Bulletin of Mathematical Biology

, 71:1914

A Geometric Buildup Algorithm for the Solution of the Distance Geometry Problem Using Least-Squares Approximation

Original Article

DOI: 10.1007/s11538-009-9431-9

Cite this article as:
Sit, A., Wu, Z. & Yuan, Y. Bull. Math. Biol. (2009) 71: 1914. doi:10.1007/s11538-009-9431-9


We propose a new geometric buildup algorithm for the solution of the distance geometry problem in protein modeling, which can prevent the accumulation of the rounding errors in the buildup calculations successfully and also tolerate small errors in given distances. In this algorithm, we use all instead of a subset of available distances for the determination of each unknown atom and obtain the position of the atom by using a least-squares approximation instead of an exact solution to the system of distance equations. We show that the least-squares approximation can be obtained by using a special singular value decomposition method, which not only tolerates and minimizes small distance errors, but also prevents the rounding errors from propagation effectively, especially when the distance data is sparse. We describe the least-squares formulations and their solution methods, and present the test results from applying the new algorithm for the determination of a set of protein structures with varying degrees of availability and accuracy of the distances. We show that the new development of the algorithm increases the modeling ability, and improves stability and robustness of the geometric buildup approach significantly from both theoretical and practical points of view.


Biomolecular modeling Protein structure determination Distance geometry Linear and nonlinear systems of equations Linear and nonlinear optimization 

Copyright information

© Society for Mathematical Biology 2009

Authors and Affiliations

  1. 1.Department of Mathematics, Program on Bioinformatics and Computational BiologyIowa State UniversityAmesUSA
  2. 2.Laboratory of Scientific and Engineering ComputingChinese Academy of ScienceBeijingChina

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