Isometric and Isotensional Force-Length Profiles in Polymethylene Chains

Energy/entropy partition of force at DNA stretching

We compute by molecular simulation the energy/entropic partition of the force in a stretched double-stranded (ds)DNA molecule that is not yet available from the single-molecule measurements. Simulation using the coarse-grained wormlike chain (WLC) model predicts a gradual decrease in the internal (bending) energy of DNA at stretching. The ensuing negative energy contribution to force f_U is outweighed by the positive entropy contribution f_S . The ratio f_U /f, used to assess the polymer elasticity, is about -1 at the moderate extension of DNA. At the high extension, the extra energy expenses due to the contour length elongation make the ratio f_U /f less negative. The simulation findings of the hybrid energy/entropy nature of DNA elasticity at weak and moderate forces are supported by computations using the thermoelastic method mimicking the polymer experiments in bulk. It is contended that the observation of the negative energy elasticity in DNA can be generalized to other semiflexible polymers described by the WLC model.

Force-displacement relations at compression of dsDNA macromolecules

The elasticity of dsDNA molecules is investigated by Monte Carlo simulations based on a coarse-grained model of DNA. The force-displacement (f-r) curves are computed under the constraints of the constant force (Gibbs) or the constant length (Helmholtz) ensemble. Particular attention was paid to the compressional (negative) and weak tensile forces. It was confirmed that simulations using the vector Gibbs ensemble fail to represent the compression behavior of polymers. Simulations using the scalar Gibbs protocol resulted in a qualitatively correct compressional response of DNA provided that the quadratic averages of displacements were employed. Furthermore, a well-known shortcoming of the popular Marko-Siggia relation for DNA elasticity at weak tensile forces is elucidated. Conversely, the function f-r from the simulation at the constant length constraint, as well as the new closed-form expressions, provides a realistic depiction of the DNA elasticity over the wide range of negative and positive forces. Merely a qualitative resemblance of the compression functions f-r predicted by the employed approaches supports the notion that the elastic response of DNA molecules may be greatly affected by the specifics of the experimental setups and the kind of averaging of the measured variable.

Stretching and compression of DNA by external forces under nanochannel confinement

Mechanical deformation of dsDNA molecules inside square nanochannels is investigated using simulations based on a coarse-grained model of DNA. The combined action of confinement and weak external forces is explored in a variety of confinement regimes, including the transition zone relevant to nanofluidic experiments. The computed free energy and force profiles are markedly affected by the channel size. Effective elastic softening of confined DNA molecules relative to the bulk DNA is observed in the channels of intermediate widths. The extension of DNA from its bulk equilibrium length in nanofluidic devices is resolved into contributions from the passive extension due to confinement and from the active stretching induced by force. Potential implications of the very different energy costs computed for the two extension modes (extension by confinement takes much more free energy than stretching by force) for behavior of DNA in nanofluidic chips are indicated.

Size extensivity of elastic properties of alkane fragments

Using MP2, CCSD, and B3LYP methods of computational chemistry, we show length dependence in the intrinsic elastic properties of short alkane fragments. For isolated alkane fragments of finite length in the gas phase and zero temperature, the intrinsic elasticity constants are found to vary with the number of carbon atoms and its parity. From extrapolation of the elasticity constants calculations to infinite chain length, and by comparing with in-situ elasticity constant of single poly(ethylene) molecule obtained with atomic force microscopy, we estimate the softening effect of environment on the extension response of the polymer.

Ensemble inequivalence in single-molecule experiments

In bulk systems the calculation of the main thermodynamic quantities leads to the same expectation values in the thermodynamic limit, regardless of the choice of the statistical ensemble. Single linear molecules can be still regarded as statistical systems, where the thermodynamic limit is represented by infinitely long chains. The question of equivalence between different ensembles is not at all obvious and has been addressed in the literature, with sometimes contradicting conclusions. We address this problem by studying the scaling properties of the ensemble difference for two different chain models as a function of the degree of polymerization. By characterizing the scaling behavior of the difference between the isotensional (Gibbs) and isometric (Helmholtz) ensembles in the transition from the low-stretching to the high-stretching regime, we show that ensemble equivalence cannot be reached for macroscopic chains in the low force regime, and we characterize the transition from the inequivalence to the equivalence regime.

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.

A toy model of polymer stretching

We present an extremely simplified model of multiple-domain polymer stretching in an atomic force microscopy experiment. We portray each module as a binary set of contacts and decompose the system energy into a harmonic term (the cantilever) and long-range interaction terms inside each domain. Exact equilibrium computations and Monte Carlo simulations qualitatively reproduce the experimental sawtooth pattern of force-extension profiles, corresponding (in our model) to first-order phase transitions. We study the influence of the coupling induced by the cantilever and the pulling speed on the relative heights of the force peaks. The results suggest that the increasing height of the critical force for subsequent unfolding events is an out-of-equilibrium effect due to a finite pulling speed. The dependence of the average unfolding force on the pulling speed is shown to reproduce the experimental logarithmic law.