Physicochemical features of ultra-high viscosity alginates

The physicochemical characteristics of the ultra-high viscosity and highly biocompatible alginates extracted from Lessonia nigrescens (UHV_N) and Lessonia trabeculata (UHV_T) were analyzed. Fluorescence and ¹H NMR spectroscopies, viscometry, and multi-angle light scattering (MALS) were used for elucidation of the chemical structure, molar mass, and coil size. The sequential structures from NMR spectroscopy showed high guluronate content for UHV_T, but low for UHV_N. Intrinsic viscosity [η] measurements exhibited unusual high values (up to 2750 mL/g), whereas [η] of a commercial alginate was only about 970 mL/g. MALS batch measurements of the UHV-alginates yielded ultra-high values of the weight average molar mass (M_w up to 1.1 × 10⁶ g/mol) and of the z-average gyration radius (〈R_G〉_z up to191 nm). The M_w and 〈R_G〉_z distributions of UHV-alginates and of ultrasonically degraded fractions were determined using size exclusion chromatography combined with MALS and asymmetrical flow-field-flow fractionation. The M_w dependency of [η] and 〈R_G〉_z could be described by [η] = 0.059 ×  and 〈R_G〉_z = 0.103 × . (UHV_N: x = 0.52; UHV_T: x = 0.53) indicating that the monomer composition has no effect on coil expansion. Therefore, the equations can be used to calculate M_w and 〈R_G〉_z values of UHV_T- and UHV_N-alginate mixtures as used in immunoisolation. Furthermore, the simple and inexpensive capillary viscometry can be used for real-time validation of the extraction and purification process of the UHV-alginates.     

Interpretation of energy-transfer experiments by theoretical studies of model compounds using semiempirical potential functions. I. Three-linked aromatic peptide units

It is shown that theoretical conformational analysis, based on the evaluation of semiempirical potential functions, can be used to compute the quantities relevant to the interpretation of energy-transfer experiments. The relevant properties are computed for a segment of a polypeptide chain with the sequence Tyr-Tyr. In particular, the average value of the orientation factor 〈κ²〉 and its distribution ?(κ²) are examined. It appears that the degrees of freedom for rotation of the side chains are not sufficient to randomize completely the orientation factor of the transition dipoles. Two additional degrees of freedom, namely the torsion angles around the valence bonds of the backbone, ψ₁ and ?₂, bring 〈κ²〉 close to the value that corresponds to randomly oriented transition dipoles.     

Coordination chemistry of lanthanides with cryptands. An X-ray and spectroscopic study of the complex Nd2(NO3)6 [C18H36O6N2]·H2O

By reacting neodymium nitrate hexahydrate with the cryptand 〈222〉 in methanol, the complex Nd₂-(NO₃)₆[C₁₈H₃₆O₆N₂]·H₂O was obtained and analyzed by single-crystal X-ray diffraction. The cell is triclinic P$\text{1}$ with a = 14.870(2) Å, b = 13.261(2) Å, c = 8.832(1) Å, α = 91.2(1)°, β = 93.4(1)°, γ = 87.6(1)°, Z = 2 and U = 1736.6 ų. The structure was refined by least-squares methods to the conventional R = 0.039 for 6177 observed reflections. The compound contains the cations [Nd〈222〉(NO₃)]²⁺ and the anions [Nd(NO₃)₅·H₂O]^2?, and is isostructural with the samarium analogue. Solid state fluorescence spectra of the title complex were measured at room and liquid nitrogen temperature, and the transitions ⁴F_3/2 → ⁴I_9/2 and ⁴F_3/2 → ⁴I_11/2 analyzed.     

Variance of actual inbreeding

The variances of actual inbreeding and coancestry in terms of their corresponding identities by descent were studied for finite populations. For inbreeding at a single locus, the total variance σ² = F(1 ? F) (F is the inbreeding coefficient) is comprised of a component σ_w² within populations and a component σ_b² between replicate populations. These variances increase in time to a maximum at about 1.1N_e generations for σ_w², about 2.3N_e generations for σ_b², and about 1.4N_e generations for σ², and decrease thereafter (N_e is effective population size). The ratio $\text{σ}{}_{\mathrm{<mtext>b</mtext>}}{}^2\text{σ}{}^2$ is ever increasing to an asymptote in the range 0.4-0.5 depending on N_e and the mating system. For finite populations with variation in pedigree F's, there are contributions σ_wF² within and σ_bF² between populations. The component σ_bF² is insignificant except for very small populations, and σ_wF² is largest in the early generations and then decreases roughly as $\text{(1 ? F)}{}^2\text{KN}{}_{\mathrm{<mtext>e</mtext>}}\text{where}\text{K}$ is formulated in terms of the mating strategy and the degree of avoidance of mating relatives. An additional degree of avoidance increases K by a factor of 4. In a large population at equilibrium with respect to mixed self and random mating, σ_wF² accounts for onehalf to two-thirds of σ_w². Bringing in more loci leads to the decomposition of the total variance into four components whose values are affected by linkages among the loci. The relationships between these components and σ_w², σ_b², σ_wF², and σ_bF², are elaborated in terms of tight and loose linkage. The exact computations of σ_wF² and σ_bF² require the use of two locus descent measures without linkage. The variances of various averages of actual identities by descent, such as the proportions for individuals or populations, are formulated for a sample of individuals.     

Effects of increasing nutrient supply and omnivorous feeding on the size spectrum slope: a size-based nutrient-phytoplankton-zooplankton model

Size spectrum slope has been considered as an indicator for system productivity and size-dependent trophic interactions in plankton communities. We investigated the effect of new nutrient flux (N _in ) and feeding breadth of zooplankton (σ²) on spectral slopes of the plankton community using a size-structured nutrient-phytoplankton-zooplankton model. We studied two types of plankton systems (1) at a steady state and (2) with fluctuating plankton populations. For the steady state systems, the spectral slopes increased with N _in and σ². In contrast, for the systems in fluctuation, spectral slopes constructed from long-term average plankton populations decreased with increasing N _in and σ². In addition to spectral slopes constructed from long-term average population densities, we investigated slope variability in systems with fluctuating plankton populations. The variability of spectral slopes was found to increase with N _in and σ², indicating that spectral slope variation is large in a eutrophic system or when zooplankton feed on a wide size range of prey. Empirically, because N _in is difficult to measure, nutrient concentration is investigated instead. Our model predicts that the spectral slope is positively correlated with nutrient concentration due to the accumulated mesozooplankton biomass, which was confirmed by our study in plankton community in a subtropical reservoir in Taiwan.     

Human Microtubule-Associated-Protein Tau Regulates the Number of Protofilaments in Microtubules: A Synchrotron X-Ray Scattering Study

Microtubules (MTs), a major component of the eukaryotic cytoskeleton, are 25 nm protein nanotubes with walls comprised of assembled protofilaments built from αβ heterodimeric tubulin. In neural cells, different isoforms of the microtubule-associated-protein (MAP) tau regulate tubulin assembly and MT stability. Using synchrotron small angle x-ray scattering (SAXS), we have examined the effects of all six naturally occurring central nervous system tau isoforms on the assembly structure of taxol-stabilized MTs. Most notably, we found that tau regulates the distribution of protofilament numbers in MTs as reflected in the observed increase in the average radius 〈R^MT〉 of MTs with increasing Φ, the tau/tubulin-dimer molar ratio. Within experimental scatter, the change in 〈R^MT〉 seems to be isoform independent. Significantly, 〈R^MT〉 was observed to rapidly increase for 0 < Φ < 0.2 and saturate for Φ between 0.2-0.5. Thus, a local shape distortion of the tubulin dimer on tau binding, at coverages much less than a monolayer, is spread collectively over many dimers on the scale of protofilaments. This implies that tau regulates the shape of protofilaments and thus the spontaneous curvature C_o^MT of MTs leading to changes in the curvature C^MT (=1/R^MT). An important biological implication of these findings is a possible allosteric role for tau where the tau-induced shape changes of the MT surface may effect the MT binding activity of other MAPs present in neurons. Furthermore, the results, which provide insight into the regulation of the elastic properties of MTs by tau, may also impact biomaterials applications requiring radial size-controlled nanotubes.     

Synthesis of new (σ-N,N′-diazadiene)(η-alkene)platinum(0) compounds

Novel, thermally stable, dark-red to orange Pt⁰(σ²-N,N′-diazadiene)(η²-alkene) compounds have been synthesized in good yields from Pt⁰(COD)₂ or Pt⁰(NBE)₃, by stepwise substitution of the respective dienes or alkenes by an electron-poor alkene (dimethyl fumarate, maleic anhydride or fumaronitrile), followed by the appropriate diazadiene ligand in dry diethyl ether at 20 °C (diazadiene=various N,N′-disubstitued-1,4-diaza-1,3-dienes). The complex Pt(DBA)₂ is less suited as a precursor for the synthesis of Pt⁰(σ²-N,N′-diazadiene)(η²-alkene) compounds. These zerovalent Pt(diazadiene)(η²-alkene) compounds constitute a useful category of starting materials for synthetic organoplatinum chemistry and catalysis.     

The nucleic acid distribution function: evaluation of the loop closure probability

We present a detailed theoretical study of nucleic acid distance distribution functions for chain lengths up to thirty-five nucleotides. The distribution functions were found by the Monte Carlo techniques described previously and, where they are symmetric, by reconstruction from their even moments. A comparison of the two approaches allows an assessment of the utility of expansion procedures for stiff chains (C_∞ ≈ 17), as a function of length and extension. It was found that for chains with fewer than fourteen nucleotides over seventy even moments were required to obtain a reliable function for extensions R ≥ (〈R²〉)^1/2. On the other hand at thirty-five nucleotides the first ten even moments were sufficient to reconstruct the distribution for all but extreme extensions. The other feature of the calculation is the prediction of a loop weighting function. It was found that for a thirty-five nucleotide chain, the form of the distribution function is very nearly gaussian for R < (〈R²〉)^1/2. Consequently a loop weighting function based on detailed crystallographic data is now known for all values of N. The first derivative of the function is within 8% of the Jacobson-Stockmayer value at 170 nucleotides, but differs severely from the latter for chains with less than twenty nucleotides.     

MonodentateN coordination of 1aza4oxo1,3butadienes [R1NC(R2)C(R3)O] to platinum(II). X-ray structure of trans-[PtCl2(PEt3){σ-N-(t-BuNCHC(Me)O)}]

Reaction of dimeric trans-[PtCl₂(PR₃)]₂ with 1-aza-4-oxo-1,3-butadienes [R¹NC(R²)C(R³)O, R³ = Me, Ph, OMe, NEt₂] in a 1:2 molar ratio results in almost quantitative formation of mononuclear complexes trans·[PtCl₂(PR₃){σ-N-(R¹NC(R²)C(R³)O)}]. The ligands are bonded in the monodentate σ-N bonding mode to the platinum(II) centre. This has been established by an X-ray structure determination of trans-[PtCl₂(PEt₃){σ-N-(t-BuNCHC(Me)O)}]. Crystals of the latter compound are orthorhombic with space group Pc2₁n; cell constants are a = 14.712(3), b = 15.053(2), c = 9.025(5) Å, Z= 4 and R_w = 0.056 for 3281 reflections. The 1aza4oxol,3butadiene (α-iminoketone for R³ is alkyl or aryl) has the E-configuration about the imine bond (CN 1.34(4) Å), with a C(5)C(6) distance of 1.44(5) Å and a NC(5)/ C(6)O torsion angle of 89(4)°. As a result of this ligand conformation, the acetyl hydrogen atoms are positioned (on average) into the neighbourhood of the Pt-atom above the Pt-coordination plane. Infrared and NMR (¹H, ¹³C, ³¹p) data show that these structural features are also predominant in solution.     

Manganese(II) complexes of di-2-pyridinylmethylene-1,2-diimine di-Schiff base ligands: Structures and reactivity

Manganese(II) complexes [Mn(L)X₂] were prepared and characterized, where L is a neutral di-Schiff base ligand incorporating pyridylimine donor arms, including (1R,2R)-N,N′-bis(2-pyridylmethylidene)-1,2-diphenylethylenediimine (L¹), (1R,2R)-N,N′-bis(6-methyl-2-pyridylmethylidene)-1,2-cyclohexyldiimine (L²), or (1R,2R)-, (1S,2S)- or racemic N,N′-bis(2-pyridylmethylidene)-1,2-cyclohexyldiimine (L³), and X⁻ =  or Cl⁻. Product complexes were structurally characterized, specifically including [Mn(R,R-L¹)(NCCH₃)₃](ClO₄)₂, [Mn(R,R-L²)(OH₂)₂](ClO₄)₂ and racemic [Mn(L³)Cl₂]. The first of these complexes features a heptacoordinate ligand field in a distorted pentagonal bipyramid, and the latter two are hexacoordinate, but retain equatorially monovacant pentagonal bipyramidal structures. Complexes [Mn(L³)X₂] (X⁻ = Cl⁻, ) were reacted with the primary phosphine FcCH₂PH₂ (Fc = -C₅H₄FeC₅H₅), H₂O and ethyldiazoacetate (EDA). The first two substrates prompted reactivity at a single ligand imine bond, resulting in hydrophosphination and hydrolysis, respectively. Complexes of the derivative ligands were also structurally characterized. Evidence for EDA activation was obtained by electrospray ionization mass spectrometry, but catalytic carbene transfer was not obtained.     

Fluctuations of an alpha-helix.

Fluctuations in backbone dihedral angles in the α-helical conformation of homopolypeptides are studied based on an assumption that the conformational energy function of a polypeptide consisting of n amino-acid residues can be approximated by a 2n-dimensional parabola around the minimum point in the range of fluctuations. A formula is derived that relates 〈Δθ_iΔθ_j〉, the mean value of the product of deviations of dihedral angles ?_i and ψ_i (collectively designated by θ_i) from their energy minimum values, with a matrix inverse to the second derivative matrix F ,_n of the conformational energy function at the minimum point. A method of calculating the inverse matrix F _n^?1 explicitly is given. The method is applied to calculating 〈Δθ_iΔθ_j〉 for the α-helices of poly(L -alanine) and polyglycine. The autocorrelations 〈(Δ?_i)²〉 and 〈(Δψ_i)²〉 at 300°K are found to be about 66 deg² and 49 deg², respectively, for poly(L -alanine), and 84 deg² and 116 deg², respectively, for polyglycine. The length of correlations of fluctuations along the chain is found for both polypeptides to be about eight residues long.     

Backscattering of gyrotron radiation and short-wavelength turbulence during electron cyclotron resonance plasma heating in the L-2M stellarator

Backscattering of gyrotron radiation (θ = π) by short-wavelength density fluctuations (k _⊥ = 30 cm^?1) in the plasma of the L-2M stellarator was studied under conditions of electron cyclotron resonance (ECR) plasma heating at the second harmonic of the electron gyrofrequency (75 GHz). The scattering of the O-wave emerging due to the splitting of the linearly polarized gyrotron radiation into the X- and O-waves was analyzed. The signal obtained after homodyne detection of scattered radiation is a result of interference of the reference signal, the quasi-steady component, and the fast oscillating component. The coefficients of reflection of the quasi-steady component, R ₌ ² (Y), and fast oscillating component, R _～ ² (Y), of scattered radiation are estimated. The growth of the R _～ ² (Y) coefficient from 3.7 × 10^?4 to 5.2 × 10^?4 with increasing ECR heating power from 190 to 430 kW is found to correlate with the decrease in the energy lifetime from 1.9 to 1.46 ms. The relative density of short-wavelength fluctuations is estimated to be 〈n _～ ² 〉/〈n _e ² 〉 = 3 × 10^?7. It is shown that the frequencies of short-wavelength fluctuations are in the range 10–150 kHz. The recorded short-wavelength fluctuations can be interpreted as structural turbulence, the energy of which comprises ～10% of the total fluctuations energy. Simulations of transport processes show that neoclassical heat fluxes are much smaller than anomalous ones. It is suggested that short-wavelength turbulence plays a decisive role in the anomalous heat transport.     

Determination of molecular size of O-(2-hydroxyethyl)cellulose (HEC) and its relationship to the mechanism of enzymatic hydrolysis by cellulases

Z-average root mean square end-to-end distance 〈r_o²〉_z^1/2 and radius of gyration 〈s_o²〉_z^1/2 for 13 samples of O-(2-hydroxyethyl)cellulose (HEC) of different molecular weights were derived from Gel Permeation Chromatography and intrinsic viscosity measurements with water as a solvent. At 40 °C and pH 4.5, contraction of chain dimensions is observed, compared with the sizes observed under neutral conditions at room temperature. The effect is lower for samples with higher molecular weights. Values of 〈r_o²〉₄₀/DP_z also indicate that chain flexibility increases at higher temperature and acidic conditions. From the analysis of molecular weight dependence of 〈s_o²〉 _z^1/2, Flory exponent υ was derived at 40 °C and pH 4.5. A value of υ = 0.70 ± 0.02 was recorded, which indicates that a relatively stiff chain is present under these conditions. Finally, different equations to calculate persistence length L_p were evaluated. Values in the range of 260-400 Å were derived for persistence length. Implications of chain conformation in the enzymatic action of cellulases are also discussed.     

Assessing the impact of inductive electronic effects on the metrical parameters and reactivity of a series of ferrous complexes

Reported are four iron(II) complexes with N-benzyl-N,N′-bis(2-pyridylmethyl)-1,2-ethanediamine (L^H) and three electronically modified derivatives: N-(4-methoxy)benzyl-N,N′-bis(2-pyridylmethyl)-1,2-ethanediamine (L^OMe), N-(4-chloro)benzyl-N,N′-bis(2-pyridylmethyl)-1,2-ethanediamine (L^Cl), and N-(4-nitro)benzyl-N,N′-bis(2-pyridylmethyl)-1,2-ethanediamine (L^NO₂). The four ligands react with FeCl₂ to form a series of mononuclear species with the general formula [Fe(L^R)Cl₂]. The cis-α conformation of the ligand places the amine N-donors trans to the Fe-Cl bonds. The identity of the 4-benzyl substituent has profound influences on the lengths of the iron-ligand bonds, the optical spectra, and the redox activities of the [Fe(L^R)Cl₂] compounds.     

Kerr constants of amides and peptides

Molar Kerr contants _mK have been determined for N-methylacetamide, N-ethyl-acatamide, N-methylpropionamide, N-acetylglycine-N′-methylamide, N-acetyl-L -ala-nine-N′-methylamide, and N-acetyl-L -leucine-N′-methylamide from electric birefringence measurements on dilute solutions in dioxane. The resultes are compared with configurational averatges 〈_mK〉 calculated on the basis of conformational energies. Values of_mK calculated for various fixed confromations on the peptides vary over a wide range depending on the choice of conformation; hece, the configurational averages 〈_mK〉 are sensitive to smalll changes in the conformational enerey. Kerr constants are calculated for random coiled oligoglycine and oligoalanine peptides as functions of chain length. The Kerr constant is an especially acute index of the average conformation.     

Non-phenotypic selection of N-methyl-N′-nitro-N-nitrosoguanidine-directed mutation at a predicted hotspot site

The striking mutational specificity of N-methyl-N′-nitro-N-nitrosoguanidine (MNNG) exhibited in the lacI gene in Escherichia coli allows comment on the phenotypic consequences of mutation at specific sequences that are not recovered after MNNG mutagenesis. We predict that the I⁺ phenotype is maintained when such silent positions are substituted by amino acids whose codons are generated by the MNNG-directed G:C → A:T transition. We chose the mutationally silent Gly200 codon (an MNNG hotspot motif sequence) to test this prediction. Through MNNG mutagenesis we have generated, identified and isolated a G:C → A:T transition at position 627 (5′-GG-C3′) under non-selective conditions which creates the Gly200→Asp substitution. The I⁺ phenotype is retained for this altered repressor.     

Nucleotide excision repair of 2-acetylaminofluorene- and 2-aminofluorene-(C8)-guanine adducts: molecular dynamics simulations elucidate how lesion structure and base sequence context impact repair efficiencies

Nucleotide excision repair (NER) efficiencies of DNA lesions can vary by orders of magnitude, for reasons that remain unclear. An example is the pair of N-(2′-deoxyguanosin-8-yl)-2-aminofluorene (dG-C8-AF) and N-(2′-deoxyguanosin-8-yl)-2-acetylaminofluorene (dG-C8-AAF) adducts that differ by a single acetyl group. The NER efficiencies in human HeLa cell extracts of these lesions are significantly different when placed at G₁, G₂ or G₃ in the duplex sequence (5′-CTCG₁G₂CG₃CCATC-3′) containing the NarI mutational hot spot. Furthermore, the dG-C8-AAF adduct is a better substrate of NER than dG-C8-AF in all three NarI sequence contexts. The conformations of each of these adducts were investigated by Molecular dynamics (MD) simulation methods. In the base-displaced conformational family, the greater repair susceptibility of dG-C8-AAF in all sequences stems from steric hindrance effects of the acetyl group which significantly diminish the adduct-base stabilizing van der Waals stacking interactions relative to the dG-C8-AF case. Base sequence context effects for each adduct are caused by differences in helix untwisting and minor groove opening that are derived from the differences in stacking patterns. Overall, the greater NER efficiencies are correlated with greater extents of base sequence-dependent local untwisting and minor groove opening together with weaker stacking interactions.     

Effects of Na+and Mg2+on the Structures of Supercoiled DNAs: Comparison of Simulations with Experiments

Recent cryo-electron microscopy (cryo-EM) results suggest that sufficient NaCl concentration (≤0.1 M) and superhelix density (≤−0.05) cause circular DNAs to adopt highly extended, tightly interwound configur ations, in which the strands are laterally contiguous along almost their entire length. Millimolar levels of MgCl₂reportedly act synergistically with NaCl to produce similar conformations. However, Monte Carlo simulations with purely repulsive interduplex forces failed to reproduce such structures. In the present work, solution measurements of particular physical properties were performed both to characterize the effects of Na⁺and Mg²⁺on DNA structure and to provide quantitative tests of Monte Carlo simulations of circular DNAs. Supercoiled p30δ DNAs in 10 mM Tris plus 0, 0.122, and 0.1 M NaCl, and 0.1 M NaCl plus 4 mM Mg²⁺were examined by static and dynamic light scattering (LS and DLS), time- resolved fluorescence polarization anisotropy (FPA) of intercalated ethidium, and circular dichroism (CD) spectroscopy. Upon addition of 0.122 M NaCl, the radius of gyration (R_g) decreased substantially, which indicates that p30δ adopts a more compact structure. This contradicts the cryo-EM studies, where molecular extension andR_gboth increase upon adding 0.1 M NaCl. In 0.1 M NaCl, the torsion constant measured by FPA is practically invariant to superhelix density, and the plateau diffusion coefficient at large scattering vector (D_plat) is likewise nearly the same at both relaxed and native superhelix densities. Such invariance is difficult to reconcile with any transition from relaxed circles to tightly interwound structures with laterally contiguous strands. Metropolis Monte Carlo simulations were performed to generate canonically distributed sets of structures, from which averageD₀values and scattered intensity ratios,〈I(0)〉/〈I(k)〉, were calculated. Agreement between simulations and experiments in regard to 〈I(0)|〉/〈I(k)〉,D₀and the supercoiling free energy, ΔG_sc(Δl ), is remarkably good for the most extensively studied p30δ samples. The simulated structures exhibit no sign of very tight interwinding with extensive lateral contacts, but instead exhibit most probable superhelix diameters of 85 to 90 Å. When 4 mM Mg²⁺was added to native supercoiled p30δ in 0.1 M NaCl,R_gdecreased,D₀increased, and the longest internal relaxation rate (1/τ₂(0)) increased, all of which indicate a further overall contraction of the molecular envelope. The torsion constant exhibited a slight increase that is hardly statistically significant. In this case, agreement between the simulations and experiments was only semi-quantitative for most samples investigated, although the predicted contraction was exhibited by all five samples of p30δ and one of pBR322 DNA. The simulated structures in 0.1 M NaCl plus 4 mM Mg²⁺again showed no sign of extensive lateral contacts. A plausible explanation is proposed for the highly extended, tightly interwound structures seen in cryo-EM, and explicitly tested by Monte Carlo simulations of a 1000 bp circular DNA at +25 and −50°C. Structures identical to those seen in cyro-EM are in fact the equilibrium structures in the simulations at −50°C, and the estimated time for equilibration (2.3×10⁻⁶second) is much smaller than the estimated time for vitrification (1×10⁻⁴second).     

Dark-field light microscopic study of the flexibility of F-actin complexes

The flexibility of F-actin complexed with saturating amounts of myosin subfragments has been measured by the use of a dark-field light microscope and a high-sensitivity television camera. When dilute solutions of F-actin complexes were observed in the microscope, single filaments in flexural thermal motion were visible to the eye. Images of the fluctuating filaments were recorded on videotapes using the high-sensitivity camera, and these records were used for the analysis of fluctuation to calculate flexibility in the framework of statistical mechanics of thermal fluctuation in semi-flexible rods. The analysis was carried out by two different methods. In method A, we selected many filaments (the entire length appeared near focus occasionally in the limited period of 10 to 100 seconds), measured the mean square end-to-end distance 〈R²〉 of each filament during the period and also its contour length L, and calculated a parameter λ representing flexibility by the equation given by Landau & Lifshitz (1958): $\text{〈R}{}^2\text{〉 =}\text{[2λL ? 1 +}\text{exp}\text{(?2λL)]}\text{2λ}{}^2$. Then, we obtained a value for λ = 0.040 ± 0.010 μm^?1 for the acto-heavy meromyosin filament at 24.0 °C ± 1.0 deg. C, and λ = 0.027 ± 0.005 μm^?1 for the acto-tropomyosin-heavy meromyosin filament at the same temperature.In method B, still photographs were taken of the video screen to collect a great number of filaments or parts of filaments which appeared just in focus over their length, and the contour length L of each filament and the angle θ(L) between the tangents at its two ends were measured, on the basis of the assumption that the whole length of each filament was in a plane perpendicular to the direction of view. The data were treated statistically and the results were approximated with 〈cosθ(L)〉 = exp(?λL), which holds for an ensemble of filaments with flexibility λ but in two-dimensional thermal motion (Landau & Lifshitz, 1958). The λ-values obtained by this method for acto-heavy meromyosin and acto-tropomyosin-heavy meromyosin filaments were both in good agreements with those obtained by method A, confirming the reliability of our measurement.F-actin complexed with a saturating amount of myosin subfragment-1 was examined by method B, and its flexibility was shown to be little different from that of acto-heavy meromyosin filaments.     

Estimation of heritability by parent-offspring regression

Summary The implications of bias due to previous inbreeding of parents and genotype x environmental interaction on narrow sense heritability (h²) estimates by parent-offspring regression are enumerated. To remove the bias caused by genotype x environment interaction, an analysis of covariance model could be used. In special cases, where phenotypic expression is a result of two organisms interacting, such as in symbiotic N₂ fixation, an analysis of covariance model with a test of heterogeneity of slopes is recommended. When host genotype x strain interactions are significant, separate heritability estimates for each strain are suggested to take advantage of genotype x strain interaction, which may be a major factor contributing to the expression of N₂ fixation traits.