Ion aggregates in biomolecular simulations: A force field problem C9926: Problems and Issues of Molecular Modeling Rahul Deb CEITEC MUNI 2021 • Empirical force fields are developed and validated by experimental and ab initio computational data • Fine-tuning of Lennard-Jones (LJ) parameters for monovalent ions (Na+, K+, and Cl-) • Some of these parameters, in conjunction with different water models, have been evaluated • Large dispersion of calculated properties, which is mainly due to incomplete experimental knowledge of ionic aqueous solutions at finite molarity Spontaneous formation of NaCl aggregates in a simulation of “A-to-B” DNA transitions in >1 M salt solution using the AMBER adopted ion parameters and TIP3P water model. Example: Lennard-Jones (LJ) potential MD simulations of aqueous KCl solutions - three salt concentrations (1.0, 0.25, and 0.10 M) - two water models (TIP3P and SPC/E) - two LJ parameter sets for K+ (AMBER and Dang-Kollman) Ion-ion radial distribution functions Highly ordered ionic structure Dissociated salt solution High salt concentration 0.1M Rapid formation of KCL clusters in AMBER K-Cl radial distribution functions High salt concentration 0.1M Low salt concentration 0.01M No aggregation numbers of ions of opposite charge surrounding a given ion revealing the occurrence of KCl contact pairs K-Cl radial distribution functions Converging Ion-water coordination numbers number of water molecules located in the first shell is larger for Dang, reflecting that AMBER favors the formation of ion pairs and aggregates Issues of electronic polarizability using non-polarizable force fields AMBER, CHARMM, GROMOS and OPLS have been successful in modeling many complex molecular systems. The hydration free energies can be computed accurately. • For example, the dielectric constant of the inner part of Cytochrome c was found to be only about 1.5, which is lower than pure electronic dielectric constant 2.0 • in low-polar solvents, e.g., ethers, and non-polar solvents, e.g., alkanes • low-dielectric protein environment and lipid membranes Electrostatic interactions of ions (point charges) are described as if they are in vacuum, completely disregarding the effect of electronic dielectric screening inherent to the condensed phase medium, where all charges are immersed in the electronic continuum, which weakens their interactions by a factor of about 2. Therefore, all the interactions are overestimated by a factor of about 2. • Coulomb interaction of ions • Interactions of ions with water molecules, or with partial atomic charges of a protein • Interaction of charged residues in proteins Arg+/Lys+ with Glu-/AspSerious problems: MDEC model • Uniform charge scaling based on the idea of uniform electronic continuum with an effective dielectric constant εel of 2, and point charges moving in it • Model combines a non-polarizable (fixed-charge) force field for molecular dynamics (MD) with a phenomenological electronic continuum (EC) • The interactions between charges are scaled by a factor 1/εel (i.e., individual charges are scaled by a factor of 1/√εel) Interaction energies of charged species Electronic screening effect of the dielectric environment on the interaction energies can be accurately reproduced by a simple scaling of charges ab initio calculations in gas-phase HF/6-31(d) calculation in dielectric of 2.0 standard CHARMM and TIP3P CHARMM with scaled charges (εel = 2.0), and TIP3P TIP3P and SPC/E are MDEC models Water models Dipole moment of water in vacuum ~ 1.85D and in liquid state ~ 2.9D to 3.2D. This significant increase in dipole is also supported by the Kirkwood-Onsager model, which estimates the enhanced polarization of a molecule due to the reaction field of the polarized environment. Yet, the dipole moment of TIP3P water model is 2.35D. This was understood as a scaled dipole, so that the dipole–dipole interactions are screened by the electronic continuum by a factor 1/εel (i.e., each dipole is scaled by a factor 1/√εel). Considering the interaction of effective dipoles, μeff= μ/√εel ~ 2:35D (where εel 1.78 is the electronic high-frequency dielectric constant of water). In the high-dielectric region, ε0 >20, the water polarization is almost constant and like the water molecule in the bulk ε0 = 80. At low-dielectric region (proteins or membranes), ε0 <20, there is a significant dependence. Dependence of water dipole on the polarity of the environment Solvation free energy MDEC and the conventional non-polarizable MD reproduce experimental data within the experimental error in a high-dielectric media such as water. Solvation free energy consists of two parts: the nuclear part evaluated by MD, and the pure electronic polarization part evaluated by using the polarizable continuum model (i.e., by solving the Poisson equation with corresponding boundary conditions, with dielectric constant ε = 1 inside the solute region, and ε = εel outside. However, the traditional non-polarizable MD significantly underestimate the solvation free energy in the low-dielectric media such as liquid cyclohexane or protein interior of protein Cytochrome c oxidase. Microscopic interactions When the space between ionic spheres is larger than a size of solvent molecules, the effects of solvent microscopic structure becomes unimportant, and the average interaction, both in polarizable and non-polarizable models of benzene, can be approximated by a simple Coulomb law with an effective dielectric constant. Polarizable Drude oscillator model Traditional non-polarizable CHARMM MD Traditional non-polarizable CHARMM MD with scaled charges PMF for an ion pair A+ and A- in benzene Dynamics of salt bridges in proteins Salt bridge is observed 98% or even 63% of the time in MD with scaled charges without and with water molecules in the cavity, respectively. Distribution functions of the distance d between the atoms forming saltbridge Standard non-polarizable MD MD with scaled charges of the ionized groups no water in the catalytic cavity 4 water molecules in the cavity Salt bridge formed = no water in the cavity Standard non-polarizable MD with and without water in the cavity lead to the conclusion that the salt bridge is formed 100% of the time .