Improved calculations of compactness and a reevaluation of continuous compact units

A new method for calculating compactness (Z) that uses look-up table-based algorithms for area and volume computations is introduced. These algorithms can be used in any iterative area or volume calculation, are more than 1000 times faster than the original algorithms, and have equal or better precision. With the faster algorithms it is now possible to calculate the compactness of all continuous units in a protein, and to precisely locate the optimal compact units without the screening functions and limited resolution used previously. These methods have been incorporated into a fully automatic domain finding algorithm, and this method has been applied to the 21 proteins originally analyzed as well as 12 additional proteins. This method is robust, and yields similar units even when applied to coordinates of protein crystals grown under different experimental conditions.