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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.<\/jats:p><\/jats:sec><jats:sec><jats:title>Results<\/jats:title><jats:p>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<jats:italic>inverse potential<\/jats:italic>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.<\/jats:p><\/jats:sec><jats:sec><jats:title>Conclusion<\/jats:title><jats:p>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.<\/jats:p><\/jats:sec>","DOI":"10.1186\/1471-2105-7-326","type":"journal-article","created":{"date-parts":[[2006,9,19]],"date-time":"2006-09-19T06:26:17Z","timestamp":1158647177000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":28,"title":["A maximum likelihood framework for protein design"],"prefix":"10.1186","volume":"7","author":[{"given":"Claudia L","family":"Kleinman","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nicolas","family":"Rodrigue","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"C\u00e9cile","family":"Bonnard","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Herv\u00e9","family":"Philippe","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nicolas","family":"Lartillot","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2006,6,29]]},"reference":[{"key":"1065_CR1","doi-asserted-by":"publisher","first-page":"5275","DOI":"10.1073\/pnas.78.9.5275","volume":"78","author":"KE Drexler","year":"1981","unstructured":"Drexler KE: Molecular engineering: an approach to the development of general capabilities for molecular manipulation. 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