The noisy and marvelous molecular world of biology

At the molecular level biology is intrinsically noisy. The forces that regulate the myriad of molecular reactions in the cell are tiny, on the order of piconewtons (10−12 Newtons), yet they proceed in concerted action making life possible. Understanding how this is possible is one of the most fundamental questions biophysicists would like to understand. Single molecule experiments offer an opportunity to delve into the fundamental laws that make biological complexity surface in a physical world governed by the second law of thermodynamics. Techniques such as force spectroscopy, fluorescence, microfluidics, molecular sequencing, and computational studies project a view of the biomolecular world ruled by the conspiracy between the disorganizing forces due to thermal motion and the cosmic evolutionary drive. Here we will digress on some of the evidences in support of this view and the role of physical information in biology

Temperature-dependent elastic properties of DNA

Knowledge of the elastic properties, e.g., the persistence length or interphosphate distance, of single-stranded (ss) and double-stranded (ds) DNA under different experimental conditions is critical to characterizing molecular reactions studied with single-molecule techniques. While previous experiments have addressed the dependence of the elastic parameters upon varying ionic strength and contour length, temperature-dependent effects are less studied. Here, we examine the temperature-dependent elasticity of ssDNA and dsDNA in the range 5°C-50°C using a temperature-jump optical trap. We find a temperature softening for dsDNA and a temperature stiffening for ssDNA. Our results highlight the need for a general theory explaining the phenomenology observed

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 thisproblem, in which a limit procedure may send the extension of memory effects to arbitrarytimes in the past. This method allows us to compute average position, work, their variancesand the entropy production rate of a particle dragged in a complex fluid by an harmonicpotential, which could represent the effect of moving optical tweezers. For initial conditionsin equilibrium we generalise the results by van Zon and Cohen, finding the variance of thework for generic protocols of the trap. In addition, we study a particle dragged for a longtime captured in an optical trap with constant velocity in a steady state. Our formulas openthe door to thermodynamic uncertainty relations in systems with memory

Vidres de spins i xarxes neuronals

Un deis interessos més gran de la física és l'estudi de les propietats dels sistemes macroscòpics amb molts graus de llibertat. D'aquesta branca de la física s'encarrega la mecànica estadística, 1'objectiu de la qual és la derivació de les propietats globals d'un sistema conegudes les interaccions al nivell de les seves partícules constituents. La mecànica estadística, encara que es va iniciar ja fa molt temps amb els primers resultats de L. Boltzmann i J.W. Gibbs ara farà uns cent anys, ha anat obrint el seu camp d'influència i actualment compren un gran nombre de temes de recerca, que van des de l'estat sòlid fins a la turbulència deis fluids passant per tota una fenomenologia molt vasta. La mecànica estadística s'ha revelat també de molta utilitat en permetre un llenguatge comú amb la teoria quàntica de camps fins al punt de parlar-se avui en dia de teoria estadística deis camps per fer referencia a totes dues

Experimental test of ensemble inequivalence and the fluctuation theorem in the force ensemble in DNA pulling experiments

We experimentally test the validity of the Crooks fluctuation theorem (CFT) in the force ensemble by pulling DNA hairpins, first with magnetic tweezers, next with optical tweezers using force feedback. The CFT holds when using the definition of work Wf=−∫xdf, where x is the molecular extension and f is the force. In contrast, it does not hold when using the usual definition, appropriate for the constant extension ensemble, Wx=∫fdx, showing the importance of the contribution of boundary terms to the full entropy production in a clear example of statistical ensemble inequivalence in small systems. We also evaluate the differences in the average dissipated work in the force ensemble as compared to the extension ensemble, highlighting ensemble inequivalence also at the level of molecular kinetics

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 °C, 25 °C, and 45 °C) exhibiting largely varying kinetic rates. As expected, we find that equilibrium hopping experiments in the CFM and PM perform well at 6 °C (where kinetics are slow), whereas the CFM overestimates molecular parameters at 45 °C (where kinetics are 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

Closure of the Monte Carlo dynamical equation in the spherical Sherrington-Kirkpatrick model

We study the analytical solution of the Monte Carlo dynamics in the spherical Sherrington-Kirkpatrick model using the technique of the generating function. Explicit solutions for one-time observables (like the energy) and two-time observables (like the correlation and response function) are obtained. We show that the crucial quantity which governs the dynamics is the acceptance rate. At zero temperature, an adiabatic approximation reveals that the relaxational behavior of the model corresponds to that of a single harmonic oscillator with an effective renormalized mass

Derivation of nearest-neighbor DNA parameters in magnesium from single-molecule experiments

DNA hybridization is an essential molecular reaction in biology with many applications. The nearest-neighbor (NN) model for nucleic acids predicts DNA thermodynamics using energy values for the different base pair motifs. These values have been derived from melting experiments in monovalent and divalent salt and applied to predict melting temperatures of oligos within a few degrees. However, an improved determination of the NN energy values and their salt dependencies in magnesium is still needed for current biotechnological applications seeking high selectivity in the hybridization of synthetic DNAs. We developed a methodology based on single molecule unzipping experiments to derive accurate NN energy values and initiation factors for DNA. A new set of values in magnesium is derived, which reproduces unzipping data and improves melting temperature predictions for all available oligo lengths, in a range of temperature and salt conditions where correlation effects between the magnesium bound ions are weak. The NN salt correction parameters are shown to correlate to the GC content of the NN motifs. Our study shows the power of single-molecule force spectroscopy assays to unravel novel features of nucleic acids such as sequence-dependent salt corrections

The Kuramoto model: A simple paradigm for synchronization phenomena

Synchronization phenomena in large populations of interacting elements are the subject of intense research efforts in physical, biological, chemical, and social systems. A successful approach to the problem of synchronization consists of modeling each member of the population as a phase oscillator. In this review, synchronization is analyzed in one of the most representative models of coupled phase oscillators, the Kuramoto model. A rigorous mathematical treatment, specific numerical methods, and many variations and extensions of the original model that have appeared in the last few years are presented. Relevant applications of the model in different contexts are also included

From free energy measurements to thermodynamic inference in nonequilibrium small systems

Fluctuation theorems (FTs), such as the Crooks or Jarzynski equalities (JEs), have become an important tool in single-molecule biophysics where they allow experimentalists to exploit thermal fluctuations and measure free-energy differences from non-equilibrium pulling experiments. The rich phenomenology of biomolecular systems has stimulated the development of extensions to the standard FTs, to encompass different experimental situations. Here we discuss an extension of the Crooks fluctuation relation that allows the thermodynamic characterization of kinetic molecular states. This extension can be connected to the generalized JE under feedback. Finally we address the recently introduced concept of thermodynamic inference or how FTs can be used to extract the total entropy production distribution in nonequilibrium systems from partial entropy production measurements. We discuss the significance of the concept of effective temperature in this context and show how thermodynamic inference provides a unifying comprehensive picture in several nonequilibrium problems