arXiv subjects

Felix Ritort

Publications and source records attributed to Felix Ritort.

At least 37 records · Page 2Linked to original sources

arXiv2020

Explicit solution of the generalised Langevin equation

Generating an initial condition for a Langevin equation with memory is a non trivial issue. We introduce a generalisation of the Laplace transform as a useful tool for solving this problem, in which a limit procedure may send the extension of memory effects to arbitrary times in the past. This method allows us to compute average position, work, their variances and the entropy production rate of a particle dragged in a complex fluid by an harmonic potential, which could represent the effect of moving optical tweezers. For initial conditions in equilibrium we generalise the results by van Zon and Cohen, finding the variance of the work for generic protocols of the trap. In addition, we study a particle dragged for a long time captured in an optical trap with constant velocity in a steady state. Our formulas open the door to thermodynamic uncertainty relations in systems with memory.

cond-mat.stat-mech↗

arXiv2020

Experimental evidence of symmetry breaking of transition-path times

While Kramers' rates have been studied for almost a century, the transition path time between states has only recently received attention. Transition paths between different energy levels are expected to be indistinguishable in shape and have equal uphill and downhill lengths. This fundamental symmetry often prevents directional sensing in experiments. Here, we report experimental evidence for transition path time symmetry and its breakdown on the single-molecule and mesoscale. In automated Brownian dynamics experiments, we establish first-passage time symmetries of colloids driven by femtoNewton-range forces in holographically-created optical landscapes confined in microchannels. Conversely, we show that transitions which couple in a path-dependent manner to fluctuating forces exhibit asymmetry. We reproduce this asymmetry in folding transitions of DNA-hairpins driven out of equilibrium and suggest a topological mechanism for the symmetry breakdown. Our results can reveal directionality in molecular transitions or translocations through membrane channels and nanopores.

cond-mat.stat-mech↗

arXiv2020

Work extraction, information-content and the Landauer bound in the continuous Maxwell Demon

In a recent paper we have introduced a continuous version of the Maxwell demon (CMD) that is capable of extracting large amounts of work per cycle by repeated measurements of the state of the system. Here we underline its main features such as the role played by the Landauer limit in the average extracted work, the continuous character of the measurement process and the differences between our continuous Maxwell demon and an autonomous Maxwell demon. We demonstrate the reversal of Landauer's inequality depending on the thermodynamical and mechanical stability of the work extracting substance. We also emphasise the robustness of the Shannon definition of the information-content of the stored sequences in the limit where work extraction is maximal and fuelled by the large information-content of rare events.

cond-mat.stat-mech↗

arXiv2020

Large work extraction and the Landauer limit in a continuous Maxwell demon

The relation between entropy and information dates back to the classical Maxwell demon (MD) paradox, a thought experiment proposed in 1867 by J. C. Maxwell to violate the second law of thermodynamics. A variant of the classical MD is the Szilard engine proposed by L. Szilard in 1926 in which the demon observes, at a given time, the compartment occupied by a single molecule in a vessel and extracts work by operating a pulley device. Here we introduce the Continuous Maxwell Demon (CMD), a device capable of extracting arbitrarily large amounts of work per cycle by repeated measurements of the state of a system, and experimentally test it in single DNA hairpin pulling experiments. In the CMD the demon monitors the state of the DNA hairpin (folded or unfolded) by observing it at equally spaced time intervals but extracts work only when the molecule changes state. We demonstrate that the average maximum work per cycle that can be extracted by the CMD is limited by the information-content of the stored sequences, in agreement with the second law. Work extraction efficiency is found to be maximal in the large information-content limit where work extraction is fuelled by rare events.

cond-mat.stat-mech↗

arXiv2020

Optical Tweezers: A Comprehensive Tutorial from Calibration to Applications

Since their invention in 1986 by Arthur Ashkin and colleagues, optical tweezers have become an essential tool in several fields of physics, spectroscopy, biology, nanotechnology, and thermodynamics. In this Tutorial, we provide a primer on how to calibrate optical tweezers and how to use them for advanced applications. After a brief general introduction on optical tweezers, we focus on describing and comparing the various available calibration techniques. Then, we discuss some cutting-edge applications of optical tweezers in a liquid medium, namely to study single-molecule and single-cell mechanics, microrheology, colloidal interactions, statistical physics, and transport phenomena. Finally, we consider optical tweezers in vacuum, where the absence of a viscous medium offers vastly different dynamics and presents new challenges. We conclude with some perspectives for the field and the future application of optical tweezers. This Tutorial provides both a step-by-step guide ideal for non-specialists entering the field and a comprehensive manual of advanced techniques useful for expert practitioners. All the examples are complemented by the sample data and software necessary to reproduce them.

physics.optics↗

arXiv2019

Efficient methods for determining folding free energies in single-molecule pulling experiments

The remarkable accuracy and versatility of single-molecule techniques make possible new measurements that are not feasible in bulk assays. Among these, the precise estimation of folding free energies using fluctuation theorems in nonequilibrium pulling experiments has become a benchmark in modern biophysics. In practice, the use of fluctuation relations to determine free energies requires a thorough evaluation of the usually large energetic contributions caused by the elastic deformation of the different elements of the experimental setup (such as the optical trap, the molecular linkers and the stretched-unfolded polymer). We review and describe how to optimally estimate such elastic energy contributions to extract folding free energies, using DNA and RNA hairpins as model systems pulled by laser optical tweezers. The methodology is generally applicable to other force-spectroscopy techniques and molecular systems.

q-bio.BM↗

arXiv2019

Force Feedback Effects on Single Molecule Hopping and Pulling Experiments

Single-molecule experiments with optical tweezers have become an important tool to study the properties and mechanisms of biological systems, such as cells and nucleic acids. In particular, force unzipping experiments have been used to extract the thermodynamics and kinetics of folding and unfolding reactions. In hopping experiments, a molecule executes transitions between the unfolded and folded states at a preset value of the force (constant force mode -CFM- under force feedback) or trap position (passive mode -PM- without feedback) and the force-dependent kinetic rates extracted from the lifetime of each state (CFM) and the rupture force distributions (PM) using the Bell-Evans model. However, hopping experiments in the CFM are known to overestimate molecular distances and folding free energies for fast transitions compared to the response time of the feedback. In contrast, kinetic rate measurements from pulling experiments have been mostly done in the PM while the CFM is seldom implemented in pulling protocols. Here, we carry out hopping and pulling experiments in a short DNA hairpin in the PM and CFM at three different temperatures (6$^\circ$C, 25$^\circ$C and 45$^\circ$C) exhibiting largely varying kinetic rates. As expected, we find that equilibrium hopping experiments in the CFM and PM perform well at 6$^\circ$C (where kinetics is slow) whereas the CFM overestimates molecular parameters at 45$^\circ$C (where kinetics is fast). In contrast, nonequilibrium pulling experiments perform well in both modes at all temperatures. This demonstrates that the same kind of feedback algorithm in the CFM leads to more reliable determination of the folding reaction parameters in irreversible pulling experiments.

physics.bio-ph↗

arXiv2017

Finite-time generalization of the thermodynamic uncertainty relation

For fluctuating currents in non-equilibrium steady states, the recently discovered thermodynamic uncertainty relation expresses a fundamental relation between their variance and the overall entropic cost associated with the driving. We show that this relation holds not only for the long-time limit of fluctuations, as described by large deviation theory, but also for fluctuations on arbitrary finite time scales. This generalization facilitates applying the thermodynamic uncertainty relation to single molecule experiments, for which infinite timescales are not accessible. Importantly, often this finite-time variant of the relation allows inferring a bound on the entropy production that is even stronger than the one obtained from the long-time limit. We illustrate the relation for the fluctuating work that is performed by a stochastically switching laser tweezer on a trapped colloidal particle.

cond-mat.stat-mech↗

arXiv2017

Experimental measurement of binding energy, selectivity and allostery using fluctuation theorems

Thermodynamic bulk measurements of binding reactions critically rely on the validity of the law of mass action and the assumption of a dilute solution. Yet important biological systems such as allosteric ligand-receptor binding, macromolecular crowding, or misfolded molecules may not follow this fundamental law and require a particular reaction model. Here we introduce a fluctuation theorem for ligand binding and an experimental approach using single-molecule force-spectroscopy to determine binding energies, selectivity and allostery of nucleic acids, proteins and peptides in a model-independent fashion. This work extends the use of fluctuation theorems beyond unimolecular folding reactions, bridging the thermodynamics of small systems and the basic laws of chemical equilibrium.

physics.bio-ph↗

arXiv2015

Free energy inference from partial work measurements in small systems

Fluctuation relations (FRs) are among the few existing general results in non-equilibrium systems. Their verification requires the measurement of the total work (or entropy production) performed on a system. Nevertheless in many cases only a partial measurement of the work is possible. Here we consider FRs in dual-trap optical tweezers where two different forces (one per trap) are measured. With this setup we perform pulling experiments on single molecules by moving one trap relative to the other. We demonstrate that work should be measured using the force exerted by the trap that is moved. The force that is measured in the trap at rest fails to provide the full dissipation in the system leading to a (incorrect) work definition that does not satisfy the FR. The implications to single-molecule experiments and free energy measurements are discussed. In the case of symmetric setups a new work definition, based on differential force measurements, is introduced. This definition is best suited to measure free energies as it shows faster convergence of estimators. We discuss measurements using the (incorrect) work definition as an example of partial work measurement. We show how to infer the full work distribution from the partial one via the FR. The inference process does also yield quantitative information, e.g. the hydrodynamic drag on the dumbbell. Results are also obtained for asymmetric dual-trap setups. We suggest that this kind of inference could represent a new and general application of FRs to extract information about irreversible processes in small systems.

cond-mat.stat-mech↗

arXiv2015

Universal Axial Fluctuations in Optical Tweezers

Optical tweezers allow the measurement of fluctuations at the nano-scale, in particular fluctuations in the end-to-end distance in single molecules. Fluctuation spectra can yield valuable information, but they can easily be contaminated by instrumental effects. We identify axial fluctuations, i.e. fluctuations of the trapped beads in the direction of light propagation, as one of these instrumental effects. Remarkably, axial fluctuations occur on a characteristic timescale similar to that of conformational (folding) transitions, which may lead to misinterpretation of the experimental results. We show that a precise measurement of the effect of force on both axial and conformational fluctuations is crucial to disentangle them. Our results on axial fluctuations are captured by a simple and general formula valid for all optical tweezers setups and provide experimentalists with a general strategy to distinguish axial fluctuations from conformational transitions.

physics.bio-ph↗

arXiv2014

Electrostatic Binding and Hydrophobic Collapse of Peptide-Nucleic Acid Aggregates Quantified Using Force Spectroscopy

Knowledge of the mechanisms of interaction between self-aggregating peptides and nucleic acids or other polyanions is key to the understanding of many aggregation processes underlying several human diseases (e.g. Alzheimer's and Parkinson's diseases). Determining the affinity and kinetic steps of such interactions is challenging due to the competition between hydrophobic self-aggregating forces and electrostatic binding forces. Kahalalide F (KF) is an anticancer hydrophobic peptide which contains a single positive charge that confers strong aggregative properties with polyanions. This makes KF an ideal model to elucidate the mechanisms by which self-aggregation competes with binding to a strongly charged polyelectrolyte such as DNA. We use optical tweezers to apply mechanical forces to single DNA molecules and show that KF and DNA interact in a two-step kinetic process promoted by the electrostatic binding of DNA to the aggregate surface followed by the stabilization of the complex due to hydrophobic interactions. From the measured pulling curves we determine the spectrum of binding affinities, kinetic barriers and lengths of DNA segments sequestered within the KF-DNA complex. We find there is a capture distance beyond which the complex collapses into compact aggregates stabilized by strong hydrophobic forces, and discuss how the bending rigidity of the nucleic acid affects such process. We hypothesize that within an in vivo context, the enhanced electrostatic interaction of KF due to its aggregation might mediate the binding to other polyanions. The proposed methodology should be useful to quantitatively characterize other compounds or proteins in which the formation of aggregates is relevant.

physics.bio-ph↗

arXiv2013

Force Spectroscopy with Dual-Trap Optical Tweezers: Molecular Stiffness Measurements and Coupled Fluctuations Analysis

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 paper 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 novel dual trap optical tweezers setup which 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 ds-DNA 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.

physics.bio-ph↗

arXiv2013

Counter-propagating dual-trap optical tweezers based on linear momentum conservation

We 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.

physics.bio-ph↗

arXiv2013

Experimental free energy measurements of kinetic molecular states using fluctuation theorems

Recent advances in non-equilibrium statistical mechanics and single molecule technologies make it possible to extract free energy differences from irreversible work measurements in pulling experiments. To date, free energy recovery has been focused on native or equilibrium molecular states, whereas free energy measurements of kinetic states (i.e. finite lifetime states that are generated dynamically and are metastable) have remained unexplored. Kinetic states can play an important role in various domains of physics, such as nanotechnology or condensed matter physics. In biophysics, there are many examples where they determine the fate of molecular reactions: protein and peptide-nucleic acid binding, specific cation binding, antigen-antibody interactions, transient states in enzymatic reactions or the formation of transient intermediates and non-native structures in molecular folders. Here we demonstrate that it is possible to obtain free energies of kinetic states by applying extended fluctuation relations. This is shown by using optical tweezers to mechanically unfold and refold DNA structures exhibiting intermediate and misfolded kinetic states.

physics.bio-ph↗

arXiv2011

Improving free-energy estimates from unidirectional work measurements: theory and experiment

We derive analytical expressions for the bias of the Jarzynski free-energy estimator from N nonequilibrium work measurements, for a generic work distribution. To achieve this, we map the estimator onto the Random Energy Model in a suitable scaling limit parametrized by (log N)/m, where m measures the width of the lower tail of the work distribution, and then compute the finite-N corrections to this limit with different approaches for different regimes of (log N)/m. We show that these expressions describe accurately the bias for a wide class of work distributions, and exploit them to build an improved free-energy estimator from unidirectional work measurements. We apply the method to optical tweezers unfolding/refolding experiments on DNA hairpins of varying loop size and dissipation, displaying both near-Gaussian and non-Gaussian work distributions.

cond-mat.stat-mech↗

arXiv2011

Folding and unfolding of a triple-branch DNA molecule with four conformational states

Single-molecule experiments provide new insights into biological processes hitherto not accessible by measurements performed on bulk systems. We report on a study of the kinetics of a triple-branch DNA molecule with four conformational states by pulling experiments with optical tweezers and theoretical modelling. Three distinct force rips associated with different transitions between the conformational states are observed in the folding and unfolding trajectories. By applying transition rate theory to a free energy model of the molecule, probability distributions for the first rupture forces of the different transitions are calculated. Good agreement of the theoretical predictions with the experimental findings is achieved. Furthermore, due to our specific design of the molecule, we found a useful method to identify permanently frayed molecules by estimating the number of opened basepairs from the measured force jump values.

physics.bio-ph↗

arXiv2011

Recent progress in fluctuation theorems and free energy recovery

In this note we review recent progress about fluctuation relations and their applicability to free energy recovery in single molecule experiments. We underline the importance of the operational definition for the mechanical work and the non-invariance of fluctuation relations under Galilean transformations, both aspects currently amenable to experimental test. Finally we describe a generalization of the Crooks fluctuation relation useful to recover free energies of partially equilibrated states and thermodynamic branches.

cond-mat.stat-mech↗