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.
We present the derivation of the macroscopic equations for systems with an axial dynamic preferred direction. In addition to the usual hydrodynamic variables, we introduce the time derivative of the local preferred direction as a new variable and discuss its macroscopic consequences including new crosscoupling terms. Such an approach is expected to be useful for a number of systems for which orientational degrees of freedom are important including, for example, the formation of dynamic macroscopic patterns shown by certain bacteria such a Proteus mirabilis. We point out similarities in symmetry between the additional macroscopic variable discussed here, and the magnetization density in magnetic systems as well as the so-called ˆl vector in superfluid 3He-A. Furthermore we investigate the coupling to a gel-like system for which one has the strain tensor and relative rotations between the new variable and the network as additional macroscopic variables.
Pentatomid bugs communicate using substrate-borne vibrational signals that are transmitted along herbaceous plant stems in the form of bending waves with a regular pattern of minimal and maximal amplitude values with distance. We tested the prediction that amplitude variation is caused by resonance, by measuring amplitude profiles of different vibrational pulses transmitted along the stem of a Cyperus alternifolius plant, and comparing their patterns with calculated spatial profiles of corresponding eigenfrequencies of a model system. The measured distance between nodes of the amplitude pattern for pulses with different frequencies matches the calculated values, confirming the prediction that resonance is indeed the cause of amplitude variation in the studied system. This confirmation is supported by the resonance profile obtained by a frequency sweep, which matches theoretical predictions of the eigenfrequencies of the studied system. Signal bandwidth influences the amount of amplitude variation. The effect of both parameters on signal propagation is discussed in the context of insect vibrational communication.