DNA Equation of State: In Vitro vs In Viro

Temperature-induced DNA density transition in phage λ capsid revealed with contrast-matching SANS

Structural details of a genome packaged in a viral capsid are essential for understanding how the structural arrangement of a viral genome in a capsid controls its release dynamics during infection, which critically affects viral replication. We previously found a temperature-induced, solid-like to fluid-like mechanical transition of packaged λ-genome that leads to rapid DNA ejection. However, an understanding of the structural origin of this transition was lacking. Here, we use small-angle neutron scattering (SANS) to reveal the scattering form factor of dsDNA packaged in phage λ capsid by contrast matching the scattering signal from the viral capsid with deuterated buffer. We used small-angle X-ray scattering and cryoelectron microscopy reconstructions to determine the initial structural input parameters for intracapsid DNA, which allows accurate modeling of our SANS data. As result, we show a temperature-dependent density transition of intracapsid DNA occurring between two coexisting phases-a hexagonally ordered high-density DNA phase in the capsid periphery and a low-density, less-ordered DNA phase in the core. As the temperature is increased from 20 °C to 40 °C, we found that the core-DNA phase undergoes a density and volume transition close to the physiological temperature of infection (~37 °C). The transition yields a lower energy state of DNA in the capsid core due to lower density and reduced packing defects. This increases DNA mobility, which is required to initiate rapid genome ejection from the virus capsid into a host cell, causing infection. These data reconcile our earlier findings of mechanical DNA transition in phage.

Fluctuation-induced dispersion forces on thin DNA films

In this work, the calculation of Casimir forces across thin DNA films is carried out based on the Lifshitz theory. The variations of Casimir forces due to the DNA thicknesses, volume fractions of containing water, covering media, and substrates are investigated. For a DNA film suspended in air or water, the Casimir force is attractive, and its magnitude increases with decreasing thickness of DNA films and the water volume fraction. For DNA films deposited on a dielectric (silica) substrate, the Casimir force is attractive for the air environment. However, the Casimir force shows unusual features in a water environment. Under specific conditions, switching sign of the Casimir force from attractive to repulsive can be achieved by increasing the DNA-film thickness. Finally, the Casimir force for DNA films deposited on a metallic substrate is investigated. The Casimir force is dominated by the repulsive interactions at a small DNA-film thickness for both the air and water environments. In a water environment, the Casimir force turns out to be attractive for a large DNA-film thickness, and a stable Casimir equilibrium can be found. The influences of electrolyte screening on the Casimir pressure of DNA films are also discussed at the end. In addition to the adhesion stability, our finding could be applicable to the problems of condensation and decondensation of DNA, due to fluctuation-induced dispersion forces.

Observations of three "re-entrant" twisted structures in double-stranded DNA dispersion particles

In this work we report on observations of new twisted (cholesteric-like) structures in liquid-crystalline dispersion particles with a hexagonal packing of double-stranded (ds) DNA molecules. Heating up to 80 °C of the DNA dispersion formed in a aqueous-salt solution with a high osmotic pressure (concentration) of poly(ethylene glycol) induces the formation of a new, optically active, spirally twisted structure of these molecules ("re-entrant" cholesteric structure (rest-A structure)). Cooling of this dispersion up to 22 °C is accompanied by the formation of an additional "re-entrant" cholesteric structure (rest-B). Modification of particles of the ds DNA dispersion (with rest-B structure) by replacing Na⁺ cations by multi-charged Gd³⁺ cations results in the third " re-entrant" structure (rest-C) despite a high density packing of ds nucleic acid molecules.

Hydrophobic interactions control the self-assembly of DNA and cellulose

Desoxyribosenucleic acid, DNA, and cellulose molecules self-assemble in aqueous systems. This aggregation is the basis of the important functions of these biological macromolecules. Both DNA and cellulose have significant polar and nonpolar parts and there is a delicate balance between hydrophilic and hydrophobic interactions. The hydrophilic interactions related to net charges have been thoroughly studied and are well understood. On the other hand, the detailed roles of hydrogen bonding and hydrophobic interactions have remained controversial. It is found that the contributions of hydrophobic interactions in driving important processes, like the double-helix formation of DNA and the aqueous dissolution of cellulose, are dominating whereas the net contribution from hydrogen bonding is small. In reviewing the roles of different interactions for DNA and cellulose it is useful to compare with the self-assembly features of surfactants, the simplest case of amphiphilic molecules. Pertinent information on the amphiphilic character of cellulose and DNA can be obtained from the association with surfactants, as well as on modifying the hydrophobic interactions by additives.

Buckling transitions and soft-phase invasion of two-component icosahedral shells

What is the optimal distribution of two types of crystalline phases on the surface of icosahedral shells, such as of many viral capsids? We here investigate the distribution of a thin layer of soft material on a crystalline convex icosahedral shell. We demonstrate how the shapes of spherical viruses can be understood from the perspective of elasticity theory of thin two-component shells. We develop a theory of shape transformations of an icosahedral shell upon addition of a softer, but still crystalline, material onto its surface. We show how the soft component "invades" the regions with the highest elastic energy and stress imposed by the 12 topological defects on the surface. We explore the phase diagram as a function of the surface fraction of the soft material, the shell size, and the incommensurability of the elastic moduli of the rigid and soft phases. We find that, as expected, progressive filling of the rigid shell by the soft phase starts from the most deformed regions of the icosahedron. With a progressively increasing soft-phase coverage, the spherical segments of domes are filled first (12 vertices of the shell), then the cylindrical segments connecting the domes (30 edges) are invaded, and, ultimately, the 20 flat faces of the icosahedral shell tend to be occupied by the soft material. We present a detailed theoretical investigation of the first two stages of this invasion process and develop a model of morphological changes of the cone structure that permits noncircular cross sections. In conclusion, we discuss the biological relevance of some structures predicted from our calculations, in particular for the shape of viral capsids.

Spontaneous Domain Formation in Spherically Confined Elastic Filaments

Although the free energy of a genome packing into a virus is dominated by DNA-DNA interactions, ordering of the DNA inside the capsid is elasticity driven, suggesting general solutions with DNA organized into spool-like domains. Using analytical calculations and computer simulations of a long elastic filament confined to a spherical container, we show that the ground state is not a single spool as assumed hitherto, but an ordering mosaic of multiple homogeneously ordered domains. At low densities, we observe concentric spools, while at higher densities, other morphologies emerge, which resemble topological links. We discuss our results in the context of metallic wires, viral DNA, and flexible polymers.

Chromosome Translocation Inflates Bacillus Forespores and Impacts Cellular Morphology

The means by which the physicochemical properties of different cellular components together determine bacterial cell shape remain poorly understood. Here, we investigate a programmed cell-shape change during Bacillus subtilis sporulation, when a rod-shaped vegetative cell is transformed to an ovoid spore. Asymmetric cell division generates a bigger mother cell and a smaller, hemispherical forespore. The septum traps the forespore chromosome, which is translocated to the forespore by SpoIIIE. Simultaneously, forespore size increases as it is reshaped into an ovoid. Using genetics, timelapse microscopy, cryo-electron tomography, and mathematical modeling, we demonstrate that forespore growth relies on membrane synthesis and SpoIIIE-mediated chromosome translocation, but not on peptidoglycan or protein synthesis. Our data suggest that the hydrated nucleoid swells and inflates the forespore, displacing ribosomes to the cell periphery, stretching septal peptidoglycan, and reshaping the forespore. Our results illustrate how simple biophysical interactions between core cellular components contribute to cellular morphology.

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.

Open-Boundary Molecular Dynamics of a DNA Molecule in a Hybrid Explicit/Implicit Salt Solution

The composition and electrolyte concentration of the aqueous bathing environment have important consequences for many biological processes and can profoundly affect the behavior of biomolecules. Nevertheless, because of computational limitations, many molecular simulations of biophysical systems can be performed only at specific ionic conditions: either at nominally zero salt concentration, i.e., including only counterions enforcing the system's electroneutrality, or at excessive salt concentrations. Here, we introduce an efficient molecular dynamics simulation approach for an atomistic DNA molecule at realistic physiological ionic conditions. The simulations are performed by employing the open-boundary molecular dynamics method that allows for simulation of open systems that can exchange mass and linear momentum with the environment. In our open-boundary molecular dynamics approach, the computational burden is drastically alleviated by embedding the DNA molecule in a mixed explicit/implicit salt-bathing solution. In the explicit domain, the water molecules and ions are both overtly present in the system, whereas in the implicit water domain, only the ions are explicitly present and the water is described as a continuous dielectric medium. Water molecules are inserted and deleted into/from the system in the intermediate buffer domain that acts as a water reservoir to the explicit domain, with both water molecules and ions free to enter or leave the explicit domain. Our approach is general and allows for efficient molecular simulations of biomolecules solvated in bathing salt solutions at any ionic strength condition.

Interactions between charged particles with bathing multivalent counterions: experiments vs. dressed ion theory

We compare the recent experimentally measured forces between charged colloidal particles, as well as their effective surface potentials (surface charge) in the presence of multivalent counterions in a bathing monovalent salt solution, with the predictions of the dressed ion theory of strongly charged colloidal systems. The benchmark for comparison is provided by the DLVO theory and the deviations from its predictions at small separations are taken as an indication of the additional non-DLVO attractions that can be fitted by an additional phenomenological exponential term. The parameters characterizing this non-DLVO exponential term as well as the dependencies of the effective potential on the counterion concentration and valency predicted by the dressed ion theory are well within the experimental values. This suggests that the deviations from the DLVO theory are probably caused by ion correlations as formalized within the dressed ion theory.

Order and interactions in DNA arrays: Multiscale molecular dynamics simulation

While densely packed DNA arrays are known to exhibit hexagonal and orthorhombic local packings, the detailed mechanism governing the associated phase transition remains rather elusive. Furthermore, at high densities the atomistic resolution is paramount to properly account for fine details, encompassing the DNA molecular order, the contingent ordering of counterions and the induced molecular ordering of the bathing solvent, bringing together electrostatic, steric, thermal and direct hydrogen-bonding interactions, resulting in the observed osmotic equation of state. We perform a multiscale simulation of dense DNA arrays by enclosing a set of 16 atomistically resolved DNA molecules within a semi-permeable membrane, allowing the passage of water and salt ions, and thus mimicking the behavior of DNA arrays subjected to external osmotic stress in a bathing solution of monovalent salt and multivalent counterions. By varying the DNA density, local packing symmetry, and counterion type, we obtain osmotic equation of state together with the hexagonal-orthorhombic phase transition, and full structural characterization of the DNA subphase in terms of its positional and angular orientational fluctuations, counterion distributions, and the solvent local dielectric response profile with its order parameters that allow us to identify the hydration force as the primary interaction mechanism at high DNA densities.

Quantitative computational models of molecular self-assembly in systems biology

Molecular self-assembly is the dominant form of chemical reaction in living systems, yet efforts at systems biology modeling are only beginning to appreciate the need for and challenges to accurate quantitative modeling of self-assembly. Self-assembly reactions are essential to nearly every important process in cell and molecular biology and handling them is thus a necessary step in building comprehensive models of complex cellular systems. They present exceptional challenges, however, to standard methods for simulating complex systems. While the general systems biology world is just beginning to deal with these challenges, there is an extensive literature dealing with them for more specialized self-assembly modeling. This review will examine the challenges of self-assembly modeling, nascent efforts to deal with these challenges in the systems modeling community, and some of the solutions offered in prior work on self-assembly specifically. The review concludes with some consideration of the likely role of self-assembly in the future of complex biological system models more generally.