Somatic vs. dendritic responses to hypercapnia in chemosensitive locus coeruleus neurons from neonatal rats

Cardiorespiratory control is mediated in part by central chemosensitive neurons that respond to increased CO₂ (hypercapnia). Activation of these neurons is thought to involve hypercapnia-induced decreases in intracellular pH (pH_i). All previous measurements of hypercapnia-induced pH_i changes in chemosensitive neurons have been obtained from the soma, but chemosensitive signaling could be initiated in the dendrites of these neurons. In this study, membrane potential (V_m) and pH_i were measured simultaneously in chemosensitive locus coeruleus (LC) neurons from neonatal rat brain stem slices using whole cell pipettes and the pH-sensitive fluorescent dye pyranine. We measured pH_i from the soma as well as from primary dendrites to a distance 160 µm from the edge of the soma. Hypercapnia [15% CO₂, external pH (pH_o) 7.00; control, 5% CO₂, pH_o 7.45] resulted in an acidification of similar magnitude in dendrites and soma (0.26 pH unit), but acidification was faster in the more distal regions of the dendrites. Neither the dendrites nor the soma exhibited pH_i recovery during hypercapnia-induced acidification; but both regions contained pH-regulating transporters, because they exhibited pH_i recovery from an NH₄Cl prepulse-induced acidification (at constant pH_o 7.45). Exposure of a portion of the dendrites to hypercapnic solution did not increase the firing rate, but exposing the soma to hypercapnic solution resulted in a near-maximal increase in firing rate. These data show that while the pH_i response to hypercapnia is similar in the dendrites and soma, somatic exposure to hypercapnia plays a major role in the activation of chemosensitive LC neurons from neonatal rats. acid; brain stem; intracellular pH; pyranine; respiratory control; whole cell     

Digestion time and reemergence in the desert grassland scorpion Paruroctonus utahensis (Williams) (Scorpionida,Vaejovidae)

Summary The desert grassland scorpion Paruroctonus utahensis spends most of its life in its burrow. During the active season, only about 5% of the individuals in a population appear on the surface each night. Individuals do not appear on the surface for several nights following a meal. To determine if physiological digestion time could account for this delay in reemergence after eating, I measured changes in oxygen consumption immediately following a meal. Oxygen consumption exceeded 125 l O₂g^-1h^-1 just after completion of a meal, then dropped to normal levels (53 l O₂g^-1h^-1) within 6 h. I also measured the interval between completion of the meal and subsequent defecation. All individuals defecated by 72 h following ingestion (median 12 h). In field enclosures, scorpions returned to the surface after a mean of 20.3 days (median=16) following a successful predation event. Lack of correspondence between estimates of physiological digestion time and the reappearance interval lead me to reject the idea of a long digestive pause in Paruroctonus utahensis. This conclusion lends support to the hypothesis that scorpions remain in their burrows to minimize exposure to predation.     

Growth and physiology of potassium-limited chemostat cultures of Paracoccus denitrificans

In potassium-limited chemostat cultures of Paracoccus denitrificans the maximum specific growth rate (µ_max) was found to depend on the input potassium concentration: At 0.21mM µ_max was 0.10–0.11 h^-1; at 0.44 mM 0.15–0.16 h^-1 and at 0.66 mM 0.20–0.21 h^-1. The plots of the specific rates of oxygen-, succinate-and potassium consumption against gave straight lines. The intracellular potassium concentration was a linear function of and varied from 1% (0.13 M) at a value of 0.034 h^-1 to 2.2% (0.29 M) at =0.26 h^-1; the potassium concentration gradient and the potassium concentration in the culture fluid in the steady state were dependent on the input potassium concentration. The potassium concentration gradient varied from 8,900-1,200. At all values 20–25% of the total energy production was used for potassium transport. 350,100 and 30 ATP molecules were calculated to be required to maintain one potassium ion intracellular during 1 h at values of 0.034, 0.197 and 0.257 h^-1 respectively. It is concluded that the amount of circulation of potassium is dependent on the potassium concentration gradient or on the potassium concentration in the culture in the steady state. The dependency of µ_max on the input potassium concentration was explained by the assumption that at low input potassium concentrations the net uptake of potassium (influx-efflux) is not rapidly enough to maintain the high potassium gradient in the existing cells and to establish it in the newly formed cells. At high values and at high input potassium concentrations µ_max is limited by the specific rate of oxygen consumption, which was found to be 11–12 mmol O₂ g dry weight^-1 h^-1 at µ_max for potassium-, succinate-and sulphate-limited chemostat cultures.     

Modulation of inwardly rectifying Na+-K+ channels by serotonin and cyclic nucleotides in salivary gland cells of the leech,Haementeria

Summary The electrically excitable salivary cells of the giant Amazon leech, Haementeria, display a time-dependent inward rectification. Under voltage clamp, hyperpolarizing steps to membrane potentials negative to about –70 mV were associated with the activation of a slow inward current (I _h) which showed no inactivation with time. The time course of activation of I _hwas described by a single-exponential function and was strongly voltage dependent. The activation curve of_hranged from –72 to –118 mV, with half-activation occurring at –100 mV. Ion-substitution experiments indicated that I _his carried by both Na⁺ and K⁺ ions. 5-Hydroxytryptamine (5-HT) increased the amplitude of I _hand its rale of activation. It also produced a positive shift of the activation curve of the conductance underlying I _h G_hwithout altering the slope factor, thus indicating that the voltage dependence of I _hwas modulated by 5-HT. Cs⁺ blocked both I _hand the 5-HT-polentiated current in a voltage-independent manner, whereas Ba²⁺ had little effect. It is concluded that 5-HT increases I _hby modulating the inwardly rectifying Na⁺-K⁺ channels in the salivary cells. The effect of 5-HT may be mediated by an increase in adenylate cyclase activity since I _hwas increased by 8-bromocyclic AMP and by the phosphodiesterase inhibitor, 3-isobutyl-l-methylxanthine. In contrast, I _hwas reduced by 8-bromo-cyclic GMPand by zaprinast (an inhibitor of cyclic GMP-scnsitive phosphodieslerase). Cyclic GMP itself also reduced I _h, and the effect was specific to the 3,5 form; 2,3-cyclic GMP was inactive. The results suggest that the inward-rectifier channel may be modulated in opposite directions by cyclic AMP and cyclic GMPThis work was supported by a grant from the Science and Engineering Research Council (no. GR/F/17087). We are grateful to the SmithKline (1982) Foundation for provision of a pulse generator     

Dendritic analysis of lobster stretch receptor neurons: Electrotonic properties with single and distributed inputs

Using steady-state cable analysis as derived by Rall, electrotonic properties of the dendritic trees of the tonic stretch receptor neuron of the spiny lobster, Panulirus interruptus,have been examined. By directly measuring the somatic input resistance and by visualizing the dendritic trees of this neuron by backfilling the axon with cobalt, the electrotonic properties of the dendritic trees have been derived. The calculated membrane resistivity is 800-3600 -cm ². Voltage and current transfer functions were calculated for (a) single dendritic tips the size observed in the cobalt preparations and (b) for processes 2 µm or smaller, as observed in electron microscopy. Current transfer to the soma was high in both cases (greater than 80%). Voltage transfer was 22% for large and 4% for small dendrites. When a more natural simultaneous conductance change at the tips of all major dendrites was modeled, voltage transfer was 84% and current transfer 56%. But the dynamic range of the cell (rheobase to saturation) is well-predicted by varying the simultaneous inputs, not by scaling up a single input, thus illustrating that convenient indices of electrotonic properties may not prove useful in appreciating the integrative properties of a neuron.     

Linkage studies of the h gene with plant weight in flax genotrophs

Summary The association of the H-h (hairy-hairless septa) character with plant weight was studied in the coupling and repulsion phases in F₂ of reciprocal crosses between large (L) and small (S) genotrophs of flax variety Stormont Cirrus. F₂ plants of reciprocal crosses in coupling (L^H x S^h) and in repulsion (L^h x S^H) giving H-h segregations were grown with their parents at two sowing times. Significant positive and negative associations between h and plant weight were obtained. A model is proposed based on the hypothesis that the H phenotype had changed to the h phenotype at the time of induction by a heterochromatic region extending over this locus. In the heterozygote, stable equilibria of the homozygotes are destroyed and transfer of heterochromatin, or number of reiterated sequences, or a decrease in one homologue and an increase in the other, occur in this region between homologous chromosomes. The amount and direction of the association is dependent upon the frequency of transfer: 0% transfer gives complete positive association; 50% transfer, no association; 100% transfer, complete negative association. This mechanism or heterochromatic transfer preserves the Mendelian ratio of 31 of Hh in the F₂. It is also supposed that there must be other controlling elements present as well.     

Growth kinetics of Thermus thermophilus

Summary The nonsporulating extreme thermophile Thermus thermophilus was grown in continuous culture at dilution rates up to 2.65 h^–1 at 75°C and pH 6.9 on complex medium. Concomitantly very low yield (Y=0.12 g cell dry weight g^–1 utilized organic carbon) and incomplete substrate utilization (always less than 45%) were found. In batch cultures T. thermophilus could be grown with _max =h^–1, in shake flasks only with _max =h^–1 with the same low yield and incomplete substrate utilization. Stable steady states at 84C and 45°C were realized at a dilution rate of 0.3 h^–1 whereas at 86°C and 40°C no growth could be detected. Artefacts arising from wall growth (in bioreactors) or improper materials must be ruled out. Inhibition of growth by organic substrates was demonstrated at low concentrations: a decrease in the yield obtained was found when more than 0.7 gl^–1 of meat extract were supplied in the medium. The maintenance requirement for oxygen is potentially very high and was determined to be 10 to 15 mmol g^–1 h^–1.     

Isothermic variation of the specific growth rate of Saccharomyces cerevisiae in batch culture

The specific growth rate () of a respiration-deficient mutant of Saccharomyces cerevisiae growing under defined experimental conditions in batch culture (mineral medium plus glucose and vitamins at 25°C) varied from experiment to experiment over a wide range (0.10–0.24 h^-1) and showed a normal distribution. Neither the age of the culture, the history of the inoculum, nor experimental error accounted wholy for the variability of . The variation was positively correlated with the specific rate of glucose transfer and negatively with the specific rate of production of non-fermentative CO₂. The yield decreased with implying higher maintenance requirements in batch culture (4.7 mmoles g^-1 h^-1) than in continuous culture (0.8 mmoles g^-1 h^-1). It was concluded that the strain is capable of establishing any one of several steady states of growth under the same experimental conditions, each steady state displaying some buildin inertia with respect to change. The variations of the specific rates of glucose transfer and non-fermentative CO₂ production, and of the yield appeared to be consequences rather than causes of the variation of . The ultimate causes of the variation of remained unidentified.Part of a doctoral thesis submitted by J. Martinez-Peinado to the University of Navarra Spain     

Pyramidal cell-to-inhibitory cell spike transduction explicable by active dendritic conductances in inhibitory cell

In the guinea-pig hippocampal CA3 region, the synaptic connection from pyramidal neurons tostratum pyramidale inhibitory neurons is remarkable. Anatomically, the connection usually consists of a single release site on an interneuronal dendrite, sometimes 200 m or more from the soma. Nevertheless, the connection is physiologically powerful, in that a single presynaptic action potential can evoke, with probability 0.1 to 0.6, a postsynaptic action potential with latency 2 to 6 ms. We construct a model interneuron and show that the anatomical and physiological observations can be reconciled if the interneuron dendrites are electrically excitable. Excitable dendrites could also account for depolarization-induced amplification of the pyramidal cell-interneuron EPSP in the voltage range subthreshold for spike generation.     

Voltage-imaging and simulation of effects of voltage- and agonist-activated conductances on soma-dendritic voltage coupling in cerebellar Purkinje cells

We investigated the spread of membrane voltage changes from the soma into the dendrites of cerebellar Purkinje cells by using voltage-imaging techniques in combination with intracellular recordings and by performing computer simulations using a detailed compartmental model of a cerebellar Purkinje cell. Fluorescence signals from single Purkinje cells in cerebellar cultures stained with the styryl dye di-4-ANEPPS were detected with a 10 × 10 photodiode array and a charge coupled device (CCD). Fluorescence intensity decreased and increased with membrane depolarization and hyperpolarization, respectively. The relation between fractional fluorescence change (F/F) and membrane potential could be described by a linear function with a slope of up to – 3%/100 mV. Hyperpolarizing and depolarizing voltage jumps applied to Purkinje cells voltage-clamped with an intrasomatic recording electrode induced dendritic dye signals, demonstrating that these voltage transients invaded the dendrites. Dye signals induced by depolarizing somatic voltage jumps were weaker in the dendrites, when compared with those induced by hyperpolarizing voltage jumps. Dendritic responses to hyperpolarizing voltage steps applied at the soma were attenuated when membrane conductance was increased by muscimol, an agonist for GABA_Areceptors.Corresponding experimental protocols were applied to a previously developed detailed compartmental model of a Purkinje cell. In the model, as in the electrophysiological recordings, voltage attenuation from soma to dendrites increased under conditions where membrane conductance is increased by depolarization or by activation of GABA_A receptors, respectively.We discuss how these results affect voltage clamp studies of synaptic currents and synaptic integration in Purkinje cells.     

Structured segregated models and analysis of self-oscillating yeast continuous cultures

A structured segregated model of budding yeast (Saccharomyces cerevisiae) populations is analysed in order to verify its ability to predict the spontaneous oscillations arising in continuous cultures. To obtain tractable and useful information about the relationships among the metabolic modifications during the cell cycle, the control over division and the occurrence of oscillations, very simple assumptions are considered and added to the model. The cell metabolism has been taken into account by assuming a diversification in the yield coefficient during the cell cycle. Moreover, in the oscillatory range, the cell mass is assumed to be constant at budding and to depend on the limiting substrate concentration at division. For a suitable range of parameter values, sustained oscillations are obtained, which can be compared to the experimental ones.List of Symbols D dilution rate - K _h critical substrate for h - K _s saturation constant - h ratio between size at division and size at budding - h _max maximum h value - h _min minimum h value - s substrate concentration - s _in substrate concentration in the input flow - x budded biomass concentration - y unbudded biomass concentration - Y _x yield coefficient for budded biomass - Y _y yield coefficient for unbudded biomass - specific growth rate - _max maximum specific growth rate     

Improvement on laboratory fermentation equipment to study Saccharomyces cerevisiae metabolism

Beside being an ordinary fermenter, the present equipment was conceived to sample the medium, to store the samples and to record photographs of the yeasts. Ten sensors were used to measure gas exchanges. During the growth of ScM1 (a Saccharomyces cerevisiae strain) on glucose, we could observe two different linear decreases of CO₂ production rates (18.17±0.12 mmol CO₂ h^–2 (g biomass)^–1 and 8.67±0.12 mmol CO₂ h^–2 (g biomass)^–1), together with a sudden variation of slope during the respiro-fermentative phase. Nomenclature F_in InletairFlowl h ^–1 F_out OutletgasFlowl h ^–1 _in Inletairtemperature°C_out Outletgastemperature°CP _atm AtmosphericPressuremmHgP _in InletairOverPressuremmHgP _out OutletgasOverPressuremmHgDODissolvedO ₂ mg l^–1 pO₂ PartialPressureO ₂ in Outlet gas % (v/v) pCO₂ PartialPressureCO ₂ in Outlet gas % (v/v) Int(t) Whole number of hours     

Die Manifestation des FaktorsH in Abh?ngigkeit vom genetischen Milieu

Zusammenfassung Die Befunde der Keimversuche mit Samen derOenothera berteriana (B ·l) und derOe. odorata (v · I) sowie ihrer hellgrünen Mutanten (B_h·l _h und v_h · I_h) legten die Vermutung nahe, daß der Faktorh im B-Komplex die entgegengesetzte Wirkung hat wie der nämliche Faktor im v-Komplex. Durch die Versuche mit Samen aus geeigneten Kreuzungen konnte dies bestätigt werden. Der Komplex B_h verglichen mit dem Komplex B erniedrigt beispielsweise die Lichtbedürftigkeit der Samen und beschleunigt den Keimverlauf; möglicherweise schlägt seine Wirkung im Lauf eines Jahres zeitlich ins Gegenteil um. Der Komplex v_h dagegen erhöht gegenüber dem Komplex v die Lichtbedürftigkeit der Samen und verlangsamt den Keimverlauf.Mit 12 TextabbildungenMit Unterstützung der Deutschen Forschungsgemeinschaft.     

Modelling continuous culture of Rhodospirillum rubrum in photobioreactor under light limited conditions

Rhodospirillum rubrum was grown continuously and photoheterotrophically under light limitation using a cylindrical photobioreactor in which the steady state biomass concentration was varied between 0.4 to 4 kg m^–3 at a constant radiant incident flux of 100 W m^–2. Kinetic and stoichiometric models for the growth are proposed. The biomass productivities, acetate consumption rate and the CO₂ production rate can be quantitatively predicted to a high level of accuracy by the proposed model calculations. Nomenclature: C _X, biomass concentration (kg m^–3) D, dilution rate (h^–1) Ea, mean mass absorption coefficient (m² kg^–1) I , total available radiant light energy (W m^–2) K, half saturation constant for light (W m^–2) R _W, boundary radius defining the working illuminated volume (m) r _X, local biomass volumetric rate (kg m^–3 h^–1) <r _X>, mean volumetric growth rate (kg m^–3 h^–1) V _W, illuminated working volume in the PBR (m^–3). Greek letters: , working illuminated fraction (–) _M, maximum quantum yield (–) bar, mean energetic yield (kg J^–1).     

Two mathematical models for the development of a single microbial pellet

A mathematical model for pellet development of filamentous microorganisms is presented, which simulates in detail location and growth of single hyphal elements. The basic model for growth, septation and branching of discrete hyphae is adopted from Yang et al. [2, 23]. Exact solutions to the intracellular mass-balance equations of a growth-limiting key component is given for two types of either branched or unbranched cellular compartments. Furthermore, the growth model was extended in regard to the external mass-balance equations of limiting substrates (oxygen, glucose) under the assumption that the substrates can enter the denser regions of the pellet only diffusively. Penetration of the substrates into the more porous outer regions of the pellet occurs more easily due to microeddies in the surrounding fluid. Chipping of hyphae from the pellet surface by shear forces was included in the model as well. The application of shear forces leads to a marked smoothing of the simulated pellet surface. The development of pellets from spore germination up to late stages with cell-lysis due to shortage of substrates in the pellet centre can be described. The effects of various model parameters are discussed.List of Symbols A _i algebraic coefficient (i = 1, 2,..., 6) - B _i algebraic coefficient (i = 1, 2,..., 6) - C _i mass-concentration of component i (i = O₂, S) (gl^–1) - C _i,crit concentration of substance i critical for lysis (i=O₂, S) (gl^–1) - C _i,stop concentration of substance i below which cells are inactivated (gl^–1) - C(l _i,t) intracellular concentration of the key component at site l _i and time t (gl^–1) - C _m maximal intracellular concentration of the key component (gl^–1) - C _X Concentration of dry biomass (gl^–1) - D intracellular diffusion coefficient of the key component (m² h^–1) - D _max,i maximal molecular diffusion coefficient of substrate i (i = O₂, S) (m² h^–1) - D _eff,i effective diffusion coefficient of component i (i = O₂) (m² h^–1) - d _h cross-sectional diameter of hyphae (m) - k production coefficient for the key component (h^–1) - K _s Monod coefficient for glucose (gl^–1) - k ₀ Monod coefficient for oxygen (gl^–1) - L _c total length of a compartment (m) - L _i total length of branch i (i=1, 2, 3) (m) - l _i position on branch i (i=1, 2, 3) - L _m maximal length of a segment (m) - m _i maintenance coefficient of substrate i (h^–1) - N _m maximal number of segments in a compartment - n _iR number of tips of type i in layer R, i=1, 2 - p auxiliary variable (see Eq. (7)) - P _Br probability that a hypha is chipped off (%h^–1) - pO ₂ partial pressure of oxygen in the liquid phase (%) - Q auxiliary variable (see Eq. (8)) - Q _i uptake rate of substrate i (i = O₂, S) (gl^–1 h^–1) - q auxiliary variable (see Eq. (7)) - R index of radial layer (R=1, 2, 3,..., R _max) - r radius (m) - r _crit critical radius, Eq. (15) (m) - r _max pellet radius (m) - r _tip distance from the pellet centre to the tip position (m) - r _thr threshold radius (m) - s auxiliary variable (see Eq. (7)) - S index for glucose - t time (h) - v _R volume of layer R (1) - Y _Mi observable yield coefficient of biomass on substrate i (gg^–1) - Y _Xi yield coefficient of biomass on substrate i (gg^–1) Greek Letters _i actual tip expansion rate (m h^–1) - _i,m actual maximal extension rate of tip i (i=1, 2) (m h^–1) - _1y lysis rate (h^–1) - _m maximal tip extension rate (m h^–1) - auxiliary variable in Eq. (2) - auxiliary variable in Eq. (3) - auxiliary variable defined in Eq. (4) (m^–1) - _shear shear force parameter - _R overall specific growth rate in layer R (h^–1) - _m maximal specific hyphal growth rate (h^–1) - cell volume density (l cell volume per 1) - _crit critical cell volume density in Eq. (15) - _S shear force parameter - _X cell mass density (g dry weight per 1 wet cells) - (C _i) growth kinetics on substrate i - proportional factor in Eq. (34) (l g^–1) We thank the Deutsche Forschungsgemeinschaft (DFG) for financially supporting parts of this work.We thank the Deutsche Forschungsgemeinschaft (DFG) for financially supporting parts of this work.     

Inhibition of the acidogenic dissimilation of glucose in anaerobic continuous cultures by free butyric acid

Summary In anaerobic wastewater treatment the separation of fermentative and methanogenic bacteria is aimed at an increased performance of the total digestion process. It is known that the attainable growth rate of the acidogenic population in continuous culture decreases at increasing influent concentrations of glucose. To account for this phenomenon, a new kinetic model was developed that combines substrate and product inhibition. In the present research product inhibition was investigated quantitatively in a continuous culture fermenting 50 mmol/l glucose. Extra acetate and butyrate were added up to 200 mmol/l at different pH values, and it turned out that only free butyric acid inhibited growth. The lower attainable growth rates of cultures producing comparable amounts of butyrate when fed with concentrated influents, strongly indicated substrate inhibition. Evidence is presented that transitions to low-conversion steady states predicted by the kinetic model, play a role and decrease the stability of the culture.Nomenclature D dilution rate, h^-1 - D_att highest D using certain experimental procedure h^-1 - K_i substrate inhibition constant, mol·m^-3 - K_p product inhibition constant mol·m^-3 - K_s substrate saturation constant, mol·m^-3 - P concentration inhibitory product mol·m^-3 - S substrate concentration, mol·m^-3 - S_o influent substrate concentration, mol·m^-3 - S _max ^c substrate concentration at _max ^c , mol·m^-3 - S _max ^h substrate concentration at _max ^h , mol·m^-3 - specific growth rate, h^-1 - experimental realization of at D_att, h^-1 - _max maximum specific growth rate, h^-1 - _max ^c maximum attainable specific growth rate according to combined substrate/product inhibition model, h^-1 - _h ⁰ specific growth rate at S₀ according to Haldane kinetics, h^-1 - _max ^c maximum attainable specific growth rate according to Haldane kinetics, h^-1 - Y_p yield inhibitory product, mol·mol^-1 - Y_x yield biomass, kg dry weight·kg^-1 - bio biomass - EtOH ethanol - gluc glucose - HAc acetate - HBt butyrate - HCap caproate - HFo formate - HPr propionate - HVal valerate - prod produced - lact lactate     

Using Multi-Compartment Ensemble Modeling As an Investigative Tool of Spatially Distributed Biophysical Balances: Application to Hippocampal Oriens-Lacunosum/Moleculare (O-LM) Cells

Multi-compartmental models of neurons provide insight into the complex, integrative properties of dendrites. Because it is not feasible to experimentally determine the exact density and kinetics of each channel type in every neuronal compartment, an essential goal in developing models is to help characterize these properties. To address biological variability inherent in a given neuronal type, there has been a shift away from using hand-tuned models towards using ensembles or populations of models. In collectively capturing a neuron''s output, ensemble modeling approaches uncover important conductance balances that control neuronal dynamics. However, conductances are never entirely known for a given neuron class in terms of its types, densities, kinetics and distributions. Thus, any multi-compartment model will always be incomplete. In this work, our main goal is to use ensemble modeling as an investigative tool of a neuron''s biophysical balances, where the cycling between experiment and model is a design criterion from the start. We consider oriens-lacunosum/moleculare (O-LM) interneurons, a prominent interneuron subtype that plays an essential gating role of information flow in hippocampus. O-LM cells express the hyperpolarization-activated current (I _h). Although dendritic I _h could have a major influence on the integrative properties of O-LM cells, the compartmental distribution of I _h on O-LM dendrites is not known. Using a high-performance computing cluster, we generated a database of models that included those with or without dendritic I _h. A range of conductance values for nine different conductance types were used, and different morphologies explored. Models were quantified and ranked based on minimal error compared to a dataset of O-LM cell electrophysiological properties. Co-regulatory balances between conductances were revealed, two of which were dependent on the presence of dendritic I _h. These findings inform future experiments that differentiate between somatic and dendritic I _h, thereby continuing a cycle between model and experiment.     

Modelling of alcohol fermentation in a tubular reactor with high biomass recycle

Fermentation in tubular recycle reactors with high biomass concentrations is a way to boost productivity in alcohol production. A computer model has been developed to investigate the potential as well as to establish the limits of this process from a chemical engineering point of view. The model takes into account the kinetics of the reaction, the nonideality of flow and the segregation in the bioreactor. In accordance with literature, it is shown that tubular reactors with biomass recycle can improve productivity of alcohol fermentation substantially.With the help of the computer based reactor model it was also possible to estimate the detrimental effects of cell damage due to pumping. These effects are shown to play a major role, if the biomass separation is performed by filtration units which need high flow rates, e.g. tangential flow filters.List of Symbols Bo d Bodenstein number - c kg/m³ concentration of any component - CPFR continuous plug flow reactor - CSTR continuous stirred tank reactor - d _h m hydraulic diameter - D _eff m²/s dispersion coefficient - f residence time distribution function - K _s kg/m³ monod constant for biomass production - K _s kg/m³ monod constant for alcohol production - p kg/m³ product concentration - P _i kg/m³ lower inhibition limit concentration for biomass production - p _i kg/m³ lower inhibition limit concentration for alcohol production - p _m kg/m³ maximum inhibition limit concentration for biomass production - p _m kg/m³ maximum inhibition limit concentration for alcohol production - q _p h^–1 specific production rate - q _p,max h^–1 maximum specific production rate for alcohol production - q _s h^–1 specific substrate consumption rate - Q _L m _gas ³ /m³h specific gas rate - r _p , r _s , r _x kg/(m³ · h) reaction rate for ethanol production substrate consumption and cell growth, respectively - S _F kg/m³ substrate concentration in feed stream - s kg/m³ substrate concentration - t h time - x kg/m³ biomass concentration - x _max kg/m³ maximum biomass concentration for biomass production - Y _p/s yield coefficient - h^–1 specific growth rate - _max h^–1 maximum specific growth rate - dimensionless time (t/) - h mean residence time - _s glucose conversion     

The electromotor system of the electric catfish (Malapterurus electricus): A fine-structural analysis

Summary The electromotor system of the electric catfish (Malapterurus electricus) consists of two large ganglion cells situated in the spinal cord, two single axons containing electric nerves and two large electric organs with several million electroplaque cells. The small, irregularly stacked electroplaque cells possess at their center a crater-like indentation from which a stalk like protrusion arises. Many synaptic contacts derived from a single axon collateral are carried on lobe-like protrusions at the terminal knob of this stalk. The electric nerve consists of a large myelinated axon (diameter: 25 m) surrounded by many layers of connective tissue cells. The two ganglion cells (200 m in diameter) are rich in elements of the rough endoplasmic reticulum, Golgi apparatus and lysosomal structures. The cytoplasm of the soma changes its appearance towards the voluminous axon hillock (50 m in diameter) which these organelles do not enter. The cell soma is perforated in a tunnel-like manner by blood capillaries, axons and processes of glial cells. The cell soma and dendrites are covered with two types of synapse. One type forms mixed chemical and electrical (gap junctions) contacts with intermediate attachment plaques. The other type is only chemical in nature. This system may be useful in the study of an identified vertebrate giant neuron.     

Zur Unterscheidung zwischen multifaktoriellem Erbgang mit Schwellenwerteffekt und einfachem diallelen Erbgang

Zusammenfassung und Schlußfolgerungen Die Feststellung, daß eine Anomalie einem einfachen Erbgang folgt, hat nach unsern heutigen Kenntnissen über den Wirkungsmechanismus der Gene eine schwerwiegende Konsequenz: die Anomalie muß dann eine einfache biochemische Ursache haben, nämlich die Veränderung oder das Fehlen des primären Produkts (Polypeptidkette) eines bestimmten Gens. Wenn die Anomalie die formalen Kriterien eines einfachen Erbgangs nicht zwanglos erfüllt, sondern nur nach Heranziehung von Zusatzannahmen, wie.z. B. der von unvollständiger Penetranz des anomalen Allels, so sollten daher, um nicht zu einer aussichtslosen Suche nach einer einfachen biochemischen Ursache zu verleiten, auch noch konservativere Erbgangshypothesen in Betracht gezogen werden. In dieser Arbeit wird einem einfachen diallelen Erbgang mit unvollständiger Penetranz des anomalen Allels (Modell EDEUP) eine davon extrem abweichende konservativere Alternativhypothese gegenübergesteein multifaktorieller Erbgang mit Schwellenwerteffekt (Modell MFVSE), bei dem kleine unspezifische Effekte der Genpaare an einer Vielzahl von Loci, evtl. in Verbindung mit einem Umweltbeitrag, additiv eine phänotypisch latente kontinuierliche Variable (die Disposition für die Anomalie) determinieren, die bei Überschreiten eines bestimmten Schwellenwertes die Anomalie manifest werden läßt.Die beiden Modelle haben als gemeinsamen Parameter die Populationsfrequenz P des Merkmals (der Anomalie); weitere Parameter sind beim Modell EDEUP die Penetranzen w ₁ und w ₂ des anomalen Allels im homozygoten bzw. heterozygoten Zustand, beim Modell MFVSE die Heritabilität h ²und der Grad der genetischen Bestimmtheit ² der Disposition. Von den 3-Parameter-Modellen werden in der Arbeit nur zweiparametrige Spezialfälle betrachtet: vom Modell EDEUP der durch w ₁=1, w ₂=w definierte Spezialfall EDEUP1 (vollständige Penetranz des anomalen Allels im homozygoten Zustand), vom Modell MFVSE in erster Linie der durch ² = h² definierte Spezialfall MFVSE1 (keine Dominanzeffekte an den beteiligten Loci) und in zweiter Linie der durch ² = 1 definierte Spezialfall MFVSE2 (kein Umweltbeitrag zur Disposition, aber Dominanzeffekte möglich). Von Interesse ist, unter welchen Bedingungen die Modelle EDEUP1 und MFVSEi (i = 1 oder 2) sich gegenseitig bezüglich gewisser phänotypischer Teilaspekte simulieren können, und ob es Kriterien gibt, welche die Unterscheidung zwischen den beiden Modellen gestatten. Als solche phänotypischen Teilaspekte werden herangezogen: erstens die Merkmalsfrequenzen Q ₁, Q ₂, Q ₃ bei Eltern (oder Kindern), Geschwistern (bzw. ZZ-Partnern) und EZ-Partnern von Merkmalsträgern (Probanden), zweitens die Merkmalsfrequenzen Q ₁₁, Q ₂₁ und Q ₂₂ bei Probandengeschwistern mit gegebener Phänotypenkombination der Eltern (-X-,+x-oder+x+, wobei - = merkmalsfrei und + = merkmalstragend); hier wird angenommen, daß die Probandenerfassung den Bedingungen der Einzelauslese genügt. Ein Modell EDEUP1 (P, w) (Realisation des Modells EDEUP1 mit spezifizierten Parameterwerten P und w) simuliert ein Modell MFVSEi (P, h ²) (i = 1 oder 2) bezüglich einer Merkmalsfrequenz Q (und umgekehrt das letztere das erstere Modell), wenn die Erwartungswerte von Q in den beiden Modellen (bei gleicher Populationsfrequenz P) übereinstimmen. Ein Modell EDEUP1 (P, w) ist bezüglich Q durch das Modell MFVSEi simulierbar, wenn es eine Realisation MFVSEi (P, h ²) von MFVSEi gibt, die EDEUP1 (P, w) bezüglich Q simuliert; andernfalls ist EDEUP1 (P, w) auf Grund von Q vom Modell MFVSEi unterscheidbar. Entsprechend ist die Simulierbarkeit eines Modells MFVSEi (P, h ²) durch das Modell EDEUP1 erklärt.Es werden zunächst eingehend die Methoden beschrieben, nach denen die Erwartungswerte der Merkmalsfrequenzen Q ₁, Q ₂, Q ₃, Q ₁₁, Q ₂₁ und Q ₂₂ für die Modelle EDEUP und MFVSE in Abhängigkeit von den Modellparametern berechnet werden können. Beim Modell MFVSE stehen dabei jeweils mehrere Methoden zur Auswahl: Für die Berechnung der Erwartungswerte von Q ₁, Q ₂ und Q ₃ werden neben dem in dieser Arbeit verwendeten, auf numerischer Integration mittels der Gaußschen Quadraturformel beruhenden Verfahren Methoden von Pearson (1901), Crittenden (1961) und Falconer (1965) sowie von Smith (1970) angegeben. Für die Berechnung der Erwartungswerte von Q ₁₁, Q ₂₁ und Q ₂₂ steht neben der in dieser Arbeit benutzten, durch leichte Modifikation eines Verfahrens von Steck (1958) erhaltenen Methode im Spezialfall MFVSE1 eine Methode von Smith (1971b) zur Verfügung.Die tatsächliche Berechnung der Erwartungswerte der genannten 6 Merkmalsfrequenzen in den gegenübergestellten Modellen erfolgte stets für die Werte der Populationsfrequenz P zwischen 0,01 und 10% (P-Bereich). Der Vergleich der Erwartungswerte der 6 Merkmalsfrequenzen für die Modelle EDEUP1 und MFVSE1 liefert folgende Ergebnisse: Das Modell EDEUP1 (P, 1) (einfacher dominanter Erbgang mit vollständiger Penetranz) ist im ganzen P-Bereich auf Grund jeder der Merkmalsfrequenzen Q ₁, Q ₂, Q ₁₁ Q ₂₁ und Q ₂₂ allein vom Modell MFVSE1 unterscheidbar. Der andere Grenzfall EDEUP1 (P, 0) von EDEUP1 (einfacher recessiver Erbgang) ist auf Grund jeder der Merkmalsfrequenzen Q ₂, Q ₁₁, Q ₂₁ und Q ₂₂ ebenfalls im ganzen P-Bereich vom Modell MFVSE1 zu unterscheiden. Für 0,5w<1 kann das Modell EDEUP1 (P, w) im ganzen P-Bereich auf Grund von Q ₁, Q ₂ oder Q ₁₁ von MFVSE1 unterschieden werden; auf Grund von Q ₂₁ ist die Unterscheidung noch möglich, wenn P1%, oder im ganzen P-Bereich, sofern w0,7. Im Gegensatz dazu ist für 0<w<0,5 das Modell EDEUP1 (P, w) im ganzen P-Bereich lediglich auf Grund der Merkmalsfrequenz Q ₁₁ von MFVSE1 unterscheidbar; sieht man von den biologisch wenig sinnvollen sehr kleinen Penetranzen (0<w<0,1) ab, so ist eine Unterscheidung auf Grund von Q ₁, Q ₂ oder Q ₂₁ nur bei kleiner Populationsfrequenz P möglich, und zwar bei um so kleinerem P, je kleiner w ist. Ein Modell EDEUP1 (P, w) mit 0,1w<0,5 ist also bezüglich jeder der 5 Merkmalsfrequenzen Q ₁, Q ₂, Q ₃, Q ₂₁ und Q ₂₂ durch das Modell MFVSE1 simulierbar, zumindest wenn P hinreichend groß ist. Das hei\t: es besteht Veranlassung, bei der Annahme eines einfachen dominanten Erbgangs mit kleiner Penetranz (0,1w<0,5) vorsichtig zu sein, wenn die Populationsfrequenz nicht klein ist. Auf der anderen Seite ist das Modell MFVSE1 (P, h ²) für jeden Wert von h ² im ganzen P-Bereich auf Grund von Q ₁₁ vom Modell EDEUP1 unterscheidbar. Bezüglich jeder der übrigen Merkmalsfrequenzen Q ₁, Q ₂, Q ₃, Q ₂₁ und Q ₂₂ ist das Modell MFVSE1 (P, h ²) für große Werte von h ² (insbesondere für h ²=1) bei hinreichend großem Wert von P durch das Modell EDEUP1 simulierbar. Für mittlere und kleine Werte von h ² dagegen ist MFVSE1 (P, h ²) im ganzen P-Bereich auf Grund jeder dieser 5 Merkmalsfrequenzen von EDEUP1 unterscheidbar: auf Grund von Q ₃ und Q ₂₁ für h ²0,6, auf Grund von Q ₁ und Q ₂₂ für h ²0,7 und auf Grund von Q ₂ für h ²0,8. Die Betrachtung der beiden Quotienten R ₁ =Q ₃/Q ₂ und R ₂=Q ₂₁/Q ₁₁ führt zu zwei Kriterien zur Unterscheidung der Modelle: Ein Wert R ₁>4 schließt das Modell EDEUP1 aus und spricht für das Modell MFVSE1, sofern nur diese beiden Modelle zur Auswahl stehen (Zwillingskriterium von Penrose, 1953); das zweite Kriterium macht die gleiche Aussage in Verbindung mit der Bedingung R ₂2,5. Beide Kriterien enthalten lediglich eine hinreichende und keine notwendige Bedingung: ein Wert R ₁4 bzw. ein Wert R ₂<2,5 spricht nicht für, aber auch nicht gegen das Modell MFVSE1.Der Vergleich der Erwartungswerte der betrachteten 6 Merkmalsfrequenzen für die Modelle EDEUP1 und MFVSE2 liefert qualitativ fast die gleichen Ergebnisse wie der entsprechende Vergleich bei den Modellen EDEUP1 und MFVSE1; es bestehen lediglich quantitative Unterschiede: Dominanz (an einigen der beteiligten Loci oder an allen) wirkt sich auf die 6 Merkmalsfrequenzen ähnlich aus wie eine Umweltbeteiligung an der Disposition. Insbesondere ist es nicht möglich, auf Grund der Merkmalsfrequenzen zwischen den Modellen MFVSE1 und MFVSE2 zu unterscheiden.Die Unterscheidung eines vorliegenden Erbgangs von einem der Modelle EDEUP1 und MFVSE1 auf Grund einer Merkmalsfrequenz Q (bei einem bestimmten Typ von Verwandten von Probanden) im obengenannten Sinne setzt voraus, daß sowohl die Populationsfrequenz P des Merkmals als auch der Erwartungswert Q von Q bei dem vorliegenden Erbgang genau bekannt ist. Praktisch stehen jedoch sowohl für P als auch für Q nur Schätzwerte zur Verfügung, die aus Stichproben gewonnen wurden. Zunächst wird noch vorausgesetzt, daß wenigstens P exakt bekannt ist, und behandelt, wie auf Grund eines Stichprobenergebnisses für Q (Schätzwert mit zugehörigen Vertrauensgrenzen für Q) entschieden werden kann, ob zwischen dem vorliegenden Erbgang und einem der Modelle EDEUP1 und MFVSE1, etwa EDEUP1, ein Unterschied besteht: es wird ein Unterschied angenommen, wenn der Erwartungswert von Q für jedes Modell EDEUP1 (P, w), dessen P-Wert gleich der vorliegenden Populationsfrequenz ist, außerhalb des Vertrauensintervalls für Q liegt. Das ist eine Entscheidung im Sinne eines statistischen Tests, und es wird ausführlich auf die Problematik dieses Tests eingegangen. Abgesehen von der Voraussetzung, daß genau bekannt sein muß, hat dieses Vorgehen den Nachteil, daß die genannte Entscheidung auf Grund eines Stichprobenergebnisses für immer nur eine der 6 in die Untersuchung einbezogenen Merkmalsfrequenzen vorgenommen wird: auch wenn in keinem Fall ein Unterschied konstatiert werden kann, ist immer noch denkbar, daß sich auf Grund der Stichprobenergebnisse für alle Merkmalsfrequenzen gemeinsam ein Unterschied zwischen dem vorliegenden Erbgang und einem der Modelle EDEUP1 und MFVSE1 feststellen läßt. Beide Nachteile vermeidet eine von Morton et al. (1970) angegebene, auf dem Maximum-Likelihood-Verfahren und dem ² beruhende Methode, die auf unseren Fall zugeschnitten eingehend dargestellt wird.Zum Abschluß werden unsere Ergebnisse hinsichtlich der Unterscheidbarkeit der Modelle EDEUP1 und MFVSE1 mit den Ergebnissen von Smith (1971a) verglichen, der die Unterscheidbarkeit zwischen einem allgemeineren Modell des einfachen diallelen Erbgangs (GTSLM) und dem Modell MFVSE1 mit einer von der unsrigen abweichenden, dem Vorgehen von Morton et al. (1970) ähnlichen Methode untersucht hat; das Modell GTSLM sieht noch zusätzlich die Manifestation des merkmals aus nichtgenetischer Ursache (mit der Wahrscheinlichkeit z) vor und enthält das Modell EDEUP als Spezialfall (z=0). Unsere Ergebnisse stehen mit denen von Smith im Einklang, soweit sie überhaupt mit diesen vergleichbar sind. Es ist auch kein Widerspruch, daß sich in einigen Fällen ein Modell MFVSE1 (P, h ²) bei Smith nicht vom Modell GTSLM unterscheiden läßt, obwohl es bei uns vom Modell EDEUP1 unterscheidbar ist. Denn dies ist wegen der größeren Allgemeinheit des Modells GTSLM zu erwarten, und tatsächlich weicht in einem solchen Fall die Parameterkonstellation der MFVSE1 (P, h ²) optimal angepaßten Realisation von GTSLM mehr oder weniger stark von den Parameterkombinationen ab, die dem Modell EDEUP1 entsprechen. Vielfach ist diese Parameterkonstellation jedoch biologisch wenig sinnvoll, indem die Penetranzen klein sind oder die Wahrscheinlichkeit z groß ist (oder beides zutrifft); in einem solchen Fall ist das multifaktorielle Modell überzeugender als das davon formal nicht unterscheidbare Modell GTSLM.Der in dieser Arbeit durchgeführten Untersuchung haftet in zweierlei Weise etwas unvermeidbar Künstliches an. Zum ersten sind die gegenübergestellten Modelle EDEUP1 und MFVSE1 künstlich, indem bei ihrer Spezifikation eine Reihe von Voraussetzungen gemacht werden mußte, um die Berechnung der Erwartungswerte der in die Untersuchung einbezogenen Merkmalsfrequenzen bei Verwandten von Probanden für diese Modelle zu ermöglichen und die Komplexität der Modelle in Grenzen zu halten. Diese Voraussetzungen sind zwar zum Teil plausibel, wie z. B. die Annahme einer Normalverteilung für die Disposition in der Population, aber zum Teil auch einschränkend, wie die Annahme, daß der Umweltbeitrag zur Disposition mit dem genotypischen Wert der Disposition nicht korreliert ist, oder die Annahme, daß zwischen den Umweltbeiträgen zu den Dispositionen von Verwandten keine Korrelation besteht. Eine Einschränkung bedeutet auch die in der Arbeit stets gemachte Voraussetzung, daß in der Population bezüglich des zugrundeliegenden Locus bzw. aller beteiligten Loci Panmixie besteht und insbesondere die Eltern der Probanden nicht verwandt sind; beim multifaktoriellen Modell wirkt sich diese Voraussetzung so aus, daß die Dispositionen der Eltern nicht korreliert sind. Wenn man durch Fallenlassen einiger dieser Voraussetzungen bei einem der Modelle, etwa bei MFVSE1, zu einem allgemeineren Modell übergeht (was prinzipiell möglich ist, allerdings die Untersuchung erheblich komplizieren würde), so wird eine zwischen einem Modell EDEUP1 (P, w) und dem Modell MFVSE1 auf Grund einer Merkmalsfrequenz bestehende Unterscheidbarkeit eventuell verlorengehen, während eine Simulierbarkeit von EDEUP1 (P, w) bezüglich einer Merkmalsfrequenz sicher erhalten bleibt. Aus den Ergebnissen der Arbeit können demnach nur Schlüsse auf die Simulierbarkeit durch allgemeinere Modelle, nicht auf die Unterscheidbarkeit von solchen Modellen gezogen werden. Insbesondere wird durch einen Wert R ₁>4 des Quotienten R ₁=Q ₃/Q ₂ oder einen Wert R ₂2,5 des Quotienten R ₂ =Q ₂₁/Q ₁₁ wohl das Modell EDEUP1 ausgeschlossen, aber nicht unbedingt jedes allgemeinere Modell eines einfachen diallelen Erbgangs. Zum zweiten ist künstlich, daß, in die Untersuchung nur die 6 Merkmalsfrequenzen Q ₁, Q ₂, Q ₃, Q ₁₁, Q ₂₁ und Q ₂₂ bei den engsten Verwandten (Kleinfamilie) der Probanden einbezogen werden. Durch Hinzunahme von Merkmalsfrequenzen bei entfernteren Verwandten der Probanden werden sich vermutlich zusätzliche Möglichkeiten zur Unterscheidung zwischen den Modellen EDEUP1 und MFVSE1 ergeben. Eine solche Ausweitung ist aber auch im Hinblick auf die Unterscheidung zwischen allgemeineren Modellen des einfachen bzw. multifaktoriellen Erggangs wichtig. Als entferntere Verwandte kommen in erster Linie Onkel und Tanten sowie Großeltern der Probanden in Betracht. Hier bietet sich die Trennung in Verwandte des Vaters und Verwandte der Mutter an, und man kann, zumindest prinzipiell, die Wahrscheinlichkeiten für die möglichen Verteilungen von 2 Merkmalsträgern auf eine bestimmte Gruppe von väterlichen Verwandten und eine solche von mütterlichen Verwandten (etwa auf v (2) väterliche und m (2) mütterliche Geschwister) in den Modellen EDEUP1 und MFVSE1 berechnen. Slater (1966) hat nämlich die Vermutung geäußert (und diese an Hand eines grob annähernden Rechenmodells zu bestätigen versucht), daß das Verhältnis der Wahrscheinlichkeit der einseitigen Verteilungen (beide Merkmalsträger entweder auf der väterlichen oder auf der mütterlichen Seite) zur Wahrscheinlichkeit der zweiseitigen Verteilungen beim einfachen Erbgang (Modell EDEUP1) größer ist als beim multifaktoriellen Erbgang (Modell MFVSE1), und das wäre eine weitere Hilfe bei der Unterscheidung zwischen den beiden Modellen. Darüber hinaus könnte man daran denken, aus einer bestimmten Gruppe von Verwandten des Probanden (etwa seinen Geschwistern, seinen Eltern und deren Geschwistern) bestehende Stammbäume nach den Stellen im Staummbaum, an denen das Merkmal auftritt, in Typen einzuteilen und die Wahrscheinlichkeiten dieser Typen für die beiden Modelle EDEUP1 und MFVSE1 zu berechnen, in der Hoffnung, daß hinsichtlich der Verteilung der Typen zwischen den beiden Modellen charakteristische Unterschiede bestehen. Klunker (1960) hat die Verteilung solcher Stammbaumtypen für das Modell EDEUP1 unter einer speziellen Annahme über die Genotypen der Eltern und Großeltern des Probanden (die bei seltenen Merkmalen annähernd zutrifft) berechnet; grundsätzlich ist die Berechnung auch ohne diese Annahme möglich, wird dann aber sehr kompliziert. Die Verteilung der Stammbaumtypen für das Modell MFVSE1 kann mit Hilfe einer von Smith (1971b, Anhang) angegebenen Näherungsmethode berechnet werden.

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Discrimination between multifactoria inheritance with threshold effect and two-allele single-locus hypothesis

Summary and Conclusions According to our present knowledge of the mechanism of gene action, the statement that an anomaly follows a simple mode of inheritance (single-locus hypothesis) implies that the anomaly has a simple biochemical cause, namely the alteration or absence of the primary product (polypeptide chain) of a certain gene. Therefore, if the anomaly does not satisfy the formal criteria of a single-locus model except with the help of additional assumptions, such as that of incomplete penetrance of the anomalous allele, a more conservative hypothesis of inheritance should also be considered, to avoid a hopeless search for a simple biochemical cause. In this paper a two-allele single-locus hypothesis with incomplete penetrance of the anomalous allele (model EDEUP) is contrasted with a more conservative alternative hypothesis which is extremely different from the first: a multifactorial mode of inheritance with threshold effect (model MFVSE). In this model slight and non-specific effects of the gene pairs at a great many loci, and perhaps some environmental influence, combine to determine a phenotypically latent continuous variable (the disposition or liability to the anomaly), with the anomaly becoming manifest when the variable exceeds a certain threshold level.A parameter common to both models is the population frequency P of the trait (the anomaly); further parameters are: the penetrances w ₁and w ₂of the anomalous allele in the homozygous and heterozygous states respectively in the EDEUP model, the heritability h ²and the degree of genetic determination ² of the disposition in the MFVSE model. In the paper only 2-parametric special cases of the 3-parameter models are considered: the EDEUP model is restricted to the special case EDEUP1, defined by w ₁=1, w ₂=w (complete penetrance of the anomalous allele in the homozygous state), and the MFVSE model to first the special case MFVSE1, defined by ² = h² (no dominance effects at the loci involved), and then to the special case MFVSE2, defined by ² = 1 (no environmental contribution, but possible dominance effects). It is interesting to consider what conditions allow the two models EDEUP1 and MFVSEi (i=1 or 2) to simulate each other in certain partial aspects of the phenotype, and whether there are criteria allowing discrimination between the two models. The partial aspects of the phenotype used are firstly the trait frequencies (incidences) Q ₁,Q ₂, and Q ₃in parents (or children), sibs (or DZ twins), and MZ twins of affected persons (probands), secondly the incidences Q ₁₁, Q ₂₁, and Q ₂₂in sibs of probands with a given phenotype combination of the parents (-x-, +x-, or +x+, where - and + mean normal and affected respectively); here it is assumed that the procedure for recording probands fulfils the conditions of single selection. A model EDEUP1 (P, w) (realization of the EDEUP1 model with specified values of the parameters P and w) simulates a model MFVSEi (P, h²) (i=1 or 2) (and conversely the latter the first model) relative to an incidence Q if the expectations of Q in the two models (with the same population frequency P in both models) coincide. A model EDEUP1 (P, w) can be simulated by the MFVSEi model relative to Q if there is a realization MFVSEi (P, h ²) simulating EDEUP1 (P, w) relative to Q; otherwise EDEUP1 (P, w) is distinguishable from the MFVSEi model by means of Q. Whether a model MFVSEi (P, h ²) can be simulated by the EDEUP1 model or not, is decided in the same way.First the methods for calculation of the expectations of the incidences Q ₁, Q ₂, Q ₃,Q ₁₁, Q ₂₁, and Q ₂₂in the models EDEUP and MFVSE in dependence on the model parameters are described in detail. There are several possible methods for the MFVSE model: For calculating the expectations of Q ₁, Q ₂, and Q ₃, the methods of Pearson (1901), Crittenden (1961) and Falconer (1965), as well as of Smith (1970) are mentioned, besides the procedure used in this paper, which is based on numerical integration by means of the Gaussian quandrature formula. The method actually used for calculating the expectations of Q ₁₁, Q ₂₁, and Q ₂₂, was obtained by a slight modification to a procedure described by Steck (1958), and there is another method (Smith, 1971b) which is applicable only to the special case MFVSE1.The factual calculation of the expectations of the 6 incidences mentioned in the contrasted models was always carried out for the values of population frequency P between 0.01% and 10% (P-range). Comparison of the expectations of the 6 incidences in the models EDEUP1 and MFVSE1 yields the following results: The model EDEUP1 (P, 1) (simple dominant inheritance with complete penetrance) can be distinguished from the EDEUP1 model throughout the range of P by means of each of the incidences Q ₁, Q ₂, Q ₁₁, Q ₂₁and Q ₂₂. The other limiting case of EDEUP1, the model EDEUP1 (P, 0) (simple recessive inheritance), is distinguishable from the MFVSE1 model by each of the incidences Q ₂, Q ₁₁, Q ₂₁, and Q ₂₂, also throughout the P-range. For 0.5w<1, the model EDEUP1 (P, w) can be distinguished from MFVSE1 throughout the range of P by Q ₁, Q ₂, or Q ₁₁; discrimination by means of Q ₂₁is still possible if P1%, or throughout the range of P if w0.7. For 0<w<0.5, in contrast, the model EDEUP1 (P, w) is distinguishable from MFVSE1 throughout the range of P only by means of the incidence Q ₁₁; disregarding the very low penetrances (0<w<0.1) which are biologically not very reasonable, discrimination by means of Q ₁, Q ₂, or Q ₂₁is possible only for low population frequency P; in fact, the lower the value of w is, the lower P must be. Thus a model EDEUP1 (P, w) with 0.1w<0.5 can be simulated by the MFVSE1 model relative to each of the 5 incidences Q ₁, Q ₂, Q ₃, Q ₂₁, and Q ₂₂, at least when P is sufficiently high; for this reason one has to be cautious in assuming a simple dominant inheritance with low penetrance (0.1w<0.5) if the population frequency is not low. On the other hand, the model MFVSE1 (P, h ²) is distinguishable from the EDEUP1 model by means of Q ₁₁at every value of h ²and throughout the range of P. Relative to each of the remaining 5 incidences Q ₁, Q ₂, Q ₃, Q ₂₁, and Q ₂₂, the model MFVSE1 (P, h ²) can be simulated by EDEUP1 at high values of h ²(especially for h ²=1) and a sufficiently high value of P. At medium and low values of h ², in contrast, the model MFVSE1 (P, h ²) is distinguishable from the EDEUP1 model by means of each of these 5 incidences: by means of Q ₃and Q ₂₁when h ²0.6, of Q ₁and Q ₂₂when h ²0.7, and of Q ₂when h ²0.8. The investigation of the two ratios R ₁=Q ₃/Q ₂and R ₂=Q ₂₁/Q ₁₁leads to two criteria for differentiation between the models: A value R ₁<4 excludes the EDEUP1 model and indicates the MFVSE1 model, if the choice is between these two models only (twin criterium of Penrose, 1953); the second criterion states the same in the case of R ₂2.5. Both criteria contain only a sufficient and not a necessary condition: a value R ₁4 or a value R ₂<2.5 is not indicative of the MFVSE1 model but nor does it exclude it.Comparison of the values expected for the 6 incidences in the models EDEUP1 and MFVSE2 yields results which are almost the same qualitatively as those of the corresponding comparison of EDEUP1 with MFVSE1; there are only some quantitative differences: Dominance (at some or all of the loci involved) has a similar effect on the 6 incidences as an environmental contribution to the disposition. More specifically, it is not possible to discriminate between the models MFVSE1 and MFVSE2 by means of the incidences considered.The discrimination of a mode of inheritance under discussion from one of the models EDEUP1 and MFVSE1 by means of an incidence Q (in a certain type of relatives of probands) in the sense mentioned above presupposes that not only the population frequency P of the trait but also Q, the value expected for Q in the mode of inheritance under discussion, is known exactly. In practice, however, only estimates obtained from samples are available for both P and Q. First it is still assumed that at least P is known exactly, and the method of deciding by means of a sample result for Q (estimate for Q with confidence limits) whether there is a difference between the mode of inheritance under discussion and one of EDEUP1 and MFVSE1, say EDEUP1, is discussed: a difference is accepted when the expectation of Q in each model EDEUP1 (P, w) with P-value equal to the existing population frequency lies outside the confidence interval for Q. This is a decision in the sense of a statistical test, and we go into the problems of this test in detail. Apart from the condition that P must be exactly known, this procedure has the added disadvantage that the decision mentioned is always made by means of a sample result for only one of the 6 incidences included in the investigation: even if it is not possible to establish a difference in any of the cases, it is still conceivable that a difference can be stated between the mode of inheritance under discussion and one of the models EDEUP1 and MFVSE1 by means of the sample results of all incidences together. A method given by Morton et al. (1970) which is based on the maximum likelihood principle and the ²-test for goodness of fit avoids both disadvantages; the method, modified for our case, is presented in detail.Finally, our results on the possibility of discrimination between the models EDEUP1 and MFVSE1 are compared with those obtained by Smith (1971a), who investigated the discrimination between a generalized two-allele single-locus model (GTSLM) and the MFVSE1 model by a different method from ours, which resembles that used by Morton et al. (1970). The GTSLM model also provides for the manifestation of the trait from non-genetic causes (with a probability z) and contains the EDEUP model as a special case (z=0). Our results are consistent with Smith's results, insofar as they are at all comparable with them. In particular, it is no contradiction that in some cases a model MFVSE1 (P, h ²) in Smith's results cannot be distinguished from the GTSLM model although it is distinguishable from the EDEUP1 model in our results. This is to be expected because of the greater generality of the GTSLM model, and actually in such a case the parameter constellation of the realization of GTSLM which gives the best fit to the model MFVSE1 (P, h ²) deviates more or less strongly from the parameter combinations appropriate to the EDEUP1 model. Frequently, however, this parameter constellation is not very reasonable biologically, in that the penetrances are low or the probability z is high (or both); in such a case the multifactorial model is more convincing than the GTSLM model though it is formally not distinguishable from the latter.Two kinds of inevitable artificiality are inherent in the investigation described in this paper. Firstly, the contrasted models EDEUP1 and MFVSE1 are artificial in that their specification involved a series of assumptions to facilitate the calculation of the values expected in these models for the incidences in relatives of probands included in the investigation and to limit the complexity of the models. It is true that some of these assumptions are plausible, for instance the assumption of a normal distribution of the disposition in the population, but some are restricting, such as the assumption that the environmental contribution to the disposition is not correlated with the genotypic value of the disposition, or that there is no correlation between the environmental contributions to the dispositions of relatives. A further restriction is imposed by the assumption always made in this paper that there is random mating in the population relative to the underlying locus resp. all the loci involved and, especially, that the parents of the probands are not related; in the multifactorial model, this implies that the dispositions of the parents are not correlated. If by ceasing to insist on some of these assumptions in one of the models, say in MFVSE1, one adopts a more general model (a procedure which is possible in theory but would considerably complicate the investigation), the possiblility of discrimination existing between a model EDEUP1 (P, w) and the MFVSE1 model by means of an incidence will eventually be lost, while the possibility of simulation of EDEUP1 (P, w) relative to an incidence will certainly be preserved. From the results of this paper, therefore, we can draw inferences only about the possibility of simulation by more general models and not about the possibility of discrimination from such models. In particular, it is true that when R ₁>4 for the ratio R ₁=Q ₃/Q ₂or when R ₂2.5 for the ratio R ₂=Q ₂₁/Q ₁₁the EDEUP1 model is excluded, but not necessarily every more general two-allele single-locus model. A second kind of artificiality is introduced by the inclusion of only the 6 incidences Q ₁, Q ₂, Q ₃, Q ₁₁, Q ₂₁, and Q ₂₂in the closest relatives (small family) of the probands in the investigation. The inclusion of incidences in more remote relatives of the probands will probably yield additional possibilities for discriminating between models EDEUP1 and MFVSE1. But widening of the investigation in this way is also important with regard to discrimination between more general models of simple or multifactorial inheritance. More remote relatives means primarily the uncles and aunts and the grand-parents of the probands. Separation into maternal and paternal relatives may then be considered, and, at least in theory, the probabilities for the possible distributions of two affected persons in a certain group of paternal relatives and in a corresponding group of maternal relatives (say, on v (2) paternal and m (2) maternal sibs) in the models EDEUP1 and MFVSE1 can be calculated. Slater (1966) has advanced the supposition (and has attempted to verify it by means of a approximative computational model) that the ratio of the probability of the one-sided distributions (both affected persons on the paternal side or both on the maternal side) to the probability of the two-sided distributions is higher in simple inheritance (EDEUP1 model) than in multifactorial inheritance (MFVSE1 model), and this would be a further help in distinguishing between the two models. In addition, one could classify the pedigrees consisting of a particular group of the proband's relatives (say his sibs, his parents, and his parents' sibs) into types according to the positions where the trait occurs in the pedigree. Then, it would be interesting to calculate the probabilities of these types for the two models EDEUP1 and MFVSE1, in the hope of finding characteristic differences between the two models as to the distribution of the types. Klunker (1960) has calculated the distribution of such pedigree types for the EDEUP1 model with a specific assumption about the genotypes of the parents and grand-parents of the proband (which is approximately correct for rare traits); in principle, the calculation is also possible without this assumption but then it becomes very complicated. The distribution of the pedigree types in the MFVSE1 model can be calculated by means of an approximation method described by Smith (1971b, Appendix).