Introduction to Molecular Simulation Chih-Hao Lu Associate Professor China Medical University

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Molecular dynamics (MD) is a form of computer simulation in which atoms and molecules are allowed to interact for a period of time by approximations of known physics, giving a view of the motion of the particles.

This kind of simulation is frequently used in the study of proteins and biomolecules. It is tempting, though not entirely accurate, to describe the technique as a "virtual microscope" with high temporal and spatial resolution.

Richard Feynman once said that Richard Phillips Feynman (1918–1988) Richard Feynman once said that "If we were to name the most powerful assumption of all, which leads one on and on in an attempt to understand life, it is that all things are made of atoms, and that everything that living things do can be understood in terms of the jigglings and wigglings of atoms."

Molecular dynamics lets scientists peer into the motion of individual atoms in a way which is not possible in laboratory experiments.

John Desmond Bernal (1901-1971) in 1962: "... I took a number of rubber balls and stuck them together with rods of a selection of different lengths ranging from 2.75 to 4 inches. I tried to do this in the first place as casually as possible, working in my own office, being interrupted every five minutes or so and not remembering what I had done before the interruption."

Because molecular systems generally consist of a vast number of particles, it is in general impossible to find the properties of such complex systems analytically.

MD simulation circumvents the analytical intractability by using numerical methods.

Babylonian clay tablet YBC 7289 (1800–1600 BC) ? Tip: Sexagesimal

Babylonian clay tablet YBC 7289 (1800–1600 BC) 42,25,35 = 42/60 + 25/602 + 35/603 = 0.707106

long MD simulations are mathematically ill-conditioned, generating cumulative errors in numerical integration that can be minimized with proper selection of algorithms and parameters, but not eliminated entirely.

Current potential functions are, in many cases, not sufficiently accurate to reproduce the dynamics of molecular systems, so the much more computationally demanding ab Initio Molecular Dynamics method must be used.

Design of a molecular dynamics simulation should account for the available computational power. Simulation size (n=number of particles), timestep and total time duration must be selected so that the calculation can finish within a reasonable time period.

However, the simulations should be long enough to be relevant to the time scales of the natural processes being studied.

Most scientific publications about the dynamics of proteins and DNA use data from simulations spanning nanoseconds (1E-9 s) to microseconds (1E-6 s).

A molecular dynamics simulation requires the definition of a potential function, or a description of the terms by which the particles in the simulation will interact. In chemistry and biology this is usually referred to as a force field.

Most force fields consist of a summation of bonded forces associated with chemical bonds, bond angles, and bond dihedrals, and non-bonded forces associated with van der Waals forces and electrostatic charge.

These potentials contain free parameters such as atomic charge, van der Waals parameters reflecting estimates of atomic radius, and equilibrium bond length, angle, and dihedral

In addition to the functional form of the potentials, a force field defines a set of parameters for each type of atom.

For example, a force field would include distinct parameters for an oxygen atom in a carbonyl functional group and in a hydroxyl group.

How many types of bonds? C-C 2 C-H 8 10 bonds ?? angle terms ?? torsional terms ?? non-bonded interactions

How many types of angles? C-C-C 1 C-C-H 10 H-C-H 7 10 bonds 18 angle terms ?? torsional terms ?? non-bonded interactions

How many types of torsions? H-C-C-H 12 H-C-C-C 6 10 bonds 18 angle terms 18 torsional terms ?? non-bonded interactions

How many types of nonbonded ineractions? H-H 28 C-H 16 C-C 1 10 bonds 18 angle terms 18 torsional terms 45 non-bonded interactions

Molecular dynamics simulation Molecular dynamics simulation of 30 proteins ~50 years CPU (Rueda, PNAS 2007)

1CZT Our method (no force field) < 1 sec CPU ~1.7 yr CPU

The Protein Fixed-Point Model (A) (B) Large B-factor 1FUP:A Small B-Factor 0.924 (C) (D) 2BF5:A 0.880 Computational profile X-Ray B-factor profile

(E) (F) (G) (H) 0.851 0.873 1DQZ:A 1O6V:A Computational profile X-Ray B-factor profile

Protein complexes 0.920 0.120

Protein complexes 0.801 0.416

Multi-domain proteins 0.348 0.781 0.800

Correlation Coefficient ≥0.5 PFP Model New PFP Model GNM Mean 0.53 0.59 0.56 Correlation Coefficient ≥0.5 61% 75% 69%

The (Weighted) Contact Number Model flavocytochrome c3 (1Y0P:A) WCN CN Computational profile X-Ray B-factor profile

The (Weighted) Contact Number Model human ppGalNAcT-2 (2FFU:A) WCN CN Computational profile X-Ray B-factor profile

The 50S ribosomal subunit (1YJW) 3774 residues WCN profile X-Ray B-factor profile

CN: GNM: WCN:

? Bonds ? C-H ? C-C ? Angle terms ? C-C-C ? H-C-H ? H-C-C ? Torsional terms ? H-C-C-H ? H-C-C-C ? Non-bonded interactions ? H-H

13 Bonds 10 C-H 3 C-C 24 Angle terms 3 C-C-C 9 H-C-H 12 H-C-C 27 Torsional terms 9 H-C-C-H 18 H-C-C-C 78 Non-bonded interactions 30 C-H 45 H-H

Chih-Hao Lu chlu@mail.cmu.edu.tw Thank you! Chih-Hao Lu chlu@mail.cmu.edu.tw