Efficient Enumeration and Visualization of Helix-coil Ensembles

Helix-coil models are routinely used to interpret CD data of helical peptides or predict the helicity of naturally-occurring and designed polypeptides. However, a helix-coil model contains significantly more information than mean helicity alone, as it defines the entire ensemble - the equilibrium population of every possible helix-coil configuration - for a given sequence. Many desirable quantities of this ensemble are either not obtained as ensemble averages, or are not available using standard helicity-averaging calculations. Enumeration of the entire ensemble can allow calculation of a wider set of ensemble properties, but the exponential size of the configuration space typically renders this intractable. We present an algorithm that efficiently approximates the helix-coil ensemble to arbitrary accuracy, by sequentially generating a list of the M highest populated configurations in descending order of population. Truncating this list of (configuration, population) pairs at a desired accuracy provides an approximating sub-ensemble. We demonstrate several uses of this approach for providing insight into helix-coil ensembles and folding mechanisms, including landscape visualization. O_TEXTBOXSIGNIFICANCE Helix-coil models define the probability distribution of helix-coil configurations for a polypeptide (a helix-coil ensemble). Each configuration specifies which residues are -helical and which are not. We used an accurate helix-coil model, paired with concepts from the field of probabilistic graphical modeling, to devise an algorithm capable of enumerating helix-coil configurations in order of decreasing probability. By enumerating ensembles for a representative set of peptides we find that helix-coil ensembles tend to be highly concentrated, with the vast majority of probability mass assigned to a relatively small set of configurations from a configuration space that is often astronomical in size. This result facilitates the development of new and accurate methods for analyzing and predicting the behavior of helical polypeptides. C_TEXTBOX