Force-extension curves of bacterial flagella

Bacterial flagella assume different helical shapes during the tumbling phase of a bacterium but also in response to varying environmental conditions. Force-extension measurements by Darnton and Berg explicitly demonstrate a transformation from the coiled to the normal helical state (N.C. Darnton, H.C. Berg, Biophys. J. 92, 2230 (2007)). We here develop an elastic model for the flagellum based on Kirchhoff's theory of an elastic rod that describes such a polymorphic transformation and use resistive force theory to couple the flagellum to the aqueous environment. We present Brownian-dynamics simulations that quantitatively reproduce the force-extension curves and study how the ratio G \Gamma of torsional to bending rigidity and the extensional rate influence the response of the flagellum. An upper bound for G \Gamma is given. Using clamped flagella, we show in an adiabatic approximation that the mean extension, where a local coiled-to-normal transition occurs first, depends on the logarithm of the extensional rate.     

Force-extension curves for a single polymer chain under varying solvent conditions

We show that Langevin dynamics can be used to obtain force-extension curves for a single polymer chain under varying solvent conditions. We find that the chains obey Hooke-type and Pincus regime behavior for Theta and good solvents. However, in poor solvents a coil-strand coexistence is observed in the equilibrium state and this leads to a quite different type of deformation behavior.     

Superstructure-mechanical property relationships of polyglutamic acid esters

A study has been made of the relaxation phenomena in a series of poly-γ-n-alkyl-D-glutamates having linear side chains of different lengths in the temperature range from ?170 to 250°C. The solid-state films of poly-γ-n-alkyl-D-glutamate were cast from solutions in α-helix and random coil forming solvents. The technique of dynamic mechanical relaxation at various frequencies up to 110 Hz was used in the investigation. X-ray, IR, and density measurements were used as supplements to the mechanical measurements in order to determine the relationships between the mechanical properties and superstructures. Six relaxation regions are discernible in the temperature range investigated, and these are labeled α, β, γ, δ, ε, and ζ in order of decreasing temperature. The following mechanisms are assigned to these relaxations: (1) The α-relaxation arises from the thermal molecular motion of the α-helices in the crystalline region. (2) The β relaxation arises from micro-Brownian segmental motion of the disordered region or the distorted part of the a-helices, (3) The γ and δ relaxations are associated with motions of the entire side-chain groups in the crystalline and the disordered regions, respectively. (4) The ε and ζ relaxations involve the conformational rearrangements of n-alkyl groups including carboxyl group and n-alkyl groups alone, respectively.     

Force-extension behavior of folding polymers

The elastic response of flexible polymers made of elements which can be either folded or unfolded, having different lengths in these two states, is discussed. These situations are common for biopolymers as a result of folding interactions intrinsic to the monomers, or as a result of binding of other smaller molecules along the polymer length. Using simple flexible-chain models, we show that even when the energy ε associated with maintaining the folded state is comparable to k _B T, the elastic response of such a chain can mimic usual polymer linear elasticity, but with a force scale enhanced above that expected from the flexibility of the chain backbone. We discuss recent experiments on single-stranded DNA, chromatin fiber and double-stranded DNA with proteins weakly absorbed along its length which show this effect. Effects of polymer semiflexiblity and torsional stiffness relevant to experiments on proteins binding to dsDNA are analyzed. We finally discuss the competition between electrostatic self-repulsion and folding interactions responsible for the complex elastic response of single-stranded DNA. Received 7 August 2002 and Received in final form 7 March 2003 / Published online: 15 April 2003 RID="a" ID="a"e-mail: jmarko@uic.edu     

Force-extension relationship of cell-cell contacts

Adherens junctions (AJ) are adhesive motifs joining neighboring cells. The physical contacts are fingerlike structures which grow perpendicular to the cell-cell interface. While their length may vary with the applied force, their density is independent of length. Here we measure AJ contact lengths while varying the mean contractile force of the cell using nocodazole. Using this assay and a simple mechanical model, we measure an effective spring constant of about 30 pN/microm per finger. This measurement may enable the estimation of cell monolayer force distributions from a simple AJ image.     

Non-Hermitian quasicrystal in dimerized lattices

Non-Hermitian quasicrystals possess PT and metal–insulator transitions induced by gain and loss or nonreciprocal effects. In this work, we uncover the nature of localization transitions in a generalized Aubry–André–Harper model with dimerized hopping amplitudes and complex onsite potential. By investigating the spectrum, adjacent gap ratios and inverse participation ratios, we find an extended phase, a localized phase and a mobility edge phase, which are originated from the interplay between hopping dimerizations and non-Hermitian onsite potential. The lower and upper bounds of the mobility edge are further characterized by a pair of topological winding numbers, which undergo quantized jumps at the boundaries between different phases. Our discoveries thus unveil the richness of topological and transport phenomena in dimerized non-Hermitian quasicrystals.     

Force-extension curve of a polymer in a high-frequency electric field

We study theoretically the conformation and force-extension curve of a semiflexible polymer in a spatially uniform ac electric field. The polymer backbone minimizes its energy by aligning along one of two orientations parallel to the field. In a strong ac field, hairpin kinks develop between regions of opposite alignment. These kinks are mathematically described as sine-Gordon solitons. We calculate the equation of state of the one-dimensional kink gas, which yields the force-extension curve of the polymer. A sufficiently strong ac field causes the polymer to extend spontaneously to almost its full contour length. The theory is applied to recent experiments on dielectrophoretic stretching of DNA.     

Investigation of frustrated and dimerized classical Heisenberg chains

We have considered the 1D dimerized frustrated antiferromagnetic (ferromagnetic) Heisenberg model with arbitrary spin S$S$. The exact classical magnetic phase diagram at zero temperature is determined using the LK cluster method. The cluster method results show that the classical ground-state phase diagram of the model is very rich, including first-order and second-order phase transitions. In the absence of dimerization, a second-order phase transition occurs between antiferromagnetic (ferromagnetic) and spiral phases at the critical frustration _αc=±0.25${\alpha }_c=\pm 0.25$, a well-known result. In the vicinity of the critical points _αc${\alpha }_c$, the exact classical critical exponent of the spiral order parameter is found to be 1/2$1/2$. In the case of a dimerized chain (δ≠0$\delta \ne 0$), the spiral order shows stability and exists in some part of the ground-state phase diagram. We have found two first-order phase boundaries separating antiferromagnetic (uud and duu) phases from the spiral phase.     

Persistence of magnons in a site-diluted dimerized frustrated antiferromagnet

We present inelastic neutron scattering and thermodynamic measurements characterizing the magnetic excitations in a disordered spin-liquid antiferromagnet with non-magnetic substitution. The parent compound Ba(3)Mn(2)O(8) is a dimerized, quasi-two-dimensional geometrically frustrated quantum disordered antiferromagnet. We substitute this compound with non-magnetic V(5+) for the S=1 Mn(5+) ions, Ba(3)(Mn(1-x)V (x))(2)O(8), and find that the singlet-triplet excitations which dominate the spectrum of the parent compound persist for the full range of substitution examined, up to x=0.3. We also observe additional low-energy magnetic fluctuations which are enhanced at the greatest substitution values.     

On the theory of the magnetization of dimerized magnets

To describe a quantum phase transition in a dimerized antiferromagnet, the formalism of the Landau theory of phase transitions has been applied. The energy of the ground state is minimized by varying the parameter of the mixing of the wavefunctions with different multiplicities. The critical behavior of the parameter of the wavefunction is responsible for the critical behavior of the observables.     

Dielectric constant of a dimerized interrupted strand model

The static electronic polarizability has been calculated in a one-electron tight-binding approximation for dimerized linear chains of various lengths, L. When dimerization creates a Peierls gap that is comparable to or greater than the intrinsic level splitting, the electronic polarization is reduced and increases less rapidly with chain length than N², the result obtained for a non-dimerized chain. One can infer, therefore, that an organic material composed of strands of such chains will exhibit a dielectric constant that increases with sample perfection or with average chain length. The dielectric constant is also shown to increase significantly with temperature at temperatures well below the half gap at the Fermi level. This reflects the relatively large amount of polarization carried by the states in the vicinity of the Fermi level for the dimerized chain.     

The electronic structure of polymerized fullerenes and dimerized heterofullerenes

\chem{Rb_1C_{60}} and dimerised using electron energy-loss spectroscopy in transmission. From the excitation spectra a reduced density of states is observed for polymerized . This is in contrast to and can be explained by the different type of \squt{doping} and by the different bonding between the fullerene molecules in the two systems. Additional information about the optical properties was obtained from the low energy loss function. Using a Kramers-Kronig analysis, the dielectric function, (), and the optical conductivity, (), have been derived. and the onset of the spectral weight have been compared between the polymer, the dimer and . This onset of spectral weight is found to be at and for o- and for , respectively. Received: 28 October 1996/Accepted: 13 December 1996     

Antiferromagnetic spin-S chains with exactly dimerized ground states

We show that spin S Heisenberg spin chains with an additional three-body interaction of the form (S(i-1)·S(i))(S(i)·S(i+1))+H.c. possess fully dimerized ground states if the ratio of the three-body interaction to the bilinear one is equal to 1/[4S(S+1)-2]. This result generalizes the Majumdar-Ghosh point of the J1-J2 chain, to which the present model reduces for S=1/2. For S=1, we use the density matrix renormalization group method to show that the transition between the Haldane and the dimerized phases is continuous with a central charge c=3/2. Finally, we show that such a three-body interaction appears naturally in a strong-coupling expansion of the Hubbard model, and we discuss the consequences for the dimerization of actual antiferromagnetic chains.     

Spin-liquid versus dimerized ground states in a frustrated Heisenberg antiferromagnet

We present a density matrix renormalization group study of the ground-state properties of spin-1/2 frustrated J1-J3 Heisenberg n(l)-leg ladders (with n(l) up to 8). For strong frustration (J(3)/J(1) approximately 0.5), both even-leg and odd-leg ladders display a finite gap to spin excitations, which we argue remains finite in the two-dimensional limit. In this regime, on odd-leg ladders the ground state is spontaneously dimerized, in agreement with the Lieb-Schultz-Mattis prediction, while on even-leg ladders the dimer correlations decay exponentially. The magnitude of the dimer order parameter decreases as the number of legs increases, consistent with a two-dimensional spin-liquid ground state.     

A calorimetric study of the dimerized phase of C60 fullerene

The temperature dependence of the heat capacity at a constant pressure C _p ⁰ = f(T) for the dimerized phase of the C₆₀ fullerene in the temperature range 300–575 K and the thermodynamic characteristics for depolymerization of this phase under normal pressure are investigated using precision differential scanning calorimetry. It is established that thermal depolymerization is a kinetically hindered process. The final products of thermal depolymerization are identified as a partially crystalline monomer face-centered cubic phase of C₆₀ with a degree of crystallinity α = 67 mol %. The results obtained in this study and our previous experimental data on the low-temperature heat capacity are used in the calculations of standard thermodynamic functions for the (C₆₀)₂ crystalline dimer, namely, the heat capacity C _p ⁰ (T), the enthalpy H ⁰(T) ? H ⁰(0), the entropy S ⁰(T), and the Gibbs function G ⁰(T) ? H ⁰(0) in the temperature range from T → 0 to 394 K.     

Frustration and intermediate dimerized phase in spin ladder system

This paper studies a spin ladder model which possesses frustrating interactions.By using both the bosonization and the density matrix renormalization group techniques,it shows that the intermediate columnar dimerized phase,which exists in a narrow parameter region of the so-called J 1 J 2 model,vanishes if the interchain frustration is weak and anisotropic.Therefore,it concludes that the frustrating interaction indeed plays an important role in producing such a phase.As a complementary to our previous investigation,it reaches a more complete picture of the quantum phase transition in the frustrated spin ladder systems.