Stability of stationary distributions in a space-dependent population growth process

We consider a spatial population growth process which is described by a reaction-diffusion equation c(x)u _t = (a ²(x)u _x ) _x +f(u), c(x) >0, a(x) > 0, defined on an interval [0, 1] of the spatial variable x. First we study the stability of nonconstant stationary solutions of this equation under Neumann boundary conditions. It is shown that any nonconstant stationary solution (if it exists) is unstable if a _xx0 for all x[0, 1], and conversely ifa _xx>0 for some x[0, 1], there exists a stable nonconstant stationary solution. Next we study the stability of stationary solutions under Dirichlet boundary conditions. We consider two types of stationary solutions, i.e., a solution u ₀(x) which satisfies u ₀ x0 for all x[0, 1] (type I) and a solution u ₀(x) which satisfies u _0x = 0 at two or more points in [0, 1] (type II). It is shown that any stationary solution of type I [type II] is stable [unstable] if a _xx 0 [a _xx 0] for all x[0, 1]. Conversely, there exists an unstable [a stable] stationary solution of type I [type II] if a _xx <0 [a _xx >0] for some x[0, 1].     

The influence of yeast metabolism on dispersion in a fluidised yeast bed

Summary The effect of yeast metabolism on the dispersion characteristics of a fluidised bed fermentor containing flocs of the yeast Saccharomyces carlsbergensis was investigated. Dispersion in the metabolizing fluidised yeast floc system was compared with the dispersion in an inert yeast floc system and in a glass bead system. Breakdown in plug-flow was found to occur in the metabolically active yeast bed when the flow rate was increased over a relatively narrow operating range (up to a dilution rate of 0.08 h^-1). The superficial liquid velocity at which perfect mixing was approximated was some 18 times greater in the inert yeast floc system than in the metabolizing yeast floc system.Abbreviations C Tracer concentration - C ₀ Concentration of tracer at time t=0 - V Mixing chamber volume - v Volumetric flow rate - l Time - t Mean residence time - N Number of tanks in series - D/l Dispersion number - ² variance     

A self-dual network derived from a single neuronic equation

A model of a neuron with memory was viewed from the realibizability of a given periodic sequence of typeR _n R _n =u ₁ u ₂...u _{n 1 2}... _n(u _j = 0 or 1, _j = 1 –u _j). It is easily shown that the periodic sequenceR _n R _n is always obtained as an output of the model with memory of lengthn. However it is not so easy to decide the realizability of the given sequence in the case of the memory of length less thann. The necessary and sufficient condition for the realizability was given in a practical form. The condition is concerned with the determinant of a matrix associated with the given sequence.     

A novel immobilised design for the production of the heterologous protein lysozyme by a genetically engineered Aspergillus niger strain

Abstract A novel immobilisation design for increasing the final concentration of the heterologous protein lysozyme by a genetically engineered fungus, Aspergillus niger B1, was developed. A central composition design was used to investigate different immobilised polymer types (alginate and pectate), polymer concentration [24% and 4% (w/v)], inoculum support ratios (1:2 and 1:4) and gel-inducing agent concentration [CaCl₂, 2% and 3.5% (w/v)]. Studies of the kinetics of production showed that optimum lysozyme productivity occurred after 10 days. Lysozyme production was significantly affected by polymer type, polymer concentration, and inoculum support ratio. Overall, immobilisation in Ca-pectate resulted in higher lysozyme production compared to that in Ca-alginate. Similar effects were observed when the polymer concentration was reduced. Regardless of polymer type and concentration, increasing the fungal inoculum level increased lysozyme production. A significantly higher lysozyme yield was achieved with Ca-pectate in comparison to Ca-alginate (approximately 20–23 mg l^–1 and 0.5–2 mg l^–1, respectively). The maximum lysozyme yield achieved was about 23 mg l^–1 by immobilisation in Ca-pectate 2% (w/v) with 33% (v/v) mycelium and 3.5% (w/v) gel-inducing agent (CaCl₂). Response surface methodology was used to investigate the effect of pH and water activity (a_w). The best medium pH was 4.5–5.0, and bead a_w for optimum lysozyme yield was 0.94, regardless of polymer type.     

The growth analysis of water hyacinth,Eichhornia crasipes solms,in different water temperature conditions

A 40-day culture experiment of water hyacinth was made in 4 different water temperatures, 15, 20, 25 and 30°C, which were combined with 4 levels of concentration of culture solution, 1/3, 1, 3 and 9-fold of the standard solution containing 28 ppm of totalN and 7.7 ppm of totalP. The optimum condition for obtaining the maximum plant growth shifted from 30°C: 3-fold condition in the early stage to 20–25°C: 3-fold condition in the later stages of the experiment. The relation between the fresh weight biomass per 100-l tank,w, and the concentration of culture solution,f, was expressed successfully by a reciprocal equation,1/w=A F/f+A F ^′f/(1-f/C F)+B F, in whichA f,A f′, andB f are time dependent coefficients andC f is the upper limit of the concentration to permit plant growth which can change with time. The relation betweenw and water temperature,T, was expressed by another reciprocal equation,1/w=A T/e ^aT+A T^′e^bT+B T, in whicha andb are constants andAt At′ andB t are time dependent coefficients. The latter formulation shows that the temperature can be breated as an exponential factor, and it suggests the possibility of the growth coefficient of the logistic growth equation, ψ, being affected by temperature.     

The production of cyclopiazonic acid by Penicillium commune and cyclopiazonic acid and aflatoxins by Aspergillus flavus as affected by water activity and temperature on maize grains

The combined effects of water activity (a_w) and temperature on mycotoxin production by Penicilium commune (cyclopiazonic acid — CPA) and Aspergillus flavus (CPA and aflatoxins — AF) were studied on maize over a 14-day period using a statistical experimental design. Analysis of variance showed a highly significant interaction (P 0.001) between these factors and mycotoxin production. The minimum a_w/temperature for CPA production (2264 ng g^–1 P. commune, 709 ng g^–1 A. flavus) was 0.90 a_w/30 °C while greatest production (7678 ng g^–1 P. commune, 1876 ng g^–1 A. flavus) was produced at 0.98 a_w/20 °C. Least AF (411 ng g^–1) was produced at 0.90 a_w/20 °C and most (3096 ng g^–1) at 0.98 a_w/30 °C.     

Chemotactic collapse for the Keller-Segel model

 This work is concerned with the system (S) {u _t =Δu − χ∇ (u∇v) for x∈Ω, t>0Γ v _t =Δv+(u−1) for x∈Ω, t>0 where Γ, χ are positive constants and Ω is a bounded and smooth open set in ℝ². On the boundary ∂Ω, we impose no-flux conditions: (N) ∂u∂n =∂v∂n =0 for x∈∂ Ω, t>0 Problem (S), (N) is a classical model to describe chemotaxis corresponding to a species of concentration u(x, t) which tends to aggregate towards high concentrations of a chemical that the species releases. When completed with suitable initial values at t=0 for u(x, t), v(x, t), the problem under consideration is known to be well posed, locally in time. By means of matched asymptotic expansions techniques, we show here that there exist radial solutions exhibiting chemotactic collapse. By this we mean that u(r, t) →Aδ(y) as t→T for some T<∞, where A is the total concentration of the species. Received 9 March 1995; received in revised form 25 December 1995     

Optimal control of continuous fermentation processes

Three layer control structure is proposed for optimal control of continuous fermentation processes. The start-up optimization problems are solved as a first step for optimization layer building. A steady state optimization problem is solved by a decomposition method using prediction principle. A discrete minimum time optimal control problem with state delay is formulated and a decomposition method, based on an augmented Lagrange's function is proposed to solve it. The problem is decomposed in time domain by a new coordinating vector. The obtained algorithms are used for minimum time optimal control calculation of Baker's Yeast fermentation process.List of Symbols x(t) g/l biomass concentration - s(t) g/l limiting substrate concentration - x ⁰ g/l inlet biomass concentration - s ⁰(t) g/l inlet substrate concentration - D(t) h^–1 dilution rate - (t) h^–1 specific growth rate - Y g/g yield coefficient - (t) h^–1 specific limiting substrate consumption rate - k _D h^–1 disappearing constant - w ₁, w ₂ known constant or piece-wise disturbances - _m h^–1 maximum specific growth rate - k _s g/l Michaelis-Menten's parameter - h time delay - x ₀, s ₀ g/l initial concentrations - ¯x, ¯s, ¯D optimal steady state value - V _min , V _max , v=x,s,d,t bounds of variables - t h sampling period - K number of steps in the optimization horison - Js, J _d performance indexes - L _s Lagrange's function - L _d Lagrange's functional - ₀ weighting coefficient for the amount of the limiting substrate throwing out of the fermentor - ₁, ₂ dual variables of Lagrange's function - steps in steady state coordination procedure - errors values for steady state coordination process - _v , v=x, s conjugate variables of Lagrange's functional - _v , v=x,s penalty coefficients of augmented Lagrange's functional - _v , v=x, s interconnections of the time - e _v , v=x,s, D, _x , _s gradients of Lagrange's functional - j, l indexes of calculation procedures - values of errors in calculations The researches was supported by National Scientific Research Foundation under grants No NITN428/94 and No NITN440/94     

Intensity of microcarrier collisions in turbulent flow

A model is developed, allowing estimation of the share of inelastic interparticle collisions in total energy dissipation for stirred suspensions. The model is restricted to equal-sized, rigid, spherical particles of the same density as the surrounding Newtonian fluid. A number of simplifying assumptions had to be made in developing the model. According to the developed model, the share of collisions in energy dissipation is small.List of Symbols b parameter in velocity distribution function (Eq. (28)) - c _K factor in Kolmogoroff spectrum law (Eq. (20)) - D _t(r _p ) m²/s characteristic dispersivity at particle radius scale (Eq. (13)) - E(k, t) m³/s² energy spectrum as function of k and t (Eq. (16)) - E _K (k) m³/s² energy spectrum as function of k in Kolmogoroff-region (Eq. (20)) - E _p dimensionless mean kinetic energy of a colliding particle (Eq. (36)) - E _cp dimensionless kinetic energy exchange in a collision (Eq. (37)) - G(x, s) dimensionless energy spectrum as function of x and s (Eq. (16)) - G _B(x) dimensionless energy spectrum as function of x for boundary region (Eq. (29)) - G _K(x) dimensionless energy spectrum as function of x for Kolmogoroff-region (Eq. (21)) - g m/s² gravitational acceleration - I _cp dimensionless collision intensity per particle (Eq. (38)) - I _cv dimensionless volumetric collision intensity (Eq. (39)) - k l/m reciprocal of length scale of velocity fluctuations (Eq. (17)) - K dimensionless viscosity (Eq. (13)) - n(2) dimensionless particle collision rate (Eq. (12)) - n(r) l/s particle exchange rate as function of distance from observatory particle center (Eq. (7)) - r m vector describing position relative to observatory particle center (Eq. (2)) - r m scalar distance to observatory particle center (Eq. (3)) - r _pm particle radius (Eq. (1)) - s dimensionless time (Eq. (10)) - SC kg/ms³ Severity of collision (Eq. (1)) - t s time (Eq. (2)) - u(r, t) m/s velocity vector as function of position vector and time (Eq. (2)) - u(r, t) m/s magnitude of velocity vector as function of position vector and time (Eq. (3)) - u _r(r, t) m/s radial component of velocity vector as function of position vector and time (Eq. (3)) - u _r (r, t) m/s magnitude of radial component of velocity vector as function of position vector and time (Eq. (3)) - u (r, t) m/s latitudinal component of velocity vector as function of position vector and time (Eq. (3)) - u (r, t) m/s magnitude of latitudinal component of velocity vector as function of position vector and time (Eq. (3)) - u (r, t) m/s longitudinal component of velocity vector as function of position vector and time (Eq. (3)) - u (r, t) m/s magnitude of longitudinal component of velocity vector as function of position vector and time (Eq. (3)) - u _gsm/s superficial gas velocity - u(r) m/s root mean square velocity as function of distance from observatory particle center (Eq. (3)) - u_r(r) m/s root mean square radial velocity component as function of distance from observatory particle center (Eq. (4)) - u (r) m/s root mean square latitudinal velocity component as function of distance from observatory particle center (Eq. (4)) - u (r) m/s Root mean square longitudinal velocity component as function of distance from observatory particle center (Eq. (4)) - w(x) dimensionless root mean square velocity as function of dimensionless distance from observatory particle center (Eq. (11)) - V _pm³ particle volume (Eq. (36)) - w(2) dimensionless root mean square collision velocity (Eq. (34)) - w ^* parameter in boundary layer velocity equation (Eq. (24)) - x dimensionless distance to particle center (Eq. (9)) - x ^* value of x where G _Band G _K-curves touch (Eq. (32)) - x _K dimensionless micro-scale (Kolmogoroff-scale) of turbulence (Eq. (15)) - volumetric particle hold-up - m²/s³ energy dissipation per unit of mass - m²/s kinematic viscosity - kg/m³ density - (r) m³/s fluid-exchange rate as function of distance to observatory particle center - Latitudinal co-ordinate (Eq. (5)) - Longitudinal co-ordinate (Eq. (5))     

Multiple liquid-liquid partition: II. Theory of Martin-Synge distribution (MSD)

The theory of Martin-Synge distribution (MSD) was refined, with special attention being focused upon the derivation of the separation functions. The separation function for the fundamental distribution of MSD was obtained in the form v = t²(αk₁ + 1)(αk₁ + β)[(αk₁ + 1)^1/2 + (αk₁ + β)^1/2]²/αk₁(β ? 1)², where ν is the number of aliquots v_m driven through the apparatus, t the abscissa of the standard normal distribution, α = v_m/v₈ the phase ratio, β = k₁/k₂≥ 1 the separation factor, and k₁ the partition coefficient of the more rapidly moving component; ν was shown to have minima at given αk₁ values. The separation function of the single withdrawal of MSD was presented in the form N = u + 1 = t²(2αk₁ + β + 1)²/(β ? 1)²+ 1, where N is the number of partition units; N is minimal when αk₁ = 0. The elution volumes and standard deviations of the two compounds to be separated were mathematically analyzed in a manner similar to that previously presented when dealing with the theory of counter-current distribution (CCD). As in CCD, the elution volumes in MSD were found to have minima at given αk₁ values. However, the standard deviations of the elution curves also have minima in respect to αk₁ in MSD, which is a different situation as compared to CCD. The selection of optimal operating conditions was found to be more critical in MSD than in CCD.     

Existence and uniqueness of a sharp travelling wave in degenerate non-linear diffusion Fisher-KPP equations

In this paper we use a dynamical systems approach to prove the existence of a unique critical value c ^* of the speed c for which the degenerate density-dependent diffusion equation u _ct = [D(u)u _x ] _x + g(u) has: 1. no travelling wave solutions for 0 < c < c ^*, 2. a travelling wave solution u(x, t) = (x - c ^* t) of sharp type satisfying (– ) = 1, () = 0 ^*; '(^*–) = – c ^*/D'(0), '(^*+) = 0 and 3. a continuum of travelling wave solutions of monotone decreasing front type for each c > c ^*. These fronts satisfy the boundary conditions (– ) = 1, '(– ) = (+ ) = '(+ ) = 0. We illustrate our analytical results with some numerical solutions.     

Verification studies of a simplified model for the removal of dichloromethane from waste gases using a biological trickling filter

The removal of dichloromethane from waste gases in a biological trickling filter was studied experimentally as well as theoretically within the concentration range of 0–10,000 ppm. A stable dichloromethane elimination performance was achieved during two years of operation, while the start-up of the system only amounted to several weeks at constant inlet concentrations. The trickling filter system was operated co-currently as well as counter-currently.However, experimental and theoretical results revealed that the relative flow direction of the mobile phases did not significantly affect the elimination performance. Moreover, it was found that the gas-liquid mass-transfer resistance in the trickling filter bed applied was negligible, which leaves the biological process inside the biofilm to be the rate limiting step.A simplified model was developed, the Uniform-Concentration-Model, which showed to predict the filter performance close to the numerical solutions of the model equations. This model gives an analytical expression for the degree of conversion and can thus be easily applied in practice.The dichloromethane eliminating performance of the trickling filter described in this paper, is reflected by a maximum dichloromethane elimination capacity EC _max=157 g/(m³ · h) and a critical liquid concentration C _lcr=45 g/m³ at a superficial liquid velocity of 3.6 m/h, inpendent of the gas velocity and temperature.List of Symbols a _s m²/m³ specific area - a _w m²/m³ specific wetted area - A m² cross-sectional area - C _g g/m³ gas phase concentration - C _go g/m³ inlet gas phase concentration - C _gocr g/m³ critical gas phase concentration - C _g ^* C_g/C_go dimensionless gas concentration - C _l g/m³ liquid concentration - C _lcr g/m³ critical liquid concentration - C _lcr ^* mC_lcr/C_go dimensionless critical concentration - c _li g/m³ substrate concentration at liquid-biofilm interface - C _l ^* mC_l/C_go dimensionless liquid concentration - C _o g/m³ oxygen concentration inside the biofilm - C _oi g/m³ oxygen concentration at liquid-biofilm interface - C_s g/m³ substrate concentration inside the biofilm - C _si g/m³ substrate concentration at liquid-biofilm interface - D _eff m²/h effective diffusion coefficient in the biofilm - D _o m²/h effective diffusion coefficient for oxygen in the biolayer - E mu_g/u_l extraction factor - E _act kJ/mol activation energy for the biological reaction - EC g/(m³· h) K _o a _w : elimination capacity, or the amount of substrate degraded per unit of reactor volume and time - EC _max g/(m³ · h) K _o a_w: maximum elimination capacity - f degree of conversion - h m coordinate in height - H m height of the packed bed - K ₀ g/(m³ · h) _maxX_b/Y zeroth order reaction defined per unit of biofilm volume - k _og m/h overall gas phase mass transfer coefficient - K ^* dimensionless constant given by Eq. (A.5) - K _l ^* dimensionless constant given by Eq. (A.6) - K ₂ ^* dimensionless constant given by Eq. (A.6) - m C _g /C_l gas liquid distribution coefficient - N g/(m² · h) liquid-biofilm interfacial flux of substrate - N _og k_oga_wH/u_g number of gas phase transfer units - N _r k_o a_w H/u_g C_go number of reaction units - OL g/(m³· h) u _g C _go /H organic load - r _s g/(m³ ·h) zeroth order substrate degradation rate given by Eq. (1) - R _s g/(g TSS ·h) specific activity - T K absolute temperature - u _g m/h superficial gas velocity - u _t m/h superficial liquid velocity - X _b g TSS/m₃ biomass concentration inside biofilm - X _s g TSS/m₃ liquid suspended biomass concentration - x m coordinate inside the biofilm - Y g TSS/(g_DCM) yield coefficient Greek Symbols dimensionless parameter given by Eq. (2) - m averaged biofilm thickness - biofilm effectiveness factor given by Eqs. (7a)–(7c) - m penetration depth of substrate into the biofilm - _max d^–1 microbiological maximum growth rate - v _o stoichiometric utilization coefficient for oxygen - v _s stoichiometric utilization coefficient for substrate - dimensionless height in the filter bed - h H/u _g superficial gas phase contact time - _o (K ₀ /DC _ii )^1/2 - _o C _o /C _oi dimensionless oxygen concentration inside the biofilm - _s C _s /C _si dimensionless substrate concentration inside the biofilm Experimental results, verifying the model presented will be discussed Part II (to be published in Vol. 6, No. 4)     

Basic functions of variability of simple pre-planned movements

A model of a pre-planned single joint movements performed without feedback is considered. Modifications of this movement result from transformation of a trajectory pattern f(t) in space and time. The control system adjusts the movement to concrete external conditions specifying values of the transform parameters before the movement performance. The preplanned movement is considered to be simple one, if the transform can be approximated by an affine transform of the movement space and time. In this case, the trajectory of the movement is x(t) = Af(t/ + s) +p, were A and 1/ are space and time scales, s and p are translations. The variability of movements is described by time profiles of variances and covariances of the trajectory x(t), velocity v(t), and acceleration a(t). It is assumed that the variability is defined only by parameters variations. From this assumption follows the main finding of this work: the variability time profiles can be expanded on a special system of basic functions corresponding to established movement parameters. Particularly, basic functions of variance time profiles, reflecting spatial and temporal scaling, are x ²(t) and t ² v ²(t) for trajectory, v ²(t) and (v(t) + t · a(t))² for velocity, and a ²(t) and (2a(t) +t · j(t))², where j(t) = d³ x(t)/dt ³, for acceleration. The variability of a model of a reaching movement was studied analytically. The model predicts certain peculiarities of the form of time profiles (e.g., the variance time profile of velocity is bi-modal, the one of acceleration is tri-modal, etc.). Experimental measurements confirmed predictions. Their consistence allows them to be considered invariant properties of reaching movement. A conclusion can be made, that reaching movement belongs to the type of simple preplanned movements. For a more complex movement, time profiles of variability are also measured and explained by the model of movements of this type. Thus, a movement can be attributed to the type of simple pre-planned ones by testing its variability.     

Theory of transport in linear biological systems: I. Fundamental integral equation

The conditions under which the output,γ _b (t), of a biological system is related to the input,γ _a (t), by an integral equation of the typeγ _b (t) = ∫ ₀ ^t γ _a (ω)w(t−ω)dω, where ω(t) is a transport functioncharacteristic of the system, are analyzed in detail. Methods of solving this type of integral equation are briefly discussed. The theory is then applied to problems in tracer kinetics in which input and output are sums of exponentials, and explicit formulae, which are applicable whether or not the pool is uniformly mixed, are derived for “turnover time” and “pool” size.     

Visible light-induced H2 production from cellulose using photosensitization of Mg chlorophyll a

A photoinduced-H₂ production system, coupling cellulose degradation by cellulase and glucose dehydrogenase (GDH) and H₂ production with colloidal Pt as a catalyst using the visible light-induced photosensitization of Mg chlorophyll a, has been developed. When the sample solution containing methylcellulose, cellulase, GDH, NAD⁺, Mg chlorophyll a, Methyl viologen and colloidal Pt was irradiated, continuous H₂ production was observed. The amount of H₂ production was about 12 mol after 4 h irradiation.     

A new method to determine the aw range in which immobilized lipases display optimum activity in organic media

Summary We describe a qualitative method to predict the pre-equilibration a_w, system value in which, covalent immobilized lipase B from Candida antarctica to sepharose and silica, displayed best synthetic activity. The methodology is based in the analysis of the water adsorption isotherms of the biocatalyst in air and in the organic solvent. The biocatalyst is active at pre-equilibration a_w values higher than the divergence point between both isotherms. In addition, native and immobilized lipase display highest activity if the biocatalyst is pre-equilibrated at a_w=P point. For preparative purposes, the validity of the method was proved in the esterification of racemic 2-(4-isobutyl phenyl) propionic acid with 1-propanol in isooctane at long reaction time.     

The initial reaction velocities of lactate dehydrogenase in various cell types

Summary The initial reaction velocities (v _v ) of lactate dehydrogenase in hepatocytes, cardiac muscle fibres, skeletal (gastrocnemius) muscle fibres, gastric parietal cells, ductal epithelial and acinar cells of the parotid gland, and oocytes were determined, by computer-assisted image analysis, in unfixed sections of these tissues incubated at 37°C on substrate-containing agarose gel films. They were found to fit the equations v _i = a₁A (equation 1) and v _i – v = a₂A (equation 2) reported previously for mouse hepatocytes (Nakae & Stoward, 1993a, b), where v and A are, respectively, the gradients (or steady-state velocities) and the intercepts on the absorbance axis of the linear regression lines of the absorbance (A) of the finalreaction product on incubation times between 1 and 3 min, and a ₁ and a ₂ are constants. Both equations 1 and 2 fitted the observed v _i closely for mouse (a ₁ = 2.7, a ₂ = 2.2) and human (a ₁ = 3.0, a ₂ = 1.9) hepatocytes. However, equation 2 fitted the observed v _i better than equation 1 for mouse cardiac muscle fibres (a ₂ = 1.5), skeletal muscle fibres (a ₂ = 1.2), gastric parietal cells (a ₂ = 1.7), acinar (a ₂ = 1.4) and striated ductal (a ₂ = 2.2) epithelial cells of the parotid gland, and oocytes (a ₂ = 1.6). The values of v _i calculated from the two equations agreed with the observed v _i to within about 11%. They ranged from 105 mole hydrogen equivalents/cm³ cell/min units in hepatocytes to 24 units in parotid acinar cells, but for other cell types they were between 46 and 61 units. These are all considerably higher than values reported previously.     

BB rat diabetes susceptibility and body weight regulation genes colocalize on Chromosome 2

The genetic etiology of Type 1 (insulin-dependent) diabetes mellitus is complicated by the apparent presence of several diabetes susceptibility genetic regions. Type 1 diabetes in the inbred BioBreeding (BB) rat closely resembles the human disorder and was previously shown to involve two genes: the lymphopenia (lyp) region on Chromosome (Chr) 4 and RT1 ^u in the major histocompatibility complex (MHC) on Chr 20. In addition, a segregation analysis of an F₂ intercross between the diabetes-prone congenic BB DR ^lyp/lyp,u/u and F344^{+/+, lv/lv} rats indicated that at least one more genetic factor was responsible for Type 1 diabetes. In this study, we generated F₂N₂ progeny in a cross between non-diabetic F₂(DR ^lyp/lyp,u/u × F344) ^lyp/lyp,u/u and diabetic DR ^lyp/lyp,u/u rats. In a subsequent total genome scan, a third factor was mapped to the 21.3-cM region on Chr 2 between D2Mit14 and D2Mit15 (peak LOD score 4.7 with 67% penetrance). Interestingly, the homozygosity of the BB allele (b/b) for the Chr 2 region was significantly associated with a greater weight reduction after fasting than the homozygosity of the F344 allele (f/f, p < 0.008). In conclusion, the development of Type 1 diabetes in the congenic DR ^lyp/lyp rat is controlled by at least three genes: lymphopenia, MHC, and a third factor that may play a role in metabolism and body weight regulation. Received: December 1998 / Accepted: 10 May 1999     

Sodium/calcium selectivity of cloned calcium T-type channels

We studied the peculiarities of permeability with respect to the main extracellular cations, Na⁺ and Ca²⁺, of cloned low-threshold calcium channels (LTCCs) of three subtypes, Ca_v3.1 (α1G), Ca_v3.2 (α 1H), and Ca_v3.3 (α1I), functionally expressed in Xenopus oocytes. In a calcium-free solution containing 100 mM Na⁺ and 5 mM calcium-chelating EGTA buffer (to eliminate residual concentrations of Ca²⁺) we observed considerable integral currents possessing the kinetics of inactivation typical of LTCCs and characterized by reversion potentials of −10 ± 1, −12 ± 1, and −18 ± 2 mV, respectively, for Ca_v3.1, Ca_v3.2, and Ca_v3.3 channels. The presence of Ca²⁺ in the extracellular solution exerted an ambiguous effect on the examined currents. On the one hand, Ca²⁺ effectively blocked the current of monovalent cations through cloned LTCCs (K _d = 2, 10, and 18 μM for currents through channels Ca_v3.1, Ca_v3.2, and Ca_v3.3, respectively). On the other hand, at the concentration of 1 to 100 mM, Ca²⁺ itself functioned as a carrier of the inward current. Despite the fact that the calcium current reached the level of saturation in the presence of 5 mM Ca²⁺ in the external solution, extracellular Na⁺ influenced the permeability of these channels even in the presence of 10 mM Ca²⁺. The Ca_v3.3 channels were more permeable with respect to Na⁺ (P _Ca/P _Na ∼ 21) than Ca_v3.1 and Ca_v3.2 (P _Ca/P _Na ∼ 66). As a whole, our data indicate that cloned LTCCs form multi-ion Ca²⁺-selective pores, as these ions possess a high affinity for certain binding sites. Monovalent cations present together with Ca²⁺ in the external solution modulate the calcium permeability of these channels. Among the above-mentioned subtypes, Ca_v3.3 channels show the minimum selectivity with respect to Ca²⁺ and are most permeable for monovalent cations. Neirofiziologiya/Neurophysiology, Vol. 38, No. 3, pp. 183–192, May–June, 2006.