Pathways and kinetic barriers in mechanical unfolding and refolding of RNA and proteins

Using self-organized polymer models, we predict mechanical unfolding and refolding pathways of ribo-zymes, and the green fluorescent protein. In agreement with experiments, there are between six and eight unfolding transitions in the Tetrahymena ribozyme. Depending on the loading rate, the number of rips in the force-ramp unfolding of the Azoarcus ribozymes is between two and four. Force-quench refolding of the P4-P6 subdomain of the Tetrahymena ribozyme occurs through a compact intermediate. Subsequent formation of tertiary contacts between helices P5b-P6a and P5a/P5c-P4 leads to the native state. The force-quench refolding pathways agree with ensemble experiments. In the dominant unfolding route, the N-terminal a helix of GFP unravels first, followed by disruption of the N terminus b strand. There is a third intermediate that involves disruption of three other strands. In accord with experiments, the force-quench refolding pathway of GFP is hierarchic, with the rate-limiting step being the closure of the barrel.Comment: 33 pages 7 figure

Size, shape, and flexibility of RNA structures

Determination of sizes and flexibilities of RNA molecules is important in understanding the nature of packing in folded structures and in elucidating interactions between RNA and DNA or proteins. Using the coordinates of the structures of RNA in the Protein Data Bank we find that the size of the folded RNA structures, measured using the radius of gyration, $R_G$, follows the Flory scaling law, namely, $R_G =5.5 N^{1/3}$ \AA where N is the number of nucleotides. The shape of RNA molecules is characterized by the asphericity $\Delta$ and the shape $S$ parameters that are computed using the eigenvalues of the moment of inertia tensor. From the distribution of $\Delta$, we find that a large fraction of folded RNA structures are aspherical and the distribution of $S$ values shows that RNA molecules are prolate ($S>0$). The flexibility of folded structures is characterized by the persistence length $l_p$. By fitting the distance distribution function $P(r)$ to the worm-like chain model we extracted the persistence length $l_p$. We find that $l_p\approx 1.5 N^{0.33}$ \AA. The dependence of $l_p$ on $N$ implies the average length of helices should increases as the size of RNA grows. We also analyze packing in the structures of ribosomes (30S, 50S, and 70S) in terms of $R_G$, $\Delta$, $S$, and $l_p$. The 70S and the 50S subunits are more spherical compared to most RNA molecules. The globularity in 50S is due to the presence of an unusually large number (compared to 30S subunit) of small helices that are stitched together by bulges and loops. Comparison of the shapes of the intact 70S ribosome and the constituent particles suggests that folding of the individual molecules might occur prior to assembly.Comment: 28 pages, 8 figures, J. Chem. Phys. in pres

Tubulin bond energies and microtubule biomechanics determined from nanoindentation in silico

Microtubules, the primary components of the chromosome segregation machinery, are stabilized by longitudinal and lateral non-covalent bonds between the tubulin subunits. However, the thermodynamics of these bonds and the microtubule physico-chemical properties are poorly understood. Here, we explore the biomechanics of microtubule polymers using multiscale computational modeling and nanoindentations in silico of a contiguous microtubule fragment. A close match between the simulated and experimental force-deformation spectra enabled us to correlate the microtubule biomechanics with dynamic structural transitions at the nanoscale. Our mechanical testing revealed that the compressed MT behaves as a system of rigid elements interconnected through a network of lateral and longitudinal elastic bonds. The initial regime of continuous elastic deformation of the microtubule is followed by the transition regime, during which the microtubule lattice undergoes discrete structural changes, which include first the reversible dissociation of lateral bonds followed by irreversible dissociation of the longitudinal bonds. We have determined the free energies of dissociation of the lateral (6.9+/-0.4 kcal/mol) and longitudinal (14.9+/-1.5 kcal/mol) tubulin-tubulin bonds. These values in conjunction with the large flexural rigidity of tubulin protofilaments obtained (18,000-26,000 pN*nm^2), support the idea that the disassembling microtubule is capable of generating a large mechanical force to move chromosomes during cell division. Our computational modeling offers a comprehensive quantitative platform to link molecular tubulin characteristics with the physiological behavior of microtubules. The developed in silico nanoindentation method provides a powerful tool for the exploration of biomechanical properties of other cytoskeletal and multiprotein assemblie

Mechanism of Fibrin(ogen) Forced Unfolding

SummaryFibrinogen, upon enzymatic conversion to monomeric fibrin, provides the building blocks for fibrin polymer, the scaffold of blood clots and thrombi. Little has been known about the force-induced unfolding of fibrin(ogen), even though it is the foundation for the mechanical and rheological properties of fibrin, which are essential for hemostasis. We determined mechanisms and mapped the free energy landscape of the elongation of fibrin(ogen) monomers and oligomers through combined experimental and theoretical studies of the nanomechanical properties of fibrin(ogen), using atomic force microscopy-based single-molecule unfolding and simulations in the experimentally relevant timescale. We have found that mechanical unraveling of fibrin(ogen) is determined by the combined molecular transitions that couple stepwise unfolding of the γ chain nodules and reversible extension-contraction of the α-helical coiled-coil connectors. These findings provide important characteristics of the fibrin(ogen) nanomechanics necessary to understand the molecular origins of fibrin viscoelasticity at the fiber and whole clot levels