Structure of toroidal DNA collapsed inside the phage capsid

Genome organization in double-stranded DNA viruses observed by cryoET

Double-stranded DNA (dsDNA) viruses package their genetic material into protein cages with diameters usually a few hundred times smaller than the length of their genome. Compressing the relatively stiff and highly negatively charged dsDNA into a small volume is energetically costly and mechanistically enigmatic. Multiple models of dsDNA packaging have been proposed based on various experimental evidence and simulation methods, but direct observation of any viral genome organization is lacking. Here, using cryoET and an improved data processing scheme that utilizes information from the encaging protein shell, we present 3D views of dsDNA genome inside individual viral particles at resolution that densities of neighboring DNA duplexes are readily separable. These cryoET observations reveal a "rod-and-coil" fold of the dsDNA that is conserved among herpes simplex virus type 1 (HSV-1) with a spherical capsid, bacteriophage T4 with a prolate capsid, and bacteriophage T7 with a proteinaceous core inside the capsid. Finally, inspired by the genome arrangement in partially packaged T4 particles, we propose a mechanism for the genome packaging process in dsDNA viruses.

Protamine folds DNA into flowers and loop stacks

DNA in sperm undergoes an extreme compaction to almost crystalline packing levels. To produce this dense packing, DNA is dramatically reorganized in minutes by protamine proteins. Protamines are positively charged proteins that coat negatively charged DNA and fold it into a series of toroids. The exact mechanism for forming these ∼50-kbp toroids is unknown. Our goal is to study toroid formation by starting at the "bottom" with folding of short lengths of DNA that form loops and working "up" to more folded structures that occur on longer length scales. We previously measured folding of 200-300 bp of DNA into a loop. Here, we look at folding of intermediate DNA lengths (L = 639-3003 bp) that are 2-10 loops long. We observe two folded structures besides loops that we hypothesize are early intermediates in the toroid formation pathway. At low protamine concentrations (∼0.2 μM), we see that the DNA folds into flowers (structures with multiple loops that are positioned so they look like the petals of a flower). Folding at these concentrations condenses the DNA to 25% of its original length, takes seconds, and is made up of many small bending steps. At higher protamine concentrations (≥2 μM), we observe a second folded structure-the loop stack-where loops are stacked vertically one on top of another. These results lead us to propose a two-step process for folding at this length scale: 1) protamine binds to DNA, bending it into loops and flowers, and 2) flowers collapse into loop stacks. These results highlight how protamine uses a bind-and-bend mechanism to rapidly fold DNA, which may be why protamine can fold the entire sperm genome in minutes.

DNA-protamine condensates under low salt conditions: molecular dynamics simulation with a simple coarse-grained model focusing on electrostatic interactions

Protamine, a small, strongly positively-charged protein, plays a key role in achieving chromatin condensation inside sperm cells and is also involved in the formulation of nanoparticles for gene therapy and packaging of mRNA-based vaccines against viral infection and cancer. The detailed mechanisms of such condensations are still poorly understood especially under low salt conditions where electrostatic interaction predominates. Our previous study, with a refined coarse-grained model in full consideration of the long-range electrostatic interactions, has demonstrated the crucial role of electrostatic interaction in protamine-controlled reversible DNA condensation. Therefore, we herein pay our attention only to the electrostatic interaction and devise a coarser-grained bead-spring model representing the right linear charge density on protamine and DNA chains but treating other short-range interactions as simply as possible, which would be suitable for real-scale simulations. Effective pair potential calculations and large-scale molecular dynamics simulations using this extremely simple model reproduce the phase behaviour of DNA in a wide range of protamine concentrations under low salt conditions, again revealing the importance of the electrostatic interaction in this process and providing a detailed nanoscale picture of bundle formation mediated by a charge disproportionation mechanism. Our simulations also show that protamine length alters DNA overcharging and in turn redissolution thresholds of DNA condensates, revealing the important role played by entropies and correlated fluctuations of condensing agents and thus offering an additional opportunity to design tailored nanoparticles for gene therapy. The control mechanism of DNA-protamine condensates will also provide a better microscopic picture of biomolecular condensates, i.e., membraneless organelles arising from liquid-liquid phase separation, that are emerging as key principles of intracellular organization. Such condensates controlled by post-translational modification of protamine, in particular phosphorylation, or by variations in protamine length from species to species may also be responsible for the chromatin-nucleoplasm patterning observed during spermatogenesis in several vertebrate and invertebrate species.

A microfluidic platform for the controlled synthesis of architecturally complex liquid crystalline nanoparticles

Soft-matter nanoparticles are of great interest for their applications in biotechnology, therapeutic delivery, and in vivo imaging. Underpinning this is their biocompatibility, potential for selective targeting, attractive pharmacokinetic properties, and amenability to downstream functionalisation. Morphological diversity inherent to soft-matter particles can give rise to enhanced functionality. However, this diversity remains untapped in clinical and industrial settings, and only the simplest of particle architectures [spherical lipid vesicles and lipid/polymer nanoparticles (LNPs)] have been routinely exploited. This is partially due to a lack of appropriate methods for their synthesis. To address this, we have designed a scalable microfluidic hydrodynamic focusing (MHF) technology for the controllable, rapid, and continuous production of lyotropic liquid crystalline (LLC) nanoparticles (both cubosomes and hexosomes), colloidal dispersions of higher-order lipid assemblies with intricate internal structures of 3-D and 2-D symmetry. These particles have been proposed as the next generation of soft-matter nano-carriers, with unique fusogenic and physical properties. Crucially, unlike alternative approaches, our microfluidic method gives control over LLC size, a feature we go on to exploit in a fusogenic study with model cell membranes, where a dependency of fusion on particle diameter is evident. We believe our platform has the potential to serve as a tool for future studies involving non-lamellar soft nanoparticles, and anticipate it allowing for the rapid prototyping of LLC particles of diverse functionality, paving the way toward their eventual wide uptake at an industrial level.

Energetic preference and topological constraint effects on the formation of DNA twisted toroidal bundles

DNA toroids are compact torus-shaped bundles formed by one or multiple DNA molecules being condensed from the solution due to various condensing agents. It has been shown that the DNA toroidal bundles are twisted. However, the global conformations of DNA inside these bundles are still not well understood. In this study, we investigate this issue by solving different models for the toroidal bundles and performing replica-exchange molecular dynamics (REMD) simulations for self-attractive stiff polymers of various chain lengths. We find that a moderate degree of twisting is energetically favorable for toroidal bundles, yielding optimal configurations of lower energies than for other bundles corresponding to spool-like and constant radius of curvature arrangements. The REMD simulations show that the ground states of the stiff polymers are twisted toroidal bundles with the average twist degrees close to those predicted by the theoretical model. Constant-temperature simulations show that twisted toroidal bundles can be formed through successive processes of nucleation, growth, quick tightening, and slow tightening of the toroid, with the two last processes facilitating the polymer threading through the toroid's hole. A relatively long chain of 512 beads has an increased dynamical difficulty to access the twisted bundle states due to the polymer's topological constraint. Interestingly, we also observed significantly twisted toroidal bundles with a sharp U-shaped region in the polymer conformation. It is suggested that this U-shaped region makes the formation of twisted bundles easier by effectively reducing the polymer length. This effect can be equivalent to having multiple chains in the toroid.

Self-Assembled Micro-Sized Hexagons Built from Short DNA in a Crowded Environment

DNA programmable structures of various morphologies have attracted extensive attention due to their potential for materials science and biomedical applications. Here, we report the formation of micro-sized hexagons via assembly of only one pair of short double-stranded DNA in buffer-salt poly(ethylene glycol) solution. Each DNA strand had complementary bases with a two-base overhang. The procedure of heating and subsequent cooling of blunt-ended double-stranded DNA resulted in different assemblies. These results indicated that end-to-end adhesion at the terminals induced by complementary overhangs were required to construct the hexagonal DNA assemblies. The stable formation of the hexagons was highly dependent on heating temperature. In addition, concentration adjustments of DNA and poly(ethylene glycol) were essential. Circular dichroism spectral measurements and polarization microscopy observations indicated parallel alignment of double-stranded DNA in the hexagonal platelet. Self-assembled micro-sized hexagons composed of simple building blocks may have great potential for future biomedical device development.

Toroidal nuclei of columnar lyotropic chromonic liquid crystals coexisting with an isotropic phase

Nuclei of ordered materials emerging from the isotropic state usually show a shape topologically equivalent to a sphere; the well-known examples are crystals and nematic liquid crystal droplets. In this work, we explore experimentally and theoretically the toroidal in shape nuclei of columnar lyotropic chromonic liquid crystals coexisting with the isotropic phase. The geometry of these toroids depends strongly on concentrations of the disodium cromoglycate (DSCG) and the crowding agent, polyethylene glycol (PEG). High concentrations of DSCG and PEG result in thick toroids with small central holes, while low concentrations yield thin toroids with wide holes. The multitude of the observed shapes is explained by the balance of bending elasticity and anisotropic interfacial tension.

Spontaneous Condensation of RNA into Nanoring and Globular Structures

The effect of polyvalent cations, like spermine, on the condensation of DNA into very well-defined toroidal shapes has been well studied and understood. A great effort has been made to obtain similar condensed structures from RNA molecules, but so far, it has been elusive. In this work, we show that single-stranded RNA (ssRNA) molecules can easily be condensed into nanoring and globular structures on a mica surface, where each nanoring structure is formed mostly by a single RNA molecule. The condensation occurs in a concentration range of different cations, from monovalent to trivalent, but at a higher concentration, globular structures appear. RNA nanoring structures were observed on mica surfaces by atomic force microscopy (AFM). The samples were observed in tapping mode and were prepared by drop evaporation of a solution of RNA in the presence of one type of the different cations used. As far as we know, this is the first time that nanorings or any other well-defined condensed RNA structures have been reported in the presence of simple salts. The RNA nanoring formation can be understood by an energy competition between the hydrogen bonding forming hairpin stems-weakened by the salts-and the hairpin loops. This result may have an important biological relevance since it has been proposed that RNA is the oldest genome-coding molecule, and the formation of these structures could have given it stability against degradation in primeval times. Even more, the nanoring structures could have the potential to be used as biosensors and functionalized nanodevices.

Evaluation of DNA-mediated electron transfer using a hole-trapping nucleobase under crowded conditions

The effects of a crowded environment on DNA-mediated electron transfer were evaluated using a pyrene-modified oligonucleotide containing a hole-trapping nucleobase in poly(ethylene glycol) mixed solutions. Rapid decompositions of hole-trapping bases in condensed and noncondensed DNA showed that more efficient electron transfer occurred under crowded conditions than in dilute solutions.

Mechanics of Metric Frustration in Contorted Filament Bundles: From Local Symmetry to Columnar Elasticity

Bundles of filaments are subject to geometric frustration: certain deformations (e.g., bending while twisted) require longitudinal variations in spacing between filaments. While bundles are common-from protein fibers to yarns-the mechanical consequences of longitudinal frustration are unknown. We derive a geometrically nonlinear formalism for bundle mechanics, using a gaugelike symmetry under reptations along filament backbones. We relate force balance to orientational geometry and assess the elastic cost of frustration in twisted-toroidal bundles.

Condensed Supramolecular Helices: The Twisted Sisters of DNA

Condensation of DNA helices into hexagonally packed bundles and toroids represents an intriguing example of functional organization of biological macromolecules at the nanoscale. The condensation models are based on the unique polyelectrolyte features of DNA, however here we could reproduce a DNA‐like condensation with supramolecular helices of small chiral molecules, thereby demonstrating that it is a more general phenomenon. We show that the bile salt sodium deoxycholate can form supramolecular helices upon interaction with oppositely charged polyelectrolytes of homopolymer or block copolymers. At higher order, a controlled hexagonal packing of the helices into DNA‐like bundles and toroids could be accomplished. The results disclose unknown similarities between covalent and supramolecular non‐covalent helical polyelectrolytes, which inspire visionary ideas of constructing supramolecular versions of biological macromolecules. As drug nanocarriers the polymer–bile salt superstructures would get advantage of a complex chirality at molecular and supramolecular levels, whose effect on the nanocarrier assisted drug efficiency is a still unexplored fascinating issue.

Protamine-Controlled Reversible DNA Packaging: A Molecular Glue

Packaging paternal genome into tiny sperm nuclei during spermatogenesis requires 10⁶-fold compaction of DNA, corresponding to a 10-20 times higher compaction than in somatic cells. While such a high level of compaction involves protamine, a small arginine-rich basic protein, the precise mechanism at play is still unclear. Effective pair potential calculations and large-scale molecular dynamics simulations using a simple idealized model incorporating solely electrostatic and steric interactions clearly demonstrate a reversible control on DNA condensates formation by varying the protamine-to-DNA ratio. Microscopic states and condensate structures occurring in semidilute solutions of short DNA fragments are in good agreement with experimental phase diagram and cryoTEM observations. The reversible microscopic mechanisms induced by protamination modulation should provide valuable information to improve a mechanistic understanding of early and intermediate stages of spermatogenesis where an interplay between condensation and liquid-liquid phase separation triggered by protamine expression and post-translational regulation might occur. Moreover, recent vaccines to prevent virus infections and cancers using protamine as a packaging and depackaging agent might be fine-tuned for improved efficiency using a protamination control.

Ion-dependent DNA configuration in bacteriophage capsids

Bacteriophages densely pack their long double-stranded DNA genome inside a protein capsid. The conformation of the viral genome inside the capsid is consistent with a hexagonal liquid crystalline structure. Experiments have confirmed that the details of the hexagonal packing depend on the electrochemistry of the capsid and its environment. In this work, we propose a biophysical model that quantifies the relationship between DNA configurations inside bacteriophage capsids and the types and concentrations of ions present in a biological system. We introduce an expression for the free energy that combines the electrostatic energy with contributions from bending of individual segments of DNA and Lennard-Jones-type interactions between these segments. The equilibrium points of this energy solve a partial differential equation that defines the distributions of DNA and the ions inside the capsid. We develop a computational approach that allows us to simulate much larger systems than what is possible using the existing molecular-level methods. In particular, we are able to estimate bending and repulsion between the DNA segments as well as the full electrochemistry of the solution, both inside and outside of the capsid. The numerical results show good agreement with existing experiments and with molecular dynamics simulations for small capsids.

Chromonic liquid crystals and packing configurations of bacteriophage viruses

We study equilibrium configurations of hexagonal columnar liquid crystals in the context of characterizing packing structures of bacteriophage viruses in a protein capsid. These are viruses that infect bacteria and are currently the focus of intense research efforts, with the goal of finding new therapies for bacteria-resistant antibiotics. The energy that we propose consists of the Oseen-Frank free energy of nematic liquid crystals that penalizes bending of the columnar directions, in addition to the cross-sectional elastic energy accounting for distortions of the transverse hexagonal structure; we also consider the isotropic contribution of the core and the energy of the unknown interface between the outer ordered region of the capsid and the inner disordered core. The problem becomes of free boundary type, with constraints. We show that the concentric, azimuthal, spool-like configuration is the absolute minimizer. Moreover, we present examples of toroidal structures formed by DNA in free solution and compare them with the analogous ones occurring in experiments with other types of lyotropic liquid crystals, such as food dyes and additives. This article is part of the theme issue 'Topics in mathematical design of complex materials'.

DNA looping by protamine follows a nonuniform spatial distribution

DNA looping plays an important role in cells in both regulating and protecting the genome. Often, studies of looping focus on looping by prokaryotic transcription factors like lac repressor or by structural maintenance of chromosomes proteins such as condensin. Here, however, we are interested in a different looping method whereby condensing agents (charge ≥+3) such as protamine proteins neutralize the DNA, causing it to form loops and toroids. We considered two previously proposed mechanisms for DNA looping by protamine. In the first mechanism, protamine stabilizes spontaneous DNA fluctuations, forming randomly distributed loops along the DNA. In the second mechanism, protamine binds and bends the DNA to form a loop, creating a distribution of loops that is biased by protamine binding. To differentiate between these mechanisms, we imaged both spontaneous and protamine-induced loops on short-length (≤1 μm) DNA fragments using atomic force microscopy. We then compared the spatial distribution of the loops to several model distributions. A random looping model, which describes the mechanism of spontaneous DNA folding, fit the distribution of spontaneous loops, but it did not fit the distribution of protamine-induced loops. Specifically, it failed to predict a peak in the spatial distribution of loops at an intermediate location along the DNA. An electrostatic multibinding model, which was created to mimic the bind-and-bend mechanism of protamine, was a better fit of the distribution of protamine-induced loops. In this model, multiple protamines bind to the DNA electrostatically within a particular region along the DNA to coordinate the formation of a loop. We speculate that these findings will impact our understanding of protamine’s in vivo role for looping DNA into toroids and the mechanism of DNA condensation by condensing agents more broadly.

Local structure of DNA toroids reveals curvature-dependent intermolecular forces

In viruses and cells, DNA is closely packed and tightly curved thanks to polyvalent cations inducing an effective attraction between its negatively charged filaments. Our understanding of this effective attraction remains very incomplete, partly because experimental data is limited to bulk measurements on large samples of mostly uncurved DNA helices. Here we use cryo electron microscopy to shed light on the interaction between highly curved helices. We find that the spacing between DNA helices in spermine-induced DNA toroidal condensates depends on their location within the torus, consistent with a mathematical model based on the competition between electrostatic interactions and the bending rigidity of DNA. We use our model to infer the characteristics of the interaction potential, and find that its equilibrium spacing strongly depends on the curvature of the filaments. In addition, the interaction is much softer than previously reported in bulk samples using different salt conditions. Beyond viruses and cells, our characterization of the interactions governing DNA-based dense structures could help develop robust designs in DNA nanotechnologies.

Guanine damage by singlet oxygen from SYBR Green I in liquid crystalline DNA

It is known that double-stranded DNA (dsDNA) turns into a liquid crystalline phase by the addition of a high concentration of polymer with salt. SYBR Green I (SG) is a well-known sensitive fluorescent stain for dsDNA, and is intercalated in liquid crystalline DNA. Formation of the liquid crystalline dsDNA-SG complex has been confirmed by CD spectral measurements, fluorescence spectral measurements and confocal fluorescence microscopy. SG in dsDNA was also used as a singlet oxygen generator. We conducted photoirradiation experiments using three kinds of 42-mer oligonucleotides with SG. The amount of guanine decomposition by selective irradiation of SG was analyzed using HPLC after digestion of dsDNA in each sample solution. We found that singlet oxygen produced in liquid crystalline DNA promoted guanine damage much more efficiently than in homogeneous solution.

Structure-guided DNA-DNA attraction mediated by divalent cations

Probing the role of surface structure in electrostatic interactions, we report the first observation of sequence-dependent dsDNA condensation by divalent alkaline earth metal cations. Disparate behaviors were found between two repeating sequences with 100% AT content, a poly(A)-poly(T) duplex (AA-TT) and a poly(AT)-poly(TA) duplex (AT-TA). While AT-TA exhibits non-distinguishable behaviors from random-sequence genomic DNA, AA-TT condenses in all alkaline earth metal ions. We characterized these interactions experimentally and investigated the underlying principles using computer simulations. Both experiments and simulations demonstrate that AA-TT condensation is driven by non-specific ion–DNA interactions. Detailed analyses reveal sequence-enhanced major groove binding (SEGB) of point-charged alkali ions as the major difference between AA-TT and AT-TA, which originates from the continuous and close stacking of nucleobase partial charges. These SEGB cations elicit attraction via spatial juxtaposition with the phosphate backbone of neighboring helices, resulting in an azimuthal angular shift between apposing helices. Our study thus presents a distinct mechanism in which, sequence-directed surface motifs act with cations non-specifically to enact sequence-dependent behaviors. This physical insight allows a renewed understanding of the role of repeating sequences in genome organization and regulation and offers a facile approach for DNA technology to control the assembly process of nanostructures.

Structural Polymorphism of Single pDNA Condensates Elicited by Cationic Block Polyelectrolytes

DNA folding is a core phenomenon in genome packaging within a nucleus. Such a phenomenon is induced by polyelectrolyte complexation between anionic DNA and cationic proteins of histones. In this regard, complexes formed between DNA and cationic polyelectrolytes have been investigated as models to gain insight into genome packaging. Upon complexation, DNA undergoes folding to reduce its occupied volume, which often results in multi-complex associated aggregates. However, when cationic copolymers comprising a polycation block and a neutral hydrophilic polymer block are used instead, DNA undergoes folding as a single molecule within a spontaneously formed polyplex micelle (PM), thereby allowing the observation of the higher-order structures that DNA forms. The DNA complex forms polymorphic structures, including globular, rod-shaped, and ring-shaped (toroidal) structures. This review focuses on the polymorphism of DNA, particularly, to elucidate when, how, and why DNA organizes into these structures with cationic copolymers. The interactions between DNA and the copolymers, and the specific nature of DNA in rigidity; i.e., rigid but foldable, play significant roles in the observed polymorphism. Moreover, PMs serve as potential gene vectors for systemic application. The significance of the controlled DNA folding for such an application is addressed briefly in the last part.

Fine structure of viral dsDNA encapsidation

Unraveling the mechanisms of packing of DNA inside viral capsids is of fundamental importance to understanding the spread of viruses. It could also help develop new applications to targeted drug delivery devices for a large range of therapies. In this article, we present a robust, predictive mathematical model and its numerical implementation to aid the study and design of bacteriophage viruses for application purposes. Exploiting the analogies between the columnar hexagonal chromonic phases of encapsidated viral DNA and chromonic aggregates formed by plank-shaped molecular compounds, we develop a first-principles effective mechanical model of DNA packing in a viral capsid. The proposed expression of the packing energy, which combines relevant aspects of the liquid crystal theory, is developed from the model of hexagonal columnar phases, together with that describing configurations of polymeric liquid crystals. The method also outlines a parameter selection strategy that uses available data for a collection of viruses, aimed at applications to viral design. The outcome of the work is a mathematical model and its numerical algorithm, based on the method of finite elements, and computer simulations to identify and label the ordered and disordered regions of the capsid and calculate the inner pressure. It also presents the tools for the local reconstruction of the DNA "scaffolding" and the center curve of the filament within the capsid.

Adenovirus major core protein condenses DNA in clusters and bundles, modulating genome release and capsid internal pressure

Some viruses package dsDNA together with large amounts of positively charged proteins, thought to help condense the genome inside the capsid with no evidence. Further, this role is not clear because these viruses have typically lower packing fractions than viruses encapsidating naked dsDNA. In addition, it has recently been shown that the major adenovirus condensing protein (polypeptide VII) is dispensable for genome encapsidation. Here, we study the morphology and mechanics of adenovirus particles with (Ad5-wt) and without (Ad5-VII-) protein VII. Ad5-VII- particles are stiffer than Ad5-wt, but DNA-counterions revert this difference, indicating that VII screens repulsive DNA-DNA interactions. Consequently, its absence results in increased internal pressure. The core is slightly more ordered in the absence of VII and diffuses faster out of Ad5-VII– than Ad5-wt fractured particles. In Ad5-wt unpacked cores, dsDNA associates in bundles interspersed with VII-DNA clusters. These results indicate that protein VII condenses the adenovirus genome by combining direct clustering and promotion of bridging by other core proteins. This condensation modulates the virion internal pressure and DNA release from disrupted particles, which could be crucial to keep the genome protected inside the semi-disrupted capsid while traveling to the nuclear pore.

A multiscale analysis of DNA phase separation: from atomistic to mesoscale level

DNA condensation and phase separation is of utmost importance for DNA packing in vivo with important applications in medicine, biotechnology and polymer physics. The presence of hexagonally ordered DNA is observed in virus capsids, sperm heads and in dinoflagellates. Rigorous modelling of this process in all-atom MD simulations is presently difficult to achieve due to size and time scale limitations. We used a hierarchical approach for systematic multiscale coarse-grained (CG) simulations of DNA phase separation induced by the three-valent cobalt(III)-hexammine (CoHex³⁺). Solvent-mediated effective potentials for a CG model of DNA were extracted from all-atom MD simulations. Simulations of several hundred 100-bp-long CG DNA oligonucleotides in the presence of explicit CoHex³⁺ ions demonstrated aggregation to a liquid crystalline hexagonally ordered phase. Following further coarse-graining and extraction of effective potentials, we conducted modelling at mesoscale level. In agreement with electron microscopy observations, simulations of an 10.2-kb-long DNA molecule showed phase separation to either a toroid or a fibre with distinct hexagonal DNA packing. The mechanism of toroid formation is analysed in detail. The approach used here is based only on the underlying all-atom force field and uses no adjustable parameters and may be generalised to modelling chromatin up to chromosome size.

Real-Time Assembly of Viruslike Nucleocapsids Elucidated at the Single-Particle Level

While the structure of a multitude of viral particles has been resolved to atomistic detail, their assembly pathways remain largely elusive. Key unresolved issues are particle nucleation, particle growth, and the mode of genome compaction. These issues are difficult to address in bulk approaches and are effectively only accessible by the real-time tracking of assembly dynamics of individual particles. This we do here by studying the assembly into rod-shaped viruslike particles (VLPs) of artificial capsid polypeptides. Using fluorescence optical tweezers, we establish that small oligomers perform one-dimensional diffusion along the DNA. Larger oligomers are immobile and nucleate VLP growth. A multiplexed acoustic force spectroscopy approach reveals that DNA is compacted in regular steps, suggesting packaging via helical wrapping into a nucleocapsid. By reporting how real-time assembly tracking elucidates viral nucleation and growth principles, our work opens the door to a fundamental understanding of the complex assembly pathways of both VLPs and naturally evolved viruses.

Polyamine-induced, chiral expression from liquid crystalline peptide nanofilaments to long-range ordered nanohelices

We reported the condensation and transformation of peptide micelles into well-defined nanohelices through the incorporation of natural polyamines. The liquid-crystalline peptide micelles are assembled by a short dipeptide amphiphile driven by strong electrostatic repulsions and aromatic stacking attractions. By incorporating polyamines into the peptide solutions, like-charge attractions were achieved to induce the condensation of the like-charged nanofilaments into giant bundles. Intriguingly, by increasing the temperature or electrostatic screening effects, the nanofilaments within the bundles fuse with each other into well-defined flat ribbons which then spontaneously twisted into macroscopically aligned nanohelices. Moreover, the chiral interactions between the aromatic groups of adjacent peptides are inverted from right-handedness to left-handedness during the formation of nanohelices. The results provide new insights into the chiral evolution during peptide self-assembly and offer opportunities for the design of peptide materials with new properties, such as anisotropic hydrogels and long-range ordered chiral nanostructures.

Cryo-EM structure and in vitro DNA packaging of a thermophilic virus with supersized T=7 capsids

Understanding molecular events during virus assembly and genome packaging is important for understanding viral life cycles, and the functioning of other protein–nucleic acid machines. The model system developed for the thermophilic bacteriophage P23-45 offers advantages over other systems. Cryo-EM reconstructions reveal modifications to a canonical capsid protein fold, resulting in capsids that are abnormally large for this virus class. Structural information on the portal protein, through which the genome is packaged, demonstrates that the capsid influences the portal’s conformation. This has implications for understanding how processes inside and outside the capsid can be coordinated.

Double-stranded DNA viruses, including bacteriophages and herpesviruses, package their genomes into preformed capsids, using ATP-driven motors. Seeking to advance structural and mechanistic understanding, we established in vitro packaging for a thermostable bacteriophage, P23-45 of Thermus thermophilus. Both the unexpanded procapsid and the expanded mature capsid can package DNA in the presence of packaging ATPase over the 20 °C to 70 °C temperature range, with optimum activity at 50 °C to 65 °C. Cryo-EM reconstructions for the mature and immature capsids at 3.7-Å and 4.4-Å resolution, respectively, reveal conformational changes during capsid expansion. Capsomer interactions in the expanded capsid are reinforced by formation of intersubunit β-sheets with N-terminal segments of auxiliary protein trimers. Unexpectedly, the capsid has T=7 quasi-symmetry, despite the P23-45 genome being twice as large as those of known T=7 phages, in which the DNA is compacted to near-crystalline density. Our data explain this anomaly, showing how the canonical HK97 fold has adapted to double the volume of the capsid, while maintaining its structural integrity. Reconstructions of the procapsid and the expanded capsid defined the structure of the single vertex containing the portal protein. Together with a 1.95-Å resolution crystal structure of the portal protein and DNA packaging assays, these reconstructions indicate that capsid expansion affects the conformation of the portal protein, while still allowing DNA to be packaged. These observations suggest a mechanism by which structural events inside the capsid can be communicated to the outside.

Influence of Microscopic Interactions on the Flexible Mechanical Properties of Viral DNA

During the packaging and ejection of viral DNA, its mechanical properties play an essential role in viral infection. Some of these mechanical properties originate from different microscopic interactions of the encapsulated DNA in the capsid. Based on an updated mesoscopic model of the interaction potential by Parsegian et al., an alternative continuum elastic model of the free energy of the confined DNA in the capsid is developed in this work. With this model, we not only quantitatively identify the respective contributions from hydration repulsion, electrostatic repulsion, entropy and elastic bending but also predict the ionic effect of viral DNA's mechanical properties during the packaging and ejection. The relevant predictions are quantitively or qualitatively consistent with the existing experimental results. Furthermore, the nonmonotonous or monotonous changes in the respective contributions of microscopic interactions to the ejection force and free energy at different ejection stages are revealed systematically. Among these, the nonmonotonicity in the entropic contribution implies a transition of viral DNA structure from order to disorder during the ejection.

Peptide-Induced DNA Condensation into Virus-Mimicking Nanostructures

A series of surfactant-like peptides have been designed for inducing DNA condensation, which are all comprised of the same set of amino acids in different sequences. Results from experiments and molecular dynamics simulations show that the peptide's self-assembly and DNA-interaction behaviors can be well manipulated through sequence variation. With optimized pairing modes between the β-sheets, the peptide of I₃V₃A₃G₃K₃ can induce efficient DNA condensation into virus-mimicking structures. The condensation involves two steps; the peptide molecules first bind onto the DNA chain through electrostatic interactions and then self-associate into β-sheets under hydrophobic interactions and hydrogen bonding. In such condensates, the peptide β-sheets act as scaffolds to assist the ordered arrangement of DNA, mimicking the very nature of the virus capsid in helping DNA packaging. Such a hierarchy affords an extremely stable structure to attain the highly condensed state and protect DNA against enzymatic degradation. Moreover, the condensate size can be well tuned by the DNA length. The condensates with smaller sizes and narrow size distribution can deliver DNA efficiently into cells. The study helps not only for probing into the DNA packaging mechanism in virus but also delineating the role of peptide self-assembly in DNA condensation, which may lead to development of peptide-based gene vectors for therapeutic applications.

Block Copolymer Micelles in Nanomedicine Applications

Polymeric micelles are demonstrating high potential as nanomedicines capable of controlling the distribution and function of loaded bioactive agents in the body, effectively overcoming biological barriers, and various formulations are engaged in intensive preclinical and clinical testing. This Review focuses on polymeric micelles assembled through multimolecular interactions between block copolymers and the loaded drugs, proteins, or nucleic acids as translationable nanomedicines. The aspects involved in the design of successful micellar carriers are described in detail on the basis of the type of polymer/payload interaction, as well as the interplay of micelles with the biological interface, emphasizing on the chemistry and engineering of the block copolymers. By shaping these features, polymeric micelles have been propitious for delivering a wide range of therapeutics through effective sensing of targets in the body and adjustment of their properties in response to particular stimuli, modulating the activity of the loaded drugs at the targeted sites, even at the subcellular level. Finally, the future perspectives and imminent challenges for polymeric micelles as nanomedicines are discussed, anticipating to spur further innovations.

Toroidal Condensates by Semiflexible Polymer Chains: Insights into Nucleation, Growth and Packing Defects

Deciphering the principles of DNA condensation is important to understand problems such as genome packing and DNA compaction for delivery in gene therapy. DNA molecules condense into toroids and spindles upon the addition of multivalent ions. Nucleation of a loop in the semiflexible DNA chain is critical for both the toroid and spindle formation. To understand the structural differences in the nucleated loop, which cause bifurcation in the condensation pathways leading to toroid or spindle formation, we performed molecular dynamics simulations using a coarse-grained bead-spring polymer model. We find that the formation of a toroid or a spindle is correlated with the orientation of the chain segments close to the loop closure in the nucleated loop. Simulations show that toroids grow in size when spindles in solution interact with a pre-existing toroid and merge into it by spooling around the circumference of the toroid, forming multimolecular toroidal condensates. The merging of spindles with toroids is facile, indicating that this should be the dominant pathway through which the toroids grow in size. The Steinhardt bond order parameter analysis of the toroid cross section shows that the chains pack in a hexagonal fashion. In agreement with the experiments there are regions in the toroid with good hexagonal packing and also with considerable disorder. The disorder in packing is due to the defects, which are propagated during the growth of toroids. In addition to the well-known crossover defect, we have identified three other forms of defects, which perturb hexagonal packing. The new defects identified in the simulations are amenable to experimental verification.

Drop-on-coilable-fibre systems exhibit negative stiffness events and transitions in coiling morphology

We investigate the mechanics of elastic fibres carrying liquid droplets. In such systems, buckling may localize inside the drop cavity if the fibre is thin enough. This so-called drop-on-coilable-fibre system exhibits a surprising liquid-like response under compression and a solid-like response under tension. Here we analyze this unconventional behavior in further detail and find theoretical, numerical and experimental evidence of negative stiffness events. We find that the first and main negative stiffness regime owes its existence to the transfer of capillary-stored energy into mechanical curvature energy. The following negative stiffness events are associated with changes in the coiling morphology of the fibre. Eventually coiling becomes tightly locked into an ordered phase where liquid and solid deformations coexist.

Evidence of protein-free homology recognition in magnetic bead force-extension experiments

Earlier theoretical studies have proposed that the homology-dependent pairing of large tracts of dsDNA may be due to physical interactions between homologous regions. Such interactions could contribute to the sequence-dependent pairing of chromosome regions that may occur in the presence or the absence of double-strand breaks. Several experiments have indicated the recognition of homologous sequences in pure electrolytic solutions without proteins. Here, we report single-molecule force experiments with a designed 60 kb long dsDNA construct; one end attached to a solid surface and the other end to a magnetic bead. The 60 kb constructs contain two 10 kb long homologous tracts oriented head to head, so that their sequences match if the two tracts fold on each other. The distance between the bead and the surface is measured as a function of the force applied to the bead. At low forces, the construct molecules extend substantially less than normal, control dsDNA, indicating the existence of preferential interaction between the homologous regions. The force increase causes no abrupt but continuous unfolding of the paired homologous regions. Simple semi-phenomenological models of the unfolding mechanics are proposed, and their predictions are compared with the data.

A route to self-assemble suspended DNA nano-complexes

Highly charged polyelectrolytes can self-assemble in presence of condensing agents such as multivalent cations, amphiphilic molecules or proteins of opposite charge. Aside precipitation, the formation of soluble micro- and nano-particles has been reported in multiple systems. However a precise control of experimental conditions needed to achieve the desired structures has been so far hampered by the extreme sensitivity of the samples to formulation pathways. Herein we combine experiments and molecular modelling to investigate the detailed microscopic dynamics and the structure of self-assembled hexagonal bundles made of short dsDNA fragments complexed with small basic proteins. We suggest that inhomogeneous mixing conditions are required to form and stabilize charged self-assembled nano-aggregates in large excess of DNA. Our results should help re-interpreting puzzling behaviors reported for a large class of strongly charged polyelectrolyte systems.

The structure and intermolecular forces of DNA condensates

Spontaneous assembly of DNA molecules into compact structures is ubiquitous in biological systems. Experiment has shown that polycations can turn electrostatic self-repulsion of DNA into attraction, yet the physical mechanism of DNA condensation has remained elusive. Here, we report the results of atomistic molecular dynamics simulations that elucidated the microscopic structure of dense DNA assemblies and the physics of interactions that makes such assemblies possible. Reproducing the setup of the DNA condensation experiments, we measured the internal pressure of DNA arrays as a function of the DNA–DNA distance, showing a quantitative agreement between the results of our simulations and the experimental data. Analysis of the MD trajectories determined the DNA–DNA force in a DNA condensate to be pairwise, the DNA condensation to be driven by electrostatics of polycations and not hydration, and the concentration of bridging cations, not adsorbed cations, to determine the magnitude and the sign of the DNA–DNA force. Finally, our simulations quantitatively characterized the orientational correlations of DNA in DNA arrays as well as diffusive motion of DNA and cations.

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.

Theory and simulations of toroidal and rod-like structures in single-molecule DNA condensation

DNA condensation by multivalent cations plays a crucial role in genome packaging in viruses and sperm heads, and has been extensively studied using single-molecule experimental methods. In those experiments, the values of the critical condensation forces have been used to estimate the amplitude of the attractive DNA-DNA interactions. Here, to describe these experiments, we developed an analytical model and a rigid body Langevin dynamics assay to investigate the behavior of a polymer with self-interactions, in the presence of a traction force applied at its extremities. We model self-interactions using a pairwise attractive potential, thereby treating the counterions implicitly. The analytical model allows to accurately predict the equilibrium structures of toroidal and rod-like condensed structures, and the dependence of the critical condensation force on the DNA length. We find that the critical condensation force depends strongly on the length of the DNA, and finite-size effects are important for molecules of length up to 10(5)μm. Our Langevin dynamics simulations show that the force-extension behavior of the rod-like structures is very different from the toroidal ones, so that their presence in experiments should be easily detectable. In double-stranded DNA condensation experiments, the signature of the presence of rod-like structures was not unambiguously detected, suggesting that the polyamines used to condense DNA may protect it from bending sharply as needed in the rod-like structures.

Mechanics of Viral Chromatin Reveals the Pressurization of Human Adenovirus

Tight confinement of naked genomes within some viruses results in high internal pressure that facilitates their translocation into the host. Adenovirus, however, encodes histone-like proteins that associate with its genome resulting in a confined DNA-protein condensate (core). Cleavage of these proteins during maturation decreases core condensation and primes the virion for proper uncoating via unidentified mechanisms. Here we open individual, mature and immature adenovirus cages to directly probe the mechanics of their chromatin-like cores. We find that immature cores are more rigid than the mature ones, unveiling a mechanical signature of their condensation level. Conversely, intact mature particles demonstrate more rigidity than immature or empty ones. DNA-condensing polyamines revert the mechanics of mature capsid and cores to near-immature values. The combination of these experiments reveals the pressurization of adenovirus particles induced by maturation. We estimate a pressure of ∼30 atm by continuous elasticity, which is corroborated by modeling the adenovirus mini-chromosome as a confined compact polymer. We propose this pressurization as a mechanism that facilitates initiating the stepwise disassembly of the mature particle, enabling its escape from the endosome and final genome release at the nuclear pore.

Which way up? Recognition of homologous DNA segments in parallel and antiparallel alignments

Homologous gene shuffling between DNA molecules promotes genetic diversity and is an important pathway for DNA repair. For this to occur, homologous genes need to find and recognize each other. However, despite its central role in homologous recombination, the mechanism of homology recognition has remained an unsolved puzzle of molecular biology. While specific proteins are known to play a role at later stages of recombination, an initial coarse grained recognition step has, however, been proposed. This relies on the sequence dependence of the DNA structural parameters, such as twist and rise, mediated by intermolecular interactions, in particular, electrostatic ones. In this proposed mechanism, sequences that have the same base pair text, or are homologous, have lower interaction energy than those sequences with uncorrelated base pair texts. The difference between the two energies is termed the "recognition energy." Here, we probe how the recognition energy changes when one DNA fragment slides past another, and consider, for the first time, homologous sequences in antiparallel alignment. This dependence on sliding is termed the "recognition well." We find there is a recognition well for anti-parallel, homologous DNA tracts, but only a very shallow one, so that their interaction will differ little from the interaction between two nonhomologous tracts. This fact may be utilized in single molecule experiments specially targeted to test the theory. As well as this, we test previous theoretical approximations in calculating the recognition well for parallel molecules against MC simulations and consider more rigorously the optimization of the orientations of the fragments about their long axes upon calculating these recognition energies. The more rigorous treatment affects the recognition energy a little, when the molecules are considered rigid. When torsional flexibility of the DNA molecules is introduced, we find excellent agreement between the analytical approximation and simulations.

Controlling the extent of viral genome release by a combination of osmotic stress and polyvalent cations

While several in vitro experiments on viral genome release have specifically studied the effects of external osmotic pressure and of the presence of polyvalent cations on the ejection of DNA from bacteriophages, few have systematically investigated how the extent of ejection is controlled by a combination of these effects. In this work we quantify the effect of osmotic pressure on the extent of DNA ejection from bacteriophage lambda as a function of polyvalent cation concentration (in particular, the tetravalent polyamine spermine). We find that the pressure required to completely inhibit ejection decreases from 38 to 17 atm as the spermine concentration is increased from 0 to 1.5 mM. Further, incubation of the phage particles in spermine concentrations as low as 0.15 mM--the threshold for DNA condensation in bulk solution-is sufficient to significantly limit the extent of ejection in the absence of osmolyte; for spermine concentrations below this threshold, the ejection is complete. In accord with recent investigations on the packaging of DNA in the presence of a condensing agent, we observe that the self-attraction induced by the polyvalent cation affects the ordering of the genome, causing it to get stuck in a broad range of nonequilibrated structures.

Confined polyelectrolytes: The complexity of a simple system

The interaction between polyelectrolytes and counterions in confined situations and the mutual relationship between chain conformation and ion condensation is an important issue in several areas. In the biological field, it assumes particular relevance in the understanding of the packaging of nucleic acids, which is crucial in the design of gene delivery systems. In this work, a simple coarse-grained model is used to assess the cooperativity between conformational change and ion condensation in spherically confined backbones, with capsides permeable to the counterions. It is seen that the variation on the degree of condensation depends on counterion valence. For monovalent counterions, the degree of condensation passes through a minimum before increasing as the confining space diminishes. In contrast, for trivalent ions, the overall tendency is to decrease the degree of condensation as the confinement space also decreases. Most of the particles reside close to the spherical wall, even for systems in which the density is higher closer to the cavity center. This effect is more pronounced, when monovalent counterions are present. Additionally, there are clear variations in the charge along the concentric layers that cannot be totally ascribed to polyelectrolyte behavior, as shown by decoupling the chain into monomers. If both chain and counterions are confined, the formation of a counterion rich region immediately before the wall is observed. Spool and doughnut-like structures are formed for stiff chains, within a nontrivial evolution with increasing confinement.

Modeling Viral Capsid Assembly

I present a review of the theoretical and computational methodologies that have been used to model the assembly of viral capsids. I discuss the capabilities and limitations of approaches ranging from equilibrium continuum theories to molecular dynamics simulations, and I give an overview of some of the important conclusions about virus assembly that have resulted from these modeling efforts. Topics include the assembly of empty viral shells, assembly around single-stranded nucleic acids to form viral particles, and assembly around synthetic polymers or charged nanoparticles for nanotechnology or biomedical applications. I present some examples in which modeling efforts have promoted experimental breakthroughs, as well as directions in which the connection between modeling and experiment can be strengthened.

Modeling DNA condensation on freestanding cationic lipid membranes

Motivated by recent experimental observations of a rapid spontaneous DNA coil-globule transition on freestanding cationic lipid bilayers, we propose simple theoretical models for DNA condensation on cationic lipid membranes. First, for a single DNA rod, we examine the conditions of full wrapping of a cylindrical DNA-like semi-flexible polyelectrolyte by an oppositely charged membrane. Then, for two parallel DNA rods, we self-consistently analyze the shape and the extent of the membrane enveloping them, focusing on membrane elastic deformations and the membrane-DNA embracing angle, which enables us to compute the membrane-mediated DNA-DNA interactions. We examine the effects of the membrane composition and its charge density, which are the experimentally tunable parameters. We show that membrane-driven rod-rod attraction is more pronounced for higher charge densities and for smaller surface tensions of the membrane. Thus, we demonstrate that for a long DNA chain adhered to a cationic lipid membrane, such membrane-induced DNA-DNA attraction can trigger compaction of DNA.

Saddle-splay screening and chiral symmetry breaking in toroidal nematics

We present a theoretical study of director fields in toroidal geometries with degenerate planar boundary conditions. We find spontaneous chirality: despite the achiral nature of nematics the director configuration shows a handedness if the toroid is thick enough. In the chiral state the director field displays a double twist, whereas in the achiral state there is only bend deformation. The critical thickness increases as the difference between the twist and saddle-splay moduli grows. A positive saddle-splay modulus prefers alignment along the meridian of the bounding torus, and hence promotes a chiral configuration. The chiral-achiral transition mimics the order-disorder transition of the mean-field Ising model. The role of the magnetisation in the Ising model is played by the degree of twist. The role of the temperature is played by the aspect ratio of the torus. Remarkably, an external field does not break the chiral symmetry explicitly, but shifts the transition. In the case of toroidal cholesterics, we do find a preference for one chirality over the other - the molecular chirality acts as a field in the Ising analogy.

Repulsive DNA-DNA interactions accelerate viral DNA packaging in phage Phi29

We use optical tweezers to study the effect of attractive versus repulsive DNA-DNA interactions on motor-driven viral packaging. Screening of repulsive interactions accelerates packaging, but induction of attractive interactions by spermidine(3+) causes heterogeneous dynamics. Acceleration is observed in a fraction of complexes, but most exhibit slowing and stalling, suggesting that attractive interactions promote nonequilibrium DNA conformations that impede the motor. Thus, repulsive interactions facilitate packaging despite increasing the energy of the theoretical optimum spooled DNA conformation.

An elastic rod model to evaluate effects of ionic concentration on equilibrium configuration of DNA in salt solution

As a coarse-gained model, a super-thin elastic rod subjected to interfacial interactions is used to investigate the condensation of DNA in a multivalent salt solution. The interfacial traction between the rod and the solution environment is determined in terms of the Young-Laplace equation. Kirchhoff's theory of elastic rod is used to analyze the equilibrium configuration of a DNA chain under the action of the interfacial traction. Two models are established to characterize the change of the interfacial traction and elastic modulus of DNA with the ionic concentration of the salt solution, respectively. The influences of the ionic concentration on the equilibrium configuration of DNA are discussed. The results show that the condensation of DNA is mainly determined by competition between the interfacial energy and elastic strain energy of the DNA itself, and the interfacial traction is one of forces that drive DNA condensation. With the change of concentration, the DNA segments will undergo a series of alteration from the original configuration to the condensed configuration, and the spiral-shape appearing in the condensed configuration of DNA is independent of the original configuration.

RELATIONSHIP BETWEEN THE GENOME PACKING IN THE BACTERIOPHAGE CAPSID AND THE KINETICS OF DNA EJECTION

We present a general survey of experimental and theoretical observations of DNA structure and in vitro ejection kinetics for different bacteriophage species. In some species, like T5, the ejection may present pauses and arrests that have not been detected in others species like Lambda. We propose hypotheses to explain such differences and we discuss how the experimental conditions may be important for their detection. Our work highlights the role of DNA organization inside the bacteriophage capsid on the stochastic and out of equilibrium nature of the ejection process.