\end{figure}
-\section{Implicit solvation\index{implicit solvation}\index{Generalized Born methods}}
-\label{sec:gbsa}
-Implicit solvent models provide an efficient way of representing
-the electrostatic effects of solvent molecules, while saving a
-large piece of the computations involved in an accurate, aqueous
-description of the surrounding water in molecular dynamics simulations.
-Implicit solvation models offer several advantages compared with
-explicit solvation, including eliminating the need for the equilibration of water
-around the solute, and the absence of viscosity, which allows the protein
-to more quickly explore conformational space.
-
-Implicit solvent calculations in {\gromacs} can be done using the
-generalized Born-formalism, and the Still~\cite{Still97}, HCT~\cite{Truhlar96},
-and OBC~\cite{Case04} models are available for calculating the Born radii.
-
-Here, the free energy $G_{\mathrm{solv}}$ of solvation is the sum of three terms,
-a solvent-solvent cavity term ($G_{\mathrm{cav}}$), a solute-solvent van der
-Waals term ($G_{\mathrm{vdw}}$), and finally a solvent-solute electrostatics
-polarization term ($G_{\mathrm{pol}}$).
-
-The sum of $G_{\mathrm{cav}}$ and $G_{\mathrm{vdw}}$ corresponds to the (non-polar)
-free energy of solvation for a molecule from which all charges
-have been removed, and is commonly called $G_{\mathrm{np}}$,
-calculated from the total solvent accessible surface area
-multiplied with a surface tension.
-The total expression for the solvation free energy then becomes:
-
-\beq
-G_{\mathrm{solv}} = G_{\mathrm{np}} + G_{\mathrm{pol}}
-\label{eqn:gb_solv}
-\eeq
-
-Under the generalized Born model, $G_{\mathrm{pol}}$ is calculated from the generalized Born equation~\cite{Still97}:
-
-\beq
-G_{\mathrm{pol}} = \left(1-\frac{1}{\epsilon}\right) \sum_{i=1}^n \sum_{j>i}^n \frac {q_i q_j}{\sqrt{r^2_{ij} + b_i b_j \exp\left(\frac{-r^2_{ij}}{4 b_i b_j}\right)}}
-\label{eqn:gb_still}
-\eeq
-
-In {\gromacs}, we have introduced the substitution~\cite{Larsson10}:
-
-\beq
-c_i=\frac{1}{\sqrt{b_i}}
-\label{eqn:gb_subst}
-\eeq
-
-which makes it possible to introduce a cheap transformation to a new
-variable $x$ when evaluating each interaction, such that:
-
-\beq
-x=\frac{r_{ij}}{\sqrt{b_i b_j }} = r_{ij} c_i c_j
-\label{eqn:gb_subst2}
-\eeq
-
-In the end, the full re-formulation of~\ref{eqn:gb_still} becomes:
-
-\beq
-G_{\mathrm{pol}} = \left(1-\frac{1}{\epsilon}\right) \sum_{i=1}^n \sum_{j>i}^n \frac{q_i q_j}{\sqrt{b_i b_j}} ~\xi (x) = \left(1-\frac{1}{\epsilon}\right) \sum_{i=1}^n q_i c_i \sum_{j>i}^n q_j c_j~\xi (x)
-\label{eqn:gb_final}
-\eeq
-
-The non-polar part ($G_{\mathrm{np}}$) of Equation~\ref{eqn:gb_solv} is calculated
-directly from the Born radius of each atom using a simple ACE type
-approximation by Schaefer {\em et al.}~\cite{Karplus98}, including a
-simple loop over all atoms.
-This requires only one extra solvation parameter, independent of atom type,
-but differing slightly between the three Born radii models.
-
% LocalWords: GROningen MAchine BIOSON Groningen GROMACS Berendsen der Spoel
% LocalWords: Drunen Comp Phys Comm ROck NS FFT pbc EM ifthenelse gmxlite ff
% LocalWords: octahedra triclinic Ewald PME PPPM trjconv xy solvated