Solvation Solvent Influence Bulk Solvent Effect Example Solvation Treatment Explicit Water Models Implicit Solvent Models

n Solvent influence levels Solvation n Direct interaction (or reaction) with solute n Solvent provides environment (anisotropic, for example) that influences solute behavior (mean field effect)

CHEM8711/7711 n Solvent acts as bulk medium affecting solute properties

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Bulk Solvent Effect Example Solvation Treatment

Butane n Explicit Conformation n System includes actual solvent molecules Distribution n Required for any direct solvent-solute interaction

n Problems

n System becomes quite large if long-range effects are to be handled well

n Sampling of solvent configurations required

n Simulation times increase n Implicit

n System does not include actual solvent molecules

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Explicit Water Models Implicit Solvent Models n Simple Pairwise Potentials n Dielectric Screening n Interaction sites defined on atoms, atoms and lone pairs, or atoms and bisector of HOH angle n Continuum Representations q(lp) q(lp) q(O) n Attempt to represent three contributions to solvation free energy: q(H) q(H) q(H) q(M) q(H) q(H) q(H) SPC, SPC/E, TIP3P TIP4P, BF ST2 DGsol = DGelec + DGvdw + DGcav n Widely used methods addressing G : n VDW interactions may be simplified to one per pair of D elec water molecules n Born model (we will discuss generalized Born model,

n Individual molecule dipole moments (~2.25D) which also addresses DGvdw and DGcav)

approximate liquid water (2.6D) rather than gas phase n Poisson-Boltzmann (1.85D) n Polarizable CHEM8711/7711: 5 CHEM8711/7711: 6

1 Dielectric Screening Limitation n Polar solvents screen (reduce) electrostatic n The influence of solvent includes an interactions electrostatic and an entropic contribution q1q2 n Electrostatic function: V = n The electrostatic component is due to solvent Dr polarization (and screening of charge interactions due to intervening solvent molecules) n Common solvent dielectric constants: n Entropic contributions are due to formation of n gas phase: 1 solvent cavities around solutes

n water: 78.3 n The solvent dielectric only reflects the screening

n alkanes: 3 of charge interactions

n aqueous/membrane interface: 10

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Class Exercise Exercise Analysis n Compute the conformational populations for n Consider the following questions:

either butane or 1,4-butanedione (coordinate n Are the lowest energy conformations the same with another student to make sure both are with different solvent dielectrics?

covered) with the solvent dielectric set to 1 n If not, how do they differ (structurally)? n Recompute the conformational populations with the solvent dielectric set to 80 if you have a database of conformations, you can reset the dielectric using Window->Potential Control and then get energies for reminimized structures: db_ComputeEnergy [‘database.mdb’,’source field’,’destination field’,1]

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Generalized Born Method Implicit Solvation of Butane

n Solvation free energies can be expressed as a sum of a e=1 e =80 solvent cavity term, a solvent-solute van derWaals term and an electrostatic polarization term Anti 23.4317 25.6143 G = G + G + G sol cav VDW pol (99.98421%) (99.98420%) n The cavity and van derWaals terms are related to the solvent-accessible surface area Gauche+ 24.3669 26.5494

Gcav + GVDW = ? skSAk (0.00789%) (0.00790%) solvent accessible surface area for parameter for atom type k atoms of type k Gauche- 24.3669 26.5494 n Electrostatic term form: (0.00789%) (0.00790%) N N q q 1 æ 1 ö i j Changes in conformational distribution due to solvation of DGelec = - ç1- ÷å å 2 è e ø i=1 j=1 f (rij ,aij ) hydrophobic molecules are largely NOT electrostatic in nature Interparticle distance Born radii CHEM8711/7711: 11 CHEM8711/7711: 12

2 GB/SA Results for Butane Poisson Equation Charge density No Solvent GB/SA water 4pr(r) Ñ2f(r) = - Anti -5.076 -3.04947 e (99.92605%) (99.88116%) Variation in potential (f) Medium constant dielectric Gauche+ -4.29374 -2.31422 (0.03697%) (0.05942%) Ñ ·e (r)Ñf(r) = -4pr(r) Gauche- -4.29374 -2.31422 (0.03697%) (0.05942%) Dielectric field varies with position Inclusion of the cavity and van derWaals effects of solvation improves the calculated influence of solvent

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Linearized Poisson-Boltzmann Boltzmann Distribution of Ions Equation

Ñ ·e (r)Ñf(r)-k 'f(r) = -4pr(r) Energy change of ion Number density of ions at r transfer from infinity to r 8pN e2 I Bulk number density k ' = A 1000k T æ -u(r)ö B n(r) = N expç ÷ è kBT ø n Must be solved numerically

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Finite Difference Method Reading

Constant charge density in cube:

q0 r = n Chapter 4, section 14 0 h3 n Chapter 11, sections 9-12 Potential at grid point 0: q e f + 4p 0 å i i h f0 = '2 åei + k0 potential influenced by surrounding grid points – iterate until consistent solution achieved

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