DNA Curvature Research Articles

Intrinsic DNA curvature in trypanosomes

BackgroundTrypanosoma cruzi and Trypanosoma brucei are protozoan parasites causing Chagas disease and African sleeping sickness, displaying unique features of cellular and molecular biology. Remarkably, no canonical signals for RNA polymerase II promoters, which drive protein coding genes transcription, have been identified so far. The secondary structure of DNA has long been recognized as a signal in biological processes and more recently, its involvement in transcription initiation in Leishmania was proposed. In order to study whether this feature is conserved in trypanosomatids, we undertook a genome wide search for intrinsic DNA curvature in T. cruzi and T. brucei.ResultsUsing a region integrated intrinsic curvature (RIIC) scoring that we previously developed, a non-random distribution of sequence-dependent curvature was observed. High RIIC scores were found to be significantly correlated with transcription start sites in T. cruzi, which have been mapped in divergent switch regions, whereas in T. brucei, the high RIIC scores correlated with sites that have been involved not only in RNA polymerase II initiation but also in termination. In addition, we observed regions with high RIIC score presenting in-phase tracts of Adenines, in the subtelomeric regions of the T. brucei chromosomes that harbor the variable surface glycoproteins genes.ConclusionsIn both T. cruzi and T. brucei genomes, a link between DNA conformational signals and gene expression was found. High sequence dependent curvature is associated with transcriptional regulation regions. High intrinsic curvature also occurs at the T. brucei chromosome subtelomeric regions where the recombination processes involved in the evasion of the immune host system take place. These findings underscore the relevance of indirect DNA readout in these ancient eukaryotes.

Modulation of extracytoplasmic function (ECF) sigma factor promoter selectivity by spacer region sequence.

The ability of bacteria to adapt to stress depends on the conditional expression of specific sets of genes. Bacillus subtilis encodes seven extracytoplasmic function (ECF) sigma (σ) factors that regulate functions important for survival under conditions eliciting cell envelope stress. Of these, four have been studied in detail: σM, σW, σX and σV. These four σ factors recognize overlapping sets of promoters, although the sequences that determine this overlapping recognition are incompletely understood. A major role in promoter selectivity has been ascribed to the core −10 and −35 promoter elements. Here, we demonstrate that a homopolymeric T-tract motif, proximal to the −35 element, functions in combination with the core promoter sequences to determine selectivity for ECF sigma factors. This motif is most critical for promoter activation by σV, and contributes variably to activation by σM, σX and σW. We propose that this motif, which is a feature of the deduced promoter consensus for a subset of ECF σ factors from many species, imparts intrinsic DNA curvature to influence promoter activity. The differential effect of this region among ECF σ factors thereby provides a mechanism to modulate the nature and extent of regulon overlap.

Carcinogen susceptibility is regulated by genome architecture and predicts cancer mutagenesis.

The development of many sporadic cancers is directly initiated by carcinogen exposure. Carcinogens induce malignancies by creating DNA lesions (i.e., adducts) that can result in mutations if left unrepaired. Despite this knowledge, there has been remarkably little investigation into the regulation of susceptibility to acquire DNA lesions. In this study, we present the first quantitative human genome-wide map of DNA lesions induced by ultraviolet (UV) radiation, the ubiquitous carcinogen in sunlight that causes skin cancer. Remarkably, the pattern of carcinogen susceptibility across the genome of primary cells significantly reflects mutation frequency in malignant melanoma. Surprisingly, DNase-accessible euchromatin is protected from UV, while lamina-associated heterochromatin at the nuclear periphery is vulnerable. Many cancer driver genes have an intrinsic increase in carcinogen susceptibility, including the BRAF oncogene that has the highest mutation frequency in melanoma. These findings provide a genome-wide snapshot of DNA injuries at the earliest stage of carcinogenesis. Furthermore, they identify carcinogen susceptibility as an origin of genome instability that is regulated by nuclear architecture and mirrors mutagenesis in cancer.

DNA structural features of eukaryotic TATA‐containing and TATA‐less promoters

Eukaryotic genes can be broadly classified as TATA‐containing and TATA‐less based on the presence of TATA box in their promoters. Experiments on both classes of genes have revealed a disparity in the regulation of gene expression and cellular functions between the two classes. In this study, we report characteristic differences in promoter sequences and associated structural properties of the two categories of genes in six different eukaryotes. We have analyzed three structural features, DNA duplex stability, bendability, and curvature along with the distribution of A‐tracts, G‐quadruplex motifs, and CpG islands. The structural feature analyses reveal that while the two classes of gene promoters are distinctly different from each other, the properties are also distinguishable across the six organisms.

Analyzing DNA curvature and its impact on the ionic environment: application to molecular dynamics simulations of minicircles.

We propose a method for analyzing the magnitude and direction of curvature within nucleic acids, based on the curvilinear helical axis calculated by Curves+. The method is applied to analyzing curvature within minicircles constructed with varying degrees of over- or under-twisting. Using the molecular dynamics trajectories of three different minicircles, we are able to quantify how curvature varies locally both in space and in time. We also analyze how curvature influences the local environment of the minicircles, notably via increased heterogeneity in the ionic distributions surrounding the double helix. The approach we propose has been integrated into Curves+ and the utilities Canal (time trajectory analysis) and Canion (environmental analysis) and can be used to study a wide variety of static and dynamic structural data on nucleic acids.

Quaternion modeling of the helical path for analysis of the shape of the DNA molecule

The three­dimensional shape of a DNA molecule is a key property influencing its functional specificity and the nature of its molecular interactions. The characteristic shape into which a DNA molecule folds under certain conditions is a manifestation of its micromechanical and structural features, which are sequence­dependent. DNA shape­related properties can there fore be determined in a predictable manner. A number of models have been designed to describe intrinsic DNA curvature, incorporating a set of helical parameters which can be applied to operative three­dimensional reconstruction of the DNA structures. Alternatively, desired base pair parameters can be computed based on publicly available information about atomic DNA structures. Further, taking the base pairs as rigid bodies, their relative location in space can be estimated based on these parameters. Matrices are a common method to implement any rigid body transformations and are widely used in the modeling of DNA structures. Quaternions are the more straightforward and robust alternative for matrices. Unit quaternions can represent only a rotation, whereas dual quaternions combine rotation and translation into a single state. In the present guide, the algebra of unit and dual quaternions is applied for the first time to modeling of the DNA helical path, based on conformational parameters of the base pair steps. Although dual quaternions are preferable for modeling of DNA structure in detail, the use of unit quaternions is sufficient to predict the DNA trajectory and all calculations of DNA shape features. In order to analyze DNA shape and chain sta ­ tistics, and predict the micromechanical properties of DNA molecules based on coordinates of the helical path, the widely used as well as original algorithms for computing DNA curvature, radius of gyration, persistence length and phasing of DNA bends are described. Taken together, these algorithms will be useful both in the in silico analysis of relatively short DNA fragments as well as in topological mapping of whole genomes.

DNA minicircles clarify the specific role of DNA structure on retroviral integration.

Chromatin regulates the selectivity of retroviral integration into the genome of infected cells. At the nucleosome level, both histones and DNA structure are involved in this regulation. We propose a strategy that allows to specifically study a single factor: the DNA distortion induced by the nucleosome. This strategy relies on mimicking this distortion using DNA minicircles (MCs) having a fixed rotational orientation of DNA curvature, coupled with atomic-resolution modeling. Contrasting MCs with linear DNA fragments having identical sequences enabled us to analyze the impact of DNA distortion on the efficiency and selectivity of integration. We observed a global enhancement of HIV-1 integration in MCs and an enrichment of integration sites in the outward-facing DNA major grooves. Both of these changes are favored by LEDGF/p75, revealing a new, histone-independent role of this integration cofactor. PFV integration is also enhanced in MCs, but is not associated with a periodic redistribution of integration sites, thus highlighting its distinct catalytic properties. MCs help to separate the roles of target DNA structure, histone modifications and integrase (IN) cofactors during retroviral integration and to reveal IN-specific regulation mechanisms.

DNA Sequence Determinants Controlling Affinity, Stability and Shape of DNA Complexes Bound by the Nucleoid Protein Fis.

The abundant Fis nucleoid protein selectively binds poorly related DNA sequences with high affinities to regulate diverse DNA reactions. Fis binds DNA primarily through DNA backbone contacts and selects target sites by reading conformational properties of DNA sequences, most prominently intrinsic minor groove widths. High-affinity binding requires Fis-stabilized DNA conformational changes that vary depending on DNA sequence. In order to better understand the molecular basis for high affinity site recognition, we analyzed the effects of DNA sequence within and flanking the core Fis binding site on binding affinity and DNA structure. X-ray crystal structures of Fis-DNA complexes containing variable sequences in the noncontacted center of the binding site or variations within the major groove interfaces show that the DNA can adapt to the Fis dimer surface asymmetrically. We show that the presence and position of pyrimidine-purine base steps within the major groove interfaces affect both local DNA bending and minor groove compression to modulate affinities and lifetimes of Fis-DNA complexes. Sequences flanking the core binding site also modulate complex affinities, lifetimes, and the degree of local and global Fis-induced DNA bending. In particular, a G immediately upstream of the 15 bp core sequence inhibits binding and bending, and A-tracts within the flanking base pairs increase both complex lifetimes and global DNA curvatures. Taken together, our observations support a revised DNA motif specifying high-affinity Fis binding and highlight the range of conformations that Fis-bound DNA can adopt. The affinities and DNA conformations of individual Fis-DNA complexes are likely to be tailored to their context-specific biological functions.

Boundary conditions for free A-DNA in solution and the relation of local to global DNA structures at reduced water activity

Because of repeated claims that A-DNA cannot exist without aggregation or condensation, the state of DNA restriction fragments with 84–859 bp has been analyzed in aqueous solutions upon reduction of the water activity. Rotational diffusion times τd measured by electric dichroism at different water activities with a wide variation of viscosities are normalized to values τc at the viscosity of water, which indicate DNA structures at a high sensitivity. For short helices (chain lengths {ell} ≤ persistence length p), cooperative formation of A-DNA is reflected by the expected reduction of the hydrodynamic length; the transition to the A-form is without aggregation or condensation upon addition of ethanol at monovalent salt ≤1 mM. The aggregation boundary, indicated by a strong increase of τc, is shifted to higher monovalent salt (≥4 mM) when ethanol is replaced by trifluoroethanol. The BA transition is not indicated anymore by a cooperative change of τc for {ell} » p; τc values for these long chains decrease upon reduction of the water activity continuously over the full range, including the BA transition interval. This suggests a non-cooperative BC transition, which induces DNA curvature. The resulting wide distribution of global structures hides changes of local length during the BA transition. Free A-DNA without aggregation/condensation is found at low-salt concentrations where aggregation is inhibited and/or very slow. In an intermediate range of solvent conditions, where the A-form starts to aggregate, a time window remains that can be used for analysis of free A-DNA in a quasi-equilibrium state.

Novel alleles of the VERNALIZATION1 genes in wheat are associated with modulation of DNA curvature and flexibility in the promoter region.

BackgroundIn wheat, the vernalization requirement is mainly controlled by the VRN genes. Different species of hexaploid and tetraploid wheat are widely used as genetic source for new mutant variants and alleles for fundamental investigations and practical breeding programs. In this study, VRN-A1 and VRN-B1 were analysed for 178 accessions representing six tetraploid wheat species (Triticum dicoccoides, T. dicoccum, T. turgidum, T. polonicum, T. carthlicum, T. durum) and five hexaploid species (T. compactum, T. sphaerococcum, T. spelta, T. macha, T. vavilovii).ResultsNovel allelic variants in the promoter region of VRN-A1 and VRN-B1 were identified based on the change in curvature and flexibility of the DNA molecules. The new variants of VRN-A1 (designated as Vrn-A1a.2, Vrn-A1b.2 – Vrn-A1b.6 and Vrn-A1i) were found to be widely distributed in hexaploid and tetraploid wheat, and in fact were predominant over the known VRN-A1 alleles. The greatest diversity of the new variants of VRN-B1 (designated as VRN-B1.f, VRN-B1.s and VRN-B1.m) was found in the tetraploid and some hexaploid wheat species.For the first time, minor differences within the sequence motif known as the VRN-box of VRN1 were correlated with wheat growth habit. Thus, vrn-A1b.3 and vrn-A1b.4 were revealed in winter wheat in contrast to Vrn-A1b.2, Vrn-A1b.5, Vrn-A1b.6 and Vrn-A1i. It was found that single nucleotide mutation in the VRN-box can influence the vernalization requirement and growth habit of wheat. Our data suggest that both the A-tract and C-rich segment within the VRN-box contribute to its functionality, and provide a new view of the hypothesised role of the VRN-box in regulating transcription of the VRN1 genes. Specifically, it is proposed that combination of mutations in this region can modulate vernalization sensitivity and flowering time of wheat.ConclusionsNew allelic variants of the VRN-A1 and VRN-B1 genes were identified in hexaploid and tetraploid wheat. Mutations in A-tract and C-rich segments within the VRN-box of VRN-A1 are associated with modulation of the vernalization requirement and flowering time. New allelic variants will be useful in fundamental investigations into the regulation of VRN1 expression, and provide a valuable genetic resource for practical breeding of wheat.Electronic supplementary materialThe online version of this article (doi:10.1186/s12870-015-0691-2) contains supplementary material, which is available to authorized users.

Conserved Curvature of RNA Polymerase I Core Promoter Beyond rRNA Genes: The Case of the Tritryps

In trypanosomatids, the RNA polymerase I (RNAPI)-dependent promoters controlling the ribosomal RNA (rRNA) genes have been well identified. Although the RNAPI transcription machinery recognizes the DNA conformation instead of the DNA sequence of promoters, no conformational study has been reported for these promoters. Here we present the in silico analysis of the intrinsic DNA curvature of the rRNA gene core promoters in Trypanosoma brucei, Trypanosoma cruzi, and Leishmania major. We found that, in spite of the absence of sequence conservation, these promoters hold conformational properties similar to other eukaryotic rRNA promoters. Our results also indicated that the intrinsic DNA curvature pattern is conserved within the Leishmania genus and also among strains of T. cruzi and T. brucei. Furthermore, we analyzed the impact of point mutations on the intrinsic curvature and their impact on the promoter activity. Furthermore, we found that the core promoters of protein-coding genes transcribed by RNAPI in T. brucei show the same conserved conformational characteristics. Overall, our results indicate that DNA intrinsic curvature of the rRNA gene core promoters is conserved in these ancient eukaryotes and such conserved curvature might be a requirement of RNAPI machinery for transcription of not only rRNA genes but also protein-coding genes.

Insights into the interaction between Cren7 and DNA: the role of loop β3-β4.

Sulfolobus synthesizes large amounts of small chromatin proteins Cren7 and Sul7d. The two proteins share overall structural similarity, but differ distinctly in the DNA-binding region between β3- and β4-strands. While Sul7d possesses a hinge of two amino acid residues, Cren7 contains a flexible seven-residue loop (loop β3-β4) in the region. Here, we report the role of loop β3-β4 in the interaction of Cren7 with duplex DNA. We show that all residues with a large side chain on the loop, i.e., Pro30, Lys31, Arg33 and Lys34, contributed significantly to the binding of Cren7 to DNA. The three basic amino acids affected the ability of Cren7 to constrain negative DNA supercoils in a residue number-dependent manner. The crystal structure of a complex between a mutant Cren7 protein (GR) with loop β3-β4 replaced by two residues (Gly and Arg) to mimic the hinge at the corresponding position in Sul7d and an 8-bp dsDNA has been determined. Structural comparison between the GR-DNA and Cren7-DNA complexes shows that GR resembles Sul7d more than Cren7 in DNA-binding size and in the effect on the width of the major groove of DNA and the pattern of DNA bending. However, GR induces smaller DNA curvature than Sul7d. Our results suggest that Cren7 and Sul7d package chromosomal DNA in a slightly different fashion, presumably permitting different chromosomal accessibility by proteins functioning in DNA transactions.

Unraveling the Structural, Dynamic, Thermodynamic, and Kinetic Heterogeneity in DNA Site Recognition by Structurally Homologous ETS Transcription Factors

Despite increasing awareness of their biological importance, mechanisms of DNA site discrimination by structurally homologous and functionally non-redundant transcription factors remain poorly defined concepts. Members of the ETS family of transcription factors, which regulate the differentiation of hematopoietic stem cells to the gamut of blood cell lineages, exemplify this conundrum. While the ETS-family members PU.1 and Ets-1 share structurally superimposable DNA-binding domains, the two homologs direct distinct cohorts of genes and induce mutually exclusive outcomes in hematopoietic cell-fate decisions. Using an array of biochemical, spectroscopic, and calorimetric techniques, we have compared DNA site recognition by PU.1 and Ets-1. The data indicate a startling level of structural, dynamic, thermodynamic, and kinetic heterogeneity associated with DNA site recognition by these proteins, which may be traced to their differential coupling of molecular hydration and counter-ion release with site-specific binding. Whereas site recognition by Ets-1 appears homogeneous with respect to DNA sequence identity, high- and low-affinity sites unmask major heterogeneity in PU.1 binding by all experimental observations. These differences are intrinsic to the two homologous DNA-binding domains; additional intramolecular interactions in adjacent domains exert no effect on the apparent homogeneity in Ets-1/DNA binding. The emerging evidence suggests a strong coupling between molecular hydration, DNA curvature, conformational dynamics, electrostatics as a mechanism for PU.1 to enforce different sequence preferences and kinetic behavior relative to Ets-1, and offer new insight into the functional differences between the two homologs. [This investigation is supported by NIH R15GM112002-01 to GMKP, NIH R01AI083803 to JKB, and NSF MCB1411502 to GMKP and WDW.]

Coarse-grained modeling of DNA curvature.

The interaction of DNA with proteins occurs over a wide range of length scales, and depends critically on its local structure. In particular, recent experimental work suggests that the intrinsic curvature of DNA plays a significant role on its protein-binding properties. In this work, we present a coarse grained model of DNA that is capable of describing base-pairing, hybridization, major and minor groove widths, and local curvature. The model represents an extension of the recently proposed 3SPN.2 description of DNA [D. M. Hinckley, G. S. Freeman, J. K. Whitmer, and J. J. de Pablo, J. Chem. Phys. 139, 144903 (2013)], into which sequence-dependent shape and mechanical properties are incorporated. The proposed model is validated against experimental data including melting temperatures, local flexibilities, dsDNA persistence lengths, and minor groove width profiles.

Search by proteins for their DNA target site: 1. The effect of DNA conformation on protein sliding.

The recognition of DNA-binding proteins (DBPs) to their specific site often precedes by a search technique in which proteins slide, hop along the DNA contour or perform inter-segment transfer and 3D diffusion to dissociate and re-associate to distant DNA sites. In this study, we demonstrated that the strength and nature of the non-specific electrostatic interactions, which govern the search dynamics of DBPs, are strongly correlated with the conformation of the DNA. We tuned two structural parameters, namely curvature and the extent of helical twisting in circular DNA. These two factors are mutually independent of each other and can modulate the electrostatic potential through changing the geometry of the circular DNA conformation. The search dynamics for DBPs on circular DNA is therefore markedly different compared with linear B-DNA. Our results suggest that, for a given DBP, the rotation-coupled sliding dynamics is precluded in highly curved DNA (as well as for over-twisted DNA) because of the large electrostatic energy barrier between the inside and outside of the DNA molecule. Under such circumstances, proteins prefer to hop in order to explore interior DNA sites. The change in the balance between sliding and hopping propensities as a function of DNA curvature or twisting may result in different search efficiency and speed.

Search by proteins for their DNA target site: 2. The effect of DNA conformation on the dynamics of multidomain proteins.

Multidomain transcription factors, which are especially abundant in eukaryotic genomes, are advantageous to accelerate the search kinetics for target site because they can follow the intersegment transfer via the monkey-bar mechanism in which the protein forms a bridged intermediate between two distant DNA regions. Monkey-bar dynamics highly depends on the properties of the multidomain protein (the affinity of each of the constituent domains to the DNA and the length of the linker) and the DNA molecules (their inter-distance and inter-angle). In this study, we investigate using coarse-grained molecular dynamics simulations how the local conformation of the DNA may affect the DNA search performed by a multidomain protein Pax6 in comparison to that of the isolated domains. Our results suggest that in addition to the common rotation-coupled translation along the DNA major groove, for curved DNA the tethered domains may slide in a rotation-decoupled sliding mode. Furthermore, the multidomain proteins move by longer jumps on curved DNA compared with those performed by the single domain protein. The long jumps originate from the DNA curvature bringing two sequentially distant DNA sites into close proximity with each other and they suggest that multidomain proteins may move on highly curved DNA faster than linear DNA.

A functional variant in the 5'-flanking region of the chicken serotonin transporter gene is associated with increased body weight and locomotor activity.

In this study, we identified a polymorphism in the 5'-flanking region of the chicken serotonin transporter (5-HTT) gene. Sequencing analysis revealed that in comparison with the wild-type variant (W), a deleted variant (D) is generated by deletion of four nucleotides (5'-AATT-3') and a single nucleotide change (A→T). Using a polyacrylamide gel electrophoresis system, we found that the 360-bp DNA fragment containing the W variant with the wild-type sequence 5'-AATTAATT-3' shows intrinsic DNA curvature while the 356-bp fragment containing the D variant lacking the four base pairs AATT is not curved. Quantitative real-time RT-PCR and ELISA demonstrated that the expression of 5-HTT in D/D chickens was higher than that in W/W and W/D chickens. In addition, transient transfection experiments with chloramphenicol acetyltransferase reporter gene constructs revealed increased 5-HTT promoter activity mediated by the D variant and a silencer activity of the W variant. Interestingly, females and males with D/D genotype showed significant greater increase in body weight from 6 weeks and 16 weeks of age, respectively, and higher body mass index. Moreover, we found that D/D chickens of both genders were physically more active than W/W and W/D chickens.

Investigating the Interplay between Nucleoid-Associated Proteins, DNA Curvature, and CRISPR Elements Using Comparative Genomics

Many prokaryotic and eukaryotic genomes feature a characteristic periodic signal in distribution of short runs of A or T (A-tracts) phased with the DNA helical period of ∼10–11 bp. Such periodic spacing of A-tracts has been associated with intrinsic DNA curvature. In eukaryotes, this periodicity is a major component of the nucleosome positioning signal but its physiological role in prokaryotes is not clear. One hypothesis centers on possible role of intrinsic DNA bends in nucleoid compaction. We use comparative genomics to investigate possible relationship between the A-tract periodicity and nucleoid-associated proteins in prokaryotes. We found that genomes with DNA-bridging proteins tend to exhibit stronger A-tract periodicity, presumably indicative of more prevalent intrinsic DNA curvature. A weaker relationship was detected for nucleoid-associated proteins that do not form DNA bridges. We consider these results an indication that intrinsic DNA curvature acts collaboratively with DNA-bridging proteins in maintaining the compact structure of the nucleoid, and that previously observed differences among prokaryotic genomes in terms DNA curvature-related sequence periodicity may reflect differences in nucleoid organization. We subsequently investigated the relationship between A-tract periodicity and presence of CRISPR elements and we found that genomes with CRISPR tend to have stronger A-tract periodicity. This result is consistent with our earlier hypothesis that extensive A-tract periodicity could help protect the chromosome against integration of prophages, possibly due to its role in compaction of the nucleoid.

Assessing Diversity of DNA Structure-Related Sequence Features in Prokaryotic Genomes

Prokaryotic genomes are diverse in terms of their nucleotide and oligonucleotide composition as well as presence of various sequence features that can affect physical properties of the DNA molecule. We present a survey of local sequence patterns which have a potential to promote non-canonical DNA conformations (i.e. different from standard B-DNA double helix) and interpret the results in terms of relationships with organisms' habitats, phylogenetic classifications, and other characteristics. Our present work differs from earlier similar surveys not only by investigating a wider range of sequence patterns in a large number of genomes but also by using a more realistic null model to assess significant deviations. Our results show that simple sequence repeats and Z-DNA-promoting patterns are generally suppressed in prokaryotic genomes, whereas palindromes and inverted repeats are over-represented. Representation of patterns that promote Z-DNA and intrinsic DNA curvature increases with increasing optimal growth temperature (OGT), and decreases with increasing oxygen requirement. Additionally, representations of close direct repeats, palindromes and inverted repeats exhibit clear negative trends with increasing OGT. The observed relationships with environmental characteristics, particularly OGT, suggest possible evolutionary scenarios of structural adaptation of DNA to particular environmental niches.

Total positive curvature of circular DNA

The properties of double-stranded DNA and other chiral molecules depend on the local geometry, i.e., on curvature and torsion, yet the paths of closed chain molecules are globally restricted by topology. When both of these characteristics are to be incorporated in the description of circular chain molecules, e.g., plasmids, it is shown to have implications for the total positive curvature integral. For small circular micro-DNAs it follows as a consequence of Fenchel's inequality that there must exist a minimum length for the circular plasmids to be double stranded. It also follows that all circular micro-DNAs longer than the minimum length must be concave, a result that is consistent with typical atomic force microscopy images of plasmids. Predictions for the total positive curvature of circular micro-DNAs are given as a function of length, and comparisons with circular DNAs from the literature are presented.