Protein Modelling and Surface Folding by Limiting the Degrees of Freedom - Computational Modeling in Tissue Engineering - page 34

protein size and additional terms would be required to account for this based on
species size. These changes can readily be accomplished within the software and
hence numerous further applications are possible.
One limitation that we encountered with our approach was an objective func-
tion that required readjustment when distances approached gapping in the protein
structure that were over 10 %. A solution for this would be to add the functionality
of AMBER software (Assistance Model Building with Energy Refinement) where
the energy for the distance is predicted and can therefore control or refine the
distance [ 16 , 18 , 59 , 62 ]. The added approach does not consider the atoms, but
simply the distance, and can deal with large or small sequences.

6 Conclusion

We present a new model to solve three-dimensional modelling of proteins that can
create supra structures within tissues. By considering amino acid peptides as
beads, hydrogen bond distances, the surface and distance geometry as functional
components, and by focusing on folding, the Ab initio protocols can successfully
model complex proteins in three dimensions with minimal computational load.

Acknowledgments The authors thank: Isabella Verdinelli and Lauren Ernst for the discussions
related to the model and Troy Wymore from the Pittsburgh Supercomputing Center for his
suggestions in verifying the models and a special thanks to Dr. Alex Cohen from ProteoRubix
Systems who developed the minimizer and for discussion and development of ProteoRubix TM
software for the Geometry Modelling. Chris Holm for editing the manuscript.

Appendix 1

NP
Suppose the bead involves d dihedral angles. Let / ¼ / 1 ; ... ; / n

2 0 ; 360

d ½ be

an optimal solution to the constrained optimization problem
(1.1) min

/ 2 0 ; 360

f v ð / : / is arotation about the bond i Þ g

d ½

Then there is a maximal number n [ 0.
(1.2) The p n hard problem of an exhaustive se ar ch over the angles
0 / i \ \/ i 360 to find an approximate optimizer / to / may be possible
for a modern computer.
(1.3) There is exactly one solution to (4) in / i p ; / i þ p

which would be /
and can be approximated using a given constrained optimization algorithm (B1).
The convergence ball for the constrained optimization algorithm provides a
candidate for p in the proposition. Using this proposition, we can obtain an
acceptable initial condition for a constrained optimization algorithm.