Theory of DNA condensation: collapse versus aggregation

ISWI catalyzes nucleosome sliding in condensed nucleosome arrays

How chromatin enzymes work in condensed chromatin and how they maintain diffusional mobility inside remains unexplored. Here we investigated these challenges using the Drosophila ISWI remodeling ATPase, which slides nucleosomes along DNA. Folding of chromatin fibers did not affect sliding in vitro. Catalytic rates were also comparable in- and outside of chromatin condensates. ISWI cross-links and thereby stiffens condensates, except when ATP hydrolysis is possible. Active hydrolysis is also required for ISWI's mobility in condensates. Energy from ATP hydrolysis therefore fuels ISWI's diffusion through chromatin and prevents ISWI from cross-linking chromatin. Molecular dynamics simulations of a 'monkey-bar' model in which ISWI grabs onto neighboring nucleosomes, then withdraws from one before rebinding another in an ATP hydrolysis-dependent manner, qualitatively agree with our data. We speculate that monkey-bar mechanisms could be shared with other chromatin factors and that changes in chromatin dynamics caused by mutations in remodelers could contribute to pathologies.

Liquid-liquid phase separation (LLPS) in DNA and chromatin systems from the perspective of colloid physical chemistry

DNA is a highly charged polyelectrolyte and is prone to associative phase separation driven by the presence of multivalent cations, charged surfactants, proteins, polymers and colloids. The process of DNA phase separation induced by positively charged species is often called DNA condensation. Generally, it refers to either intramolecular DNA compaction (coil-globule transition) or intermolecular DNA aggregation with macroscopic phase separation, but the formation of a DNA liquid crystalline system is also displayed. This has traditionally been described by polyelectrolyte theory and qualitative (Flory-Huggins-based) polymer theory approaches. DNA in the cell nucleus is packed into chromatin wound around the histone octamer (a protein complex comprising two copies each of the four histone proteins H2A, H2B, H3 and H4) to form nucleosomes separated by linker DNA. During the last decade, the phenomenon of the formation of biomolecular condensates (dynamic droplets) by liquid-liquid phase separation (LLPS) has emerged as a generally important mechanism for the formation of membraneless organelles from proteins, nucleic acids and their complexes. DNA and chromatin droplet formation through LLPS has recently received much attention by in vitro as well as in vivo studies that established the importance of this for compartmentalisation in the cell nucleus. Here, we review DNA and chromatin LLPS from a general colloid physical chemistry perspective. We start with a general discussion of colloidal phase separation in aqueous solutions and review the original (pre-LLPS era) work on DNA (macroscopic) phase separation for simpler systems with DNA in the presence of multivalent cations and well-defined surfactants and colloids. Following that, we discuss and illustrate the similarities of such macroscopic phase separation with the general behaviour of LLPS droplet formation by associative phase separation for DNA-protein systems, including chromatin; we also note cases of segregative association. The review ends with a discussion of chromatin LLPS in vivo and its physiological significance.

ISWI catalyzes nucleosome sliding in condensed nucleosome arrays

How chromatin enzymes work in condensed chromatin and how they maintain diffusional mobility inside remains unexplored. We investigated these challenges using the Drosophila ISWI remodeling ATPase, which slides nucleosomes along DNA. Folding of chromatin fibers did not affect sliding in vitro. Catalytic rates were also comparable in- and outside of chromatin condensates. ISWI cross-links and thereby stiffens condensates, except when ATP hydrolysis is possible. Active hydrolysis is also required for ISWI's mobility in condensates. Energy from ATP hydrolysis therefore fuels ISWI's diffusion through chromatin and prevents ISWI from cross-linking chromatin. Molecular dynamics simulations of a 'monkey-bar' model in which ISWI grabs onto neighboring nucleosomes, then withdraws from one before rebinding another in an ATP hydrolysis-dependent manner qualitatively agree with our data. We speculate that 'monkey-bar' mechanisms could be shared with other chromatin factors and that changes in chromatin dynamics caused by mutations in remodelers could contribute to pathologies.

Conformation-dependent UV inactivation efficiency of a conjugative, multi-drug resistant plasmid

A conjugative, multi-drug-resistant plasmid was irradiated in-vivo and in-vitro with a 265-nm UV-light emitting diode (UV-LED) to investigate the gene inactivation efficiency of a plasmid deoxyribonucleic acid (pDNA) carrying DNA transfer and replication genes. The clinical-isolate 60 kb RP4 plasmid of the IncPα group containing the traG gene, was irradiated intracellularly in E. coli DH5α and extracellularly in a water medium at pH 8.5. Real-time quantitative polymerase chain reaction (RT-qPCR) measurements of the UV-fluence response gene inactivation rate constants revealed a decreasing pattern via a pseudo-1st-order inactivation kinetics in all forms examined. Our findings showed that the intracellular-supercoiled conformation, with k = 6.1 × 10-3 cm2/mJ, has the lowest UV susceptibility (lowest inactivation rate). UV absorbance measurements and a computational approach showed that the host's RNA provides the photo-shielding, demonstrating this high UV resistance. When UV exposure was measured in-vitro, the condensed DNA exhibited a self-shielding effect over supercoiled and denatured DNA due to the hypochromic-hyperchromic effects. This study has shown that large-sized conjugative plasmids with conformation-dependent UV/UV-LED-based gene inactivation play a significant role in preventing the spread of antibiotic resistance.

Condensation Goes Viral: A Polymer Physics Perspective

The past decade has seen a revolution in our understanding of how the cellular environment is organized, where an incredible body of work has provided new insights into the role played by membraneless organelles. These rapid advancements have been made possible by an increasing awareness of the peculiar physical properties that give rise to such bodies and the complex biology that enables their function. Viral infections are not extraneous to this. Indeed, in host cells, viruses can harness existing membraneless compartments or, even, induce the formation of new ones. By hijacking the cellular machinery, these intracellular bodies can assist in the replication, assembly, and packaging of the viral genome as well as in the escape of the cellular immune response. Here, we provide a perspective on the fundamental polymer physics concepts that may help connect and interpret the different observed phenomena, ranging from the condensation of viral genomes to the phase separation of multicomponent solutions. We complement the discussion of the physical basis with a description of biophysical methods that can provide quantitative insights for testing and developing theoretical and computational models.

Machine Learning Color Feature Analysis of a High Throughput Nanoparticle Conjugate Sensing Assay

Plasmonic nanoparticles are finding applications within the single molecule sensing field in a "dimer" format, where interaction of the target with hairpin DNA causes a decrease in the interparticle distance, leading to a localized surface plasmon resonance shift. While this shift may be detected using spectroscopy, achieving statistical relevance requires the measurement of thousands of nanoparticle dimers and the timescales required for spectroscopic analysis are incompatible with point-of-care devices. However, using dark-field imaging of the dimer structures, simultaneous digital analysis of the plasmonic resonance shift after target interaction of thousands of dimer structures may be achieved in minutes. The main challenge of this digital analysis on the single-molecule scale was the occurrence of false signals caused by non-specifically bound clusters of nanoparticles. This effect may be reduced by digitally separating dimers from other nanoconjugate types. Variation in image intensity was observed to have a discernible impact on the color analysis of the nanoconjugate constructs and thus the accuracy of the digital separation. Color spaces wherein intensity may be uncoupled from the color information (hue, saturation, and value (HSV) and luminance, a* vector, and b* vector (LAB) were contrasted to a color space which cannot uncouple intensity (RGB) to train a classifier algorithm. Each classifier algorithm was validated to determine which color space produced the most accurate digital separation of the nanoconjugate types. The LAB-based learning classifier demonstrated the highest accuracy for digitally separating nanoparticles. Using this classifier, nanoparticle conjugates were monitored for their plasmonic color shift after interaction with a synthetic RNA target, resulting in a platform with a highly accurate yes/no response with a true positive rate of 88% and a true negative rate of 100%. The sensor response of tested single stranded RNA (ssRNA) samples was well above control responses for target concentrations in the range of 10 aM-1 pM.

Shelterin Components Modulate Nucleic Acids Condensation and Phase Separation in the Context of Telomeric DNA

Telomeres are nucleoprotein complexes that protect the ends of chromosomes and are essential for chromosome stability in Eukaryotes. In cells, individual telomeres form distinct globules of finite size that appear to be smaller than expected for bare DNA. Moreover, telomeres can cluster together, form telomere-induced-foci or co-localize with promyelocytic leukemia (PML) nuclear bodies. The physical basis for collapse of individual telomeres and coalescence of multiple ones remains unclear, as does the relationship between these two phenomena. By combining single-molecule force spectroscopy measurements, optical microscopy, turbidity assays, and simulations, we show that the telomere scaffolding protein TRF2 can condense individual DNA chains and drives coalescence of multiple DNA molecules, leading to phase separation and the formation of liquid-like droplets. Addition of the TRF2 binding protein hRap1 modulates phase boundaries and tunes the specificity of solution demixing while simultaneously altering the degree of DNA compaction. Our results suggest that the condensation of single telomeres and formation of biomolecular condensates containing multiple telomeres are two different outcomes driven by the same set of molecular interactions. Moreover, binding partners, such as other telomere components, can alter those interactions to promote single-chain DNA compaction over multiple-chain phase separation.

Co-condensation of proteins with single- and double-stranded DNA

Biomolecular condensates are intracellular organelles that are not bounded by membranes and often show liquid-like, dynamic material properties. They typically contain various types of proteins and nucleic acids. How the interaction of proteins and nucleic acids finally results in dynamic condensates is not fully understood. Here we use optical tweezers and fluorescence microscopy to study how the prototypical prion-like protein Fused-in-Sarcoma (FUS) condenses with individual molecules of single- and double-stranded DNA. We find that FUS adsorbs on DNA in a monolayer and hence generates an effectively sticky FUS–DNA polymer that collapses and finally forms a dynamic, reversible FUS–DNA co-condensate. We speculate that protein monolayer-based protein–nucleic acid co-condensation is a general mechanism for forming intracellular membraneless organelles.

Biomolecular condensates provide distinct compartments that can localize and organize biochemistry inside cells. Recent evidence suggests that condensate formation is prevalent in the cell nucleus. To understand how different components of the nucleus interact during condensate formation is an important challenge. In particular, the physics of co-condensation of proteins together with nucleic acids remains elusive. Here we use optical tweezers to study how the prototypical prion-like protein Fused-in-Sarcoma (FUS) forms liquid-like assemblies in vitro, by co-condensing together with individual DNA molecules. Through progressive force-induced peeling of dsDNA, buffer exchange, and force measurements, we show that FUS adsorbing in a single layer on DNA effectively generates a sticky FUS–DNA polymer that can collapse to form a liquid-like FUS–DNA co-condensate. Condensation occurs at constant DNA tension for double-stranded DNA, which is a signature of phase separation. We suggest that co-condensation mediated by protein monolayer adsorption on nucleic acids is an important mechanism for intracellular compartmentalization.

DNA length tunes the fluidity of DNA-based condensates

Living organisms typically store their genomic DNA in a condensed form. Mechanistically, DNA condensation can be driven by macromolecular crowding, multivalent cations, or positively charged proteins. At low DNA concentration, condensation triggers the conformational change of individual DNA molecules into a compacted state, with distinct morphologies. Above a critical DNA concentration, condensation goes along with phase separation into a DNA-dilute and a DNA-dense phase. The latter DNA-dense phase can have different material properties and has been reported to be rather liquid-like or solid-like depending on the characteristics of the DNA and the solvent composition. Here, we systematically assess the influence of DNA length on the properties of the resulting condensates. We show that short DNA molecules with sizes below 1 kb can form dynamic liquid-like assemblies when condensation is triggered by polyethylene glycol and magnesium ions, binding of linker histone H1, or nucleosome reconstitution in combination with linker histone H1. With increasing DNA length, molecules preferentially condense into less dynamic more solid-like assemblies, with phage λ-DNA with 48.5 kb forming mostly solid-like assemblies under the conditions assessed here. The transition from liquid-like to solid-like condensates appears to be gradual, with DNA molecules of roughly 1–10 kb forming condensates with intermediate properties. Titration experiments with linker histone H1 suggest that the fluidity of condensates depends on the net number of attractive interactions established by each DNA molecule. We conclude that DNA molecules that are much shorter than a typical human gene are able to undergo liquid-liquid phase separation, whereas longer DNA molecules phase separate by default into rather solid-like condensates. We speculate that the local distribution of condensing factors can modulate the effective length of chromosomal domains in the cell. We anticipate that the link between DNA length and fluidity established here will improve our understanding of biomolecular condensates involving DNA.

Nucleosome Positioning and Spacing: From Mechanism to Function

Eukaryotes associate their genomes with histone proteins, forming nucleosome particles. Nucleosomes regulate and protect the genetic information. They often assemble into evenly spaced arrays of nucleosomes. These regular nucleosome arrays cover significant portions of the genome, in particular over genes. The presence of these evenly spaced nucleosome arrays is highly conserved throughout the entire eukaryotic domain. Here, we review the mechanisms behind the establishment of this primary structure of chromatin with special emphasis on the biogenesis of evenly spaced nucleosome arrays. We highlight the roles that transcription, nucleosome remodelers, DNA sequence, and histone density play towards the formation of evenly spaced nucleosome arrays and summarize our current understanding of their cellular functions. We end with key unanswered questions that remain to be explored to obtain an in-depth understanding of the biogenesis and function of the nucleosome landscape.

Archaeal Histone Contributions to the Origin of Eukaryotes

The eukaryotic lineage arose from bacterial and archaeal cells that underwent a symbiotic merger. At the origin of the eukaryote lineage, the bacterial partner contributed genes, metabolic energy, and the building blocks of the endomembrane system. What did the archaeal partner donate that made the eukaryotic experiment a success? The archaeal partner provided the potential for complex information processing. Archaeal histones were crucial in that regard by providing the basic functional unit with which eukaryotes organize DNA into nucleosomes, exert epigenetic control of gene expression, transcribe genes with CCAAT-box promoters, and a manifest cell cycle with condensed chromosomes. While mitochondrial energy lifted energetic constraints on eukaryotic protein production, histone-based chromatin organization paved the path to eukaryotic genome complexity, a critical hurdle en route to the evolution of complex cells.

The folding pathways and thermodynamics of semiflexible polymers

Inspired by the protein folding and DNA packing, we have systematically studied the thermodynamic and kinetic behaviors of single semiflexible homopolymers by Langevin dynamics simulations. In line with experiments, a rich variety of folding products, such as rod-like bundles, hairpins, toroids, and a mixture of them, are observed in the complete diagram of states. Moreover, knotted structures with a significant population are found in a certain range of bending stiffness in thermal equilibrium. As the solvent quality becomes poorer, the population of the intermediate occurring in the folding process increases, which leads to a severe chevron rollover for the folding arm. However, the population of the intermediates in the unfolding process is very low, insufficient to induce unfolding arm rollover. The total types of folding pathways from the coil state to the toroidal state for a semiflexible polymer chain remain unchanged by varying the solvent quality or temperature, whereas the kinetic partitioning into different folding events can be tuned significantly. In the process of knotting, three types of mechanisms, namely, plugging, slipknotting, and sliding, are discovered. Along the folding evolution, a semiflexible homopolymer chain can knot at any stage of folding upon leaving the extended coil state, and the probability to find a knot increases with chain compactness. In addition, we find rich types of knotted topologies during the folding of a semiflexible homopolymer chain. This study should be helpful in gaining insight into the general principles of biopolymer folding.

Crowding Induces Entropically-Driven Changes to DNA Dynamics That Depend on Crowder Structure and Ionic Conditions

Macromolecular crowding plays a principal role in a wide range of biological processes including gene expression, chromosomal compaction, and viral infection. However, the impact that crowding has on the dynamics of nucleic acids remains a topic of debate. To address this problem, we use single-molecule fluorescence microscopy and custom particle-tracking algorithms to investigate the impact of varying macromolecular crowding conditions on the transport and conformational dynamics of large DNA molecules. Specifically, we measure the mean-squared center-of-mass displacements, as well as the conformational size, shape, and fluctuations, of individual 115 kbp DNA molecules diffusing through various in vitro solutions of crowding polymers. We determine the role of crowder structure and concentration, as well as ionic conditions, on the diffusion and configurational dynamics of DNA. We find that branched, compact crowders (10 kDa PEG, 420 kDa Ficoll) drive DNA to compact, whereas linear, flexible crowders (10, 500 kDa dextran) cause DNA to elongate. Interestingly, the extent to which DNA mobility is reduced by increasing crowder concentrations appears largely insensitive to crowder structure (branched vs. linear), despite the highly different configurations DNA assumes in each case. We also characterize the role of ionic conditions on crowding-induced DNA dynamics. We show that both DNA diffusion and conformational size exhibit an emergent non-monotonic dependence on salt concentration that is not seen in the absence of crowders.

Single-molecule compaction of megabase-long chromatin molecules by multivalent cations

To gain insight into the conformational properties and compaction of megabase-long chromatin molecules, we reconstituted chromatin from T4 phage DNA (165 kb) and recombinant human histone octamers (HO). The unimolecular compaction, induced by divalent Mg2+ or tetravalent spermine4+ cations, studied by single-molecule fluorescence microscopy (FM) and dynamic light scattering (DLS) techniques, resulted in the formation of 250-400 nm chromatin condensates. The compaction on this scale of DNA size is comparable to that of chromatin topologically associated domains (TAD) in vivo. Variation of HO loading revealed a number of unique features related to the efficiency of chromatin compaction by multivalent cations, the mechanism of compaction, and the character of partly compact chromatin structures. The observations may be relevant for how DNA accessibility in chromatin is maintained. Compaction of saturated chromatin, in turn, is accompanied by an intra-chain segregation at the level of single chromatin molecules, suggesting an intriguing scenario of selective activation/deactivation of DNA as a result of chromatin fiber heterogeneity due to the nucleosome positioning. We suggest that this chromatin, reconstituted on megabase-long DNA because of its large size, is a useful model of eukaryotic chromatin.

Collapse of DNA in packaging and cellular transport

The dawn of molecular biology and recombinant DNA technology arose from our ability to manipulate DNA, including the process of collapse of long extended DNA molecules into nanoparticles of approximately 100 nm diameter. This condensation process is important for the packaging of DNA in the cell and for transporting DNA through the cell membrane for gene therapy. Multivalent cations, such as natural polyamines (spermidine and spermine), were initially recognized for their ability to provoke DNA condensation. Current research is targeted on molecules such as linear and branched polymers, oligopeptides, polypeptides and dendrimers that promote collapse of DNA to nanometric particles for gene therapy and on the energetics of DNA packaging.

Conformational and phase transitions in DNA--photosensitive surfactant solutions: Experiment and modeling

DNA binding to trans- and cis-isomers of azobenzene containing cationic surfactant in 5 mM NaCl solution was investigated by the methods of dynamic light scattering (DLS), low-gradient viscometry (LGV), atomic force microscopy (AFM), circular dichroism (CD), gel electrophoresis (GE), flow birefringence (FB), UV-Vis spectrophotometry. Light-responsive conformational transitions of DNA in complex with photosensitive surfactant, changes in DNA optical anisotropy and persistent length, phase transition of DNA into nanoparticles induced by high surfactant concentration, as well as transformation of surfactant conformation under its binding to macromolecule were studied. Computer simulations of micelles formation for cis- and trans-isomers of azobenzene containing surfactant, as well as DNA-surfactant interaction, were carried out. Phase diagram for DNA-surfactant solutions was designed. The possibility to reverse the DNA packaging induced by surfactant binding with the dilution and light irradiation was shown.

Coexistence of coil and globule domains within a single confined DNA chain

The highly charged DNA chain may be either in an extended conformation, the coil, or condensed into a highly dense and ordered structure, the toroid. The transition, also called collapse of the chain, can be triggered in different ways, for example by changing the ionic conditions of the solution. We observe individual DNA molecules one by one, kept separated and confined inside a protein shell (the envelope of a bacterial virus, 80 nm in diameter). For subcritical concentrations of spermine (4+), part of the DNA is condensed and organized in a toroid and the other part of the chain remains uncondensed around. Two states coexist along the same DNA chain. These ‘hairy’ globules are imaged by cryo-electron microscopy. We describe the global conformation of the chain and the local ordering of DNA segments inside the toroid.

Polyethylene glycol and divalent salt-induced DNA reentrant condensation revealed by single molecule measurements

In this study, we investigated the DNA condensation induced by polyethylene glycol (PEG) with different molecular weights (PEG 600 and PEG 6000) in the presence of NaCl or MgCl2 by using magnetic tweezers (MT) and atomic force microscopy (AFM). The MT measurements show that with increasing NaCl concentration, the critical condensation force in the PEG 600-DNA or PEG 6000-DNA system increased approximately linearly. PEG 6000 solution has a larger critical force than PEG 600 solution at a given NaCl concentration. In comparison, a parabolic trend of the critical condensation force was observed with increasing MgCl2 concentration, indicating that DNA undergoes a reentrant condensation. The AFM results show that the morphologies of the compacted DNA-PEG complexes depended on the salt concentration and were consistent with the MT results.

Substitution-inert trinuclear platinum complexes efficiently condense/aggregate nucleic acids and inhibit enzymatic activity

The trinuclear platinum complexes (TriplatinNC-A [{Pt(NH3 )3 }2 -μ-{trans-Pt(NH3 )2 (NH2 (CH2 )6 NH2 )2 }](6+) , and TriplatinNC [{trans-Pt(NH3 )2 (NH2 (CH2 )6 NH3 (+) )}2 -μ-{trans-Pt(NH3 )2 (NH2 (CH2 )6 NH2 )2 }](8+) ) are biologically active agents that bind to DNA through noncovalent (hydrogen bonding, electrostatic) interactions. Herein, we show that TriplatinNC condenses DNA with a much higher potency than conventional DNA condensing agents. Both complexes induce aggregation of small transfer RNA molecules, and TriplatinNC in particular completely inhibits DNA transcription at lower concentrations than naturally occurring spermine. Topoisomerase I-mediated relaxation of supercoiled DNA was inhibited by TriplatinNC-A and TriplatinNC at concentrations which were 60 times and 250 times lower than that of spermine. The mechanisms for the biological activity of TriplatinNC-A and TriplatinNC may be associated with their ability to condense/aggregate nucleic acids with consequent inhibitory effects on crucial enzymatic activities.

Effective and reversible DNA condensation induced by a simple cyclic/rigid polyamine containing carbonyl moiety

The transfection of DNA in gene therapy largely depends on the possibility of obtaining its condensation. The details of nanoparticle formation are essential for functioning, as mediated by the diverse elements containing molecular structure, ionic strength in mediums, and condensing motivator. Here, we report two kinds of DNA condensing agents based on simple cyclic/rigid polyamine molecules, having evaluated their structural effect on nanoparticle formation. The reversible condensation-dissociation process was achieved by ion-switching, attributing to a possible condensing mechanism-competitive building of external hydrogen bonds. Using poly[(dA-dT)2] and poly[(dG-dC)2] as substrates, respectively, circular dichroism (CD) signals clearly presented dissimilar interactions between polyamines and both rich sequences, implying potential preference for G-C sequence. The presence of divalent ion Zn(2+) as an efficient motivator accelerated the achievement of DNA condensation, and an accessible schematic model was depicted to explain the promotion in detail. In addition, by comparison with the behaviors of linear polyamines, differences between condensation and aggregation were explicitly elucidated in aspects of morphology and surface charges, as well as induced condition. The present work may have the potential to reveal the precise mechanism of DNA nanoparticle formation and, in particular, be applied to gene delivery as an efficient nonviral vector.

The role of solvent in protein folding and in aggregation

We discuss features of the effect of solvent on protein folding andaggregation, highlighting the physics related to the particulate nature and the peculiar structure of the aqueous solvent, and the biological significance of interactions between solvent and proteins. To this purpose we use a generalized energy landscape of extended dimensionality. A closer look at the properties of solvent induced interactions and forces proves useful for understanding the physical grounds of `ad hoc' interactions and for devising realistic ways of accounting for solvent effects. The solvent has long been known to be a crucially important part of biological systems, and times appear mature for it to be adequately accounted for in the protein folding problem. Use of the extended dimensionality energy landscape helpseliciting the possibility of coupling among conformational changes and aggregation, such as proved by experimental data in the literature.

Critical behavior of megabase-size DNA toward the transition into a compact state

We studied the changes in the higher-order structure of a megabase-size DNA (S120-1 DNA) under different spermidine (SPD) concentrations through single-molecule observations using fluorescence microscopy (FM) and atomic force microscopy (AFM). We examined the difference between the folding transitions in S120-1 DNA and sub-megabase-size DNA, T4 DNA (166 kbp). From FM observations, it is found that S120-1 DNA exhibits intra-chain segregation as the intermediate state of transition, in contrast to the all-or-none nature of the transition on T4 DNA. Large S120-1 DNA exhibits a folding transition at lower concentrations of SPD than T4 DNA. AFM observations showed that DNA segments become aligned in parallel on a two-dimensional surface as the SPD concentration increases and that highly intense parallel alignment is achieved just before the compaction. S120-1 DNA requires one-tenth the SPD concentration as that required by T4 DNA to achieve the same degree of parallel ordering. We theoretically discuss the cause of the parallel ordering near the transition into a fully compact state on a two-dimensional surface, and argue that such parallel ordering disappears in bulk solution.

A universal description for the experimental behavior of salt-(in)dependent oligocation-induced DNA condensation

We report a systematic study of the condensation of plasmid DNA by oligocations with variation of the charge, Z, from +3 to +31. The oligocations include a series of synthetic linear ε-oligo(L-lysines), (denoted εKn, n = 3–10, 31; n is the number of lysines with the ligand charge Z = n+1) and branched α-substituted homologues of εK10: εYK10, εLK10 (Z = +11); εRK10, εYRK10 and εLYRK10 (Z = +21). Data were obtained by light scattering, UV absorption monitored precipitation assay and isothermal titration calorimetry in a wide range concentrations of DNA and monovalent salt (KCl, CKCl). The dependence of EC50 (ligand concentration at the midpoint of DNA condensation) on C(KCl) shows the existence of a salt-independent regime at low C(KCl) and a salt-dependent regime with a steep rise of EC50 with increase of C(KCl). Increase of the ligand charge shifts the transition from the salt-independent to salt-dependent regime to higher C(KCl). A novel and simple relationship describing the EC50 dependence on DNA concentration, charge of the ligand and the salt-dependent dissociation constant of the ligand–DNA complex is derived. For the ε-oligolysines εK6–εK10, the experimental dependencies of EC50 on C(KCl) and Z are well-described by an equation with a common set of parameters. Implications from our findings for understanding DNA condensation in chromatin are discussed.

Condensed DNA: condensing the concepts

DNA is stored in vivo in a highly compact, so-called condensed phase, where gene regulatory processes are governed by the intricate interplay between different states of DNA compaction. These systems often have surprising properties, which one would not predict from classical concepts of dilute solutions. The mechanistic details of DNA packing are essential for its functioning, as revealed by the recent developments coming from biochemistry, electrostatics, statistical mechanics, and molecular and cell biology. Different aspects of condensed DNA behavior are linked to each other, but the links are often hidden in the bulk of experimental and theoretical details. Here we try to condense some of these concepts and provide interconnections between the different fields. After a brief description of main experimental features of DNA condensation inside viruses, bacteria, eukaryotes and the test tube, main theoretical approaches for the description of these systems are presented. We end up with an extended discussion of the role of DNA condensation in the context of gene regulation and mention potential applications of DNA condensation in gene therapy and biotechnology.

Cation-induced polyelectrolyte-polyelectrolyte attraction in solutions of DNA and nucleosome core particles

The paper reviews our current studies on the experimentally induced cation compaction and aggregation in solutions of DNA and nucleosome core particles and the theoretical modelling of these processes using coarse-grained continuum models with explicit mobile ions and with all-atom molecular dynamics (MD) simulations. Recent experimental results on DNA condensation by cationic oligopeptides and the effects of added salt are presented. The results of MD simulations modelling DNA-DNA attraction due to the presence of multivalent ions including the polyamine spermidine and fragments of histone tails, which exhibit bridging between adjacent DNA molecules, are discussed. Experimental data on NCP aggregation, using recombinantly prepared systems are summarized. Literature data and our results of studying of the NCP solutions are compared with predictions of coarse-grained MD simulations, including the important ion correlation as well as bridging mechanisms. The importance of the results to chromatin folding and aggregation is discussed.

A universal description for the experimental behavior of salt-(in)dependent oligocation-induced DNA condensation

We report a systematic study of the condensation of plasmid DNA by oligocations with variation of the charge, Z, from +3 to +31. The oligocations include a series of synthetic linear epsilon-oligo(l-lysines), (denoted epsilonKn, n = 3-10, 31; n is the number of lysines equal to the ligand charge) and branched alpha-substituted homologues of epsilonK10: epsilonYK10, epsilonLK10 (Z = +10); epsilonRK10, epsilonYRK10 and epsilonLYRK10 (Z = +20). Data were obtained by light scattering, UV absorption monitored precipitation assay and isothermal titration calorimetry in a wide range concentrations of DNA and monovalent salt (KCl, C(KCl)). The dependence of EC(50) (ligand concentration at the midpoint of DNA condensation) on C(KCl) shows the existence of a salt-independent regime at low C(KCl) and a salt-dependent regime with a steep rise of EC(50) with increase of C(KCl). Increase of the ligand charge shifts the transition from the salt-independent to salt-dependent regime to higher C(KCl). A novel and simple relationship describing the EC(50) dependence on DNA concentration, charge of the ligand and the salt-dependent dissociation constant of the ligand-DNA complex is derived. For the epsilon-oligolysines epsilonK3-epsilonK10, the experimental dependencies of EC(50) on C(KCl) and Z are well-described by an equation with a common set of parameters. Implications from our findings for understanding DNA condensation in chromatin are discussed.

Folding transition of a single semiflexible polyelectrolyte chain through toroidal bundling of loop structures

We consider how the DNA coil-globule transition progresses via the formation of a toroidal ring structure. We formulate a theoretical model of this transition as a phenomenon in which an unstable single loop generated as a result of thermal fluctuation is stabilized through association with other loops along a polyelectrolyte chain. An essential property of the chain under consideration is that it follows a wormlike chain model. A toroidal bundle of loop structures is characterized by a radius and a winding number. The statistical properties of such a chain are discussed in terms of the free energy as a function of the fraction of unfolded segments. We also present an actual experimental observation of the coil-globule transition of single giant DNA molecules, T4 DNA (165.5 kbp), with spermidine (3+), where intrachain phase segregation appears at a NaCl concentration of more than 10 mM. Both the theory and experiments lead to two important points. First, the transition from a partially folded state to a completely folded state has the characteristics of a continuous transition, while the transition from an unfolded state to a folded state has the characteristics of a first-order phase transition. Second, the appearance of a partially folded structure requires a folded structure to be less densely packed than in the fully folded compact state.

The phase behavior of polyethylene ring chains

The equilibrium properties of an isolated polyethylene ring chain are studied by using molecular dynamics (MD) simulations. The results of an 80-bond linear chain are also presented, which are in agreement with previous studies of square-well chains and Lennard-Jones (LJ) homopolymers. Mainly, we focus on the collapse of polyethylene ring chains. At high temperatures, a fully oblate structure is observed for the ring chains with different chain lengths. For such an oblate structure, a shape factor of delta(*)=0.25 and a rodlike scaling relation between the radius of gyration and chain lengths could be deduced easily in theory, and the same results are obtained by our MD simulations. Such an oblate structure can be obtained by Monte Carlo simulation only for sufficient stiff ring chains. When the temperature decreases, an internal energy barrier is observed. This induces a strong peak in the heat capacity, denoting a gas-liquid-like transition. This energy barrier comes mainly from the local monomer-monomer interactions, i.e., the bond-stretching, the bond-bending, and the torsion potentials. A low temperature peak is also observed in the same heat capacity curve, representing a liquid-solid-like transition. These numerical simulation results support a two-stage collapse of polyethylene ring chains; however, the nature should be different from the square-well and LJ ring chains.

Role of chain stiffness on the conformation of single polyelectrolytes in salt solutions

Conformation of single polyelectrolytes in tetravalent salt solutions is investigated under the framework of a coarse-grained model, using Langevin dynamics simulations. The chain size, studied by the radius of gyration, shows three different variational behaviors with salt concentration, depending on the chain stiffness. According to the size variations, polyelectrolytes of fixed chain length are classified into three categories: (1) flexible chain, for which the variation shows a curve similar to a tilted L, (2) semiflexible chain, whose curve resembles U, and (3) rigid chain, for which the curve is a straight line. The wormlike chain model with persistence length predicted by the Odijk-Skolnick-Fixman theory is found to be able to qualitatively describe the end-to-end distance at low salt concentration not only for semiflexible and rigid chains but also for flexible chain. In a low salt region, a flexible polyelectrolyte extends more significantly than a semiflexible chain, in reference of the size of their uncharged counterparts, and in a high salt region, regardless of chain stiffness, a chain attains a dimension comparable to that of its neutral polymer. The chain stiffness influences both the local and the global chain structures. A flexible chain exhibits a zigzagged local structure in the presence of salt ions, and the condensed structure is a disordered, random globule. A semiflexible chain is locally smooth, and the condensed structure is orderly packed, taking a form such as hairpin or toroid. Moreover, the chain stiffness can also affect the nature of the coil-globule transition. The transition occurred in a discrete manner for semiflexible chain, whereas it occurred in a continuous way for flexible chain. This discrete feature happened not only at low salt concentration when a semiflexible chain collapsed but also at high salt concentration when the collapsed chain is reexpanded. At the end, the effects of chain stiffness and salt concentration on the conformation of single polyelectrolytes are summarized in a schematic state diagram.

On the formation of rings-on-a-string conformations in a single polyelectrolyte chain: A possible scenario

Recent single-molecular observations have revealed that a single giant DNA molecule assumes (micro) phase separated structures upon the addition of condensing agents. Electron and atomic force microscopy have clearly shown the coexistence of ordered tori and disordered coil structures within a single DNA molecule. Motivated by these experimental findings, we theoretically investigated the collapse transition of a single polyelectrolyte chain driven by the addition of condensing guest molecules. We found that the transition behavior critically depends on the degree of the surviving charge inside the torus. When the torus is charged, even slightly, "rings-on-a-string" structures are expected for a sufficiently long chain, owing to the combinational entropy of segment state distribution along the chain and the unique property of the stability of charged torus.

How are small ions involved in the compaction of DNA molecules?

DNA is a genetic material found in all life on Earth. DNA is composed of four types of nucleotide subunits, and forms a double-helical one-dimensional polyelectrolyte chain. If we focus on the microscopic molecular structure, DNA is a rigid rod-like molecule. On the other hand, with coarse graining, a long-chain DNA exhibits fluctuating behavior over the whole molecule due to thermal fluctuation. Owe to its semiflexible nature, individual giant DNA molecule undergoes a large discrete transition in the higher-order structure. In this folding transition into a compact state, small ions in the solution have a critical effect, since DNA is highly charged. In the present article, we interpret the characteristic features of DNA compaction while paying special attention to the role of small ions, in relation to a variety of single-chain morphologies generated as a result of compaction.

Depletion-induced instability in protein-DNA mixtures: Influence of protein charge and size

While there is abundant experimental and theoretical work on polymer-induced DNA condensation, it is still unclear whether globular proteins can condense linear DNA or not. We develop a simple analytical approximation for the depletion attraction between rodlike segments of semiflexible polyelectrolytes such as DNA, induced by nonbinding globular proteins. Monte Carlo simulations show that the approximation works well up to protein volume fractions of at least 20%. From the expression for the depletion attraction we estimate instability thresholds by computing the effective virial coefficient of DNA segments in protein solutions. While globular proteins are found to be much poorer depletion agents than flexible polymers, it should be possible to condense linear DNA with small highly charged globular proteins, at relatively low ionic strengths.

Ligand-induced DNA condensation: choosing the model

We test and compare different models for ligand-induced DNA condensation. Using 14C-labeled spermidine3+, we measure the binding to condensed DNA at micromolar to molar polyamine concentrations. DNA aggregates at a critical polyamine concentration. Spermidine3+ binding becomes highly cooperative at the onset of aggregation. At higher concentrations, spermidine3+ binding to condensed DNA reaches a plateau with the degree of binding equal to 0.7 (NH(4+)/PO3-). Condensed DNA exists in a wide range of spermidine concentrations with the roughly constant degree of ligand binding. At greater concentrations, the degree of binding increases again. Further spermidine penetration between the double helices causes DNA resolubilization. We show that a simple two-state model without ligand-ligand interactions qualitatively predicts the reentrant aggregation-resolubilization behavior and the dependence on the ligand, Na+, and DNA concentrations. However, such models are inconsistent with the cooperative ligand binding to condensed DNA. Including the contact or long-range ligand-ligand interactions improves the coincidence with the experiments, if binding to condensed DNA is slightly more cooperative than to the starting DNA. For example, in the contact interaction model it is equivalent to an additional McGhee-von Hippel cooperativity parameter of approximately 2. Possible physical mechanisms for the observed cooperativity of ligand binding are discussed.

DNA structural transitions induced by divalent metal ions in aqueous solutions

Using methods of IR spectroscopy, light scattering, gel-electrophoresis DNA structural transitions are studied under the action of Cu2+, Zn2+, Mn2+, Ca2+ and Mg2+ ions in aqueous solution. Cu2+, Zn2+, Mn2+ and Ca2+ ions bind both to DNA phosphate groups and bases while Mg2+ ions-only to phosphate groups of DNA. Upon interaction with divalent metal ions studied (except for Mg2+ ions) DNA undergoes structural transition into a compact form. DNA compaction is characterized by a drastic decrease in the volume occupied by DNA molecules with reversible formation of DNA dense particles of well-defined finite size and ordered morphology. The DNA secondary structure in condensed particles corresponds to the B-form family. The mechanism of DNA compaction under Mt2+ ion action is not dominated by electrostatics. The effectiveness of the divalent metal ions studied to induce DNA compaction correlates with the affinity of these ions for DNA nucleic bases: Cu2+>>Zn2+>Mn2+>Ca2+>>Mg2+. Mt2+ ion interaction with DNA bases (or Mt2+ chelation with a base and an oxygen of a phosphate group) may be responsible for DNA compaction. Mt2+ ion interaction with DNA bases can destabilize DNA causing bends and reducing its persistent length that will facilitate DNA compaction.

Contribution of hydrophobicity to thermodynamics of ligand-DNA binding and DNA collapse

The importance of understanding the dynamics of DNA condensation is inherent in the biological significance of DNA packaging in cell nuclei, as well as for gene therapy applications. Specifically, the role of ligand hydrophobicity in DNA condensation has received little attention. Considering that only multivalent cations can induce true DNA condensation, previous studies exploring monovalent lipids have been unable to address this question. In this study we have elucidated the contribution of the hydrophobic effect to multivalent cation- and cationic lipid-DNA binding and DNA collapse by studying the thermodynamics of cobalt hexammine-, spermine-, and lipospermine-plasmid DNA binding at different temperatures. Comparable molar heat capacity changes (DeltaC(p)) associated with cobalt hexammine- and spermine-DNA binding (-23.39 cal/mol K and -17.98 cal/mol K, respectively) suggest that upon binding to DNA, there are insignificant changes in the hydration state of the methylene groups in spermine. In contrast, the acyl chain contribution to the DeltaC(p) of lipospermine-DNA binding (DeltaC(p ) = DeltaC(p lipospermine) - DeltaC(p spermine)) is significant (-220.94 cal/mol K). Although lipopermine induces DNA ordering into "tubular" suprastructures, such structures do not assume toroidal dimensions as observed for spermine-DNA complexes. We postulate that a steric barrier posed by the acyl chains in lipospermine precludes packaging of DNA into dimensions comparable to those found in nature.

Information content and complexity in the high-order organization of DNA

Nucleic acids are characterized by a vast structural variability. Secondary structural conformations include the main polymorphs A, B, and Z, cruciforms, intrinsic curvature, and multistranded motifs. DNA secondary motifs are stabilized and regulated by the primary base sequence, contextual effects, environmental factors, as well as by high-order DNA packaging modes. The high-order modes are, in turn, affected by secondary structures and by the environment. This review is concerned with the flow of structural information among the hierarchical structural levels of DNA molecules, the intricate interplay between the various factors that affect these levels, and the regulation and physiological significance of DNA high-order structures.