Force Fields for MD simulations

Transcription

1 Force Fields for MD simulations Topology/parameter files Where do the numbers an MD code uses come from? ow to make topology files for ligands, cofactors, special amino acids, ow to obtain/develop missing parameters.

2 Classical Molecular Dynamics U ( r) = 1 4!" 0 q q Coulomb interaction i r ij j U ( r) =. ij &, R $ * $ % + r min, ij ij ) ' ( 12, R - 2* + r van der Waals interaction min, ij ij ) ' ( 6 #!! "

3 Classical Molecular Dynamics Bond definitions, atom types, atom names, parameters,.

4 Energy Terms Described in the CARMm Force Field Bond Angle Dihedral Improper

5 The Potential Energy Function U bond = oscillations about the equilibrium bond length U angle = oscillations of 3 atoms about an equilibrium bond angle U dihedral = torsional rotation of 4 atoms about a central bond U nonbond = non-bonded energy terms (electrostatics and Lenard-Jones)

6 Interactions between bonded atoms V angle = K " ( ) 2 " #" o V bond = K b ( b " b o ) 2 V dihedral = K ( 1+ cos( n"! )) " #

7 ( b b ) 2 V = K! bond b o Chemical type K bond b o C-C 100 kcal/mole/å Å C=C 200 kcal/mole/å Å C=C 400 kcal/mole/å Å Bond Energy versus Bond length 400 Potential Energy, kcal/mol Single Bond Double Bond Triple Bond Bond length, Å Bond angles and improper terms have similar quadratic forms, but with softer spring constants. The force constants can be obtained from vibrational analysis of the molecule (experimentally or theoretically).

8 Dihedral Potential V dihedral = K ( 1+ cos( n"! )) " # Dihedral energy versus dihedral angle 20 Potential Energy, kcal/mol K=10, n=1 K=5, n=2 K=2.5, = Dihedral Angle, degrees δ = 0

9 onbonded Parameters. nonbonded q q + / &, R $ * $ % + i j min, ij min, ij ij 40Drij rij rij ) ' ( 12, R - 2* + ) ' ( 6 #!! " q i : partial atomic charge D: dielectric constant ε: Lennard-Jones (LJ, vdw) well-depth R min : LJ radius (R min /2 in CARMM) Combining rules (CARMM, Amber) R min i,j = R min i + R min j ε i,j = SQRT(ε i * ε j )

10 Electrostatic Energy versus Distance Interaction energy, kcal/mol q1=1, q2=1 q1=-1, q2= Distance, Å From MacKerell ote that the effect is long range.

11 Charge Fitting Strategy CARMM- Mulliken* AMBER(ESP/RESP) Partial atomic charges C O *Modifications based on interactions with TIP3 water

12 CARMM Potential Function PDB file geometry Topology PSF file parameters Parameter file

13 File Format/Structure The structure of a pdb file The structure of a psf file The topology file The parameter file Connection to potential energy terms

14 Structure of a PDB file index name resname chain resid X Y Z segname ATOM 22 ALA B B ATOM 23 ALA B B ATOM 24 CA ALA B B ATOM 25 A ALA B B ATOM 26 CB ALA B B ATOM 27 B1 ALA B B ATOM 28 B2 ALA B B ATOM 29 B3 ALA B B ATOM 30 C ALA B B ATOM 31 O ALA B B ATOM 32 ALA B B ATOM 33 ALA B B ATOM 34 CA ALA B B ATOM 35 A ALA B B ATOM 36 CB ALA B B ATOM 37 B1 ALA B B ATOM 38 B2 ALA B B ATOM 39 B3 ALA B B ATOM 40 C ALA B B ATOM 41 O ALA B B >>> It is an ascii, fixed-format file <<< o connectivity information

15 Checking file structures PDB file Topology file PSF file Parameter file

16 Parameter Optimization Strategies Check if it has been parameterized by somebody else Literature Google Minimal optimization By analogy (i.e. direct transfer of known parameters) Quick, starting point Maximal optimization Time-consuming Requires appropriate experimental and target data Choice based on goal of the calculations Minimal database screening MR/X-ray structure determination Maximal free energy calculations, mechanistic studies, subtle environmental effects

17 Getting Started Identify previously parameterized compounds Access topology information assign atom types, connectivity, and charges annotate changes CARMM topology (parameter files) top_all22_model.inp (par_all22_prot.inp) top_all22_prot.inp (par_all22_prot.inp) top_all22_sugar.inp (par_all22_sugar.inp) top_all27_lipid.rtf (par_all27_lipid.prm) top_all27_na.rtf (par_all27_na.prm) top_all27_na_lipid.rtf (par_all27_na_lipid.prm) top_all27_prot_lipid.rtf (par_all27_prot_lipid.prm) top_all27_prot_na.rtf (par_all27_prot_na.prm) toph19.inp (param19.inp) A and lipid force fields have new LJ parameters for the alkanes, representing increased optimization of the protein alkane parameters. Tests have shown that these are compatible (e.g. in protein-nucleic acid simulations). For new systems is suggested that the new LJ parameters be used. ote that only the LJ parameters were changed; the internal parameters are identical

18 Break Desired Compound into 3 Smaller Ones O O A B C O O Indole ydrazine Phenol When creating a covalent link between model compounds move the charge on the deleted into the carbon to maintain integer charge (i.e. methyl (q C =-0.27, q =0.09) to methylene (q C =-0.18, q =0.09) From MacKerell

19 From top_all22_model.inp RESI PE 0.00! phenol, adm jr. GROUP ATOM CG CA ! ATOM G P 0.115! D1 E1 GROUP! ATOM CD1 CA ! CD1--CE1 ATOM D1 P 0.115! // \\ GROUP! G--CG CZ--O ATOM CD2 CA ! \ / \ ATOM D2 P 0.115! CD2==CE2 GROUP! ATOM CE1 CA ! D2 E2 ATOM E1 P GROUP ATOM CE2 CA ATOM E2 P GROUP ATOM CZ CA ATOM O O ATOM BOD CD2 CG CE1 CD1 CZ CE2 CG G CD1 D1 BOD CD2 D2 CE1 E1 CE2 E2 CZ O O DOUBLE CD1 CG CE2 CD2 CZ CE1 Top_all22_model.inp contains all protein model compounds. Lipid, nucleic acid and carbohydate model compounds are in the full topology files. G will ultimately be deleted. Therefore, move G (hydrogen) charge into CG, such that the CG charge becomes 0.00 in the final compound. Use remaining charges/atom types without any changes. Do the same with indole From MacKerell

20 Creation of topology for central model compound RESI Mod1! Model compound 1 Group ATOM C1 CT ATOM 11 A ATOM 12 A ATOM 13 A GROUP ATOM C2 C 0.51 ATOM O2 O GROUP ATOM ATOM ATOM 4 R1 0.16!new atom ATOM C5 CEL ATOM 51 EL ATOM C6 CT ATOM 61 A 0.09 ATOM 62 A 0.09 ATOM 63 A 0.09 BOD C1 11 C1 12 C1 13 C1 C2 C2 O2 C BOD 3 4 C5 51 C5 C6 C6 61 C6 62 C6 63 DOUBLE 4 C5 (DOUBLE only required for MMFF) O Start with alanine dipeptide. ote use of new aliphatic LJ parameters and, importantly, atom types. R1 from histidine unprotonated ring nitrogen. Charge (very bad) initially set to yield unit charge for the group. ote use of large group to allow flexibility in charge optimization. From MacKerell

21 Partial Atomic Charge Determination Method Dependent Choices 1. RESP: F/6-31G overestimates dipole moments (AMBER) 2. Interaction based optimization (CARMM) From MacKerell For a particular force field do OT change the QM level of theory. This is necessary to maintain consistency with the remainder of the force field.

22 C 3 O Starting charges?? Mulliken population analysis Analogy comparison C 3 Final charges (methyl, vary q C to maintain integer charge, q = 0.09) interactions with water (F/6-31G*, monohydrates!) From MacKerell

23 Comparison of analogy and optimized charges ame Type Analogy Optimized C1 CT A A A C2 C O2 O R C5 CEL EL C6 CT A A A O

24 Dihedral optimization based on QM potential energy surfaces (F/6-31G* or MP2/6-31G*). O O O O 2 O O O From MacKerell

25 Parameterization of unsaturated lipids All C=C bonds are cis, what does rotation about neighboring single bonds look like? Courtesy of Scott Feller, Wabash College

26 DA conformations from MD rotational barriers are extremely small many conformers are accessible w/ short lifetimes Courtesy of Scott Feller, Wabash College

27 Dynamics of saturated vs. polyunsaturated lipid chains sn1 stearic acid = blue sn2 DA = yellow 500 ps of dynamics Movie courtesy of Mauricio Carrillo Tripp Courtesy of Scott Feller, Wabash College

28 Lipid-protein interactions Radial distribution around protein shows distinct layering of acyl chains DA penetrates deeper into the protein surface Courtesy of Scott Feller, Wabash College

29 Lipid-protein interactions Decomposition of non-bonded interaction shows rhodopsin is strongly attracted to unsaturated chain All hydrophobic residues are stabilized by DA resname PE ILE VAL LEU MET TYR ALA TRP U DA U stearic ratio Courtesy of Scott Feller, Wabash College

30 Origin of protein:da attraction Flexibility of the DA chain allows solvation of the rough protein surface to occur with little intra-molecular energy cost Courtesy of Scott Feller, Wabash College

31 Retinal Proteins -- Rhodopsins Me Me Me Me Me Me Me Me Me Me Chromophore Covalently linked to a lysine Usually protonated Schiff base all-trans and 11-cis isomers

32 Unconventional chemistry Me Me Me Me Me Me Me Me Me Me

33 Isomerization Barriers in retinal Lys C 15 C 14 C 13 C 12 C 11 C 10 C 9 C 8 C 7 C 5 C 6 C 4 C 1 C 2 C 3 DFT/6-31G**

34 Coupling of electronic excitation and conformational change in br S 1 S 0 BR K C 13 =C 14 -trans C 13 =C 14 -cis Me Me Me Me Me 13 15

35 Inducing isomerization 500 nm ~50 kcal/mole

36 Classical Retinal Isomerization in Rhodopsin Twist Propagation

37 QM/MM calculations MM O MM Lys216-RET QM QM QM ˆ = p 2 i i + " + V 1 2 "" q r i p ip MM QM! MM + p "" + + V i A ia A p Ap MM MM Z r "" A Z 1 + " + " r A r q i> j ij A> B p Z AZ r AB B dummy atom O MM Asp85, 212 O O QM

38 Ab Initio QM/MM Excited State MD Simulation QM Quantum mechanical (QM) treatment of the chromophore, and force field (MM) treatment of the embedding protein

39 QM/MM calculation of ATP hydrolysis

40 Coarse grain modeling of lipids 150 particles 9 particles!