G the neutral solute. There are several different implicit solvent models discussed below: the Poisson oltzmann model and the generalized Born model, 3-bromo-α-methyl- which differ in how Gel is obtained. Poisson oltzmann model Solving Poisson’s equation, which is valid under conditions where ions are absent, gives a second order differential equation describing the electrostatic environment that is modeled with a dielectric continuum model [145], r ??-4 ? ?2?where (r) is the electrostatic potential, (r) is the dielectric constant and (r) is the charge density. Poisson’s equation cannot be solved analytically for most systems, and must be solved using computers and adopting numerical methods. The Boltzmann contribution, along with the assumptions of the Debye kel theory, describes the charge density due to ions in solution. This results in the (non-linearized) Poisson oltzmann (PB) equation [146]: r ? s kT S ?2 sinh ?kT ?-4 ? e ?3?where denotes the Debye kel parameter, s is the solvent dielectric constant, S(r) is a « masking » function with value 1 in the region accessible to the ions in the solvent and value 0 elsewhere; e is the protonic charge; k is Boltzmann’s constant; T is the absolute temperature. Here, the charge density on the right represents the partial chargesTuszynski et al. Theoretical Biology and Medical Modelling 2014, 11:52 http://www.tbiomed.com/content/11/1/Page 22 ofin the cavity. When the ionic strength of the solution or the potential is low, Equation (33) can Methyl 5-amino-2,4-difluorobenzoate be linearized by expanding the second term on the left into a Taylor series and retaining only the first term: r ?s 2 S r ??-4 ? ?4?The non-electrostatic contribution (Gnonel) to the solvation free energy is calculated by empirical methods and is proportional to the solvent accessible surface area. This is PubMed ID:https://www.ncbi.nlm.nih.gov/pubmed/25386826 added to the electrostatic part to yield the solvation free energy. Although the PB approach is mathematically rigorous, it is computationally expensive to calculate without approximations [141,147,148]. The generalized Born model provides a more efficient means of including solvent in biomolecular simulations. Generalized born model The generalized Born (GB) model is based on the Born approximation of point charges, modeling solute atoms as charged spheres with an internal dielectric (generally equal to 1) that differs from the solvent (external) dielectric. The polarization effects of the solvent are represented by a dielectric continuum represents the polarization effects of the solvent. Numerical methods are used to determine the charges on the solute spheres that result in the same electrostatic potential on the cavity PubMed ID:https://www.ncbi.nlm.nih.gov/pubmed/13485127 surface that mimics that of the solute in a vacuum. By making approximations to the linear Poisson-Boltzmann equation (Equation 31), the electrostatic contribution of the generalized Born model is obtained: qi qj 1 1 1 X – ?5?Gel ?- . !1=2 ; 2 int ext ij 2 ? exp – r 2 r ij i j ij 4 ij where i is effective Born radius of particle i, rij is the distance between atoms i and j, int and ext the internal and external dielectric constants, respectively, and qi is the electrostatic charge on particle i. Like the PB method, Gnonel is calculated from the solvent-accessible surface area [140,141,147,149-151].Reference interaction site modelAnother type of solvation model is a probabilistic method known as the 3D reference interaction site 5-Bromo[1,2,4]triazolo[1,5-a]pyridin-2-amine model (3D-RISM) [140,152-158]. This molecular theory of solvation simulates the solvent distributions.