Destructive effect of fluctuations on the performance of a Brownian gyrator.

The Brownian gyrator (BG) is often called a minimal model of a nano-engine performing a rotational motion, judging solely upon the fact that in non-equilibrium conditions its torque, specific angular momentum  and specific angular velocity  have non-zero mean values. For a time-discretised (with time-step δt) model we calculate here the previously unknown probability density functions (PDFs) of  and . We show that for finite δt, the PDF of  has exponential tails and all moments are therefore well-defined. At the same time, this PDF appears to be effectively broad - the noise-to-signal ratio is generically bigger than unity meaning that  is strongly not self-averaging. Concurrently, the PDF of  exhibits heavy power-law tails and its mean is the only existing moment. The BG is therefore not an engine in the common sense: it does not exhibit regular rotations on each run and its fluctuations are not only a minor nuisance - on contrary, their effect is completely destructive for the performance. Our theoretical predictions are confirmed by numerical simulations and experimental data. We discuss some plausible improvements of the model which may result in a more systematic rotational motion.

Quantum duets working as autonomous thermal motors.

We study the dynamic properties of a thermal autonomous machine made up of two quantum Brownian particles, each of which is in contact with an environment at different temperature and moves on a periodic sinusoidal track. When such tracks are shifted, the center of mass of the system exhibits a nonvanishing velocity, for which we provide an exact expression in the limit of small track undulations. We discuss the role of the broken spatial symmetry in the emergence of directed motion in thermal machines. We then consider the case in which external deterministic forces are applied to the system, and we characterize its steady-state velocity. If the applied external force opposes the system motion, work can be extracted from such a steady-state thermal machine, without any external cyclic protocol. When the two particles are not interacting, our results reduce to those of Fisher and Zwerger [Phys. Rev. B 32, 6190 (1985)PRBMDO0163-182910.1103/PhysRevB.32.6190] and Aslangul, Pottier, and Saint-James [J. Phys. France 48, 1093 (1987)JOPQAG0302-073810.1051/jphys:019870048070109300] for a single particle moving in a periodic tilted potential. We finally use our results for the motor velocity to check the validity of the quantum molecular dynamics algorithm in the nonlinear, nonequilibrium regime.

Out-of-Equilibrium Clock Model at the Verge of Criticality.

We consider an out-of-equilibrium lattice model consisting of 2D discrete rotators, in contact with heat reservoirs at different temperatures. The equilibrium counterpart of such a model, the clock model, exhibits three phases: a low-temperature ordered phase, a quasiliquid phase, and a high-temperature disordered phase, with two corresponding phase transitions. In the out-of-equilibrium model the simultaneous breaking of spatial symmetry and thermal equilibrium gives rise to directed rotation of the spin variables. In this regime the system behaves as a thermal machine converting heat currents into motion. In order to quantify the susceptibility of the machine to the thermodynamic force driving it out of equilibrium, we introduce and study a dynamical response function. We show that the optimal operational regime for such a thermal machine occurs when the out-of-equilibrium disturbance is applied around the critical temperature at the boundary between the first two phases, namely, where the system is mostly susceptible to external thermodynamic forces and exhibits a sharper transition. We thus argue that critical fluctuations in a system of interacting motors can be exploited to enhance the machine overall dynamic and thermodynamic performances.

Exact firing time statistics of neurons driven by discrete inhibitory noise.

Neurons in the intact brain receive a continuous and irregular synaptic bombardment from excitatory and inhibitory pre- synaptic neurons, which determines the firing activity of the stimulated neuron. In order to investigate the influence of inhibitory stimulation on the firing time statistics, we consider Leaky Integrate-and-Fire neurons subject to inhibitory instantaneous post- synaptic potentials. In particular, we report exact results for the firing rate, the coefficient of variation and the spike train spectrum for various synaptic weight distributions. Our results are not limited to stimulations of infinitesimal amplitude, but they apply as well to finite amplitude post-synaptic potentials, thus being able to capture the effect of rare and large spikes. The developed methods are able to reproduce also the average firing properties of heterogeneous neuronal populations.

Non-Boltzmann stationary distributions and nonequilibrium relations in active baths.

Most natural and engineered processes, such as biomolecular reactions, protein folding, and population dynamics, occur far from equilibrium and therefore cannot be treated within the framework of classical equilibrium thermodynamics. Here we experimentally study how some fundamental thermodynamic quantities and relations are affected by the presence of the nonequilibrium fluctuations associated with an active bath. We show in particular that, as the confinement of the particle increases, the stationary probability distribution of a Brownian particle confined within a harmonic potential becomes non-Boltzmann, featuring a transition from a Gaussian distribution to a heavy-tailed distribution. Because of this, nonequilibrium relations (e.g., the Jarzynski equality and Crooks fluctuation theorem) cannot be applied. We show that these relations can be restored by using the effective potential associated with the stationary probability distribution. We corroborate our experimental findings with theoretical arguments.

Pushing the limit: investigation of hydrodynamic forces on a trapped particle kicked by a laser pulse.

We introduce a new optical technique where a train of short optical pulses is utilized to disturb a trapped microscopic particle. Using fast (250 kHz) and accurate (nm) detection of the position of the particle, accurately synchronized to the repetition rate of the laser pulses, we can coherently superimpose the displacement caused by each individual laser pulse. Thereby we are able to both bypass the influence from the Brownian motion of the trapped particle and to simultaneously increase the ability to localize its average trajectory by √n, where n is the number of repetitive pulses. In the results presented here we utilize a train of 1200 pulses to kick a 5 µm polystyrene sphere and obtain a spatial resolution corresponding to 0.09 nm and a time resolution of 4 µs. The magnitude of the optical force pushing the particle corresponds to ∼ 10(4)g and enables an investigation of both the hydrodynamical drag and the inertial effects caused by the particle and the surrounding liquid. Our results enables a more accurate testing of the existing extended models for the hydrodynamic drag and we discuss the observed agreement between experiments and theory.

Exact fluctuation theorem without ensemble quantities.

Evaluating the entropy production (EP) along a stochastic trajectory requires the knowledge of the system probability distribution, an ensemble quantity notoriously difficult to measure. In this paper we show that the EP of nonautonomous systems in contact with multiple reservoirs can be expressed solely in terms of physical quantities measurable at the single-trajectory level with a suitable preparation of the initial condition. As a result, we identify universal energy and particle fluctuation relations valid for any measurement time. We apply our findings to an electronic junction model, which may be used to verify our prediction experimentally.

Sisyphus effect in pulse-coupled excitatory neural networks with spike-timing-dependent plasticity.

The collective dynamics of excitatory pulse-coupled neural networks with spike-timing-dependent plasticity (STDP) is studied. Depending on the model parameters stationary states characterized by high or low synchronization can be observed. In particular, at the transition between these two regimes, persistent irregular low frequency oscillations between strongly and weakly synchronized states are observable, which can be identified as infraslow oscillations with frequencies ≃0.02-0.03 Hz. Their emergence can be explained in terms of the Sisyphus effect, a mechanism caused by a continuous feedback between the evolution of the coherent population activity and of the average synaptic weight. Due to this effect, the synaptic weights have oscillating equilibrium values, which prevents the neuronal population from relaxing into a stationary macroscopic state.

Single-molecule folding mechanism of an EF-hand neuronal calcium sensor.

EF-hand calcium sensors respond structurally to changes in intracellular Ca(2+) concentration, triggering diverse cellular responses and resulting in broad interactomes. Despite impressive advances in decoding their structure-function relationships, the folding mechanism of neuronal calcium sensors is still elusive. We used single-molecule optical tweezers to study the folding mechanism of the human neuronal calcium sensor 1 (NCS1). Two intermediate structures induced by Ca(2+) binding to the EF-hands were observed during refolding. The complete folding of the C domain is obligatory for the folding of the N domain, showing striking interdomain dependence. Molecular dynamics results reveal the atomistic details of the unfolding process and rationalize the different domain stabilities during mechanical unfolding. Through constant-force experiments and hidden Markov model analysis, the free energy landscape of the protein was reconstructed. Our results emphasize that NCS1 has evolved a remarkable complex interdomain cooperativity and a fundamentally different folding mechanism compared to structurally related proteins.

Emergence of slow collective oscillations in neural networks with spike-timing dependent plasticity.

The collective dynamics of excitatory pulse coupled neurons with spike-timing dependent plasticity is studied. The introduction of spike-timing dependent plasticity induces persistent irregular oscillations between strongly and weakly synchronized states, reminiscent of brain activity during slow-wave sleep. We explain the oscillations by a mechanism, the Sisyphus Effect, caused by a continuous feedback between the synaptic adjustments and the coherence in the neural firing. Due to this effect, the synaptic weights have oscillating equilibrium values, and this prevents the system from relaxing into a stationary macroscopic state.

A highly compliant protein native state with a spontaneous-like mechanical unfolding pathway.

The mechanical properties of proteins and their force-induced structural changes play key roles in many biological processes. Previous studies have shown that natively folded proteins are brittle under tension, unfolding after small mechanical deformations, while partially folded intermediate states, such as molten globules, are compliant and can deform elastically a great amount before crossing the transition state barrier. Moreover, under tension proteins appear to unfold through a different sequence of events than during spontaneous unfolding. Here, we describe the response to force of the four-α-helix acyl-CoA binding protein (ACBP) in the low-force regime using optical tweezers and ratcheted molecular dynamics simulations. The results of our studies reveal an unprecedented mechanical behavior of a natively folded protein. ACBP displays an atypical compliance along two nearly orthogonal pulling axes, with transition states located almost halfway between the unfolded and folded states. Surprisingly, the deformability of ACBP is greater than that observed for the highly pliant molten globule intermediate states. Furthermore, when manipulated from the N- and C-termini, ACBP unfolds by populating a transition state that resembles that observed during chemical denaturation, both for structure and position along the reaction coordinate. Our data provide the first experimental evidence of a spontaneous-like mechanical unfolding pathway of a protein. The mechanical behavior of ACBP is discussed in terms of topology and helix propensity.

Motion analysis of optically trapped particles and cells using 2D Fourier analysis.

Motion analysis of optically trapped objects is demonstrated using a simple 2D Fourier transform technique. The displacements of trapped objects are determined directly from the phase shift between the Fourier transform of subsequent images. Using end- and side-view imaging, the stiffness of the trap is determined in three dimensions. The Fourier transform method is simple to implement and applicable in cases where the trapped object changes shape or where the lighting conditions change. This is illustrated by tracking a fluorescent particle and a myoblast cell, with subsequent determination of diffusion coefficients and the trapping forces.

Mechanical stress affects glucagon fibrillation kinetics and fibril structure.

Mechanical stress can strongly influence the capability of a protein to aggregate and the kinetics of aggregation, but there is little insight into the underlying mechanism. Here we study the effect of different mechanical stress conditions on the fibrillation of the peptide hormone glucagon, which forms different fibrils depending on temperature, pH, ionic strength, and concentration. A combination of spectroscopic and microscopic data shows that fibrillar polymorphism can also be induced by mechanical stress. We observed two classes of fibrils: a low-stress and a high-stress class, which differ in their kinetic profiles, secondary structure as well as morphology and that are able to self-propagate in a template-dependent fashion. The bending rigidity of the low-stress fibrils is sensitive to the degree of mechanical perturbation. We propose a fibrillation model, where interfaces play a fundamental role in the switch between the two fibrillar classes. Our work also raises the cautionary note that mechanical perturbation is a potential source of variability in the study of fibrillation mechanisms and fibril structures.

Discrete breathers in a realistic coarse-grained model of proteins.

We report the results of molecular dynamics simulations of an off-lattice protein model featuring a physical force-field and amino-acid sequence. We show that localized modes of nonlinear origin, discrete breathers (DBs), emerge naturally as continuations of a subset of high-frequency normal modes residing at specific sites dictated by the native fold. DBs are time-periodic, space-localized vibrational modes that exist generically in nonlinear discrete systems and are known for their resilience and ability to concentrate energy for long times. In the case of the small ß-barrel structure that we consider, DB-mediated localization occurs on the turns connecting the strands. At high energies, DBs stabilize the structure by concentrating energy on a few sites, while their collapse marks the onset of large-amplitude fluctuations of the protein. Furthermore, we show how breathers develop as energy-accumulating centres following perturbations even at distant locations, thus mediating efficient and irreversible energy transfers. Remarkably, due to the presence of angular potentials, the breather induces a local static distortion of the native fold. Altogether, the combination of these two nonlinear effects may provide a ready means for remotely controlling local conformational changes in proteins.

Unfolding times for proteins in a force clamp.

The escape process from the native valley for proteins subjected to a constant stretching force is examined using a model for a beta barrel. For a wide range of forces, the unfolding dynamics can be treated as one-dimensional diffusion, parametrized in terms of the end-to-end distance. In particular, the escape times can be evaluated as first passage times for a Brownian particle moving on the protein free-energy landscape, using the Smoluchowski equation. At strong forces, the unfolding process can be viewed as a diffusive drift away from the native state, while at weak forces thermal activation is the relevant mechanism. An escape-time analysis within this approach reveals a crossover from an exponential to an inverse Gaussian escape-time distribution upon passing from weak to strong forces. Moreover, a single expression valid at weak and strong forces can be devised both for the average unfolding time as well as for the corresponding variance. The analysis offers a possible explanation of recent experimental findings for the proteins ddFLN4 and ubiquitin.

Changing the mechanical unfolding pathway of FnIII10 by tuning the pulling strength.

We investigate the mechanical unfolding of the tenth type III domain from fibronectin (FnIII(10)) both at constant force and at constant pulling velocity, by all-atom Monte Carlo simulations. We observe both apparent two-state unfolding and several unfolding pathways involving one of three major, mutually exclusive intermediate states. All three major intermediates lack two of seven native beta-strands, and share a quite similar extension. The unfolding behavior is found to depend strongly on the pulling conditions. In particular, we observe large variations in the relative frequencies of occurrence for the intermediates. At low constant force or low constant velocity, all three major intermediates occur with a significant frequency. At high constant force or high constant velocity, one of them, with the N- and C-terminal beta-strands detached, dominates over the other two. Using the extended Jarzynski equality, we also estimate the equilibrium free-energy landscape, calculated as a function of chain extension. The application of a constant pulling force leads to a free-energy profile with three major local minima. Two of these correspond to the native and fully unfolded states, respectively, whereas the third one can be associated with the major unfolding intermediates.

Free-energy landscape of mechanically unfolded model proteins: extended Jarzinsky versus inherent structure reconstruction.

The equilibrium free-energy landscape of off-lattice model heteropolymers as a function of an internal coordinate, namely the end-to-end distance, is reconstructed from out-of-equilibrium steered molecular dynamics data. This task is accomplished via two independent methods: By employing an extended version of the Jarzynski equality and the inherent structure formalism. A comparison of the free energies estimated with these two schemes with equilibrium results obtained via the umbrella sampling technique reveals a good quantitative agreement among all the approaches in a range of temperatures around the "folding transition" for the two examined sequences. In particular, for the sequence with good foldability properties, the mechanically induced structural transitions can be related to thermodynamical aspects of folding. Moreover, for the same sequence the knowledge of the landscape profile allows for a good estimation of the lifetimes of the native configuration for temperatures ranging from the folding to the collapse temperature. For the random sequence, mechanical and thermal unfolding appear to follow different paths along the landscape.

Reconstructing the free-energy landscape of a mechanically unfolded model protein.

The equilibrium free-energy landscape of an off-lattice model protein as a function of an internal (reaction) coordinate is reconstructed from out-of-equilibrium mechanical unfolding manipulations. This task is accomplished via two independent methods: by employing an extended version of the Jarzynski equality (EJE) and the protein inherent structures (ISs). In a range of temperatures around the "folding transition" we find a good quantitative agreement between the free energies obtained via EJE and IS approaches. This indicates that the two methodologies are consistent and able to reproduce equilibrium properties of the examined system. Moreover, for the studied model the structural transitions induced by pulling can be related to thermodynamical aspects of folding.

Surface tension in bilayer membranes with fixed projected area.

We study the elastic response of bilayer membranes with fixed projected area to both the stretching and shape deformations. A surface tension is associated to each of these deformations. By using model amphiphilic membranes and computer simulations, we are able to observe both the types of deformation, and thus, both the surface tensions, related to each type of deformation, are measured for the same system. These surface tensions are found to assume different values in the same bilayer membrane, in particular, they vanish for different values of the projected area. We introduce a simple theory which relates the two quantities and successfully apply it to the data obtained with computer simulations.