In this study, we estimate the statistical significance of structure predic
tion by threading, We introduce a single parameter epsilon that serves as a
universal measure determining the probability that the best alignment is i
ndeed a native-like analog, Parameter epsilon takes into account both lengt
h and composition of the query sequence and the number of decoys in threadi
ng simulation, It can be computed directly from the query sequence and pote
ntial of interactions, eliminating the need for sequence reshuffling and re
alignment. Although our theoretical analysis is general, here we compare it
s predictions with the results of gapless threading. Finally we estimate th
e number of decoys from which the native structure can be found by existing
potentials of interactions, We discuss how this analysis can be extended t
o determine the optimal gap penalties for any sequence-structure alignment
(threading) method, thus optimizing it to maximum possible performance.