Chloride secretion by canine tracheal epithelium: II. The cellular electrical potential profile

Summary We used intracellular microelectrode techniques to study the mechanisms responsible for Cl secretion by canine tracheal epithelium. Tissues were treated with indomethacin (10^–6 m, added to the mucosal solution) to reduce the baseline rate of Cl secretion and then stimulated by addition of epinephrine (10^–6 m) or prostaglandin E₁ (10^–6 m) to the submucosal solution.Three conclusions emerged from our findings: First, secretagogues enhance the rate of transepithelial Cl transport primarily by increasing apical membrane Cl permeability, since: (i) stimulation of secretion produced parallel decreases in transepithelial resistance (R _t) and the membrane resistance ratioR _a/R_b, whereR _a andR _b refer to the resistances of the apical and basolateral membranes; (ii) there was an inverse relation between the short-circuit current andR _a/R_b; (iii) secretagogues depolarized the electrical potential difference across the apical membrane (_a) and produced an equivalent hyperpolarization of the transepithelial electrical potential difference (₁) so that, in the steady-state, the basolateral membrane potential (_b) was unchanged; and (iv) substitution of sulfate or gluconate for Cl in the bathing solutions prevented secretagogue-induced changes inR _t, R_a/R_b, (_a) and (₁).Second, Cl entry into the cell across the basolateral membrane appears to be electrically-neutral since omission of Cl from the submucosal solution had no effect on (_b) and did not decreaseR _a/R_b as would be expected if Cl entered the cell by a conductive process.Third, secretagogues decreaseR _b. Approximately 20 sec after the onset of the secretory responseR _a/R_b underwent a secondary increase whileR _t continued to fall. The decrease inR _b may reflect an increase in basolateral membrane K permeability.     

COMPUTATION OF MODEL-DEPENDENT TOLERANCE BANDS FOR AMBULATORILY MONITORED BLOOD PRESSURE

The construction of time-specified reference limits requires systematic sampling in clinical health, particularly for those variables characterized by a circadian rhythm of large amplitude, as it is the case for blood pressure (BP). For the detection of false negatives, tolerance intervals (limits that will include at least a specified proportion of the population with a stated confidence) are important and should substitute when possible for prediction limits. We have previously described a nonparametric method for the computation of model-independent tolerance intervals that are constructed by first dividing the sampling range in several time spans in which no appreciable changes in population characteristics (namely, mean and variance) take place. The tolerance interval is then computed for each of the time spans. The limits thus computed, as well as results of any comparison of a given individual's profile against such tolerance intervals, are highly dependent on the sampling scheme of both the reference individuals and the test subject. To avoid this problem, we have developed an alternative method that allows the computation of model-dependent tolerance bands for hybrid time series. Assuming that a set X of longitudinal series monitored from a given group of reference individuals can be fitted with the same individual model, a population model C(X,t) can be also determined, as well as the deviation S(X,t) of each individual curve from the population model. The tolerance band will then have the form C(X,t) ± kS(X,t), where k is here estimated following a nonparametric approach based on bootstrap techniques. Alternatively, two different values of k can be estimated (for the lower and upper limits of the tolerance interval, respectively) in cases for which we cannot assume symmetry. The method is generally applicable for any population model describing the reference population (including the fit of multiple significant components, nonsinusoidal waveforms, and/or trends). The method was used to establish time-specified tolerance bands for time series of blood pressure monitored automatically in healthy individuals of both genders. Model-dependent intervals are preferred to the model-independent limits when reliance on a specified sampling rate needs to be avoided. These limits may serve for an objective and positive definition of health, for the screening and diagnosis of disease, and for gauging the subject's response to treatment. (Chronobiology International, 17(4), 567–582, 2000)     

Frequency-domain order parameters for the burst and spike synchronization transitions of bursting neurons

We are interested in characterization of synchronization transitions of bursting neurons in the frequency domain. Instantaneous population firing rate (IPFR) R(t), which is directly obtained from the raster plot of neural spikes, is often used as a realistic collective quantity describing population activities in both the computational and the experimental neuroscience. For the case of spiking neurons, a realistic time-domain order parameter, based on R(t), was introduced in our recent work to characterize the spike synchronization transition. Unlike the case of spiking neurons, the IPFR R(t) of bursting neurons exhibits population behaviors with both the slow bursting and the fast spiking timescales. For our aim, we decompose the IPFR R(t) into the instantaneous population bursting rate R_b(t) (describing the bursting behavior) and the instantaneous population spike rate R_s(t) (describing the spiking behavior) via frequency filtering, and extend the realistic order parameter to the case of bursting neurons. Thus, we develop the frequency-domain bursting and spiking order parameters which are just the bursting and spiking “coherence factors” β_b and β_s of the bursting and spiking peaks in the power spectral densities of R_b and R_s (i.e., “signal to noise” ratio of the spectral peak height and its relative width). Through calculation of β_b and β_s, we obtain the bursting and spiking thresholds beyond which the burst and spike synchronizations break up, respectively. Consequently, it is shown in explicit examples that the frequency-domain bursting and spiking order parameters may be usefully used for characterization of the bursting and the spiking transitions, respectively.     

Measurement of the chlorophyll fluorescence induction kinetics with a 10 µs time resolution and its application in the forest decline research

Summary Measurement methods are described which determine the initial phase of the fluorescence induction kinetics with a maximum time resolution of 10 µs simultaneously for the two fluorescence componentsF ₆₈₅(t) andF ₁₃₀(t) selected by filters at the wavelengths 685 nm and 730 nm, respectively. The excitation light provided by a He-Ne laser (632.8 nm) is switched on within 0.3 µs (maximum intensityI _e=12 mW/cm²).F _o,F _p, andF _s, the initial-, peak-, and steady-state intensity and the initial valueR _o of the ratioR(t)=F ₇₃₀(t)/F ₆₈₅(t) can accurately be determined as well as the initial time derivativeF _o ^* of the fluorescence intensity.F _o andF _o ^* are related to the quantum yield _a of the antenna and to the photochemical quantum yield _pc, respectively. Spruce, oak, birch, poplar, and soy bean show a decline ofR(t) fromR _o to a first minimumR _b at some 10 ms which has a similar value as the second minimumR _p in the time range of seconds. Furthermore, the initial valueR _o and the steady-state valueR _S ofR(t) are also very similar. Measurements on spruce with water deficiency and with varying excitation light intensityI _e show effects on the initial phase of the fluorescence induction kinetics. Further measurements on spruce of different damage classes indicate that for the current year's needles the ratioF _p/F_o, is the most sensitive parameter to differentiate between the damage classes and thatF _o/F_s andR _o/R_b are also affected. As demonstrated by measurements on leaves of soy beans, the initial decrease ofR(t) fromR _o toR _b originates from a change of the fluorescence spectrum because no change of the leaf transmission can be observed in the time range between 10 µs and 1 ms.     

Annual patterns of phytoplankton density and primary production in a large, shallow lake: the central role of light

1. We studied the seasonal dynamics of suspended particulate matter in a turbid, large shallow lake during an annual period (2005–06). We relate the patterns of seston concentration (total suspended solids), phytoplankton biomass and water transparency to the seasonal pattern of incident solar radiation (I₀). We also report the seasonal trends of phytoplankton primary production (PP) and photosynthesis photoinhibition due to photosynthetically active radiation (PAR) and ultraviolet radiation (UVR) (I_β and UV₅₀). 2. We first collected empirical evidence that indicated the conditions of light limitation persisted during the study period. We found that the depth‐averaged irradiance estimated for the time of the day of maximum irradiance (I_mean–noon) was always lower than the measured onset of light saturation of photosynthesis (I_k). 3. We then contrasted the observations with theoretical expectations based on a light limitation scenario. The observed temporal patterns of seston concentration, both on a volume and area basis, were significantly explained by I₀ (R² = 0.39 and R² = 0.37 respectively). The vertical diffuse attenuation coefficient (kd_PAR) (R² = 0.55) and the depth‐averaged irradiance (I_mean) (R² = 0.66), significantly increased with the I₀; while the irradiance reaching the lake bottom (I_out) significantly decreased with the incident irradiance (R² = 0.49). However, phytoplankton biovolume maxima were not coincident with the time of the year of maximum irradiance. 4. A significant positive relationship was observed between PP estimated on an area basis and I₀ (R² = 0.51, P < 0.001). In addition, the parameters describing the photosynthetic responses to high irradiances displayed marked seasonal trends. The photosynthesis photoinhibition due to PAR as well as to UV were significantly related to incident solar radiation (PAR: R² = 0.73; UV: R² = 0.74). These results suggest adaptation of the phytoplankton community in response to changes in incident solar radiation.     

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.     

On the control of tooth replacement in reptiles and its relationship to growth

The teeth of nearly all non-mammalian vertebrates are replaced in waves which sweep through alternate tooth positions. It is argued that tooth replacement in these animals represents growth of the dentition. It is shown that the pattern of tooth replacement could be described by the exponential equation t_(n)r, = k e^ar+bn when t(n)r is the time at which the rth replacement erupts in the nth position and k, a and b are constants. The length of a replacement wave (w) which is visible in the mouth, can be calculated from the equation w = 2(a?b)/a?2b for forward travelling waves. The effect of different ratios, $\text{a}\text{b}$, on wavelength is described. The model can be interpreted as describing the effect of a zone of inhibition which (it is argued) temporarily surrounds any newly initiated tooth. The increasing time required to dissipate the inhibition around successive replacement teeth is related to the age of the animal. This increasing time permits successive teeth to grow for longer periods than their predecessors and can account for a gradual increase in the size of successive teeth. A similar mechanism could account for the phasic nature of bone growth. It is indicated that the model could be difficult to test.     

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     

A simulation program based on a structured population model for biotechnological yeast processes

Summary A segregated population model for budding yeasts and a simulation program based on it are presented. They enable the study of bioprocesses utilizing yeasts in steady and perturbed conditions and in particular the comparison between the model predictions and the experimental results obtained by flow cytometry, which allows the measurement of segregated parameters of cell populations.Nomenclature a genealogical age - A parameter of the budding law - CV coefficient of variation - F _in(t) volumetric input flow - F _out(t) volumetric output flow - h parameter of the division law - K _s parameter of the Monod's law - m cell mass - M _i discretized cell mass - m _b (a,s) critical mass level for budding - m _p cell mass at the time of budding - n(t) cell number per unit volume - n _p number of sub-populations - n _c number of channels - p (a, i, j, k) discrete density function - Q parameter of the budding law - s(t) substrate concentration - S _in(t) substrate concentration in the input flow - t time - T _m minimal length of the budded phase - V(t) culture volume - x(t) biomass concentration - Y yield coefficient - channel width - (s) specific growth rate - _max parameter of the Monod's law     

Interaction of maturation delay and nonlinear birth in population and epidemic models

 A population with birth rate function B(N) N and linear death rate for the adult stage is assumed to have a maturation delay T>0. Thus the growth equation N′(t)=B(N(t−T)) N(t−T) e⁻ d ₁ T−dN(t) governs the adult population, with the death rate in previous life stages d ₁≧0. Standard assumptions are made on B(N) so that a unique equilibrium N _e exists. When B(N) N is not monotone, the delay T can qualitatively change the dynamics. For some fixed values of the parameters with d ₁>0, as T increases the equilibrium N _e can switch from being stable to unstable (with numerically observed periodic solutions) and then back to stable. When disease that does not cause death is introduced into the population, a threshold parameter R ₀ is identified. When R ₀<1, the disease dies out; when R ₀>1, the disease remains endemic, either tending to an equilibrium value or oscillating about this value. Numerical simulations indicate that oscillations can also be induced by disease related death in a model with maturation delay. Received: 2 November 1998 / Revised version: 26 February 1999     

Cell cycle control at the first restriction point and its effect on tissue growth

Cell cycle is controlled at two restriction points, R ₁ and R ₂. At both points the cell will commit apoptosis if it detects irreparable damage. But at R ₁ an undamaged cell also decides whether to proceed to the S phase or go into a quiescent mode, depending on the environmental conditions (e.g., overpopulation, hypoxia). We consider the effect of this decision at the population level in a spherical tissue {r < R(t)}. We prove that if the cells have full control at R ₁, they can manipulate the size of R(t) to ensure that 0 < c ≤ R(t) ≤ C < ∞; simulations further show that R(t) can be made nearly stationary. In the absence of such control, R(t) will either increase to ∞ or decrease to 0. The mathematical model and analysis involve a system of PDEs in {r < R(t)}.     

An approach for parameter estimation of biotechnological processes

An approach for parameter estimators design of biotechnological processes (BTP) is presented in case of lack of real time information about state variables. It is based on general reaction rate models and measurements of at least one reaction rate. A general parameter estimator of BTP is designed with the help of which specific rate estimators are synthesized. Stability and convergence of an estimator of specific growth rate for a class of aerobic batch processes are proved. Its effectiveness is illustrated by simulation results. The proposed on-line parameter estimation approach can be used for design of BTP on-line variable estimation algorithms (variable observers of BTP).List of Symbols X, S, P g/l biomass, substrate and product concentrations - C g/l oxygen concentration in the culture broth - C _sg/l saturation concentration of oxygen in the culture broth - C _in, C_outg/l oxygen concentrations in the input air flow and in the outlet gasphase - F _in, F_outl/h the input air flow in the fermenter and output air flow - OUR g/(lh) oxygen consumption rate - OUR _mg/(lh) measured values of OUR - V l volume - , , l/h specific growth, consumption and synthesis rates - K _La(o) l/h specific volumetric mass transfer coefficient - D l/h dilution rate - R _X, R_S, R_Pg/(lh) biomass growth, substrate consumption and product synthesis rates - K _b matrix of yield coefficients - H_b(), H() matrices of known functions of - H(R) matrix of known functions of R - and gain matrices - a vector of the state variables - () a reactions rates vector, describing qualitative relations among the components - R() a reactions rates vector, describing qualitative and quantitative relations among the components - F a feed rates vector - Q a gaseous outflow rates vector - _b () a vector of unknown functions of - ₁() a vector of functions - (t) a vector of unknown time-varying parameters - ₂(, ) an auxiliary vector-function of and - Y _X/S, Y_X/C, Y_X/P substrate, oxygen and product yield coefficients - b maintenence coefficient - k _i(i=1...6) kinetic coefficients - C _i(i=1,2) design parameters estimate     

The Role of CEC and pH in Cd Retention from Soils of North of Iran

Cadmium (Cd) is a critical environmental chemical in which sorption reactions control its entry into soil solution. The aim of the present study was to evaluate Cd sorption characteristics of some soils of the northern part of Iran with a wide range of physicochemical properties. Duplicates of each sample were equilibrated with solutions containing 5 to 500 mg Cd L^?1 with 0.01 M CaCl₂ as background solution. The quantity of Cd retention was calculated as the difference between initial and equilibrated Cd concentration. Sorption isotherms including Freundlich, Langmuir, Temkin, Dubinin-Radushkevich, and Redlich-Peterson were used to evaluate the behavior of Cd sorption. Cadmium sorption data were well fitted to Langmuir, Freundlich, and Redlich-Peterson isotherms. The constant of Freundlich equation (k_F ) and adsorption maxima (b_L ) of Langmuir equation were related to pH and cation exchange capacity (CEC). The maximum buffering capacity (K_d ) was significantly correlated with pH (R² = 0.52, p ≤ 0.001) and calcium carbonate equivalent (CCE) (R² = 0.63, p ≤ 0.001). Redlich-Peterson constants (k_RP and a_RP ) were significantly correlated with pH (R² k_RP = 0.30, p ≤ 0.007) and (R² a_RP = 0.27, p ≤ 0.012). It seemed that pH, CEC, and CCE were the main soil properties regulating Cd retention behavior of the studied soils.     

Calcium-calcium and calcium-strontium exchange across the membrane of human red cell ghosts

Summary Stationary and nonstationary state⁴⁵Ca fluxes as well as Sr–Ca exchange movements were studied in energy-depleted human erythrocyte ghosts at different intra-and extracellular Ca concentrations. Influx and efflux followed the kinetics of a closed two-compartment system. The influx and efflux rate constants (k _in andk _out, respectively, fractions of total extra- or intracellular⁴⁵Ca that move in one direction per unit time) were similar in magnitude. They decreased with increasing Ca concentration on the cisside and increased with increasing Ca concentration on the trans-side of the membrane. Hence, the fluxes in both directions were characterized by saturation kinetics and appeared to be partially caused by an exchange diffusion mechanism. In the presence of a moderate inward (up to 8mm) or outward (up to 2mm) Ca concentration gradient, k_in andk _out did not vary in the course of an experiment and did not differ significantly from rates which were measured under stationary state conditions. Extracellular Sr induced an outward transport of intracellular Ca against the concentration gradient (counter-transport). The resulting inward Ca concentration gradient (maximal inside-to-outside concentration ratio as 1 to 3) persisted since extra- and intracellular Sr did not equilibrate. Analogous results were obtained studying⁴⁵Ca–⁴⁰Ca countertransport. In net flow experiments Ca–Sr exchange proved to occur on a one-for-one basis. Ca–Sr exchange was additive to the noncoupled Ca and Sr net downhill movements. The experimental results suggest that a specific ATP-independent Ca transfer system exists in the erythrocyte membrane which acts symmetrically on the two sides of the membrane and is restricted to a tightly coupled one-for-one exchange diffusion.     

The Status and the Role of Glutathione under Disturbed Ionic Balance and pH Homeostasis in Escherichia coli

The study of glutathione status in aerobically grown Escherichia coli cultures showed that the total intracellular glutathione (GSH_in + GSSG_in) level falls by 63% in response to a rapid downshift in the extracellular pH from 6.5 to 5.5. The incubation of E. coli cells in the presence of 50 mM acetate or 10 g/ml gramicidin S decreased the total intracellular glutathione level by 50 and 25%, respectively. The fall in the total intracellular glutathione level was accompanied by a significant decrease in the (GSH_in : GSSG_in) ratio. The most profound effect on the extracellular glutathione level was exerted by gramicidin S, which augmented the total glutathione level by 1.8 times and the (GSH_out : GSSG_out) ratio by 2.1 times. The gramicidin S treatment and acetate stress inhibited the growth of mutant E. coli cells defective in glutathione synthesis 5 and 2 times more severely than the growth of the parent cells. The pH downshift and the exposure of E. coli cells to gramicidin S and 50 mM acetate enhanced the expression of the sodA gene coding for superoxide dismutase SodA.     

Stability of the analytical solution of Penna model of biological aging

There are some analytical solutions of the Penna model of biological aging; here, we discuss the approach by Coe et al. (Phys. Rev. Lett. 89, 288103, 2002), based on the concept of self-consistent solution of a master equation representing the Penna model. The equation describes transition of the population distribution at time t to next time step (t + 1). For the steady state, the population n(a, l, t) at age a and for given genome length l becomes time-independent. In this paper we discuss the stability of the analytical solution at various ranges of the model parameters—the birth rate b or mutation rate m. The map for the transition from n(a, l, t) to the next time step population distribution n(a + 1, l, t + 1) is constructed. Then the fix point (the steady state solution) brings recovery of Coe et al. results. From the analysis of the stability matrix, the Lyapunov coefficients, indicative of the stability of the solutions, are extracted. The results lead to phase diagram of the stable solutions in the space of model parameters (b, m, h), where h is the hunt rate. With increasing birth rate b, we observe critical b ₀ below which population is extinct, followed by non-zero stable single solution. Further increase in b leads to typical series of bifurcations with the cycle doubling until the chaos is reached at some b _c. Limiting cases such as those leading to the logistic model are also discussed.     

Regulation of the basolateral potassium conductance of theNecturus proximal tubule

Summary Two methods, the measurement of the response of the basolateral membrane potential (V _bl) of proximal tubule cells ofNecturus to step changes in basolateral K⁺ concentration, and cellular cable analysis, were used to assess the changes in basolateral potassium conductance (G _K) caused by a variety of maneuvers. The effects of some of these maneuvers on intracellular K⁺ activity (a _K ⁱ ) were also evaluated using double-barreled ion-selective electrodes. Perfusion with 0mm K⁺ basolateral solution for 15 min followed by 45 min of 1mm K⁺ solution resulted in a fall in basolateral potassium (apparent) transference number (t _K),V _bl anda _K ⁱ . Results of cable analysis showed that total basolateral resistance,R _b , rose. The electrophysiological effects of additional manipulations, known to inhibit net sodium reabsorption across the proximal tubular epithelium ofNecturus, were also investigated. Ouabain caused a fall int _K accompanied by large decreases ina _K ⁱ andV _bl. Lowering luminal sodium caused a fall int _K and a small reduction inV _bl. Selective reduction of peritubular sodium, a maneuver that has been shown to block sodium transport from lumen to peritubular fluid, also resulted in a significant decrease int _K. These results suggest thatG _K varies directly with rate of transport of the sodium pump, irrespective of the mechanism of change in pump turnover.Part of this material has been presented at the 10th International Conference on Biological Membranes (Cohen & Giebisch, 1984).     

Kinetics of Catalase Inactivation Induced by Ultrasonic Cavitation

Kinetic patterns of sonication-induced inactivation of bovine liver catalase (CAT) were studied in buffer solutions (pH 4.0–11.0) within the temperature range from 36 to 55^o. Solutions of CAT were exposed to LF (20.8 kHz) ultrasound (specific power, 48–62 W/cm²). The kinetics of CAT inactivation was characterized by effective first-order rate constants (s^–1) of total inactivation (k _in), thermal inactivation (*k _in), and ultrasonic inactivation (k _in(us)). In all cases, the following inequality was valid: k _in > *k _in. The value of k _in(us) increased with the ultrasound power (range, 48–62 W/cm²) and exhibited a strong dependence on the pH of the medium. On increasing initial concentration of CAT (0.4–4.0 nM), k _in(us) decreased. The three rate constants were minimum within the range pH 6.5–8.0; their values increased considerably at pH < 6.0 and pH > 9.0. At 36–55^o, the temperature dependence of k _in(us) was characterized by an activation energy (E _act) of 19.7 kcal/mol, whereas the value of E _act for CAT thermoinactivation was equal to 44.2 kcal/mol. Bovine and human serum albumins (BSA and HSA, respectively) inhibited sonication-induced CAT inactivation; complete prevention was observed at concentrations above 2.5 g/ml. Dimethyl formamide (DMFA), a scavenger of hydroxyl radicals (O ), prevented sonication-induced CAT inactivation at 10% (k _in and *k _in increased with the content of DMFA at concentrations in excess of 3%). The results obtained indicate that free radicals generated in the field of ultrasonic cavitation play a decisive role in the inactivation of CAT, which takes place when its solutions are exposed to low-frequency ultrasound. However, the efficiency of CAT inactivation by the radicals is determined by (1) the degree of association between the enzyme molecules in the reaction medium and (2) the composition thereof.     

On the Analysis and Synthesis of a Four-Field-Table

The real four-field-table measure k is calculable as follows: K₁ for V(a, b, c, d) with k₁ = (arc K₁)/100, K₁₁ for V(a, b, 0, 0) with k₁₁ = (arc K₁₁)/100, K₁₂ for V(c, d, 0, 0) with k₁₂ = (arc K₁₂)/100 and K₁₂₁ for V(0, 0, c, d) with k₁₂₁ = – k₁₂. The equation k₁ = k₁₁ – k₁₂ holds good. It is possible to calculate the probability of error of a four-field-table with small frequencies, indirectly from component values. Two examples are given.     

Almost-one Parameter Hypothesis of Individuality in Height Growth

Thus far an individual height growth curve h_ij(t) of the i-th person in the j-th period, t being his (or her) age, has been studied as a function of t associated with its velocity curve. In this note we introduce a natural scale X(t) in place of t, which linearizes this personal curve and facilitates its analysis, in the sense that this equation of growth contains apparently two personal parameters for one period but one of them plays an essential role. The effectiveness of this approach will be seen in four figures.