Three-dimensional bead position histograms reveal single-molecule nanomechanics Nils B. Becker, 1, * Stephan M. Altmann, 2 Tim Scholz, 3 J. K. Heinrich Hörber, 4 Ernst H. K. Stelzer, 1 and Alexander Rohrbach 1,² 1 European Molecular Biology Laboratory, Meyerhofstrabe 1, 69117 Heidelberg, Germany 2 BASF AG, Carl-Bosch-Strabe 38, 67056 Ludwigshafen, Germany 3 Medizinische Hochschule Hannover, Carl-Neuberg-Strabe 1, 30625 Hannover, Germany 4 Wayne State University, Detroit, Michigan 48202, USA sReceived 12 July 2004; published 22 February 2005; corrected 28 February 2005d We describe a method to investigate the structure and elasticity of macromolecules by a combination of single molecule experiments and kinematic modeling. With a photonic force microscope, we recorded spatial position histograms of a fluctuating microsphere tethered to full-length myosin-II. Assuming only that the molecule consists of concatenated rigid segments, a model derived from robot kinematics allows us to relate these histograms to the molecule’s segment lengths and bending stiffnesses. Both our calculated position distributions and the experimental data show an asymmetry characteristic of a mixed entropic-enthalpic spring. Our model that fits best to experimental line profiles has two intramolecular hinges, one at the bound head domain, and another about 50 nm down the myosin tail, with a summed bending stiffness of about 3 k B T / rad. DOI: 10.1103/PhysRevE.71.021907 PACS numberssd: 87.15.La, 87.15.Aa, 87.15.Ya, 87.80.Cc I. INTRODUCTION In the study of motor molecules, optical single molecule techniques have been widely used to measure properties of the mechanochemical cycle, such as step size and load- dependent speed f1–3g. Motor function depends on ATPase activity at the head domains of the protein. However, any force acting at the head domain in such experiments is bal- anced by the elastic response of the whole molecular con- struct used. The tail elasticity therefore influences the statis- tics of the force and torque that act at the head domains of the molecule. Also for myosin function in muscle f4,5g, the passive elasticity of the myosin cross bridge is essential. To understand the mechanochemical cycle in depth, it seems important to characterize the passive elastic response of the complete motor molecules including the tail domains. The analysis of three-dimensional s3Dd elastic properties of rodlike single macromolecules is also interesting as a test of polymer physics models and for nanotechnology applications. These elastic properties can be measured in single- molecule experiments f6g using a photonic force microscope sPFMdf7,8g. Here, a submicrometer-sized bead is tethered to a coverslip by a single rodlike molecule and confined in a weak optical trap. The bead explores the local free energy landscape by thermal motion, while its 3D position is re- corded interferometrically. The spatial resolution of the po- sition histogram achieved is on the order of 2–5 nm in 3D with a sampling rate higher than 100 kHz. Since the bead moves diffusively in a predefined volume, it will probe the tether elasticity in a wide range of directions and on multiple time scales at once, in contrast to the situation using atomic force microscopy or conventional optical tweezers. By re- cording histograms of the bead position, an energy resolution on the order of 0.1k B T can be achieved, depending on bin size and recording time. Another method that can provide 2D f9,10g or 3D f11g position histograms is video tracking, but with a lower temporal resolution in the millisecond range, leading to motion blur for fast fluctuations of small trapped beads and thereby limiting the spatial resolution. To relate the measured histograms to molecular elasticity, a model for the mechanics of the bead-molecule tether is required. The simplest assumption of a swiveling, radial Hookean spring f6,12g with a rigidly attached bead fails to account for the experimentally observed asymmetry in radial line profiles ssee belowd. To explain this asymmetry, the internal nanome- chanics of the molecule has to be taken into account. One possible model for the tail of a rodlike motor mol- ecule such as conventional kinesin or myosin-II is a semi- flexible polymer, e.g., a wormlike chain sWLCdf13g, char- acterized by a contour length and a persistence length l p . This corresponds to a uniform distribution of bending com- pliance along the molecule. There is evidence from structural and electron-microscopy studies, however, that the tail re- gion of kinesin can bend strongly at a single point about midway along the tail f14g. Also, myosin-II can be enzymati- cally split into heavy sHMMd and light meromyosin sLMMd at a point on the tail about 50 nm from the head domain, indicating an interruption of the regular coiled-coil structure f15g. Therefore, a complementary description is considered here; in the opposite limit of maximally concentrated bend- ing compliance, one obtains a segmentally flexible molecule with a few rigid subunits connected by pointlike joints. This view is supported by a molecular dynamics study of the leu- cine zipper of the SNARE complex, which indicated a high rigidity for this structurally similar coiled-coil domain f16g. In the present article, we describe a mechanical model for the passive elastic properties of segmentally flexible, rodlike macromolecules attached to a single bead. In Sec. II a math- ematical framework f17g is introduced to conveniently de- scribe the relative configurations of the rigid segments of *Electronic address: nbecker@mpipks-dresden.mpg.de ² Electronic address: rohrbach@embl.de PHYSICAL REVIEW E 71, 021907 s2005d 1539-3755/2005/71s2d/021907s7d/$23.00 ©2005 The American Physical Society 021907-1