26 research outputs found
Averaging and large deviation principles for fully--coupled piecewise deterministic Markov processes and applications to molecular motors
No full textAveraging and large deviation principles for fully-coupled pieceweise deterministic Markov processes and applications to molecular motors
No full textWe consider Piecewise Deterministic Markov Processes (PDMPs) with a
finite set of discrete states. In the regime of fast jumps between discrete states, we prove
a law of large number and a large deviation principle. In the regime of fast and slow
jumps, we analyze a coarse–grained process associated to the original one and prove its
convergence to a new PDMP with effective force fields and jump rates. In all the above
cases, the continuous variables evolve slowly according to ODEs. Finally, we discuss some
applications related to the mechanochemical cycle of macromolecules, including strained–
dependent power–stroke molecular motors. Our analysis covers the case of fully–coupled
slow and fast motions
Non-equilibrium Thermodynamics of Piecewise Deterministic Markov Processes
No full textWe consider a class of stochastic dynamical systems, called piecewise deterministic
Markov processes, with states (x, σ) ∈ × , being a region in Rd or the
d-dimensional torus, being a finite set. The continuous variable x follows a piecewise
deterministic dynamics, the discrete variable σ evolves by a stochastic jump dynamics
and the two resulting evolutions are fully-coupled. We study stationarity, reversibility
and time-reversal symmetries of the process. Increasing the frequency of the σ-jumps,
the system behaves asymptotically as deterministic and we investigate the structure of its
fluctuations (i.e. deviations from the asymptotic behavior), recovering in a non Markovian
frame results obtained by Bertini et al. (Phys. Rev. Lett. 87(4):040601, 2001; J. Stat.
Phys. 107(3–4):635–675, 2002; J. Stat. Mech. P07014, 2007; Preprint available online at
http://www.arxiv.org/abs/0807.4457, 2008), in the context of Markovian stochastic interacting
particle systems. Finally, we discuss a Gallavotti–Cohen-type symmetry relation with
involution map different from time-reversal
Non-equilibrium Thermodynamics of Piecewise Deterministic Markov Processes
No full textWe consider a class of stochastic dynamical systems, called piecewise deterministic Markov processes, with states (x, sigma) is an element of Omega x Gamma, Omega being a region in R(d) or the d-dimensional torus, Gamma being a finite set. The continuous variable x follows a piecewise deterministic dynamics, the discrete variable sigma evolves by a stochastic jump dynamics and the two resulting evolutions are fully-coupled. We study stationarity, reversibility and time-reversal symmetries of the process. Increasing the frequency of the sigma-jumps, the system behaves asymptotically as deterministic and we investigate the structure of its fluctuations (i.e. deviations from the asymptotic behavior), recovering in a non Markovian frame results obtained by Bertini et al. (Phys. Rev. Lett. 87(4): 040601, 2001; J. Stat. Phys. 107(3-4): 635-675, 2002; J. Stat. Mech. P07014, 2007; Preprint available online at http://www.arxiv.org/abs/0807.4457, 2008), in the context of Markovian stochastic interacting particle systems. Finally, we discuss a Gallavotti-Cohen-type symmetry relation with involution map different from time-reversal
Force Spectroscopy with Dual-Trap Optical Tweezers: Molecular Stiffness Measurements and Coupled Fluctuations Analysis
No full textABSTRACT Dual-trap optical tweezers are often used in high-resolution measurements in single-molecule biophysics. Such measurements can be hindered by the presence of extraneous noise sources, the most prominent of which is the coupling of fluctuations along different spatial directions, which may affect any optical tweezers setup. In this article, we analyze, both from the theoretical and the experimental points of view, the most common source for these couplings in dual-trap optical-tweezers setups: the misalignment of traps and tether. We give criteria to distinguish different kinds of misalignment, to estimate their quantitative relevance and to include them in the data analysis. The experimental data is obtained in a, to our knowledge, novel dual-trap optical-tweezers setup that directly measures forces. In the case in which misalignment is negligible, we provide a method to measure the stiffness of traps and tether based on variance analysis. This method can be seen as a calibration technique valid beyond the linear trap region. Our analysis is then employed to measure the persistence length of dsDNA tethers of three different lengths spanning two orders of magnitude. The effective persistence length of such tethers is shown to decrease with the contour length, in accordance with previous studies
Force Spectroscopy with Dual-Trap Optical Tweezers: Molecular Stiffness Measurements and Coupled Fluctuations Analysis
No full textABSTRACT Dual-trap optical tweezers are often used in high-resolution measurements in single-molecule biophysics. Such measurements can be hindered by the presence of extraneous noise sources, the most prominent of which is the coupling of fluctuations along different spatial directions, which may affect any optical tweezers setup. In this article, we analyze, both from the theoretical and the experimental points of view, the most common source for these couplings in dual-trap optical-tweezers setups: the misalignment of traps and tether. We give criteria to distinguish different kinds of misalignment, to estimate their quantitative relevance and to include them in the data analysis. The experimental data is obtained in a, to our knowledge, novel dual-trap optical-tweezers setup that directly measures forces. In the case in which misalignment is negligible, we provide a method to measure the stiffness of traps and tether based on variance analysis. This method can be seen as a calibration technique valid beyond the linear trap region. Our analysis is then employed to measure the persistence length of dsDNA tethers of three different lengths spanning two orders of magnitude. The effective persistence length of such tethers is shown to decrease with the contour length, in accordance with previous studies
Counter-propagating dual-trap optical tweezers based on linear momentum conservation
No full textWe present a dual-trap optical tweezers setup which directly measures forces using linear momentum conservation. The setup uses a counter-propagating geometry, which allows momentum measurement on each beam separately. The experimental advantages of this setup include low drift due to all-optical manipulation, and a robust calibration (independent of the features of the trapped object or buffer medium) due to the force measurement method. Although this design does not attain the high-resolution of some co-propagating setups, we show that it can be used to perform different single molecule measurements: fluctuation-based molecular stiffness characterization at different forces and hopping experiments on molecular hairpins. Remarkably, in our setup it is possible to manipulate very short tethers (such as molecular hairpins with short handles) down to the limit where beads are almost in contact. The setup is used to illustrate a novel method for measuring the stiffness of optical traps and tethers on the basis of equilibrium force fluctuations, i.e., without the need of measuring the force vs molecular extension curve. This method is of general interest for dual trap optical tweezers setups and can be extended to setups which do not directly measure forces
Counter-propagating dual-trap optical tweezers based on linear momentum conservation
No full textWe present a dual-trap optical tweezers setup which directly measures forces using linear momentum conservation. The setup uses a counter-propagating geometry, which allows momentum measurement on each beam separately. The experimental advantages of this setup include low drift due to all-optical manipulation, and a robust calibration (independent of the features of the trapped object or buffer medium) due to the force measurement method. Although this design does not attain the high-resolution of some co-propagating setups, we show that it can be used to perform different single molecule measurements: fluctuation-based molecular stiffness characterization at different forces and hopping experiments on molecular hairpins. Remarkably, in our setup it is possible to manipulate very short tethers (such as molecular hairpins with short handles) down to the limit where beads are almost in contact. The setup is used to illustrate a novel method for measuring the stiffness of optical traps and tethers on the basis of equilibrium force fluctuations, i.e., without the need of measuring the force vs molecular extension curve. This method is of general interest for dual trap optical tweezers setups and can be extended to setups which do not directly measure forces
Nonequilibrium thermodynamics of single DNA hairpins in a dual-trap optical tweezers setup
No full text
