Volume and Surface Types

This program can calculate different types of volume and surface area related to molecular structures.

For clarity, we are defining here the different types of volume and surface.

Types of surface

• The van der Waals surface (S_vdw) is simply the surface defined by atoms if they were rigid spheres with a van der Waals radius (for more information see Van der Waals surface).

• The probe accessible surface (S_acc) is the surface defined by the center of a spherical probe rolling around the atoms. It is related to the concept of solvent accessible surface (or Lee-Richards surface) where the probe would be a solvent molecule like water (see Solvent accessible surface).

• The probe excluded surface (S_exc) is the surface defined by the contact point of a spherical probe rolling around the atoms. It is related to the concept of solvent excluded surface (or Connolly surface or "molecular surface") where the probe would be a solvent molecule like water (see Solvent excluded surface).

Note that when a cavity is present inside the molecular structure and isolated from the outside (i.e. the probe cannot enter the cavity from outside), there are special considerations that are further discussed below.

The image below gives a general idea of the three types of surfaces seen in 2D:

Types of volume

There are two main categories of volume with several variants or subcategories:

• Molecular volumes which correspond to the space occupied by the atoms
  • Van der Waals molecular volume (V_vdw) corresponding to the space delimited by the S_vdw and containing the atoms.
  • Probe excluded molecular volume (V_mol-exc) corresponding to the space delimited by the S_exc and containing the atoms.
  • Probe accessible molecular volume (V_mol-acc) corresponding to the space delimited by the S_acc and containing the atoms. This type of volume can be defined but, to the best of our knowledge, has no interesting physical meaning and is not used. This volume is not provided by the program but can be manually calculated if desired ( V_mol-acc = V_mol-exc + V_probe-shell ).
• Void volumes which correspond to the empty space unoccupied by atoms (the "negative" of the molecular volumes):
  • Complete void (V_void-total) corresponding to the space unoccupied by atoms, delimited by the S_vdw.
  • Probe excluded void (V_void-exc) corresponding to the space not covered by the atoms nor the probes between S_vdw and S_exc.
  • Probe occupied void (V_void-occ) corresponding to the space that can be covered by the full probe floating around atoms and delimited by S_exc.
  • Probe accessible void (V_void-acc) corresponding to the space that can be covered by the center of the probe floating around atoms and delimited by S_acc.

Surfaces and volumes when using two probes

As seen in the image above, the surface and volume of isolated cavities can be easily defined but pockets that go inside molecules and are connected to the "outside" don't have a clear limit when using the rolling probe concept. To circumvent this issue, a special mode involving two probes was introduced to the program MoloVol where a second large probe is rolling around the exterior of the molecule (see Two probes modes). While the surface and volume types defined above remain valid for this two probe mode, some of these surfaces are divided into sub-types. For instance, the probe excluded molecular volume will be divided into two sub-types: probes excluded molecular volume and probe 2 excluded molecular volume (sometimes referred as the shell volume, see program ³V article and website). The following image describes the new types of surface and volume considered in the two probe modes.

Note that more types could be considered (e.g. probe 1 excluded molecular volume) but they were deemed useless and are therefore not described.

Special considerations regarding isolated cavities

In some cases, it can be interesting to calculate a molecular volume or surface that is only delimited by a probe coming from the outside, i.e. considering the isolated cavities as part of the molecular volume. It is often the case for biomacromolecules such as proteins because the isolated cavities are considered useless for their activity (assuming that the cavity does not become accessible during conformational change).

The program MoloVol provides the following volume and surface area values in the report file:

• outside probe excluded surface area = S_exc-total - S_exc-cavities (only provided in single probe mode, not for unit cell analysis)
• outside probe accessible surface area = S_acc-total - S_acc-cavities (only provided in single probe mode, not for unit cell analysis)
• outside probe excluded molecular volume = V_mol-exc + V_{void-occ-cavities} (not for unit cell analysis)

The following volume has no useful physical meaning and is not provided but can be manually calculated from other values if desired:

• outside probe accessible molecular volume = V_mol-acc + V_{void-acc-cavities}

The image below illustrate what would corresponds to the outside probe excluded molecular volume sometimes simply referred as the molecular volume in biochemistry.