Stretching and unfolding of multidomain biopolymers: a statistical mechanics theory of titin

Abstract

Single-molecule manipulation has allowed the forced unfolding of multidomain proteins. Here we develop a theory that not only explains these experiments, but also points out a number of difficulties in their interpretation and makes suggestions for further experiments. Our theory is valid for essentially any molecule that can be unfolded in the AFM: as an example we present force-extension curves for the unfolding of both titin and RNA hairpins. For titin we reproduce force-extension curves, the dependence of break force on pulling speed, and break-force distributions, and also validate two common experimental views: unfolding titin Ig domains can be explained as stepwise increases in contour length, and increasing force peaks in native Ig sequences represent a hierarchy of bond strengths.

Full Statistics of Conjugated Thermodynamic Ensembles in Chains of Bistable Units

“…Each step corresponds to the switching of a unit induced by the increasing extension of the chain. This behavior agrees with previous theoretical and experimental results obtained with hard devices [66][67][68][69][70][71][72][73].…”

“…The process represents a realization of the Helmholtz statistical ensemble of the statistical mechanics, and the corresponding force-extension curve shows a sawtooth-like shape. This behavior proves that the units unfold sequentially in response to the increasing extension [39,41,[66][67][68][69][70][71][72][73]. In any case, the differences between isotensional and isometric force-extension curves, or equivalently between Gibbs ans Helmholtz ensembles, disappear if the number of units is very large since, in the thermodynamic limit, the Gibbs and Helmholtz ensembles are statistically equivalent, as largely discussed in the recent literature [3,6].…”

Isotensional and isometric force-extension response of chains with bistable units and Ising interactions

“…On the one side, isotensional experiments (conducted at constant applied force by soft devices) correspond to the Gibbs statistical ensemble, and lead to a plateau-like force-extension curve with a threshold force characterizing the synchronized unfolding of all chain units [37,[50][51][52][53][54][55]. On the other side, isometric experiments (conducted at prescribed displacement by hard devices) represent a realization of the Helmholtz statistical ensemble, and the corresponding force-extension curve shows a sawtoothlike shape, proving that the units unfold sequentially in reaction to the increasing extension [30,32,[54][55][56][57][58][59][60][61]. In any case, the differences between isotensional and isometric force-extension curves disappear whenever the number of units is very large since, in the thermodynamic limit, the Gibbs and Helmholtz ensembles become statistically equivalent [62,63].…”

Thermodynamics of small systems with conformational transitions: The case of two-state freely jointed chains with extensible units

“…Theories for titin, RNA hairpins, and other macromolecules have been elaborated through Landaulike free energies, first-order phase transition, Langevin equations, and Ising models. [62][63][64][65][66][67] A more general point of view about two-state systems driven by hard or soft devices can be found in the mechanical literature concerning discrete systems with multi-basin energy landscapes, Fermi-Pasta-Ulam chains of bistable elements, and structures undergoing discrete phase transformations. [68][69][70][71] We present in this paper, a general methodology to cope with the problem of analyzing the response of a system composed of two-state units and subjected to different boundary conditions.…”