Holling's “hungry mantid” model for the invertebrate functional response considered as a Markov process. Part II: Negligible handling time

In this paper we analyse a stochastic model for invertebrate predation taking account of the predator's satiation. This model approximates Holling's hungry mantid model when handling time is negligible (see Part I). For this model we derive equations from which we can calculate the functional response and the variance of the total catch. Moreover we study a number of approximations which can be used to calculate these quantities in practical cases in a relatively simple manner.List of Notation a rate constant of digestion - b maximum of rate constant of prey encounter in the mantid - c satiation threshold for search - c satiation threshold for pursuit in the mantid - c _i (w^1/2(N- N)ⁱ) - expectation operator - f rate of change of satiation during search - F functional response: mean number of prey eaten per unit of time - g rate constant of prey capture - h probability generating function of N conditional on S = s times p - H probability generating function of N - m_i ¹ - n, N number of prey caught - p probability density of S - p_n simultaneous probability (density) of N and S - q probability of strike success - r dummy variable in generating function - s, S satiation - T _s search time - T _d digestion time - v asymptotic rate of increase of var v - V asymptotic rate of increase of var N - w weight of edible part of prey - W standard Wiener process - x prey density - z (N{S = s}-N)p - rate constant of prey escape time maximum pursuit time - (v{S = + w ^1/2}-v) - present time as a fraction of the time from the start to the end of the experiment - hazard rate of T _s - mean time between (downward) passages of S through c - v w_–1/2(N-) - edible prey biomass density - probability density of , number pi - parameter of Weibull distribution of T _s = (1/2acx(-g(c)))_1/2 - w_–1/2(S -) - satiation in the guzzler approximation: solution to d/dt = f() + g(), (0)=S(0). - biomass functional response: wF - total biomass catch in the guzzler approximation: solution to d/dt = g(), (0) = 0     

Role of mitochondria in ethanol tolerance of Saccharomyces cerevisiae

The presence of active mitochondria and oxidative metabolism is shown to be essential to maintain low inhibition levels by ethanol of the growth rate (), fermentation rate (v) or respiration rate () of Saccharomyces cerevisiae wild type strain S288C. Cells which have respiratory metabolism show K _i (ethanol inhibition constant) values for , v and , higher (K _i>1 M) than those of petite mutants or grande strains grown in anaerobiosis (K _i=0.7 M). In addition, the relationship between or v and ethanol concentration is linear in cells with respiratory metabolism and exponential in cells lacking respiration. When functional mitochondria are transferred to petite mutants, the resulting strain shows K _i values similar to those of the grande strain and the inhibition of and v by increasing ethanol concentrations becomes linear.     

Protocol-dependence of equivalent circuit parameters of toad urinary bladder

Summary Determinations of current-voltage relationships are widely employed in the characterization of epithelial sodium transport. In order to determine the protocol dependence of transport parameters in the toad urinary bladder, studies were carried out in the presence and absence of amiloride, an inhibitor of active sodium transport. With symmetric positive and negative perturbations of the transepithelial electrical potential difference (0±100 mV) for 30 sec, the amiloride-sensitive current-voltage (i ^a -) relationship was near linear over the range –75+100 mV, indicating constancy of the conductance ^a and the apparent electromotive force E _Na, lumped parameters of the standard electrical equivalent circuit model of the active transport system. With a reverse protocol (±1000 mV) or 15 min perturbations thei ^a - relationships were highly nonlinear. Nonlinearity reflected voltage dependence of parameters: perturbations that increased active transport decreased E _Na and increased ^a, as evaluated from 10 sec perturbations of ; slowing of active transport produced the converse changes. These effects are usefully analyzed in both quasi-steady states and true steady states by means of a detailed equivalent circuit incorporating the significant ionic currents across each plasma membrane. Precise understanding of the significance of ^a and E _Na will require characterization of the partial ionic conductances on perturbation of .     

The relation of proton motive force,adenylate energy charge and phosphorylation potential to the specific growth rate and efficiency of energy transduction inBacillus licheniformis under aerobic growth conditions

The magnitude of the proton motive force (p) and its constituents, the electrical () and chemical potential (-ZpH), were established for chemostat cultures of a protease-producing, relaxed (rel ^–) variant and a not protease-producing, stringent (rel ⁺) variant of an industrial strain ofBacillus licheniformis (respectively referred to as the A- and the B-type). For both types, an inverse relation of p with the specific growth rate was found. The calculated intracellular pH (pH_in) was not constant but inversely related to . This change in pH_in might be related to regulatory functions of metabolism but a regulatory role for pH_in itself could not be envisaged. Measurement of the adenylate energy charge (EC) showed a direct relation with for glucose-limited chemostat cultures; in nitrogen-limited chemostat cultures, the EC showed an approximately constant value at low and an increased value at higher . For both limitations, the ATP/ADP ratio was directly related to .The phosphorylation potential (G'p) was invariant with . From the values for G'p and p, a variable H⁺/ATP-stoichiometry was inferred: H⁺/ATP=1.83+0.52µ, so that at a given H⁺/O-ratio of four (4), the apparent P/O-ratio (inferred from regression analysis) showed a decline of 2.16 to 1.87 for =0 to _max (we discuss how more than half of this decline will be independent of any change in internal cell-volume). We propose that the constancy of G'p and the decrease in the efficiency of energy-conservation (P/O-value) with increasing are a way in which the cells try to cope with an apparent less than perfect coordination between anabolism and catabolism to keep up the highest possible with a minimum loss of growth-efficiency. Protease production in nitrogen-limited cultures as compared to glucose-limited cultures, and the difference between the A- and B-type, could not be explained by a different energy-status of the cells.Abbreviations CCCP carbonylcyanide-p-trichloromethoxyphenylhydrazone - DW dry weight of biomass - F Faraday's constant, 96.6 J/(mV × mol) - Fo chemostat outflow-rate (ml/h) - FCCP carbonylcyanide-p-trifluoromethoxyphenylhydrazone - G'p phosphorylation potential, the Gibbs energy change for ATP-synthesis from ADP and P_i - G'⁰p standard Gibbs energy change at specified conditions - H⁺/ATP number of protons translocated through - ATP synthase in synthesis of one ATP - H⁺/O protons translocated during transfer of 2 electrons from substrate to oxygen - specific growth rate (1/h) - _H+ transmembrane electrochemical proton potential, J/mol - M_b molar weight (147.6 g/mol) of bacteria with general cell formula C_6.0H_10.8O_3.0N_1.2 - pH_out,in extracellular, intracellular pH - P_i (intracellular) inorganic phosphate - p proton motive force, mV - pH transmembrane pH-difference - transmembrane electrical potential, mV - P/O number of ADP phosphorylated to ATP upon reduction of one O^2– to H₂O by two electrons transferred through the electron transfer chain - P/O (H⁺/O) × (H⁺/ATP)^–1 - P/O_F, P/O_N P/O with the two electrons donated by resp. (NADH + H⁺) and FADH - q specific rate of consumption or production (mol/g DW × h) - rel ⁺,rel ^– stringent, relaxed genotype - R universal gas constant, 8.36 J/(mol × degree) - T absolute temperature - TPMP⁺ triphenylmethylphosphonium ion - TPP⁺ tetraphenyl phosphonium ion - Y growth yield, g DW/mol - Z conversion constant=61.8 mV for 310 K (37 °C) - ZpH transmembrane proton potential or chemical potential, mV     

Effects of α-galactosidase digestion on lectin staining in human pancreas

Summary Effects of -galactosidase (from green coffee beans) digestion on lectin staining were examined in formalin-fixed, paraffin-embedded human pancreatic tissues from individuals of blood-group B and AB. Digestion with the enzyme resulted in almost complete loss of Griffonia simplicifolia agglutinin I-B₄(GSAI-B₄) staining in the acinar cells with concomitant appearance of Ulex europaeus agglutinin-I(UEA-I) staining in the corresponding cells. In addition, reactivity with soybean agglutinin(SBA) was also imparted by the enzyme digestion in GSAI-B₄ positive acinar cells. -Galactosidase digestion following -galactosidase digestion neither reduced the reactivity with SBA nor induced the reactivity with Griffonia simplicifolia agglutinin-II(GSA-II) in GSAI-B₄ positive cells, while in UEA-I positive cells, both reduction of SBA reactivity and appearance of GSA-II reactivity occurred after simple -galactosidase digestion as well as sequential digestion with - and -galactosidase. However, when -l-fucosidase digestion procedure was inserted between - and -galactosidase digestion, UEA-I staining imparted by -galactosidase digestion was markedly decreased in intensity and GSA-II reactivity was appeared in GSAI-B₄ positive acinar cells. Furthermore, after sequential digestion with -galactosidase and fucosidase, reactivity with peanut agglutinin(PNA) was revealed in GSAI-B₄ positive acinar cells as well as UEA-I positive cells in secretors. In non-secretors, strong PNA staining was usually observed in the acinar cells throughout the glands without enzyme digestion. These results confirmed that the -galactosidase induced GSA-II reactivity and the fucosidase induced PNA reactivity are due to precursors of different kinds of blood-group determinants and suggest that at least two kinds of B antigen determinants, i.e. Gal(1-3)[Fuc(1-2)]Gal(1-3,4)GlcNac and Gal(1-3)-[Fuc(1-2)]Gal(1-3)GalNAc are produced in GSAI-B₄ positive acinar cells. The synthesis of the latter type of B antigen is assumed to be controlled under the secretory gene in human pancreas.Abbreviation GalNAc N-acetyl-d-galactosamine - Gal d-galactose - GlcNAc N-acetyl-d-glucosamine - Fuc l-fucose - NeuNAc N-acetylneuraminic acid (sialic acid)     

Proteolysis alters the spectral properties of 124 kdalton phytochrome from Avena

Native phytochrome from Avena sativa L. is homogeneous with a monomeric molecular weight of 124 kdalton; 6–10 kdalton larger than the heterogeneous 120 kdalton preparations previously considered to be undegraded (Vierstra and Quail, 1982, Proc. Natl. Acad. Sci. USA, 79: 5272–5276). The phototransformation difference spectrum (Pr-Pfr) of 124 kdalton phytochrome measured in crude extracts has a minimum in the farred region at 730 nm, the same as that observed in vivo. These spectral properties contrast with those of 120 kdalton phytochrome purified by column immunoaffinity chromatography where the difference minimum is at 724 nm. When 124 kdalton phytochrome is incubated as Pr in crude extracts, the difference minimum shifts progressively to shorter wavelengths (from 730 to 722 nm) concomitant with the proteolytic degradation of the chromoprotein to the mixture of 118 and 114 kdalton species that comprise 120 kdalton phytochrome preparations. These two effects are inhibited in concert by the serine protease inhibitor, phenylmethylsulfonylfluoride, and or maintenance of the phytochrome in the Pfr form. These results provide further evidence that 124 kdalton phytochrome is the native molecule in Avena and indicate that the peptide segments removed by proteolysis of the Pr form are important to the pigment's spectral integrity. The present data thus resolve the previously unsettled question of why the Pfr form of 120 kdalton phytochrome isolated by various procedures from Avena has been found to absorb at shorter wavelengths than that observed in vivo. Previous spectral studies with 120 kdalton phytochrome preparations are open to reexamination.Abbreviations, symbols PMSF phenylmethylsulfonylfluoride - SDS-PAGE sodium dodecyl sulfate polyacrylamide gel electrophoresis - Ig immunoglobulin - A_minimum, A_maximum phototransformation difference spectrum (Pr-Pfr) minimum and maximum - A_r/A_fr ratio spectral change ratio     

β-Ether cleavage of the lignin model compound 4-ethoxy-3-methoxyphenylglycerol-β-guaiacyl ether and derivatives by Phanerochaete chrysosporium

The white rot basidiomycete Phanerochaete chrysosporium metabolized 4-ethoxy-3-methoxyphenyl-glycerol--guaiacyl ether (V) in low nitrogen, stationary cultures under which conditions the ligninolytic enzyme system is expressed. 4-Ethoxy-3-methoxyphenylglycerol XIII, guaicol and 4-ethoxy-3-methoxybenzyl alcohol (II) were isolated as metabolic products. Exogenously added XIII was rapidly converted to 4-ethoxy-3-methoxybenzyl alcohol indicating that it is an intermediate in the metabolism of V. P. chrysosporium also metabolized 1-(4-ethoxy-3-methoxyphenyl)-2-(2-methoxyphenoxy)-3-hydroxypropane VI. The degradation pathway for this dimer also included initial -ether cleavage and -hydroxylation of the diol product 1-(4-ethoxy-3-methoxyphenyl) 2,3 dihydroxypropane (XI) to yield the triol XIII which was cleaved at the , bond to yield 4-ethoxy-3-methoxybenzyl alcohol. Finally P. chrysosporium also cleaved the dimer 1-(4-ethoxy-3-methoxyphenyl)-2-(2-methoxyphenoxy)-1-hydroxypropane (VIII) at the -ether linkage yielding 1-(4-ethoxy-3-methoxyphenyl) 1,2 dihydroxypropane (IX) which was subsequently cleaved at the , bond to yield II. All of the results indicate that oxidative -ether cleavage is an important initial reaction in the metabolism of -aryl ether lignin substructure dimeric compounds. Metabolities were identified after comparison with chemically synthesized standards by gas liquid chromatography-mass spectrometry.Abbreviations GLC Gas liquid chromatography - TMSi trimethylsilyl - TLC thin layer chromatography     

Orientation of the porphyrin ring in artificial chlorophyll membranes

Summary A sensitive photometric method is described by which the dichroism of lipid bilayer membranes in aqueous phase can be measured. The method is applied to black films with incorporated chlorophylla andb. With chlorophylla a relatively large dichroism is found in the Soret band and a much weaker dichroism in the red band. From the experimental data, the angles _B and _R between the blue and red transition moments and the membrane can be obtained. _B and _R are then used to calculate the angle of the porphyrin ring with respect to the membrane surface. For chlorophylla and three different lipids, values of between 44 and 49° are found.     

Comparative Study of Effects of Various Sterols and Triterpenoids on Permeability of Model Lipid Membranes

Using permeability to labeled glucose as a criterion of stability for liposomal membranes, a comparative study on stabilizing properties of different sterols and triterpenes in phospholipid bilayer has been carried out as well as on structural peculiarities of sterols responsible for membranolytic properties of cucumarioside G₁ from the cucumaria Eupentacta fraudatris. Stabilizing action of the studied sterols and triterpenoides incorporated in the bilayer decreases in the following order: cholesterol sulfate > cholesterol > ⁵-sterols > -sitosterol > ergosterols > ⁷-sterols > epicholesterol > pregnane > androstane > coprosterol > 14-methylcholest-9(11)-en-3-ol > 4, 14-dimethylcholest-9(11)-en-3-ol > holothurinogenin A₁ > glucoside of cholesterol > -xylosidase of ⁷-sterols > betulin > protopanaxatriol > phosphatidylcholine liposomes without sterol > protopanaxadiol > oleanolic acid. Sterol-dependent membranolytic cucumarioside G₁ practically loses its ability to increase permeability of phospholipid membranes containing sterols obtained from this holothuria as well as coprosterol, epicholestrol, sulfated and glycosylated forms of sterols. The obtained results confirm the sterol hypothesis of the mechanism of membranotropic action of holothuria glycosides and of resistance to them of holothuria cell membranes.     

Modelling based method for pharmacokinetic hypotheses test

The aim of this work is to propose methods to test mechanism of synergy of toxic agents in bees. A synergy between prochloraz, an imidazole fungicide, and deltamethrin, a pyrethroid insecticide, was demonstrated experimentally. The hypothesis is that prochloraz modifies the penetration or the metabolism of deltamethrin. This hypothesis is tested using a pharmacokinetic box model. A previous experimental work showed that bee instantaneous mortalities were higher, from the time t ₁ to the time t ₂ after spraying, in groups sprayed with deltamethrin at dose D ₀ in the presence of prochloraz (+P) than in those sprayed with deltamethrin alone at a dose time as high (). We postulate that accrued mortality is proportional to the cumulated internal deltamethrin (ID ₂). ID ₂ of treatment (+P) had to be greater than ID ₂ of treatment () during the period from t ₁ to t ₂ so that the hypothesis would be consistent with the experimental data. The limit, for which the hypothesis is conceivable, is the ID ₂₍₎ = ID _2(+P ) curve. We study, in particular, the asymptotic behaviour of the limit curve when different parameters of the kinetic model tend to 0 or . These limits allow to verify quickly and easily whether a mechanism is conceivable or not As the limits are calculated with algebraic values, the test can be used for other synergies.     

Some improvements in calculating the plant stand surface albedo and its influence on ground surface temperature

It is shown that better results are obtained in calculating the surface albedo of a plant stand for near-infrared solar radiation using the modified two-stream approximation in favor of the Schwarzschild one. These evaluations of the plant stand surface albedo were obtained by assuming the values for scattering parameters of upward ₀ and diffusive solar radiation in the plant stand, by applying the delta-Eddington approximation. However, more accurate evaluations of ₀ and can be obtained by using Rayleigh's phase scattering functions for radiative scattering in a plant stand. Furthermore, much attention is devoted to testing the influence of the plant stand albedo for the visible part of solar radiation (for which the Schwarzchild approximation is valid) on ground surface temperature. The ground surface temperature was calculated by the force-restore method; the greatest ground surface temperature corrections were obtained in cases where the surface beneath the plant stand is covered with snow. The influence on ground surface temperature of high absorption and scattering in dense plant stands with horizontal foliage was also tested. Again significant corrections of ground surface temperature were obtained, taking into consideration the given characteristics of a plant stand compared to a standard albedo value.List of symbols A albedo of direct radiation in plant canopy - A _D albedo of diffuse radiation in plant canopy - A _p albedo of the ground surface - A _Q total albedo in plant canopy - a proportion of gaps in plant canopy characteristic of surface evaporation - _w constant - parameter of upward scattering diffuse radiation - ₀ parameter of upward scattering direct radiation - C _g soil volumetric heat capacity - C _p air specific heat - C _DH aerodynamic transfer coefficient for heat - C _DE aerodynamic transfer coefficient for moisture - d depth of soil - sun's declination - azimuth of incident radiation - azimuth of diffuse radiation - characteristic of the radiative sources - G foliage orientation function - g parameter in delta-Eddington approximation - g _z parameter for near-infrared radiation - _L scattering phase function radiation - _D diffuse solar radiation flux - _G soil heat flux - _H air sensible heat flux - _L air latent heat flux - _O solar constant - _R net longwave radiation flux - _S direct solar radiation flux - h _o height of the sun - i intensity of diffuse radiation - k von Karman constant - L leaf area index - L _v coefficient for latent heat of evaporation - _g soil heat conductivity - n/N relative cloudiness - solid angle - frequency of temperature wave - Q _a specific humidity of air - Q _w specific humidity of saturated air - R _L coefficient of plant reflectivity - r direction of diffuse radiation - direction of incident radiation - r _o direction of solar radiation - r _s resistance of the leaf stomata - p _o air density - S intensity of direct solar radiation - Stefan-Boltzman constant - T _a air temperature - T _G ground surface temperature - T _c cloud temperature - T ₁ feaf temperature - T _* air temperature scale - t time - t time step - zenith angle of diffuse radiation - zenith angle of incident radiation - ₀ zenith angle of solar radiation - U _* friction velocity scale - V near-surface wind velocity - W _g soil water content - W _L scattering coefficient in plant canopy - W _sat saturated soil water content - z vertical direction     

Restriction fragment analysis of ‘null’ forms at the Gli-1 loci of bread and durum wheats

Summary Wheat accessions lacking some of the - and -gliadin components encoded by the Gli-1 loci on the short arm of chromosome 1D in bread wheat and chromosome 1A in durum wheat were studied by two-dimensional polyacrylamide gel electrophoresis and restriction fragment analysis. Digested genomic DNAs of normal and null forms were probed with a cDNA clone related to -/-gliadins and with a genomic clone encoding an LMW subunit of glutenin. The hybridisation patterns with the -/-gliadin probe were similar to those of cvs Chinese Spring and Langdon used as standards for bread and durum wheats, respectively, but several restriction fragments located on the 1D chromosome of bread wheat and the 1A chromosome of durum wheat were absent in the null forms. In addition, specific LMW glutenin fragments encoded by the same chromosomes were also absent in the null forms, suggesting that simultaneous deletions of blocks of genes for both -/-gliadins and LMW glutenins had occurred. Comparisons of the protein and RFLP patterns enabled some proteins to be mapped to specific restriction fragments.     

New ganglioside analogs that inhibit influenze virus sialidase

Synthetic thioglycoside-analogs of gangliosides such as Neu5Ac)2-S-6)Glc-(1-1)Ceramide (1) and the GM3 analog Neu5Ac(2-S-6)Gal-(1–4)Glc(1-1)Ceramide (2), competitively inhibited GM3 hydrolysis by the sialidase of different subtypes of human and animal influenza viruses with an apparent K_i value of 2.8×10^–6 and 1.5×10^–5 M, respectively. The inhibitory activity of the ganglioside GM4 analog [Neu5Ac-(2-S-6)Gal-(1-1)Ceramide (3)], in which the glucose of 1 was substituted by galactose, was lower than that of 1 (K_i =1.0×10^–4 M). The thioglycoside-analogs (1, 2, 3) of the gangliosides were nonhydrolyzable substrates for influenza virus sialidase. The inhibitory activity of 1 to bacterial sialidases fromClostridium perfringens andArthrobacter ureafaciens was considerably lower than that to influenza virus sialidase, indicating that the structure of the active site in bacterial and influenza virus sialidase may be different and the analogs may be useful to determine the orientation of the substrate to the active site of sialidases, especially of influenza viruses.Abbreviations Cer ceramide - GM3 Neu5Ac(2–3)Gal(1–4)Glc(1-1)Cer - GM4 Neu5Ac(2–3)Gal(1-1)Cer Gangliosides were abbreviated according to Svennerholm [1] and the recommendation of the IUPAC-IUB Commission on Biochemical Nomenclature [2].     

Purification and characterization of β‐methylaspartase from Fusobacterium varium

Methylaspartase (EC 4.3.1.2) was purified 20fold in 35% yield from Fusobacterium varium, an obligate anaerobe. The purification steps included heat treatment, fractional precipitation with ammonium sulfate and ethanol, gel filtration, and ion exchange chromatography on DEAESepharose. The enzyme is dimeric, consisting of two identical 46 kDa subunits, and requires Mg²⁺ (K_m = 0.27 ± 0.01 mM) and K⁺ (K_m = 3.3 ± 0.8 mM) for maximum activity. Methylaspartasecatalyzed addition of ammonia to mesaconate yielded two diastereomeric amino acids, identified by HPLC as (2S,3S)3methylaspartate (major product) and (2S,3R)3methylaspartate (minor product). Optimal activity for the deamination of (2S,3S)3methylaspartate (K_m = 0.51 ± 0.04 mM) was observed at pH 9.7. The Nterminal protein sequence (30 residues) of the F. varium enzyme is 83% identical to the corresponding sequence of the clostridial enzyme.     

Osmotic potential and turgor maintenance in Spartina alterniflora Loisel.

Summary The dependence of leaf water potential (), osmotic potential () and turgor pressure (P) on relative water content (RWC) was determined for leaves of tall and short growth forms of Spartina alterniflora Loisel. from a site on Canary Creek marsh in Lewes, Delaware. Tall plants (ca. 1.5 m) occured along a drainage ditch where interstitial water salinity was approximately 20, and short plants (ca. 0.2 m) were 13 m away near a pan and exposed to 80 salinity during the most stressful period. Leaves were collected at dawn and pressure-volume measurements were made as they desiccated in the laboratory. Pressure equilibrium was used to measure , RWC was determined from weight loss and dry weight, was determined from the pressure volume curve, and P was calculated as the difference between and . Physical properties of the bulk leaf tissue that have a role in regulating water balance of the two growth forms were estimated: relative water content of apoplastic water (RWC_a) relative water content at zero turgor (RWC₀), the bulk modulus of elasticity (E), and water capacity (C _w). There were no detectable temporal trends in any of the parameters measured from Nune through September and no significant differences between the two growth forms when compared on the basis of RWC_a, RWC₀, E, and C _w. There was a clear difference between the two growth forms with respect to ; at RWC₀, was-4.5±0.40 MPa for short form plants and-3.3±0.40 MPa for tall form.Turgor pressure of plants in the field (P) was lower in leaves from short form than for the tall form plants with average difference of about 0.4 MPa. In July, P in short form leaves dropped to zero by mid-morning as expected for leaves experiencing water stress.These results show that S. alterniflora is capable of reducing osmotic potential in response to increased salinity and that turgor pressure was lower in short growth form than in tall forms.     

Holling's “hungry mantid” model for the invertebrate functional response considered as a Markov process. Part I: The full model and some of its limits

In this paper we give an analytical reformulation of Holling's (1966) simulation model for invertebrate predatory behaviour. To this end we represent a population of predators as a frequency distribution over a space of (physiological) states. The functional response of a predator is calculated from the (stable) equilibrium distribution of its state as a function of prey density.Starting from the general model various other models are obtained by limit processes, some of them new and some of them old. The more interesting of which will be studied in further papers in this series.List of Notation a rate constant of digestion - b maximum of rate constant of prey encounter in the mantid - b maximum pursuit duration in the mantid (_p(0)) - c satiation threshold for search - c satiation threshold for pursuit in the mantid: c=c(b-D_s/v)/b - D _m maximum sighting distance - D _p pursuit distance - D _s strike distance - expectation operator - f, f ₀ rate of change of satiation during search - f ₁ rate of change of satiation during prey handling - F functional response: number of prey eaten per unit of time by one predator - g rate constant of effective prey encounter in the gobbler and sucker - g₀ rate constant of prey encounter - g₁ probability of no prey loss from pursuit - g₂ probability of no prey escaping during pursuit - H Holling secretary correction factor in the sucker: fraction of the time spent searching - k _R density of R - k_T probability density of maximum prey handling time - K probability that maximum prey handling time is _e, i.e. pursuit duration is zero - K _R distribution function of R - N number of prey caught - p (marginal) density of S - p₀ density of S in search - p₁ simultaneous density of S and T - P probability - p ₁ marginal density of S in handling prey - q probability of strike success - R ratio of realized to maximum sighting distance - s, S satiation - satiation axis - t time - handling time axis - u eating speed - U homogeneous(0,1) random variable - v pursuit speed - V exponential(1) random variable - w prey weight - W exponential(_m) random variable - x prey density - ratio of maximum successful pursuit duration to meal duration (_pm/_e) - _pm - relative duration of successful pursuit (_p/_pm) - ratio of shortest to largest sighting distance - x_e - time already spent handling a prey item - rate of prey loss during prey handling - prey escape rate during pursuit - prey biomass density (xw) - , T maximum time still to be spent handling a prey item - _e meal duration - _m maximum handling time ( _e+ _p) - _p duration of successful pursuit - _pm maximum duration of successful pursuit (_p(0)) - hazard rate - _m maximum of hazard rate - scaled functional response (wF) - minimal i-state space     

Synthesis of Aminoethyl Glycosides of the Ganglioside GM1 and Asialo-GM1 Oligosaccharide Chains

4-O-Glycosylation of 2-azidoethyl 2,3,6-tri-O-benzyl-4-O-(2,3-di-O-benzyl-6-O-benzoyl--D-galactopyranosyl)--D-glucopyranoside with a disaccharide donor, 4-trichloroacetamidophenyl 4,6-di-O-acetyl-2-deoxy-3-O-(2,3,4,6-tetra-O-acetyl--D-galactopyranosyl)-1-thio-2-trichloroacetamido--D-galactopyranoside, in dichloromethane in the presence of N-iodosuccinimide and trifluoromethanesulfonic acid resulted in a tetrasaccharide, 2-azidoethyl (2,3,4,6-tetra-O-acetyl--D-galactopyranosyl)-(1 3)-(4,6-di-O-acetyl-2-deoxy-2-trichloroacetamido--D-galactopyranosyl)-(1 4)-(2,3-di-O-benzyl-6-O-benzoyl--D-galactopyranosyl)-(1 4)-2,3,6-tri-O-benzyl--D-glucopyranoside, in 69% yield. The complete removal of O-protecting groups in the tetrasaccharide, the replacement of N-trichloroacetyl by N-acetyl group, and the reduction of the aglycone azide group to amine led to the target aminoethyl glycoside of -D-Gal-(1 3)--D-GalNAc-(1 4)--D-Gal-(1 4)--D-Glc-OCH₂CH₂NH₂ containing the oligosaccharide chain of asialo-GM₁ ganglioside in 72% overall yield. Selective 3-O-glycosylation of 2-azidoethyl 2,3,6-tri-O-benzyl-4-O-(2,6-di-O-benzyl--D-galactopyranosyl)--D-glucopyranoside with thioglycoside methyl (ethyl 5-acetamido-4,7,8,9-tetra-O-acetyl-3,5-dideoxy-2-thio-D-glycero--D-galacto-2-nonulopyranosyl)oate in acetonitrile in the presence of N-iodosuccinimide and trifluoromethanesulfonic acid afforded 2-azidoethyl [methyl (5-acetamido-4,7,8,9-tetra-O-acetyl-3,5-dideoxy-D-glycero--D-galacto-2-nonulopyranosyl)oate]-(2 3)-(2,6-di-O-benzyl--D-galactopyranosyl)-(1 4)-2,3,6-tri-O-benzyl--D-glucopyranoside, the selectively protected derivative of the oligosaccharide chain of GM₃ ganglioside, in 79% yield. Its 4-O-glycosylation with a disaccharide glycosyl donor, (4-trichloroacetophenyl-4,6-di-O-acetyl-2-deoxy-3-O-(2,3,4,6-tetra-O-acetyl--D-galactopyranosyl) 1-thio-2-trichloroacetamido--D-galactopyranoside in dichloromethane in the presence of N-iodosuccinimide and trifluoromethanesulfonic acid gave 2-azidoethyl (2,3,4,6-tetra-O-acetyl--D-galactopyranosyl)-(1 3)-(4,6-di-O-acetyl-2-deoxy-2-trichloroacetamido--D-galactopyranosyl)-(1 4)-{[methyl (5-acetamido-4,7,8,9-tetra-O-acetyl-3,5-dideoxy-D-glycero--D-galacto-2-nonulopyranosyl)onate]-(2 3)}-(2,6-di-O-benzyl--D-galactopyranosyl)-(1 4)-2,3,6-tri-O-benzyl--D-glucopyranoside in 85% yield. The resulting pentasaccharide was O-deprotected, its N-trichloroacetyl group was replaced by N-acetyl group, and the aglycone azide group was reduced to afford in 85% overall yield aminoethyl glycoside of -D-Gal-(1 3)--D-GalNAc-(1 4)-[-D-Neu5Ac-(2 3)]--D-Gal-(1 4)--D-Glc-OCH₂CH₂NH₂ containing the oligosaccharide chain of GM₁ ganglioside.     

Distance-constraint approach to protein folding. I. Statistical analysis of protein conformations in terms of distances between residues

A statistical analysis of protein conformations in terms of the distance between residues, represented by their C atoms, is presented. We consider four factors that contribute to the determination of the distanced _i,i+k between a given pair ofith and(i+k)th residues in the native conformation of a globular protein: (1) the distancek along the chain, (2) the size of the protein, (3) the conformational states of theith to(i+k)th residues, and (4) the amino acid types of the and(i+k)th residues. In order to account for the dependence on the distancek along the chain, the statistics are taken for three ranges, viz., short, medium, and long ranges (k8; 9k20; andk21; respectively). In the statistics of short-range distances, a mean distanceD _k and its standard deviationS _k are calculated for each value ofk, with and without taking into account the conformational states of all residues fromi toi+k (factors 1 and 3). As an Appendix, the relations for converting from the distances between residues into other conformational parameters are discussed. In the statistics of long-range distances, a reduced distanced* _ij (the actual distance divided by the radius of gyration) is used to scale the data so that they become independent of protein size, and then a mean reduced distanceD _l (a, a) and its standard deviation _l (a, a) are calculated for each amino acid pair (a, a) (factors 2 and 4). The effect of the neighboring residues along the chain on the value of the distanced* _ij is explored by a linear regression analysis between the actual reduced distanced* _ij and the mean value over theD _l for all possible pairs of residues in the two segments of the (i–2)th to the (i+2)th and the (j–2)th to the (j+2)th residues. The effect is assessed in terms of the tangentA _l (a, a) of the calculated regression line for each amino acid pair (a, a). In the statistics of medium-range distances, only factors 1 and 4 are considered, to simplify the analysis. The scaled distanced _i,i+k =(d _i,i+k -D _k )/S _k is used to eliminate the dependence onk, the distance along the chain. The propertiesD _m (a, a), _m (a, a) andA _m (a, a) corresponding toD _l (a, a), _l (a, a), andA _l (a, a), and also calculated for each amino acid pair (a, a). The results are interpreted as follows: the smaller values ofD _l (a, a) andD _m (a, a) indicate a preference of the pair (a, a) for a contact (e.g., pairs between hydrophobic amino acids, and pairs of Cys with aromatic amino acids), and the larger values of these quantities indicate a preference for distant mutual location (e.g., pairs between strong hydrophilic amino acids); the smaller values of _l (a, a) and _m (a, a) indicate a strong preference for either contact or noncontact (e.g., pairs between hydrophobic amino acids, and pairs between strong hydrophobic and hydrophilic amino acids, respectively), and the larger values of these quantities indicate the ambivalent/neutral nature of the preference for contact and noncontact (e.g., pairs containing Ser or Thr); the smaller values ofA _l (a, a) andA _m (a, a) indicate that the distance of an (a, a) pair is determined independently of the amino acid character of the neighboring residues along the chain (e.g., some pairs of Cys or Met with other amino acids) and the larger values of these quantities indicare that such amino acid character contributes strongly to the determination of the distance (e.g., pairs containing Ser or Thr, and pairs between amino acids with small side chains). The difference between the statistics for the long- and medium-range distances is also discussed; the former reflect the difference between the hydrophobic and hydrophilic character of the residues, but the latter cannot be easily interpretable only in terms of hydrophobicity and hydrophilicity. The data analyzed here are used in the optimization of an object function to compute protein conformation in a subsequent paper.