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.

The DNA contained in every living cell not only stores the genetic information; it functions in a complex molecular network that can condense, transcribe, replicate and repair genes. The essential role played by the sequence dependent structure and deformability of DNA in these basic processes of life, has received increasing attention over the past years. The present work aims at better understanding sequence dependent elasticity of double stranded DNA elasticity, across biologically relevant length scales. A theoretical description is developed that makes is possible to relate structural, biochemical and biophysical experiments and simulation. It is based on the rigid base–pair chain (rbc) model which captures all basic deformation modes on the scale of individual base–pair (bp) steps. Existing microscopic parametrizations of the rbc model rely on indirect methods. A way to relate them to biochemical experiments is provided by the indirect readout mechanism, where DNA elasticity determines protein–DNA complexation affinities. By correlating theoretical affinity predictions with in vitro measurements in a well–studied test case, different parameter sets were evaluated. As a result a new, hybrid parameter set is proposed which greatly reduces prediction errors. Indirect readout occurs mostly at particular binding subsites in a complex. A statistical marker is developed which localizes indirect readout subsites, by detecting elastically optimized sub-sequences. By a systematic coarse–graining of the rbc to the well–characterized worm–like chain (wlc) model, a quantitative connection between microscopic and kbp scale elasticity is established. The general helical rbc geometry is mapped to an effective, linear ‘on-axis’ version, yielding the full set of wlc elastic parameters for any given sequence repeat. In the random sequence case, structural variability adds conformational fluctuations which are correlated by sequence continuity. The sequence disorder correction to entropic elasticity in the rbc model is shown to coincide with the conformational correction. The results show remarkable overall agree- ment of the coarse–grained with the mesoscale wlc parameters, lending support to the model and to the microscopic parameter sets. A continuum version of the rbc is formulated as Brownian motion on the rigid motion group. Analytic expressions for angular correlation functions and moments of the end–to–end distance distribution are given. In an equivalent Lagrangian approach, conserved quantities along, and the linear response around, a general equilibrium shape are explored. / Die in jeder lebenden Zelle enthaltene DNS speichert nicht nur die genetische Information; Sie funktioniert innerhalb eines komplexen molekularen Netzwerks, das in der Lage ist, Gene zu kondensieren, transkribieren, replizieren und reparieren. Die zentrale Rolle, welche der sequenzabhängigen Struktur und Deformierbarkeit von DNS in diesen grundlegenden Lebensprozessen zukommt, erregte in den letzten Jahren zunehmendes Interesse. Die vorliegende Arbeit hat ein besseres Verständnis der sequenzabhängigen elastischen Eigenschaften von DNS auf biologisch relevanten Längenskalen zum Ziel. Es wird eine theoretische Beschreibung entwickelt, die es ermöglicht, strukturbiologische, biochemische und biophysikalische Experimente und Simulationen in Beziehung zu setzen. Diese baut auf dem Modell einer Kette aus starren Basenpaaren (rbc) auf, das alle wichtigen Deformationsmoden von DNS auf der Ebene von einzelnen Basenpaar (bp)–Schritten abbildet. Bestehende Parametersätze des rbc-Modells beruhen auf indirekten Methoden. Eine direkte Beziehung zu biochemischen Experimenten kann mithilfe des indirekten Auslese-Mechanismus hergestellt werden. Hierbei bestimmt die DNS– Elastizität Komplexierungsaffinitäten von Protein–DNS–Komplexen. Durch eine Korrelation von theoretischen Vorhersagen mit in vitro Messungen in einem gut untersuchten Beispielfall werden verschiedene Parametersätze bewertet. Als Resultat wird ein neuer Hybrid–Parametersatz vorgeschlagen, der die Vorhersagefehler stark reduziert. Indirektes Auslesen tritt meistens an speziellen Teilbindungsstellen innerhalb eines Komplexes auf. Es wird eine statistische Kenngröße entwickelt, die indirektes Auslesen durch Detektion elastisch optimierter Subsequenzen erkennt. Durch ein systematisches Coarse–Graining des rbc-Modells auf das gut charakterisierte Modell der wurmartigen Kette (wlc) wird eine quantitative Beziehung zwischen der mikroskopischen und der Elastizität auf einer kbp-Skala hergestellt. Die allgemeine helikale Geometrie wird auf eine effektive, lineare Version der Kette ‘auf der Achse’ abgebildet. Dies führt zur Berechnung des vollen Satzes von wlc-elastischen Parameters für eine beliebig vorgegebene periodische Sequenz. Im Fall zufälliger Sequenz führt die Strukturvariabilität zu zusätzlichen Konformationsfluktuationen, die durch die Kontinuität der Sequenz kurzreichweitig korreliert sind. Es wird gezeigt, daß die Sequenzunordnungs-Korrektur zur entropischen Elastizität im rbc-Modell identisch ist zur Korrektur der Konformationsstatistik. Die Ergebnisse zeigen eine bemerkenswerte Übereinstimmung der hochskalierten mikroskopischen mit den mesoskopischen wlc-Parameter und bestätigen so die Wahl des Modells und seiner mikroskopischen Parametrisierung. Eine Kontinuumsversion des rbc-Modells wird formuliert als Brownsche Bewegung auf der Gruppe der Starrkörpertransformationen. Analytische Ausdrücke für Winkelkorrelationsfunktionen und Momente der Verteilung des End-zu-End–Vektors werden angegeben. In einem äquivalenten Lagrange-Formalismus werden Erhaltungsgrößen entlang von Gleichgewichtskonformationen und die lineare Antwort in ihrer Umgebung untersucht.

Anisotropic molecules confined on a spherical or other curved surface can display coupled positional and orientational orderings, which make possible applications in physics, chemistry, biology, and material science. Therefore, controlling the order of such system has attracted much attention recently. Several distinct conformations of rod-like or chain-like molecules confined on a spherical surface have been predicted, including states such as tennis-ball, rectangle, and cut-and-rotate splay. These conformations have four +1/2 defects and are suggested to dominate over the splay conformation that has two +1 defects. For the purpose of investigating the conformations of 2-fold anisotropic molecules confined on the spherical surface, the author of this thesis utilizes the Onsager model to study the system of rigid rods and conducts Monte Carlo simulations on the bead-bond model to research the system of semiflexible polymer chains. At low surface coverage density, no particular pattern of the molecules would form. However, coupled positional and orientational ordering begins to emerge beyond a transition density. On the basis of the numerical solutions of the Onsager model of rigid rods, the splay conformation is shown to be the only stable state. On the other hand, Monte Carlo simulations on a polymer system indicate that the ordered state always accompanies the tennis-ball symmetry. With comparison to the continuous isotropic-nematic transition of a fluid of hard rods embedded in a flat two-dimensional space, the disorder-order transition for both the system of rigid rods and the system of polymer chains confined on the spherical surface has first-order phase-transition characteristics.

Anisotropic molecules confined on a spherical or other curved surface can display coupled positional and orientational orderings, which make possible applications in physics, chemistry, biology, and material science. Therefore, controlling the order of such system has attracted much attention recently. Several distinct conformations of rod-like or chain-like molecules confined on a spherical surface have been predicted, including states such as tennis-ball, rectangle, and cut-and-rotate splay. These conformations have four +1/2 defects and are suggested to dominate over the splay conformation that has two +1 defects. For the purpose of investigating the conformations of 2-fold anisotropic molecules confined on the spherical surface, the author of this thesis utilizes the Onsager model to study the system of rigid rods and conducts Monte Carlo simulations on the bead-bond model to research the system of semiflexible polymer chains. At low surface coverage density, no particular pattern of the molecules would form. However, coupled positional and orientational ordering begins to emerge beyond a transition density. On the basis of the numerical solutions of the Onsager model of rigid rods, the splay conformation is shown to be the only stable state. On the other hand, Monte Carlo simulations on a polymer system indicate that the ordered state always accompanies the tennis-ball symmetry. With comparison to the continuous isotropic-nematic transition of a fluid of hard rods embedded in a flat two-dimensional space, the disorder-order transition for both the system of rigid rods and the system of polymer chains confined on the spherical surface has first-order phase-transition characteristics.

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.

Entangled semiflexible polymer networks are usually described by the tube model, although this concept has not been able to explain all experimental observations. One of its major shortcomings is neglecting the thermal fluctuations of the polymers surrounding the examined test filament, such that disentanglement effects are not captured. In this study, we present experimental evidence that correlated constraint release which has been predicted theoretically occurs in entangled, but not in crosslinked semiflexible polymer networks. By tracking single semiflexible DNA nanotubes embedded both in entangled and crosslinked F-actin networks, we observed different reptation dynamics in both systems, emphasizing the need for a revision of the classical tube theory for entangled polymer solutions.

No description available.

Bundles and networks of semiflexible biopolymers are key elements in cells, lending them mechanical integrity while also enabling dynamic functions. Networks have been the subject of many studies, revealing a variety of fundamental characteristics often determined via bulk measurements. Although bundles are equally important in biological systems, they have garnered much less scientific attention since they have to be probed on the mesoscopic scale. Here, we review theoretical as well as experimental approaches, which mainly employ the naturally occurring biopolymer actin, to highlight the principles behind these structures on the single bundle level.