We calculate the forces required to package (or, equivalently, acting to eject) DNA into (from) a bacteriophage capsid, as a function of the loaded (ejected) length, under conditions for which the DNA is either self-repelling or self-attracting. Through computer simulation and analytical theory, we find the loading force to increase more than 10-fold (to tens of piconewtons) during the final third of the loading process; correspondingly, the internal pressure drops 10-fold to a few atmospheres (matching the osmotic pressure in the cell) upon ejection of just a small fraction of the phage genome. We also determine an evolution of the arrangement of packaged DNA from toroidal to spool-like structures.T he classic Hershey-Chase experiment (1) of almost 50 years ago is best known for confirming DNA as the genetic material. But it was significant also as the demonstration that a bacterial virus (phage) leaves its protein capsid outside the cell it infects. More explicitly, upon binding to its receptor protein in the outer membrane of the bacterial cell, the viral capsid is opened and its DNA is injected into the cytoplasm. Obviously, this transfer can only happen as a passive process if the DNA is sufficiently pressurized in the capsid. For the past several decades, a great deal of experimental work has been devoted to determining the arrangement of ''packaged'' DNA in phage capsids through techniques that include x-ray scattering (2, 3), Raman spectroscopy (4), chemical cross-linking (5, 6), and electron microscopy (7,8,9). Various competing models have been proposed in which the DNA molecule is organized in concentric rings as a ''spool'' (3), in parallel segments joined at sharp kinks (10), or as a folded toroid (11). The most recent electron microscopy results on bacteriophages T7 (8) and T4 (9) show concentric ring structures that lend support to a spool-like structural motif. The underlying theoretical problem is also formidable, because one is confronted with the statistical-mechanical challenge of accounting for how a semif lexible, highly charged chain can be confined in dimensions comparable to its persistence length and yet hundreds of times smaller than its overall (contour) length L (12, 13). Although some estimates have been made of the pressure and elastic stress in a fully loaded capsid (12, 14), we are not aware of any attempt to treat the driving pressures during the course of ejection or the loading forces as a function of the extent of packaging (15). ¶In the present work, we connect the processes of loading DNA into, and ejecting it from, a phage capsid by calculating the energy of the chain as a function of the degree of loading or ejection. As already mentioned, the initial ejection is a passive process, being driven directly by the pressure difference inside and outside the capsid (16).ʈ Indeed, we shall show that the energy decreases monotonically as successively shorter lengths of DNA are left confined in the capsid; this rate of decrease corresponds to a force driving the chain outside. By ...

In a previous communication (Kindt et al., 2001) we reported preliminary results of Brownian dynamics simulation and analytical theory which address the packaging and ejection forces involving DNA in bacteriophage capsids. In the present work we provide a systematic formulation of the underlying theory, featuring the energetic and structural aspects of the strongly confined DNA. The free energy of the DNA chain is expressed as a sum of contributions from its encapsidated and released portions, each expressed as a sum of bending and interstrand energies but subjected to different boundary conditions. The equilibrium structure and energy of the capsid-confined and free chain portions are determined, for each ejected length, by variational minimization of the free energy with respect to their shape profiles and interaxial spacings. Numerical results are derived for a model system mimicking the lambda-phage. We find that the fully encapsidated genome is highly compressed and strongly bent, forming a spool-like condensate, storing enormous elastic energy. The elastic stress is rapidly released during the first stage of DNA injection, indicating the large force (tens of pico Newtons) needed to complete the (inverse) loading process. The second injection stage sets in when approximately 1/3 of the genome has been released, and the interaxial distance has nearly reached its equilibrium value (corresponding to that of a relaxed torus in solution); concomitantly the encapsidated genome begins a gradual morphological transformation from a spool to a torus. We also calculate the loading force, the average pressure on the capsid's walls, and the anisotropic pressure profile within the capsid. The results are interpreted in terms of the (competing) bending and interaction components of the packing energy, and are shown to be in good agreement with available experimental data.

Cell-cell communication, which enables cells to coordinate their activity and is essential for growth, development and function, is usually ascribed a chemical or electrical origin. However, cells can exert forces and respond to environment elasticity and to mechanical deformations created by their neighbours 1-13 . The extent to which this mechanosensing ability facilitates intercellular communication remains unclear. Here we demonstrate mechanical communication between cells directly for the first time, providing evidence for a long-range interaction that induces long-lasting alterations in interacting cells. We show that an isolated cardiac cell can be trained to beat at a given frequency by mechanically stimulating the underlying substrate. Deformations are induced using an oscillatory mechanical probe that mimics the deformations generated by a beating neighbouring cardiac cell. Unlike electrical field stimulation, the probe-induced beating rate is maintained by the cell for an hour after the stimulation stops, implying that long-term modifications occur within the cell. These long-term alterations provide a mechanism for cells that communicate mechanically to be less variable in their electromechanical delay. Mechanical coupling between cells therefore ensures that the final outcome of action potential pacing is synchronized beating. We further show that the contractile machinery is essential for mechanical communication.Here we sought to separate the mechanical component of intercellular communication from indirect effects, such as a change in the amount or type of secreted chemo-attractants. We did so by introducing a 'mechanical cell' . The 'mechanical cell' consists of a probe that mimics the mechanical aspect of a cell by generating substrate deformations identical to the ones induced by a neighbouring beating cell. Previous studies have shown that mechanical stimulation of a quiescent cell or an engineered cardiac construct can induce beating 12,14 . However, in those studies, the magnitude and direction of forces applied were not controlled as to mimic the magnitude and direction of forces applied by cells. In addition, the duration of stimulation was extremely brief and the cells did not synchronize with the probe. These studies therefore did not provide a demonstration or characterization of cellular mechanical communication.Here, we use a 'mechanical cell' to apply deformations identical to those generated by an aligned beating cardiac cell both in magnitude and in directionality. We show that such deformations can synchronize cell beating. This provides clear evidence for mechanical cellular communication. Training of both quiescent and spontaneously beating cells takes up to 10-15 min and the induced beating frequency persists for over an hour after stimulation had stopped. These results demonstrate that mechanical communication is a unique type of interaction that is both long ranged and induces long-lasting alterations in interacting cells. We further demonstrate that mechanical communication...

We present a simple statistical thermodynamic model for budding of viral nucleocapsids at the cell membrane. The membrane is modeled as a flexible lipid bilayer embedding linker (spike) proteins, which serve to anchor and thus wrap the membrane around the viral capsids. The free energy of a single bud is expressed as a sum of the bending energy of its membrane coat, the spike-mediated capsid-membrane adhesion energy, and the line energy associated with the bud's rim, all depending on the extent of wrapping (i.e., bud size), and density of spikes in the curved membrane. This self-energy is incorporated into a simple free energy functional for the many-bud system, allowing for different spike densities, and hence entropy, in the curved (budding) and planar membrane regions, as well as for the configurational entropy of the polydisperse bud population. The equilibrium spike densities in the coexisting, curved and planar, membrane regions are calculated as a function of the membrane bending energy and the spike-mediated adhesion energy, for different spike and nucleocapsid concentrations in the membrane plane, as well as for several values of the bud's rim energy. We show that complete budding (full wrapping of nucleocapsids) can only take place if the adhesion energy exceeds a certain, critical, bending free energy. Whenever budding takes place, the spike density in the mature virions is saturated, i.e., all spike adhesion sites are occupied. The rim energy plays an important role in determining the size distribution of buds. The fraction of fully wrapped buds increases as this energy increases, resulting eventually in an all-or-nothing mechanism, whereby nucleocapsids at the plasma membrane are either fully enveloped or completely naked (just touching the membrane). We also find that at low concentrations all capsids arriving at the membrane get tightly and fully enveloped. Beyond a certain concentration, corresponding approximately to a stoichiometric spike/capsid ratio, newly arriving capsids cannot be fully wrapped; i.e., the budding yield decreases.