title: A maximum likelihood framework for protein design.
abstract: BACKGROUND
  The aim of protein design is to predict amino-acid sequences compatible with a given target structure. Traditionally envisioned as a purely thermodynamic question, this problem can also be understood in a wider context, where additional constraints are captured by learning the sequence patterns displayed by natural proteins of known conformation. In this latter perspective, however, we still need a theoretical formalization of the question, leading to general and efficient learning methods, and allowing for the selection of fast and accurate objective functions quantifying sequence/structure compatibility.
  
  
  RESULTS
  We propose a formulation of the protein design problem in terms of model-based statistical inference. Our framework uses the maximum likelihood principle to optimize the unknown parameters of a statistical potential, which we call an inverse potential to contrast with classical potentials used for structure prediction. We propose an implementation based on Markov chain Monte Carlo, in which the likelihood is maximized by gradient descent and is numerically estimated by thermodynamic integration. The fit of the models is evaluated by cross-validation. We apply this to a simple pairwise contact potential, supplemented with a solvent-accessibility term, and show that the resulting models have a better predictive power than currently available pairwise potentials. Furthermore, the model comparison method presented here allows one to measure the relative contribution of each component of the potential, and to choose the optimal number of accessibility classes, which turns out to be much higher than classically considered.
  
  
  CONCLUSIONS
  Altogether, this reformulation makes it possible to test a wide diversity of models, using different forms of potentials, or accounting for other factors than just the constraint of thermodynamic stability. Ultimately, such model-based statistical analyses may help to understand the forces shaping protein sequences, and driving their evolution.
authors.affiliation: Canadian Institute for Advanced Research, Département de Biochimie, Université de Montréal, Montréal, Québec, Canada. cl.kleinman@umontreal.ca
authors.forename: Claudia L
authors.initials: CL
authors.lastname: Kleinman
authors.forename: Nicolas
authors.initials: N
authors.lastname: Rodrigue
authors.forename: Cécile
authors.initials: C
authors.lastname: Bonnard
authors.forename: Hervé
authors.initials: H
authors.lastname: Philippe
authors.forename: Nicolas
authors.initials: N
authors.lastname: Lartillot
mesh_terms: D000595:Amino Acid Sequence; D001665:Binding Sites; D003198:Computer Simulation; D016503:Drug Delivery Systems / Q000379:methods*; D015195:Drug Design; D016013:Likelihood Functions; D008958:Models, Molecular; D015233:Models, Statistical; D008969:Molecular Sequence Data; D011485:Protein Binding; D015202:Protein Engineering / Q000379:methods; D011506:Proteins / Q000737:chemistry* / Q000145:classification; D016415:Sequence Alignment / Q000379:methods*; D020539:Sequence Analysis, Protein / Q000379:methods*
chemical_list: D011506:Proteins