A semiflexible polymer confined to a spherical surface is used as a basic model for understanding DNA conformation in restricted space. By means of Monte Carlo simulation for a bead-rod chain generated on a spherical surface, we find an ordered helicoidal phase at sufficiently high surface density and determine the critical density of the isotropic-helicoidal phase transition for various persistence lengths. We verify that the excluded volume effect is the key factor to cause the helicoidal state. In addition to Monte Carlo simulations, we utilize the model of wormlike chain with Onsager's excluded volume interaction and examine the Landau expansion of the free energy involving both the orientational and spatial order parameters. We also analytically figure out the critical density and transition gap for various ratios of persistence lengths of the polymer chain and the radius of spherical surface. The results from both simulation and analysis are consistent with each other.

A semiflexible polymer confined to a spherical surface is used as a basic model for understanding DNA conformation in restricted space. By means of Monte Carlo simulation for a bead-rod chain generated on a spherical surface, we find an ordered helicoidal phase at sufficiently high surface density and determine the critical density of the isotropic-helicoidal phase transition for various persistence lengths. We verify that the excluded volume effect is the key factor to cause the helicoidal state. In addition to Monte Carlo simulations, we utilize the model of wormlike chain with Onsager's excluded volume interaction and examine the Landau expansion of the free energy involving both the orientational and spatial order parameters. We also analytically figure out the critical density and transition gap for various ratios of persistence lengths of the polymer chain and the radius of spherical surface. The results from both simulation and analysis are consistent with each other.

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.

In der vorliegenden Arbeit wird die Mechanik von Netzwerken semiflexibler Polymere behandelt. Insbesondere wird der Zusammenhang zwischen der Steifigkeit des Einzelfilaments und der Steifigkeit des Gesamtnetzwerks experimentell untersucht. Der Hintergrund aktueller, einschlägiger theoretische Modelle wird zusammengefasst. Die Möglichkeiten und Limitierungen bisheriger experimenteller Modellsysteme werden diskutiert. Zur Untersuchung des eingangs genannten Zusammenhangs wird ein neuartiges, vielfältiges Modellsystem für semiflexible Polymere auf Basis von DNA Röhren eingeführt und umfassend auf Einzelfilament- und Netzwerkebene charakterisiert. Die Steifigkeit des Netzwerks lässt sich damit und unter Einsatz von Quervernetzern über einen weiten Bereich einstellen. Es zeigt sich, dass bisherige einschlägige Modelle in der korrekten Vorhersage des o.g. Zusammenhangs scheitern. Mögliche Auswege in der Modellierung werden skizziert, sowie konkrete, weitere Anwendungen der DNA Röhren benannt.:Chapter 1 Introduction Chapter 2 Background Section 2.1 Theoretical Models Section 2.2 Rheology Section 2.3 Experimental Model Systems Section 2.4 Existing G_0(l_p) Studies Chapter 3 Materials & Methods Section 3.1 Microscopy Section 3.2 Atomic Force Microscopy Section 3.3 Shear Rheology Section 3.4 Actin Section 3.5 DNA Assembly Section 3.6 Statistical Analysis Tools Chapter 4 Results Section 4.1 Persistence Length of Individual Filaments Section 4.2 Entangled Networks Section 4.3 Reptation Section 4.4 Inextensibility Section 4.5 Cross-Linked DNA n-Helix Tubes Chapter 5 Discussion Section 5.1 Limitations of Established Semiflexible Model Systems Section 5.2 DNA $n$-Helix Tubes as a Tunable Model System Section 5.3 Validation as an Entangled Semiflexible Model System Section 5.4 Impact on Existing Theories Section 5.5 DNA n-Helix Tubes as a Tunable Material Section 5.6 Summary Section 5.7 Outlook Chapter A Further Calculations Section A.1 Detailed Calculations on Worm-Like Chains. Chapter B Protocols Section B.1 Actin Section B.2 DNA n-Helix Tubes Chapter Bibliography Chapter List of Own Publications Chapter Acknowledgments Chapter Zusammenfassung nach §11(4) Promotionsordnung

Semiflexible Polymere erfüllen als Hauptbausteine intrazellulärer Gerüste und extrazellulärer Matrizen eine zentrale Rolle in biologischen Systemen. In der vorgelegten Arbeit wird der Einfluss kollektiver Effekte auf die physikalischen Eigenschaften semiflexibler Polymerstrukturen untersucht. Mikrorheologische Messungen sowohl an verwickelten als auch an quervernetzten Aktinfilamentnetzweken enthüllen, dass Aktingele drastisch durch die Belichtung fluoreszierender Kügelchen mit der entsprechenden Anregungswellenlänge erweicht werden. Dies beeinflusst die Resultate bei der Untersuchung von Aktinnetzwerken mit Mikrorheologie und kann zu großen Unterschieden zwischen mikro- und makrorheologischen Messungen führen. Messungen an mehrfaserigen Aktinbündlen mit Hilfe optischer Pinzetten enthüllen kontraktile Kräfte mit einem harmonischen Potential beim Auseinanderziehen und Kontrahieren der Bündel. Die beobachteten Dynamiken werden durch ein analytisches Modell als emergentes, kollektives Phänomen erklärt welches durch additive, paarweise Interaktionen der Filamente im Bündel verursacht wird. Auf der Netzwerkebene wird gezeigt, dass Kompositnetzwerke aus rekonstituierten Aktin- und Vimentinproteinen als Superposition zweier nichtinteragierender Gerüste beschrieben werden können. Hierbei entstehende Effekte werden durch die Verbindung von Einzelfilamentdynamiken mit makrorheologischen Netzwerkeigenschaften dargestellt und innerhalb eines inelasitschen Glassy Wormlike Chain Modells erfasst. Dies bereitet den Weg um die mechanischen Eigenschaften des Zytoskeletts auf der Basis der Eigenschaften der Einzelkomponenten vorherzusagen. Weitere Untersuchungen an Netzwerken bestehend aus Aktinfilamenten, Intermediärfilamenten und synthetischen DNS Nanoröhren zeigen, dass Mengeneigenschaften durch diverse Interfilamentinterkationen beeinflusst werden. Es wird vorgeschlagen, dass diese Interaktionen in einen einzelnen Parameter im Rahmen des Glassy Wormlike Chain Modells zusammengefasst werden können. Die Interpretation dieses Parameters als polymerspezifische 'Stickiness' ist sowohl für makrorheologische Beobachtungen als auch im Reptationsverhalten konsistent. Diese Erkenntnisse zeigen, dass Stickiness im Allgemeinen nicht in semiflexiblen Polymermodellen ignoriert werden sollte. / Semiflexible polymers play a central role in biological systems as major building blocks of intracellular scaffolds and extracellular matrices. The presented thesis investigates the influence of collective effects on the physical properties of semiflexible polymer structures. Microrheological measurements on both entangled and cross-linked actin filament networks reveal that illumination of fluorescent beads with their appropriate excitation wavelength leads to a drastic softening of actin gels. This impairs results when studying the microrheology of actin networks and can cause large discrepancies between micro and macro-rheological measurements. Optical tweezers measurements on multifilament actin bundles reveal contractile forces with a harmonic potential upon bundle extension and contraction. The observed dynamics are explained as an emergent, collective phenomenon stemming from the additive, pairwise interactions of filaments within a bundle through an analytical model. On the network level, it is shown that composite networks reconstituted from actin and vimentin can be described by a superposition of two non-interacting scaffolds. Arising effects are demonstrated in a scale-spanning frame connecting single filament dynamics to macro-rheological network properties and are captured within an inelastic glassy wormlike chain model. This paves the way to predict the mechanics of the cytoskeleton based on the properties of its single structural components. Further investigations on networks assembled from filamentous actin, intermediate filaments and synthetic DNA nanotubes show bulk properties are affected by various inter-filament interactions. It is proposed that these interactions can be merged into a single parameter in the frame of the glassy wormlike chain model. The interpretation of this parameter as a polymer specific stickiness is consistent with observations from macro-rheological measurements and reptation behavior. These findings demonstrate that stickiness should generally not be ignored in semiflexible polymer models.

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.

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