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<Paper uid="W06-1635">
  <Title>Sydney, July 2006. c(c)2006 Association for Computational Linguistics Protein folding and chart parsing</Title>
  <Section position="3" start_page="0" end_page="293" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> In statistical parsing, the task is to find the most likely syntactic structure for an input string of words, given a grammar and a probability model over the analyses defined by that grammar. Proteins are sequences of amino acids (polypeptide chains) that form unique, sequence-specific three-dimensional structures. The structure into which a particular protein folds has a lower energy than all other possible structures. In protein structure prediction, the task is thus to find the lowest-energy physical structure for an input sequence of amino acids, given a representation of possible structures and a function that assigns an energy score to these structures. There is therefore a natural analogy between these two seemingly unrelated computational problems. Based on this analogy, we propose an adaptation of the CKY chart parsing algorithm to protein structure prediction, using a well-known simplified model of proteins as proof of concept.</Paragraph>
    <Paragraph position="1"> Models of protein folding additionally aim to explain the process by which this structure formation takes place, and their validity depends not only on the accuracy of the predicted structures, but also on their physical plausibility. One common proposal in the biophysical literature is that the folding process is hierarchical, and that folding routes are tree-shaped. CKY provides an explicit computational recipe to efficiently search (and return) all possible folding routes. This sets it apart from existing folding algorithms, which are typically based on Monte Carlo simulations, and can only sample one possible trajectory.</Paragraph>
    <Paragraph position="2"> Since we believe that there is much scope for future work in applying statistical parsing techniques to more detailed models of proteins, a secondary aim of this paper is to provide an introduction to the research questions that arise in protein folding to the NLP community.</Paragraph>
    <Paragraph position="3"> Proteins are essential components of the cells of any living organism, and their biological function (eg. as enzymes that catalyze certain reactions) depends on their three-dimensional structure. However, genes only specify the linear, sequence of the amino acids, and the ribosome (the cell's &amp;quot;protein factory&amp;quot;) uses this information to assemble the polypeptide chain. Under &amp;quot;natural&amp;quot; conditions, these polypeptide chains then fold rapidly and spontaneously into their unique final structures, or native states. Therefore, protein folding is often referred to as the second half of the genetic code, and the ability to predict the native state for a primary sequence is great practical importance, eg. in drug design, or in our understanding of the genome.</Paragraph>
    <Paragraph position="4"> Levinthal (1968), who was the first to frame the folding process as a search problem, showed that folding cannot be guided by a random, exhaustive search: he argued that a chain of 150 amino acids has on the order of 10300 possible structures, but since folding takes only a few seconds, not more 108 of these structures can be searched. Under the assumption that a better understanding of the physical folding process will ultimately be required to design accurate structure prediction techniques, this observation has lead researchers to try to identify sequence-specific pathways along which folding may proceed or a general mechanism that makes this process so fast and reliable. Our aim of understanding the folding process is different from a number of approaches which have  used formal grammars to represent the structure of biological molecules such as RNAs or proteins (Searls, 2002; Durbin et al., 1998; Chiang, 2004).</Paragraph>
    <Paragraph position="5"> These studies have typically focused on a specific classes of protein folds, and are not generally applicable yet. Our folding algorithm restricts the possible order of folding events, but places no explicit restrictions on the structures it can account for (other than those imposed by the spatial model used to represent them, and those that are implied by the hierarchical nature of the folding process).</Paragraph>
  </Section>
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