In Vitro Assembly Kinetics of Cytoplasmic Intermediate Filaments: A Correlative Monte Carlo Simulation Study.

Intermediate filament (IF) elongation proceeds via full-width "mini-filaments", referred to as "unit-length" filaments (ULFs), which instantaneously form by lateral association of extended coiled-coil complexes after assembly is initiated. In a comparatively much slower process, ULFs longitudinally interact end-to-end with other ULFs to form short filaments, which further anneal with ULFs and with each other to increasingly longer filaments. This assembly concept was derived from time-lapse electron and atomic force microscopy data. We previously have quantitatively verified this concept through the generation of time-dependent filament length-profiles and an analytical model that describes assembly kinetics well for about the first ten minutes. In this time frame, filaments are shorter than one persistence length, i.e. ~1 µm, and thus filaments were treated as stiff rods associating via their ends. However, when filaments grow several µm in length over hours, their flexibility becomes a significant factor for the kinetics of the longitudinal annealing process. Incorporating now additional filament length distributions that we have recorded after extended assembly times by total internal reflection fluorescence microscopy (TIRFM), we developed a Monte Carlo simulation procedure that accurately describes the underlying assembly kinetics for large time scales.

Kinetic lattice Monte Carlo simulation of viscoelastic subdiffusion.

We propose a kinetic Monte Carlo method for the simulation of subdiffusive random walks on a cartesian lattice. The random walkers are subject to viscoelastic forces which we compute from their individual trajectories via the fractional Langevin equation. At every step the walkers move by one lattice unit, which makes them differ essentially from continuous time random walks, where the subdiffusive behavior is induced by random waiting. To enable computationally inexpensive simulations with n-step memories, we use an approximation of the memory and the memory kernel functions with a complexity O(log n). Eventual discretization and approximation artifacts are compensated with numerical adjustments of the memory kernel functions. We verify with a number of analyses that this new method provides binary fractional random walks that are fully consistent with the theory of fractional brownian motion.

Chromosome dynamics, molecular crowding, and diffusion in the interphase cell nucleus: a Monte Carlo lattice simulation study.

Using Monte Carlo simulations, we have investigated the decondensation of chromosomes during interphase and the diffusive transport of spherical probe particles in the chromatin network. The chromatin fibers are modeled as semiflexible polymer chains on a fixed three-dimensional grid, taking into account their flexibility and eventual chain crossing by the aid of topoisomerases. The network thus created will obstruct the diffusion of macromolecules. A result of our simulations is that crowding of diffusing molecules leaves the dynamics of the chromosomes and the behavior of other diffusing molecules qualitatively unaffected. Furthermore, the capability of the simulated chromatin network to trap diffusing molecules over long times is lower than that measured in microrheological experiments. Microrheology is a technique that allows to determine the viscoelastic properties of a material by the motion of embedded tracer particles. Long-time trapping requires a stiff network, as only such a network quickly responds to the diffusive fluctuations of tracers and prevents them from squeezing through meshes. A high degree of crosslinking amplifies this effect. The presence of a flexible and uncrosslinked polymer simply increases the effective viscosity sensed by tracer particles. The diffusion of tracers in our simulations reveals rather viscous than elastic chromatin networks, suggesting that chromatin alone cannot account for the high elasticity of the cell nucleus.

Histone depletion facilitates chromatin loops on the kilobasepair scale.

The packing of eukaryotic DNA in the nucleus is decisive for its function; for instance, contact between remote genome sites constitutes a basic feature of gene regulation. Interactions among regulatory proteins, DNA binding, and transcription activation are facilitated by looping of the intervening chromatin. Such long-range interactions depend on the bending flexibility of chromatin, i.e., the ring-closure probability is a directly measurable indicator of polymer flexibility. The applicability of a wormlike chain model to naked DNA has been widely accepted. However, whether this model also suffices to describe the flexibility of eukaryotic interphase chromatin is still a matter of discussion. Here we compare both 5C data from a gene desert and data from fluorescence in situ hybridization with the results of a Monte Carlo simulation of chromatin fibers with and without histone depletion. We then estimate the ring-closure probabilities of simulated fibers with estimates from analytical calculations and show that the wormlike chain model grossly underestimates chromatin flexibility for sharp bends. Most importantly, we find that only fibers with random depletion of linker histones or nucleosomes can explain the probability of random chromatin contacts on small length scales that play an important role in gene regulation. It is possible that missing linker histones and nucleosomes are not just simple, unavoidable, randomly occurring defects, but instead play a regulatory role in gene expression.

Dynamics of a fluorophore attached to superhelical DNA: FCS experiments simulated by Brownian dynamics.

We investigated the dynamics of a single-fluorophore-labeled pUC18 plasmid through a Brownian dynamics algorithm, followed by a simulation of the fluorescence correlation spectroscopy (FCS) process. Recent experimental FCS measurements indicated a sensitivity of the monomer mean square displacements in DNA circles towards superhelicity. Simulations with homogeneous DNA elasticity and local straight equilibrium are not sufficient to reproduce this observed behavior. But inserting permanently bent sequences into the DNA, which favor end loop formation, caused a dependence of the calculated FCS correlation curves on superhelical density. Furthermore, our simulations allow us to take into account the orientation of the fluorophore in polarized excitation, which might explain the observed appearance of a Rouse-like regime at intermediate time scales.

Computational modeling of the chromatin fiber.

The packing of the genomic DNA in the living cell is essential for its biological function. While individual aspects of the genome architecture, such as DNA and nucleosome structure or the arrangement of chromosome territories are well studied, much information is missing for a unified description of cellular DNA at all its structural levels. Computer modeling can contribute to such a description. We present here some typical approaches to models of the chromatin fiber, including different amounts of detail in the description of the local nucleosome structure. The main results from our simulations are that the physical properties of the chromatin fiber can be well described by a simplified model consisting of cylinder-like nucleosomes connected by flexible DNA segments, with a geometry determined by the bending and twisting angles between nucleosomes. Randomness in the local geometry - such as random absence of linker histone H1 - leads to a dramatic increase in the chromatin fiber flexibility. Furthermore, we show that chromatin is much more flexible to bending than to stretching, and that the structure of the chromatin fiber favors the formation of sharp bends.

Monte Carlo simulation of chromatin stretching.

We present Monte Carlo (MC) simulations of the stretching of a single chromatin fiber. The model approximates the DNA by a flexible polymer chain with Debye-Hückel electrostatics and uses a two-angle zigzag model for the geometry of the linker DNA connecting the nucleosomes. The latter are represented by flat disks interacting via an attractive Gay-Berne potential. Our results show that the stiffness of the chromatin fiber strongly depends on the linker DNA length. Furthermore, changing the twisting angle between nucleosomes from 90 degrees to 130 degrees increases the stiffness significantly. An increase in the opening angle from 22 degrees to 34 degrees leads to softer fibers for small linker lengths. We observe that fibers containing a linker histone at each nucleosome are stiffer compared to those without the linker histone. The simulated persistence lengths and elastic moduli agree with experimental data. Finally, we show that the chromatin fiber does not behave as an isotropic elastic rod, but its rigidity depends on the direction of deformation: Chromatin is much more resistant to stretching than to bending.

Kinetics of site-site interactions in supercoiled DNA with bent sequences.

A curved DNA segment is known to adopt a preferred end loop localization in superhelical (sc) DNA and thus may organize the overall conformation of the molecule. Through this process it influences the probability of site juxtaposition. We addressed the effect of a curvature on site-site interactions quantitatively by measuring the kinetics of cross-linking of two biotinylated positions in scDNA by streptavidin. The DNA was biotinylated at either symmetric or asymmetric positions with respect to a curved insert via triplex-forming oligonucleotides (TFOs) modified with biotin. We used a quench-flow device to mix the DNA with the protein and scanning force microscopy to quantify the reaction products. As a measure of the interaction probability, rate constants of cross-linking and local concentrations j(M) of one biotinylated site in the vicinity of the other were determined and compared to Monte Carlo simulations for corresponding DNAs. In good agreement with the simulations, a j(M) value of 1.74 microM between two sites 500bp apart was measured for an scDNA without curvature. When a curvature was centered between the sites, the interaction probability increased about twofold over the DNA without curvature, significantly less than expected from the simulations. However, the relative differences of the interaction probabilities due to varied biotin positions with respect to the curvature agreed quantitatively with the theory.

Computer simulation of the 30-nanometer chromatin fiber.

A new Monte Carlo model for the structure of chromatin is presented here. Based on our previous work on superhelical DNA and polynucleosomes, it reintegrates aspects of the "solenoid" and the "zig-zag" models. The DNA is modeled as a flexible elastic polymer chain, consisting of segments connected by elastic bending, torsional, and stretching springs. The electrostatic interaction between the DNA segments is described by the Debye-Hückel approximation. Nucleosome core particles are represented by oblate ellipsoids; their interaction potential has been parameterized by a comparison with data from liquid crystals of nucleosome solutions. DNA and chromatosomes are linked either at the surface of the chromatosome or through a rigid nucleosome stem. Equilibrium ensembles of 100-nucleosome chains at physiological ionic strength were generated by a Metropolis-Monte Carlo algorithm. For a DNA linked at the nucleosome stem and a nucleosome repeat of 200 bp, the simulated fiber diameter of 32 nm and the mass density of 6.1 nucleosomes per 11 nm fiber length are in excellent agreement with experimental values from the literature. The experimental value of the inclination of DNA and nucleosomes to the fiber axis could also be reproduced. Whereas the linker DNA connects chromatosomes on opposite sides of the fiber, the overall packing of the nucleosomes leads to a helical aspect of the structure. The persistence length of the simulated fibers is 265 nm. For more random fibers where the tilt angles between two nucleosomes are chosen according to a Gaussian distribution along the fiber, the persistence length decreases to 30 nm with increasing width of the distribution, whereas the other observable parameters such as the mass density remain unchanged. Polynucleosomes with repeat lengths of 212 bp also form fibers with the expected experimental properties. Systems with larger repeat length form fibers, but the mass density is significantly lower than the measured value. The theoretical characteristics of a fiber with a repeat length of 192 bp where DNA and nucleosomes are connected at the core particle are in agreement with the experimental values. Systems without a stem and a repeat length of 217 bp do not form fibers.