CiteULike: norris Sinha

Elasticity of Stiff Biopolymers

Abhijit Ghosh — 2007-11-25T22:48:28-00:00

(8 Oct 2007)

We present a statistical mechanical study of stiff polymers, motivated by experiments on actin filaments and the considerable current interest in polymer networks. We obtain simple, approximate analytical forms for the force-extension relations and compare these with numerical treatments. We note the important role of boundary conditions in determining force-extension relations. The theoretical predictions presented here can be tested against single molecule experiments on neurofilaments and cytoskeletal filaments like actin and microtubules. Our work is motivated by the buckling of the cytoskeleton of a cell under compression, a phenomenon of interest to biology.

Inequivalence of statistical ensembles in single molecule measurements

Supurna Sinha — 2007-11-25T22:45:25-00:00

Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), Vol. 71, No. 2. (2005)

We study the role of fluctuations in single molecule experimental measurements of force-extension (f-) curves. We use the wormlike chain (WLC) model to bring out the connection between the Helmholtz ensemble characterized by the free energy [F()] and the Gibbs ensemble characterized by the free energy [G(f)]. We consider the rigid rod limit of the WLC model as an instructive special case to bring out the issue of ensemble inequivalence. We point out the need for taking into account the free energy of transition when one goes from one ensemble to another. We also comment on the "phase transition" noticed in an isometric setup for semiflexible polymers and propose a realization of its thermodynamic limit. We present general arguments which rule out nonmonotonic force-extension curves in some ensembles and note that these do not apply to the isometric ensemble.

Molecular elasticity and the geometric phase.

J Samuel — 2007-09-13T12:51:25-00:00

Phys Rev Lett, Vol. 90, No. 9. (7 March 2003)

We present a method for solving the wormlike-chain (WLC) model for twisting semiflexible polymers to any desired accuracy. We show that the WLC free energy is a periodic function of the applied twist with period 4pi. We develop an analogy between WLC elasticity and the geometric phase of a spin-1 / 2 system. These analogies are used to predict elastic properties of twist-storing polymers. We graphically display the elastic response of a single molecule to an applied torque. This study is relevant to mechanical properties of biopolymers such as DNA.

Molecular Elasticity and the Geometric Phase

Joseph Samuel — 2007-09-12T19:01:41-00:00

Physical Review Letters, Vol. 90, No. 9. (6 March 2003), 098305.

We present a method for solving the wormlike-chain (WLC) model for twisting semiflexible polymers to any desired accuracy. We show that the WLC free energy is a periodic function of the applied twist with period 4π. We develop an analogy between WLC elasticity and the geometric phase of a spin-1 / 2 system. These analogies are used to predict elastic properties of twist-storing polymers. We graphically display the elastic response of a single molecule to an applied torque. This study is relevant to mechanical properties of biopolymers such as DNA.

Elasticity of semiflexible polymers

Joseph Samuel — 2006-08-09T13:52:28-00:00

Physical Review E, Vol. 66, No. 5. (21 November 2002), 050801.

We present a method for solving the wormlike chain model for semiflexible polymers to any desired accuracy over the entire range of polymer lengths . Our results are in excellent agreement with recent computer simulations and reproduce important qualitatively interesting features observed in simulations of polymers of intermediate lengths. We also make a number of predictions that can be tested in a variety of concrete experimental realizations. The expected level of finite size fluctuations in force-extension curves is also estimated. This study is relevant to mechanical properties of biological molecules.

A 3D cylindrical PML/FDTD method for elastic waves in fluid-filled pressurized boreholes in triaxially stressed formations

Qing Liu — 2006-12-05T16:39:52-00:00

Geophysics, Vol. 68, No. 5. (2003), pp. 1731-1743.

A new 3D cylindrical perfectly matched layer (PML) formulation is developed for elastic wave propagation in a pressurized borehole surrounded by a triaxially stressed solid formation. The linear elastic formation is altered by overburden and tectonic stresses that cause significant changes in the wave propagation characteristics in a borehole. The 3D cylindrical problem with both radial and azimuthal heterogeneities is suitable for numerical solutions of the wave equations by finite-difference time-domain (FDTD) and pseudospectral time-domain (PSTD) methods. Compared to the previous 2.5D formulation with other absorbing boundary conditions, this 3D cylindrical PML formulation allows modeling of a borehole-conformal, full 3D description of borehole elastic waves in a stress-induced heterogeneous formation. We have developed an FDTD method using this PML as an absorbing boundary condition. In addition to the ability to solve full 3D problems, this method is found to be advantageous over the previously reported 2.5D finite-difference formulation because a borehole can now be adequately simulated with fewer grid points. Results from the new FDTD technique confirm the principle of superposition of the influence of various stress components on both the borehole monopole and dipole dispersions. In addition, we confirm that the increase in shear-wave velocity caused by a uniaxial stress applied in the propagation direction is the same as that applied parallel to the radial polarization direction.