Stretching a macromolecule in an atomic force microscope: Statistical mechanical analysis

Kreuzer, H. J.; Payne, S.H.

doi:10.1103/physreve.63.021906

Cited by 50 publications

(70 citation statements)

References 12 publications

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“…Such force-dependent reactivity is thought to account for the behaviour of polymeric materials, melts and solutions under load, may be exploited to yield new stress-responsive, actuating and energy transducing materials [1][2][3][4][5][6][7][8][9][10] and may even allow characterization of transition states. 11 Considerable theoretical, 3,[12][13][14][15][16][17][18][19] computational 13,[20][21][22][23][24][25][26] and experimental [27][28][29][30][31][32][33][34] effort has been devoted to refine and validate a model of forcedependent kinetics for elementary (single-barrier) reactions. Yet many reactions proceed through one or more intermediates, that is, multiple activation barriers separate the reactant(s) from the product(s).…”

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“…A stretched polymer in single-molecule force or elongational flow experiments can be thought of as a molecule coupled, at two of its atoms, to a constraining potential that exerts a stretching force on these two atoms. 3,5,13,18,45,46 An activation barrier for a reaction in such a polymer will depend on stretching force if the strain energy of the constraining potential is different at the top and the bottom of the barrier (that is, at the transition state and reactant or intermediate). To a good approximation, this strain energy change between two points on the energy surface (also known as work potential) is proportional to the difference of the separation of the two atoms at which the potential acts (so called pulling axis) at these points.…”

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Model studies of force-dependent kinetics of multi-barrier reactions

et al. 2013

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According to transition state theory, the rate of a reaction that traverses multiple energy barriers is determined by the least stable (rate-determining) transition state. The preceding ('inner') energy barriers are kinetically 'invisible' but mechanistically significant. Here we show experimentally and computationally that the reduction rate of organic disulphides by phosphines in water, which in the absence of force proceeds by an equilibrium formation of a thiophosphonium intermediate, measured as a function of force applied on the disulphide moiety yields a usefully accurate estimate of the height of the inner barrier. We apply varying stretching force to the disulphide by incorporating it into a series of increasingly strained macrocycles. This force accelerates the reduction, even though the strain-free rate-determining step is orthogonal to the pulling direction. The observed rate-force correlation is consistent with the simplest model of force-dependent kinetics of a multibarrier reaction.

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Model studies of force-dependent kinetics of multi-barrier reactions

et al. 2013

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“…In the former case, the Gibb's free energy is relevant while it is the Helmholtz in the second case. This point has been carefully analyzed by Kreuzer and Payne in the context of atomic force microscope experiments [4]. Theoretically, the constant-force ensemble is easier to treat, and infact an exact numerical solution has been obtained [5] (though only for t >> 1).…”

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Triple Minima in the Free Energy of Semiflexible Polymers

Dhar

Chaudhuri

2002

Phys. Rev. Lett.

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We study the free energy of the worm-like-chain model, in the constant-extension ensemble, as a function of the stiffness λ for finite chains of length L. We find that the polymer properties obtained in this ensemble are qualitatively different from those obtained using constant-force ensembles. In particular we find that as we change the stiffness parameter, t = L/λ, the polymer makes a transition from the flexible to the rigid phase and there is an intermediate regime of parameter values where the free energy has three minima and both phases are stable. This leads to interesting features in the force-extension curves.PACS numbers: 87.15.-v, 05.20.-y, 36.20.-r, 05.40.-a The simplest model for describing semiflexible polymers without self-avoidance is the so called Worm-LikeChain (WLC) model [1][2][3]. In this model the polymer is modeled as a continuous curve that can be specified by a d−dimensional (d > 1) vectorx(s), s being the distance, measured along the length of the curve, from one fixed end. The energy of the WLC model is just the energy due to curvature and is given bywhereû(s) = ∂x/∂s is the tangent vector and satisfieŝ u 2 = 1. The parameter κ specifies the stiffness of the chain and is related to the persistence length λ defined through û(s).û(s ′ ) = e −|s−s ′ |/λ . It can be shown thatThe thermodynamic properties of such a chain can be obtained from the free energy which can be either the Helmholtz's (F ) free energy or the Gibb's (G) energy. In the former case one considers a polymer whose ends are kept at a fixed distance r [one end fixed at the origin and the other end atr = (0, ...0, r)] by an average force f = ∂F (r, L)/∂r, while in the latter case one fixes the force and the average extension is given by r = −∂G(f, L)/∂f . It can be shown that in the thermodynamic limit L → ∞ the two ensembles are equivalent and related by the usual Legendre transform G = F −f r. For a system with finite L/λ, the equivalence of the two ensembles is not guaranteed, especially when fluctuations become large. We note that real polymers come with a wide range of values of the parameter t = L/λ [e.g. λ ≈ 0.1µm for DNA while λ ≈ 1µm for Actin and their lengths can be varied] and fluctuations in r (or f ) can be very large. Then the choice of the ensemble depends on the experimental conditions. Experiments on stretching polymers are usually performed by fixing one end of the polymer and attaching the other end to a bead which is then pulled by various means (magnetic, optical, mechanical, etc.). In such experiments one can either fix the force on the bead and measure the average polymer extension, or, one could constrain the bead's position and look at the average force on the polymer. In the former case, the Gibb's free energy is relevant while it is the Helmholtz in the second case. This point has been carefully analyzed by Kreuzer and Payne in the context of atomic force microscope experiments [4]. Theoretically, the constant-force ensemble is easier to treat, and infact an exact numerical solution has been o...

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“…We neglect the coupling to the probing device, as is justified for sufficiently stiff cantilevers or optical traps [14,15]. In the presence of an external force F z acting along the vertical direction, the total free energy in units of…”

Section: Fixed Contact Pointmentioning

confidence: 99%

Pulling adsorbed polymers from surfaces with the AFM: stick vs. slip, peeling vs. gliding

Serr¹,

Netz²

2006

Europhys. Lett.

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We consider the response of an adsorbed polymer that is pulled by an AFM within a simple geometric framework. We separately consider the cases of i) fixed polymer-surface contact point, ii) sticky case where the polymer is peeled off from the substrate, and iii) slippery case where the polymer glides over the surface. The resultant behavior depends on the value of the surface friction coefficient and the adsorption strength. Our resultant force profiles in principle allow to extract both from non-equilibrium force-spectroscopic data. After its introduction in the 1980s [1], the atomic-force microscope (AFM) has been intensely used to study the mechanical properties of single molecules [2]. Applications range from sequential unfolding of collapsed biopolymers over stretching of coiled synthetic polymers to breaking individual covalent bonds [3,4,5,6]. In recent experiments, the desorption of polyelectrolytes such as DNA, poly-(vinylamines), and poly-(acrylicacid) and polymers in varying solvent conditions physisorbed to different substrates was investigated [7,8,9,10].Depending on the adsorption strength between polymer and substrate, AFM single-polymer studies split in two classes: In the first, the applied forces are relatively weak so that the attachment on the cantilever tip and on the substrate is irreversible up to a certain maximal force and over the typical experimental time-scales; in this case the measured distance-force traces contain information on the polymer that is being stretched and can be used to extract the polymer elasticity by comparison with molecular models [11,12]. In the second class, the applied force is strong enough to detach the polymer from the substrate. In this case, the measured force-distance relation contains information about the strength of the surface-polymer interaction and, as we will show in this paper, about the nanoscopic friction effects at the substrate. In fact, assuming that the polymer glides very easily over the surface and surface friction can be neglected, plateau forces are measured the heights of which correspond to the adsorption free energy per unit length [7,8,13]. In the presence of finite surface-polymer friction, the force-distance curves exhibit more complex behavior.In the interpretation of force-distance curves it is often assumed that the polymer is vertically attached between cantilever tip and surface. This is not necessarily true, and in this paper we point out the consequences of a non-zero attachment angle φ as defined schematically in fig. 1. In the case of irreversible attachment between polymer and substrate, i.e. where the polymer-substrate contact point is immobile, the angle φ is fixed for a given vertical distance between the polymer-substrate and polymer-cantilever contact points and determined by their lateral distance. This distance is typically not controlled in experiments, but the resulting force-distance curve decisively depends on this angle. In the case of reversible attachment between polymer and substrate, the resultant ...

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Stretching a macromolecule in an atomic force microscope: Statistical mechanical analysis

Cited by 50 publications

References 12 publications

Model studies of force-dependent kinetics of multi-barrier reactions

Model studies of force-dependent kinetics of multi-barrier reactions

Triple Minima in the Free Energy of Semiflexible Polymers

Pulling adsorbed polymers from surfaces with the AFM: stick vs. slip, peeling vs. gliding

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