DNA,Flexibly Flexible

Investigators have constructed dsDNA molecules with several different base modifications and have characterized their bending and twisting flexibilities using atomic force microscopy, DNA ring closure, and single-molecule force spectroscopy with optical tweezers. The three methods provide persistence length measurements that agree semiquantitatively, and they show that the persistence length is surprisingly similar for all of the modified DNAs. The circular dichroism spectra of modified DNAs differ substantially. Simple explanations based on base stacking strength, polymer charge, or groove occupancy by functional groups cannot explain the results, which will guide further high-resolution theory and experiments.Real double-stranded DNA molecules differ from the idealized zero-Kelvin A, B, and Z forms. They can adopt deformed average conformations, as in bent A-tract DNA or protein-DNA complexes. The path of the DNA helix axis also varies due to thermal energy, so at very long lengths DNA behaves as a random coil. The term “long lengths” is relative to the persistence length P of the wormlike chain model. P is the average offset of the end of a chain along its initial direction, or alternatively the length over which the unit vectors μ1→ and μ2→ tangent to the helix axis lose colinearity according to〈μ1→⋅μ2→〉=〈cosθ〉=e−d12/P,where d₁₂ is the contour length from point 1 to point 2, as in Fig. 1. P can be measured by hydrodynamics (1), atomic force microscopy (AFM) (2), DNA ring closure (3) or protein-DNA looping (4), tethered particle microscopy (5), or single-molecule optical tweezers experiments (6). The long-range loss of memory of DNA direction grows out of local variations in the helix axis direction specified by roll, tilt, and twist angles that parameterize changes in the helix axis direction. For harmonic bending potentials, the bending persistence length is related to roll and tilt according toσroll2+σtilt2=2ℓ/P,where ℓ = 3.4 Å, so for P ∼ 50 nm (147 bp) the average standard deviations in the roll and tilt angles σ_roll and σ_tilt are ∼4.7°, although in real DNA, roll varies more than tilt. Similar relationships hold for twist flexibility (7).Open in a separate windowFigure 1The base modifications studied by Peters et al. (13,14) affect both Watson-Crick hydrogen bonding and groove occupancy. They used AFM, DNA ring closure, single-molecule force spectroscopy, and circular dichroism spectroscopy (not shown) to characterize the resulting changes in bending and twisting flexibility. DNA molecules are not shown to scale. To see this figure in color, go online.DNA flexibility can be studied at contour length scales from Ångstroms to microns. Flexibility at the atomic scale accessed by nuclear magnetic resonance, x-ray crystallography, cryo-electron microscopy, and molecular dynamics simulations (8) refers to many aspects of conformational variability. One active thread of research at this scale concerns interconversion among helical forms, base flipping, DNA kinking, changes in backbone torsion angles, and the sequence dependence of all of these local properties. Local fluctuations in the basepair roll, tilt, and twist angles do seem to predict the correct long-range behavior (9). A second thread asks whether the wormlike chain model holds at DNA lengths shorter than P (2,10); the active controversy concerning enhanced bendability at short lengths has recently been reviewed by Vologodskii and Frank-Kamenetskii (11). A third thread asks whether we can understand the underlying biophysical causes of long-range DNA flexibility. These presumably include base stacking, electrostatic repulsion along the backbone, changes in the counterion atmosphere (12), occupancy of the major and minor grooves by functional groups, conformational entropy, the strength of Watson-Crick hydrogen bonding, and water structure. Helical polymorphisms and the junctions between polymorphs presumably affect the sequence dependence of the persistence length.Peters et al. (13,14) have attempted to understand bending and twisting flexibility by characterizing a variety of modified nucleic acids using DNA ring closure, AFM, and optical tweezer methods, sketched in Fig. 1. In previous work (13), they used ring closure to show that major groove substituents that alter the charge on the polymer do not have substantial effects on the bending persistence length, and that the effects were not correlated in an obvious way to the stacking propensity of the modified bases. The work described in this issue of the Biophysical Journal (14) uses all three methods to demonstrate that DNA with 2-amino-adenosine (a.k.a., 2,6-diaminopurine) substituted for adenosine has an increased persistence length, whereas inosine substitution for guanosine reduces the persistence length, as would be expected if groove occupancy (or the number of Watson-Crick hydrogen bonds) affects flexibility. However, the authors did one experiment too many—when they measured the effects of the earlier major groove substituents (13) using AFM, the correlation with groove occupancy disappeared. This could be because changes in helical geometry, as evidenced by the circular dichroism spectroscopy also reported in the article, alter the grooves sufficiently to prevent a straightforward connection to flexibility.The magnitude of the effect of base modifications on P is the largest for the optical tweezers and the smallest for DNA ring closure, showing that no more than one of the experiments is perfect. The Supporting Material for both articles (13,14) offers valuable resources for the careful evaluation of experimental results and possible sources of error within and between experiments. For example, the DNA lengths and the ionic conditions required by the different methods differ. Ring closure results depend critically on the purity of the DNA and appropriate ligation conditions. Analysis of AFM results averaged several different statistical measures of decaying angular correlations and end-to-end distance, which did not individually always agree. In force spectroscopy there are variations in the bead attachment for each molecule, errors in the stretch modulus can affect the measured persistence length, force can induce DNA melting, and very few molecules can be observed. Rare kinking events proposed to explain enhanced bendability should affect the cyclization experiment most markedly; no evidence for enhanced flexibility was seen. Finally, Peters et al. (14) have observed that DNA twist and twisting flexibility seem to be more sensitive than the persistence length to base modifications.Taken as a whole, this extremely thorough series of experiments shows that we still do not understand the fundamental origins of the remarkable stiffness of double-stranded DNA. There may be compensating effects that make the dissection difficult. For example, changing the charge on the polymer may induce a corresponding adjustment in the counterion condensation atmosphere, leading to a relatively constant residual charge. Groove substituents that enhance basepair stability could enhance bendability for steric reasons. Stacking thermodynamics may not change very much for the very small bend angles at any individual basepair. Locally stiff regions may introduce nearby junctions that are flexible.The stiffness of DNA relative to other biopolymers inspired the development of DNA nanotechnology (although that field has adopted bridged synthetic constructs that are even more rigid). Further research on the biophysics, and specifically the long-range mechanical properties of DNA, will be essential as we build better models of DNA in the cell, which has evolved many proteins that act to increase apparent flexibility. The various aspects of DNA flexibility influence the protein-DNA complexes that mediate DNA’s informational role, the induction of and responses to supercoiling used for long-range communication among sites (15), and chromosome structure and genome organization.     

Flexible docking of DNA fragments and actinocin derivatives

We have applied molecular docking methods to systems containing nucleic acids as targets and biologically active substances as ligands. The complexes of DNA fragments and actinocin derivatives with different lengths of aminoalkyl side chains were obtained by molecular docking. It was observed that actinocin derivatives could form energetically favourable complexes with DNA both as intercalators and minor groove binders. It was shown that small changes in the binding energy (～1?kcal/mol) could result in complexes with substantially different structure. The complexes of actinocin derivatives and DNA fragments were stabilized by hydrogen bonding upon intercalation and minor groove binding. It was found that the change of solvent-accessible surface area upon binding of the actinocin derivative to DNA linear increased with the growth of methylene groups' number in ligand side chains. The solvation energy change upon binding of actinocin derivatives to DNA calculated by the WSAS method was favourable in the case of small uncharged ligands and unfavourable for positively charged ligands.     

Nano-Scale Alignment of Proteins on a Flexible DNA Backbone

Nano-scale alignment of several proteins with freedom of motion is equivalent to an enormous increase in effective local concentration of proteins and will enable otherwise impossible weak and/or cooperative associations between them or with their ligands. For this purpose, a DNA backbone made of six oligodeoxynucleotide (ODN) chains is designed in which five double-stranded segments are connected by four single-stranded flexible linkers. A desired protein with an introduced cysteine is connected covalently to the 5′-end of azido-ODN by catalyst-free click chemistry. Then, six protein-ODN conjugates are assembled with their complementary nucleotide sequences into a single multi-protein-DNA complex, and six proteins are aligned along the DNA backbone. Flexible alignment of proteins is directly observed by high-speed AFM imaging, and association of proteins with weak interaction is demonstrated by fluorescence resonance energy transfer between aligned proteins.     

Flexible 5-guanidino-4-nitroimidazole DNA lesions: structures and thermodynamics

5-Guanidino-4-nitroimidazole (NI), derived from guanine oxidation by reactive oxygen and nitrogen species, contains an unusual flexible ring-opened structure, with nitro and guanidino groups which possess multiple hydrogen bonding capabilities. In vitro primer extension experiments with bacterial and mammalian polymerases show that NI incorporates C as well as A and G opposite the lesion, depending on the polymerase. To elucidate structural and thermodynamic properties of the mutagenic NI lesion, we have investigated the structure of the modified base itself and the NI-containing nucleoside with high-level quantum mechanical calculations and have employed molecular modeling and molecular dynamics simulations in solution for the lesion in B-DNA duplexes, with four partner bases opposite the NI. Our results show that NI adopts a planar structure at the damaged base level. However, in the nucleoside and in DNA duplexes, steric hindrance between the guanidino group and its linked sugar causes NI to be nonplanar. The NI lesion can adopt both syn and anti conformations on the DNA duplex level, with the guanidino group positioned in the DNA major and minor grooves, respectively; the specific preference depends on the partner base. On the basis of hydrogen bonding and stacking interactions, groove dimensions, and bending, we find that the least distorted NI-modified duplex contains partner C, consistent with observed incorporation of C opposite NI. However, hydrogen bonding interactions between NI and partner G or A are also found, which would be compatible with the observed mismatches.     

Flexible polymer-induced condensation and bundle formation of DNA and F-actin filaments

A simple semi-empirical theory is developed for the ionic strength dependence of the flexible polymer-induced condensation of semiflexible polyelectrolytes such as DNA and F-actin filaments. Critical concentrations of flexible polymer needed for condensation are calculated by comparing the free energies of inserting the semiflexible polyelectrolytes in a solution of flexible polymers, respectively, in their free state, and in their condensed state. Predictions of the theory are compared to experimental data on the condensation of DNA and F-actin filaments induced by the flexible polymer poly(ethylene oxide). The theory also predicts that reentrant decollapse is possible at low ionic strength and high concentrations of flexible polymer, as observed for DNA.     

Actin Filament Length Tunes Elasticity of Flexibly Cross-Linked Actin Networks

Networks of the cytoskeletal biopolymer actin cross-linked by the compliant protein filamin form soft gels that stiffen dramatically under shear stress. We demonstrate that the elasticity of these networks shows a strong dependence on the mean length of the actin polymers, unlike networks with small, rigid cross-links. This behavior is in agreement with a model of rigid filaments connected by multiple flexible linkers.     

A Simple,Flexible Failure Model

A new failure model is introduced in the form of a four-parameter nonlinear differential equation, with failure probability as the dependent variable and failure time as the independent variable. The first parameter characterizes the location, the second the scale, and the other two the shape of the model. The type of the accompanying hazard function is immediately read off the shape parameters. The new model approximates the classical failure models with rather high precision, but also models cases where the failure density is skewed to the left. It can be used to analyze survival data objectively, based on the shape of the failure distribution. The computation of quantiles and moments is easy and fast. Nonlinear regression methods are used to estimate parameter values.     

Flexible DNA target site recognition by divergent homing endonuclease isoschizomers I-CreI and I-MsoI

Homing endonucleases are highly specific catalysts of DNA strand breaks that induce the transposition of mobile intervening sequences containing the endonuclease open reading frame. These enzymes recognize long DNA targets while tolerating individual sequence polymorphisms within those sites. Sequences of the homing endonucleases themselves diversify to a great extent after founding intron invasion events, generating highly divergent enzymes that recognize similar target sequences. Here, we visualize the mechanism of flexible DNA recognition and the pattern of structural divergence displayed by two homing endonuclease isoschizomers. We determined structures of I-CreI bound to two DNA target sites that differ at eight of 22 base-pairs, and the structure of an isoschizomer, I-MsoI, bound to a nearly identical DNA target site. This study illustrates several principles governing promiscuous base-pair recognition by DNA-binding proteins, and demonstrates that the isoschizomers display strikingly different protein/DNA contacts. The structures allow us to determine the information content at individual positions in the binding site as a function of the distribution of direct and water-mediated contacts to nucleotide bases, and provide an evolutionary snapshot of endonucleases at an early stage of divergence in their target specificity.     

Improved Protocol for the Synthesis of Flexibly Protected Morpholino Monomers from Unprotected Ribonucleosides

An inexpensive and much improved protocol has been developed for the synthesis of protected morpholino monomers from unprotected ribonucleosides in high overall yield, using oxidative glycol cleavage and reductive amination strategy. Unlike the previous methods, the present strategy allows installing the exocyclic amine protections at a later stage, and thus avoids the use of expensive, or commercially unavailable, exocyclic amine-protected ribonucleosides as starting materials. To demonstrate the flexibility of the present method in choosing protecting groups, the monomers have been protected with several such groups of different deblocking properties at the exocyclic amine position.     

Production Capacity Modeling of Alternative, Nonidentical, Flexible Machines

Analyzing the production capacity of a flexible manufacturing system consisting of a number of alternative, nonidentical, flexible machines, where each machine is capable of producing several different part types simultaneously (by flexibly allocating its production capacity among these part types), is not a trivial task. The production capacity set of such a system is naturally expressed in terms of the machine-specific production rates of all part types. In this paper we also express it in terms of the total production rates of all part types over all machines. More specifically, we express the capacity set as the convex hull of a set of points corresponding to all possible assignments of machines to part types, where in each assignment each machine allocates all its capacity to only one part type. First, we show that within each subset of assignments having a given number of machines assigned to each part type, there is a unique assignment that corresponds to an extreme point of the capacity set. Then, we propose a procedure for generating all the extreme points and facets of the capacity set. Numerical experience shows that when the number of part types is less than four, the size of the capacity set (measured in terms of the number of variables times the number of constraints) is smaller, if the capacity set is expressed in terms of the total production rates of all part types over all machines than if it is expressed in terms of the machine-specific production rates of all part types. When the number of part types is four or more, however, the opposite is true.     

Flexible structural comparison allowing hinge-bending, swiveling motions

We present an efficient method for flexible comparison of protein structures, allowing swiveling motions. In all currently available methodologies developed and applied to the comparisons of protein structures, the molecules are considered to be rigid objects. The method described here extends and generalizes current approaches to searches for structural similarity between molecules by viewing proteins as objects consisting of rigid parts connected by rotary joints. During the matching, the rigid subparts are allowed to be rotated with respect to each other around swiveling points in one of the molecules. This technique straightforwardly detects structural motifs having hinge(s) between their domains. Whereas other existing methods detect hinge-bent motifs by initially finding the matching rigid parts and subsequently merging these together, our method automatically detects recurring substructures, allowing full 3 dimensional rotations about their swiveling points. Yet the method is extremely fast, avoiding the time-consuming full conformational space search. Comparison of two protein structures, without a predefinition of the motif, takes only seconds to one minute on a workstation per hinge. Hence, the molecule can be scanned for many potential hinge sites, allowing practically all C(alpha) atoms to be tried as swiveling points. This algorithm provides a highly efficient, fully automated tool. Its complexity is only O(n2), where n is the number of C(alpha) atoms in the compared molecules. As in our previous methodologies, the matching is independent of the order of the amino acids in the polypeptide chain. Here we illustrate the performance of this highly powerful tool on a large number of proteins exhibiting hinge-bending domain movements. Despite the motions, known hinge-bent domains/motifs which have been assembled and classified, are correctly identified. Additional matches are detected as well. This approach has been motivated by a technique for model based recognition of articulated objects originating in computer vision and robotics.     

Chimpanzees (Pan troglodytes) Flexibly Adjust Their Behaviour in Order to Maximize Payoffs,Not to Conform to Majorities

Chimpanzees have been shown to be adept learners, both individually and socially. Yet, sometimes their conservative nature seems to hamper the flexible adoption of superior alternatives, even to the extent that they persist in using entirely ineffective strategies. In this study, we investigated chimpanzees’ behavioural flexibility in two different conditions under which social animals have been predicted to abandon personal preferences and adopt alternative strategies: i) under influence of majority demonstrations (i.e. conformity), and ii) in the presence of superior reward contingencies (i.e. maximizing payoffs). Unlike previous nonhuman primate studies, this study disentangled the concept of conformity from the tendency to maintain one’s first-learned strategy. Studying captive (n=16) and semi-wild (n=12) chimpanzees in two complementary exchange paradigms, we found that chimpanzees did not abandon their behaviour in order to match the majority, but instead remained faithful to their first-learned strategy (Study 1a and 1b). However, the chimpanzees’ fidelity to their first-learned strategy was overridden by an experimental upgrade of the profitability of the alternative strategy (Study 2). We interpret our observations in terms of chimpanzees’ relative weighing of behavioural options as a function of situation-specific trade-offs. More specifically, contrary to previous findings, chimpanzees in our study abandoned their familiar behaviour to maximize payoffs, but not to conform to a majority.     

Epidemiological transitions, reproductive health, and the Flexible Response Model

In concert with improving standards of living since the mid-19th century, chronic and non-infectious diseases replaced infectious diseases as the major causes of mortality in more developed countries. Thus, economic development has been seen as one strategy to improve women's reproductive health. However, rates of two of the major contributors to women's illness, maternal mortality and breast cancer, do not correspond well with the level of economic development. Drawing upon our longitudinal study of reproductive functioning among rural Bolivians (Project Reproduction and Ecology in Provincia Aroma (REPA)), we propose an evolutionary model to explain variation in certain aspects of women's reproductive health. Our findings suggest new avenues of inquiry into the determinants of reproductive health and have implications for improving the well-being of women worldwide.     

Flexible structures of SIBLING proteins, bone sialoprotein, and osteopontin

Bone sialoprotein (BSP) and osteopontin (OPN) are two members of the SIBLING (Small Integrin-Binding LIgand, N-linked Glycoprotein) family of genetically related proteins that are clustered on human chromosome 4. We present evidence that this entire family is the result of duplication and subsequent divergent evolution of a single ancient gene. The solution structures of these two post-translationally modified recombinant proteins were solved by one dimensional proton NMR and transverse relaxation times. The polypeptide backbones of both free BSP and OPN rapidly sample an ensemble of conformations consistent with them both being completely unstructured in solution. This flexibility appears to enable these relatively small glycoproteins to rapidly associate with a number of different binding partners including other proteins as well as the mineral phase of bones and teeth. These proteins often function by bridging two proteins of fixed structures into a biologically active complex.