The “Sticky Chain”: A Kinetic Model for the Deformation of Biological Macromolecules

Abstract

The deformation behavior of certain biologic macromolecules is modeled by the "sticky chain," a freely jointed chain with weak bonds between subsequent joints. Straining the chain leads to thermally assisted breaking of the weak bonds, yielding a characteristic shape of the force-elongation curve, usually with a pronounced plateau, but sometimes displaying a pseudo-Hookean behavior over a wide range of deformations. The number of individual links is assumed to be large, so the stochastic time evolution of the individual events can be approximated by a differential equation. The cases of individual and collective bond breaking are treated and formulae given for various measurable quantities. A threshold strain rate is found, below which the deformation force no longer depends on the deformation velocity. The method is applied to experimental results for the deformation of single molecules like titin or DNA and the results agree with the parameters deduced from the same experiments by the original authors using Monte Carlo (MC) calculations. Despite its intrinsic continuous character, the model, therefore, is applicable even for the deformation of macromolecules with only a few discrete unfolding elements, yielding physical quantities from experimental results using simple formulae instead of a host of MC computations.

Structural and Mechanical Properties of Klebsiella pneumoniae Type 3 Fimbriae

“…As for the later two phases, a sticky-chain model, which describes the stretched behaviors of a type 1 fimbria or a P fimbria (1,23), is suitable to describe the later two phases of a type 3 fimbria. Conceptually, in the uncoiling phase, closed layer-to-layer (LL) bonds in the helix-like structure of a type 3 fimbria are opened successively with the uncoiling force of 66 pN.…”

Sticky chain model for shear response of red blood cells

“…According to Lee and Discher (2001), x a ¼ 2.5 nm, and x d E1-3 nm; so a value of 1.6 nm will be used for x d , which is also close to the 1.59 nm as suggested by Ja¨ger (2001). For the refolding and unfolding rate constants, it is generally agreed that k d0 is very much smaller than k a0 , but their values obtained from experiments are not available.…”

“…Although the two-state model is very simple, a complete set of values for the relevant parameters are not available, and for some parameters the suggested values in some previous works are different (Ja¨ger, 2001;Lee and Discher, 2001). According to Lee and Discher (2001), x a ¼ 2.5 nm, and x d E1-3 nm; so a value of 1.6 nm will be used for x d , which is also close to the 1.59 nm as suggested by Ja¨ger (2001).…”

“…With the probability that a domain remains in the folded state under applied loads, one can find the total domains that remain in the folded state to be n(t) ¼ Np(t) if individual unfolding and refolding events are independent. According to Ja¨ger (2001), the unfolding of a spectrin chain can be described by the sticky chain model which is also appropriate for many other bio-macromolecules. If the elongation of the RBC is equal to the total length increase of the chain in the network, then we can correlate the unfolding with the elongation of the RBC by:…”

Reprint of “Biogenesis and adhesion of type 1 and P pili”

“…In Region II, these bonds are broken. They do so from the distal end, uncoiling the pilus in a stepwise fashion, the outermost subunit, with fewer neighbours to distribute the force to, experiencing the greatest force [82][83][84]. In Region III, the linearised chain is stretched still further, burdening the donor-strand exchange interactions between subunits.…”