Terminal Twist-Induced Writhe of DNA with Intrinsic Curvature

Supercoiling of a closed circular DNA rod may result from an application of terminal twist to the DNA rod by cutting the rod, rotating one of the cut faces as the other being fixed and then sealing the cut. According to White's formula, DNA supercoiling is probably accompanied by a writhe of the DNA axis. Deduced from the elastic rod model for DNA structure, an intrinsically straight closed circular DNA rod does not writhe as subject to a terminal twist, until the number of rotation exceeds a rod-dependent threshold. By contrast, a closed circular DNA rod with intrinsic curvature writhes instantly as subject to a terminal twist. This noteworthy character in fact belongs to many intrinsically curved DNA rods. By solving the dynamic equations, the linearization of the Euler–Lagrange equations governing intrinsically curved DNA rods, this paper shows that almost every clamped-end intrinsically curved DNA rod writhes instantly when subject to a terminal twist (clamped-end DNA rods include closed circular DNA rods and topological domains of open DNA rods). In terms of physical quantities, the exceptions are identified with points in ℝ⁶ whose projections onto ℝ⁵ (through ignoring the total energy density of a rod) form a subset of a quadratic hypersurface. This paper also suggests that the terminal twist induced writhe is due to the elasticity and the clamped-end boundary conditions of the DNA rods. To my sister for her 50th birthday.     

Intrinsic curvature of DNA influences LacR-mediated looping

Protein-mediated DNA looping is a common mechanism for regulating gene expression. Loops occur when a protein binds to two operators on the same DNA molecule. The probability of looping is controlled, in part, by the basepair sequence of inter-operator DNA, which influences its structural properties. One structural property is the intrinsic or stress-free curvature. In this article, we explore the influence of sequence-dependent intrinsic curvature by exercising a computational rod model for the inter-operator DNA as applied to looping of the LacR-DNA complex. Starting with known sequences for the inter-operator DNA, we first compute the intrinsic curvature of the helical axis as input to the rod model. The crystal structure of the LacR (with bound operators) then defines the requisite boundary conditions needed for the dynamic rod model that predicts the energetics and topology of the intervening DNA loop. A major contribution of this model is its ability to predict a broad range of published experimental data for highly bent (designed) sequences. The model successfully predicts the loop topologies known from fluorescence resonance energy transfer measurements, the linking number distribution known from cyclization assays with the LacR-DNA complex, the relative loop stability known from competition assays, and the relative loop size known from gel mobility assays. In addition, the computations reveal that highly curved sequences tend to lower the energetic cost of loop formation, widen the energy distribution among stable and meta-stable looped states, and substantially alter loop topology. The inclusion of sequence-dependent intrinsic curvature also leads to nonuniform twist and necessitates consideration of eight distinct binding topologies from the known crystal structure of the LacR-DNA complex.     

Twist and writhing in short circular DNAs according to first-order elasticity

The distribution of twist and writhing in a closed DNA shorter than its persistence length is examined. In this case, the only energy contribution is elastic. We have in tegrated the equations of elasticity for a homogeneous axially symmetric rod of undeformable infinitely small circular cross section with frictionless reactions, when there is no or only one self-contact. In the absence of self-contacts, the central line of the rod is drawn on a toroid. It makes ν turns around the axis of revolution of the toroid and m turns around its core. The integer, ν, is equal to one if the rod is unknotted. We prove that no infinitely thin rod with a positive Poisson ratio is stable in a toroidal conformation if there is no self-contact. However, m-leafed roses or rosettes, with but one multiple self-contact, are shown to actually be stable when their writhing is not too great. When the integer, m, is equal to two, we have figure-8 conformations. Buckling of the circle into a figure-8 conformation occurs for the constraint such that the figure-8 and the circular conformations have the same energy. This constraint is 1.845 turns for a bending-to-twisting elastic constants ratio of A/C = 1.5. For the same value of A/C, the figure-8 conformation is unstable for a constraint greater than 2.4 turns. Corrections caused by a finite value of the radius ratio, a/L, of the cross section to the length of the rod, are estimated. For instance, both the circular conformation and the infinitesimally warped circle are simultaneous solutions for particular values of the β twist. β = A/C (m² ? ν²)^½ [1 + (νπa/L)²/2]. The binding of ethidium to DNAs short enough to follow first-order elasticity has been studied. Buckling occurs at an apparent average constraint of about 0.6. How the DNA molecules are distributed in figure-8 conformations and circles has been determined as the ethidium concentration is varied.     

The study of combined action of agents using differential geometry of dose-effect surfaces

Although graphic surfaces have been used routinely in the study of combined action of agents, they are mainly used for display purposes. In this paper, it is shown that useful mechanistic information can be obtained from an analytical study of these surfaces using the tools of differential geometry. From the analysis of some simple dose-effect surfaces, it is proposed that the intrinsic curvature, referred to in differential geometry as the Gaussian curvature, of a dose-effect surface can be used as a general criterion for the classification of interaction between different agents. This is analogous to the interpretation of the line curvature of a dose-effect curve as an indication of self-interaction between doses for an agent. In this framework, the dose-effect surface would have basic uniform fabric with zero curvature in the absence of interaction, tentatively referred to as null-interaction. Pictorially speaking, this fabric is distorted locally or globally like the stretching and shrinking of a rubber sheet by the presence of interaction mechanisms between different agents. Since self-interaction with dilution dummies does not generate intrinsic curvature, this criterion of null-interaction would describe the interaction between two trulydifferent agents. It is shown that many of the published interaction mechanisms give rise to dose-effect surfaces with characteristic curvatures. This possible correlation between the intrinsic geometric curvature of dose-effect surfaces and the biophysical mechanism of interaction presents an interesting philosophical viewpoint for the study of combined action of agents.     

The effect of intrinsic curvature on conformational properties of circular DNA.

Both thermal fluctuations and the intrinsic curvature of DNA contribute to conformations of the DNA axis. We looked for a way to estimate the relative contributions of these two components of the double-helix curvature for DNA with a typical sequence. We developed a model and Monte Carlo procedure to simulate the Boltzmann distribution of DNA conformations with a specific intrinsic curvature. Two steps were used to construct the equilibrium conformation of the model chain. We first specified the equilibrium DNA conformation at the base pair level of resolution, using a set of the equilibrium dinucleotide angles and DNA sequence. This conformation was then approximated by the conformation of the model chain consisting of a reduced number of longer, straight cylindrical segments. Each segment of the chain corresponded to a certain number of DNA base pairs. We simulated conformational properties of nicked circular DNA for different sets of equilibrium dinucleotide angles, different random DNA sequences, and lengths. Only random sequences of DNA generated with equal probability of appearance for all types of bases at any site of the sequence were used. The results showed that for a broad range of intrinsic curvature parameters, the radius of gyration of DNA circles should be nearly independent of DNA sequence for all DNA lengths studied. We found, however, a DNA properly that should strongly depend on DNA sequence if the double helix has essential intrinsic curvature. This property is the equilibrium distribution of the linking number for DNA circles that are 300-1000 bp in length. We found that a large fraction of the distributions corresponding to random DNA sequences should have two separate maxima. The physical nature of this unexpected effect is discussed. This finding opens new opportunities for joined experimental and theoretical studies of DNA intrinsic curvature.     

Computational analysis of looping of a large family of highly bent DNA by LacI

Sequence-dependent intrinsic curvature of DNA influences looping by regulatory proteins such as LacI and NtrC. Curvature can enhance stability and control shape, as observed in LacI loops formed with three designed sequences with operators bracketing an A-tract bend. We explore geometric, topological, and energetic effects of curvature with an analysis of a family of highly bent sequences, using the elastic rod model from previous work. A unifying straight-helical-straight representation uses two phasing parameters to describe sequences composed of two straight segments that flank a common helically supercoiled segment. We exercise the rod model over this two-dimensional space of phasing parameters to evaluate looping behaviors. This design space is found to comprise two subspaces that prefer parallel versus anti-parallel binding topologies. The energetic cost of looping varies from 4 to 12 kT. Molecules can be designed to yield distinct binding topologies as well as hyperstable or hypostable loops and potentially loops that can switch conformations. Loop switching could be a mechanism for control of gene expression. Model predictions for linking numbers and sizes of LacI-DNA loops can be tested using multiple experimental approaches, which coupled with theory could address whether proteins or DNA provide the observed flexibility of protein-DNA loops.     

Investigation on chlorosomal antenna geometries: tube,lamella and spiral-type self-aggregates

Molecular mechanics calculations and exciton theory have been used to study pigment organization in chlorosomes of green bacteria. Single and double rod, multiple concentric rod, lamella, and Archimedean spiral macrostructures of bacteriochlorophyll c molecules were created and their spectral properties evaluated. The effects of length, width, diameter, and curvature of the macrostructures as well as orientations of monomeric transition dipole moment vectors on the spectral properties of the aggregates were studied. Calculated absorption, linear dichroism, and polarization dependent fluorescence-excitation spectra of the studied long macrostructures were practically identical, but circular dichroism spectra turned out to be very sensitive to geometry and monomeric transition dipole moment orientations of the aggregates. The simulations for long multiple rod and spiral-type macrostructures, observed in recent high-resolution electron microscopy images (Oostergetel et al., FEBS Lett 581:5435–5439, 2007) gave shapes of circular dichroism spectra observed experimentally for chlorosomes. It was shown that the ratio of total circular dichroism intensity to integrated absorption of the Q _y transition is a good measure of degree of tubular structures in the chlorosomes. Calculations suggest that the broad Q _y line width of chlorosomes of sulfur bacteria could be due to (1) different orientations of the transition moment vectors in multi-walled rod structures or (2) a variety of Bchl-aggregate structures in the chlorosomes. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

An elastic rod model for anguilliform swimming

We develop a model for anguilliform (eel-like) swimming as an elastic rod actuated via time-dependent intrinsic curvature and subject to hydrodynamic drag forces, the latter as proposed by Taylor (in Proc Roy Proc Lond A 214:158–183, 1952). We employ a eometrically exact theory and discretize the resulting nonlinear partial differential evolution both to perform numerical simulations, and to compare with previous models consisting of chains of rigid links or masses connected by springs, dampers, and prescribed force generators representing muscles. We show that muscle activations driven by motoneuronal spike trains via calcium dynamics produce intrinsic curvatures corresponding to near-sinusoidal body shapes in longitudinally-uniform rods, but that passive elasticity causes Taylor’s assumption of prescribed shape to fail, leading to time-periodic motions and lower speeds than those predicted Taylor (in Proc Roy Proc Lond A 214:158–183, 1952). We investigate the effects of bending stiffness, body geometry, and activation patterns on swimming speed, turning behavior, and acceleration to steady swimming. We show that laterally-uniform activation yields stable straight swimming and laterally differential activation levels lead to stable turns, and we argue that tapered bodies with reduced caudal (tail-end) activation (to produce uniform intrinsic curvature) swim faster than ones with uniform activation.     

Antagonism of morphine tolerance and dependence by metoclopramide

Metoclopramide produced significant analgesic activity when tested by acetic acid induced writhing assay. Repeated injections of metoclopramide did not result in the development of tolerance to its analgesic activity. Pretreatment with metoclopramide antagonised acute morphine tolerance and suppressed the withdrawal signs (both in acute dependence type and abrupt withdrawal type). It is suggested that metoclopramide may be a useful tool in the management of morphine dependence.     

Physical principles underlying the transduction of bilayer deformation forces during mechanosensitive channel gating

In mechanosensitive (MS) channels, gating is initiated by changes in intra-bilayer pressure profiles originating from bilayer deformation. Here we evaluated two physical mechanisms as triggers of MS channel gating: the energetic cost of protein-bilayer hydrophobic mismatches and the geometric consequences of bilayer intrinsic curvature. Structural changes in the Escherichia coli large MS channel (MscL) were studied under nominally zero transbilayer pressures using both patch clamp and EPR spectroscopic approaches. Changes in membrane intrinsic curvature induced by the external addition of lysophosphatidylcholine (LPC) generated massive spectroscopic changes in the narrow constriction that forms the channel 'gate', trapping the channel in the fully open state. Hydrophobic mismatch alone was unable to open the channel, but decreasing bilayer thickness lowered MscL activation energy, stabilizing a structurally distinct closed channel intermediate. We propose that the mechanism of mechanotransduction in MS channels is defined by both local and global asymmetries in the transbilayer pressure profile at the lipid-protein interface.     

Relating independent measures of DNA curvature: electrophoretic anomaly and cyclization efficiency

Electrophoretic methods are often used to measure DNA curvature and protein-induced DNA bending. Though convenient and widely-applied, quantitative analyses are generally limited to assays for which empirical calibration standards have been developed. Alternatively, solution-based cyclization of short DNA duplexes allows analysis of DNA curvature and bending from first principles, but a detailed understanding of this assay is still lacking. In this work, we demonstrate that calibration with an independent electrophoretic assay of DNA curvature permits interpretation of cyclization assay results in a quantitatively meaningful way. We systematically measure intrinsic DNA curvature in short duplexes using a well-established empirical ligation ladder assay. We then compare the results to those obtained from the analysis of the distribution of circular products obtained in simple enzymatic cyclization assays of the same duplexes when polymerized. A strong correlation between DNA curvature estimates from these two assays is obtained for DNA fragments between 150-300 bp in length. We discuss how this result might be used to improve quantitative analysis of protein-mediated bending events evaluated by cyclization methods. Our results suggest that measurements of DNA curvature obtained under similar conditions, in solution and in an acrylamide gel matrix, can be compared directly. The ability to correlate results of these simple assays may prove convenient in monitoring DNA curvature and flexibility.     

Crenation and cupping of the red cell: A new theoretical approach. Part II. Cupping

Typical, axisymmetrical cup shaped cells have been carefully measured and the shapes analyzed mathematically. The results show that the strain energy of a cup shaped cell is always higher than that of a biconcave cell except when the two layers of the membrane involved in resistance to bending are free to slide over one another. This is true whether intrinsic curvature of the membrane is positive, negative or zero. If the two layers can slide over one another, the cup shape becomes the lower energy form. Shear resistance, if appreciable, must cause the cup cell to buckle. Photomicrographs of cup shaped cells show buckled configurations characteristic of those of a partly deflated thin-walled rubber ball, which is a similar object having a low ratio of bending/shear strength.In light of these findings, the cup shape of the red cell can no longer be considered as evidence of intrinsic membrane curvature of opposite sign to that of the crenated cell, but appears to indicate a phase change either in the hydrophobic interior of the bimolecular membrane or in some equivalent interface.     

Selective nucleosome disruption by drugs that bind in the minor groove of DNA.

Previous studies have shown that drugs which bind in the DNA minor groove reduce the curvature of bent DNA. In this article, we examined the effects of these drugs on the nucleosome assembly of DNA molecules that display different degrees of intrinsic curvature. DAPI (4,6-diamidino-2-phenylindole) inhibited the assembly of a histone octamer onto a 192-base pair circular DNA fragment from Caenorhabditis elegans and destabilized a nucleosome that was previously assembled on this segment. The inhibitory effect was highly selective since it was not seen with nonbent molecules, bent molecules with noncircular shapes, or total genomic DNA. This marked template specificity was attributed to the binding of the ligand to multiple oligo A-tracts distributed over the length of the fragment. A likely mechanism for the effect is that the bound ligand prevents the further compression of the DNA into the minor groove which is required for assembly of DNA into nucleosomes. To further characterize the effects of the drug on chromatin formation, a nucleosome was assembled onto a 322-base pair DNA fragment that contained the circular element and a flanking nonbent segment of DNA. The position of the nucleosome along the fragment was then determined using a variety of nuclease probes including exonuclease III, micrococcal nuclease, DNase I, and restriction enzymes. The results of these studies revealed that the nucleosome was preferentially positioned along the circular element in the absence of DAPI but assembled onto the nonbent flanking sequence in the presence of the drug. DAPI also induced the directional movement of the nucleosome from the circular element onto the nonbent flanking sequence when a nucleosome preassembled onto this template was exposed to the drug under physiologically relevant conditions.     

Mean curvature as a major determinant of beta-sheet propensity

MOTIVATION: Despite the importance of beta-sheets as building blocks in proteins and also toxic elements in the pathological disorders, ranging from Alzheimer's disease to mad cow disease, the principles underlying their stability are not well understood. Non-random beta-sheet propensities of amino acids have been revealed both by their distinct statistical preferences within known protein structures and by the relative thermodynamic scales through the experimental host-guest systems. However, recent fitting analysis has proved that a native beta-sheet conforms to a minimal surface with zero mean curvature, like the physical model of soap films. RESULTS: We here suggest that the stability of a residue in the all beta-sheet proteins can be measured with its mean curvature parameter, using discrete differential geometry. The sharply decreasing mean curvature with increasing number of beta-strands identifies a significant cooperative effect whereby the interstrand interaction increases in strength with the number of beta-strands. Furthermore, strong correlations of mean curvatures with previous beta-sheet propensities of amino acids show that their intrinsic differences in adopting the ideal beta-sheet structure are affected by the water-accessible area of side-chains, and result in the distinct statistical and thermodynamic beta-sheet propensities. Therefore, we conclude that mean curvature should be considered as the significant stability index of a beta-sheet structure.     

Intrinsically bent DNA in replication origins and gene promoters

Intrinsically bent DNA is an alternative conformation of the DNA molecule caused by the presence of dA/dT tracts, 2 to 6 bp long, in a helical turn phase DNA or with multiple intervals of 10 to 11 bp. Other than flexibility, intrinsic bending sites induce DNA curvature in particular chromosome regions such as replication origins and promoters. Intrinsically bent DNA sites are important in initiating DNA replication, and are sometimes found near to regions associated with the nuclear matrix. Many methods have been developed to localize bent sites, for example, circular permutation, computational analysis, and atomic force microscopy. This review discusses intrinsically bent DNA sites associated with replication origins and gene promoter regions in prokaryote and eukaryote cells. We also describe methods for identifying bent DNA sites for circular permutation and computational analysis.     

Why is the denaturation process of super-helical DNA so uncooperative?

A theoretical model is proposed for the helix-coil transition in circular covalently closed DNA. In the melting interval the topological constrains for such a molecule are considered to affect both the inner state of the melted regions and the spatial configuration of the whole molecule ("writhing"). A good agreement is achieved between the theoretically calculated and experimentally obtained parameters of the denaturation process. A conclusion is drawn, that at the early stages of thermodenaturation (approximately till the transition midpoint) the effect of topological constrains is realised mainly through the writhing of the molecule. The denatured regions exist in the form of relaxed loops.     

Anisotropic elastic bending models of DNA

Simplified elastic rod models of DNA were developed in which the rigidity of DNA is sequence dependent and asymmetrical, i.e. the bending is facilitated towards the major groove. By subjecting the models to bending load in various directions perpendicular to the longitudinal axis of DNA, the bending deformation and the average conformation of the models can be estimated using finite element methods. Intrinsically curved sequence motifs [(aaaattttgc)_n, (tctctaaaaaatatataaaaa)_n] are found to be curved by this modelling procedure whereas the average conformation of homopolymers and straight motifs [(a)_n, (atctaatctaacacaacaca)_n] show negligible or no curvature. This suggests that sequence dependent asymmetric rigidity of DNA can provide an explanation in itself for intrinsic DNA curvature. The average rigidity of various DNA sequences was calculated and a good correlation was found with such quantities as the free energy change upon the binding of the Cro repressor, the base stacking energy and the thermal fluctuations at room temperature.     

A Possible Role of DNA Superstructures in Genome Evolution

The concept of DNA as a simple repository of the gene information has changed in that of a polymorphic macromolecule, which plays a relevant part in the management of the complex biochemical transformations in living matter. As a consequence of the slight stereochemical differences between base pairs, the direction of the DNA double helix axis undergoes deterministic writhing. A useful representation of such sequence-dependent structural distortions is the curvature diagram. Here, it is reported as an evolution simulation obtained by extensive point mutations along a biologically important DNA tract. The curvature changes, consequence of the point mutations. were compared to the related experimental gel electrophoresis mobility. The curvature of most mutants decreases and the mobility increases accordingly, suggesting the curvature of that tract is genetically selected. Moreover, DNA images by scanning force microscopy, show evidence of a sequence-dependent adhesion of curved DNA tracts to inorganic crystal surfaces. In particular, mica shows a large affinity towards the TT-rich dinucleotide sequences. This suggests a possible mechanism of selection of curved DNA regions, characterized by AA.TT dinucleotides in phase with double-helical periodicity, in the very early evolution steps.