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

A Severino, A M Monge, P Rissone and F Ritort

The remarkable accuracy and versatility of single-molecule techniques make new measurements that are not feasible in bulk assays possible. 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.

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

M Ribezzi-Crivellari and F Ritort

In a recent paper we 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 Ribezzi-Crivellari and Ritort (2019 Nat. Phys.). 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 emphasize the robustness of the Shannon definition of the information-content of the stored sequences in the limit where work extraction is maximal and fueled by the large information-content of rare events.

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The role of coupling on the statistical properties of the energy fluxes between stochastic systems at different temperatures

A Bérut, A Imparato, A Petrosyan and S Ciliberto

We experimentally study the statistical properties of the energy fluxes in two systems whose components are kept at different temperatures. The first system under consideration is an electric circuit which is composed by two resistances, kept at different temperatures and connected by a capacitance (conservative coupling) which couples the thermal noise of the two resistances. The other system is composed by two Brownian particles, trapped with optical tweezers, interacting through a dissipative hydrodynamic coupling. The particles are subjected to an effective temperature difference obtained by random forcing the position of one trap. In these two systems we measure the properties of the energy flowing between the two reservoirs. The role on these properties of the coupling and of the method used to produce the highest temperature is analyzed.

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Kinetic modeling of molecular motors: pause model and parameter determination from single-molecule experiments

José A Morin, Borja Ibarra and Francisco J Cao

Single-molecule manipulation experiments of molecular motors provide essential information about the rate and conformational changes of the steps of the reaction located along the manipulation coordinate. This information is not always sufficient to define a particular kinetic cycle. Recent single-molecule experiments with optical tweezers showed that the DNA unwinding activity of a Phi29 DNA polymerase mutant presents a complex pause behavior, which includes short and long pauses. Here we show that different kinetic models, considering different connections between the active and the pause states, can explain the experimental pause behavior. Both the two independent pause model and the two connected pause model are able to describe the pause behavior of a mutated Phi29 DNA polymerase observed in an optical tweezers single-molecule experiment. For the two independent pause model all parameters are fixed by the observed data, while for the more general two connected pause model there is a range of values of the parameters compatible with the observed data (which can be expressed in terms of two of the rates and their force dependencies). This general model includes models with indirect entry and exit to the long-pause state, and also models with cycling in both directions. Additionally, assuming that detailed balance is verified, which forbids cycling, this reduces the ranges of the values of the parameters (which can then be expressed in terms of one rate and its force dependency). The resulting model interpolates between the independent pause model and the indirect entry and exit to the long-pause state model.

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Information and thermodynamics: experimental verification of Landauer's Erasure principle

Antoine Bérut, Artyom Petrosyan and Sergio Ciliberto

We present an experiment in which a one-bit memory is constructed, using a system of a single colloidal particle trapped in a modulated double-well potential. We measure the amount of heat dissipated to erase a bit and we establish that in the limit of long erasure cycles the mean dissipated heat saturates at the Landauer bound, i.e. the minimal quantity of heat necessarily produced to delete a classical bit of information. This result demonstrates the intimate link between information theory and thermodynamics. To stress this connection we also show that a detailed Jarzynski equality is verified, retrieving the Landauer's bound independently of the work done on the system. The experimental details are presented and the experimental errors carefully discussed.

DOI

Fluctuations and response in a non-equilibrium micron-sized system

Juan Ruben Gomez-Solano, Artyom Petrosyan, Sergio Ciliberto and Christian Maes

The linear response of non-equilibrium systems with Markovian dynamics satisfies a generalized fluctuation-dissipation relation derived from time symmetry and antisymmetry properties of the fluctuations. The relation involves the sum of two correlation functions of the observable of interest: one with the entropy excess and the second with the excess of dynamical activity with respect to the unperturbed process, without recourse to anything but the dynamics of the system. We illustrate this approach in the experimental determination of the linear response of the potential energy of a Brownian particle in a toroidal optical trap. The overdamped particle motion is effectively confined to a circle, undergoing a periodic potential and driven out of equilibrium by a non-conservative force. Independent direct and indirect measurements of the linear response around a non-equilibrium steady state are performed in this simple experimental system. The same ideas are applicable to the measurement of the response of more general non-equilibrium micron-sized systems immersed in Newtonian fluids either in stationary or non-stationary states and possibly including inertial degrees of freedom.

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Experimental study of out-of-equilibrium fluctuations in a colloidal suspension of Laponite using optical traps

Pierre Jop, Juan Ruben Gomez-Solano, Artyom Petrosyan and Sergio Ciliberto

We address the issue of the validity of the fluctuation dissipation theorem and the time evolution of viscoelastic properties during ageing of aqueous suspensions of a clay (Laponite RD) in a colloidal glass phase. Given the conflicting results reported in the literature for different experimental techniques, our goal is to check and reconcile them using simultaneously passive and active microrheology techniques. For this purpose we measure the thermal fluctuations of microsized Brownian particles immersed in the colloidal glass and trapped by optical tweezers. We find that several methods based on both microrheology techniques lead to consistent and complementary results and no violation of the FDT is convincingly observed either for any frequency as low as 0.25 Hz or as an increase of the effective temperature during the formation of the viscoelastic glass. Our results are supported by the study of the probability density functions of heat fluctuations between the probe particles and the suspension transferred at different timescales. Several interesting features concerning the statistical properties and the long time correlations of the particles are observed during the transition.

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Dynamic force spectroscopy of DNA hairpins: II. Irreversibility and dissipation

M Manosas, A Mossa, N Forns, J M Huguet and F Ritort

We investigate irreversibility and dissipation in single molecules that cooperatively fold/unfold in a two-state manner under the action of mechanical force. We apply path thermodynamics to derive analytical expressions for the average dissipated work and the average hopping number in two-state systems. It is shown how these quantities only depend on two parameters that characterize the folding/unfolding kinetics of the molecule: the fragility and the coexistence hopping rate. The latter has to be rescaled to take into account the appropriate experimental set-up. Finally we carry out pulling experiments with optical tweezers in a specifically designed DNA hairpin that shows two-state cooperative folding. We then use these experimental results to validate our theoretical predictions.

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Dynamic force spectroscopy of DNA hairpins: I. Force kinetics and free energy landscapes

A Mossa, M Manosas, N Forns, J M Huguet and F Ritort

We investigate the thermodynamics and kinetics of DNA hairpins that fold/unfold under the action of applied mechanical force. We introduce the concept of the molecular free energy landscape and derive simplified expressions for the force dependent Kramers–Bell rates. To test the theory we have designed a specific DNA hairpin sequence that shows two-state cooperative folding under mechanical tension and carried out pulling experiments using optical tweezers. We show how we can determine the parameters that characterize the molecular free energy landscape of such sequences from rupture force kinetic studies. Finally we combine such kinetic studies with experimental investigations of the Crooks fluctuation relation to derive the free energy of formation of the hairpin at zero force.

DOI