Stretching type II collagen with optical tweezers

Collagens are the most abundant proteins of vertebrates and they provide mechanical and supportive functions in a wide range of connective tissues. Knowledge of the mechanical properties of single collagen molecules is essential in studying the self-assembly of collagen, the interaction between cells and extracellular matrix, the etiology of tissue degeneration and mechanism of regeneration, and the relationship between the structures and mechanical properties of tissues. Here we stretched single type II collagen molecules in neutral pH solution using optical tweezers. The molecular parameters of collagen were obtained by fitting force-extension curves into worm-like chain elasticity model. The molecule length of type II collagen monomer was 295.8 nm. The persistence length of type II collagen monomer was 11.2 nm. These observations indicate that collagen molecules are flexible rather than rigid rod molecules at neutral pH solution.     

Molecular mechanics of cardiac titin's PEVK and N2B spring elements.

Titin is a giant elastic protein that is responsible for the majority of passive force generated by the myocardium. Titin's force is derived from its extensible I-band region, which, in the cardiac isoform, comprises three main extensible elements: tandem Ig segments, the PEVK domain, and the N2B unique sequence (N2B-Us). Using atomic force microscopy, we characterized the single molecule force-extension curves of the PEVK and N2B-Us spring elements, which together are responsible for physiological levels of passive force in moderately to highly stretched myocardium. Stretch-release force-extension curves of both the PEVK domain and N2B-Us displayed little hysteresis: the stretch and release data nearly overlapped. The force-extension curves closely followed worm-like chain behavior. Histograms of persistence length (measure of chain bending rigidity) indicated that the single molecule persistence lengths are approximately 1.4 and approximately 0.65 nm for the PEVK domain and N2B-Us, respectively. Using these mechanical characteristics and those determined earlier for the tandem Ig segment (assuming folded Ig domains), we modeled the cardiac titin extensible region in the sarcomere and calculated the extension of the various spring elements and the forces generated by titin, both as a function of sarcomere length. In the physiological sarcomere length range, predicted values and those obtained experimentally were indistinguishable.     

A cooperative transition from the semi-flexible to the flexible regime of polymer elasticity: Mitoxantrone-induced DNA condensation

We report a high cooperative transition from the semi-flexible to the flexible regime of polymer elasticity during the interaction of the DNA molecule with the chemotherapeutic drug Mitoxantrone (MTX). By using single molecule force spectroscopy, we show that the force-extension curves of the DNA-MTX complexes deviate from the typical worm-like chain behavior as the MTX concentration in the sample increases, becoming straight lines for sufficiently high drug concentrations. The behavior of the radius of gyration of the complexes as a function of the bound MTX concentration was used to quantitatively investigate the cooperativity of the condensation process. The present methodology can be promptly applied to other ligands that condense the DNA molecule upon binding, opening new possibilities in the investigation of this type of process and, more generally, in the investigation of phase transitions in polymer physics.     

Nanomechanical properties of human prion protein amyloid as probed by force spectroscopy

Amyloids are associated with a number of protein misfolding disorders, including prion diseases. In this study, we used single-molecule force spectroscopy to characterize the nanomechanical properties and molecular structure of amyloid fibrils formed by human prion protein PrP90-231. Force-extension curves obtained by specific attachment of a gold-covered atomic force microscope tip to engineered Cys residues could be described by the worm-like chain model for entropic elasticity of a polymer chain, with the size of the N-terminal segment that could be stretched entropically depending on the tip attachment site. The data presented here provide direct information about the forces required to extract an individual monomer from the core of the PrP90-231 amyloid, and indicate that the β-sheet core of this amyloid starts at residue ∼164-169. The latter finding has important implications for the ongoing debate regarding the structure of PrP amyloid.     

Direct quantification of the flexibility of type I collagen monomer

Collagens are the most abundant structural proteins found in the extracellular matrix of vertebrates. Knowledge of the mechanical behavior of collagen monomers is essential for understanding the mechanical properties of collagen fibrils that constitute the main architectural framework of skin, bone, cartilage, and other connective tissues. In this study, the flexibility of type I collagen monomer was studied by stretching type I collagen monomers directly. The force-extension relationship was measured and analyzed by fitting the data into a worm-like chain elasticity model. The persistence length of collagen I monomer was determined to be 14.5 nm and the contour length was 309 nm. The results confirm that type I collagen monomer is flexible rather than rigid, rod-like molecule. Such flexibility may possibly be a consequence of the micro-unfolding of discrete domains of single collagen molecule.     

Elastin: a representative ideal protein elastomer

During the last half century, identification of an ideal (predominantly entropic) protein elastomer was generally thought to require that the ideal protein elastomer be a random chain network. Here, we report two new sets of data and review previous data. The first set of new data utilizes atomic force microscopy to report single-chain force-extension curves for (GVGVP)(251) and (GVGIP)(260), and provides evidence for single-chain ideal elasticity. The second class of new data provides a direct contrast between low-frequency sound absorption (0.1-10 kHz) exhibited by random-chain network elastomers and by elastin protein-based polymers. Earlier composition, dielectric relaxation (1-1000 MHz), thermoelasticity, molecular mechanics and dynamics calculations and thermodynamic and statistical mechanical analyses are presented, that combine with the new data to contrast with random-chain network rubbers and to detail the presence of regular non-random structural elements of the elastin-based systems that lose entropic elastomeric force upon thermal denaturation. The data and analyses affirm an earlier contrary argument that components of elastin, the elastic protein of the mammalian elastic fibre, and purified elastin fibre itself contain dynamic, non-random, regularly repeating structures that exhibit dominantly entropic elasticity by means of a damping of internal chain dynamics on extension.     

Entropic elasticity in the generation of muscle force--a theoretical model

A novel simplified structural model of sarcomeric force production in striate muscle is presented. Using some simple assumptions regarding the distribution of myosin spring lengths at different sliding velocities it is possible to derive a very simple expression showing the main components of the experimentally observed force-velocity relationship of muscle: nonlinearity during contraction (Hill, 1938), maximal force production during stretching equal to two times the isometric force (Katz, 1939), yielding at high stretching velocity, slightly concave force-extension relationship during sudden length changes (Ford et al., 1977; Lombardi & Piazzesi, 1990), accurate reproduction of the rate of ATP consumption (Shirakawa et al., 2000; He et al., 2000) and of the extra energy liberation rate (Hill, 1964a). Different assumptions regarding the force-length relationship of individual cross-bridges are explored [linear, power function and worm-like chain (WLC) model based], and it is shown that the best results are obtained if the individual myosin-spring forces are modelled using a WLC model, thus hinting that entropic elasticity could be the main source of force in myosin undergoing the conformational changes associated with the power stroke.     

Pulling-speed-dependent force-extension profiles for semiflexible chains

We present theory and simulations to describe nonequilibrium stretching of semiflexible chains that serve as models of DNA molecules. Using a self-consistent dynamical variational approach, we calculate the force-extension curves for worm-like chains as a function of the pulling speed, v(0). Due to nonequilibrium effects the stretching force, which increases with v(0), shows nonmonotonic variations as the persistence length increases. To complement the theoretical calculations we also present Langevin simulation results for extensible worm-like chain models for the dynamics of stretching. The theoretical force-extension predictions compare well with the simulation results. The simulations show that, at high enough pulling speeds, the propagation of tension along the chain conformations transverse to the applied force occurs by the Brochard-Wyart's stem-flower mechanism. The predicted nonequilibrium effects can only be observed in double-stranded DNA at large ( approximately 100 microm/s) pulling speeds.     

Stretching short DNAs in electrolytes

This paper is aimed at a combined theoretical and numerical study of the force-extension relation of a short DNA molecule stretched in an electrolyte. A theoretical formula based on a recent discrete wormlike chain (WLC) model of Kierfeld et al. (Eur Phys. J. E, Vol. 14, pp.17-34, 2004) and the classical OSF mean-field theory on electrostatic stiffening of a charged polymer is numerically verified by a set of Brownian dynamics simulations based on a generalized bead-rod (GBR) model incorporating long-ranged electrostatic interactions via the Debye-Hueckel potential (DH). The analysis indicates that the stretching of a short DNA can be well described as a WLC with a constant effective persistent length. This contrasts the behavior of long DNA chains that are known to exhibit variable persistent lengths depending on the ion concentration levels and force magnitudes.     

Unfolding mechanics of multiple OspA substructures investigated with single molecule force spectroscopy

We investigated mechanical unfolding of Borrelia burgdorferi outer surface protein A (OspA), a Lyme disease antigen containing a unique single-layer beta-sheet, with atomic force microscopy (AFM). We mechanically stretched a monomeric unit, rather than a tandem repeat, by pulling it from its N and C-terminal residues without using intervening polymer as a spacer. We detected two peaks in the force-extension profile before the final rupture of a fully extended polypeptide, which we interpreted as unfolding of multiple substructures in OspA. The double-peaked unfolding curves are consistent with results of previous thermodynamic studies showing two cooperative units in OspA. The mechanical unfolding processes were reversible, and the two substructures refolded within one second. Mutations near the boundary of the two thermodynamic cooperative units reduced the height of the first unfolding peak to undetectable levels and marginally affected the second one, indicating that the boundary between the two mechanical substructures is related to that previously assigned between the thermodynamic cooperative units. Based on a "worm-like chain" analysis of our AFM data, we propose a model for mechanical unfolding of OspA, where nearly a half of the chain is stretched with minimal resistive force, followed by sequential breakdown of C-terminal and N-terminal substructures. Based on these results, we discuss similarities and differences between mechanical and thermodynamic unfolding reactions of OspA. This work demonstrates that AFM study of monomeric proteins can elucidate details of the intramolecular mechanics of protein substructures.     

Stretching of single collapsed DNA molecules

The elastic response of single plasmid and lambda phage DNA molecules was probed using optical tweezers at concentrations of trivalent cations that provoked DNA condensation in bulk. For uncondensed plasmids, the persistence length, P, decreased with increasing spermidine concentration before reaching a limiting value 40 nm. When condensed plasmids were stretched, two types of behavior were observed: a stick-release pattern and a plateau at approximately 20 pN. These behaviors are attributed to unpacking from a condensed structure, such as coiled DNA. Similarly, condensing concentrations of hexaammine cobalt(III) (CoHex) and spermidine induced extensive changes in the low and high force elasticity of lambda DNA. The high force (5-15 pN) entropic elasticity showed worm-like chain (WLC) behavior, with P two- to fivefold lower than in low monovalent salt. At lower forces, a 14-pN plateau abruptly appeared. This corresponds to an intramolecular attraction of 0.083-0.33 kT/bp, consistent with osmotic stress measurements in bulk condensed DNA. The intramolecular attractive force with CoHex is larger than with spermidine, consistent with the greater efficiency with which CoHex condenses DNA in bulk. The transition from WLC behavior to condensation occurs at an extension about 85% of the contour length, permitting looping and nucleation of condensation. Approximately half as many base pairs are required to nucleate collapse in a stretched chain when CoHex is the condensing agent.     

A Theoretical Model for the Mechanical Unfolding of Repeat Proteins

We consider the mechanical stretching of a polypeptide chain formed by multiple interacting repeats. The folding thermodynamics and the interactions among the repeats are described by the Ising model. Unfolded repeats act as soft entropic springs, whereas folded repeats respond to a force as stiffer springs. We show that the resulting force-extension curve may exhibit a pronounced force maximum corresponding to the unfolding of the first repeat. This event is followed by the unfolding of the remaining repeats, which takes place at a lower force. As the protein extension is increased, the force-extension curve of a sufficiently long repeat protein displays a plateau, where the force remains nearly constant and the protein unfolds sequentially so that the number of unfolded repeats is proportional to the extension. Such a sequential mechanical unfolding mechanism is displayed even by the repeat proteins whose thermal denaturation is highly cooperative, provided that they are long enough. By contrast, the unfolding of short repeat progressions can be cooperative.     

Pulling geometry-induced errors in single molecule force spectroscopy measurements

In AFM-based single molecule force spectroscopy, it is tacitly assumed that the pulling direction coincides with the end-to-end vector of the molecule fragment being stretched. By systematically varying the position of the attachment point on the substrate relative to the AFM tip, we investigate empirically and theoretically the effect of the pulling geometry on force-extension characteristics of double-stranded DNA. We find that increasing the pulling angle can significantly lower the force of the characteristic overstretching transition and increase the width of the plateau feature beyond the canonical 70%. These effects, when neglected, can adversely affect the interpretation of measured force-extension relationships. We quantitatively evaluate force and extension errors originating from this "pulling angle effect" and stress the need to correct the pulling geometry when stretching rigid molecules with an AFM.     

Worm-like chain model extensions for highly stretched tropocollagen molecules

Tropocollagen plays a very important role in the load bearing functionality of soft tissues. In the context of multi-scale modeling the response of tropocollagen molecules to stretch should be very carefully predicted in order to describe the mechanical behavior of soft tissues. To this end, the worm-like chain (WLC) model is often applied, although it is restricted to the entropic force regime which is essential at moderate deformations. To describe molecular forces under larger stretches several extensions of the WLC have been proposed for deoxyribonucleic acid (DNA). This contribution aims to investigate the applicability of these models in the context of tropocollagen and discusses the feasibility of their application. Finally, the models are validated in comparison to experimental data available in the literature.     

Force-induced denaturation of RNA

We quantitatively describe an RNA molecule under the influence of an external force exerted at its two ends as in a typical single-molecule experiment. Our calculation incorporates the interactions between nucleotides by using the experimentally determined free energy rules for RNA secondary structure and models the polymeric properties of the exterior single-stranded regions explicitly as elastic freely jointed chains. We find that despite complicated secondary structures, force-extension curves are typically smooth in quasi-equilibrium. We identify and characterize two sequence/structure-dependent mechanisms that, in addition to the sequence-independent entropic elasticity of the exterior single-stranded regions, are responsible for the smoothness. These involve compensation between different structural elements on which the external force acts simultaneously and contribution of suboptimal structures, respectively. We estimate how many features a force-extension curve recorded in nonequilibrium, where the pulling proceeds faster than rearrangements in the secondary structure of the molecule, could show in principle. Our software is available to the public through an "RNA-pulling server."     

Improved resolution of tertiary structure elasticity in muscle protein

Rearrangement of tertiary structure in response to mechanical force (termed tertiary structure elasticity) in the tandem Ig chain is the first mode of elastic response for muscle protein titin. Tertiary structure elasticity occurs at low stretching forces (few tens of pN), and was described at atomic resolution in a recent molecular dynamics study, in which an originally crescent-shaped six-Ig chain was stretched into a linear chain. However, the force-extension profile that resulted from this explicit solvent simulation was dominated by the hydrodynamic drag force, and effects of tertiary structure elasticity only manifested for stretching forces above 20 pN. Here we report a slow pulling 100-ns simulation (along with other auxiliary simulations), in which hydrodynamic drag force is seen to reduce to near 0 pN, such that tertiary structure elasticity could be characterized over a 0–200 pN range. Statistical mechanical analysis showed that the stretching velocity was sufficiently low such that the protein remained significantly relaxed during the major part of its extension.     

Extension of torsionally stressed DNA by external force.

Metropolis Monte Carlo simulation was used to study the elasticity of torsionally stressed double-helical DNA. Equilibrium distributions of DNA conformations for different values of linking deficit, external force, and ionic conditions were simulated using the discrete wormlike chain model. Ionic conditions were specified in terms of DNA effective diameter, i.e., hard-core radius of the model chain. The simulations show that entropic elasticity of the double helix depends on how much it is twisted. For low amounts of twisting (less than about one turn per twist persistence length) the force versus extension is nearly the same as in the completely torsionally relaxed case. For more twisting than this, the molecule starts to supercoil, and there is an increase in the force needed to realize a given extension. For sufficiently large amounts of twist, the entire chain is plectonemically supercoiled at low extensions; a finite force must be applied to obtain any extension at all in this regime. The simulation results agree well with the results of recent micromanipulation experiments.     

The force-driven conformations of heparin studied with single molecule force microscopy

Using single molecule force spectroscopy we examine the response of heparin chains to mechanical stretching. We find that at forces below 200 pN heparin behaves as a simple entropic spring. At approximately 200 pN heparin displays a large enthalpic elasticity, which is evident as a pronounced plateau in the force-extension relationship. We determine that this enthalpic elasticity is produced by sugar rings of heparin flipping to more energetic and more extended conformations. We estimate that in vivo, the forces which stretch heparin are comparable to the forces that trigger conformational transitions in our single molecule atomic force microscopy measurements. We hypothesize that these conformational transitions have biological significance in that they provide a mechanism to finely regulate the affinity of various ligands toward heparin, for example, in secretory granules undergoing exocytosis and during the mechanical interactions between cells and the extracellular matrix.     

Reversible and irreversible unfolding of mitotic newt chromosomes by applied force

The force-extension behavior of individual mitotic newt chromosomes was studied, using micropipette surgery and manipulation, for elongations up to 80 times native length. After elongations up to five times, chromosomes return to their native length. In this regime chromosomes have linear elasticity, requiring approximately 1 nN of force to be stretched to two times native length. After more than five times stretching, chromosomes are permanently elongated, with force hysteresis during relaxation. If a chromosome is repeatedly stretched to approximately 10 times native length and relaxed, a series of hysteresis loops are obtained that converge to a single reversible elastic response. For further elongations, the linear dependence of force on extension terminates at a force "plateau" of approximately 15-20 nN, near 30 times extension. After >30 times extensions, the elastic moduli of chromosomes can be reduced by more than 20-fold, and they appear as "ghosts": swollen, elongated, and with reduced optical contrast under both phase and differential interference contrast imaging. Antibody labeling indicates that histone proteins are not being lost during even extreme extensions. Results are interpreted in terms of extension and failure of chromatin-tethering elements; the force data allow estimates of the number and size of such connectors in a chromosome.     

Stretching DNA with optical tweezers.

Force-extension (F-x) relationships were measured for single molecules of DNA under a variety of buffer conditions, using an optical trapping interferometer modified to incorporate feedback control. One end of a single DNA molecule was fixed to a coverglass surface by means of a stalled RNA polymerase complex. The other end was linked to a microscopic bead, which was captured and held in an optical trap. The DNA was subsequently stretched by moving the coverglass with respect to the trap using a piezo-driven stage, while the position of the bead was recorded at nanometer-scale resolution. An electronic feedback circuit was activated to prevent bead movement beyond a preset clamping point by modulating the light intensity, altering the trap stiffness dynamically. This arrangement permits rapid determination of the F-x relationship for individual DNA molecules as short as -1 micron with unprecedented accuracy, subjected to both low (approximately 0.1 pN) and high (approximately 50 pN) loads: complete data sets are acquired in under a minute. Experimental F-x relationships were fit over much of their range by entropic elasticity theories based on worm-like chain models. Fits yielded a persistence length, Lp, of approximately 47 nm in a buffer containing 10 mM Na1. Multivalent cations, such as Mg2+ or spermidine 3+, reduced Lp to approximately 40 nm. Although multivalent ions shield most of the negative charges on the DNA backbone, they did not further reduce Lp significantly, suggesting that the intrinsic persistence length remains close to 40 nm. An elasticity theory incorporating both enthalpic and entropic contributions to stiffness fit the experimental results extremely well throughout the full range of extensions and returned an elastic modulus of approximately 1100 pN.