München, Techn. Univ., Diss., 2004. / Computerdatei im Fernzugriff.

München, Techn. University, Diss., 2004.

Freiburg (Breisgau), Universiẗat, Diss., 2001. / Erscheinungsjahr an der Haupttitelstelle: 2001.

Halle, University, Diss., 1999.

Hamburg, Universiẗat, Diss., 2001.

We review the current state on the thermodynamic behavior and structural phases of self- and mutually-attractive dilute semiflexible polymers that undergo temperature-driven transitions. In extreme dilution, polymers may be considered isolated, and this single polymer undergoes a collapse or folding transition depending on the internal structure. This may go as far as to stable knot phases. Adding polymers results in aggregation, where structural motifs again depend on the internal structure. We discuss in detail the effect of semiflexibility on the collapse and aggregation transition and provide perspectives for interesting future investigations.

This thesis contains several contributions to the theoretical description and interpretation of biophysical single-molecule measurements: (i) For semiflexible polymers, we derive an efficient formulation of their local transverse dynamics in terms of a Generalized Langevin Equation. The elastic and frictional properties of the polymer are condensed into a memory kernel that is a function of the polymer\'s length and stiffness, the level of backbone tension, the position of the force probe along the polymer backbone and the boundary conditions at the polymer ends. At short times, the memory kernel attains a universal limiting form that depends neither on the polymer length nor on the boundary conditions; we obtain analytical results that accurately describe this regime. We discuss how to quickly and reliably evaluate the memory kernel for arbitrary times using a spectral decomposition method, and use an extensive body of numerical data to obtain analytical approximations to the memory kernel that cover the complementary long-time limit wherein polymer friction can be subsumed under a renormalized drag coefficient. (ii) Based on a systematic nonequilibrium treatment of an overdamped, one-dimensional stochastic escape process driven by external force, we develop a theory of Dynamic Force Spectroscopy (DFS) that generalizes previously available DFS theories to the high loading rates realized in novel experimental assays and in computer simulations. (iii) Extrapolating to future DFS experiments that may operate at far higher time resolution than presently achievable, we discuss the fast nonequilibrium relaxation of a semiflexible linker after bond rupture. Based on a rigorous theory of tension propagation in semiflexible polymers, we predict the relaxation of force within the force actuator, show that this relaxation is dominated by linker contraction, and demonstrate quantitative agreement of our predictions with experimental data obtained by a collaborating experimentalist group.

This work is a numerical examination of a semiflexible polymer exposed to a disorder landscape consisting of hard disks. For a small parameter range and simple constraints it is known that disorder leads to structural transitions of the equilibrium properties of polymers. The scope of this work strongly extends this range by going to both high disorder densities and large stiffnesses of the polymers. The competing length scales of polymer stiffness and average distance between the obstacles of the potential along with the way of assembling the disorder lead to a wide range of effects such as crumpling and stretching of polymer configurations due to the disorder or a modulation of the polymer’s characterizing observables with the correlation function of the potential. The high accuracy results presented in this work have been obtained by means of sophisticated Monte Carlo simulations. The refinement of a rarely applied but highly promising method to a state of the art algorithm in connection with latest numerical techniques made it possible to investigate the impact of hard-disk disorder on semiflexible polymer conformations on a broad scale.

I use an integrated approach of experiments, theory, and numerical evaluations to show that stiffening and softening/fluidization are natural consequences of the assumption that the cytoskeleton is mechanically essentially equivalent to a transiently crosslinked biopolymer network. I perform experiments on in vitro reconstituted actin/HMM networks and show that already these simple, inanimate systems display fludization and shake-down, but at the same time stress stiffening. Based on the well-established Wlc theory, I then develop a semi-phenomenological mean-field model of a transiently crosslinked biopolymer network, which I call the inelastic glassy wormlike chain (inelastic Gwlc). At the heart of the model is the nonlinear interplay between viscoelastic single-polymer stiffening and inelastic softening by bond breaking. The model predictions are in good agreement with the actin/HMM experiments. Despite of its simplicity, the inelastic Gwlc model displays a rich phenomenology. It reproduces the hallmarks of the mechanics of adherent cells such as power-law rheology, stress and strain stiffening, kinematic hardening, shake-down, fludization, and recovery. The model also may also be able to provide considerable theoretical insights into the underlying physics. For example, using the inelastic Gwlc model, I am able to resolve the apparent paradox between cell softening and stiffening in terms of a parameter-dependent competition of antagonistic nonlinear microscopic mechanisms. I further shed light on the mechanism responsible for fluidization. I identify pertinent parameters characterizing the microstructure and give criteria for the relevance of various effects, including the effect of catch-bonds on the network response. Finally, a way to incorporate irreversible plastic flow is proposed.

I use an integrated approach of experiments, theory, and numerical evaluations to show that stiffening and softening/fluidization are natural consequences of the assumption that the cytoskeleton is mechanically essentially equivalent to a transiently crosslinked biopolymer network. I perform experiments on in vitro reconstituted actin/HMM networks and show that already these simple, inanimate systems display fludization and shake-down, but at the same time stress stiffening. Based on the well-established Wlc theory, I then develop a semi-phenomenological mean-field model of a transiently crosslinked biopolymer network, which I call the inelastic glassy wormlike chain (inelastic Gwlc). At the heart of the model is the nonlinear interplay between viscoelastic single-polymer stiffening and inelastic softening by bond breaking. The model predictions are in good agreement with the actin/HMM experiments. Despite of its simplicity, the inelastic Gwlc model displays a rich phenomenology. It reproduces the hallmarks of the mechanics of adherent cells such as power-law rheology, stress and strain stiffening, kinematic hardening, shake-down, fludization, and recovery. The model also may also be able to provide considerable theoretical insights into the underlying physics. For example, using the inelastic Gwlc model, I am able to resolve the apparent paradox between cell softening and stiffening in terms of a parameter-dependent competition of antagonistic nonlinear microscopic mechanisms. I further shed light on the mechanism responsible for fluidization. I identify pertinent parameters characterizing the microstructure and give criteria for the relevance of various effects, including the effect of catch-bonds on the network response. Finally, a way to incorporate irreversible plastic flow is proposed.