Andreas Hanke

Polymer depletion effects near mesoscopic particles.

The behavior of mesoscopic particles dissolved in a dilute solution of long, flexible, and nonadsorbing polymer chains is studied by field-theoretic methods. For spherical and cylindrical particles the solvation free energy for immersing a single particle in the solution is calculated explicitly. Important features are qualitatively different for self-avoiding polymer chains as compared with ideal chains. The results corroborate the validity of the Helfrich-type curvature expansion for general particle shapes and allow for quantitative experimental tests. For the effective interactions between a small sphere and a wall, between a thin rod and a wall, and between two small spheres, quantitative results are presented. A systematic approach for studying effective many-body interactions is provided. The common Asakura-Oosawa approximation modeling the polymer coils as hard spheres turns out to fail completely for small particles and still fails by about 10% for large particles.

Probing the strong boundary shape dependence of the casimir force

We study the geometry dependence of the Casimir energy for deformed metal plates by a path integral quantization of the electromagnetic field. For the first time, we give a complete analytical result for the deformation induced change in Casimir energy delta E in an experimentally testable, nontrivial geometry, consisting of a flat and a corrugated plate. Our results show an interesting crossover for delta E as a function of the ratio of the mean plate distance H, to the corrugation length lambda: For lambda<<H we find a slower decay approximately H(-4), compared to the H(-5) behavior predicted by the commonly used pairwise summation of van der Waals forces, which is valid only for lambda>>H.

Critical Casimir Forces in Colloidal Suspensions

Some time ago, Fisher and de Gennes pointed out that long-ranged correlations in a fluid close to its critical point Tc cause distinct effective forces between immersed colloidal particles which can even lead to flocculation [C. R. Acad. Sc. Paris B287:207 (1978)]. Here we calculate such forces between pairs of spherical particles as function of both relevant thermodynamic variables, i.e., the reduced temperature t=(T−Tc)/Tc and the field h conjugate to the order parameter. This provides the basis for specific predictions concerning the phase behavior of a suspension of colloidal particles in a near-critical solvent.

Equilibrium shapes of flat knots.

We study the equilibrium shapes of prime and composite knots confined to two dimensions. Using scaling arguments we show that, due to self-avoiding effects, the topological details of prime knots are localized on a small portion of the larger ring polymer. Within this region, the original knot configuration can assume a hierarchy of contracted shapes, the dominating one given by just one small loop. This hierarchy is investigated in detail for the flat trefoil knot, and corroborated by Monte Carlo simulations.

Probing Molecular Free Energy Landscapes by Periodic Loading

Single molecule pulling experiments provide information about interactions in biomolecules that cannot be obtained by any other method. However, the reconstruction of the molecules free energy profile from the experimental data is still a challenge, in particular, for the unstable barrier regions. We propose a new method for obtaining the full profile by introducing a periodic ramp and using Jarzynskis relation for obtaining equilibrium quantities from nonequilibrium data. Our simulated experiments show that this method delivers significant more accurate data than previous methods, under the constraint of equal experimental effort.

Bubble dynamics in DNA

The formation of local denaturation zones (bubbles) in double-stranded DNA is an important example of conformational changes of biological macromolecules. We study the dynamics of bubble formation in terms of a Fokker–Planck equation for the probability density to find a bubble of size n base pairs at time t, on the basis of the free energy in the Poland–Scheraga model. Characteristic bubble closing and opening times can be determined from the corresponding first passage time problem, and are sensitive to the specific parameters entering the model. A multistate unzipping model with constant rates recently applied to DNA breathing dynamics (Altan-Bonnet et al 2003 Phys. Rev. Lett. 90 138101) emerges as a limiting case.

Kinetics and thermodynamics of salt-dependent T7 gene 2.5 protein binding to single- and double-stranded DNA

Bacteriophage T7 gene 2.5 protein (gp2.5) is a single-stranded DNA (ssDNA)-binding protein that has essential roles in DNA replication, recombination and repair. However, it differs from other ssDNA-binding proteins by its weaker binding to ssDNA and lack of cooperative ssDNA binding. By studying the rate-dependent DNA melting force in the presence of gp2.5 and its deletion mutant lacking 26 C-terminal residues, we probe the kinetics and thermodynamics of gp2.5 binding to ssDNA and double-stranded DNA (dsDNA). These force measurements allow us to determine the binding rate of both proteins to ssDNA, as well as their equilibrium association constants to dsDNA. The salt dependence of dsDNA binding parallels that of ssDNA binding. We attribute the four orders of magnitude salt-independent differences between ssDNA and dsDNA binding to nonelectrostatic interactions involved only in ssDNA binding, in contrast to T4 gene 32 protein, which achieves preferential ssDNA binding primarily through cooperative interactions. The results support a model in which dimerization interactions must be broken for DNA binding, and gp2.5 monomers search dsDNA by 1D diffusion to bind ssDNA. We also quantitatively compare the salt-dependent ssDNA- and dsDNA-binding properties of the T4 and T7 ssDNA-binding proteins for the first time.

Entropy Loss in Long-Distance DNA Looping

The entropy loss due to the formation of one or multiple loops in circular and linear DNA chains is calculated from a scaling approach in the limit of long chain segments. The analytical results allow us to obtain a fast estimate for the entropy loss for a given configuration. Numerical values obtained for some examples suggest that the entropy loss encountered in loop closure in typical genetic switches may become a relevant factor in comparison to both k(B)T and typical bond energies in biopolymers, which has to be overcome by the released bond energy between the looping contact sites.

Denaturation transition of stretched DNA

In the last two decades, single-molecule force measurements using optical and magnetic tweezers and atomic force spectroscopy have dramatically expanded our knowledge of nucleic acids and proteins. These techniques characterize the force on a biomolecule required to produce a given molecular extension. When stretching long DNA molecules, the observed force-extension relationship exhibits a characteristic plateau at approximately 65 pN where the DNA may be extended to almost twice its B-DNA length with almost no increase in force. In the present review, I describe this transition in terms of the Poland-Scheraga model and summarize recent related studies.

Tightness of slip-linked polymer chains

We study the interplay between entropy and topological constraints for a polymer chain in which sliding rings (slip links) enforce pair contacts between monomers. These slip links divide a closed ring polymer into a number of subloops which can exchange length among each other. In the ideal chain limit, we find the joint probability density function for the sizes of segments within such a slip-linked polymer chain (paraknot). A particular segment is tight (small in size) or loose (of the order of the overall size of the paraknot) depending on both the number of slip links it incorporates and its competition with other segments. When self-avoiding interactions are included, scaling arguments can be used to predict the statistics of segment sizes for certain paraknot configurations.