The Nonequilibrium Thermodynamics of Small Systems

The interactions of tiny objects with their environment are dominated by thermal fluctuations. Guided by theory and assisted by micromanipulation tools, scientists have begun to study such interactions in detail.Comment: PDF file, 13 pages. Long version of the paper published in Physics Toda

A two-state kinetic model for the unfolding of single molecules by mechanical force

We investigate the work dissipated during the irreversible unfolding of single molecules by mechanical force, using the simplest model necessary to represent experimental data. The model consists of two levels (folded and unfolded states) separated by an intermediate barrier. We compute the probability distribution for the dissipated work and give analytical expressions for the average and variance of the distribution. To first order, the amount of dissipated work is directly proportional to the rate of application of force (the loading rate), and to the relaxation time of the molecule. The model yields estimates for parameters that characterize the unfolding kinetics under force in agreement with those obtained in recent experimental results (Liphardt, J., et al. (2002) {\em Science}, {\bf 296} 1832-1835). We obtain a general equation for the minimum number of repeated experiments needed to obtain an equilibrium free energy, to within $k_BT$, from non-equilibrium experiments using the Jarzynski formula. The number of irreversible experiments grows exponentially with the ratio of the average dissipated work, \bar{\Wdis}, to $k_BT$.}Comment: PDF file, 5 page

Mechanical unfolding of RNA hairpins

Mechanical unfolding trajectories, generated by applying constant force in optical tweezer experiments, show that RNA hairpins and the P5abc subdomain of the group I intron unfold reversibly. We use coarse-grained Go-like models for RNA hairpins to explore forced-unfolding over a broad range of temperatures. A number of predictions that are amenable to experimental tests are made. At the critical force the hairpin jumps between folded and unfolded conformations without populating any discernible intermediates. The phase diagram in the force-temperature (f,T) plane shows that the hairpin unfolds by an all-or-none process. The cooperativity of the unfolding transition increases dramatically at low temperatures. Free energy of stability, obtained from time averages of mechanical unfolding trajectories, coincide with ensemble averages which establishes ergodicity. The hopping time between the the native basin of attraction (NBA) and the unfolded basin increases dramatically along the phase boundary. Thermal unfolding is stochastic whereas mechanical unfolding occurs in "quantized steps" with great variations in the step lengths. Refolding times, upon force quench, from stretched states to the NBA is "at least an order of magnitude" greater than folding times by temperature quench. Upon force quench from stretched states the NBA is reached in at least three stages. In the initial stages the mean end-to-end distance decreases nearly continuously and only in the last stage there is a sudden transition to the NBA. Because of the generality of the results we propose that similar behavior should be observed in force quench refolding of proteins.Comment: 23 pages, 6 Figures. in press (Proc. Natl. Acad. Sci.

Characterization of VKORC1L1 with respect to VKORC1

Vitamin K reduction is essential and catalyzed by two enzymes in vitro. Vitamin K 2,3-epoxide reductase complex subunit 1 (VKORC1) reduces vitamin K to sustain γ-carboxylation of vitamin K dependent (VKD) proteins. This modification is important to physiologically activate all VKD proteins, which are involved in blood coagulation, bone and glucose metabolism. Inhibition of VKORC1 by oral anticoagulants (OACs) is clini-cally used in therapy and prevention of thrombosis. However, OACs also inhibit the isozyme VKORC1-like1 (VKORC1L1), which may have antioxidative properties and is suspected to reduce vitamin K to scavenge reactive oxygen species. Specific inhibition data for various OACs were examined by means genetically engi-neered VKOR deficient HEK 293T cells. Inhibition profile differed in terms of therapeutic OACs with 4-hydroxycoumarin and 1,3-indandione backbone. In contrast, rodenti-cides investigated showed similar susceptibility for both enzymes. To explain the distinct inhibition pattern in silico and in vitro analysis was performed which identified a warfarin binding site in VKORC1L1 other than VKORC1 binding site. The function of VKORC1L1 in vivo is still unclear. In order to check the effect of the absence of the enzyme, we generated Vkorc1l1-/- mouse by CRISPR/Cas9 gene edit-ing. Those mice were viable in homozygous state, in contrast to Vkorc1-/- mice, and showed normal fertility. However, they were slender and smaller in size and showed reduced cholesterol and glucose levels in plasma compared to their wild type littermates. Further phenotyping is needed to describe those mice in more detail

Mechanically probing the folding pathway of single RNA molecules

We study theoretically the denaturation of single RNA molecules by mechanical stretching, focusing on signatures of the (un)folding pathway in molecular fluctuations. Our model describes the interactions between nucleotides by incorporating the experimentally determined free energy rules for RNA secondary structure, while exterior single stranded regions are modeled as freely jointed chains. For exemplary RNA sequences (hairpins and the Tetrahymena thermophila group I intron), we compute the quasi-equilibrium fluctuations in the end-to-end distance as the molecule is unfolded by pulling on opposite ends. Unlike the average quasi-equilibrium force-extension curves, these fluctuations reveal clear signatures from the unfolding of individual structural elements. We find that the resolution of these signatures depends on the spring constant of the force-measuring device, with an optimal value intermediate between very rigid and very soft. We compare and relate our results to recent experiments by Liphardt et al. [Science 292, 733-737 (2001)].Comment: 10 pages, 8 figures, revised version, to be published in Biophys.

Geometric effect and gauge field in nonequilibrium quantum thermostatistics

The concept of work is studied in quantum thermostatistics of a system surrounded by an environment and driven by an external force. It is found that there emerges the gauge theoretical structure in a nonequilibrium process, the field of which is referred to as the work gauge field. The thermodynamic work as the flux of the work gauge field is considered for a cyclic process in the space of the external-force parameters. As an example, the system of a spin-1/2 interacting with an external magnetic field is analyzed. This geometric effect may be observed, for example, in an NMR experiment and can be applied to the problem of cooling/heating of a small system.Comment: 11 page

Influence of Polymer Modified Binder Content from RAP on Stone Mastic Asphalt Rutting Resistance

AbstractProperties of hot mix asphalt with reclaimed asphalt pavement (RAP) mostly depends on RAP properties, especially RAP binder. It is assumed that binder from RAP is usually stiffer than virgin binder because of exploitation aging process. Use of RAP may cause stiffening of asphalt mix and improvement of rutting resistance. This paper demonstrates results of wheel tracking tests of stone mastic asphalt. Analyzed asphalt mixes were designed with six different content of RAP. Penetration and softening point of binder mix was determined and binder replacement factor for asphalt mixes was calculated. Analyses of wheel track tests with comparison to binder properties shown that increasing amount of modified binder from RPA occurs in increasing rutting resistance of asphalt mixes

SYSTEM FOR SEQUENTIALLY PROVIDING ABERATION CORRECTED ELECTROMAGNETIC RADATION TO A SPOT ON A SAMPLE AT MULTIPLE ANGLES OF INCIDENCE

A system for sequentially providing electromagnetic radia tion to a spot on a sample at different angles of incidence, and after reflection therefrom into a detector. The system includes a plurality of spherical mirrors, and a refractive element for correcting aberration