Force-induced conformational transition in a system of interacting stiff polymers: application to unfolding

Self-Attractive Semiflexible Polymers under an External Force Field

The dynamical response of a tethered semiflexible polymer with self-attractive interactions and subjected to an external force field is numerically investigated by varying stiffness and self-interaction strength. The chain is confined in two spatial dimensions and placed in contact with a heat bath described by the Brownian multi-particle collision method. For strong self-attraction the equilibrium conformations range from compact structures to double-stranded chains, and to rods when increasing the stiffness. Under the external field at small rigidities, the initial close-packed chain is continuously unwound by the force before being completely elongated. For double-stranded conformations the transition from the folded state to the open one is sharp being steeper for larger stiffnesses. The discontinuity in the transition appears in the force-extension relation, as well as in the probability distribution function of the gyration radius. The relative deformation with respect to the equilibrium case along the direction normal to the force is found to decay as the inverse of the applied force.

Polymer in wedge-shaped confinement: Effect on the θ temperature

The equilibrium properties of a finite-length linear polymer chain confined in an infinite wedge composed of two perfectly reflecting hard walls meeting at a variable apex angle (α) are presented. One end of the polymer is anchored a distance y from the apex on the conical axis of symmetry, while the other end is free. We report here, the nonmonotonic behavior of θ temperature as a function of y for a finite-length chain. Data collapse for different chain lengths indicates that such behavior will exist for all finite lengths. We delineate the origin of such nonmonotonic behavior, which may have potential applications in understanding the cellular process occurring in nanoconfined geometries.

Stiffness dependence of critical exponents of semiflexible polymer chains situated on two-dimensional compact fractals

We present an exact and Monte Carlo renormalization group (MCRG) study of semiflexible polymer chains on an infinite family of the plane-filling (PF) fractals. The fractals are compact, that is, their fractal dimension df is equal to 2 for all members of the fractal family enumerated by the odd integer b(3<or=b<infinity). For various values of stiffness parameter s of the chain, on the PF fractals (for 3<or=b<or=9 ), we calculate exactly the critical exponents nu (associated with the mean squared end-to-end distances of polymer chain) and gamma (associated with the total number of different polymer chains). In addition, we calculate nu and gamma through the MCRG approach for b up to 201. Our results show that for each particular b, critical exponents are stiffness dependent functions, in such a way that the stiffer polymer chains (with smaller values of s) display enlarged values of nu, and diminished values of gamma. On the other hand, for any specific s, the critical exponent nu monotonically decreases, whereas the critical exponent gamma monotonically increases, with the scaling parameter b. We reflect on a possible relevance of the criticality of semiflexible polymer chains on the PF family of fractals to the same problem on the regular Euclidean lattices.

Polymers in crowded environment under stretching force: Globule-coil transitions

We study flexible polymer macromolecules in a crowded (porous) environment, modeling them as self-attracting self-avoiding walks on site-diluted percolative lattices in space dimensions d=2,3 . The influence of stretching force on the polymer folding and the properties of globule-coil transitions are analyzed. Applying the pruned-enriched Rosenbluth chain-growth method, we estimate the transition temperature TTheta between collapsed and extended polymer configurations and construct the phase diagrams of the globule-coil coexistence when varying temperature and stretching force. The transition to a completely stretched state, caused by applying force, is discussed as well.

Force induced unfolding of biopolymers in a cellular environment: a model study

Effect of molecular crowding and confinement experienced by protein in the cell during unfolding has been studied by modeling a linear polymer chain on a percolation cluster. It is known that internal structure of the cell changes in time, however, they do not change significantly from their initial structure. In order to model this we introduce the correlation among the different disorder realizations. It was shown that the force-extension behavior for correlated disorder in both constant force ensemble and constant distance ensemble is significantly different than the one obtained in absence of molecular crowding.

Adsorption of externally stretched two-dimensional flexible and semiflexible polymers near an attractive wall

We study analytically a model of a two-dimensional partially directed flexible or semiflexible polymer, attached to an attractive wall which is perpendicular to the preferred direction. In addition, the polymer is stretched by an externally applied force. We find that the wall has a dramatic effect on the polymer. For wall attraction epsilon1 smaller than the nonsequential nearest-neighbor attraction epsilon, the fraction of monomers at the wall is zero and the model is the same as that of a polymer without a wall. However, for epsilon1 greater than epsilon, the fraction of monomers at the wall undergoes a first-order transition from unity at low temperature and small force, to zero at higher temperatures and forces. We present phase diagram for this transition. Our results are confirmed by Monte Carlo simulations.

Effects of molecular crowding on stretching of polymers in poor solvent

We consider a linear polymer chain in a disordered environment modeled by percolation clusters on a square lattice. The disordered environment is meant to roughly represent molecular crowding as seen in cells. The model may be viewed as the simplest representation of biopolymers in a cell. We show the existence of intermediate states during stretching arising as a consequence of molecular crowding. In the constant distance ensemble the force-extension curves exhibit oscillations. We observe the emergence of two or more peaks in the probability distribution curves signaling the coexistence of different states and indicating that the transition is discontinuous unlike what is observed in the absence of molecular crowding.

Pulling self-interacting polymers in two dimensions

We investigate a two-dimensional problem of an isolated self-interacting end-grafted polymer, pulled by one end. In the thermodynamic limit, we find that the model has only two different phases, namely a collapsed phase and a stretched phase. We show that the phase diagram obtained by Kumar [Phys. Rev. Lett. 98, 128101 (2007)] for small systems, where differences between various statistical ensembles play an important role, differs from the phase diagram obtained here in the thermodynamic limit.

Force-induced stretched state: effects of temperature

A model of self-avoiding walks with suitable constraint has been developed to study the effect of temperature on a single-stranded DNA (ssDNA) in the constant force ensemble. Our exact calculations for small chains show that the extension (reaction coordinate) may increase or decrease with the temperature depending on the applied force. The simple model developed here, which incorporates semimicroscopic details of base direction, provides an explanation of the force-induced transitions in ssDNA as observed in experiments.

Role of conformational entropy in force-induced biopolymer unfolding

A statistical mechanical description of flexible and semiflexible 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 to pulling and compressing forces has been obtained in the constant distance ensemble. We show the signature of a crossover length which increases linearly with the chain length. Below this crossover length, the critical force of unfolding decreases with temperature, while above, it increases with temperature. For stiff chains, we report for the first time sawtoothlike behavior in the force-extension curves which has been seen earlier in the case of protein unfolding.

Does changing the pulling direction give better insight into biomolecules?

Single-molecule manipulation techniques reveal that the mechanical resistance of a protein depends on the direction of the applied force. Using a lattice model of polymers, we show that changing the pulling direction leads to different phase diagrams. The simple model proposed here indicates that in one case the system undergoes a transition akin to the unzipping of a beta sheet, while in the other case the transition is of a shearing (slippage) nature. Our results are qualitatively similar to experimental results. This demonstrates the importance of varying the pulling direction since this may yield enhanced insights into the molecular interactions responsible for the stability of biomolecules.

Collapse transition of two-dimensional flexible and semiflexible polymers

The nature of the globule-coil transition of surface-confined polymers has been an issue of debate. Here this 2D collapse transition is studied through a partially directed lattice model. In the general case of polymers with positive bending stiffness (Delta>0), the collapse transition is first order; it becomes second order only in the limiting case of zero bending stiffness (Delta triple bond 0). These analytical results are confirmed by Monte Carlo simulations. We also suggest some possible future experiments.