Relationships between photosystem II efficiency and photochemical reflectance index under different levels of illumination: comparison among species grown at high- and low elevations through different seasons

Previously, we found a significant association between photosystem II efficiency (ΦPSII) and photochemical reflectance index (PRI) measured at predawn among different species at different elevations and throughout several seasons. However, this relationship has not been evaluated under varied levels of illumination. Here, we used the Taiwan species Pinus taiwanensis (a conifer distributed at 750–3,000 m a.s.l.), Stranvaesia niitakayamensis (an evergreen tree, 1,700–3,100 m) and two Miscanthus spp. (perennial C₄ Gramineae, coastline–3,200 m) to elucidate the ΦPSII–PRI relationship. We studied six levels of photosynthetic photon flux density (PPFD) (0, 200, 400, 800, 1,200 and 2,000 μmol m⁻² s⁻¹) over several growth seasons at high (2,600 m a.s.l.) and low (800 m a.s.l.) elevation sites. In comparing the same species or genus, ΦPSII and PRI were closely correlated in darkness or under the same level of PPFD, with data obtained from different seasons and elevations pooled for regression analysis. Because both the intercept and slope of the ΦPSII–PRI equation showed a negative curvilinear correlation with PPFD, we could fit an empirical regression model, ΦPSII = c + d·ln(PPFD) + e·[ln(PPFD)]² + f·PRI + g·PRI·ln(PPFD) + h·PRI·[ln(PPFD)]², for multiple regression analysis. Using this model, we found a close correlation between the estimated and measured ΦPSII (r ² = 0.842−0.937, P < 0.001) for all four species examined and for mango (Mangifera indica) measured under both artificial illumination and sunlight (data from Weng et al. 2010). This empirical regression model could simulate both seasonal and diurnal variations of leaf-scale photosynthetic efficiency at high and low elevations.     

Age and growth of Atlantic bluefin tuna, Thunnus thynnus (Osteichthyes: Thunnidae), in the Mediterranean Sea

The objective of the study was to describe the biometry of Mediterranean bluefin tuna, Thunnus thynnus, the biology of which is not yet well understood. A total of 504 specimens was collected from 1998 to 2005 in the central part of the Mediterranean basin. They were sexed and measured; fork lengths (FL) ranged from 51.0 to 255.0 cm while body weights (W) ranged from 2.6 to 247.0 kg. The first spiniform ray (spine) of the first dorsal fin was removed and cross‐sectioned near the condyle base in order to count annuli for age estimation. The regression coefficient (b) of the female FL–W relationship was significantly higher than that of the male, and both sexes displayed a negatively allometric growth (b < 3); male regression equation: ln W = ?2.942 + 2.730 ln FL; female regression equation: ln W = ?3.660 + 2.878 ln FL. Based on counts of the translucent zones in the sections of the first ray of the first dorsal fin, estimated ages ranged from 1 to 15 years for males and 1 to 14 years for females. The correlation between the spine ray (R) and FL fit the allometric model best; the R–FL regression equations of the two sexes did not differ significantly and the overall equation was: ln FL = 3.721 + 0.851 ln R. Due to the R–FL allometric correlation, estimates of fork lengths at previous ages, FL_i, were back‐calculated with a body proportional hypothesis. Von Bertalanffy growth equations were derived from both observed and back‐calculated FLs‐at‐age, which did not differ significantly. Moreover, no significant difference was found between the growth equations of the two sexes; the overall equation was FL_t = 373.08 [1?e^{?0.07(t + 1.76)}]. Weight‐at‐age values were derived from the von Bertalanffy predicted FLs‐at‐age by the FL–W correlation equations for males and females. The paper represents the first comprehensive study on the biometry, including age and growth, of bluefin tuna captured in the Mediterranean Sea.     

Influence of antifoam agents on gas hold-up and mass transfer in bubble columns with non-newtonian fluids

Summary Experimental studies on the effect of antifoam agents on the performance of bubble columns with non-Newtonian fluids have been conducted. It is found that the gas hold-up and volumetric mass transfer coefficient in the case of water were reduced due to the addition of antifoam agents. It was found that this decrease in volumetric mass trasfer coefficient is substantial but in the aqueous solutions of polymers the effect becomes weaker as the concentration of polymers becomes higher. When the concentration of polymers became higher than a certain value, the volumetric mass transfer coefficient in the aqueous solutions of polymers with antifoam agents was higher than that without antifoam agents.Nomenclature a Specific surface area, 1/m - D _c Column diameter, m - d _max Diameter of the largest bubble stable against breakup, m - d _min Diameter of the smallest bubble stable against coalescence, m - g Gravitational acceleration, m/s² - H _l Clear liquid height, m - h Rupture thickness of the liquid film, m - K Consistency index in a power-law model, Pa·s ⁿ - k _l Liquid-phase mass transfer coefficient, m/s - n Flow index in a power-law model - u _sg Superficial gas velocity, m/s Greek letters Shear rate, 1/s - Gas hold-up - Energy dissipation per unit mass, m²/s³ - Viscosity, Pa·s - p Density, kg/m³ - Surface tension, N/m - Shear stress-Pa     

Models of Plant Disease Epidemics. II: Gradients of Bean Rust

The spread of bean rust from three types of inoculum sources (area, line, and point) was studied under field conditions in two seasons. Disease intensity (y) over time was quantified as incidence of diseased plants, incidence of diseased leaves, and disease severity at distances (d) of 0.3, 0.7, 1.5, 2.7, 4.3, 6.5, and 8.7 m from the inoculum sources. Seven curvilinear models were compared and the models that best explained the gradients of bean rust were y = ad^?b exp(cd), y = a exp(–bd^c) and y = a exp(–bd); where a was proportion of disease near the source, d was distance in metres, b was the slope, and c was a shape parameter. For general analysis to compare the slopes of the gradients, the gradient curves were linearized by ln(y) versus d and the parameters ln(a) (intercept) and b (slope) were estimated. The three measures of disease intensity and the three types of inoculum sources had estimated gradient parameters that were statistically different. The incidence of diseased plants rapidly approached y = 1.0 and the gradient slopes were near zero. Also with the ln(y) linearization, the gradients of the incidence of diseased leaves had slopes flatter than the gradients of disease severity. The gradient slopes from area sources of inoculum were flatter than from line sources, which in turn were flatter than from point sources. Late in the epidemics, the b-values became similar for all combinations of inoculum sources × assessment types. The interpretation of flattening of the gradients was confounded because aberrations in transformations occurred with most models. That is, when the intensity of disease (incidence or severity) approached the maximum, the increases in the intercepts were restricted and this restriction was responsible for most of the flattening. No flattening of gradients occurred over time when the gompit gradient model [–ln(–ln(y/y_max)) = –ln(–ln(a))?b ln(d)] was used for these same disease values. The fitting of models to the gradients served little purpose except to classify the curves in a general way. A new statistic, the area under the disease gradient curve (AUDGC), is proposed to compare epidemics.     

Technetium and rhenium complexes of mercapto-containing peptides 1. Tc(V) and Re(V) complexes with mercaptoacetyl diglycine (MAG2) and X-ray structure of AsPh4[TcO(MAG2)]·C2H5OH

The reaction of mercaptoacetyl diglycine (MAG₂) with technetium(V) gluconate in aqueous solution produced [TcO(MAG₂)]⁻. A single X-ray structure determination was carried out for the tetraphenylarsonium salt. The dark brown crystals are monoclinic, space group P2(1)/n, with a=12.478(5), b=14.922(5), c=17.183(9) Å and Z=4. The [TcO(MAG₂)]⁻ ion has a square pyramidal geometry with the technetium atom displaced by 0.756 Å towards the oxo ligand from the plane formed by the equatorial S,N,N,O atoms. The rhenium complex AsPh₄[ReO(MAG₂)] was prepared analogously starting from Re(V) gluconate and characterized.     

Allometric growth relationships of East Africa highland bananas (Musa AAA-EAHB) cv. Kisansa and Mbwazirume

Highland bananas are an important staple food in East Africa, but there is little information on their physiology and growth patterns. This makes it difficult to identify opportunities for yield improvement. We studied allometric relationships by evaluating different phenological stages of highland banana growth for use in growth assessment, understanding banana crop physiology and yield prediction. Pared corms of uniform size (cv. Kisansa) were planted in a pest‐free field in Kawanda (central Uganda), supplied with fertilizers and irrigated during dry periods. In addition, tissue‐cultured plants (cv. Kisansa) were planted in an adjacent field and in Ntungamo (southwest Uganda), with various nutrient addition treatments (of N, P, K, Mg, S, Zn, B and Mo). Plant height, girth at base, number of functional leaves and phenological stages were monitored monthly. Destructive sampling allowed derivation of allometric relationships to describe leaf area and biomass distribution in plants throughout the growth cycle. Individual leaf area was estimated as LA (m²) = length (m) × maximum lamina width (m) × 0.68. Total plant leaf area (TLA) was estimated as the product of the measured middle leaf area (MLA) and the number of functional leaves. MLA was estimated as MLA (m²) = ?0.404 + 0.381 height (m) + 0.411 girth (m). A light extinction coefficient (k = 0.7) was estimated from photosynthetically active radiation measurements in a 1.0 m grid over the entire day. The dominant dry matter (DM) sinks changed from leaves at 1118 °C days (47% of DM) and 1518 °C days (46% of DM), to the stem at 2125 °C days (43% of DM) and 3383 °C days (58% of DM), and finally to the bunch at harvest (4326 °C days) with 53% of DM. The allometric relationship between above‐ground biomass (AGB in kg DM) and girth (cm) during the vegetative phase followed a power function, AGB = 0.0001 (girth)^2.35 (R² = 0.99), but followed exponential functions at flowering, AGB = 0.325 e^0.036(girth) (R² = 0.79) and at harvest, AGB = 0.069 e^0.068(girth) (R² = 0.96). Girth at flowering was a good parameter for predicting yields with R² = 0.7 (cv. Mbwazirume) and R² = 0.57 (cv. Kisansa) obtained between actual and predicted bunch weights. This article shows that allometric relationship can be derived and used to assess biomass production and for developing banana growth models, which can help breeders and agronomists to further exploit the crop's potential.     

Colony expansion model for describing the spatial distribution of populations

Two equations have been used frequently to describe the relation between the sample variance (s ²) and sample mean (m) of the number of individuals per quadrat: Taylor's power law, s ² = am ^b , and Iwao's m ^*−m regression, s ² = cm + dm ², where a, b, c, and d are constants. We can obtain biological information such as colony size and the degree of aggregation of colonies from parameters c and d of Iwao's m ^*−m regression. However, we cannot obtain such biological information from parameters a and b of Taylor's power law because these parameters have not been described by simple functions. To mitigate such in-convenience, I propose a mechanistic model that produces Taylor's power law; this model is called the colony expansion model. This model has the following two assumptions: (1) a population consists of a fixed number of colonies that lie across several quadrats, and (2) the number of individuals per unit occupied area of colony becomes v times larger in an allometric manner when the occupied area of colony becomes h times larger (v≥ 1, h≥ 1). The parameter h indicates the dispersal rate of organisms. We then obtain Taylor's power law with b = {ln[E(h)] + ln[E(v ²)]}/{ln[E(h)] + ln[E(v)]}, where E indicates the expectation. We can use the inverse of the exponent, 1/b, as an index of dispersal of individuals because it increases with increasing E(h). This model also yields a relation, known as the Kono–Sugino relation, between the proportion of occupied quadrats and the mean density per quadrat: −ln(1 −p) = fm ^g , where p is the proportion of occupied quadrats, f is a constant, and g = ln[E(h)]/{ln[E(h)] + ln[E(v)]}. We can use g as an index of dispersal as it increases with increasing E(h). The problem at low densities where Taylor's power law is not applicable is also discussed. Received: January 27, 2000 / Accepted: June 20, 2000     

Haber's Rule: The Search for Quantitative Relationships in Toxicology

Dose (or concentration) and time of exposure are both important in determining the intensity of response to a toxic agent. For a given response intensity, Haber's Rule (c×t=K) has been proposed as a law of toxicology, but this rule is just one special case of a more general relationship c×t ^m =K, where the exponent m is quite variable. For inhaled toxicants m generally has a value between 0 and 1, whereas for carcinogens m is usually between 1 and 5. The absence of a universal value for m, or one that is generally applicable to different classes of toxicants, makes it not yet possible to develop a Haber-type rule with which to extrapolate successfully between exposure scenarios.     

Flow injection chemiluminescence study of acridinium ester stability and kinetics of decomposition

Decomposition of phenyl acridinium-9-carboxylate is monitored using electrogenerated chemiluminescence in a flow system. The formation of the pseudobase from the acridinium ester [AE] is described by rate = k′₁[AE] + k″₁[AE][OH^?]^0.5, where k′₁ = 0.020 ± 0.006 s^?1 and k″₁ = 2.1 ± 0.8 (L/mol)^?0.5 s^?1. Irreversible decomposition of the pseudobase is described by rate = k′₂[AE][OH^?], where k′₂ = 20.1 ± 3.8 (L/mol s). These kinetic equations, plus measurement of variation in emission intensity for constant acridinium ester concentration, are used to predict the resulting emission intensity v. pH behaviour given various contact times (in the 0.25 to 25 s range) for the acridinium ester to be in an alkaline solution prior to initiation of the chemiluminescence reaction.     

The influence of fluid shear on the structure and material properties of sulphate-reducing bacterial biofilms

Biofilms of sulphate-reducing Desulfovibrio sp. EX265 were grown in square section glass capillary flow cells under a range of fluid flow velocities from 0.01 to 0.4 m/s (wall shear stress, τ_w, from 0.027 to 1.0 N/m²). In situ image analysis and confocal scanning laser microscopy revealed biofilm characteristics similar to those reported for aerobic biofilms. Biofilms in both flow cells were patchy and consisted of cell clusters separated by voids. Length-to-width ratio measurements (l _c:w _c) of biofilm clusters demonstrated the formation of more “streamlined” biofilm clusters (l _c:w _c=3.03) at high-flow velocity (Reynolds number, Re, 1200), whereas at low-flow velocity (Re 120), the l _c:w _c of the clusters was approximately 1 (l _c:w _c of 1 indicates no elongation in the flow direction). Cell clusters grown under high flow were more rigid and had a higher yield point (the point at which the biofilm began to flow like a fluid) than those established at low flow and some biofilm cell aggregates were able to relocate within a cluster, by travelling in the direction of flow, before attaching more firmly downstream. Received 01 February 2002/ Accepted in revised form 16 July 2002     

Interrelations of global macroecological patterns in wing and thorax size,sexual size dimorphism,and range size of the Drosophilidae

Support for macroecological rules in insects is mixed, with potential confounding interrelations between patterns rarely studied. We here investigate global patterns in body and wing size, sexual size dimorphism and range size in common fruit flies (Diptera: Drosophilidae) and explore potential interrelations and the predictive power of Allen's, Bergmann's, Rensch's and Rapoport's rules. We found that thorax length (r² = 0.05) and wing size (r² = 0.09) increased with latitude, supporting Bergmann's rule. Contrary to patterns often found in endothermic vertebrates, relative wing size increased towards the poles (r² = 0.12), a pattern against Allen's rule, which we attribute to selection for increased flight capacity in the cold. Sexual size dimorphism decreased with size, evincing Rensch's rule across the family (r² = 0.14). Yet, this pattern was largely driven by the virilis–repleta radiation. Finally, range size did not correlate with latitude, although a positive relationship was present in a subset of the species investigated, providing no convincing evidence for Rapoport's rule. We further found little support for confounding interrelations between body size, wing loading and range size in this taxon. Nevertheless, we demonstrate that studying several traits simultaneously at minimum permits better interpretation in case of multiple, potentially conflicting trends or hypotheses concerning the macroecology of insects.     

Structure and conformation of peptides: N-benzyloxycarboyl-(γ-ethyl)-L-glutamyl-(γ-ethyl)-L-glutamic acid ethyl ester

C₂₄H₃₄N₂O₉, orthorhombic, P2₁2₁2₁; a = 39.432 (10), b = 14.061 (5), c = 4.850 (2) Å, M = 494 a.m.u., Z = 4, Dm = 1.22 g cm^?3, Dx = 1.22 g cm^?3, R = 0.13 for 1205 observed reflections after refinement with isotropic thermal factors. The urethane and amide bonds are in the trans configuration, as well as all the ester groups. The φ and ψ angles of the L -glutamyl residues fall in the β-structure region of the Ramachandran's plot; the molecule is rather flat with the amide plane almost parallel to the c axis along which two hydrogen bonds hold the molecules together to form long rows in a “parallel pleated-sheet” fashion.     

Size-Dependent Variation of Carbon and Nitrogen Isotope Abundances in Epiphytic Bromeliads

Abstract: While atmospheric species of bromeliads have narrow leaves, densely covered with water‐absorbing trichomes throughout their life cycles, many tank bromeliads with broad leaves, forming phytotelmata, go through an atmospheric juvenile phase. The effect of the different habits and the phase change in tank‐forming bromeliads on water and nutrient relations was investigated by analysing the relationship between plant size, C/N ratios and the natural abundance of ¹³C and ¹⁵N in five epiphytic bromeliad species or morphospecies of a humid montane forest in Xalapa, Mexico. The atmospheric species Tillandsia juncea and T. butzii exhibited full crassulacean acid metabolism, with δ¹³C values (mean ‐ 15.3 ‰ and ‐ 14.7 ‰, respectively) independent of size. In Tillandsia species with C₃ photosynthesis, δ¹³C decreased with increasing plant size, indicating stronger drought stress in juveniles. The increase of the C/N ratio with size suggests that, at least in heteroblastic bromeliads, the availability of water is more limiting during early growth, and that limitations of nitrogen supply become more important later on, when water stored in the tank helps to bridge dry periods, reducing water shortage. δ¹⁵N values of the two atmospheric species were very negative (‐ 12.6 ‰ and ‐ 12.2 ‰, respectively) and did not change with plant size. Tank‐forming bromeliads had less negative δ¹⁵N values (c ‐ 6 ‰), and, in species with atmospheric juveniles and tank‐forming adults, δ¹⁵N values increased significantly with plant size. These differences do not appear to be an effect of the isotopic composition of N sources, but rather reflect N availability and limitation and stress‐induced changes in ¹⁵N discrimination.     

Extraordinary Thermal Stability of an Oligodeoxynucleotide Octamer Constructed from Alternating 7‐Deaza‐7‐iodo guanine and 5‐Iodocytosine Base Pairs – DNA Duplex Stabilization by Halogen Bonds?

A reinvestigation of the published X‐ray crystal‐structure analyses of 7‐halogenated (Br, I) 8‐aza‐7‐deaza‐2′‐deoxyguanosines Br⁷c⁷z⁸G_d; 1a and I⁷c⁷z⁸G_d, 1b , as well as of the structurally related 7‐deaza‐7‐iodo‐2′‐deoxy‐β‐D ‐ribofuranosyladenine (β‐I⁷c⁷A_d; 2 = 6e in Table 1) and its α‐D ‐anomer (α‐I⁷c⁷A_d; 3 ) clearly revealed the existence of halogen bonds between corresponding halogen substituents and the adjacent N(3)‐atoms of neighboring nucleoside molecules within the single crystals. These halogen bonds can be rationalized by the presence of a region of positive electrostatic potential, the σ‐hole, on the outermost portion the halogen's surface, while the three unshared pairs of electrons produce a belt of negative electrostatic potential around the central part of the halogen substituent. The N(3) atoms of the halogenated nucleosides carry a partial negative charge. This novel type of bonding between nucleosides was tentatively used to explain the extraordinary high stability of oligodeoxynucleotides constructed from halogenated nucleotide building blocks.     

Correlation of liquid dispersion and oxygen transfer in bubble column

Summary In steady state, attained by continuous aeration after oxygen saturation of water in a bubble column, vertical composition distribution of liquid and gas phases has been determined. It has been assumed that, as a result of absorption at the bottom of the column, desorption in the upper section and vertical dispersion of dissolved oxygen flux, a closed oxygen circulation is created. Determination of the axial dispersion coefficient from hydrodynamic and oxygen transfer data verifies the mathematical model proposed. The results allow conclusions to be drawn about supersaturation and desorption and other phenomena expected in biological systems.Abbreviations C[-] Dimensionless oxygen concentration Unit=0.21 bar oxygen partial pressure or dissolved oxygen level in equilibrium with latter - E[m²/s] Axial dispersion coefficient - F[m²] Horizontal cross-section area - k _L a[s^-1] Overall oxygen transfer coefficient - u; u ₂[m/s; cm/s] Superficial velocity: related to state of bubbles leaving the sparger - x; x _atm[-] Signal registered in the experiment; signal recorded in O₂ saturated water, or water vapor saturated air stream, at temperature identical to the experiment under atmospheric pressure - y[m] Water column height - [s^-1] Dimensionless oxygen flux Indices a asorption - d desorption - g gas - l liquid - k dispersion - m measured value/in the case of hydrodynamically measured E/ Dedicated to Professor Dr. H. J. Rehm on the occasion of his 60th birthday     

Averaging methods in the delayed-logistic equation

The delayed logistic equation is analyzed using the averaging method. Using the transformation of coordinates v=ln N/K it is shown that the first order term in perturbation theory yields N=K exp(r ^* cos t/2) when the delay time T exceeds some critical value T _c. The amplitude r^* is equal to (40/3 – 2)^1/2 and is an expansion parameter that is proportional to (T – T_c). Comparison of the exponential solution of N and numerical results for the ratio N _maximum/N _minimum provides a good fit for values of larger than the results using the N coordinate as the perturbed coordinate.     

Allometric changes during growth and reproduction in Eleutheria dichotoma (hydrozoa,athecata) and the problem of estimating body size in a microscopic animal

Changes in body morphology during growth and reproduction in the hydromedusa Eleutheria dichotoma are described in terms of variations in eight different characters: umbrella diameter, total surface area, tentacle area, umbrella area, tentacle knob diameter, number of embryos, and diameter and area of buds. Sexually (sex) and vegetatively (veg) reproducing medusae differ significantly in their body morphometrics. Statistically significant allometric relations exist between umbrella diameter and (1) central area (sex and veg); (2) tentacle area (veg); (3) total area (veg); (4) tentacle knob diameter (veg); (5) bud diameter; and (6) number of embryos. A significant correlation between umbrella diameter and area is also found in undetached buds. During sexual reproduction, umbrella area shows positive allometry and loses its correlations to total area, tentacle area, and tentacle knob diameter. Linear and nonlinear bivariate allometric coefficients allow estimation of total body size from only one or two easily measurable attributes, e.g., umbrella and tentacle knob diameter. Curve fitting by the classic allometric equation (y = bx^c) is only negligibly worse than that obtained with a “full” equation (y = a + ^c), and statistical confidence is better. Chemical analyses for carbon and nitrogen content allow estimation of biomass from the projection area of the body surface. The relation factors are 1.06 μgC mm^?2 (sex) and 1.14 μgC mm^?2 (veg) for carbon and 0.293 μgN mm^?2 (sex) and 0.287 μgN mm^?2 (veg) for nitrogen. The C:N ratios are 3.6 and 4.0 for sexual and vegetative medusae, respectively. The use of allometric regression formulas to calculate surface areas and to relate these to carbon content provides quick estimations of body size in a microscopic animal.     

Die Verwertung reiner Nährstoffe

Auf der Grundlage einer Analyse von Energieumsatzmessungen an ausgewachsenen Rindern (Ochsen) bei Verfütterung von 110 Rationen sehr heterogener Nährstoffzusammensetzung werden folgende Vorhersagegleichungen für Brutto‐ (y₁), verdauliche (y₂) und umsetzbare Energie (y₃) sowie für die Energieansatzwirkung von Rationen (y) (kJ) mitgeteilt:

y₁ ‐ 23.6z₁ + 34.0z₂ + 17.3z₃ + 16,0z₄ + 19, 1z₅

y₂ = 23.6x₁ + 34.0x₂ + 17.3x₃ + 16.0x₄ + 18.0x₅

y₃‐ 17.3x₁ + 34.0x₂+15.9x₃+ 15.1x₄+15.4x₅

y = (6.5x₁ + 26.6x₂ + 10.1x₃ + 7.5x₄ + 8.9x_s)( ‐ 0.5574 + 0.04050x₆ ‐ 0,0002633x₆ ²)

z₁ = Rohprotein(g) x, ‐ verdl. Rohprotein(g)

z₂ ‐ Rohfett(g) x₂ = verdl. Rohfett(g)

z₃ ‐ Stärke(g) x₃ = verdl. Stärke(g)

z₄ ‐ Zucker(g) x₄ = verdl. Zucker(g)

z₅ ‐ N‐freie Reststoffe(g) x₅ = verdl. N‐freie Reststoffe(g)

x₆ ‐ Verdaulichkeit der Energie der Ration(%) (x₆ ≤ 77)     

Analysis of derivative binding isotherms. Theoretical considerations

The basic theoretical groundwork for the use of derivative binding isotherms in the analysis of ligand binding is presented. The derivative binding isotherm is defined as Γ (Y) = df/dy where f = fractional degree of saturation and y = natural logarithm of the free ligand concentration. Since Γ (y) is a positive function, which goes to zero as y → ±∞, the mean value of y, 〈y〉, and the second and third moments, μ₂ and μ₃ about 〈y〉 are well defined. For a macromolecular system consisting of N equivalent and independent binding sites, Γ (y) is a symmetrical bell-shaped function with one maximum. The maximum occurs when y = ?ln K_assoc; μ₂ = π²/3, and μ₃ = 0. For multiple sets of independent binding sites, Γ (y) is a superposition of Γ-type functions. If the sets are sufficiently well separated in binding free energy, multiple extrema may be seen at positions corresponding to the logarithms of the dissociation constants for the individual sets. In any case, 〈y〉 is equal to the mean value of the logarithms of the dissociation constants for the sets; μ₂ > π²/3 and equal to π²/3 plus the variance of the logarithms of the dissociation constants about their mean value; and μ₃ is, except by coincidence, not equal to zero and equals the third moment of the distribution of logarithms of the dissociation constants about their mean value. Analysis of Γ(y) for the case of cooperative interactions within a set of binding sites was investigated by examining (1) the Hill model (whose mathematical representation is equivalent to that used to describe antibody heterogeneity except that in the latter case the parameter a, the Sips, constant, is constrained (0 < a ≤1);(2) a common model for cooperativity in which the cooperative free energy is a linear function of the fraction bound; and (3) a general representation of cooperative interactions within a set of sites in terms of ?(f), a smooth function that gives the interaction free energy in units of RT. For the Hill model (or Sips model) Γ(y) is a symmetrical function with one maximum at y = (?1)/a)lnK, μ₂ = π²/3a²; and μ₃ = 0. For the case in which the cooperative free energy is a linear function of f [?(f) = cf], 〈y〉 = ?ln K₀ + (c/2); μ₂ = (π²/3) + c[(c/12) + 1] where c > ?4; and μ₃ = 0. General expressions for the moments in terms of ?(f) are derived. In general, μ₂ < (π²/3) for positive cooperativity and μ₂ > (π₂/3) for negative for negative cooperativity. Γ(y) will be symmetrical if and only if the cooperative free energy is introduced symmetrically about f = 0.5.     

Membrane potential and surface potential in mitochondria: Uptake and binding of lipophilic cations

Summary The uptake and binding of the lipophilic cations ethidium⁺, tetraphenylphosphonium⁺ (TPP⁺), triphenylmethylphosphonium⁺ (TPMP⁺), and tetraphenylarsonium⁺ (TPA⁺) in rat liver mitochondria and submitochondrial particles were investigated. The effects of membrane potential, surface potentials and cation concentration on the uptake and binding were elucidated. The accumulation of these cations by mitochondria is described by an uptake and binding to the matrix face of the inner membrane in addition to the binding to the cytosolic face of the inner membrane. The apparent partition coefficients between the external medium and the cytosolic surface of the inner membrane (K' _o) and the internal matrix volume and matrix face of the inner membrane (K' _i) were determined and were utilized to estimate the membrane potential from the cation accumulation factorR _c according to the relation =RT/ZF ln [(R _cV_o–K'_o)/(V_i+K'_i)] whereV _o andV _i are the volume of the external medium and the mitochondrial matrix, respectively, andR _c is the ratio of the cation content of the mitochondria and the medium. The values of estimated from this equation are in remarkably good agreement with those estimated from the distribution of⁸⁶Rb in the presence of valinomycin. The results are discussed in relation to studies in which the membrane potential in mitochondria and bacterial cells was estimated from the distribution of lipophilic cations.