to solvent, approximated as the relative surface area (RSA) using the
Lee and Richards method implemented in the Naccess server
http://www.bioinf.manchester.ac.uk/naccess/nac_intro.html (see
Note 1)[36]. The impact of the exposition to solvent is modeled
with an exponential function in which the amino acids with:
(1) more than 55% RSA have a weight of 1 and contribute as fully
exposed; (2) less than 10% RSA have a weight of 0 and are consid-
ered as buried; (3) intermediate values of RSA (10–55%) have a
weight ranging from 0.1 to 0.99 and contribute as partially exposed
residues. In order to obtain a structurally corrected A3Dscore, the
algorithm takes into account the corrected aggregation propensi-
ties of the amino acid under evaluation “i”plus the sum of those
residues “e”included inside a projected sphere of 10 or 5 A ̊cen-
tered on its alpha carbon (Cαi) (Fig.1). Besides, the specific dis-
tance between the sphere center and the alpha carbon of other
residues within the vicinity (Cαe) is measured in A ̊ and is used to
modulate an inverse exponential function to calculate their contri-
bution to the A3Dscore. Accordingly, those amino acids at:
(1) shorter distances than 1 A ̊, receive a weight of 1 and are
predicted as strong influencers; (2) larger distances than the sphere
radius, receive a weight of 0 and are considered as distant and
non influencing residues; (3) distances between the sphere limit
and 1 A ̊receive a weight ranging from 0.1 to 0.99 and are consid-
ered as modulators. As a result of this computational scheme, the
A3D algorithm provides a value for each single protein residue,
which will be positive or negative depending on whether this
residue is predicted to contribute more to aggregation or to solu-
bility, respectively, or 0 if the amino acid is not predicted to play a
significant role.2.2 A3D Pipeline Prior to the aggregation prediction, A3D exploits FoldX algorithm
to minimize the energy of the input structure in order to remove
unfavorable energies arising from improper torsion angles, steric
Fig. 1Algorithm components.AggiandAggeare the intrinsic aggregation propensities for the central amino
acidiunder study and those amino acidsewithin the sphere, respectively;αandβare numeric parameters of
the exponential function referring to amino acid exposure;RSAiandRSAeare the relative surface area for the
central amino acidiunder study and those amino acidsewithin the sphere, respectively;δandγare numeric
parameters of the exponential function referring to the amino acid distance to the sphere center;distis the
distance between the CαCarbons of the sphere center residue and other residues encompassed in the sphere
430 Jordi Pujols et al.