Large-amplitude Deformations Research Articles

Transient elasticity and polymeric fluids: Small-amplitude deformations.

Transient elasticity (TE) is a concept useful for a systematic generalization of viscoelasticity. Due to its thermodynamic consistency, it naturally leads to a simple description of non-Newtonian effects displayed by polymeric fluids, granular media, and other soft matter. We employ a continuum-mechanical theory that is derived from TE and tailored to polymeric fluids, showing how it captures a surprisingly large number of phenomena in shear and elongational flows, including stationary, oscillatory, and transient ones, as well as the flow down an inclined channel. Even the Weissenberg effect is well accounted for. This theory is applicable for small- as well as large-amplitude deformations. We concentrate on the former in the present article, leaving the latter to a companion article.

Mesh Moving Scheme Based on Solving the Laplace Equation with Jacobian Stiffening Technique

Mesh moving scheme is an important issue in many fluid-structure interaction problems. In this paper a new mesh motion technique is presented for the effective treatment of moving mesh. The entire deformation is imposed at each time step and the motion of the internal nodes is governed by a modified Laplace equation. Finite element method is adopted to solve the Laplace equation with elemental Jacobian-based stiffening technique. Nodal coordinates are updated by using the total nodal displacements and initial coordinates. The proposed scheme has been applied to several 2D and 3D test cases involving various mesh types with the mesh quality evaluated by an index called elemental aspect ratio. With these applications, it is demonstrated that the present method still preserves good mesh quality for long-term and large amplitude oscillations or deformations.

Autonomous Motility of Active Filaments due to Spontaneous Flow-Symmetry Breaking

We simulate the nonlocal Stokesian hydrodynamics of an elastic filament which is active due a permanent distribution of stresslets along its contour. A bending instability of an initially straight filament spontaneously breaks flow symmetry and leads to autonomous filament motion which, depending on conformational symmetry, can be translational or rotational. At high ratios of activity to elasticity, the linear instability develops into nonlinear fluctuating states with large amplitude deformations. The dynamics of these states can be qualitatively understood as a superposition of translational and rotational motion associated with filament conformational modes of opposite symmetry. Our results can be tested in molecular-motor filament mixtures, synthetic chains of autocatalytic particles, or other linearly connected systems where chemical energy is converted to mechanical energy in a fluid environment.

A generalised 17-state vibronic-coupling Hamiltonian model for ethylene

In a previous work [B. Lasorne, M. A. Robb, H.-D. Meyer, and F. Gatti, "The electronic excited states of ethylene with large-amplitude deformations: A dynamical symmetry group investigation," Chem. Phys. 377, 30-45 (2010); and ibid. 382, 132 (2011) (Erratum)], we investigated the electronic structure of ethylene (ethene, C(2)H(4)) in terms of 17 dominant configurations selected at the multiconfiguration self-consistent field level of theory. These were shown to be sufficient to recover most of the static electron correlation among the first valence and Rydberg states at all geometries. We also devised a strategy to build a 17-quasidiabatic-state matrix representation of the electronic Hamiltonian for curvilinear coordinates using dynamical symmetry. Here, we present fitted surfaces in the form of a generalised vibronic-coupling Hamiltonian model for two nuclear coordinates, CC bond stretching and torsion. Dynamic electron correlation is included into the electronic structure to improve the energetics of the Rydberg states at the multireference configuration interaction level of theory. The chemical interpretation of the adiabatic states of interest does not change qualitatively, which validates our choice of underlying quasidiabatic states in the model. The absorption spectrum is calculated with quantum dynamics and partially assigned. This first two-dimensional model shows a surprisingly good agreement with the experimental spectrum.

Cyclic deformation-induced injury and differentiation of rat alveolar epithelial type II cells

The injury and differentiation of alveolar epithelial type II cells induced by alveolar epithelial deformation play important roles in the pathophysiology of ventilator-induced lung injury and repair of the lung injury, respectively. We developed an in vitro rat model to investigate the effects of deformation amplitude, peak deformation, and minimum deformation on the viability and differentiation of type II cells. Rat primary alveolar epithelial type II cells were exposed to a variety of equibiaxial cyclic stretch protocols, and deformation-induced cell survival and differentiation were analyzed. Cell death increased when deformation consisted of change in cell surface area (ΔSA) of 0-37%, 0-50%, 12-50%, 37-50% (P=0.001, P<0.001, P<0.001, and P=0.003, respectively). When ΔSA was at 12-37% and 12-50%, mRNA transcription (P=0.034 and P=0.036) and protein expressions (P=0.008 and P=0.001) of caveolin-1 (a marker for the type I phenotype) increased, in contrast to the decrease of their mRNA transcription of surfactant protein C (a marker for the type II phenotype) (P=0.011, 0.002). These results suggest that amplitude or minimum deformation ≥ 37% ΔSA is an important cause of cell death, and amplitude ≥ 25% ΔSA promotes cell differentiation. Appropriate amplitude (25% ΔSA) can not only avoid cell death but also promote cell differentiation.

Accounting for Large Amplitude Protein Deformation during in Silico Macromolecular Docking

Rapid progress of theoretical methods and computer calculation resources has turned in silico methods into a conceivable tool to predict the 3D structure of macromolecular assemblages, starting from the structure of their separate elements. Still, some classes of complexes represent a real challenge for macromolecular docking methods. In these complexes, protein parts like loops or domains undergo large amplitude deformations upon association, thus remodeling the surface accessible to the partner protein or DNA. We discuss the problems linked with managing such rearrangements in docking methods and we review strategies that are presently being explored, as well as their limitations and success.

Thermodynamic Methods and Models to Study Flexible Metal–Organic Frameworks

Much attention has recently been focused on a fascinating subclass of metal-organic frameworks that behave in a remarkable stimuli-responsive fashion. These soft porous crystals feature dynamic crystalline frameworks displaying reversible, large-amplitude structural deformations under external physical constraints such as temperature, electric field or gas exposure. The number of reported syntheses of such materials is rapidly growing and they are promising for practical applications, such as gas capture, purification and fluid separation. Herein, we summarize the recently developed thermodynamic tools that can help understand the process of fluid adsorption and fluid mixture coadsorption in these flexible nanoporous materials. These tools, which include both molecular simulation methods and analytical models, can help rationalize experimental results and predict adsorption properties over a wide range of thermodynamic conditions. A particular focus is given on how these methods can guide the experimental exploration of a large number of materials and working conditions (temperature, pressure, composition) to help design efficient processes relying on fluid adsorption in soft porous crystals.

The electronic excited states of ethylene with large-amplitude deformations: A dynamical symmetry group investigation

We show that the lowest manifold of electronic states of ethylene (ethene, C 2H 4) can be described correctly with a complete active space of 17 quasidiabatic configurations built on state-averaged orbitals. This space is stable upon large-amplitude deformations, such as torsion, pyramidalization, CC stretching and HCH bending. The properties of the nuclear coordinates and valence and Rydberg electronic states are investigated within the framework of nuclear-permutation-inversion group theory. This systematic analysis is compared to a previous model of the valence states of ethylene (R.P. Krawczyk, A. Viel, U. Manthe, W. Domcke, J. Chem. Phys. 119 (2003) 1397). Our approach is intended to be generalized to the non-adiabatic photochemistry of organic molecules where large-amplitude deformations require global vibronic Hamiltonian models to be expressed in terms of simple functions of polyspherical valence coordinates.

Two-Level Approach to Efficient Visualization of Protein Dynamics

Proteins are highly flexible and large amplitude deformations of their structure, also called slow dynamics, are often decisive to their function. We present a two-level rendering approach that enables visualization of slow dynamics of large protein assemblies. Our approach is aligned with a hierarchical model of large scale molecules. Instead of constantly updating positions of large amounts of atoms, we update the position and rotation of residues, i.e., higher level building blocks of a protein. Residues are represented by one vertex only indicating its position and additional information defining the rotation. The atoms in the residues are generated on-the-fly on the GPU, exploiting the new graphics hardware geometry shader capabilities. Moreover, we represent the atoms by billboards instead of tessellated spheres. Our representation is then significantly faster and pixel precise. We demonstrate the usefulness of our new approach in the context of our collaborative bioinformatics project.

Liquid jet response to internal modulated ultrasonic radiation pressure and stimulated drop production

Experimental evidence shows that a liquid jet in air is an acoustic waveguide having a cutoff frequency inversely proportional to the jet diameter. Ultrasound applied to the jet supply liquid can propagate within the jet when the acoustic frequency is near to or above the cutoff frequency. Modulated radiation pressure is used to stimulate large amplitude deformations and the breakup of the jet into drops. The jet response to the modulated internal ultrasonic radiation pressure was monitored along the jet using (a) an optical extinction method and (b) images captured by a video camera. The jet profile oscillates at the frequency of the radiation pressure modulation and where the response is small, the amplitude was found to increase in proportion to the square of the acoustic pressure amplitude as previously demonstrated for oscillating drops [P.L. Marston and R.E. Apfel, J. Acoust. Soc. Am. 67, 27-37 (1980)]. Small amplitude deformations initially grow approximately exponentially with axial distance along the jet. Though aspects of the perturbation growth can be approximated from Rayleigh's analysis of the capillary instability, some detailed features of the observed jet response to modulated ultrasound are unexplained neglecting the effects of gravity.

Light-induced deformation and instability of a liquid interface. II. Dynamics

We study the dynamics of the deformation of a soft liquid-liquid interface by the optical radiation pressure of a focused cw Gaussian laser beam. We measured the temporal evolution of both the hump height and the hump curvature by direct observation and by detecting the focusing effect of the hump acting as a lens. Extending the results of Yoshitake [J. Appl. Phys. 97, 024901 (2005)] to the case of liquid-liquid interfaces and to the Bo approximately =1 regime [Bo=(omega0/lc)2, , where omega0 is the beam waist and lc the capillary length], we show that, in the Bo<<1 and Bo approximately =1 ranges, the small-amplitude deformations are correctly described by a linear hydrodynamic theory predicting an overdamped dynamics. We also study the dynamics of the large-amplitude interface deformations at the onset of optohydrodynamic instability [Phys. Rev. Lett. 90, 144503 (2003)]. Using a simple, phenomenological model for the nonlinear evolution of the hump height, we interpret the observed interface dynamics at the instability onset as the signature of an imperfect subcritical instability.

Macromolecular Assemblies Highlighted

The functional units in cells are often assemblies of macromolecules, including proteins and nucleic acids. Therefore, the knowledge of structure, dynamics, and energetics of macromolecular complexes is necessary for a mechanistic description of biochemical and cellular processes. This special issue of Structure , "Macromolecular Assemblies Highlighted," presents ten research articles and five reviews on the determination, representation, visualization, archival, and dissemination of assembly structure and dynamics.

Shear Instability of a Gyroid Diblock Copolymer

The stability of the gyroid phase of diblock copolymers has been studied using combined oscillatory shear and small-angle neutron scattering (SANS) techniques. It is shown that the gyroid phase of polystyrene-polyisoprene (PS-PI) is unstable when exposed to combined large-amplitude and highfrequency shear deformations. The bicontinuous cubic gyroid structure (G) transforms to the hexagonally cylinder phase (HEX). The transition is perfectly reversible, but with a significant difference in time constants. Upon application of shear the G → HEX transition is instantaneous within experimental resolution, while the HEX → G relaxation after cessation of shear takes hours. The texture of the shear-induced cylinder phase is shown to be a near ideal monodomain, while the relaxed gyroid phase constitutes a two-dimensional powder with the characteristic 10-spot scattering pattern. The shear-induced destabilization is discussed in relation to analogous observations on shear-induced order-to-order and disorder-to-order transitions observed in related block copolymer systems and in microemulsions. It is discussed whether these phenomena originate in shear-reduced fluctuations or shear-induced dislocations.

Optical detection of the response of liquid jets to internal modulated ultrasonic radiation pressure

A liquid jet in air is an acoustic waveguide having a cutoff frequency inversely proportional to the jet diameter. Ultrasound applied to the jet supply liquid can propagate down the jet when the carrier frequency is near-to or above the cutoff frequency. The jet response to the internal acoustic radiation pressure of amplitude modulated ultrasound was monitored along the jet using an optical pseudo-extinction method. The jet profile oscillates at the frequency of the radiation pressure modulation and, where the response is small, the amplitude was found to increase in proportion to the square of the acoustic pressure amplitude as previously demonstrated for oscillating drops [P. L. Marston and R. E. Apfel, J. Acoust. Soc. Am. 67, 27–37 (1980)]. Small amplitude deformations initially grow approximately exponentially with axial distance along the jet. Modulated radiation pressure can be used to stimulate large amplitude deformations and the breakup of the jet into drops. [Work supported by NASA.]

Geometry of the DNA strands within the RecA nucleofilament: role in homologous recombination.

Homologous recombination consists of exchanging DNA strands of identical or almost identical sequence. This process is important for both DNA repair and DNA segregation. In prokaryotes, it involves the formation of long helical filaments of the RecA protein on DNA. These filaments incorporate double-stranded DNA from the cell's genetic material, recognize sequence homology and promote strand exchange between the two DNA segments. DNA processing by these nucleofilaments is characterized by large amplitude deformations of the double helix, which is stretched by 50% and unwound by 40% with respect to B-DNA. In this article, information concerning the structure and interactions of the RecA, DNA and ATP molecules involved in DNA strand exchange is gathered and analyzed to present a view of their possible arrangement within the filament, their behavior during strand exchange and during ATP hydrolysis, the mechanism of RecA-promoted DNA deformation and the role of DNA deformation in the process of homologous recombination. In particular, the unusual characteristics of DNA within the RecA filament are compared to the DNA deformations locally induced by architectural proteins which bind in the DNA minor groove. The possible role and location of two flexible loops of RecA are discussed.

Ab initio investigation of the potential energy surfaces involved in the photophysics of s- trans-1,3-butadiene

The potential energy surfaces of the 1 1 A g , 2 1 A g , and 1 1 B u electronic states of trans-butadiene have been investigated with the complete-active-space self-consistent-field (CASSCF) method as well as second-order perturbation theory based on the CASSCF reference (CASPT2). Symmetry-adapted valence internal coordinates are employed to describe large-amplitude deformations from the ground-state equilibrium geometry. Both in-plane and out-of-plane deformations have systematically been explored. Four coordinates are identified as particularly effective in inducing a crossing of the 1 1 B u and 2 1 A g surfaces: two totally symmetric coordinates (symmetric C–C double-bond stretching and symmetric C–C–C bending) as well as the conrotatory and disrotatory torsions of the terminal CH 2 groups. A single coordinate of b u symmetry is found to be active as 1 1 B u – 2 1 A g coupling mode. On the basis of these ab initio results, a simple five-mode vibronic coupling model of the 1 1 B u – 2 1 A g conical intersection is proposed.

Deformation-induced injury of alveolar epithelial cells. Effect of frequency, duration, and amplitude.

The onset of ventilator-induced lung injury (VILI) is linked to a number of possible mechanisms. To isolate the possible role of alveolar epithelial deformation in the development of VILI, we have developed an in vitro system in which changes in alveolar epithelial cell viability can be measured after exposure to tightly controlled and physiologically relevant deformations. We report here a study of the relative effect of deformation frequency, duration, and amplitude on cell viability. We exposed rat primary alveolar epithelial cells to a variety of biaxial stretch protocols, and assessed deformation-induced cell injury quantitatively, using a fluorescent cell viability assay. Deformation-induced injury was found to depend on repetitive stretching, with cyclic deformations significantly more damaging than tonically held deformations. In cyclically deformed cells, injury occurred rapidly, with the majority of cell death occurring during the first 5 min of deformation. Deformation-induced injury was increased with the frequency of sustained cyclic deformations, but was not dependent on the deformation rate during a single stretch. Reducing the amplitude of cell deformations by superimposing small cyclic deformations on a tonic deformation significantly reduced cell death as compared with large-amplitude deformations with the same peak deformation.

Mathematical models of compaction, consolidation and regional groundwater flow

A 3-D theory of groundwater flow and consolidation that allows for compressibility of the soil or sediment matrix is that due to Biot (1941). However, this theory is inapplicable to virgin consolidation tests, where the deformation of the soil along the critical state surface is accomplished by elastic–plastic flow. In fact, Biot's model cannot even be applied to overconsolidated soils where the deformation is elastic, as it does not conserve the mass of the solid. In this paper, we provide a modified version of the model, and show how it can be extended to allow for elastic–plastic deformation and large-amplitude deformations in elastic–plastic compaction. A particular example of the potential application of this theory is to the groundwater flow induced by the compaction of sediments by an overriding ice sheet, and we show how the commonly used Dupuit approximation can be employed to simplify the theory.

Thermodynamic and structural properties of r(ACC) as revealed by ultraviolet electronic absorption, circular dichroism, 1H-NMR spectroscopy and Monte Carlo simulations.

UV absorption, circular dichroism (CD) and 1H NMR, associated with Monte Carlo (MC) molecular structure simulations have been applied to the study of the trinucleoside diphosphate: r(ACC). The MC study which has been conducted as a function of temperature, is based on random variations of the nucleotide conformational angles, i.e. phosphodiester chain torsional angles and sugar pucker pseudorotational angles. All of the chemical bond lengths and valence angles remained fixed during the structural simulation, except those of the sugar pucker. Six different initial structures have been selected in order to explore the molecular conformational space as completely as possible. This simulation procedure led to distinct families of equilibrium conformations at 283, 298 and 318 K. The thermodynamical parameters such as variations in entropy, enthalpy and also melting temperature (delta SX0, delta HX0 and Tm) of the stacking (X) equilibrium were obtained from UV absorption and circular dichroism (CD) spectra recorded over a 80K temperature range. Chemical shifts (delta), vicinal coupling constants (3Jk,l), and cross-relaxation rate (sigma k,l) of trimers were measured at 400.13 MHz over a range of concentrations (2-13 mM) and temperatures (283-333K). Least-squares fitting of the experimental chemical shifts to simple models of association (A) and stacking equilibria allowed separation of the variations in the delta values (delta delta X and delta delta A) due to either phenomenon. The three NMR data sets (delta delta X, 3Jk,l, and sigma k,l) were then evaluated for the minima conformers obtained with the MC stimulations. Theoretical values of delta delta X were estimated using the results of an ab initio study while the coupling constant data were simulated with Karplus-type equations. Finally, the relaxation data were simulated from the distance matrices using treatment for cases of both slow conformational exchange accompanied by rapid small-amplitude fluctuations about the minima structures. A consistent picture of the large amplitude deformations (torsional angle variation) of these trimers has emerged from the present study. Optimized conformational blends at 283,296 and 318K were obtained by least-squares fitting of the experimental data to the theoretical ones, while considering the populations as adjustable parameters. As it would be expected, the right-handed helical conformation (A-RNA type) is found to be the major stacked species, in the temperature range of 283 to 318K. Limited evidence for bulged structures has been obtained, whereas novel reverse-stacked and half-stacked conformers also presented theoretical data compatible with the NMR observables of aqueous r(ACC).

A weak-mode representation of floppy molecules

Abstract The eigenstates of a model floppy molecule (i.e. a molecule for which large-amplitude isomerization-like deformations are possible) are variationally calculated. The Hamiltonian operator and the Hamiltonian matrix are established in following the adiabatic weak-mode approach that has been recently proposed. The model consists of a triatomic molecule with two linear isomers, roughly connected with HCN ⇌ CNH: the atomic masses are the appropriate ones, but the isomerization reaction profile does not present the shoulder that is typical of CNH, and the model potential energy surface is a simplified version of the one by Murrell et al. Indeed, the actual high-energy vibrational level distribution of both HCN and CNH turns out to be particularly complicated because of this shoulder and, in order to test new theoretical arguments for analyzing the vibrational eigenstates, using a model with no shoulder is simpler. For zero total angular momentum, the eigenvalues converge up to 20000 cm−1. An adiabatic model, based on the separation of hard (radial) and soft (angular) Jacobi coordinates, is used. The adiabatic representation (in which the analytical radial basis functions parametrically depend on the angle) is interesting from the physical viewpoint: it allows discriminating between various types of eigenstates, depending on (i) the angular distribution of the amplitude and (ii) the value of the projection of the state over the subspace corresponding to a given couple of adiabatic stretching quantum numbers. Many spectroscopic states (both energetically low- and high-lying) are localizated on one isomer side. Several other states are quantally delocalized on both sides, i.e. are linear combinations (interference pattern) of two or more contributions (at least one for each isomer), separated from each other by an angular range where the eigenfunction is very small. We call these states “composite”. Finally, high-lying states (for energies equal to or higher than well identified adiabatic isomerization barriers) are intrinsically delocalized, i.e. with noticeable amplitude almost everywhere. They are very well described within the framework of the adiabatic approach: large-amplitude bending motion of the light atom around the strongly bound diatomic core takes place. Only these states we term “floppy”. The adiabatic weak-mode description allows obtaining quasi-automatically a spectroscopic assignment (as far as it is meaningful) of the molecular states, by means of adiabatic quantum numbers, consistently from the low-lying levels (where the adiabatic quantum numbers are equivalent to standard normal-mode quantum numbers) up to the floppy states, for which normal-mode quantum numbers would be meaningless. The adiabatic quantum numbers appropriately indicate what part of the dynamics can be described as quasi-regular in the molecular states (basically the adiabatic stretching vibrations, and, in localized and floppy states, also the bending motion) and what other part (if any) can be deeply perturbed.