A Quantitative Theory of Mechanical Unfolding of a Homopolymer Globule (original) (raw)
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Mechanical Unfolding of a Homopolymer Globule Studied by Self-Consistent Field Modeling
Macromolecules, 2009
We present results of numerical Self-Consistent Field (SCF) calculations for the equilibrium mechanical unfolding of a globule formed by a single flexible polymer chain collapsed in a poor solvent. In accordance with earlier scaling theory and stochastic dynamics simulations findings we have identified three regimes of extensional deformation: (i) a linear response regime characterized by a weakly elongated (ellipsoidal) shape of the globule at small deformations; (ii) a tadpole structure with a globular "head" co-existing with a stretched "tail" at intermediate ranges of deformations and (iii) an uniformly stretched chain at strong extensions. The conformational transition from the tadpole to the stretched chain is accompanied by an abrupt unfolding of the depleted globular head and a corresponding jump-wide drop in the intra-chain tension. The unfolding-refolding cycle demonstrates a hysteresis loop in the vicinity of the transition point. These three regimes of deformation, as well as the first-order like transition between the tadpole and the stretched chain conformations, can be experimentally observable provided that the number of monomer units in the chain is large and/or the solvent quality is sufficiently poor. For short chains, on the other hand, at moderately poor solvent strength conditions the unfolding transition is continuous. Upon an increase in the imposed end-to-end distance the extended globule retains a longitudinally uniform shape at any degree of deformation. In all cases the system exhibits a negative extensional modulus in the intermediate range of deformations. We anticipate that predictions of patterns in force-deformation curves for polymer molecules in poor solvent can be observed in single molecule atomic spectroscopy experiments.
Mechanical Unfolding of a Homopolymer Globule: Applied Force versus Applied Deformation
Modern Trends in Polymer Science-Epf 09, 2010
We propose the quantitative mean-field theory of mechanical unfolding of a globule formed by long flexible homopolymer chain collapsed in poor solvent and subjected to an extensional force We show that with an increase in the applied force the globule unfolds as a whole without formation of an intermediate state. The value of the threshold force and the corresponding jump in the distance between chain ends increase with a deterioration of the solvent quality and / or with an increase in the degree of polymerization. This way of globule unfolding is compared with that in the Densemble, when the distance between chain ends is imposed.
Macromolecules, 2011
Equilibrium mechanical unfolding of a globule formed by long flexible homopolymer chain collapsed in a poor solvent and subjected to an extensional force f (force-clamp mode) or extensional deformation D (position-clamp mode) is studied theoretically. Our analysis, like all previous analysis of this problem, shows that the globule behaves essentially differently in two modes of extension. In the force-clamp mode, mechanical unfolding of the globule with increasing applied force occurs without intramolecular microphase segregation, and at certain threshold value of the pulling force the globule unfolds as a whole ("all-or-none" transition). The value of the threshold force and the corresponding jump in the distance between the chain ends increase with a deterioration of the solvent quality and / or with an increase in the degree of polymerization. In the position-clamp mode, the globule unfolding occurs via intramolecular microphase coexistence of globular and extended microphases followed by an abrupt unraveling transition. Reaction force in the microphase segregation regime demonstrates an "anomalous" decrease with increasing extension. Comparison of deformation curves in force and position-clamp modes demonstrates that at weak and strong extensions the curves for two modes coincide, differences are observed in the intermediate extension range. Another unfolding scenario is typical for short globules: in both modes of extension they unfold continuously, without jumps or intramolecular microphase coexistence, by passing a sequence of uniformly elongated configurations. The values of the the critical chain length, Ncr, separating long and short chain behavior are slightly different for two extension modes: N cr,f < Ncr,D.
Unfolding of globular polymers by external force
The Journal of Chemical Physics, 2015
We examine the problem of a polymer chain, folded into a globule in poor solvent, subjected to a constant tensile force. Such a situation represents a Gibbs thermodynamic ensemble and is useful for analysing forceclamp atomic force microscopy measurements, now very common in molecular biophysics. Using a basic Flory mean-field theory, we account for surface interactions of monomers with solvent. Under an increasing tensile force a first-order phase transition occurs from a compact globule to a fully extended chain, in an 'all-ornothing' unfolding event. This contrasts with the regime of imposed extension, first studied by Halperin and Zhulina, where there is a regime of coexistence of a partial globule with an extended chain segment. We relate the transition forces in this problem to the solvent quality and degree of polymerisation, and also find analytical expressions for the energy barriers present in the problem. Using these expressions, we analyse the kinetic problem of a force-ramp experiment, and show that the force at which a globule ruptures depends on the rate of loading.
Stepwise unfolding of collapsed polymers
The European Physical Journal E, 2004
Motivated by recent experimental data on DNA stretching in presence of polyvalent counterions, we study the force-induced unfolding of a homopolymer on and off lattice. In the fixed force ensemble the globule unravels via a series of steps due to surface effects which play an important role for finite-size chains. This holds both for flexible and stiff polymers. We discuss in a qualitative way how this result may impact on the interpretation of DNA stretching experiments showing peaks in the characteristic curves, by extracting from the raw data the corresponding elongation-versus-force characteristic curves. Furthermore, approximate analytical and numerical calculations, valid in a quasi-equilibrium fixed stretch ensemble, and if the initial low-temperature state is ordered in a spool, show that the average force versus elongation displays peaks related to the geometry of the initial configuration. We finally argue how the proposed mechanisms identified for the arising of peaks may couple in the experiments, and comment on the role of dynamic effects. PACS. 82.35.Lr Physical properties of polymers -87.15.-v Biomolecules: structure and physical properties -36.20.Ey Conformation (statistics and dynamics)
Modeling force-induced bio-polymer unfolding
Journal of Mathematical Chemistry, 2009
We study the conformations of polymer chains in a poor solvent, with and without bending rigidity, by means of a simple statistical mechanics model. This model can be exactly solved for chains of length up to N = 55 using exact enumeration techniques. We analyze in details the differences between the constant force and constant distance ensembles for large but finite N . At low temperatures, and in the constant force ensemble, the force-extension curve shows multiple plateaus (intermediate states), in contrast with the abrupt transition to an extended state prevailing in the N → ∞ limit. In the constant distance ensemble, the same curve provides a unified response to pulling and compressing forces, and agrees qualitatively with recent experimental results. We identify a cross-over length, proportional to N , below which the critical force of unfolding decreases with temperature, while above, it increases with temperature.
Role of Conformational Entropy in Force-Induced Biopolymer Unfolding
Physical Review Letters, 2007
A statistical mechanical description of flexible and semi-flexible polymer chains in a poor solvent is developed in the constant force and constant distance ensembles. We predict the existence of many intermediate states at low temperatures stabilized by the force. A unified response of pulling and compressing force has been obtained in the constant distance ensemble. We show the signature of a cross-over length which increases linearly with the chain length. Below this cross-over length, the critical force of unfolding decreases with temperature, while above, it increases with temperature. For stiff chains, we report for the first time a "saw-tooth" like behavior in the force-extension curves which has been seen earlier in the case of protein unfolding.
Unwinding globules under tension and polymer collapse
Physical Review E, 2002
Polymer collapse is known to be mediated by the formation of pearls. These intermediate structures behave as small globules under tension. The globule size is studied by molecular dynamic simulations as a function of the strength of an external stretching force applied to its ends, for different values of the chain length. A very strong first-order-like transition from a compact globule state to a stretched one is observed. A model of this transition in terms of a globule-chain system is presented. The critical force, above which the globule unwinds, is shown to satisfy a power law scaling like N 1/3 in the number of monomers.
Early stages of homopolymer collapse
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 2000
Interest in the protein folding problem has motivated a wide range of theoretical and experimental studies of the kinetics of the collapse of flexible homopolymers. In this paper, a phenomenological model is proposed for the kinetics of the early stages of homopolymer collapse following a quench from temperatures above to below the straight theta temperature. In the first stage, nascent droplets of the dense phase are formed, with little effect on the configurations of the bridges that join them. The droplets then grow by accreting monomers from the bridges, thus causing the bridges to stretch. During these two stages, the overall dimensions of the chain decrease only weakly. Further growth of the droplets is accomplished by the shortening of the bridges, which causes the shrinking of the overall dimensions of the chain. The characteristic times of the three stages scale as N0, N(1/5), and N(6/5), respectively, where N is the degree of polymerization of the chain.
Statistical mechanics of stretching of biopolymers
We developed a simple model of polymers on a triangular lattice to study the force-induced transitions related to biopolymers. Using an exact enumeration technique, we calculate various thermodynamic quantities associated with it. We show here, by including different parameters, e.g. bending and paring interactions in the model system, that one can understand the qualitative differences in the force-extension curves exhibited by different biopolymers. Our study also shows that the solvent plays an important role in the unfolding of proteins.