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.     

Diurnal water storage in the stems of Picea sitchensis (Bong.) Carr.

Abstract. Two models of the relationship between diurnal variation in shoot water potential and transpiration in 14-year-old Picea sitchensis (Bong.) Carr. were compared. The first model was a physiologically based resistance-capacitance (R-C) analogue with its associated differential equations. The second was a non-physiological discrete-difference (D-D) or stochastic transfer function model. The RC model included only the effect of water storage in the phloem and bark while the D-D model implicity included all storage mechanisms. The R-C and D-D models explained similar fractions (62% and 68% respectively) of the variation in shoot water potential due to diurnal changes in transpiration rate. However, the D-D model had fewer parameters than the R-C model. The results from the D-D model showed that the resistance to flow from soil to shoots along the trunk, (RT), was 5 × 10³ MPa kg^-1s and the capacitance of the phloem and bark treated as a single store, (C_s), was 1.6 kg MPa^-1. It is suggested that the resistance to flow into storage (R_s) is much greater than R_T and can be disregarded. A non-linear version of the D-D model suggested [hat resistance to flow in the trunk increases with increasing transpiration rate.     

Resonance electroconformational coupling: A proposed mechanism for energy and signal transductions by membrane proteins

Recent experiments show that membrane ATPases are capable of absorbing free energy from an applied oscillating electric field and converting it to chemical bond energy of ATP or chemical potential energy of concentration gradients. Presumably these enzymes would also respond to endogenous transmembrane electric fields of similar intensity and waveform. A mechanism is proposed in which energy coupling is achieved via Coulombic interaction of an electric field and the conformational equilibria of an ATPase. Analysis indicates that only an oscillating or fluctuating electric field can be used by an enzyme to drive a chemical reaction away from equilibrium.In vivo, the stationary transmembrane potential of a cell must be modulated to become locally oscillatory if it is to derive energy and signal transduction processes.     

Regulation of the distribution of excitation energy in Ochromonas danica,an organism containing a chlorophyll-A/C/carotenoid light harvesting antenna

A chlorophyll a, c-fucoxanthin pigment-protein complex8 functions as the major light harvesting antenna in the Chrysophyte Ochromonas danica. The regulated distribution of excitation energy between the two photosystems was investigated in these organisms and was shown to be strongly wavelength dependent. A light state transition was induced by pre-illumination of cells using light 2 (640 nm) and light 1 (700 nm) of equal absorbed intensity, and detected by reversible changes in the 77 K chlorophyll fluorescence emission spectra. Peaks at 690 nm and 720 nm in the low temperature spectra are most likely associated with PS2 and PS1 respectively. A room temperature fluorescence emission at 680 nm induced by modulated light 2 (500 nm) was strongly quenched in the presence of background light 1 (720 nm). Removal of light 1 led to an increase in fluorescence followed by a slow quenching. The room temperature fluorescence changes were directly correlated with changes in the 77 K emission spectra that indicated a change in the distribution of excitation energy between the two photosystems. It was established that DCMU (1 mol) prevented the state 2. The conversion to state 1 followed a simple photochemical dose dependence and had a half-time of 20 s-1.5 min at 6 W m^-2. In contrast, the conversion to state 2 was independent of light intensity. These data indicate that O. danica undergoes a light state transition in response to the preferential excitation of PS2 or PS1.Abbreviations PS2 photosystem 2 - PS1 photosystem 1 - LHC light harvesting chlorophyll a/b protein - fx fucoxanthin - PQ plastoquinone - DCMU 3-(3,4-dichlorophenyl)-1,1-dimethyl urea     

State transitions,photosystem stoichiometry adjustment and non-photochemical quenching in cyanobacterial cells acclimated to light absorbed by photosystem I or photosystem II

Cells of the cyanobacterium Synechococcus 6301 were grown in yellow light absorbed primarily by the phycobilisome (PBS) light-harvesting antenna of photosystem II (PS II), and in red light absorbed primarily by chlorophyll and, therefore, by photosystem I (PS I). Chromatic acclimation of the cells produced a higher phycocyanin/chlorophyll ratio and higher PBS-PS II/PS I ratio in cells grown under PS I-light. State 1-state 2 transitions were demonstrated as changes in the yield of chlorophyll fluorescence in both cell types. The amplitude of state transitions was substantially lower in the PS II-light grown cells, suggesting a specific attenuation of fluorescence yield by a superimposed non-photochemical quenching of excitation. 77 K fluorescence emission spectra of each cell type in state 1 and in state 2 suggested that state transitions regulate excitation energy transfer from the phycobilisome antenna to the reaction centre of PS II and are distinct from photosystem stoichiometry adjustments. The kinetics of photosystem stoichiometry adjustment and the kinetics of the appearance of the non-photochemical quenching process were measured upon switching PS I-light grown cells to PS II-light, and vice versa. Photosystem stoichiometry adjustment was complete within about 48 h, while the non-photochemical quenching occurred within about 25 h. It is proposed that there are at least three distinct phenomena exerting specific effects on the rate of light absorption and light utilization by the two photoreactions: state transitions; photosystem stoichiometry adjustment; and non-photochemical excitation quenching. The relationship between these three distinct processes is discussed.Abbreviations Chl chlorophyll - DCMU 3-(3,4-dichlorophenyl)-1,1-dimethylurea - F relative fluorescence intensity at emission wavelength nm - F _o fluorescence intensity when all PS II traps are open - light 1 light absorbed preferentially by PS I - light 2 light absorbed preferentially by PS II - PBS phycobilisome - PS photosystem     

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.