Estimation of uncertainties in X-ray refinement results by use of perturbed structures

The uncertainties in the refined parameters for a 1.5-A X-ray structure of carbon-monoxy (FeII) myoglobin are estimated by combining energy minimization with least-squares refinement against the X-ray data. The energy minimizations, done without reference to the X-ray data, provide perturbed structures which are used to restart conventional X-ray refinement. The resulting refined structures have the same, or better, R-factor and stereochemical parameters as the original X-ray structure, but deviate from it by 0.13 A rms for the backbone atoms and 0.31 A rms for the sidechain atoms. Atoms interacting with a disordered sidechain, Arg 45 CD3, are observed to have larger positional uncertainties. The uncertainty in the B-factors, within the isotropic harmonic motion approximation, is estimated to be 15%. The resulting X-ray structures are more consistent with the energy parameters used in simulations.     

Volume estimation of biological objects by systematic sections

The absolute volume of biological objects is often estimated stereologically from an exhaustive set of systematic sections. The usual volume estimator is the sum of the section contents times the distance between sections. For systematic sectioning with a random start, it has been recently shown that is unbiased when m, the ratio between projected object length and section distance, is an integer number (Cruz-Orive 1985). As this quantity is no integer in the real world, we have explored the properties of in the general and realistic situation m . The unbiasedness of under appropriate sampling conditions is demonstrated for the arbitrary compact set in 3 dimensions by a rigorous proof. Exploration of further properties of for the general triaxial ellipsoid leads to a new class of non-elementary real functions with common formal structure which we denote as np-functions. The relative mean square error (CE ²) of in ellipsoids is an oscillating differentiable np-function, which reduces to the known result CE ²= 1/(5m ⁴) for integer m. As a biological example the absolute volumes of 10 left cardiac ventricles and their internal cavities were estimated from systematic sections. Monte Carlo simulation of replicated systematic sectioning is shown to be improved by using m instead of m . In agreement with the geometric model of ellipsoids with some added shape irregularities, mean empirical CE was proportional to m ^–1.36 and m^–1.73 in the cardiac ventricle and its cavity. The considerable variance reduction by systematic sectioning is shown to be a geometric realization of the principle of antithetic variates.     

Revision of the theory of phototropism in plants: a new interpretation of a classical experiment

Went's classical experiment on the diffusion of auxin activity from unilaterally illuminated oat coleoptile tips (Went 1928), was repeated as precisely as possible. In agreement with Went's data with theAvena curvature assay, the agar blocks from the illuminated side of oat (Avena sativa L. cv. Victory) coleoptile tips had, on an average, 38% of the auxin activity of those from the shaded side. However, determination of the absolute amounts of indole-3-acetic acid (IAA) in the agar blocks, using a physicochemical assay following purification, showed that the IAA was evenly distributed in the blocks from the illuminated and shaded sides. In the blocks from the shaded and dark-control halves the amounts of IAA were 2.5 times higher than the auxin activity measured by theAvena curvature test, and in those from the illuminated half even 7 times higher. Chromatography of the diffusates prior to theAvena curvature test demonstrated that the amounts of two growth inhibitors, especially of the more polar one, were significantly higher in the agar blocks from the illuminated side than in those from the shaded side and the dark control. These results show that the basic experiment from which the Cholodny-Went theory was derived, does not justify this theory. The data rather indicate that phototropism is caused by the light-induced, local accumulation of growth inhibitors against a background of even auxin distribution, the diffusion of auxin being unaffected.Abbreviation IAA indole-3-acetic acid     

Application of the Fröhlich theory to the modelling of rouleau formation in human erythrocytes

The details of Fröhlich's theory and some recent experiments on the rouleau formation of human erythrocytes which exhibit a strong interaction that appears to satisfy the prerequisites of the Fröhlich theory, are summarized. To verify whether the Fröhlich theory of long-range coherence in biological systems is applicable to the phenomenon of rouleau formation in human erythrocytes, the interactions between erythrocytes are modelled as those between two large, coupled oscillating dipoles. Relevant expressions for the resonant long-range and the van der Waals interaction are then derived. Using the available numerical data, the eigenfrequencies and the interaction energies corresponding to the experimental conditions are then derived. In the range of postulated frequencies (10¹¹–10¹² Hz) the effective interaction coefficient due to the resonant long-range forces is, indeed, found to agree with its experimental value of 3.0. However, the same value of can also be achieved through the ordinary van der Waals interactions between dipoles oscillating at lower frequencies. It is concluded that the resonant long-range interaction between erythrocytes may be responsible for the onset of rouleau formation. However, other mechanisms cannot be ruled out at this stage, especially since the Fröhlich mechanism requires a number of unconfirmed preconditions.     

Exciton interactions in synthetic porphyrin dimers

The Soret absorption spectra of six synthetic rigid porphyrin dimers whose crystal structures have been determined are simulated using simple exciton theory. The objective is to test the validity of the point dipole and associated approximations; the electronic interaction parameters are thus calculated using data obtained from the monomer spectra, with no adjustable parameters. Satisfactory agreement between theory and experiment is obtained for one class of dimers but not for a second. This poses a challenge for semiempirical electronic structure methods as to whether improvements over the point dipole calculations can be obtained.     

Obligation and the new naturalism

Although it has become increasingly evident that an adequate theory of obligation must rest on evolutionary biology and human ethology, attempts toward this end need to explore the full range of personal, cultural, and political obligations observed in our species. The new naturalism reveals the complexity of social behavior and the defects of reductionist models that oversimplify the foundations of human duties and rights. Ultimately, this approach suggest a return to the Aristotelian concept of natural justice.