Despi
te much s
tudy, biomolecule folding coopera
tivi
ty is no
t well unders
tood. There arequan
ti
ta
tive models for helix-coil
transi
tions and for coil-
to-globule
transi
tions, bu
t no accura
te models ye
ttrea
t bo
th chain collapse and secondary s
truc
ture forma
tion
toge
ther. We develop here a dynamicprogramming approach
to s
ta
tis
tical mechanical par
ti
tion func
tions of foldamer chain molecules. We call i
tthe ascending levels model. We apply i
t to helix-coil and helix-bundle folding and coopera
tivi
ty. For 14-
to50-mer
Baldwin pep
tides,
the model gives good predic
tions for
the hea
t capaci
ty and helici
ty versus
tempera
ture and urea. The model also gives good fi
ts for
the dena
tura
tion of Oas's
three-helix bundle Bdomain of pro
tein A (F13W*) and syn
the
tic pro
tein
3C by
tempera
ture and guanidine. The model predic
ts
the conforma
tional dis
tribu
tions. I
t shows
tha
t these pro
teins fold wi
th
transi
tions
tha
t are
two-s
ta
te, al
though
the
transi
tions in
the Baldwin helices are nearly higher order. The model shows
tha
t the recen
tly developed
three-helix bundle polypep
toids of Lee e
t al. fold
anti-cooperatively, wi
th a predic
ted value of
![](/images/gifchars/Del<font color=)
ta.gif" BORDER=0 >
HvH/
![](/images/gifchars/Del<font color=)
ta.gif" BORDER=0 >
Hcal =0.72. The model also predic
ts
tha
t two-helix bundles are uns
table in pro
teins bu
t s
table in pep
toids. Ourdynamic programming approach provides a general way
to explore coopera
tivi
ty in complex foldablepolymers.