Theory of antigen-antibody induced particulate aggreagation—I. General assumptions and basic theory

A theory of antigen-antibody induced particulate aggregation is developed by investigating the stability of model systems of particles. Conditions for the formation of large aggregates are derived by imposing the requirement that at equilibrium a statistically significant number of redundant bonds would occur in a reduced monomer-dimer model system. A relationship is obtained which predicts the fractional agglutination in the reduced dimer system as a function of the antigen, antibody and particulate concentrations: $$\frac{g}{{2f c_0 (1 - g)^{2^ - } }} = \frac{{s_1 }}{r} + \frac{{s_1 s_2 }}{{2!r^2 }} + ... + \frac{{s_1 s_2 ...s_j }}{{j!r^j }},$$ wherec ₀ is the initial concentration of monomer,f is a proximity factor,g is the fractional agglutination,s _i is the average rate of formation of theith bond from an (i?1)th bound dimer, andr is the average rate of dissociation of a single antibody-antigen bond.     

Kinetics of ultrafiltration hemodialysis

The expressions of Wolfet al. (1951) and Renkin (1956) for the kinetics of artificial kidneys are generalized to include the effects of filtration. IfB is the bath volume,b the relevant volume of distribution,f the filtration rate,t the time, andA ₀,B ₀,b ₀ representA, B, andb at timet=0, then the plasma concentrationA is given by

$$\frac{A}{{A_0 }} = \frac{{B_0 }}{{B_0 + b_0 }}e^{ - \frac{{\left( {B_0 + b_0 } \right)}}{{B_0 }}\frac{{D_f }}{{b_0 }}K\left( {ft} \right)t} + \frac{{b_0 }}{{B_0 + b_0 }}$$     

Weber's theory of the kernleiter

The potential distribution about a kernleiter is determined according to Weber's method. It is shown that the distribution reduces to the solution of a telegrapher's equation when the volume of the external medium is small. The velocity of propagation as a function of the external volume is determined approximately. This involves the solution of the equation

$$\frac{{\left[ {Y_0 (k\xi )} \right]^\prime }}{{\left[ {J_0 (k\xi )} \right]^\prime }} = \frac{{\left[ {\xi ^{ - a} Y_0 (\xi )} \right]^\prime }}{{\left[ {\xi ^{ - a} J_0 (\xi )} \right]^\prime }}$$     

Toward a gibbsian approach to the problems of growth and cancer

Summary Certain sections ofJosiah Willard Gibbs's thermodynamics papers might be applicable to biological equilibrium and growth, normal or abnormal.Gibbs added terms _i dm _i to the differential of the internal energy d=td–pd, (t=temperature,p=pressure,=entropy,=volume) where is the potential of substancem _i , to provide for chemical as well as thermal and mechanical equilibrium. In this article a further generalization is suggested, to include biological equilibrium by adding to de terms of the form GdN, the variableN being the number of cells, where is a growth potential that measures exactly the resistance toward spontaneous growth. The functionG, like _i is intensive in nature (i.e. depends on intensive variables only) except for a conversion factor ,M=m _i , affording possible insight into why incipient abnormal growth is often independent of the number of cells. Useful applications might follow from identities between , or and or respectively. The following new function is studied, , a natural generalization of theGibbs free energy function , the possibility of measuring it electrically, and comparison of its role with that of for the possible experimental determination ofG. Gibbs's necessary and sufficient conditions for heterogeneous equilibrium ofn components inm phases are generalized and also modified to include broader restraining conditions like ,j=1,f,n, the > being characteristic of only living cellular phases. Careful appraisal of the term biological stability is followed by new criteria for stability, instability, and limits of stability, (neutral equilibrium) in terms of derivatives ofG, with possible medical applications. Three different sections of Gibbs's works tend to indicate that, for a biological phase, lower pressure usually increases its stability. The equation , where =surface tension,p, p = pressures,r, r=radii of curvature, is applied to possible control of tissue growth at interfaces. Methods of altering the equilibrum between three phasesA, B, C by varying the interfacial tensions _AB , _BC , _AC , using relations like _AB < _AC + _BC for stability of theA, B interface, suggest different means for shifting biological equilibrium between normal and abnormal cells through the introduction of new third phases at the interface. Various devices are mentioned for possible control of growth through proper channeling of surface or other equivalent forms of energy.     

Evaluation of surface colonization kinetics in continuous culture

Two equations, describing surface colonization, were evaluated and compared using suspended glass slides in a continuous culture ofPseudomonas aeruginosa. These equations were used to determine surface growth rates from the number and distribution of cells present on the surface after incubation. One of these was the colonization equation which accounts for simultaneous attachment and growth of bacteria on surfaces: $$N = (A/\mu )e^{\mu t} - A/\mu $$ where N=number of cells on surface (cells field^?1); A=attachment rate (cells field^?1h^?1);μ=specific growth rate (h^?1); t=incubation period (h). The other was the surface growth rate equation which assumes that the number of colonies of a given size (C_i) will reach a constant value (C_max) which is equal to A divided byμ: $$\mu = \frac{{\ln \left( {\frac{N}{{C_i }} + 1} \right)}}{t}$$ Both equations gave similar results and the time required to approximate C_max may not be as long as was previously thought. In all cases both A andμ continuously decreased throughout the incubation period. These decreases may be due to various effects of microbial accumulation on the surface. Both equations accurately determined surface growth rates despite highly variable attachment rates. Growth rates were similar for both the liquid phase of the culture and the solid-liquid interface (0.4 h^?1). Use of the surface growth rate equation is favored over the use of the colonization equation since the former does not require a computer to solve forμ and the counting procedure is simplified.     

Derivation of a growth rate equation describing microbial surface colonization

A surface growth rate equation is derived which describes simultaneous growth and attachment during microbial surface colonization. The equation simplifies determination of attachment and growth rate, and does not require a computer program for solution. This rate equation gives the specific growth rate (Μ) as a function of the number of cells on the surface (N), the incubation period (t), and the number of colonies (C_i) containing either one cell, two cells, four cells, etc, as shown below. $$\mu = \frac{{\ln (\frac{N}{{C_i }} + 1)}}{t}$$ The attachment rate (A) is given by the following relationship: $$A = \mu C_i $$ The proposed colonization kinetics are compared with exponential growth kinetics using 3-dimensional computer plots. Colonization kinetics diverged most from exponential kinetics when the growth rate was low or the attachment rate was high. Using these kinetics, it is possible to isolate the effects of growth and attachment on microbial surface colonization.     

The secant condition for instability in biochemical feedback control—II. Models with upper hessenberg jacobian matrices

We consider ann-component biochemical system whose Jacobian matrixJ is of upper Hessenberg form, with principal subdiagonal elementsb ₁,b ₂, ...,b _n?1 and upper right-hand corner element ?f. The open-loop Jacobian matrixJ ₀ is formed fromJ by settingf=0. It is shown that if the characteristic roots of ?J ₀ are real and non-negative then a necessary condition for instability at a critical point (steady state) is $$\frac{{b_1 b_2 ...b_{n - 1} f}}{{\left| { - J_0 } \right|}} \geqslant (\sec \pi /n)^n $$ This condition is analyzed in terms of reaction orders. For a metabolic sequence with some reversible steps, no loss of intermediate metabolites, and competitive inhibition of the first enzyme by the last metabolite, the above necessary condition becomes $$\frac{{\beta _{N - 1} X_{n + 1} }}{{\xi _{N - 1} E_{0T} }} \geqslant (\sec \pi /N)^N $$ whereN is the number of components (metabolites, enzyme-substrate complexes, and enzyme-inhibitor complex),β _N-1 the order of the enzyme-inhibitor reaction (with respect to the inhibitor),ξ _N-1 the order of reaction for the removal of the last metabolite, andX _n+1 /E _0T the fraction of first enzyme blocked by inhibitor. It is shown that, under certain assumptions, a critical point is always stable in a single two-step enzymatic process (formation of enzyme-substrate complex, followed by conversion to product, then loss of product) with slow negative feedback by competitive product inhibition. A model is constructed showing that stable oscillations can occur in a feedback system with only two metabolic steps and negative feedback by competitive inhibition with no cooperativity. The instability is due to a slow feedback reaction and saturable removal of the second metabolite.     

Measurement of eight scalar and dipolar couplings for methine–methylene pairs in proteins and nucleic acids

A new 3D, spin-state-selective coherence transfer NMR experiment is described that yields accurate measurements for eight scalar or dipolar couplings within a spin system composed of a methylene adjacent to a methine group. Implementations of the experiment have been optimized for proteins and for nucleic acids. The experiments are demonstrated for C–C moieties of the third IgG-binding domain from Streptococcal Protein G (GB3) and for C –C groups in a 24-nt RNA oligomer. Chemical shifts of C, C and H (respectively C , C and H ) are dispersed in the three orthogonal dimensions, and the absence of heteronuclear decoupling leads to distinct and well-resolved E.COSY multiplet patterns. In an isotropic sample, the E.COSY displacements correspond to ¹J_CH, ²J_CH2+²J_CH3, ²J_CH, ¹J_CH2+¹J_CH3, ¹J_CH2–²J_H2H3, ¹J_CH3–²J_H2H3, ³J_HH2 and ³J_HH3 for proteins, and ¹J , ²J J , ²J , ¹J +¹J , ¹J J , ¹J J , ³J and ³J in nucleic acids. The experiment, based on relaxation-optimized spectroscopy, yields best results when applied to residues where the methine–methylene group corresponds to a reasonably isolated spin system, as applies for C, F, Y, W, D, N and H residues in proteins, or the C –C groups in nucleic acids. Splittings can be measured under either isotropic or weakly aligned conditions, yielding valuable structural information both through the ³J couplings and the one-, two- and three-bond dipolar interactions. Dipolar couplings for 10 out of 13 sidechains in GB3 are found to be in excellent agreement with its X-ray structure, whereas one residue adopts a different backbone geometry, and two residues are subject to extensive ₁ rotamer averaging. The abundance of dipolar couplings can also yield stereospecific assignments of the non-equivalent methylene protons. For the RNA oligomer, dipolar data yielded stereospecific assignments for six out of the eight C H₂ groups in the loop region of the oligomer, in all cases confirmed by ¹J ^{1} $$" align="middle" border="0"> J , and H resonating downfield of H .Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1007/s10858-005-0175-z.     

Prognose des Stoffhaushaltes von Staugewässern mit Hilfe kontinuierlicher und semikontinuierlicher biologischer Modelle. II. Prüfung der Prognosegenauigkeit. Prediction of the Balance of Matter in Storage Reservoirs by Means of Continuous or Semicontinuous Biological Models. II. Reliability of the Prediction Method

The phosphate removal in small, completely mixed storage reservoirs (preimpoundment basins) mainly is a function of the production of biomass by the phytoplankton. The knowledge of the critical detention time of the water is the most important premise to the prediction. The critical detention time t̄ is computed from the equation: \documentclass{article}\pagestyle{empty}\begin{document}$ \overline t _c = \frac{1}{{\mu ^* - 0,1}} $\end{document} and the growth rate μ* at a given combination of the light intensity J, temperature T and phosphate concentration P is computed from: \documentclass{article}\pagestyle{empty}\begin{document}$ \mu ^* = \frac{{\mu T \cdot \mu J \cdot \mu P}}{{\mu \max ^2 }}\mu \max \cdot \frac{P}{{K_p + P}}\frac{J}{{K_j + J}}\frac{T}{{T_{opt} }}, $\end{document} (μmax = maximum possible growth rate of the dominant species; K_p, K_j and T_opt are constants computed from batch cultures). The quotient \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{{\bar t_{act.} }}{{\bar t_c }}(\bar t_{act.} = {\rm actual detention time in the water body)} $\end{document} enables prediction of the phosphate removal. A comparison of the predicted results from semicontinuous cultures and from the preimpoundment basin of the Weida reservoir revealed a satisfactory degree of conformity.     

Kinetics of ethanol inhibition in alcohol fermentation

The inhibitory effect of ethanol on yeast growth and fermentation has been studied for the strain Saccharomyces cerevisiae ATCC No. 4126 under anaerobic batch conditions. The results obtained reveal that there is no striking difference between the response of growth and ethanol fermentation. Two kinetic models are also proposed to describe the kinetic pattern of ethanol inhibition on the specific rates of growth and ethanol fermentation: \documentclass{article}\pagestyle{empty}\begin{document}$$\begin{array}{*{20}c} {\frac{{\mu _i }}{{\mu _0 }} = 1{\rm } - {\rm }\left( {\frac{P}{{P_m }}} \right);\alpha } \hfill & {\left( {{\rm for}\ {\rm growth}} \right)} \hfill \\ {\frac{{\nu _i }}{{\nu _0 }} = 1{\rm } - {\rm }\left( {\frac{P}{{P'_m }}} \right);\beta } \hfill & {\left( {{\rm for}\ {\rm ethanol}\ {\rm production}} \right)} \hfill \\ \end{array}$$\end{document} The maximum allowable ethanol concentration above which cells do not grow was predicted to be 112 g/L. The ethanol-producing capability of the cells was completely inhibited at 115 g/L ethanol. The proposed models appear to accurately represent the experimental data obtained in this study and the literature data.     

(H)NCAHA and (H)CANNH experiments for the determination of vicinal coupling constants related to the ϕ-torsion angle

Summary A set of three-dimensional triple-resonance experiments is described which provide , , and coupling constants. The pulse sequences generate E.COSY-like multiplet patterns and comprise a magnetization transfer from the amide proton to the α-proton or vice versa via the directly bound heteronuclei. For residues with the ¹H^α spin resonating close to the H₂O signal, a modified HNCA experiment can be employed to measure the vicinal ¹H^N,¹H^α couplings. Ambiguities associated with the conversion of values into ϕ-angle constraints for protein structure determination can be resolved with the knowledge of the heteronuclear ³J-couplings. In favourable cases, stereospecific assignments of glycine α-protons can be obtained by employing the experiments described here in combination with NOE data. The methods are applied to flavodoxin from Desulfovibrio vulgaris.     

Photosynthetic limitation by CO<Subscript>2</Subscript> diffusion in drought stressed orange leaves on three rootstocks

Photosynthetic limitations under moderate water deficit were evaluated in ‘Valência’ orange trees grafted on three different rootstocks, in pots. Net CO₂ assimilation rate (A _N), stomatal conductance (g _s), and photosystem II (PS II) operating efficiency ( ) in response to changing intercellular CO₂ partial pressure (C _i) were analyzed under controlled conditions. Drought decreased A _N and g _s, whereas remained unchanged. This resulted in a higher ratio between electron transport rate (ETR) and gross CO₂ assimilation rate (A _G). Since the comparison of A _N–C _i gas exchange curves can lead to incorrect conclusions, a normalization of C _i values () of stressed leaves was applied. Then, the relationship established for irrigated trees between the ETR/A _G ratio and C _i was used to estimate the from ETR/A _G ratios measured under water stress. The response of A _N to suggests that the CO₂ diffusional restriction is the main factor that limits photosynthesis in orange leaves under moderate water deficit.     

Sampling bias in estimating Design II variance components with S1 families

Summary The use of several S₁ individuals to represent an S₀ individual permits the use of a Design II mating scheme for plants with only one pistillate flower per plant. Estimates of additive (V _A ) and dominance (V _D ) variance from this mating scheme will be biased upwards, when a small number (10) of individuals of each S₁ line are used. This bias can be computed, and the additive and dominance estimates can be corrected. Of particular interest is the observation that the additive genetic variance contributes to bias in estimates of V _D . When S₀ plants are non inbred and their selfedprogeny (S₁ lines) are used to represent them in developing families for use in the Design II, where m₁ is the number of individuals used to represent an S₁ line in developing half sib-families and m₂ is the number of individuals used to represent the S₁ line in making up full sib-families. For example, in a 3×3 Design II, with about 10 individuals used to represent each S₁ line in each cross, m₂ = 10 and m₁ = 30. When m₁ = m₂ = 1, and Joint contribution from Department of Agronomy, University of Nebraska 68583, and the S. S. Cameron Laboratory, Werribee, Victoria 3030, Australia. Published as paper No. 7395, Journal Series     

Determination of heteronuclear three-bond J-coupling constants in peptides by a simple heteronuclear relayed E.COSY experiment

Summary A simple heteronuclear relayed E.COSY pulse sequence with a minimum number of pulses is proposed for the quantitative determination of heteronuclear three-bond J-coupling constants in uniformly ¹³C-enriched polypeptide samples. Numerous heteronuclear three-bond coupling constants, including , , , and , can be determined for each residue from a single heteronuclear relayed E.COSY spectrum. Couplings relevant for stereospecific assignments as well as for the determination of dihedral angles in the amino acid backbone and in side chains are obtained. The method is demonstrated on the uniformly ¹³C-enriched decapeptide antamanide (-Val¹-Pro²-Pro³-Ala⁴-Phe⁵-Phe⁶-Pro⁷-Pro⁸-Phe⁹-Phe¹⁰-).     

Energy requirements of Adélie penguin (Pygoscelis adeliae) chicks

Summary The energy requirements of Adélie penguin (Pygoscelis adeliae) chicks were analysed with respect to body mass (W, 0.145–3.35 kg, n=36) and various forms of activity (lying, standing, minor activity, locomotion, walking on a treadmill). Direct respirometry was used to measure O₂ consumption ( ) and CO₂ production. Heart rate (HR, bpm) was recorded from the ECG obtained by both externally attached electrodes and implantable HR-transmitters. The parameters measured were not affected by hand-rearing of the chicks or by implanting transmitters. HR measured in the laboratory and in the field were comparable. Oxygen uptake ranged from in lying chicks to at maximal activity, RQ=0.76. Metabolic rate in small wild chicks (0.14–0.38 kg) was not affected by time of day, nor was their feeding frequency in the colony (Dec 20–21). Regressions of HR on were highly significant (p< 0.0001) in transmitter implanted chicks (n=4), and two relationships are proposed for the pooled data, one for minor activities ( ), and one for walking ( ). Oxygen consumption, mass of the chick (2–3 kg), and duration of walking (T, s) were related as , whereas mass-specific O₂ consumption was related to walking speed (S, m·s^-1) as .Abbreviations bpm beats per minute - D distance walked (m) - ECG electrocardiogram - HR heart rate (bpm) - ns number of steps - RQ respiratory quotient - S walking speed (m·s^-1) - T time walked (s) - W body mass (kg)     

Hydrogen-isotope composition of leaf water in C3 and C4 plants: its relationship to the hydrogen-isotope composition of dry matter

The natural abundance hydrogen-isotope composition of leaf water ( ) and leaf organic matter ( _D ^org ) was measured in leaves of C₃ and C₄ dicotyledons and monocotyledons. The value of leaf water showed a marked diurnal variation, greatest enrichment being observed about midday. However, this variation was greater in the more slowly transpiring C₄ plants than in C₃ plants under comparable environmental conditions. A model based on analogies with a constant feed pan of evaporating water was developed and the difference between C₃ and C₄ plants expressed in terms of either differences in kinetic enrichment or different leaf morphology. Microclimatic and morphological features of the leaves which may be associated with this factor are discussed. There was no daily excursion in the _D ^org value in leaves of either C₃ or C₄ plants. When _D ^org values were referenced to the mean values during the period of active photosynthesis, the discrimination against deuterium during photosynthetic metabolism (D) was greater in C₃ plants (-117 to -121) than in C₄ plants (-86 to -109).These results show that the different water use strategies of C₃ and C₄ plants are responsible for the measured difference in deuterium-isotope composition of leaf water. However, it is unlikely that these physical processes account fully for the differences in hydrogen-isotope composition of the products of C₃ and C₄ photosynthetic metabolism.Symbols Hydrogen-isotope composition of leaf water - _D ^org hydrogen-isotope composition of leaf organic matter     

The qualitative analysis of a difference equation of population growth

The difference equation f _b :[0,1]–[0,1] defined by f _b (x)=b x(1–x) is studied. In particular complete qualitative information is obtained for the parameter value b=3.83. For example the number of fixed points of (f _b )ⁱ is given by

Energetics of the growth of Methanobacterium thermoautotrophicum and Methanococcus thermolithotrophicus on ammonium chloride and dinitrogen

Methanobacterium thermoautotrophicum was grown in continuous culture in a fermenter gassed with H₂ and CO₂ as sole carbon and energy sources, and in a medium which contained either NH₄Cl or gaseous N₂ as nitrogen source. Growth was possible with N₂. Steady states were obtained at various gas flow rates with NH₄Cl and with and the maintenance coefficient varied with the gas input and with the nitrogen source. Growth of Methanococcus thermolithotrophicus in continuous culture in a fermenter gassed with H₂, CO₂ as nitrogen, carbon and energy sources was also examined.Abbreviations molecular growth yield (g dry weight of cells per mol of CH₄ evolved) - growth rate (h^-1) - D dilution rate (h^-1) - rate (h_-1); relation of Neijssel and Tempest and of Stouthamer and Bettenhaussen - energy