The trajectory of a stiff rod in a curved potential energy trough

The equilibrium trajectory of the axis of a rod subject to an externally imposed curved potential energy trough tends to conform to the shape of the curved trough, but also tends to be straight because of elastic resistance to bending. The actual path of the axis is a balance between the two extremes. We consider a potential energy trough centered along a circular arc of radiusR. For a rod of small length compared toR, we show that the axis at equilibrium forms an arc of a circle of radius greater thanR. The value of the radius of the axial path depends on the relative values of the Hooke’s Law bending constant for the rod and the depth and width of the trough. Motivation for the calculation is provided by nucleosomal DNA, which conforms to the surface of a roughtly cylindrical histone core at physiological ionic strength, but is observed to unwind into a partially extended conformation at very low ionic strength. We suggest that the rigidity to bending of short DNA segments becomes sufficiently great at low ionic strength to overcome attractive interactions with the histone surface. Alternately, of course, if during the cell cycle mutually attractive forces between DNA and histone core are weakened at constant ionic strength, the same type of unfolding would be expected to occur as the strength of the DNA-histone contacts drops below the level required to overcome elastic resistance to bending of the DNA rod.     

Theoretical significance of the condition δ=2μ in bacterial chemotaxis

First-order spatial gradients are reliquished in the Schrödinger-Bloch equation for bacterial chemotaxis if and only if the flux coefficient-motility ratio equals 2, the precise value measured in recent experiments onEscherichia coli attracted by oxygen. Moreover, for δ/μ=2 the Schrödinger-Bloch function Ψ is simply equal to the number of bacteria cells per unit volume divided by the chemoattractant concentration.     

In Vitro Studies of α-Carboxyl-3-Thienylmethyl Penicillin,a New Semisynthetic Penicillin

The activity of a new semisynthetic penicillin, α-carboxyl-3-thienylmethyl penicillin (BRL-2288) was determined against 535 clinical isolates of gram-negative bacilli, by using the tube dilution technique. Nearly 80% of isolates of Proteus spp. were inhibited by 3.12 μg or less of this antibiotic per ml. BRL-2288 was as active as ampicillin against Escherichia coli. It was slightly more active than carbenicillin or 6-(d-α-sulfoaminophenylacetamido)-penicillanic acid against Pseudomonas sp., with over half of the isolates being inhibited by 50 μg or less of BRL-2288 per ml. Isolates of Klebsiella sp. were routinely resistant to this antibiotic. The drug was bactericidal against most sensitive organisms. BRL-2288 was less active against large inocula. A strain of Pseudomonas sp. which developed resistance to carbenicillin also developed resistance to BRL-2288 simultaneously.     

The origin of lift forces in fluttering flight

A two-dimensional nonlinear integro-differential equation with time-varying coefficients describing the behavior of the fluttering wing-body systems typical of natural flight mechanisms has been deduced from the Navier-Stokes equation which generalizes local pressure and velocity distributions in the externally oscillating air field. The resulting equation for the wing forces is combined with an analogous expression for the forces of gravitation and acceleration associated with the body. The air acceleration force, not previously considered in bio-physical models of insect and bird flight, is shown to arise from a formal analysis of unsteady or time-varying contributions to the velocity field, while the square form of the conventional steady state aerodynamic forces is derived from the intertial terms in the Navier-Stokes equation with the aid of the approximations of Newtonian impact theory. Previous calculations (Houghton, 1964) have indicated that the contribution to gravitational stability of air acceleration and aerodynamic life are roughly in the ratio of 3:1.