From Protein Structure to Function with Bioinformatics.pdf

2 Fold Recognition 37dependent on the quality of the initial alignment, which again was the problem inthe first place. To avoid some of this dependence on the initial alignment theprocess is iterated several times, realigning the sequence with a contribution fromthe threading score on the previous iteration.A quite complex approach was developed by (Jones et al. 1992) called ‘doubledynamic programming’ used in the program THREADER. This approach provedquite successful in the early days of CASP. A full description of this technique isbeyond the scope of this chapter. However in summary, the idea is to align a singleposition in the query sequence with a single position in the template structure. Thenone uses a conventional alignment algorithm to align the remainder of the sequenceto optimise the potential with respect to this one fixed position. The optimal alignmentfound is then added to a scoring matrix. This process is repeated for everypossible (or at least a large reasonable subset) pair of residues in the sequence andstructure, each time accumulating the optimal alignments in the secondary scoringmatrix. Finally, the secondary scoring matrix is used to generate a final alignment,attempting to pass through as much of the accumulated alignments as possible. Itis this dual-level alignment that accounts for the name double-dynamic programming.It is essentially a method to break down the threading problem into a largenumber of simple problems whose solutions are combined to produce a singleanswer – a theme repeated in many of the methods described below.The Gibbs Sampling Algorithm was applied by Bryant (1996) to the problem ofthreading. The technique begins with a random alignment. At each step it randomlychooses a core secondary structure element C, generates all possible alternativealignments for it, calculates each new alignment score S and chooses a new alignmentwith probability proportional to exp(−S/kT), where k is the Boltzmann constantand T is a notional ‘temperature’ of the system. At every iteration a differentrandomly chosen core element is the target for alignment. A simulated annealingprotocol is used whereby the ‘temperature’ of the system is slowly reduced overtime. Thus, starting with an initial high temperature means poorly scoring alignmentsare accepted almost as frequently as good scoring alignments. This is suitableduring the beginning of the simulation as it is highly unlikely to have an overallgood alignment by chance. However, as the temperature drops, it becomes progressivelyless likely that poorly scoring alignments are accepted and the system gradually‘settles’ on a globally low energy alignment. Simulated annealing is a widelyused approach to many optimisation problems in bioinformatics and elsewhere. Themethod does not guarantee a global optimum alignment, but is very fast and givesgood performance.The divide and conquer threading algorithm (Xu et al. 1998) repeatedlydivides the structure model into sub-models, solves the alignment problem forsub-models, and combines the sub-solutions to find a globally optimal alignment.Similarly the branch and bound search algorithm (Lathrop and Smith 1996)repeatedly divides the threading search space into smaller subsets and alwayschooses the most promising subset to split next. Eventually the most promisingsubset contains only one alignment, which is a global optimum. Finding the globaloptimum is extremely time-consuming, so a so-called ‘anytime’ version