Conformational transitions of heteropolymers in dilute solutions

Abstract

In this paper we extend the Gaussian self-consistent method to permit study of the equilibrium and kinetics of conformational transitions for heteropolymers with any given primary sequence. The kinetic equations earlier derived by us are transformed to a form containing only the mean squared distances between pairs of monomers. These equations are further expressed in terms of instantaneous gradients of the variational free energy. The method allowed us to study exhaustively the stability and conformational structure of some periodic and random aperiodic sequences. A typical phase diagram of a fairly long amphiphilic heteropolymer chain is found to contain phases of the extended coil, the homogeneous globule, the micro-phase separated globule, and a large number of frustrated states, which result in conformational phases of the random coil and the frozen globule. We have also found that for a certain class of sequences the frustrated phases are suppressed. The kinetics of folding from the extended coil to the globule proceeds through non-equilibrium states possessing locally compacted, but partially misfolded and frustrated, structure. This results in a rather complicated multistep kinetic process typical of glassy systems.Comment: 15 pages, RevTeX, 20 ps figures, accepted for publication in Phys. Rev.

Polymer association in poor solvents: from monomolecular micelles to clusters of chains and phase separation

“…9) and references therein). Here we only add that very recently Timoshenko et al 15) studied the kinetics of collapse and the final equilibrium states of random copolymers using a model quite similar to ours. However, they considered both solvophobic and solvophilic beads, respectively having attractive and repulsive long-range two-body interactions of varying strength.…”

“…Such procedure was followed by Dawson et al 14) to study the collapse of periodic ring copolymers with the alternating structure (AB) n ; however, see also refs. 15,16) We considered copolymers having fixed sequences of 20% to 60% mutually attractive {1}-beads, generated at random in chains with up to N T = 40 total beads 17) . The parameters of the repulsive interactions are equal to those of chain I discussed in Section 3A.…”

Conformations of dendrimers in dilute solution

“…(7), applied until the stationary limit is reached, presents one of the most efficient techniques for finding the global free energy minimum. This, based on the fifth order adaptive step Runge-Kutta integrator 16 , is used for obtaining the results from the GSC technique.…”

“…A version of the Gaussian variational theory 15 , which relies on a somewhat problematic 16 virial representation of the excluded volume interactions 17,18 , has been used by Ganazzoli et al for describing the size, shape and intrinsic viscosity of dendrimers in a good solvent 19 . Based on this approach the dynamic properties such as the relaxation times spectrum, dynamic structure factor and the viscoelastic moduli, 20 , as well as the inter-chain theta-temperature 21 have been also investigated.…”

Pathway to copolymer collapse in dilute solution: Uniform versus random distribution of comonomers

“…Theory and simulations show that collapse of flexible random copolymers is preceded by microphase separation due to aggregation of the sticky comonomers, and that the chain can exhibit frozen, folded, and collapsed states depending on its stiffness, the "stickiness" of comonomer interactions, and the distribution of comonomers along the chain ͑viz., chain microstructure͒. 3,7,8 It is interesting to examine the role played by copolymer microstructure on collapse-especially since copolymers with precisely tailored microstructures can now be experimentally realized using recent advances in synthetic techniques. 9 There are relatively few reports that investigate how copolymer microstructure influences collapse.…”