We present an experimental system suitable for producing spherical crystals and for observing the distribution of lattice defects (disclinations and dislocations) on a significant fraction (50%) of the sphere. The introduction of fluorescently labeled particles enables us to determine the location and orientation of grain boundary scars. We find that the total number of scars and the number of excess dislocations per scar agree with theoretical predictions and that the geometrical centers of the scars are roughly positioned at the vertices of an icosahedron.

Loops are abundant in native RNA structures and proliferate close to the unfolding transition. By including a statistical weight approximately l(-c) for loops of length l in the recursion relation for the partition function, we show that the heat capacity depends sensitively on the presence and value of the exponent c, even for a short explicit tRNA sequence. For long homo-RNA, we analytically calculate the critical temperature and critical exponents which exhibit a nonuniversal dependence on c.

Secondary structure formation of nucleic acids strongly depends on salt concentration and temperature. We develop a theory for RNA folding that correctly accounts for sequence effects, the entropic contributions associated with loop formation, and salt effects. Using an iterative expression for the partition function that neglects pseudoknots, we calculate folding free energies and minimum free energy configurations based on the experimentally derived basepairing free energies. The configurational entropy of loop formation is modeled by the asymptotic expression -clnm, where m is the length of the loop and c the loop exponent, which is an adjustable constant. Salt effects enter in two ways: first, we derive salt-induced modifications of the free energy parameters for describing basepairing, and second, we include the electrostatic free energy for loop formation. Both effects are modeled on the Debye-Hückel level including counterion condensation. We validate our theory for two different RNA sequences. For tRNA-phe, the resultant heat capacity curves for thermal denaturation at various salt concentrations accurately reproduce experimental results. For the P5ab RNA hairpin, we derive the global phase diagram in the three-dimensional space spanned by temperature, stretching force, and salt concentration and obtain good agreement with the experimentally determined critical unfolding force. We show that for a proper description of RNA melting and stretching, both salt and loop entropy effects are needed.

PACS 82.35.Gh -Polymers on surfaces; adhesion PACS 83.50.-v -Deformation and flow PACS 82.37.Gk -STM and AFM manipulations of a single moleculeAbstract. -The adsorption of a single polymer to a flat surface in shear is investigated using Brownian hydrodynamics simulations and scaling arguments. Competing effects are disentangled: in the absence of hydrodynamic interactions, shear drag flattens the chain and thus enhances adsorption. Hydrodynamic lift on the other hand gives rise to long-ranged repulsion from the surface which preempts the surface-adsorbed state via a discontinuous desorption transition, in agreement with theoretical arguments. Chain flattening is dominated by hydrodynamic lift, so overall, shear flow weakens the adsorption of flexible polymers. Surface friction due to smallwavelength surface potential corrugations is argued to weaken the surface attraction as well.

We introduce a three-state model for a single DNA chain under tension that distinguishes among B-DNA, S-DNA, and M (molten or denatured) segments and at the same time correctly accounts for the entropy of molten loops, characterized by the exponent c in the asymptotic expression S approximately -c ln n for the entropy of a loop of length n. Force extension curves are derived exactly by employing a generalized Poland-Scheraga approach and then compared to experimental data. Simultaneous fitting to force-extension data at room temperature and to the denaturation phase transition at zero force is possible and allows us to establish a global phase diagram in the force-temperature plane. Under a stretching force, the effects of the stacking energy (entering as a domain-wall energy between paired and unpaired bases) and the loop entropy are separated. Therefore, we can estimate the loop exponent c independently from the precise value of the stacking energy. The fitted value for c is small, suggesting that nicks dominate the experimental force extension traces of natural DNA.

The dynamics of proteins and biopolymers play a crucial role in their function. By using Brownian dynamics we show that polymer globules, which serve as a model system for proteins, undergo a size-dependent dynamical transition from a liquid-like state at high T to a frozen state at low T with a relaxation time that diverges at the transition point. Furthermore, a stretch-induced melting transition is shown to be readily controlled by external forces that exploit the polymer connectivity to modify the size of the globule. This pathway could be a general route to enhance the rate of conformational changes in naturally occurring biopolymers.

We study the conformational dynamics within homopolymer globules by solvent-implicit Brownian dynamics simulations. A strong dependence of the internal chain dynamics on the Lennard-Jones cohesion strength ε and the globule size N (G) is observed. We find two distinct dynamical regimes: a liquid-like regime (for ε < ε(s) with fast internal dynamics and a solid-like regime (for ε > ε(s) with slow internal dynamics. The cohesion strength ε(s) of this freezing transition depends on N (G) . Equilibrium simulations, where we investigate the diffusional chain dynamics within the globule, are compared with non-equilibrium simulations, where we unfold the globule by pulling the chain ends with prescribed velocity (encompassing low enough velocities so that the linear-response, viscous regime is reached). From both simulation protocols we derive the internal viscosity within the globule. In the liquid-like regime the internal friction increases continuously with ε and scales extensive in N (G) . This suggests an internal friction scenario where the entire chain (or an extensive fraction thereof) takes part in conformational reorganization of the globular structure.

Loops are essential secondary structure elements in folded DNA and RNA molecules and proliferate close to the melting transition. Using a theory for nucleic acid secondary structures that accounts for the logarithmic entropy -c ln m for a loop of length m, we study homopolymeric single-stranded nucleic acid chains under external force and varying temperature. In the thermodynamic limit of a long strand, the chain displays a phase transition between a low-temperature/low-force compact (folded) structure and a high-temperature/high-force molten (unfolded) structure. The influence of c on phase diagrams, critical exponents, melting, and force extension curves is derived analytically. For vanishing pulling force, only for the limited range of loop exponents 2 < c ≲ 2.479 a melting transition is possible; for c ≤ 2 the chain is always in the folded phase and for 2.479 ≲ c always in the unfolded phase. A force-induced melting transition with singular behavior is possible for all loop exponents c < 2.479 and can be observed experimentally by single-molecule force spectroscopy. These findings have implications for the hybridization or denaturation of double-stranded nucleic acids. The Poland-Scheraga model for nucleic acid duplex melting does not allow base pairing between nucleotides on the same strand in denatured regions of the double strand. If the sequence allows these intra-strand base pairs, we show that for a realistic loop exponent c ≈ 2.1 pronounced secondary structures appear inside the single strands. This leads to a lower melting temperature of the duplex than predicted by the Poland-Scheraga model. Further, these secondary structures renormalize the effective loop exponent [Formula: see text], which characterizes the weight of a denatured region of the double strand, and thus affect universal aspects of the duplex melting transition.