Developing Monovalent Ion Parameters for the Optimal Point Charge (OPC) Water Model. John Dood Hope College

Developing Monovalent Ion Parameters for the Optimal Point Charge (OPC) Water Model John Dood Hope College

What are MD simulations? Model and predict the structure and dynamics of large macromolecules. Force field equation implemented in AMBER + V = + n atoms ε ij i<j n bonds b i r i r i,eq i n dihedral i n 2 + i n angles a i θ i θ i,eq n i,max V i,n/2[1 + cos nφ i γ i,n ] R min,ij r ij 12 2 R min,ij r ij 6 + n atoms i<j 2 q i q j 4πε 0 r ij

What are Water Models? 3 point Mass Charge vdw 4 point Mass vdw 5 point Mass vdw O H 1 H 2 EP 1 EP 2 Mass Charge Mass Charge Mass Charge Mass Charge Mass Charge Mass Charge Charge Charge Charge 3 point model i.e. TIP3P and SPC 4 point model i.e. TIP4P-Ew and OPC 5 point model i.e. TIP5P

What is OPC? Optimal point charge (OPC) Saeed Izadi, Ramu Anandakrishnan and Alexey V. Onufriev, Published 2014 Derived to reproduce quantum mechanical electrostatic potential Simulates the bulk properties of water better than other models Izadi, Anandakrishnan, Onufriev, J. Phys. Chem. Lett., 2014, 5, 3863-3871

What are ion parameters? + V = + n atoms ε ij i<j n bonds b i r i r i,eq i n dihedral i n 2 + i n angles a i θ i θ i,eq n i,max V i,n/2[1 + cos nφ i γ i,n ] R min,ij r ij 12 2 R min,ij r ij 6 + n atoms i<j 2 q i q j 4πε 0 r ij

What are Ion Parameters? Ions must be parameterized in order to provide coefficients for energy calculations in AMBER. E LJ = ε ij R min,ij r ij 12 2 R min,ij r ij 6 Two parameters must be created for each ion, ε and R min /2. Lennard-Jones (LJ) potential has a well depth of ε at a distance of R min. Energy ( ) 1.5 1.0 0.5 0.0-0.5-1.0 0.5 1.0 1.5 2.0 2.5 3.0 Distance (R min )

How are Ion Parameters Developed? Most ion parameters are developed empirically. Parameters are chosen that produce the most realistic test results. In Suk Joung and Tomas E. Cheatham TIP3P, SPC, and TIP4P-Ew ion parameters Kasper P. Jenson and William L. Jorgenson SPC and TIP3P ion parameters

Lattice Constants (LC s) The lattice constant is the spacing between unit cells. For FCC crystals this value is twice the interionic distance.

Lattice Constants LE (kcal/mol) -3.40x10 7-3.60x10 7-3.80x10 7-4.00x10 7-4.20x10 7-4.40x10 7-4.60x10 7-4.80x10 7-5.00x10 7 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 LC (Å) -4.80x10 7-4.82x10 7 Na + R min /2 = 1.369Å Cl R min /2 = 2.513Å LE (kcal/mol) -4.84x10 7-4.86x10 7-4.88x10 7-4.90x10 7 5.5 5.6 5.7 5.8 5.9 6.0 LC (Å)

Hydration Free Energy Gives the energy from the interactions of the ion with water. Produced by slowly bringing the charges and Van der Waals to zero (thermodynamic integration). G Hyd = 0 1 V λ dλ λ = 0 λ = 1

V/ λ V/ λ Thermodynamic Integration (TI) TI is performed in two steps, charge elimination and Van der Waals (vdw) elimination Various intermediate states are produced (λ) and fit to a curve for each step The curve is integrated for each step and the two areas are added to produce a hydration free energy Charge V/ λ vdw V/ λ 200 150 100 50 0 0 0.2 0.4 0.6 0.8 1 λ 4 2 0-2 -4-6 -8 0 0.2 0.4 0.6 0.8 1 λ 90.96+0.2360=91.20 kcal/mol

Radial Distribution Functions

Radial Distribution Functions Show the density of the oxygen atom in water with respect to radius from the ion The ion-oxygen distance of the first peak is characteristic for each ion 5 Frequency of O 4 3 2 1 0 3 4 5 6 7 8 Distance (Å)

Experimental Comparison Lattice Constants Hydration Free Energy G Hyd = 0 1 V λ dλ λ = 0 λ = 1 Radial Distribution Function

Convergence Test Run a large number of LC simulations for different R min, R min pairs for NaCl KCl LiCl. Run TI & RDF simulations for a variety of R min, ε Pick R min s that minimize error in LC for each crystal Pick ε s that minimize error in RDF & TI for each crystal Collect Parameters Run Test Simulations

Convergence Test Run a large number of LC simulations for different R min, R min pairs for NaCl KCl LiCl. Pick R min s that minimize error in LC for each crystal Run TI & RDF simulations for a variety of R min, ε Pick ε s that minimize error in RDF & TI for each crystal Collect Parameters Run Test Simulations

Convergence Test Run a large number of LC simulations for different R min, R min pairs for NaCl KCl LiCl. Run TI & RDF simulations for a variety of R min, ε Pick R min s that minimize error in LC for each crystal LiF LiCl LiBr NaF NaCl NaBr KF KCl KBr Collect Parameters Pick ε s that minimize error in RDF & TI for each crystal Run Test Simulations

Lattice Calculations Involve no simulation only energy evaluation so list is short Particle mesh Ewald Non-bonded cutoff Total system size

Non-bonded Cutoff LC (Å) 8 7 6 5 0 5 10 15 20 6.00 5.95 5.90 5.85 5.80 5.75 5.70 5.65 5.60 5.55 5.50 0 5 10 15 20 5.700 5.698 5.696 5.694 5.692 5.690 5.688 5.686 5.684 5.682 5.680 0 5 10 15 20 NB Cutoff (Å) NB Cutoff (Å) NB Cutoff (Å)

Lattice Calculations Particle Mesh Ewald (Default Settings OK) Non-bonded Cutoff (12Å) Total System Size (No dependence)

TI convergence testing Electrostatics play a big role Computation is more expensive NTWX Equilibration Time Buffer Size Production Time Number of λ values Non bonded Cutoff

Hydration Free Energy Buffer Size/Production Time 92.4 92.3 92.2 92.1 92 91.9 91.8 0 5 10 15 20 25 30 35 40 45 Time (s) 15 A 17.5 A 20 A 22.5 A 25 A 30 A 40 A 50 A

TI Convergence Testing NTWX (50ps) Equilibration Time (2ns) Buffer Size (in process) Production Time (in process) Number of λ Values (3 for testing, 9 for production more work for vdw) Non-Bonded Cutoff (last step)

RDF Convergence Testing Equilibration time Sampling time Period between samples Size of the periodic box

Density of O Density of O Equilibration Time 9 8 7 6 5 4 3 2 1 0 First 10ns Middle 10ns Last 10ns 0 1 2 3 4 5 6 7 8 9 10 R (Å) 8.5 First 10ns 8 Middle 10ns 7.5 Last 10ns 7 6.5 6 5.5 5 4.5 2.4 2.45 2.5 2.55 2.6 R (Å) First 10ns Middle 10ns Last 10ns STDEV Range 2.483852 2.483645 2.483822 0.000112.000207

Density of O Density of O Sampling Time 9 8 7 6 5 4 3 2 1 0 1ns 2ns 5ns 10ns 0 1 2 3 4 5 6 7 8 9 10 R (Å) 8.5 1ns 8 2ns 7.5 5ns 7 10ns 6.5 6 5.5 5 4.5 2.4 2.45 2.5 2.55 2.6 R (Å) 1ns 2ns 5ns 10ns STDEV Range 2.481208 2.483100 2.483755 2.483822 0.001219 0.002614

Ion-Oxygen Distance (Å) Density of O Density of O Buffer Size 9 8 7 6 5 4 3 2 1 0 14.3 Buffer 16 Buffer 18 Buffer 20 Buffer 25 Buffer 0 1 2 3 4 5 6 7 8 9 10 R (Å) 8.5 14.3 Buffer 8 16 Buffer 7.5 18 Buffer 7 20 Buffer 6.5 25 Buffer 6 5.5 5 4.5 2.4 2.45 2.5 2.55 2.6 R (Å) 2.485 2.484 Na + RDF 2.483 14 16 18 20 22 24 26 Buffer Size (Å)

RDF Convergence Testing Equilibration time (520ps minimum; 100ns used) Sampling time (10ns) Period between samples (500fs) Size of the periodic box (15Å buffer zone 26Å truncated octahedron)

RDF surfaces Chose values about ±15% relative to TIP4P-Ew parameters by Joung and Cheatham 2.65 3.1 2.60 3.0 2.55 RDF (Å) 2.50 2.45 RDF (Å) 2.9 2.8 2.40 2.7 2.35 2.30 1.40 1.35 1.30 1.25 1.20 1.15 R min /2 (Å) 1.10 1.05 0.15 0.16 0.18 0.17 (kcal/mol) 2.6 1.8 1.7 1.6 R min /2 (Å) 1.5 1.4 1.3 0.24 0.26 0.30 0.28 (kcal/mol) Na + Exp: 2.356Å K + Exp: 2.798Å Joung, I. S.; Cheatham T. E. J. Phys. Chem. B 2008, 112, 9020 Marcus, Y. Chem. Rev. 1988, 88, 1475

RDF Surfaces 3.5 3.4 RDF(Å) 3.4 3.3 3.2 3.1 3.0 2.9 RDF (Å) 3.3 3.2 3.1 3.0 2.9 2.8 0.013 2.8 0.035 2.7 3.1 3.0 2.9 2.8 R min /2 (Å) 2.7 2.6 2.5 2.4 0.010 0.012 0.011 (kcal/mol) 2.8 2.7 2.6 R min /2 (Å) 2.5 2.4 2.3 0.025 0.030 (kcal/mol) Cl Exp: 3.187Å Br Exp: 3.373Å

Future Work Run lattice calculations for all nine crystals Finish TI convergence testing Run simulations out to 60 ns to finalize box size, and production time Determine non-bonded cutoff Run a large number of lambda values to prove convergence Produce TI surfaces Test parameters

Acknowledgements NSF-MRI #CHE-1039925 NSF-RUI #CHE-1058981 Dr. Krueger Lab partners Past Krueger students Hope CIT and Daniel Yonker Dr. Polik and Mike Poublon Saeed Izadi, Dr. Onufriev Ross Walker, AMBER development team, CUDA development team