Abstract
In 1951, before the first experimental determination of a complete protein structure, Corey and Pauling predicted that certain typical local structural motifs would arise from specific hydrogen bond patterns [121]. These motifs, referred to as α-helices and β-sheets, were later confirmed experimentally, and are now known to exist in almost all proteins. The fact that proteins display such strong local structural preferences has an immediate consequence for protein structure simulation and prediction. The efficiency of simulations can be enhanced by focusing on candidate structures that exhibit realistic local structure, thus effectively reducing the conformational search space. Probabilistic models that capture local structure are also the natural building blocks for the development of more elaborate models of protein structure.
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Notes
- 1.
This follows directly from the definition of the spherical coordinate system. Note that the sphere is the two-dimensional surface of the three-dimensional ball.
- 2.
The models can equally well be considered as multi-track HMMs, but the graphical formalism for DBNs is more convenient for the TORUSDBN and FB5HMM models, since they use fully connected transition matrices (see Chap. 1).
- 3.
This requires that the probability of h s − 1 is included, by taking it into consideration when filling in the first column of the forward matrix (position s).
- 4.
In random order, all hidden nodes were resampled based upon their current left and right neighboring h values and the observed emission values at that residue.
- 5.
It should be noted that these articles erroneously state that the models described in this chapter only capture the dependencies between neighboring residues. Obviously, the presence of a Markov chain of hidden nodes actually enforces dependencies along the whole sequence. In practice, such Markov chains do have a finite memory.
Acknowledgements
The authors acknowledge funding by the Danish Research Council for Technology and Production Sciences (FTP, project: Protein structure ensembles from mathematical models, 274-09-0184) and the Danish Council for Independent Research (FNU, project: A Bayesian approach to protein structure determination, 272-08-0315).
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© 2012 Springer-Verlag Berlin Heidelberg
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Boomsma, W., Frellsen, J., Hamelryck, T. (2012). Probabilistic Models of Local Biomolecular Structure and Their Applications. In: Hamelryck, T., Mardia, K., Ferkinghoff-Borg, J. (eds) Bayesian Methods in Structural Bioinformatics. Statistics for Biology and Health. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27225-7_10
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