  The respective roles of local and nonlocal interactions in the thermodynamic
cooperativity of proteins are investigated using continuum (off-lattice)
native-centric G\=o-like models with a coarse-grained C$_\alpha$ chain
representation. We study a series of models in which the (local) bond- and
torsion-angle terms have different strengths relative to the (nonlocal)
pairwise contact energy terms. Conformational distributions in these models are
sampled by Langevin dynamics. Thermodynamic cooperativity is characterized by
the experimental criteria requiring the van't Hoff to calorimetric enthalpy
ratio $\Delta H_{\rm vH}/\Delta H_{\rm cal}\approx 1$ (the calorimetric
criterion), as well as a two-state-like variation of the average radius of
gyration upon denaturation. We find that both local and nonlocal interactions
are critical for thermodynamic cooperativity. Chain models with either much
weakened local conformational propensities or much weakened favorable nonlocal
interactions are significantly less cooperative than chain models with both
strong local propensities and strong favorable nonlocal interactions. These
findings are compared with results from a recently proposed lattice model with
a local-nonlocal coupling mechanism; their relationship with experimental
measurements of protein cooperativity and chain compactness is discussed.
