1.1 Depth index

1 Atoms exposition

The depth of atom from protein surface has been proposed as a criterion to define protein structures. Current methods consist in evaluating the smaller distance between an atom and a dot of the solvent accessible surface [1] or the distance between an atom and its closest solvent accessible neighbor [2]. These methods have the drawback to lose the contribution from the three-dimensional molecular shape.

**Figure 1:** Hen egg white lysozyme: $\alpha$ -carbon 47 (red) and 58 (green) are both on the molecule surface, but accessibility of the former is quite greater

The purpose of SADIC is to calculate atoms exposition keeping into account the three-dimensional shape of the molecule. The program simulates the molecule probing by a probe of given radius and calculates the exposed volume and surface as seen by the probe, as well as the depth index.

**Figure:** Area E represents the space external to the molecule as seen by the probe

1.1 Depth index

The depth index is defined as

$\begin{displaymath}D_{i,r} = 2V_{i,r}/V_{0,r},\end{displaymath}$

where $V_{i,r}$ is the exposed volume of a sphere of radius r centered on atom i and $V_{0,r}$ is the exposed volume of the same sphere when centered on an isolated atom. Given this definition, the depth index results in a number ranging from 0 to 2: its value is 0 if the atom is completely buried inside the molecule and no external point is closer than r; a theoretical value of 2 would be obtained if the atom were completely isolated. If an atom center lied on a theoretical perfect plane -- splitting the space into an ``internal'' and an ``external'' half-space -- its $D_{i,r}$ would be exactly 1.