Statics and dynamics of condensed DNA within phages and globules

Equation of State of Charged Rod Dispersions

We study the accuracy of the theory of Stroobants, Lekkerkerker, and Odijk [Macromolecules 1986, 19, 2232-2238], called SLO theory, to describe the thermodynamic properties of an isotropic fluid of charged rods. By incorporation of the effective diameter of the rods according to SLO theory into scaled particle theory (SPT), we obtain an expression for the rod concentration-dependent free volume fraction and the osmotic pressure of a collection of charged hard spherocylinders. The results are compared to Monte Carlo simulations. We find close agreement between the simulation results and the SLO-SPT predictions for not too large values of the Debye length and for high rod charge densities. The deviations increase with rod density, particularly at concentrations above which isotropic-nematic phase transitions are expected.

Role of DNA-DNA sliding friction and nonequilibrium dynamics in viral genome ejection and packaging

Many viruses eject their DNA via a nanochannel in the viral shell, driven by internal forces arising from the high-density genome packing. The speed of DNA exit is controlled by friction forces that limit the molecular mobility, but the nature of this friction is unknown. We introduce a method to probe the mobility of the tightly confined DNA by measuring DNA exit from phage phi29 capsids with optical tweezers. We measure extremely low initial exit velocity, a regime of exponentially increasing velocity, stochastic pausing that dominates the kinetics and large dynamic heterogeneity. Measurements with variable applied force provide evidence that the initial velocity is controlled by DNA-DNA sliding friction, consistent with a Frenkel-Kontorova model for nanoscale friction. We confirm several aspects of the ejection dynamics predicted by theoretical models. Features of the pausing suggest that it is connected to the phenomenon of 'clogging' in soft matter systems. Our results provide evidence that DNA-DNA friction and clogging control the DNA exit dynamics, but that this friction does not significantly affect DNA packaging.

Role of DNA-DNA sliding friction and non-equilibrium dynamics in viral genome ejection and packaging

Many viruses eject their DNA via a nanochannel in the viral shell, driven by internal forces arising from the high-density genome packing. The speed of DNA exit is controlled by friction forces that limit the molecular mobility, but the nature of this friction is unknown. We introduce a method to probe the mobility of the tightly confined DNA by measuring DNA exit from phage phi29 capsids with optical tweezers. We measure extremely low initial exit velocity, a regime of exponentially increasing velocity, stochastic pausing that dominates the kinetics, and large dynamic heterogeneity. Measurements with variable applied force provide evidence that the initial velocity is controlled by DNA-DNA sliding friction, consistent with a Frenkel-Kontorova model for nanoscale friction. We confirm several aspects of the ejection dynamics predicted by theoretical models. Features of the pausing suggest it is connected to the phenomenon of "clogging" in soft-matter systems. Our results provide evidence that DNA-DNA friction and clogging control the DNA exit dynamics, but that this friction does not significantly affect DNA packaging.

DNA compaction and dynamic observation in a nanopore gated sub-attoliter silicon nanocavity

Confinement of biopolymers inside volumes with micro- or nanoscale lateral dimensions is ubiquitous in nature. Investigating the behavior of biopolymers in a confined environment is essential to improve our basic understanding in life sciences. In this work, we present a nanopore gated sub-attoliter silicon nanocavity device, which allows DNA compaction similar to that in virus capsids. Single DNA molecules can be electrically driven into the nanocavity, and then get compacted inside the nanocavity under certain conditions. The dynamic fluctuations of the compacted DNA can be monitored via ionic current measurements. The mechanism for the DNA compaction is elucidated by varying the DNA length or concentration, voltage polarity, nanocavity dimensions and ionic strength. Furthermore, Brownian dynamics simulations reveal the dynamic fluctuations of the compacted DNA, which are reflected in the measured ionic current. Our nanocavity device is anticipated to provide a controlled environment in extremely small volumes for investigating the physics of confined biopolymers.

Microrheological Approach for Probing the Entanglement Properties of Polyelectrolyte Solutions

The entanglement dynamics and viscoelasticity of polyelectrolyte solutions remain active research topics. Previous studies have reported conflicting experimental results when compared to Dobrynin's scaling predictions derived from the Doi-Edwards (DE) tube model for entangled polymers. Herein, by combining classical bulk shear rheometry with diffusing wave spectroscopy (DWS) microrheometry, we investigate how the key viscoelastic parameters (the specific viscosity η_sp, the plateau modulus G_e, and the ratio of the reptation time to the Rouse time of an entanglement strand τ_rep/τ_e) depend on the polymer concentration for semidilute entangled (SE) solutions containing poly(sodium styrenesulfonate) with high molecular weight. Our experimental measurements yield G_e ∝ c^1.51±0.04, in good agreement with the scaling of G_e ∝ c^1.5 predicted by Dobrynin's model for salt-free polyelectrolyte SE solutions, suggesting that the electrostatic interaction influences the viscoelastic properties of polyelectrolyte SE solutions. On the other hand, the deviation in the scaling exponent for η_sp ∝ c^2.56±0.04 and τ_rep/τ_e ∝ c^1.82±0.28 is observed between our DWS experiments and Dobrynin's model prediction (∝ c^1.5), likely due to the fact that Dobrynin's scaling model does not account for mechanisms such as the contour length fluctuation, the constraint release, and the retardation of solvent dynamics, which are known to occur for SE solutions of neutral polymers. Our results demonstrate that DWS serves as a powerful rheological tool to study the entanglement dynamics of polyelectrolyte solutions. The scaling relationships obtained in this study provide new insights to the long-standing debate on the entanglement dynamics of polyelectrolyte solutions.

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.

Density fields for branching, stiff networks in rigid confining regions

We develop a formalism to describe the equilibrium distributions for segments of confined branched networks consisting of stiff filaments. This is applicable to certain situations of cytoskeleton in cells, such as for example actin filaments with branching due to the Arp2/3 complex. We develop a grand ensemble formalism that enables the computation of segment density and polarisation profiles within the confines of the cell. This is expressed in terms of the solution to nonlinear integral equations for auxiliary functions. We find three specific classes of behaviour depending on filament length, degree of branching and the ratio of persistence length to the dimensions of the geometry. Our method allows a numerical approach for semi-flexible filaments that are networked.

A review of immune amplification via ligand clustering by self-assembled liquid-crystalline DNA complexes

We examine how the interferon production of plasmacytoid dendritic cells is amplified by the self-assembly of liquid-crystalline antimicrobial peptide/DNA complexes. These specialized dendritic cells are important for host defense because they quickly release large quantities of type I interferons in response to infection. However, their aberrant activation is also correlated with autoimmune diseases such as psoriasis and lupus. In this review, we will describe how polyelectrolyte self-assembly and the statistical mechanics of multivalent interactions contribute to this process. In a more general compass, we provide an interesting conceptual corrective to the common notion in molecular biology of a dichotomy between specific interactions and non-specific interactions, and show examples where one can construct exquisitely specific interactions using non-specific interactions.

Can Changes in Temperature or Ionic Conditions Modify the DNA Organization in the Full Bacteriophage Capsid?

We compared four bacteriophage species, T5, λ, T7, and Φ29, to explore the possibilities of DNA reorganization in the capsid where the chain is highly concentrated and confined. First, we did not detect any change in DNA organization as a function of temperature between 20 to 40 °C. Second, the presence of spermine (4+) induces a significant enlargement of the typical size of the hexagonal domains in all phages. We interpret these changes as a reorganization of DNA by slight movements of defects in the structure, triggered by a partial screening of repulsive interactions. We did not detect any signal characteristic of a long-range chiral organization of the encapsidated DNA in the presence and in the absence of spermine.

Ionic switch controls the DNA state in phage λ

We have recently found that DNA packaged in phage λ undergoes a disordering transition triggered by temperature, which results in increased genome mobility. This solid-to-fluid like DNA transition markedly increases the number of infectious λ particles facilitating infection. However, the structural transition strongly depends on temperature and ionic conditions in the surrounding medium. Using titration microcalorimetry combined with solution X-ray scattering, we mapped both energetic and structural changes associated with transition of the encapsidated λ-DNA. Packaged DNA needs to reach a critical stress level in order for transition to occur. We varied the stress on DNA in the capsid by changing the temperature, packaged DNA length and ionic conditions. We found striking evidence that the intracapsid DNA transition is 'switched on' at the ionic conditions mimicking those in vivo and also at the physiologic temperature of infection at 37°C. This ion regulated on-off switch of packaged DNA mobility in turn affects viral replication. These results suggest a remarkable adaptation of phage λ to the environment of its host bacteria in the human gut. The metastable DNA state in the capsid provides a new paradigm for the physical evolution of viruses.

Solid-to-fluid-like DNA transition in viruses facilitates infection

Releasing the packaged viral DNA into the host cell is an essential process to initiate viral infection. In many double-stranded DNA bacterial viruses and herpesviruses, the tightly packaged genome is hexagonally ordered and stressed in the protein shell, called the capsid. DNA condensed in this state inside viral capsids has been shown to be trapped in a glassy state, with restricted molecular motion in vitro. This limited intracapsid DNA mobility is caused by the sliding friction between closely packaged DNA strands, as a result of the repulsive interactions between the negative charges on the DNA helices. It had been unclear how this rigid crystalline structure of the viral genome rapidly ejects from the capsid, reaching rates of 60,000 bp/s. Through a combination of single-molecule and bulk techniques, we determined how the structure and energy of the encapsidated DNA in phage λ regulates the mobility required for its ejection. Our data show that packaged λ-DNA undergoes a solid-to-fluid-like disordering transition as a function of temperature, resulting locally in less densely packed DNA, reducing DNA-DNA repulsions. This process leads to a significant increase in genome mobility or fluidity, which facilitates genome release at temperatures close to that of viral infection (37 °C), suggesting a remarkable physical adaptation of bacterial viruses to the environment of Escherichia coli cells in a human host.

Solid-to-fluid DNA transition inside HSV-1 capsid close to the temperature of infection

DNA in the human Herpes simplex virus type 1 (HSV-1) capsid is packaged to a tight density. This leads to tens of atmospheres of internal pressure responsible for the delivery of the herpes genome into the cell nucleus. In this study we show that, despite its liquid crystalline state inside the capsid, the DNA is fluid-like, which facilitates its ejection into the cell nucleus during infection. We found that the sliding friction between closely packaged DNA strands, caused by interstrand repulsive interactions, is reduced by the ionic environment of epithelial cells and neurons susceptible to herpes infection. However, variations in the ionic conditions corresponding to neuronal activity can restrict DNA mobility in the capsid, making it more solid-like. This can inhibit intranuclear DNA release and interfere with viral replication. In addition, the temperature of the human host (37 °C) induces a disordering transition of the encapsidated herpes genome, which reduces interstrand interactions and provides genome mobility required for infection.

Morphogenesis of filaments growing in flexible confinements

Space-saving design is a requirement that is encountered in biological systems and the development of modern technological devices alike. Many living organisms dynamically pack their polymer chains, filaments or membranes inside deformable vesicles or soft tissue-like cell walls, chorions and buds. Surprisingly little is known about morphogenesis due to growth in flexible confinements--perhaps owing to the daunting complexity lying in the nonlinear feedback between packed material and expandable cavity. Here we show by experiments and simulations how geometric and material properties lead to a plethora of morphologies when elastic filaments are growing far beyond the equilibrium size of a flexible thin sheet they are confined in. Depending on friction, sheet flexibility and thickness, we identify four distinct morphological phases emerging from bifurcation and present the corresponding phase diagram. Four order parameters quantifying the transitions between these phases are proposed.

Nonequilibrium dynamics and ultraslow relaxation of confined DNA during viral packaging

Many viruses use molecular motors that generate large forces to package DNA to near-crystalline densities inside preformed viral proheads. Besides being a key step in viral assembly, this process is of interest as a model for understanding the physics of charged polymers under tight 3D confinement. A large number of theoretical studies have modeled DNA packaging, and the nature of the molecular dynamics and the forces resisting the tight confinement is a subject of wide debate. Here, we directly measure the packaging of single DNA molecules in bacteriophage phi29 with optical tweezers. Using a new technique in which we stall the motor and restart it after increasing waiting periods, we show that the DNA undergoes nonequilibrium conformational dynamics during packaging. We show that the relaxation time of the confined DNA is >10 min, which is longer than the time to package the viral genome and 60,000 times longer than that of the unconfined DNA in solution. Thus, the confined DNA molecule becomes kinetically constrained on the timescale of packaging, exhibiting glassy dynamics, which slows the motor, causes significant heterogeneity in packaging rates of individual viruses, and explains the frequent pausing observed in DNA translocation. These results support several recent hypotheses proposed based on polymer dynamics simulations and show that packaging cannot be fully understood by quasistatic thermodynamic models.

Communication: Origin of the contributions to DNA structure in phages

Cryo electron microscopy (cryo-EM) data of the interior of phages show ordering of the interior DNA that has been interpreted as a nearly perfectly ordered polymer. We show surface-induced correlations, excluded volume, and electrostatic forces are sufficient to predict most of the major features of the current structural data for DNA packaged within viral capsids without additional ordering due to elastic bending forces for the polymer. Current models assume highly-ordered, even spooled, hexagonally packed conformations based on interpretation of cryo-EM density maps. We show herein that the surface induced packing of short (6mer), unconnected DNA polymer segments is the only necessary ingredient in creating ringed densities consistent with experimental density maps. This implies the ensemble of possible conformations of polymeric DNA within the capsid that are consistent with cryo-EM data may be much larger than implied by traditional interpretations where such rings can only result from highly-ordered spool-like conformations. This opens the possibility of a more disordered, entropically-driven view of phage packaging thermodynamics. We also show the electrostatics of the DNA contributes a large portion of the internal hydrostatic and osmotic pressures of a phage virion, suggesting that nonlinear elastic anomalies might reduce the overall elastic bending enthalpy of more disordered conformations to have allowable free energies.

Heat induced capsid disassembly and DNA release of bacteriophage λ

Successive structural changes of bacteriophage λ upon heating were characterized with quantitative experimental methods. In the commonly used Tris-Mg buffer, differential scanning calorimetry measurements first established that the protein capsid of λ phage melts at 87 °C and its genomic DNA melts at 91 °C. Interestingly, prior to the capsid melting, λDNA was found to escape out of the capsid and subject to DNase digestion above ~68 °C, as concluded from light scattering, UV absorption, and electron microscopy studies. Further investigations indicated distinct temperature-dependent behaviors of the three phage proteins. Around 68 °C, disruption of the tail first occurs and leads to the escape of λ DNA; above the capsid melting temperature of 87 °C, the auxiliary protein gpD of the phage head remains soluble in solution and resists centrifugal sedimentation, whereas the major capsid protein gpE is easily precipitated and likely exists as aggregates.

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.

SCREW MOTION OF DNA DUPLEX DURING TRANSLOCATION THROUGH PORE I: INTRODUCTION OF THE COARSE-GRAINED MODEL

Based upon the structural properties of DNA duplexes and their counterion-water surrounding in solution, we have introduced here a screw model which may describe translocation of DNA duplexes through artificial nanopores of the proper diameter (where the DNA counterion–hydration shell can be intact) in a qualitatively correct way. This model represents DNA as a kind of "screw," whereas the counterion-hydration shell is a kind of "nut." Mathematical conditions for stable dynamics of the DNA screw model are investigated in detail. When an electrical potential is applied across an artificial membrane with a nanopore, the "screw" and "nut" begin to move with respect to each other, so that their mutual rotation is coupled with their mutual translation. As a result, there are peaks of electrical current connected with the mutual translocation of DNA and its counterion–hydration shell, if DNA is possessed of some non-regular base-pair sequence. The calculated peaks of current strongly resemble those observed in the pertinent experiments. An analogous model could in principle be applied to DNA translocation in natural DNA–protein complexes of biological interest, where the role of "nut" would be played by protein-tailored "channels." In such cases, the DNA screw model is capable of qualitatively explaining chemical-to-mechanical energy conversion in DNA–protein molecular machines via symmetry breaking in DNA–protein friction.

Biopolymer organization upon confinement

Biopolymers in vivo are typically subject to spatial restraints, either as a result of molecular crowding in the cellular medium or of direct spatial confinement. DNA in living organisms provides a prototypical example of a confined biopolymer. Confinement prompts a number of biophysics questions. For instance, how can the high level of packing be compatible with the necessity to access and process the genomic material? What mechanisms can be adopted in vivo to avoid the excessive geometrical and topological entanglement of dense phases of biopolymers? These and other fundamental questions have been addressed in recent years by both experimental and theoretical means. A review of the results, particularly of those obtained by numerical studies, is presented here. The review is mostly devoted to DNA packaging inside bacteriophages, which is the best studied example both experimentally and theoretically. Recent selected biophysical studies of the bacterial genome organization and of chromosome segregation in eukaryotes are also covered.

Confined nematic polymers: order and packing in a nematic drop

We investigate the tight packing of nematic polymers inside a confining hard sphere. We model the polymer via the continuum Frank elastic free energy augmented by a simple density dependent part as well as by taking proper care of the connectivity of the polymer chains when compared with simple nematics. The free energy ansatz is capable of describing an orientational ordering transition within the sample between an isotropic polymer solution and a polymer nematic phase. We solve the Euler-Lagrange equations numerically with the appropriate boundary conditions for the director and density field and investigate the orientation and density profile within a sphere. Two important parameters of the solution are the exact locations of the beginning and the end of the polymer chain. Pending on their spatial distribution and the actual size of the hard sphere enclosure we can get a plethora of various configurations of the chain exhibiting different defect geometry.

Electrostatics of strongly charged biological polymers: ion-mediated interactions and self-organization in nucleic acids and proteins

Charges on biological polymers in physiologically relevant solution conditions are strongly screened by water and salt solutions containing counter-ions. However, the entropy of these counterions can result in surprisingly strong interactions between charged objects in water despite short screening lengths, via coupling between osmotic and electrostatic interactions. Widespread work in theory, experiment, and computation has been carried out to gain a fundamental understanding of the rich, yet sometimes counterintuitive, behavior of these polyelectrolyte systems. Examples of polyelectrolyte association in biology include DNA packaging and RNA folding, as well as aggregation and self-organization phenomena in different disease states.

Buckling of stiff polymer rings in weak spherical confinement

Confinement is a versatile and well-established tool to study the properties of polymers either to understand biological processes or to develop new nanobiomaterials. We investigate the conformations of a semiflexible polymer ring in weak spherical confinement imposed by an impenetrable shell. We develop an analytic argument for the dominating polymer trajectory depending on polymer flexibility considering elastic and entropic contributions. Monte Carlo simulations are performed to assess polymer ring conformations in probability densities and by the shape measures asphericity and nature of asphericity. Comparison of the analytic argument with the mean asphericity and the mean nature of asphericity confirm our reasoning to explain polymer ring conformations in the stiff regime, where elastic response prevails.

Characterization of DNA conformation inside bacterial viruses

In this study we develop a formalism to describe the organization of DNA inside bacteriophage capsids during genome packaging. We have previously shown that DNA inside bacteriophage phi29 (phi29) is organized into folded toroids [A. S. Petrov and S. C. Harvey, Structure 15, 21 (2007)], whereas epsilon15 (epsilon15) reveals the coaxial organization of the genetic material [A. S. Petrov, K. Lim-Hing, and S. C. Harvey, Structure 15, 807 (2007)]. We now show that each system undergoes two consecutive transitions. The first transition corresponds to the formation of global conformations and is analogous to a disorder-order conformational transition. The second transition is characterized by a significant loss of DNA mobility at the local level leading to glasslike dynamic behavior. Packing genetic material inside bacteriophages can be used as a general model to study the behavior of semiflexible chains inside confined spaces, and the proposed formalism developed here can be used to study other systems of linear polymer chains confined to closed spaces.

Structure and energetics of encapsidated DNA in bacteriophage HK97 studied by scanning calorimetry and cryo-electron microscopy

Encapsidation of duplex DNA by bacteriophages represents an extreme case of genome condensation, reaching near-crystalline concentrations of DNA. The HK97 system is well suited to study this phenomenon in view of the detailed knowledge of its capsid structure. To characterize the interactions involved, we combined calorimetry with cryo-electron microscopy and native gel electrophoresis. We found that, as in other phages, HK97 DNA is organized in coaxially wound nested shells. When DNA-filled capsids (heads) are scanned in buffer containing 1 mM Mg(2+), DNA melting and capsid denaturation both contribute to the complex thermal profile between 82 degrees C and 96 degrees C. In other conditions (absence of Mg(2+) and lower ionic strength), DNA melting shifts to lower temperatures and the two events are resolved. Heads release their DNA at temperatures well below the onset of DNA melting or capsid denaturation. We suggest that, on heating, the internal pressure increases, causing the DNA to exit-probably via the portal vertex-while the capsid, although largely intact, sustains local damage that leads to an earlier onset of thermal denaturation. Heads differ structurally from empty capsids in the curvature of their protein shell, a change attributable to outwards pressure exerted by the DNA. We propose that this transition is sensed by the portal that is embedded in the capsid wall, whereupon the structure of the portal and its interactions with terminase, the packaging enzyme, are altered, thus signaling that packaging is at or approaching completion.

Shapes of semiflexible polymers in confined spaces

Biological macromolecules, living in the confines of a cell, often adopt conformations that are unlikely to occur in free space. In this paper, we investigate the effects of confinement on the shape of a semiflexible chain. Results of Monte Carlo simulations show the existence of a shape transition when the persistence length of the polymer becomes comparable to the dimensions of the box. An order parameter is introduced to quantify this behavior. A simple model is constructed to study the effect of the shape transition on the effective persistence length of the polymer.

Osmotic pressure and packaging structure of caged DNA

We present a theoretical model for aqueous solutions of double-stranded (ds) DNA with explicit consideration of electrostatic interactions, excluded-volume effects, van der Waals attractions, and salt ions. With reasonable parameters estimated from the DNA structure and experimental data for electrolytes, we are able to reproduce the DNA osmotic pressure in the bulk in good agreement with experiment. The predicted DNA osmotic pressure in lambda-bacteriophages is found to coincide with that of the PEG8000 solution that inhibits DNA ejection as reported in recent experiments. Based on the radial distributions of DNA segments and of counterions at different degrees of packaging, we find that in the presence of Mg(2+), DNA forms a multilayer structure near the inner surface of a fully loaded bacteriophage, but at low packing density the DNA segments are depleted from the surface owing to the local condensation of DNA induced by the divalent counterions. By contrast, the multilayer DNA structure is less distinctive in the presence of Na(+) despite the increase of the DNA density at contact, and the depletion near the capsid surface is not found at low packing density.

Portal motor velocity and internal force resisting viral DNA packaging in bacteriophage phi29

During the assembly of many viruses, a powerful molecular motor compacts the genome into a preassembled capsid. Here, we present measurements of viral DNA packaging in bacteriophage phi29 using an improved optical tweezers method that allows DNA translocation to be measured from initiation to completion. This method allowed us to study the previously uncharacterized early stages of packaging and facilitated more accurate measurement of the length of DNA packaged. We measured the motor velocity versus load at near-zero filling and developed a ramped DNA stretching technique that allowed us to measure the velocity versus capsid filling at near-zero load. These measurements reveal that the motor can generate significantly higher velocities and forces than detected previously. Toward the end of packaging, the internal force resisting DNA confinement rises steeply, consistent with the trend predicted by many theoretical models. However, the force rises to a higher magnitude, particularly during the early stages of packaging, than predicted by models that assume coaxial inverse spooling of the DNA. This finding suggests that the DNA is not arranged in that conformation during the early stages of packaging and indicates that internal force is available to drive complete genome ejection in vitro. The maximum force exceeds 100 pN, which is about one-half that predicted to rupture the capsid shell.

Ionic effects on viral DNA packaging and portal motor function in bacteriophage phi 29

In many viruses, DNA is confined at such high density that its bending rigidity and electrostatic self-repulsion present a strong energy barrier in viral assembly. Therefore, a powerful molecular motor is needed to package the DNA into the viral capsid. Here, we investigate the role of electrostatic repulsion on single DNA packaging dynamics in bacteriophage phi 29 via optical tweezers measurements. We show that ionic screening strongly affects the packing forces, confirming the importance of electrostatic repulsion. Separately, we find that ions affect the motor function. We separate these effects through constant force measurements and velocity versus load measurements at both low and high capsid filling. Regarding motor function, we find that eliminating free Mg(2+) blocks initiation of packaging. In contrast, Na(+) is not required, but it increases the motor velocity by up to 50% at low load. Regarding internal resistance, we find that the internal force was lowest when Mg(2+) was the dominant ion or with the addition of 1 mM Co(3+). Forces resisting DNA confinement were up to approximately 80% higher with Na(+) as the dominant counterion, and only approximately 90% of the genome length could be packaged in this condition. The observed trend of the packing forces is in accord with that predicted by DNA charge-screening theory. However, the forces are up to six times higher than predicted by models that assume coaxial spooling of the DNA and interaction potentials derived from DNA condensation experiments. The forces are also severalfold higher than ejection forces measured with bacteriophage lambda.

Biological consequences of tightly bent DNA: the other life of a macromolecular celebrity

The mechanical properties of DNA play a critical role in many biological functions. For example, DNA packing in viruses involves confining the viral genome in a volume (the viral capsid) with dimensions that are comparable to the DNA persistence length. Similarly, eukaryotic DNA is packed in DNA-protein complexes (nucleosomes), in which DNA is tightly bent around protein spools. DNA is also tightly bent by many proteins that regulate transcription, resulting in a variation in gene expression that is amenable to quantitative analysis. In these cases, DNA loops are formed with lengths that are comparable to or smaller than the DNA persistence length. The aim of this review is to describe the physical forces associated with tightly bent DNA in all of these settings and to explore the biological consequences of such bending, as increasingly accessible by single-molecule techniques.

Charge structure and counterion distribution in hexagonal DNA liquid crystal

A hexagonal liquid crystal of DNA fragments (double-stranded, 150 basepairs) with tetramethylammonium (TMA) counterions was investigated with small angle neutron scattering (SANS). We obtained the structure factors pertaining to the DNA and counterion density correlations with contrast matching in the water. Molecular dynamics (MD) computer simulation of a hexagonal assembly of nine DNA molecules showed that the inter-DNA distance fluctuates with a correlation time around 2 ns and a standard deviation of 8.5% of the interaxial spacing. The MD simulation also showed a minimal effect of the fluctuations in inter-DNA distance on the radial counterion density profile and significant penetration of the grooves by TMA. The radial density profile of the counterions was also obtained from a Monte Carlo (MC) computer simulation of a hexagonal array of charged rods with fixed interaxial spacing. Strong ordering of the counterions between the DNA molecules and the absence of charge fluctuations at longer wavelengths was shown by the SANS number and charge structure factors. The DNA-counterion and counterion structure factors are interpreted with the correlation functions derived from the Poisson-Boltzmann equation, MD, and MC simulation. Best agreement is observed between the experimental structure factors and the prediction based on the Poisson-Boltzmann equation and/or MC simulation. The SANS results show that TMA is too large to penetrate the grooves to a significant extent, in contrast to what is shown by MD simulation.

Fluid-crystal coexistence for proteins and inorganic nanocolloids: Dependence on ionic strength

We investigate theoretically the fluid-crystal coexistence of solutions of globular charged nanoparticles such as proteins and inorganic colloids. The thermodynamic properties of the fluid phase are computed via the optimized Baxter model P. Prinsen and T. Odijk [J. Chem. Phys. 121, 6525 (2004)]. This is done specifically for lysozyme and silicotungstates for which the bare adhesion parameters are evaluated via the experimental second virial coefficients. The electrostatic free energy of the crystal is approximated by supposing the cavities in the interstitial phase between the particles are spherical in form. In the salt-free case a Poisson-Boltzmann equation is solved to calculate the effective charge on a particle and a Donnan approximation is used to derive the chemical potential and osmotic pressure in the presence of salt. The coexistence data of lysozyme and silicotungstates are analyzed within this scheme, especially with regard to the ionic-strength dependence of the chemical potentials. The latter agree within the two phases provided some upward adjustment of the effective charge is allowed for.

Polymer packaging and ejection in viral capsids: shape matters

We use a mesoscale simulation approach to explore the impact of different capsid geometries on the packaging and ejection dynamics of polymers of different flexibility. We find that both packing and ejection times are faster for flexible polymers. For such polymers a sphere packs more quickly and ejects more slowly than an ellipsoid. For semiflexible polymers, however, the case relevant to DNA, a sphere both packs and ejects more easily. We interpret our results by considering both the thermodynamics and the relaxational dynamics of the polymers. The predictions could be tested with biomimetic experiments with synthetic polymers inside artificial vesicles. Our results suggest that phages may have evolved to be roughly spherical in shape to optimize the speed of genome ejection, which is the first stage in infection.

Dynamics of DNA ejection from bacteriophage

The ejection of DNA from a bacterial virus (i.e., phage) into its host cell is a biologically important example of the translocation of a macromolecular chain along its length through a membrane. The simplest mechanism for this motion is diffusion, but in the case of phage ejection a significant driving force derives from the high degree of stress to which the DNA is subjected in the viral capsid. The translocation is further sped up by the ratcheting and entropic forces associated with proteins that bind to the viral DNA in the host cell cytoplasm. We formulate a generalized diffusion equation that includes these various pushing and pulling effects and make estimates of the corresponding speedups in the overall translocation process. Stress in the capsid is the dominant factor throughout early ejection, with the pull due to binding particles taking over at later stages. Confinement effects are also investigated, in the case where the phage injects its DNA into a volume comparable to the capsid size. Our results suggest a series of in vitro experiments involving the ejection of DNA into vesicles filled with varying amounts of binding proteins from phage whose state of stress is controlled by ambient salt conditions or by tuning genome length.

Monte Carlo simulations of polyelectrolytes inside viral capsids

Structural features of polyelectrolytes as single-stranded RNA or double-stranded DNA confined inside viral capsids and the thermodynamics of the encapsidation of the polyelectrolyte into the viral capsid have been examined for various polyelectrolyte lengths by using a coarse-grained model solved by Monte Carlo simulations. The capsid was modeled as a spherical shell with embedded charges and the genome as a linear jointed chain of oppositely charged beads, and their sizes corresponded to those of a scaled-down T=3 virus. Counterions were explicitly included, but no salt was added. The encapisdated chain was found to be predominantly located at the inner capsid surface, in a disordered manner for flexible chains and in a spool-like structure for stiff chains. The distribution of the small ions was strongly dependent on the polyelectrolyte-capsid charge ratio. The encapsidation enthalpy was negative and its magnitude decreased with increasing polyelectrolyte length, whereas the encapsidation entropy displayed a maximum when the capsid and polyelectrolyte had equal absolute charge. The encapsidation process remained thermodynamically favorable for genome charges ca. 3.5 times the capsid charge. The chain stiffness had only a relatively weak effect on the thermodynamics of the encapsidation.

Forced crumpling of self-avoiding elastic sheets

Thin elastic sheets are important materials across length scales ranging from mesoscopic (polymerized membranes, clay platelets, virus capsids) to macroscopic (paper, metal foils). The crumpling of such sheets by external forces is characterized by the formation of a complex pattern of folds. We have investigated the role of self-avoidance, the fact that the sheets cannot self-intersect, for the crumpling process by large-scale computer simulations. At moderate compression, the force-compression relations of crumpled sheets for both self-avoiding and phantom sheets are found to obey universal power-law behaviours. However, self-avoiding sheets are much stiffer than phantom sheets and, for a given compression, develop many more folds. Moreover, self-avoidance is relevant already at very small volume fractions. The fold-length distribution for crumpled sheets is determined, and is found to be well-described by a log-normal distribution. The stiffening owing to self-avoidance is reflected in the changing nature of the sheet-to-sheet contacts from line-like to two-dimensionally extended with increasing compression.

The effect of genome length on ejection forces in bacteriophage lambda

A variety of viruses tightly pack their genetic material into protein capsids that are barely large enough to enclose the genome. In particular, in bacteriophages, forces as high as 60 pN are encountered during packaging and ejection, produced by DNA bending elasticity and self-interactions. The high forces are believed to be important for the ejection process, though the extent of their involvement is not yet clear. As a result, there is a need for quantitative models and experiments that reveal the nature of the forces relevant to DNA ejection. Here, we report measurements of the ejection forces for two different mutants of bacteriophage lambda, lambdab221cI26 and lambdacI60, which differ in genome length by approximately 30%. As expected for a force-driven ejection mechanism, the osmotic pressure at which DNA release is completely inhibited varies with the genome length: we find inhibition pressures of 15 atm and 25 atm, for the short and long genomes, respectively, values that are in agreement with our theoretical calculations.

Forces during bacteriophage DNA packaging and ejection

The conjunction of insights from structural biology, solution biochemistry, genetics, and single-molecule biophysics has provided a renewed impetus for the construction of quantitative models of biological processes. One area that has been a beneficiary of these experimental techniques is the study of viruses. In this article we describe how the insights obtained from such experiments can be utilized to construct physical models of processes in the viral life cycle. We focus on dsDNA bacteriophages and show that the bending elasticity of DNA and its electrostatics in solution can be combined to determine the forces experienced during packaging and ejection of the viral genome. Furthermore, we quantitatively analyze the effect of fluid viscosity and capsid expansion on the forces experienced during packaging. Finally, we present a model for DNA ejection from bacteriophages based on the hypothesis that the energy stored in the tightly packed genome within the capsid leads to its forceful ejection. The predictions of our model can be tested through experiments in vitro where DNA ejection is inhibited by the application of external osmotic pressure.

An introduction to the mechanics of DNA

This article gives an overview of recent research on the mechanical properties and spatial deformations of the DNA molecule. Globally the molecule behaves like a uniform elastic rod, and its twisting and writhing govern its compaction and packaging within a cell. Meanwhile high mechanical stresses can induce structural transitions of DNA giving, for example, a phase diagram in the space of the applied tension and torque. Locally, the mechanical properties vary according to the local sequence organization. These variations play a vital role in the biological functioning of the molecule.

Helical packaging of semiflexible polymers in bacteriophages

We investigate multilayered helical packaging of double-stranded DNA, or of a general polymer chain with persistence length lb, into an ideal, inert cylindrical container, reaching densities slightly below close packaging. We calculate the free energy as a function of the packaged length, based on the energies for bending, twisting, the suffered entropy loss, and the electrostatic energy in a Debye-Hückel model. In the absence of charges on the packaged polymer, a critical packaging force can be determined, similar to the mechanism involved in DNA unzipping models. When charges are taken into consideration, in the final packaging state the charges which are chemically distant become geometrically close, and therefore a steep rise is seen in the free energy. We argue that due to the extremely ordered and almost closely packaged final state the actual packaging geometry does not influence the behaviour of the free energy, pointing towards a certain universality of this state of the polymer. Our findings are compared to a recent simulations study, showing that the model is sensitive to the screening length.