for Modeling of Molecular Aggregation

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1 Parallel Utility for Modeling of Molecular Aggregation Peter Spijker, Bart Markvoort and Peter Hilbers BioModeling and bioinformatics Eindhoven University of Technology Eindhoven,The Netherlands City of Hope, 8-13 March 2007

2 Overview Background History, current applications, and developers Features Potential functions Constraints Integrator Design Neighbor searching method Parallel implementation File format PumMa Toolkit Future release (major upgrade) Examples 2/41

3 History (1) Origins date back to late 1980s Initialized at University of Groningen by Peter Hilbers (Turbo Pascal) Further developed at Koninklijke Shell in early 1990s Designed as efficient parallel implementation of MD program on a torodial transputer network (ANSI C) Esselink et al., J. Comp. Phys, 106: (1993) Esselink et al., J. Comp. Phys, 106: (1993) Used to study oil surfactants solutions Smit et al., Nature, 348: (1990) Smit et al., J. Phys. Chem., 95: (1991) Smit et al., Langmuir, 9:9-11 (1993) Karaborni et al., Langmuir, 9: (1993) Karaborni et al., Science, 266: (1994) 3/41

4 History (2) In the late 1990s parallelization through MPI Group of Peter Hilbers moved to the department of Biomedical Engineering in Eindhoven in 2001 Development of PumMa reinitialized Code extended beyond its original design purposes However, original parallel design has remained Specifically designed for coarse grained simulations Initially PumMa has been used in biological simulations Markvoort et al., J. Phys. Chem. B, 109: (2005) Smeijers et al., J. Phys. Chem. B, 110: (2006) Smeijers et al., J. Phys. Chem. B, 110: (2006) Markvoort et al., J. Phys. Chem. B, 110: (2006) 4/41

5 Current applications PumMa is used in many different applications: Coarse grained simulations of biological membranes, including formation, fusion and fission. Coarse grained simulations of membrane bound proteins With City of Hope, USA (Nagarajan Vaidehi) Coarse grained simulations of dendrimer complexes With Laboratory of Macromolecular and Organic Chemistry (Bert Meijer) Simulations of flow in nanochannels used in cooling devices With Energy Technology, Thermofluids Engineering (Anton van Steenhoven) Temperature Density 5/41

6 Current developers ir. Peter Spijker dr.ir. Bart Markvoort prof.dr. Peter Hilbers 6/41

7 Overview Background History, current applications, and developers Features Potential functions Constraints Integrator Design Neighbor searching method Parallel implementation File format PumMa Toolkit Future release (major upgrade) Examples 7/41

8 Features Several potential functions Non-bonded: Lennard-Jones, Coulomb Bonded: Harmonic, cosine-harmonic, cosine series expansion Constraints Berendsen temperature and pressure coupling Simulated annealing Periodic boundary conditions Fixed atoms Integrator Verlet Leap-frog scheme Energy minimization Force fields PumMa (native) CHARMM / GROMOS 8/41

9 Potentials Van der Waals Van der Waals interactions are modeled through the well known Lennard-Jones potential: where in PumMa: Interaction strength is given pair-wise, while the collision diameter is determined from the Van der Waals radii Potential is truncated at a certain cut-off distance and shifted to remain continuous 9/41

Potentials - Electrostatic Electrostatic interactions are modeled through the Coulomb relation Interaction is truncated and shifted beyond a certain cut-off

10 Potentials - Electrostatic Electrostatic interactions are modeled through the Coulomb relation Interaction is truncated and shifted beyond a certain cut-off distance No Ewald or Multipole method is incorporated q i q j = +1 q i q j = 1 How to deal with coarse grained electrostatics? r ij 10/41

11 Potentials - Bonds Bonds are modeled by the harmonic potential Force constant can be derived from the approximation of Morse potential around its minimum harmonic Morse r ij r 0 11/41

Potentials Angles Angles can are modeled in two ways in PumMa, either harmonic or cosine harmonic Besides the functional form difference of the potentials, their

12 Potentials Angles Angles can are modeled in two ways in PumMa, either harmonic or cosine harmonic Besides the functional form difference of the potentials, their implementation in the force calculating routine is equal Urey-Bradley potential is also incorporated Angle potential routine easily extendible with new functional forms 12/41

Potentials - Dihedrals Dihedral angles are modeled by either a cosine series expansion or a harmonic function 4 The cosine expansion is used in atomistic

13 Potentials - Dihedrals Dihedral angles are modeled by either a cosine series expansion or a harmonic function 4 The cosine expansion is used in atomistic simulations; however, in coarse grained simulations this form might not be valid any more, hence the harmonic form θijkl [ ] /41

14 Potentials - Impropers Improper torsions are modeled with a harmonic potential only They are used to planarize structures aromatic rings R H N R' R H N + R' O amides O N + vs. N 14/41

15 Constraints Temperature coupling To control temperature PumMa is equipped with the Berendsen thermostat Instantaneous temperature is given by For coupling target temperature T 0 and coupling constant λ c need to be known Every time step velocities are scaled with λ If λ c =0 no temperature coupling is employed, while λ c =1 is a direct coupling. Normally a loose coupling is desired 15/41

16 Constraints Pressure coupling Similar to temperature coupling, the pressure in PumMa is also coupled through the Berendsen method The instantaneous pressure is given by with the rightmost term being the virial The pressure coupling constant is subsequently given by Every so often the positions are scaled with µ 16/41

17 Constraints Periodic Bound. Cond. PumMa is equiped with different boundary conditions, but the most common to use are periodic boundary conditions Each simulation box is surrounded by exact replicas (images) The smallest distance between is calculated (minimum image conv.) Only orthorhombic cells are possible Be aware of long range interactions across periodic boundaries 17/41

18 Constraints Other Simulated Annealing: Besides the option to keep the system at a desired temperature, it is also possible to gradually heat or cool the system Fixed atoms: It is also possible to specify a set of atoms which are not allowed to move However, all nonbonded interactions with these atoms are still evaluated Non-bonded exclusion: When using bond angles or dihedrals it can be desirable to exclude the 1-3 or 1-4 Van der Waals or Coulombic interactions However, its merits can be doubted when using coarse-grained systems 18/41

19 Integrator Verlet leapfrog (1) Position of particle around time t+ t which reduces to and similar for t- t Summing and neglecting higher order terms gives Verlet 19/41

20 Integrator Verlet leapfrog (2) Difference with the Verlet integrator is that the leapfrog integrator uses velocities at half integer time steps and From Verlets algorithm we obtain and Thus, the algorithm is 1. Calculate F(t). 2. Calculate new velocities v(t+δt/2) using v(t Δt/2) and F(t). 3. Calculate new positions r(t Δt/2) using r(t) and v(t Δt/2). 4. Repeat these steps until a certain stop criterium. 20/41

Integrator Verlet leapfrog (3) Although velocities and positions are separated by half a time step, they are internally treated as being at the same time step.

21 Integrator Verlet leapfrog (3) Although velocities and positions are separated by half a time step, they are internally treated as being at the same time step. The Verlet and Leapfrog scheme are algebraically identical. However, the leapfrog scheme is numerically more stable. Still caution is be taken when choosing the size of the time step The choice of an appropriate time step is important to prevent motions that develop too slow (left) or motions leading to instabilities (middle). With the appropriate time step collisions occur smoothly (right). 21/41

22 Overview Background History, current applications, and developers Features Potential functions Constraints Integrator Design Neighbor searching method Parallel implementation File format PumMa Toolkit Future release (major upgrade) Examples 22/41

23 Design Neighbor searching meth. Divide simulation box in multiple cells Cell z y x Simulation box Minimum number of cells in one simulation box is 27 By default, size of one cell equals the maximal Verlet radius 23/41

24 Design Neighbor searching meth. Divide simulation box in multiple cells Cell Stretched cell Number of cells can be increased by applying a cell stretch Search box becomes more spherical, hence, searching for neighbors is less time consuming There is a trade-off betweenn the number of stretched cells and speed-up 24/41

25 Design Parallel implementation Design of parallel implementation is based upon a toroidial transputer network Geometrical data decomposition Slab building through projection on x-y surface On two processes: Each process gets copies of the particles reciding on its right neighbor, this is the remote area Remote area Size of remote area depends on the number of stretched cells z y x Proc. 0 Proc. 1 25/41

26 Design File format PumMa uses a set of different files as its input or output All units are reduced* Reduced units are all chosen such that they are close to one Results in less inaccuracy during the computations Default values of reduced units are: Length: 1 σ* = 0.45 nm Energy: 1 ε* = 0.47 kcal/mol Mass: 1 m* = amu Charge: 1 q* = 1.0 e All others are derived from these (see Positions and topology are decoupled Every iteration has its own set of files (except for topology and parameters) 26/41

27 Input file (1) Default file name of the input file is inp.dat Its syntax is the option followed by its value White lines and lines starting with # are treated as comments # Integrator IT 0 max_it Dt # Temperature & Pressure T 1.3 lambdac P muc Prep 25 anisopress on # File dumping Erep 25 Crep 1000 sysfile sys outpfile outp.dat 27/41

28 Input file (2) Options for the Verlet list and cut-offs Rc 2.5 # Van der Waals cutoff radius factor Rl 0.9 # Factor specifying size of additional radius for pairlist RcCB 0.0 # Cutoff radius for Coulomb interactions (in reduced units) fixedrc -1 # Cutoff radius for all particle types (in reduced units) fixedrl -1 # Pairlist radius for all particle types (in reduced units) noshifts off # Disable shift function for nonbonded interactions vlrep 0 # Frequency of building pairlist again EpsR 1.0 # Dielectric constant Excl # Exclude Van der Waals 1-3 interactions Excl # Exclude Van der Waals 1-4 interactions Simulated annealing Thold Trate Annrep 0.0 # Final temperature (in reduced units) 0.0 # Change in temperature per scaling 1000 # Temperature scaling every Annrep'th iteration And many more (see 28/41

29 Parameter file The parameter file is called pumma_parm Each parameter is identified by a letter Thereafter all specifications for that type of parameter follow A G A T A W B G G B G T B T T T G G G T G G T T G T G T G T T T T G T T T T T N G G L N G T T N G W L N T T L N T W T N W W L C G C T C W A = atom B = bond T = angle F = double angle D = dihedral I = improper N = non-bonded C = color 29/41

30 System configuration The system configuration file contains all information of the size of the system, the number of molecules and so on It is typically named sysit123.cfg The numbers are of course the current iteration number Every time an iteration is written to file a.cfg file is created DPPC 128 W /41

31 Topology file (1) For each molecule there exist a topology file The name of the topology file is X.mol Where X is the name of the molecule The topology file lists the sequence of atoms in a molecule, which atoms form bonds, angles, double angles, dihedrals, impropers. Also the charges of the atoms are in the topology file The first line is the most important line, since it tells PumMa how many lines to expect for parsing all the information 31/41

Topology file (2) 12 11 4 0 0 A1 G 0.0 A2 G 0.0 A3 G 0.0 A4 G 0.0 A5 T 0.

0 1 2 2 3 3 4 4 5 5 6 6 7 7 8 3 9 9 10 10 11 11 12 5 6 7 6 7 8 9 10 11 10 11

32 Topology file (2) A1 G 0.0 A2 G 0.0 A3 G 0.0 A4 G 0.0 A5 T 0.0 A6 T 0.0 A7 T 0.0 A8 T 0.0 A9 T 0.0 A10 T 0.0 A11 T 0.0 A12 T T ++ T ++ T ++ T - G T ++ T ++ T ++ T - G - G - G /41

33 Coordinates & Velocities The coordinates and velocities of all particles are stored in a separate file for each molecule (.pcb) The order of the lines corresponds to the order given in the topology file (for that molecule) Information is supplied per molecule (so first molecule 1, than molecule 2, and so on) The first three columns are the positions, the last three colums the velocities /41

34 Output files Depending on options set in simulation input file, multiple configuration files (both system and coordinates) are written to file (eg. sysit100.cfg, DPPCIT100.pcb, etc.) Energies are reported to the file specified by outpfile, by default outp.dat Iteration; energies (Lennard-Jones, bonded, angle, dihedral, impropers, Coulomb, kinetic, tota); density; pressure; target temperature (annealing only) 34/41

35 File format - Overview So, for a lipid bilayer (water and DPPC) system one typically has One input option file: inp.dat One parameter file: pumma_parm Two topology files: W.mol and DPPC.mol Two coordinate files: WIT0.pcb and DPPCIT0.pcb One system configuration file: sysit0.cfg A more extensive overview of the input file format and all the options can be found at the webpage 35/41

36 Overview Background History, current applications, and developers Features Potential functions Constraints Integrator Design Neighbor searching method Parallel implementation File format PumMa Toolkit Future release (major upgrade) Examples 36/41

37 PumMa Toolkit PumMaTK Next to the MD code a toolkit has been developed Written in Python, with modules in ANSI C Has both graphical front-end and command line interfaces Purpose of graphical front-end is: Easy method to construct initial configuration from scratch Adapt (merge, crop, etc.) current configurations Assign parameters Analyze current configuration (eg. velocity distribution) Purpose of command line interface: Convert PumMa files to VMD-readable DCD/PSF files Some basic analysis (eg. volume, surface area) Create POVray files for nice pictures 37/41

38 PumMaTK Graphical front-end 38/41

39 Overview Background History, current applications, and developers Features Potential functions Constraints Integrator Design Neighbor searching method Parallel implementation File format PumMa Toolkit Future release (major upgrade) Examples 39/41

40 Future release PumMa is still changing at a rapid speed Many options are now decided upon compiling the code In the next version these options will be available through the input files rather than compiling a new binary File format will probably be updated to suit the current complex topology files Possibly the format will be XML-like PumMa is currently used by three other groups than ours Energy Technology (van Steenhoven, Eindhoven) Macromolecular Chemistry (Meijer, Eindhoven) Immunology (Vaidehi, City of Hope) 40/41

41 Questions? 41/41

Molecular Dynamics Simulations. Dr. Noelia Faginas Lago Dipartimento di Chimica,Biologia e Biotecnologie Università di Perugia

Molecular Dynamics Simulations Dr. Noelia Faginas Lago Dipartimento di Chimica,Biologia e Biotecnologie Università di Perugia 1 An Introduction to Molecular Dynamics Simulations Macroscopic properties