Protein-DNA interactions determine the shapes of DNA toroids condensed in virus capsids

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.

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.

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.

Phage G Structure at 6.1 Å Resolution, Condensed DNA, and Host Identity Revision to a Lysinibacillus

Phage G has the largest capsid and genome of any known propagated phage. Many aspects of its structure, assembly, and replication have not been elucidated. Herein, we present the dsDNA-packed and empty phage G capsid at 6.1 and 9 Å resolution, respectively, using cryo-EM for structure determination and mass spectrometry for protein identification. The major capsid protein, gp27, is identified and found to share the HK97-fold universally conserved in all previously solved dsDNA phages. Trimers of the decoration protein, gp26, sit on the 3-fold axes and are thought to enhance the interactions of the hexameric capsomeres of gp27, for other phages encoding decoration proteins. Phage G's decoration protein is longer than what has been reported in other phages, and we suspect the extra interaction surface area helps stabilize the capsid. We identified several additional capsid proteins, including a candidate for the prohead protease responsible for processing gp27. Furthermore, cryo-EM reveals a range of partially full, condensed DNA densities that appear to have no contact with capsid shell. Three analyses confirm that the phage G host is a Lysinibacillus, and not Bacillus megaterium: identity of host proteins in our mass spectrometry analyses, genome sequence of the phage G host, and host range of phage G.

Biodegradable Polymers for Gene Delivery

The cellular transport process of DNA is hampered by cell membrane barriers, and hence, a delivery vehicle is essential for realizing the potential benefits of gene therapy to combat a variety of genetic diseases. Virus-based vehicles are effective, although immunogenicity, toxicity and cancer formation are among the major limitations of this approach. Cationic polymers, such as polyethyleneimine are capable of condensing DNA to nanoparticles and facilitate gene delivery. Lack of biodegradation of polymeric gene delivery vehicles poses significant toxicity because of the accumulation of polymers in the tissue. Many attempts have been made to develop biodegradable polymers for gene delivery by modifying existing polymers and/or using natural biodegradable polymers. This review summarizes mechanistic aspects of gene delivery and the development of biodegradable polymers for gene delivery.

Role of metallic core for the stability of virus-like particles in strongly coupled electrostatics

Electrostatic interactions play important roles in the formation and stability of viruses and virus-like particles (VLPs) through processes that often involve added, or naturally occurring, multivalent ions. Here, we investigate the electrostatic or osmotic pressure acting on the proteinaceous shell of a generic model of VLPs, comprising a charged outer shell and a metallic nanoparticle core, coated by a charged layer and bathed in an aqueous electrolyte solution. Motivated by the recent studies accentuating the role of multivalent ions for the stability of VLPs, we focus on the effects of multivalent cations and anions in an otherwise monovalent ionic solution. We perform extensive Monte-Carlo simulations based on appropriate Coulombic interactions that consistently take into account the effects of salt screening, the dielectric polarization of the metallic core, and the strong-coupling electrostatics due to multivalent ions. We specifically study the intricate roles these factors play in the electrostatic stability of the model VLPs. It is shown that while the insertion of a metallic nanoparticle by itself can produce negative, inward-directed, pressure on the outer shell, addition of only a small amount of multivalent counterions can robustly engender negative pressures, enhancing the VLP stability across a wide range of values for the system parameters.

Limiting shapes of confined lipid vesicles

We theoretically study the shapes of lipid vesicles confined to a spherical cavity, elaborating a framework based on the so-called limiting shapes constructed from geometrically simple structural elements such as double-membrane walls and edges. Partly inspired by numerical results, the proposed non-compartmentalized and compartmentalized limiting shapes are arranged in the bilayer-couple phase diagram which is then compared to its free-vesicle counterpart. We also compute the area-difference-elasticity phase diagram of the limiting shapes and we use it to interpret shape transitions experimentally observed in vesicles confined within another vesicle. The limiting-shape framework may be generalized to theoretically investigate the structure of certain cell organelles such as the mitochondrion.

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.

Shapes of minimal-energy DNA ropes condensed in confinement

Shapes of a single, long DNA molecule condensed in a confinement of a virus capsid are described as conformations optimizing a model free energy functional accounting for the interplay between the bending energy of the DNA and the surface energy of the DNA bundled in a “rope”. The rope is formed by bundled DNA brought together by (self-)attractive interactions. The conformations predicted by the model depend on the shape of the confinement, the total amount of the packed DNA but also on the relative contributions of the bending and surface energies. Some of the conformations found were not predicted previously, but many previously proposed DNA conformations, some of which are seemingly contradictory, were found as the solutions of the model. The results show that there are many possible packing conformations of the DNA and that the one which realizes in a particular virus depends on the capsid geometry and the nature of condensing agents.

How topoisomerase IV can efficiently unknot and decatenate negatively supercoiled DNA molecules without causing their torsional relaxation

Freshly replicated DNA molecules initially form multiply interlinked right-handed catenanes. In bacteria, these catenated molecules become supercoiled by DNA gyrase before they undergo a complete decatenation by topoisomerase IV (Topo IV). Topo IV is also involved in the unknotting of supercoiled DNA molecules. Using Metropolis Monte Carlo simulations, we investigate the shapes of supercoiled DNA molecules that are either knotted or catenated. We are especially interested in understanding how Topo IV can unknot right-handed knots and decatenate right-handed catenanes without acting on right-handed plectonemes in negatively supercoiled DNA molecules. To this end, we investigate how the topological consequences of intersegmental passages depend on the geometry of the DNA-DNA juxtapositions at which these passages occur. We observe that there are interesting differences between the geometries of DNA-DNA juxtapositions in the interwound portions and in the knotted or catenated portions of the studied molecules. In particular, in negatively supercoiled, multiply interlinked, right-handed catenanes, we detect specific regions where DNA segments belonging to two freshly replicated sister DNA molecules form left-handed crossings. We propose that, due to its geometrical preference to act on left-handed crossings, Topo IV can specifically unknot supercoiled DNA, as well as decatenate postreplicative catenanes, without causing their torsional relaxation.

Ion-mediated interactions between net-neutral slabs: Weak and strong disorder effects

We investigate the effective interaction between two randomly charged but otherwise net-neutral, planar dielectric slabs immersed in an asymmetric Coulomb fluid containing a mixture of mobile monovalent and multivalent ions. The presence of charge disorder on the apposed bounding surfaces of the slabs leads to substantial qualitative changes in the way they interact, as compared with the standard picture provided by the van der Waals and image-induced, ion-depletion interactions. While, the latter predict purely attractive interactions between strictly neutral slabs, we show that the combined effects from surface charge disorder, image depletion, Debye (or salt) screening, and also, in particular, their coupling with multivalent ions, give rise to a more diverse behavior for the effective interaction between net-neutral slabs at nano-scale separations. Disorder effects show large variation depending on the properly quantified strength of disorder, leading either to non-monotonic effective interaction with both repulsive and attractive branches when the surface charges are weakly disordered (small disorder variance) or to a dominating attractive interaction that is larger both in its range and magnitude than what is predicted from the van der Waals and image-induced, ion-depletion interactions, when the surfaces are strongly disordered (large disorder variance).

Phase diagram of the ground states of DNA condensates

The phase diagram of the ground states of DNA in a bad solvent is studied for a semiflexible polymer model with a generalized local elastic bending potential characterized by a nonlinearity parameter x and effective self-attraction promoting compaction. x=1 corresponds to the wormlike chain model. Surprisingly, the phase diagram as well as the transition lines between the ground states are found to be a function of x. The model provides a simple explanation for the results of prior experimental and computational studies and makes predictions for the specific geometries of the ground states. The results underscore the impact of the form of the microscopic bending energy at macroscopic observable scales.

Ejecting phage DNA against cellular turgor pressure

We examine in vivo ejection of noncondensed DNA from tailed bacteriophages into bacteria. The ejection is dominantly governed by the physical conditions in the bacteria. The confinement of the DNA in the virus capsid only slightly helps the ejection, becoming completely irrelevant during its last stages. A simple calculation based on the premise of condensed DNA in the cell enables us to estimate the maximal bacterial turgor pressure against which the ejection can still be fully realized. The calculated pressure (~5 atm) shows that the ejection of DNA into Gram-negative bacteria could proceed spontaneously, i.e., without the need to invoke active mechanisms.

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.

Strong coupling electrostatics for randomly charged surfaces: antifragility and effective interactions

We study the effective interaction mediated by strongly coupled Coulomb fluids between dielectric surfaces carrying quenched, random monopolar charges with equal mean and variance, both when the Coulomb fluid consists only of mobile multivalent counterions and when it consists of an asymmetric ionic mixture containing multivalent and monovalent (salt) ions in equilibrium with an aqueous bulk reservoir. We analyze the consequences that follow from the interplay between surface charge disorder, dielectric and salt image effects, and the strong electrostatic coupling that results from multivalent counterions on the distribution of these ions and the effective interaction pressure they mediate between the surfaces. In a dielectrically homogeneous system, we show that the multivalent counterions are attracted towards the surfaces with a singular, disorder-induced potential that diverges logarithmically on approach to the surfaces, creating a singular but integrable counterion density profile that exhibits an algebraic divergence at the surfaces with an exponent that depends on the surface charge (disorder) variance. This effect drives the system towards a state of lower thermal 'disorder', one that can be described by a renormalized temperature, exhibiting thus a remarkable antifragility. In the presence of an interfacial dielectric discontinuity, the singular behavior of counterion density at the surfaces is removed but multivalent counterions are still accumulated much more strongly close to randomly charged surfaces as compared with uniformly charged ones. The interaction pressure acting on the surfaces displays in general a highly non-monotonic behavior as a function of the inter-surface separation with a prominent regime of attraction at small to intermediate separations. This attraction is caused directly by the combined effects from charge disorder and strong coupling electrostatics of multivalent counterions, which dominate the surface-surface repulsion due to the (equal) mean charges on the two surfaces and the osmotic pressure of monovalent ions residing between them. These effects can be quite significant even with a small degree of surface charge disorder relative to the mean surface charge. The strong coupling, disorder-induced attraction is typically much stronger than the van der Waals interaction between the surfaces, especially within a range of several nanometers for the inter-surface separation, where such effects are predicted to be most pronounced.

Polymer Looping Is Controlled by Macromolecular Crowding, Spatial Confinement, and Chain Stiffness

We study by extensive computer simulations the looping characteristics of linear polymers with varying persistence length inside a spherical cavity in the presence of macromolecular crowding. For stiff chains, the looping probability and looping time reveal wildly oscillating patterns as functions of the chain length. The effects of crowding differ dramatically for flexible versus stiff polymers. While for flexible chains the looping kinetics is slowed down by the crowders, for stiffer chains the kinetics turns out to be either decreased or facilitated, depending on the polymer length. For severe confinement, the looping kinetics may become strongly facilitated by crowding. Our findings are of broad impact for DNA looping in the crowded and compartmentalized interior of living biological cells.

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.

Surfactant-induced ordering and wetting transitions of droplets of thermotropic liquid crystals "caged" inside partially filled polymeric capsules

We report a study of the wetting and ordering of thermotropic liquid crystal (LC) droplets that are trapped (or "caged") within micrometer-sized cationic polymeric microcapsules dispersed in aqueous solutions of surfactants. When they were initially dispersed in water, we observed caged, nearly spherical droplets of E7, a nematic LC mixture, to occupy ∼40% of the interior volume of the polymeric capsules [diameter of 6.7 ± 0.3 μm, formed via covalent layer-by-layer assembly of branched polyethylenimine and poly(2-vinyl-4,4-dimethylazlactone)] and to contact the interior surface of the capsule wall at an angle of ∼157 ± 11°. The internal ordering of LC within the droplets corresponded to the so-called bipolar configuration (distorted by contact with the capsule walls). While the effects of dodecyltrimethylammonium bromide (DTAB) and sodium dodecyl sulfate (SDS) on the internal ordering of "free" LC droplets are similar, we observed the two surfactants to trigger strikingly different wetting and configurational transitions when LC droplets were caged within polymeric capsules. Specifically, upon addition of SDS to the aqueous phase, we observed the contact angles (θ) of caged LC on the interior surface of the capsule to decrease, resulting in a progression of complex droplet shapes, including lenses (θ ≈ 130 ± 10°), hemispheres (θ ≈ 89 ± 5°), and concave hemispheres (θ < 85°). The wetting transitions induced by SDS also resulted in changes in the internal ordering of the LC to yield states topologically equivalent to axial and radial configurations. Although topologically equivalent to free droplets, the contributions that surface anchoring, LC elasticity, and topological defects make to the free energy of caged LC droplets differ from those of free droplets. Overall, these results and others reported herein lead us to conclude that caged LC droplets offer a platform for new designs of LC-droplet-based responsive soft matter that cannot be realized in dispersions of free droplets.

Dynamics and limitations of spontaneous polyelectrolyte intrusion into a charged nanocavity

We systematically investigate the spontaneous packaging mechanism of a single polyelectrolyte chain into an oppositely charged nanocavity by Langevin molecular dynamics simulations of a generic coarse-grained model. Intrusion dynamics and packaging rate, as well as the self-assembly process inside turn out to depend sensitively on the stiffness of the polyelectrolyte, the surface charge density inside the capsid, and the radius of the cavity. Further analysis shows that, depending on the stiffness, thermal fluctuations and charge inversion can be important factors to overcome barriers that slow down the intrusion and packaging dynamics. These results help advance our understanding of the function of charges on the inner surface of viral capsids and the possibility to design capsids as synthetic nanocarriers.

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.

Multivalent ion effects on electrostatic stability of virus-like nano-shells

Electrostatic properties and stability of charged virus-like nano-shells are examined in ionic solutions with monovalent and multivalent ions. A theoretical model based on a thin charged spherical shell and multivalent ions within the "dressed multivalent ion" approximation, yielding their distribution across the shell and the corresponding electrostatic (osmotic) pressure acting on the shell, is compared with extensive implicit Monte-Carlo simulations. It is found to be accurate for positive or low negative surface charge densities of the shell and for sufficiently high (low) monovalent (multivalent) salt concentrations. Phase diagrams involving electrostatic pressure exhibit positive and negative values, corresponding to an outward and an inward facing force on the shell, respectively. This provides an explanation for the high sensitivity of viral shell stability and self-assembly of viral capsid shells on the ionic environment.

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.

Nanostructure-induced DNA condensation

The control of the DNA condensation process is essential for compaction of DNA in chromatin, as well as for biological applications such as nonviral gene therapy. This review endeavours to reflect the progress of investigations on DNA condensation effects of nanostructure-based condensing agents (such as nanoparticles, nanotubes, cationic polymer and peptide agents) observed by using atomic force microscopy (AFM) and other techniques. The environmental effects on structural characteristics of nanostructure-induced DNA condensates are also discussed.

Entropy, energy, and bending of DNA in viral capsids

Inspired by novel single-molecule and bulk solution measurements, the physics underlying the forces and pressures involved in DNA packaging into bacteriophage capsids became the focus of numerous recent theoretical models. These fall into two general categories: Continuum-elastic theories (CT), and simulation studies-mostly of the molecular dynamics (MD) genre. Both types of models account for the dependence of the force, and hence the packaging free energy (ΔF), on the loaded DNA length, but differ markedly in interpreting their origin. While DNA confinement entropy is a dominant contribution to ΔF in the MD simulations, in the CT theories this role is fulfilled by interstrand repulsion, and there is no explicit entropy term. The goal of this letter is to resolve this apparent contradiction, elucidate the origin of the entropic term in the MD simulations, and point out its tacit presence in the CT treatments.

Polymorphism of DNA conformation inside the bacteriophage capsid

Double-stranded DNA bacteriophage genomes are packaged into their icosahedral capsids at the highest densities known so far (about 50 % w:v). How the molecule is folded at such density and how its conformation changes upon ejection or packaging are fascinating questions still largely open. We review cryo-TEM analyses of DNA conformation inside partially filled capsids as a function of the physico-chemical environment (ions, osmotic pressure, temperature). We show that there exists a wide variety of DNA conformations. Strikingly, the different observed structures can be described by some of the different models proposed over the years for DNA organisation inside bacteriophage capsids: either spool-like structures with axial or concentric symmetries, or liquid crystalline structures characterised by a DNA homogeneous density. The relevance of these conformations for the understanding of DNA folding and unfolding upon ejection and packaging in vivo is discussed.

Knotting of linear DNA in nano-slits and nano-channels: a numerical study

The amount and type of self-entanglement of DNA filaments is significantly affected by spatial confinement, which is ubiquitous in biological systems. Motivated by recent advancements in single DNA molecule experiments based on nanofluidic devices and by the introduction of algorithms capable of detecting knots in open chains, we investigate numerically the entanglement of linear, open DNA chains confined inside nano-slits. The results regard the abundance, type, and length of occurring knots and are compared with recent findings for DNA inside nano-channels. In both cases, the width of the confining region, D, spans the 30 nm-1 μm range and the confined DNA chains are 1-4 μm long. It is found that the knotting probability is maximum for slit widths in the 70-100 nm range. However, over the considered DNA contour lengths, the maximum incidence of knots remains below 20%, while for channel confinement it tops 50%. Further differences of the entanglement are seen for the average contour length of the knotted region, which drops significantly below D ~100 nm for channel-confinement, while it stays approximately constant for slit-like confinement. These properties ought to reverberate in different kinetic properties of linear DNA depending on confinement and could be detectable experimentally or exploitable in nano-technological applications.

Packing of charged chains on toroidal geometries

We study a strongly adsorbed flexible polyelectrolyte chain on tori. In this generalized Thomson problem, the patterns of the adsorbed chain are analyzed in the space of the toroidal coordinates and in terms of the orientation of each chain segment. Various patterns are found, including double spirals, disclination-like structures, Janus tori, and uniform wrappings, arising from the long-range electrostatic interaction and the toroidal geometry. Their broken mirror symmetry is quantitatively characterized by introducing an order parameter, an integral of the torsion. The uniform packing, which breaks the mirror symmetry the least, has the lowest value of the order parameter. In addition, it is found that the electrostatic energy of confined chains on tori conforms to a power law regardless of the screening effect in some typical cases studied. Furthermore, we study random walks on tori that generate chain configurations in the large screening limit or at large thermal fluctuation; some features associated with the toroidal geometry are discussed.

Mechanical properties of viruses

Structural biology techniques have greatly contributed to unveil the relationships between structure, properties and functions of viruses. In recent years, classic structural approaches are being complemented by single-molecule techniques such as atomic force microscopy and optical tweezers to study physical properties and functions of viral particles that are not accessible to classic structural techniques. Among these features are mechanical properties such as stiffness, intrinsic elasticity, tensile strength and material fatigue. The field of virus mechanics is contributing to materials science by investigating some physical parameters of "soft" biological matter and biological nano-objects. Virus mechanics studies are also starting to unveil the biological implications of physical properties of viruses. Growing evidence indicate that viruses are subjected to internal and external forces, and that they may have adapted to withstand and even use those forces. This chapter describes what is known on the mechanical properties of virus particles, their structural determinants, and possible biological implications, of which several examples are provided.

Direct measurement of phage phi29 stiffness provides evidence of internal pressure

Using AFM nanoindentation experiments, DNA-full phi29 phage capsids are shown to be stiffer than when empty. The presence of counterions softens full viruses in a reversible manner, indicating that pressure originates from the confined DNA. A finite element analysis of the experiments provides an estimate of the pressure of ∼40 atm inside the capsid, which is similar to theoretical predictions.

Energies and pressures in viruses: contribution of nonspecific electrostatic interactions

We summarize some aspects of electrostatic interactions in the context of viruses. A simplified but, within well defined limitations, reliable approach is used to derive expressions for electrostatic energies and the corresponding osmotic pressures in single-stranded RNA viruses and double-stranded DNA bacteriophages. The two types of viruses differ crucially in the spatial distribution of their genome charge which leads to essential differences in their free energies, depending on the capsid size and total charge in a quite different fashion. Differences in the free energies are trailed by the corresponding characteristics and variations in the osmotic pressure between the inside of the virus and the external bathing solution.

DNA movies and panspermia

There are several ways that our species might try to send a message to another species separated from us by space and/or time. Synthetic biology might be used to write an epitaph to our species, or simply “Kilroy was here”, in the genome of a bacterium via the patterns of either (1) the codons to exploit Life's non-equilibrium character or (2) the bases themselves to exploit Life's quasi-equilibrium character. We suggest here how DNA movies might be designed using such patterns. We also suggest that a search for mechanisms to create and preserve such patterns might lead to a better understanding of modern cells. Finally, we argue that the cutting-edge microbiology and synthetic biology needed for the Kilroy project would put origin-of-life studies in the vanguard of research.