Rate-dependent force-extension models for single-molecule force spectroscopy experiments.

Single-molecule force spectroscopy techniques allow for the measurement of several static and dynamic features of macromolecules of biological origin. In particular, atomic force microscopy, used with a variable pulling rate, provides valuable information on the folding/unfolding dynamics of proteins. We propose here two different models able to describe the out-of-equilibrium statistical mechanics of a chain composed of bistable units. These latter represent the protein domains, which can be either folded or unfolded. Both models are based on the Langevin approach and their implementation allows for investigating the effect of the pulling rate and of the device intrinsic elasticity on the chain unfolding response. The theoretical results (both analytical and numerical) have been compared with experimental data concerning the unfolding of the titin and filamin proteins, eventually obtaining a good agreement over a large range of the pulling rates.

Stability of radiation-damaged DNA after multiple strand breaks.

Damage to the DNA backbone occurs from natural sources, and with exceedingly large density during radiotherapy, as typically used for cancer treatment. Here, we focus on the molecular-scale dynamics of the events immediately following the production of single- and double-strand breaks, since this early-stage evolution of the damage is crucial to determine the subsequent fate of the DNA fragment. While multiple cleavage of phosphodiester bonds is the first step, however the remaining hydrogen-bond and π-stacking interactions maintain a considerable DNA cohesion, and determine further defect evolution. We use all-atom molecular dynamics to simulate the force spectra and thermal stability of different single- and multiple-defect configurations, in a random 31 bp DNA sequence. Simulations reveal a complex dynamical behaviour of the defects, where collective bond-rearrangement phenomena dominate with respect to simple bond cleavage. Defects are stable against thermal disruption, unless very closely spaced. We establish the necessary conditions for the events ultimately leading to DNA fragmentation. Such findings impact the early stages of damage recognition and signalling by specialised proteins, also implying that the identification and counting of DSBs by different experimental methods is non-unique.

Stochastic mechanical degradation of multi-cracked fiber bundles with elastic and viscous interactions.

The mechanics of fiber bundles has been largely investigated in order to understand their complex failure modes. Under a mechanical load, the fibers fail progressively while the load is redistributed among the unbroken fibers. The classical fiber bundle model captures the most important features of this rupture process. On the other hand, the homogenization techniques are able to evaluate the stiffness degradation of bulk solids with a given population of cracks. However, these approaches are inadequate to determine the effective response of a degraded bundle where breaks are induced by non-mechanical actions. Here, we propose a method to analyze the behavior of a fiber bundle, undergoing a random distribution of breaks, by considering the intrinsic response of the fibers and the visco-elastic interactions among them. We obtain analytical solutions for simple configurations, while the most general cases are studied by Monte Carlo simulations. We find that the degradation of the effective bundle stiffness can be described by two scaling regimes: a first exponential regime for a low density of breaks, followed by a power-law regime at increasingly higher break density. For both regimes, we find analytical effective expressions described by specific scaling exponents.

Scaling shift in multicracked fiber bundles.

Bundles of fibers, wires, or filaments are ubiquitous structures in both natural and artificial materials. We investigate the bundle degradation induced by an external damaging action through a theoretical model describing an assembly of parallel fibers, progressively damaged by a random population of cracks. Fibers in our model interact by means of a lateral linear coupling, thus retaining structural integrity even after substantial damage. Monte Carlo simulations of the Young's modulus degradation for increasing crack density demonstrate a remarkable scaling shift between an exponential and a power-law regime. Analytical solutions of the model confirm this behavior, and provide a thorough understanding of the underlying physics.

Theory and Monte Carlo simulations for the stretching of flexible and semiflexible single polymer chains under external fields.

Recent developments of microscopic mechanical experiments allow the manipulation of individual polymer molecules in two main ways: uniform stretching by external forces and non-uniform stretching by external fields. Many results can be thereby obtained for specific kinds of polymers and specific geometries. In this work, we describe the non-uniform stretching of a single, non-branched polymer molecule by an external field (e.g., fluid in uniform motion, or uniform electric field) by a universal physical framework, which leads to general conclusions on different types of polymers. We derive analytical results both for the freely-jointed chain and the worm-like chain models based on classical statistical mechanics. Moreover, we provide a Monte Carlo numerical analysis of the mechanical properties of flexible and semiflexible polymers anchored at one end. The simulations confirm the analytical achievements, and moreover allow to study the situations where the theory cannot provide explicit and useful results. In all cases, we evaluate the average conformation of the polymer and its fluctuation statistics as a function of the chain length, bending rigidity, and field strength.

Elasticity of flexible and semiflexible polymers with extensible bonds in the Gibbs and Helmholtz ensembles.

Stretching experiments on single molecules of arbitrary length opened the way for studying the statistical mechanics of small systems. In many cases in which the thermodynamic limit is not satisfied, different macroscopic boundary conditions, corresponding to different statistical mechanics ensembles, yield different force-displacement curves. We formulate analytical expressions and develop Monte Carlo simulations to quantitatively evaluate the difference between the Helmholtz and the Gibbs ensembles for a wide range of polymer models of biological relevance. We consider generalizations of the freely jointed chain and of the worm-like chain models with extensible bonds. In all cases we show that the convergence to the thermodynamic limit upon increasing contour length is described by a suitable power law and a specific scaling exponent, characteristic of each model.

Bulk viscosity of the Lennard-Jones system at the triple point by dynamical nonequilibrium molecular dynamics.

Nonequilibrium molecular dynamics (NEMD) calculations of the bulk viscosity of the triple point Lennard-Jones fluid are performed with the aim of investigating the origin of the observed disagreement between Green-Kubo estimates and previous NEMD data. We show that a careful application of the Doll's perturbation field, the dynamical NEMD method, the instantaneous form of the perturbation and the "subtraction technique" provides a NEMD estimate of the bulk viscosity at zero field in full agreement with the value obtained by the Green-Kubo formula. As previously reported for the shear viscosity, we find that the bulk viscosity exhibits a large linear regime with the field intensity.

Nonlinear elasticity of monolayer graphene.

By combining continuum elasticity theory and tight-binding atomistic simulations, we work out the constitutive nonlinear stress-strain relation for graphene stretching elasticity and we calculate all the corresponding nonlinear elastic moduli. Present results represent a robust picture on elastic behavior and provide the proper interpretation of recent experiments. In particular, we discuss the physical meaning of the effective nonlinear elastic modulus there introduced and we predict its value in good agreement with available data. Finally, a hyperelastic softening behavior is observed and discussed, so determining the failure properties of graphene.