Analysis of some regular systems of inbreeding

Summary A probabilistic method is used to calculate the asymptotic rate of loss of genetic variability for half-sib and first-cousin mating of an infinite number of individuals. For both systems of inbreeding, all probabilities of nonidentity by descent converge to zero at ultimate rates proportional to t ^–1/2, where t is the time in generations. The rate of decay is faster for half-sibs than for first cousins, the respective asymptotic allozygosities being 4(t)^–1/2 and 8(t)^–1/2.Supported by the National Science Foundation (Grant No. DEB77-21494).     

On-line parameter and state estimation of continuous cultivation by extended Kalman filter

Summary The on-line estimation of biomass concentration and of three variable parameters of the non-linear model of continuous cultivation by an extended Kalman filter is demonstrated. Yeast growth in aerobic conditions on an ethanol substrate is represented by an unstructured non-linear stochastic t-variant dynamic model. The filter algorithm uses easily accessible data concerning the input substrate concentration, its concentration in the fermentor and dilution rate, and estimates the biomass concentration, maximum specific growth rate, saturation constant and substrate yield coefficient. The microorganismCandida utilis, strain Vratimov, was cultivated on the ethanol substrate. The filter results obtained with the real data from one cultivation experiment are presented. The practical possibility of using this method for on-line estimation of biomass concentration, which is difficult to measure, is discussed.Nomenclature D dilution rate (h^-1) - DO₂ dissolved oxygen concentration (%) - E identity matrix - F Jacobi matrix of the deterministic part of the system equations g - g continuousn-vector non-linear real function - h m-vector non-linear real function - K Kalman filter gain matrix - K _S saturation constant (kgm^-3) - K_S expectation of the saturation constant estimate - M Jacobi matrix of the deterministic part of the measurement equations h - P(t₀) co-variance matrix of the initial values of the state - P(t_k/t_k) c-variance matrix of the error in (t _k|t _k) - P(t_k+1/t_k) co-variance matrix of the error in (t _k+1|t _k - Q co-variance matrix of the state noise - R co-variance matrix of the output noise - S substrate concentration (kgm^-3) - S _i input substrate concentration - t time - t _k discrete time instant with indexk=0, 1, 2,... - u(t) input vector - v(t_k) measurement (output) noise sequence - w(t) n-vector white Gaussian random process - x(t₀) initial state of the system - (t₀) expectation of the initial state values - x(t) n-dimensional state vector - x(t_k) state vector at the time instantt _k - (t_k|t_k) expectation of the state estimate at timet _k when measurements are known to the timet _k - (t_k+1|t_k) expectation of the state prediction - X biomass concentration (kgm^-3) - expectation of the biomass concentration estimate - y(t_k) m-dimensional output vector at the time instantt _k - Y _XIS substrate yield coefficient - _X|S expectation of the substrate yield coefficient estimate - specific growth rate (h^-1) - _M maximum specific growth rate (h^-1) - expectation of the maximum specific growth rate estimate - state transition matrix     

Estimation of specific growth rate from agitation speed in DO-stat culture

Summary A simple and effective method to estimate the specific growth rate estimation has been developed based on the observation of time changes in the agitation speed in dissolved oxygen(DO)-stat cultures of Brevibacterium ketoglutamicum. The estimation was compared with that using carbon dioxide evolution rate (CER). Estimated values of specific growth rates by both methods agreed well with the data directly calculated from cell concentration change although the use of agitation speed gave a slightly better result than CER.Nomenclature CER Carbon dioxide evolution rate (mmol/sec) - OUR Oxygen uptake rate (mmol/sec) - OTR Oxygen transfer rate (mmol/sec) - RPM Agitation speed (rev./min) - C* Saturated dissolved oxygen concentration (mmol/L) - Dissolved oxygen concentration (mmol/L) - k Time index - k _L a' Mass transfer coefficient (sec^-1) - Y _X/O2 Cellular yield based on oxygen consumed (g-cell/mmol O₂) - Specific growth rate (hr^-1) - Constant - t Fermentation time - t Sampling time for RPM and CER measurements     

The effect of sensory uncertainty due to amblyopia (lazy eye) on the planning and execution of visually-guided 3D reaching movements

Background

Impairment of spatiotemporal visual processing in amblyopia has been studied extensively, but its effects on visuomotor tasks have rarely been examined. Here, we investigate how visual deficits in amblyopia affect motor planning and online control of visually-guided, unconstrained reaching movements.

Methods

Thirteen patients with mild amblyopia, 13 with severe amblyopia and 13 visually-normal participants were recruited. Participants reached and touched a visual target during binocular and monocular viewing. Motor planning was assessed by examining spatial variability of the trajectory at 50–100 ms after movement onset. Online control was assessed by examining the endpoint variability and by calculating the coefficient of determination (R²) which correlates the spatial position of the limb during the movement to endpoint position.

Results

Patients with amblyopia had reduced precision of the motor plan in all viewing conditions as evidenced by increased variability of the reach early in the trajectory. Endpoint precision was comparable between patients with mild amblyopia and control participants. Patients with severe amblyopia had reduced endpoint precision along azimuth and elevation during amblyopic eye viewing only, and along the depth axis in all viewing conditions. In addition, they had significantly higher R² values at 70% of movement time along the elevation and depth axes during amblyopic eye viewing.

Conclusion

Sensory uncertainty due to amblyopia leads to reduced precision of the motor plan. The ability to implement online corrections depends on the severity of the visual deficit, viewing condition, and the axis of the reaching movement. Patients with mild amblyopia used online control effectively to compensate for the reduced precision of the motor plan. In contrast, patients with severe amblyopia were not able to use online control as effectively to amend the limb trajectory especially along the depth axis, which could be due to their abnormal stereopsis.     

Pharmacokinetics and biological activity in subcutaneous long-term administration of recombinant interferon-γ in cancer patients

Summary We have investigated the pharmacokinetics, tolerance, and biological activity of recombinant human interferon- (rHuIFN) administered subcutaneously to cancer patients. Twenty-one patients with lymphoma and metastatic cancer received rHuIFN (in doses of 0.1, 0.25, or 0.5 mg/m²) in two or three injections per week for up to 180 days. The most common adverse effects encountered were flu-like symptoms, fever and fatigue. The increase in body temperature after each administration ranged from 0 to 4°C depending on the individual patient, but was unrelated to the rHuIFN dose or its plasma concentration. The pharmacokinetic response of the patients after the two treatments showed a low intra-individual variability with respect to the plasma concentration/time profiles. However, as observed for the fever side-effect, the interindividual variation (CV >50%) was high for the parameters area under the data points (AUC_0-t ) and maximum plasma concentration (c _max). Despite this high interindividual variability, the mean values obtained for AUC_0-t andc _max after s.c. injection of rHuIFN were approximately proportional to the dose administered: the injection of 0.1, 0.25 or 0.5 mg/m² rHuIFN resulted in AUC_0-t values of 15.4, 31.5 or 69.6 ng h/ml, respectively andc _max was found to be 1.0, 2.4 and 4.9 ng/ml, respectively. With this s.c. administration protocol, objective antitumour responses were observed in two patients, but there was no partial or complete remission.     

Phylogenetic relationships of Triticum tauschii the D genome donor to hexaploid wheat

Summary In crosses between T. tauschii (D ^t) accesions, their polymorphic gliadin forms were inherited as blocks of gliadin components -Gli-D ^t1, Gli-D ^t2 — as single Mendelian characters. From the progeny of four tri-parental crosses (test-crosses), HMW glutenin subunits derived from T. tauschii (Glu-D ^t1) segregated as alleles of the Glu-D1 locus in bread wheat. In three of the tri-parental crosses, a small proportion (2.5%) of the progeny with atypical segregation patterns, were identified through somatic chromosome counts, to be aneuploids (1.9% hypoploids and 0.6% hyperploids). Chromosomal mapping studies revealed that the synteny of genes for HMW glutenin subunits and gliadins in T. tauschii are conserved in the D genome homologue (chromosome 1D) of T. aestivum. The map distance between the Glu-D1/-D ^t1 and Gli-D1/-D ^t1 loci was calculated to be 63.5 cM, while a linkage to the centromere of 7.7–9.7 cM was estimated for the Glu-D1/-D ^t1 locus.     

Relationship between Ca2+-transport and ATP hydrolytic activities in guinea-pig pancreatic acinar plasma membranes

Partially purified plasma membrane fractions were prepared from guinea-pig pancreatic acini. These membrane preparations were found to contain an ATP-dependent Ca²⁺-transporter as well as a heterogenous ATP-hydrolytic activity. The Ca²⁺-transporter showed high affinity for Ca²⁺ (K_Ca ²⁺ = 0.04 ± 0.01 M), an apparent requirement for Mg²⁺ and high substrate specificity. The major component of ATPase activity could be stimulated by either Ca²⁺ or Mg²⁺ but showed a low affinity for these cations. At low concentrations, Mg²⁺ appeared to inhibit the Ca²⁺-dependent ATPase activity expressed by these membranes. However, in the presence of high Mg²⁺ concentration (0.5–1 mM), a high affinity Ca²⁺-dependent ATPase activity was observed (K_Ca ²⁺ = 0.08 ± 0.02 M). The hydrolytic activity showed little specificity towards ATP. Neither the Ca²⁺-transport nor high affinity Ca²⁺-ATPase activity were stimulated by calmodulin. The results demonstrate, in addition to a low affinity Ca²⁺ (or Mg⁺)-ATPase activity, the presence of both a high affinity Ca²⁺-pump and high affinity Ca²⁺-dependent ATPase. However, the high affinity Ca²⁺-ATPase activity does not appear to be the biochemical expression of the Ca²⁺-pump.Abbreviations Ca²⁺-ATPase calcium-activated, magnesium-dependent adenosine triphosphatase - CaM calmodulin - CDTA trans-1,2-diaminocyclohexane-N,N,N,N-tetraacetate - EDTA ethylene-diaminetetraacetate - EGTA ethylene glycol bis(-aminoethyl ether)-N,N,N,N-tetraacetate - NADPH reduced form of nicotinamide adenine dinucleotide phosphate     

Slow conductance changes due to potassium depletion in the transverse tubules of frog muscle fibers during hyperpolarizing pulses

Summary When hyperpolarizing currents are applied between the inside and outside of a muscle fiber it is known that there is a slow transient decrease (300- to 600-msec time constant) in the measured fiber conductance sometimes referred to as creep which is maximal in K₂SO₄ Ringer's solutions and which disappears on disruption of the transverse tubular system. An approximate mathematical analysis of the situation indicates that these large, slow conductance changes are to be expected from changes in the K⁺ concentration in the tubular system and are due to differences in transport numbers between the walls and lumen of the tubules. Experiments using small constant-voltage and constant-current pulses (membrane p. d. changes 20 to 30 mV) on the same fibers followed by an approximate mathematical and more exact computed numerical analysis using the measured fiber parameters and published values of tubular system geometry factors showed close agreement between the conductance creep predicted and that observed, thus dispensing with the need for postulated changes in individual membrane conductances at least during small voltage pulses. It is further suggested that an examination of creep with constant-voltage and constant-current pulses may provide a useful tool for monitoring changes in tubular system parameters, such as those occurring during its disruption by presoaking the fibers in glycerol.Table of main symbols used R, T, F Gas constant, Temperature in °K and the Faraday - a Fiber radius - r Radial distance from the center of the fiber (cf. Fig. 2A) - t Time in sec - V ₁,V ₂ Voltages measured by electrodes 1 and 2 (cf. p. 248) - Longitudinal fiber space constant ( ²=R _m a/2R _i ) - R _m ,R _m (t) Total membrane resistance per unit surface area of fiber ( cm²) - R _m (0),R _m () As above att=0 (excluding capacity transient) and att= during a current or voltage pulse - G _m ,G _m (t) Total membrane conductance (mho·cm^–2) per unit area of fiber surface - G _m (0),G _m () As above att=0 (excluding the capacity transient) and att= during a current or voltage pulse - R _sm ,G _sm Surface membrane resistance ( cm²) and conductance (mho·cm^–2), respectively, excluding the TTS - R _T ,G _T Input resistance ( cm²) and conductance (mho·cm^–2) of the TTS referred to unit area of fiber surface - f _T Fraction of the K⁺ conductance in the TTS to the total K⁺ conductance of the fiber [cf. Eq. (7)] - R _i Internal resistivity of the fiber ( cm) - r _s Electrical access resistance of the TTS [ cm²;cf. Fig. 3 and Eq. (24)] - h Diffusional access resistance of the TTS [cf. Eq. (27)] - I ₀ Total current entering fiber (amp) - I _m ,i _m Total current per unit area of fiber surface (amp·cm^–2; considered positive in the hyperpolarizing direction) - i _sm Current going through the surface membrane alone (amp·cm^–2;cf. Fig. 3) - i ₀,i ₀(t) Total current entering the TTS referred to unit area of surface membrane (amp·cm^–2;cf. Fig. 3) - I _K,I _K(r) K⁺ current density crossing the equivalent TTS disc at radial distancer [cf. Fig. 2A and Eq. (23)] - i, i(r, t) Radial current in the lumen of the TTS at radial distancer and timet (cf. Fig. 2B) - C, C(r, t) K⁺ concentration within the TTS at radial distancer and timet (mEquiv·liter^–1) - C _o ,C _K Both refer to external solution and initial TTS K⁺ concentration (mEquiv·liter^–1) - V, V(r, t) The potential at radial distancer in the lumen of the TTS with respect to the external solution at timet (cf. Figs. 2 and 3) - V(a), V(a, t) The p.d. across the access resistance (cf. Figs. 3B and 3C) - V ₀,V ₀(t) The potential of the sarcoplasm with respect to the external solution (cf. Figs. 2 and 3) - E _K The K⁺ equilibrium potential between the sarcoplasm and the externa solution or across the tubular wall - t _K ^m ,t _K ^s The transport number for K⁺ in the TTS membranes and in the solution of the tubular lumen, respectively - The fraction of fiber volume occupied by tubules, and not implicitly including branches - As above but always including branches - A dimensionless network factor for the TTS - G _W Conductance per unit area of tubular wall (mho·cm^–2) - G _L Conductance of tubular lumen (mho·cm^–1) - Volume-to-surface ratio of the TTS - Effective wall conductance of TTS membranes per unit volume of fiber [mho·cm^–3;cf. Eq. (14)] - Effective radial conductance of the lumen of the TTS per unit volume of fiber [cf. Eq. (20)] - d The thickness of the equivalent disc representing the TTS [cf. Eq. (15)] - _T Space constant of the TTS [cf. Eq. (37).cp. Eq. (11)] - D _K The diffusion coefficient of K⁺ ions in the lumen of the TTS (cm² sec^–1) - The effective radial K⁺ diffusion coefficient in the TTS [cf. Eq. (28)] - J ₀,J ₁ Bessel functions of order 0 and 1, respectively - I ₀,I ₁ Modified Bessel functions of order 0 and 1, respectively - Time constants of slow conductance changes - _vc Time constant of slow conductance changes during a constant-voltage pulse - _cc Time constant of slow conductance changes during a constant-current pulse - , _m Roots of various Bessel function equations - g ₁,g ₂,g ₃,g ₄ Constants used to fit cubic equation for conductance-voltage curves [cf. Eq. (71)]     

The distribution of genetic parameter estimates and confidence intervals from small disconnected diallels

The distributions of genetic variance components and their ratios (heritability and type-B genetic correlation) from 105 pairs of six-parent disconnected half-diallels of a breeding population of loblolly pine (Pinus taeda L.) were examined. A series of simulations based on these estimates were carried out to study the coverage accuracy of confidence intervals based on the usual t-method and several other alternative methods. Genetic variance estimates fluctuated greatly from one experiment to another. Both general combining ability variance (²_g) and specific combining ability variance (²_s) had a large positive skewness. For ²_g and ²_s, a skewness-adjusted t-method proposed by Boos and Hughes-Oliver (Am Stat 54:121–128, 2000) provided better upper endpoint confidence intervals than t-intervals, whereas they were similar for the lower endpoint. Bootstrap BCa-intervals (Efron and Tibshirani, An introduction to the bootstrap. Chapman & Hall, London 436 p, 1993) and Halls transformation methods (Zhou and Gao, Am Stat 54:100–104, 2000) had poor coverages. Coverage accuracy of Fiellers interval endpoint(J R Stat Soc Ser B 16:175–185, 1954) and t-interval endpoint were similar for both h² and r_B for sample sizes n10, but for n=30 the Fiellers method is much better.     

Gas-phase influence on the mixing in a fluidized bed bio-reactor

Summary The liquid and solids mixing in fluidized bed bio-reactors containing particles with a density only slightly higher than water (1100 kg/m³) is generally consistent with the results found in previous studies for reactors with particles of higher density. The liquid mixing can be described by an axial dispersion model for a large variety of conditions while the solids follow the streamlines of the liquid. In the presence of a gas phase the degree of mixing of both the liquid and the solid phase increased. This effect became larger with increasing reactor diameter. In the extrapolation of laboratory data of three phase fluidized bed bio-reactors to pilot plant systems this effect should be taken into account. The liquid and solids mixing may have a substantial effect on overall conversion rates and on possible microbial stratification in the reactor.Nomenclature Bo Bodenstein number v L/D (-) - D _r diameter of the fluidized bed reactor (m) - D ₁ Dispersion coefficient of the liquid phase (m²/s) - D _g dispersion coefficient of the solid phase (m²/s) - E(in) normalized dye concentration function entering the ideally mixed tank reactor (-) - E(t) normalized dye concentration function as measured (-) - L length of the axial dispersed reactor (m) - t time after dye injection (s) - t _m time constant for microbial selection (s) - t _s solid mixing time constant (s) - t time interval in which a particle migrates within the bed (s) - v _t superficial gas velocity (m/s) - v _g superficial liquid velocity (m/s) - z migration distance of a particle in the bed (m) - ₁ in situ growth rate of a dominant organism (s^-1) - ₂ in situ growth rate of a recessive organism (s^-1) - average residence time in the axial dispersed reactor (s) - _t average residence time in the ideally mixed tank reactor (s)     

Optimal control of antagonistic muscle stiffness during voluntary movements

This paper presents a study on the control of antagonist muscle stiffness during single-joint arm movements by optimal control theory with a minimal effort criterion. A hierarchical model is developed based on the physiology of the neuromuscular control system and the equilibrium point hypothesis. For point-to-point movements, the model provides predictions on (1) movement trajectory, (2) equilibrium trajectory, (3) muscle control inputs, and (4) antagonist muscle stiffness, as well as other variables. We compared these model predictions to the behavior observed in normal human subjects. The optimal movements capture the major invariant characteristics of voluntary movements, such as a sigmoidal movement trajectory with a bell-shaped velocity profile, an N-shaped equilibrium trajectory, a triphasic burst pattern of muscle control inputs, and a dynamically modulated joint stiffness. The joint stiffness is found to increase in the middle of the movement as a consequence of the triphasic muscle activities. We have also investigated the effects of changes in model parameters on movement control. We found that the movement kinematics and muscle control inputs are strongly influenced by the upper bound of the descending excitation signal that activates motoneuron pools in the spinal cord. Furthermore, a class of movements with scaled velocity profiles can be achieved by tuning the amplitude and duration of this excitation signal. These model predictions agree with a wide body of experimental data obtained from normal human subjects. The results suggest that the control of fast arm movements involves explicit planning for both the equilibrium trajectory and joint stiffness, and that the minimal effort criterion best characterizes the objective of movement planning and control.     

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))     

Amplification and latency in photoreceptors: Integrated or separated phenomena?

It is shown that the models for the transduction process in photoreceptors which treat latency and amplification as integrated phenomena (integrated models) yield time scales for single photon signals (quantum bumps) which distinctly conflict with the experimentally observed ones for the ventral nerve photoreceptor of Limulus: the ratio of bump duration/ latency t _B/t _lat is predicted by integrated models to be 3 in contrast to the experimental result of 0.5. Moreover, integrated models lead to a predicted value of an extinction rate of 50%, i.e., 50% of the absorbed photons should be expected to cause no signal in the dark adapted state of the cell. In this paper it is shown that separation of latency and amplification in such a way that the latency causing process precedes amplification in the transduction process eliminates these discrepancies. In addition, the separate modeling of latency and amplification resolves the rather large ambiguity in determining the exponent n of the initial signal current J(t) ⁿreported in the literature to be between n2 (from noise analysis) up to n17 (from flash experiments). Two alternative models for the latency part of transduction are suggested which give a qualitatively much better agreement with the experimental histograms of latencies.List of Symbols A quantum bump amplitude, maximum of quantum bump signal current - latency criterion as a fraction in terms of J _max - E energy of the stimulating flash - g conductance of a single light-regulated channel - I(t) light intensity of the stimulating flash as a function of time - J(t) response current of photoreceptors to light flashes under voltage clamp - J _max maximum signal current response signal - J _min minimum current above which the signal current becomes distinguishable from the base line noise - k rate constant in models separating latency from amplification - L ligand in ligand binding model - rate constant of exponential bump decay - m number of amplification steps following gainless latency process in models separating latency and amplification - n exponent in the initial behaviour J(t)t ⁿ - Q net charge transfer of quantum bump signal current - (t) first-passage time probability density - t _B duration of quantum bump response - t _lat latency time - t _max time to peak for quantum bumps - t _r rise time for quantum bumps - U U-U _L, U=clamp voltage, U _L=reversal potential of light-regulated channels - v amplification factor - X _k intermediate conformations in transduction models This work was supported by Deutsche Forschungsgemeinschaft (SFB 160)     

Redistribution of potassium,chloride and calcium during the gravitropically induced movement of Mimosa pudica pulvinus

When the leaves of Mimosa pudica are changed from their normal position in the gravitational field, they perform reversible compensatory movements by means of pulvini. These movements are not the result of growth processes but involve reversible turgor variations. These variation are concomitant with ion migrations within pulvini: during the gravitropic movement, K⁺ and Cl^- shift towards the adaxial half of the motor organ whereas Ca²⁺ shifts towards the abaxial half. Compounds known to affect K⁺ transport, tetraethylammonium chloride and valinomycin, do not hinder the gravitropic movement but inhibit strongly the seismonastic reaction. The same general result is obtained with compounds affecting anion transport, disulfonic stilbenes and 9-anthracene carboxylic acid. Calcium chelators inhibit the gravitropic movement more efficiently than the seismonastic reaction and the calcium ionophore A 23 187 increases both movements. The data obtained with these various compounds indicate that ions do not have the same functional importance in the regulation of the two different pulvinar movements.Abbreviations abx abaxial half of the pulvinus - adx adaxial half of the pulvinus - 9-AC 9-anthracene carboxylic acid - DIDS 4,4-diisothiocyanatostilbene-2,2-disulfonic acid - EDTA ethylenediaminetetraacetic acid - EGTA ethylene glycol-bis-(-aminoethyl ether)-N,N,N,N-tetraacetic acid - SITS 4-acetamido-4-isothiocyanatostilbene-2,2-disulfonic acid - TEA tetraethylammonium chloride     

An evaluation of sensory noise in the human visual system

It is assumed that the activity of a visual channel may be represented as V(t)=g(t)+(t), where g(t) is the deterministic response of the channel due to the presentation of a stimulus and (t) is the trajectory of a wide-sense stationary Gauss process. The stimulus is detected if the event V(t)>S for at least one t[0, T] occurs. Two approximations for the probability of this event are proposed, and it is demonstrated how they may be employed to estimate (i) the value of the second spectral moment ₂ of the noise process _t , where ₂ reflects the speed of the fluctuations of the trajectories _t , and (ii) the value of the internal threshold S. The commonly made assumption of peak — detection is shown to serve as a very good first approximation in particular if the channel is of transient type or — in case of detection by a channel of sustained type — if the stimulus durations are not too long.     

A mathematical model of biological evolution

In order to understand generally how the biological evolution rate depends on relevant parameters such as mutation rate, intensity of selection pressure and its persistence time, the following mathematical model is proposed: dN _n (t)/dt=(m _n (t-)N _n (t)+N _n-1(t) (n=0,1,2,3...), where N _n (t) and m _n (t) are respectively the number and Malthusian parameter of replicons with step number n in a population at time t and is the mutation rate, assumed to be a positive constant. The step number of each replicon is defined as either equal to or larger by one than that of its parent, the latter case occurring when and only when mutation has taken place. The average evolution rate defined by is rigorously obtained for the case (i) m _n (t)=m _n is independent of t (constant fitness model), where m _n is essentially periodic with respect to n, and for the case (ii) (periodic fitness model), together with the long time average m of the average Malthusian parameter . The biological meaning of the results is discussed, comparing them with the features of actual molecular evolution and with some results of computer simulation of the model for finite populations.An early version of this study was read at the International Symposium on Mathematical Topics in Biological held in kyoto, Japan, on September 11–12, 1978, and was published in its Procedings.     

Viscous media in tower bioreactors: Hydrodynamic characteristics and mass transfer properties

Studies in tower reactors with viscous liquids on flow regime, effective shear rate, liquid mixing, gas holdup and gas/ liquid mass transfer (k _La) are reviewed. Additional new data are reported for solutions of glycerol, CMC, PAA, and xanthan in bubble columns with diameters of 0.06, 0.14 and 0.30 m diameter. The wide variation of the flow behaviour index (1 to 0.18) allows to evaluate the effective shear rate due to the gas flow. New dimensionless correlations are developed based on the own and literature data, applied to predict k _La in fermentation broths, and compared to other reactor types.List of Symbols a(a) m^–1 specific interfacial area referred to reactor (liquid) volume - Bo Bond number (g D _c ² _L/) - c _L(c _L ^* ) kmol m^–3 (equilibrium) liquid phase oxygen concentration - C coefficient characterising the velocity profile in liquid slugs - C _s m^–1 coefficient in Eq. (2) - d _B(d_vs) m bubble diameter (Sauter mean of d _B) - d ₀ m diameter of the openings in the gas distributor plate - D _c m column diameter - D _L m²s^–1 diffusivity - E _L(E_W) m² s^–1 dispersion coefficient (in water) - E ² square relative error - Fr Froude number (u _G/(g D_c)^0.5) - g m s^–2 gravity acceleration - Ga Gallilei number (g D _c ³ _L ² / _eff ² ) - h m height above the gas distributor the gas holdup is characteristic for - k Pasⁿ fluid consistency index (Eq. 1) - k _L m s^–1 liquid side mass transfer coefficient - k _La(k_La) s^–1 volumetric mass transfer coefficient referred to reactor (liquid) volume - L m dispersion height - n flow behaviour index (Eq. 1) - P W power input - Re liquid slug Reynolds number ( _L(u _G +u _L) D _c/_eff) - Sc Schmidt number ( _eff/( _L D _L )) - Sh Sherwood number (k _La D _c ² /D_L) - t s time - u _B(u_sw) m s^–1 bubble (swarm) rise velocity - u _G(u_L) m s^–1 superficial gas (liquid) velocity - V(V_L) m³ reactor (liquid) volume Greec Symbols W m^–2 K^–1 heat transfer coefficient - y(y _eff) s^–1 (effective) shear rate - _G relative gas holdup - s relaxation time of viscoelastic liquid - _L(_eff) Pa s (effective) liquid viscosity (Eq. 1) - _L kg m^–3 liquid density - N/m surface tension     

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.     

A model for continuous production of thermally induced recombinant proteins

Summary General conditions for continuous expression of heterologous genes fromP _L promoter in two fermenters connected in series have been established. The induction time of the bacterial cells is calculated as a function of the retention time in the inducing reactor. Using this model, it is possible to adapt fermentation parameters to the particular behaviour of any specific recombinant clone.Nomenclature F(t) flow at timet [ml/min] - M _T (t) culture induced, at timeT of fermentation, during a period up tot [ml] - N _T (t) culture induced, at timeT of fermentation, during a period fromt tot+dt [ml] - p(t) product yield in a discontinuous culture [units/ml] - P(t) product yield at the outlet of the fermenter [units/ml] - v(t) volume of culture entered into the inducing reactor up to timet [ml] - V volume of the inducing reactor [ml] Greek letters retention time in the inducing reactor [min] - (t) average induction time at timet [min]     

Tolerance regions with segmented fermentation processes

Many microbial fermentation processes exhibit different phases (e.g. adaption phase, main growth phase, main production phase). The process variables e.g. the biomass vary randomly about their mean. The experimentalist is interested to know the break points of the different phases, and a tolerance region, i.e. a range of possible values of the process variable that can be considered as normal. This paper deals with statistical methods for determining break points and tolerance regions.List of Symbols a _i intercept in phasei - b _i specific growth rate in phasei - e _t deviation of a measurement in timet - tEX expectation of variableX - r number of phases of fermentation - T _i break point of phaseit - t _ij time of measurementj in phasei - t _n–2.1–/2 quantile oft distribution - Y(t) logarithm of measurement at timet Greek Letters 1 – cover probability of tolerance region - 1 – part covered by the tolerance region - ² variance ofe _t - (·) standard normal distribution - quantile of chisquare distribution