Coarse-grained modeling reveals the impact of supercoiling and loop length in DNA looping kinetics

Measurements of protein-mediated DNA looping reveal that in vivo conditions favor the formation of loops shorter than those that occur in vitro, yet the precise physical mechanisms underlying this shift remain unclear. To understand the extent to which in vivo supercoiling may explain these shifts, we develop a theoretical model based on coarse-grained molecular simulation and analytical transition state theory, enabling us to map out looping energetics and kinetics as a function of two key biophysical parameters: superhelical density and loop length. We show that loops on the scale of a persistence length respond to supercoiling over a much wider range of superhelical densities and to a larger extent than longer loops. This effect arises from a tendency for loops to be centered on the plectonemic end region, which bends progressively more tightly with superhelical density. This trend reveals a mechanism by which supercoiling favors shorter loop lengths. In addition, our model predicts a complex kinetic response to supercoiling for a given loop length, governed by a competition between an enhanced rate of looping due to torsional buckling and a reduction in looping rate due to chain straightening as the plectoneme tightens at higher superhelical densities. Together, these effects lead to a flattening of the kinetic response to supercoiling within the physiological range for all but the shortest loops. Using experimental estimates for in vivo superhelical densities, we discuss our model’s ability to explain available looping data, highlighting both the importance of supercoiling as a regulatory force in genetics and the additional complexities of looping phenomena in vivo.     

Toward the equilibrium and kinetics of amyloid peptide self-assembly

Several devastating human diseases are linked to peptide self-assembly, but our understanding their onset and progression is not settled. This is a sign of the complexity of the aggregation process, which is prevented, catalyzed, or retarded by numerous factors in body fluids and cells, varying in time and space. Biophysical studies of pure peptide solutions contribute insights into the underlying steps in the process and quantitative parameters relating to rate constants (energy barriers) and equilibrium constants (population distributions). This requires methods to quantify the concentration of at least one species in the process. Translation to an in vivo situation poses an enormous challenge, and the effects of selected components (bottom up) or entire body fluids (top down) need to be quantified.     

Mechanochemical model of microtubule structure and self-assembly kinetics

Microtubule self-assembly is largely governed by the chemical kinetics and thermodynamics of tubulin-tubulin interactions. An important aspect of microtubule assembly is that hydrolysis of the beta-tubulin-associated GTP promotes protofilament curling. Protofilament curling presumably drives the transition from tip structures associated with growth (sheetlike projections and blunt ends) to those associated with shortening (rams' horns and frayed ends), and transitions between these structures have been proposed to be important for growth-shortening transitions. However, previous models for microtubule dynamic instability have not considered such structures or mechanics explicitly. Here we present a three-dimensional model that explicitly incorporates mechanical stress and strain within the microtubule lattice. First, we found that the model recapitulates three-dimensional tip structures and rates of assembly and disassembly for microtubules grown under standard conditions, and we propose that taxol may stabilize microtubule growth by reducing flexural rigidity. Second, in contrast to recent suggestions, it was determined that sheetlike tips are more likely to undergo catastrophe than blunt tips. Third, partial uncapping of the tubulin-GTP cap provides a possible mechanism for microtubule pause events. Finally, simulations of the binding and structural effects of XMAP215 produced the experimentally observed growth and shortening rates, and tip structure.     

Local rules simulation of the kinetics of virus capsid self-assembly.

A computer model is described for studying the kinetics of the self-assembly of icosahedral viral capsids. Solution of this problem is crucial to an understanding of the viral life cycle, which currently cannot be adequately addressed through laboratory techniques. The abstract simulation model employed to address this is based on the local rules theory of. Proc. Natl. Acad. Sci. USA. 91:7732-7736). It is shown that the principle of local rules, generalized with a model of kinetics and other extensions, can be used to simulate complicated problems in self-assembly. This approach allows for a computationally tractable molecular dynamics-like simulation of coat protein interactions while retaining many relevant features of capsid self-assembly. Three simple simulation experiments are presented to illustrate the use of this model. These show the dependence of growth and malformation rates on the energetics of binding interactions, the tolerance of errors in binding positions, and the concentration of subunits in the examples. These experiments demonstrate a tradeoff within the model between growth rate and fidelity of assembly for the three parameters. A detailed discussion of the computational model is also provided.     

Algorithmic self-assembly of DNA Sierpinski triangles

Algorithms and information, fundamental to technological and biological organization, are also an essential aspect of many elementary physical phenomena, such as molecular self-assembly. Here we report the molecular realization, using two-dimensional self-assembly of DNA tiles, of a cellular automaton whose update rule computes the binary function XOR and thus fabricates a fractal pattern—a Sierpinski triangle—as it grows. To achieve this, abstract tiles were translated into DNA tiles based on double-crossover motifs. Serving as input for the computation, long single-stranded DNA molecules were used to nucleate growth of tiles into algorithmic crystals. For both of two independent molecular realizations, atomic force microscopy revealed recognizable Sierpinski triangles containing 100–200 correct tiles. Error rates during assembly appear to range from 1% to 10%. Although imperfect, the growth of Sierpinski triangles demonstrates all the necessary mechanisms for the molecular implementation of arbitrary cellular automata. This shows that engineered DNA self-assembly can be treated as a Turing-universal biomolecular system, capable of implementing any desired algorithm for computation or construction tasks.     

Cytosine, the double helix and DNA self-assembly

DNA self-assembly has crucial implications in reading out the genetic information in the cell and in nanotechnological applications. In a recent paper, self-assembled DNA crystals displaying spectacular triangular motifs have been described (Zheng et al., 2009). The authors claimed that their data demonstrate the possibility to rationally design well-ordered macromolecular 3D DNA lattice with precise spatial control using sticky ends. However, the authors did not recognize the fundamental features that control DNA self-assembly in the lateral direction. By analysing available crystallographic data and simulating a DNA triangle, we show that the double helix geometry, sequence-specific cytosine–phosphate interactions and divalent cations are in fact responsible for the precise spatial assembly of DNA.     

Dynamics of membrane nanotubulation and DNA self-assembly

A localized point-like force applied perpendicular to a vesicular membrane layer, using an optical tweezer, leads to membrane nanotubulation beyond a threshold force. Below the threshold, the force-extension curve shows an elastic response with a fine structure (serrations). Above the threshold the tubulation process exhibits a new reversible flow phase for the multilamellar membrane, which responds viscoelastically. Furthermore, with an oscillatory force applied during tubulation, broad but well-resolved resonances occur in the flow phase, presumably matching the time scales associated with the vesicle-nanotubule coupled system. These nanotubules, anchored to the optical tweezer also provide, for the first time, a direct probe of the real-time dynamics of DNA self-assembly on membranes. Our studies are a step in the direction of analyzing the dynamics of membrane self-assembly and artificial nanofluidic membrane networks.     

DNA curvature influences the internal motions of supercoiled DNA.

We present evidence that short curved DNA segments can act as mediators for the ordering of large domains in superhelical DNA. Using a non-invasive solution method (dynamic light scattering), we investigated the effect of permanently curved inserts on the solution structure and on the internal motions of superhelical plasmid DNA. We find that the dynamics of superhelical DNA are strongly influenced by sequence- or protein-induced bending: in superhelical plasmids containing curved inserts the amplitude of the internal motion is lower than that of non-curved controls. Furthermore, the relative arrangement of curved sequences in the plasmids can influence the overall shape of the superhelical DNA. On linearized forms of the plasmids, these effects are not observed.     

Rapid self-assembly of DNA on a microfluidic chip

Background  

DNA self-assembly methods have played a major role in enabling methods for acquiring genetic information without having to resort to sequencing, a relatively slow and costly procedure. However, even self-assembly processes tend to be very slow when they rely upon diffusion on a large scale. Miniaturisation and integration therefore hold the promise of greatly increasing this speed of operation.     

Factors affecting the kinetics of DNA reassociation in phenol–water emulsion at high DNA concentrations

DNA reassociation kinetics using the phenol emulsion reassociation technique (PERT) [Kohne, D. E., Levison, S. A. & Byers, M. J. (1977) Biochemistry 16 , 5329–5341] has been investigated at high DNA concentrations using an endonuclease S1 assay of reaction progress. Apparent second-order rate constants fall on two intersecting straight lines when presented as a function of DNA concentrations on a log–log plot. In the low DNA concentration range, the rate constants drop about 10-fold when concentration increases 1000-fold. In the high DNA concentration range, the rate constants drop more than 10-fold when concentration increases 10-fold. The slopes of these lines are the same in different solvents and at different temperatures. The intersection between the lines occurs when the available catalytic surface is saturated. At high DNA concentrations, high-complexity heterologous denatured DNA apparently competes 2–4 times better for the surface than homologous DNA because it does not participate in a reassociation reaction. Native and partially native DNA molecules cannot compete with single-stranded DNA for a saturated surface. At high DNA concentrations, reactions using PERT become dependent on the single-strand DNA length. Increasing length lowers reassociation rates.     

Investigating the kinetics of DNA–DNA and PNA–DNA interactions using surface plasmon resonance-enhanced fluorescence spectroscopy

Plasmon surface polaritons, resonantly excited in the Kretschmann format, are used to enhance the fluorescence emission of chromophore-labeled oligonucleotides (15mers) binding to surface-attached (via biotin–streptavidin linkages) complement catcher probes. A detailed analysis of the association and dissociation kinetics as well as the affinity constants is given for a mismatch 1 hybrid, emphasizing, in particular, the experimental conditions that are required to allow for an artifact-free determination of rate constants. A first comparison between DNA- and peptide nucleic acid (PNA-) probes shows similar affinities, however, significant deviations from single-exponential kinetics predicted by a simple Langmuir model for the PNA case are found.     

A study of the influence of polysaccharides on collagen self-assembly: nanostructure and kinetics

Collagen, a critical part of the extra-cellular matrix of tissues, is a popular native material for building scaffolding for tissue-engineering applications. To mimic the structural and functional profiles of materials found in the native extra-cellular matrix, numerous efforts have been made toward developing a novel scaffold combining collagen with other biomacromolecules. All of these works have been focused on improving the mechanical or biochemical properties of the collagen-based matrix. Unfortunately, most of these studies have failed to consider the nanostructure of collagen in the complex matrix. The aim of our study was to investigate the aggregation pattern of collagen after addition of polysaccharides with positive or negative charge, the dose-response relationship, and the effect on reconstitution kinetics. Generally, collagen self-assembles into fibrils with a diameter of around 95 nm but, in the presence of various polysaccharides in varying amounts, collagen self-assembles into different shapes with larger diameters compared with collagen alone. Although the morphology and diameter of the collagen fibrils varies with reconstitution conditions, the D-periods of the fibrils all remained the same regardless of the species or concentration of polysaccharides. The kinetics of fibril formation was determined from turbidity-time curves. All turbidity curves demonstrated that polysaccharides only alter the lag time and time frame of reconstitution, but have no significant effect on the mechanism of reconstitution. Together our data indicate that the presence of biomacromolecules can alter the kinetics and the 3D fibril ultrastructure of assembled collagen and that the consequent structural changes may affect cellular responses in medical applications.     

The role of topological limitations in the kinetics of homopolymer collapse and self-assembly of biopolymers

Fast collapse of a linear homopolymer after a spasmodic temperature decrease or deterioration of the solvent quality results in the initiation of folded nonequilibrium globule. The chain line in it is a fractal with the dimension mu less than or equal to 2 at small ranges and 3 at the large ones. This is provided by non-selfintersection of the chain and initiated therefore spatial segregation from each other at all the ranges of the chain regions, globulized each in itself. Further relaxation of the folded globule proceeds very slowly only at the expense of reptation (diffusion crawling) of the chain along itself, and results in the polymer knotting. The model of the folded globule permits explanation from a single viewpoint of a number of globular proteins properties. Predictions are formulated whose checking in a real or computer experiment should reveal the adequacy of our results.     

Trafficking of the IKs‐Complex in MDCK Cells: Site of Subunit Assembly and Determinants of Polarized Localization

The voltage‐gated potassium channel K_V7.1 is regulated by non‐pore forming regulatory KCNE β‐subunits. Together with KCNE1, it forms the slowly activating delayed rectifier potassium current I_Ks. However, where the subunits assemble and which of the subunits determines localization of the I_Ks‐complex has not been unequivocally resolved yet. We employed trafficking‐deficient K_V7.1 and KCNE1 mutants to investigate I_Ks trafficking using the polarized Madin‐Darby Canine Kidney cell line. We find that the assembly happens early in the secretory pathway but provide three lines of evidence that it takes place in a post‐endoplasmic reticulum compartment. We demonstrate that K_V7.1 targets the I_Ks‐complex to the basolateral membrane, but that KCNE1 can redirect the complex to the apical membrane upon mutation of critical K_V7.1 basolateral targeting signals. Our data provide a possible explanation to the fact that K_V7.1 can be localized apically or basolaterally in different epithelial tissues and offer a solution to divergent literature results regarding the effect of KCNE subunits on the subcellular localization of K_V7.1/KCNE complexes .     

Analysis of the nucleation and crystal growth kinetics of lysozyme by a theory of self-assembly.

Concentration changes in supersaturated solutions during the nucleation and growth of the orthorhombic form of hen egg-white lysozyme crystals have been observed for 121 d at 35 degrees C and pH 4.6, and with 3% NaCl. The effect of a variation in the initial protein concentration on the rate of approach to solubility in equilibrium is analyzed, by applying a model, originally developed for the understanding of protein self-assembly. It is shown that the observed kinetics can be explained fairly well by this model, whose basic assumptions are that (a) the nucleation is induced by aggregation of i0 molecules into particular geometry, and (b) the growth proceeds via attachment of a monomer. The i0 value for this process is four, which agrees with the number of molecules in a unit cell. Similarity and dissimilarity of the observed crystal growth to that of low molecular weight substances are discussed.