A Computer Graphics Study of Sequence-Directed Bending in DNA

Abstract

We present theoretical results to account for the unusual physical properties of a 423 bp DNA restriction fragment isolated from the kinetoplast of the trypanosomatid Leishmania tarentolae. This fragment has an anomalously low electrophoretic mobility in Polyacrylamide gels and a rotational relaxation time smaller than that of normally-behaved control fragments of the same molecular weight. Our earlier work (Proc. Natl. Acad. Sci. USA 79, 7664, 1982) has attributed these anomalies to the highly periodic distribution of the dinucleotide ApA in the DNA sequence. As originally proposed by Trifonov and Sussman (Proc. Natl. Acad. Sci. USA 77, 3816,1980) local features of the DNA structure such as a small bend at ApA, if repeated with the periodicity of the helix, will cause systematic bending of the molecule.

Computer graphics representations of DNA chain trajectories are presented for different structural models. It is shown that the structural model of Calladine (J. Mol. Biol. 161, 343, 1982) which is based on crystallographic data, is unsuccessful in predicting the systematic bending of DNA in solution.     

A Refined Prediction Method for Gel Retardation of DNA Oligonucleotides from Dinucleotide Step Parameters: Reconciliation of DNA Bending Models with Crystal Structure Data

Abstract

The development and assessment of a prediction method for gel retardation and sequence dependent curvature of DNA based on dinucleotide step parameters are described. The method is formulated using the Babcock-Olson equations for base pair step geometry (1) and employs Monte Carlo simulated annealing for parameter optimization against experimental data. The refined base pair step parameters define a structural construct which, when the width of observed parameter distributions is taken into account, is consistent with the results of DNA oligonucleotide crystal structures. The predictive power of the method is demonstrated and tested via comparisons with DNA bending data on sets of sequences not included in the training set, including A-tracts with and without periodic helix phasing, phased A₄T₄ and T₄A₄ motifs, a sequence with a phased GGGCCC motif, some “unconventional” helix phasing sequences, and three short fragments of kinetoplast DNA from Crithidia fasiculata that exhibit significantly different behavior on non-denaturing polyacrylamide gels. The nature of the structural construct produced by the methodology is discussed with respect to static and dynamic models of structure and representations of bending and bendability. An independent theoretical account of sequence dependent chemical footprinting results is provided. Detailed analysis of sequences with A-tract induced axis bending forms the basis for a critical discussion of the applicability of wedge models, junction models and non A-tract, general sequence models for understanding the origin of DNA curvature at the molecular level.     

Bending and flexibility of kinetoplast DNA

We have evaluated the extent of bending at an anomalous locus in DNA restriction fragments from the kinetoplast body of Leishmania tarentolae using transient electric dichroism to measure the rate of rotational diffusion of DNA fragments in solution. We compare the rate of rotational diffusion of two fragments identical in sequence except for circular permutation, which places the bend near the center in one case and near one end of the molecule in the other. Hydrodynamic theory was used to conclude that the observed 20% difference in rotational relaxation times is a consequence of an overall average bending angle of 84 +/- 6 degrees between the end segments of the fragment that contains the bending locus near its center. If it is assumed that bending results from structural dislocations at the junctions between oligo(dA).oligo(dT) tracts and adjacent segments of B DNA, a bend angle of 9 +/- 0.5 degrees at each junction is required to explain the observations. The extent of bending is little affected by ionic conditions and is weakly dependent on temperature. Comparison of one of the anomalous fragments with an electrophoretically normal control fragment leads to the conclusion that they differ measurably in apparent stiffness, consistent with a significantly increased persistence length or contour length in the kinetoplast fragments.     

Melting of DNA Oligomers: Dynamical Models and Comparison with Experimental Results

We compare experimental melting curves of short heterogeneous DNA oligomers with theoretical curves derived from statistical mechanics. Partition functions are computed with the one-dimensional Peyrard-Bishop (PB) Hamiltonian, already used in the study of the melting of long DNA chains. Working with short chains we take into account, in the computations, not only the breaking of the interstrand hydrogen bonds, but also the complete dissociation of the double helix into separate single strands. Since this dissociation equilibrium is of general relevance, independent of the particular microscopic model, we give some details of its treatment. We discuss how the non bonded three-dimensional interactions, not explicitly considered in the one-dimensional PB model, are taken into account through the treatment of the dissociation equilibrium. We also evaluate the relevance of the dissociation as a function of the chain length.     

Which Models Are Appropriate for Six Subtropical Forests: Species-Area and Species-Abundance Models

The species-area relationship is one of the most important topic in the study of species diversity, conservation biology and landscape ecology. The species-area relationship curves describe the increase of species number with increasing area, and have been modeled by various equations. In this paper, we used detailed data from six 1-ha subtropical forest communities to fit three species-area relationship models. The coefficient of determination and F ratio of ANOVA showed all the three models fitted well to the species-area relationship data in the subtropical communities, with the logarithm model performing better than the other two models. We also used the three species-abundance distributions, namely the lognormal, logcauchy and logseries model, to fit them to the species-abundance data of six communities. In this case, the logcauchy model had the better fit based on the coefficient of determination. Our research reveals that the rare species always exist in the six communities, corroborating the neutral theory of Hubbell. Furthermore, we explained why all species-abundance figures appeared to be left-side truncated. This was due to subtropical forests have high diversity, and their large species number includes many rare species.     

A Comparison of Predictive Phosphorus Load-Concentration Models for Lakes

Lake models that predict phosphorus (P) concentrations from P-loading have provided important knowledge enabling successful restoration of many eutrophic lakes during the last decades. However, the first-generation (static) models were rather imprecise and some nutrient abatement programs have therefore produced disappointingly modest results. This study compares 12 first-generation models with three newer ones. These newer models are dynamic (time-dependent), and general in the sense that they work without any further calibration for lakes from a wide limnological domain. However, static models are more accessible to non-specialists. Predictions of P concentrations were compared with empirical long-term data from a multi-lake survey, as well as to data from transient conditions in six lakes. Dynamic models were found to predict P concentrations with much higher certainty than static models. One general dynamic model, LakeMab, works for both deep and shallow lakes and can, in contrast to static models, predict P fluxes and particulate and dissolved P, both in surface waters and deep waters. PCLake, another general dynamic model, has advantages that resemble those of LakeMab, except that it needs three or four more input variables and is only valid for shallow lakes.     

Structural Basis of Stable Bending in DNA Containing An Tracts. Different Types of Bending

Abstract

Structural determinants of DNA bending of different types have been studied by theoretical conformational analysis of duplexes. Their terminal parts were fixed either in an ordinary low-energy B-like conformation or in “anomalous” conformations with a narrowed minor groove typical of A_n tracts. The anomalous conformations had different negative tilt angles (up to about zero), different propeller twists and minor groove widths. Calculations have been performed for DNA fragments A_nT_m, T_nA_m, A_nGCT_m, A_nCGT_m, T_mGCA_n, T_mCGA_n which are the models of the junction of two anomalous structures on A_n and T_m tracts. On the AT step of the A_nT_m fragment the minor groove can be easily narrowed so that a whole unbent fragment of anomalous structure is formed on A_n T_m. According to our energy estimates, there should not be any reliable bending on A_nT_m. In contrast, in all other cases there was a pronounced roll-like bending into the major groove in the chemical symmetry region. Calculations of the junction between the anomalous and ordinary B-like structure for G_nT_m and C_nA_m have shown that there is an equilibrium bending with a tilt component towards the chain having the anomalous structure at the 5′-end. From our calculations it is impossible to determine precisely the direction of bending, though it can be suggested that the roll component of bending might be directed towards the major groove. The anomalous structure is the main reason of bending; alternations of pyrimidines and purines can modulate the value and the direction of equilibrium bending (only the value in the case of self-complemantary fragments).

The results are consistent with the experimental data and promote a better understanding of the problem of DNA bending.     

Bending modes of DNA directly addressed by cryo-electron microscopy of DNA minicircles

We use cryo-electron microscopy (cryo-EM) to study the 3D shapes of 94-bp-long DNA minicircles and address the question of whether cyclization of such short DNA molecules necessitates the formation of sharp, localized kinks in DNA or whether the necessary bending can be redistributed and accomplished within the limits of the elastic, standard model of DNA flexibility. By comparing the shapes of covalently closed, nicked and gapped DNA minicircles, we conclude that 94-bp-long covalently closed and nicked DNA minicircles do not show sharp kinks while gapped DNA molecules, containing very flexible single-stranded regions, do show sharp kinks. We corroborate the results of cryo-EM studies by using Bal31 nuclease to probe for the existence of kinks in 94-bp-long minicircles.     

A Comparison of Continuous and Discrete-time West Nile Virus Models

The first recorded North American epidemic of West Nile virus was detected in New York state in 1999, and since then the virus has spread and become established in much of North America. Mathematical models for this vector-transmitted disease with cross-infection between mosquitoes and birds have recently been formulated with the aim of predicting disease dynamics and evaluating possible control methods. We consider discrete and continuous time versions of the West Nile virus models proposed by Wonham et al. [Proc. R. Soc. Lond. B 271:501–507, 2004] and by Thomas and Urena [Math. Comput. Modell. 34:771–781, 2001], and evaluate the basic reproduction number as the spectral radius of the next-generation matrix in each case. The assumptions on mosquito-feeding efficiency are crucial for the basic reproduction number calculation. Differing assumptions lead to the conclusion from one model [Wonham, M.J. et al., [Proc. R. Soc. Lond. B] 271:501–507, 2004] that a reduction in bird density would exacerbate the epidemic, while the other model [Thomas, D.M., Urena, B., Math. Comput. Modell. 34:771–781, 2001] predicts the opposite: a reduction in bird density would help control the epidemic.     

DNA Binding and Bending Protein-Based DNA Actuator and its Practical Realization

In the life forms, the biomolecules such as DNA and protein are interacting with each other to maintain their life activity. Simultaneously, these biomolecules form DNA–protein complexes; as a result, the life forms can adjust to the external environment and continue its life activities. Therefore, using these characteristics of the DNA recognition ability of proteins, the novel molecular devices can be established. Here, we show the application of DNA binding and bending protein for design of the DNA actuator and its practical realization. The single polypeptide chain integrated host factor 2 (scIHF2), which is a DNA binding and bending protein, was used to bind to and/or bend the specific domains of DNA. Using this protein and designing the sequences of DNA, mechanical-functionalized DNA-based biomolecular device could be fabricated. Using these mechanisms, DNA binding and bending proteins have great potentials for establishing the DNA actuator for nanobiotechnology and nanotechnology applications.     

Bending and flexibility of methylated and unmethylated EcoRI DNA

We used cyclization kinetics experiments and Monte Carlo simulations to determine a structural model for a DNA decamer containing the EcoRI restriction site. Our findings agree well with recent crystal and NMR structures of the EcoRI dodecamer, where an overall bend of seven degrees is distributed symmetrically over the molecule. Monte Carlo simulations indicate that the sequence has a higher flexibility, assumed to be isotropic, compared to that of a "generic" DNA sequence. This model was used as a starting point for the investigation of the effect of cytosine methylation on DNA bending and flexibility. While methylation did not affect bend magnitude or direction, it resulted in a reduction in bending flexibility and under-winding of the methylated nucleotides. We demonstrate that our approach can augment the understanding of DNA structure and dynamics by adding information about the global structure and flexibility of the sequence. We also show that cyclization kinetics can be used to study the properties of modified nucleotides.     

A Comparison of Computational Models for Eukaryotic Cell Shape and Motility

Eukaryotic cell motility involves complex interactions of signalling molecules, cytoskeleton, cell membrane, and mechanics interacting in space and time. Collectively, these components are used by the cell to interpret and respond to external stimuli, leading to polarization, protrusion, adhesion formation, and myosin-facilitated retraction. When these processes are choreographed correctly, shape change and motility results. A wealth of experimental data have identified numerous molecular constituents involved in these processes, but the complexity of their interactions and spatial organization make this a challenging problem to understand. This has motivated theoretical and computational approaches with simplified caricatures of cell structure and behaviour, each aiming to gain better understanding of certain kinds of cells and/or repertoire of behaviour. Reaction–diffusion (RD) equations as well as equations of viscoelastic flows have been used to describe the motility machinery. In this review, we describe some of the recent computational models for cell motility, concentrating on simulations of cell shape changes (mainly in two but also three dimensions). The problem is challenging not only due to the difficulty of abstracting and simplifying biological complexity but also because computing RD or fluid flow equations in deforming regions, known as a “free-boundary” problem, is an extremely challenging problem in applied mathematics. Here we describe the distinct approaches, comparing their strengths and weaknesses, and the kinds of biological questions that they have been able to address.     

Models of bacteriophage DNA packaging motors

An ATP-dependent motor drives a DNA genome into a bacteriophage capsid during morphogenesis of double-stranded DNA bacteriophages both in vivo and in vitro. The DNA molecule enters the capsid through a channel in the center of a symmetric protein ring called a connector. Mechanisms in two classes have been proposed for this motor: (1) An ATP-driven rotating connector pulls a DNA molecule via serial power strokes. (2) The connector rectifies DNA motion that is either thermal, biased thermal, or oscillating electrical field-induced (motor-ratchet hypothesis). Mechanisms in the first class have previously been proposed to explain the detailed structure of DNA packaging motors. The present study demonstrates that the motor-ratchet hypothesis also explains the current data, including data in the following categories: biochemical genetics, energetics, structure, and packaging dynamics.