Theory of Sequence-Dependent Coil-Globule Transition in Non-Ionic AB Copolymers

The conformational transition from a coil to a globule in a single polymer chain represents a cornerstone problem in polymer physics. While this problem is fully understood for homopolymers, it becomes significantly more complex for copolymers composed of just two monomer types, A and B: both experiments [1] and simulations [2] have shown that the transition sharpness is highly sensitive to the chain’s primary sequence. A theoretical understanding of this effect has remained elusive, and this work aims to fill this gap.

We develop a statistical theory for the coil–globule transition in neutral AB copolymers. To capture the role of the primary sequence, we go beyond the mean-field approximation and include Gaussian fluctuation corrections arising from the chemical incompatibility between A and B monomers. These local compositional fluctuations lead to a reduction of the second and third virial coefficients of monomer interactions, which we derive analytically for arbitrary sequences. Increasing sequence blockiness is shown to (i) make the globule more compact, (ii) shift the transition to higher temperatures, and, crucially, (iii) narrow the transition region. The collapse becomes highly cooperative or even jump-like first order when it coincides with or closely precedes intra-globular microphase separation. The proposed theory thus provides a unified description of sequence-dependent conformational behavior in macromolecules, including Khokhlov–Khalatur protein-like copolymers that form core–shell structured globules. [1,2]

[1] H. K. Murnen, A. R. Khokhlov, P. G. Khalatur, R. A. Segalman, and R. N. Zuckermann, “Impact of Hydrophobic Sequence Patterning on the Coil-to-Globule Transition of Protein-like Polymers,” Macromolecules 45, 5229 (2012).

[2] A. R. Khokhlov and P. G. Khalatur, “Conformation-Dependent Sequence Design (Engineering) of AB Copolymers,” Phys. Rev. Lett. 82, 3456 (1999).