The proportion of mutants in bacterial cultures

The proportion of mutants in a growing culture of organisms will depend upon (a) the rate at which the wild cells produce them (with or without growth), (b) the back mutation rate, and (c) the growth rates of the wild and mutant cells. If the mutation rate without growth and the back mutation rate are neglected, the growth of a mutant is expressed by See PDF for Equation and the ratio of the mutant to wild by See PDF for Equation in which λ = mutation frequency rate constant, "mutation rate," A = growth rate constant of wild cells W, B = growth rate constant of mutant cells M. If the term [B – (1 – 2λ)A] is positive, the proportion of mutants increases continuously. If it is negative, the proportion of mutants reaches a constant value See PDF for Equation If mutation is assumed to occur without growth at the rate C, then the corresponding equations are (11), (12), and (14). See PDF for Equation If (B + C – A) is negative and t = ∞, See PDF for Equation If C << A, See PDF for Equation     

THE KINETICS OF PENETRATION : I. EQUATIONS FOR THE ENTRANCE OF ELECTROLYTES

When the only solute present is a weak acid, HA, which penetrates as molecules only into a living cell according to a curve of the first order and eventually reaches a true equilibrium we may regard the rate of increase of molecules inside as See PDF for Equation where P_M is the permeability of the protoplasm to molecules, M_o, denotes the external and M_i the internal concentration of molecules, A_i denotes the internal concentration of the anion A^- and See PDF for Equation (It is assumed that the activity coefficients equal 1.) Putting P_MF_M = V_M, the apparent velocity constant of the process, we have See PDF for Equation where e denotes the concentration at equilibrium. Then See PDF for Equation where t is time. The corresponding equation when ions alone enter is See PDF for Equation. where K is the dissociation constant of HA, P_A is the permeability of the protoplasm to the ion pair H⁺ + A^-, and A_ie denotes the internal concentration of A_i at equilibrium. Putting P_AKF_M = V_A, the apparent velocity constant of the process, we have See PDF for Equation and See PDF for Equation When both ions and molecules of HA enter together we have See PDF for Equation where S_i = M_i + A_i and S_ie is the value of S_i at equilibrium. Then See PDF for Equation V_M, V_A, and V_MA depend on F_M and hence on the internal pH value but are independent of the external pH value except as it affects the internal pH value. When the ion pair Na⁺ + A^- penetrates and Na_i = BA_i, we have See PDF for Equation and See PDF for Equation where P _NaA is the permeability of the protoplasm to the ion pair Na⁺ + A^-, Na_o and Na_i are the external and internal concentrations of Na⁺, See PDF for Equation, and V _Na is the apparent velocity constant of the process. Equations are also given for the penetration of: (1) molecules of HA and the ion pair Na⁺ + A^-, (2) the ion pairs H⁺ + A^- and Na⁺ + A^-, (3) molecules of HA and the ion pairs Na⁺ + A^- and H⁺ + A^-. (4) The penetration of molecules of HA together with those of a weak base ZOH. (5) Exchange of ions of the same sign. When a weak electrolyte HA is the only solute present we cannot decide whether molecules alone or molecules and ions enter by comparing the velocity constants at different pH values, since in both cases they will behave alike, remaining constant if F_M is constant and falling off with increase of external pH value if F_M falls off. But if a salt (e.g., NaA) is the only substance penetrating the velocity constant will increase with increase of external pH value: if molecules of HA and the ions of a salt NaA. penetrate together the velocity constant may increase or decrease while the internal pH value rises. The initial rate See PDF for Equation (i.e., the rate when M_i = 0 and A_i = 0) falls off with increase of external pH value if HA alone is present and penetrates as molecules or as ions (or in both forms). But if a salt (e.g., NaA) penetrates the initial rate may in some cases decrease and then increase as the external pH value increases. At equilibrium the value of M_i equals that of M_o (no matter whether molecules alone penetrate, or ions alone, or both together). If the total external concentration (S_o = M_o + A_o) be kept constant a decrease in the external pH value will increase the value of M_o and make a corresponding increase in the rate of entrance and in the value at equilibrium no matter whether molecules alone penetrate, or ions alone, or both together. What is here said of weak acids holds with suitable modifications for weak bases and for amphoteric electrolytes and may also be applied to strong electrolytes.     

THE COUPLED REDOX POTENTIAL OF THE LACTATE-ENZYME-PYRUVATE SYSTEM

1. The term "coupled redox potential" is defined. 2. The system lactic ion See PDF for Equation pyruvic ion + 2H⁺ + 2e is shown to be reversible (when the enzyme is lactic acid dehydrogenase) and its coupled redox potential between pH 5.2 and 7.2 at 32°C. is: See PDF for Equation 3. The free energy of the reaction: lactic ion (1m) → pyruvic ion (1m) = -ΔF = –14,572. 4. The standard free energy of formation (ΔF ₂₉₈) of pyruvic acid (l) is estimated at –108,127. This is merely an approximation as some necessary data are lacking. 5. The importance of coupled redox potentials as a factor in the regulation of the equilibrium of metabolites is indicated.     

THE EFFECT OF ADVANCE IN LACTATION AND GESTATION ON MAMMARY ACTIVITY

The rate of milk secretion in farrow cows may be expressed as See PDF for Equation, in which y = yield and t = time from calving. Pregnancy causes a decrease in yield which may be expressed as See PDF for Equation, in which i = inhibition or decrease in yield and p = time from conception. The constant K appears to be the same for various groups but b is roughly proportional to a. The decrease in yield associated with pregnancy is interpreted as due to a hormone. The hormone hypothesis also affords an interpretation of the increasing rate of milk secretion which occurs for a short time following parturition.     

THE ELECTRIC RESISTANCE AND CAPACITY OF BLOOD FOR FREQUENCIES BETWEEN 800 AND 4? MILLION CYCLES

1. The variation of the experimental values (R (ω)), (C (ω)) of the resistance and capacity of blood for increasing frequencies is approximately represented by the equation: See PDF for Equation in which R _o and C _o are the resistance and capacity of the blood at low frequency and See PDF for Equation is the resistance of the blood at infinite frequency. Formulæ (1) and (2) are derived by considering the blood as equivalent to the system shown in the diagram (a) of Fig. 1. 2. By the application of formula (1) to our experimental data the value of R(∞) can be extrapolated with high accuracy. R(∞) represents the resistance) which would have been obtained at low frequency, if the membranes around the corpuscles could have been removed. 3. The specific resistance of the corpuscle interior can be calculated by equation (5), using experimental values for R(∞), for the volume concentration of the blood and for the specific resistance of the serum. 4. The specific resistance of the interior of the red corpuscle of the calf is found to be 3.5 ± 10 per cent times the specific resistance of the serum.     

Theoretical series elastic element length in Rana pipiens sartorius muscles

Assuming a two component system for the muscle, a series elastic element and a contractile component, the analyses of the isotonic and isometric data points were related to obtain the series elastic stiffness, dP/dl_s, from the relation, See PDF for Equation From the isometric data, dP/dt was obtained and shortening velocity, v, was a result of the isotonic experiments. Substituting (P₀ - P)/T for dP/dt and (P₀ - P)/(P + a) times b for v, dP/dl_s = (P + a) /bT, where P < P₀, and a, b are constants for any lengths l ≤ l₀ (Matsumoto, 1965). If the isometric tension and the shortening velocity are recorded for a given muscle length, l₀, although the series elastic, l_s, and the contractile component, l_c, are changing, the total muscle length, l₀ remains fixed and therefore the time constant, T. Integrating, See PDF for Equation the stress-strain relation for the series elastic element, See PDF for Equation is obtained; l_sc0 - l_s + l_c0where l_co equals the contractile component length for a muscle exerting a tension of P₀. For a given P/P₀, l_s is uniquely determined and must be the same whether on the isotonic or isometric length-tension-time curve. In fact, a locus on one surface curve can be associated with the corresponding locus on the other.     

Non-Linear Current-Potential Relations in an Axon Membrane

The membrane current density, I_m, in the squid giant axon has been calculated from the measured external current applied to the axon, I_o, by the equation See PDF for Equation where V_m is the membrane potential under the current electrode and r₁ and r₂ are the external and internal longitudinal resistances. The original derivation of this equation included in one step an assumption of a linear relation between I_m and V_m. It is shown that the same equation can be obtained without this restricting assumption.     

THE ORIENTATION OF ANIMALS BY OPPOSED BEAMS OF LIGHT

When orientation is attained under the influence of beams of parallel light opposed at 180° the deflection θ from a path at right angles to the beams is given by tan See PDF for Equation, where I ₁ and I ₂ are the photic intensities and H is the average angle between the photoreceptive surfaces. This expression is independent of the units in which I is measured, and holds whether the primary photosensory effect is proportional to I or to log I. When photokinetic side-to-side motions of the head occur, H decreases with increasing total acting light intensity, but increases if higher total light intensity restricts the amplitude of random movements; in each case, H is very nearly proportional to log I ₁ I ₂. For beams of light at 90°, See PDF for Equation. The application of these equations to some particular instances is discussed, and it is shown why certain simpler empirical formulæ previously found by others yield fair concordance with the experimental data. The result is thus in complete accord with the tropism theory, since the equations are based simply on the assumption that when orientation is attained photic excitation is the same on the two sides.     

CONTRIBUTION TO THE THEORY OF PERMEABILITY OF MEMBRANES FOR ELECTROLYTES

On page 39, Vol. viii, No. 2, September 18, 1925, multiply the right-hand side of formula (2) by the factor See PDF for Equation. On page 44, immediately after formula (1) the text should be continued as follows: Let us suppose a membrane to be separated by two solutions of KCl of different concentrations K₁ and K₂ and these concentrations and the corresponding concentrations of K⁺ within the membrane, which are in equilibrium with the outside solutions, to be so high that the H⁺ ions may be neglected. When a small electric current flows across the system, practically the K⁺ ions alone are transferred and that in a reversible manner. Therefore the total P.D. is practically See PDF for Equation This P.D. is composed of two P.D.''s at the boundaries and the diffusion potential within the membrane. Suppose the immobility of the anions is not absolute but only relative as compared with the mobility of the cations, KCl would gradually penetrate into the membrane to equal concentration with the outside solution on either side and no boundary potential would be established. In this case the diffusion P.D. within the membrane is the only P.D., amounting to See PDF for Equation but, V being practically = 0, it would result that See PDF for Equation So the definitive result is the same as in the former case. Now cancel the printed text as far as page 48, line 13 from the top of the page, but retain Fig. 1. On page 50, line 19 from the top of the page, cancel the sentence beginning with the word But and ending with the words of the chain.     

THEORY AND MEASUREMENT OF VISUAL MECHANISMS : XI. ON FLICKER WITH SUBDIVIDED FIELDS

In Vol. 27, No. 5, May 20, 1944, page 403, in the eighth line from the bottom of the page, the comma after "intensity" should be a semicolon. On page 413, in the second formula from the bottom of the page, for See PDF for Equation read See PDF for Equation On the same page, formula 2 should read See PDF for Equation On page 414, line 3, at the end of the line add "or" to read "of the level of I or of F." On page 422, in the first line below the figure legend, for "illuminate" read "illuminated." On page 430, line 22, for "lighteb dars" read "lighted bars."     

THE SWELLING OF ISOELECTRIC GELATIN IN WATER : I. EQUILIBRIUM CONDITIONS.

The swelling of isoelectric gelatin in water has been found to be in agreement with the following assumptions. Gelatin consists of a network of insoluble material containing a solution of a more soluble substance. Water therefore enters owing to the osmotic pressure of the soluble material and thereby puts the network under elastic strain. The process continues until the elastic force is equal to the osmotic pressure. If the temperature is raised or the blocks of gelatin remain swollen over a period of time, the network loses its elasticity and more water enters. In large blocks this secondary swelling overlaps the initial process and so no maximum can be observed. The swelling of small blocks or films of isoelectric gelatin containing from .14 to .4 gm. of dry gelatin per gm. of water is defined by the equation See PDF for Equation in which K_e = the bulk modulus See PDF for Equation. V_e = gm. water per gm. gelatin at equilibrium; V_f = gm. water per gm. gelatin when the gelatin solidified.     

ON THE RATE OF REACTION BETWEEN ENZYME AND SUBSTRATE

1. An equation of the form: See PDF for Equation in which v_t is the time of flow of the mixture, v_w the time of flow for water, v_f the time of flow of the mixture when proteolysis is complete, v_o the time of flow at the beginning of the experiment, t the time of observation, and r a constant, has been found to describe accurately the course of change of viscosity in a mixture of gelatin and pancreatin. 2. An equation of the same general form has been found to apply similarly to the reaction between other enzymes and other substrates. 3. The equation may be derived theoretically from assuming a bimolecular reaction between enzyme and substrate obeying the mass action law.     

The proportion of terramycin-resistant mutants in B. megatherium cultures

The number of terramycin-resistant mutants in Bacillus megatherium cultures, their mutation rate, and the growth rate of the wild and mutant cells have been determined under various conditions. These values are in agreement with the following equations (Northrop and Kunitz, 1957):— See PDF for Equation λ = mutation rate, A = growth rate constant of wild cells, B = growth rate constant of mutants, See PDF for Equation equilibrium. The value of the mutation rate as determined from equation (6) agrees with that found by the null fraction method.     

Rate of excretion of N15 after feeding N15-labeled l-aspartic acid in man

1. l-Aspartic acid labeled with N¹⁵ was fed to one human adult and six infants, and the total N and N¹⁵ were determined in the urine from time to time. 2. The N¹⁵ concentration (or isotopic ratio) of urinary N reached its maximum in the adult about 2 hours and in the infants about 4 hours after feeding, then fell off logarithmically. 3. Assuming that the N of aspartic acid readily entered into equilibrium with other N compounds in the pool, the rate of turnover of the N pool was calculated from the rate of fall of the isotopic ratio of urinary N. This rate of turnover of N was about 4 per cent per hour in the adult and 6 to 12 per cent per hour in the infants. 4. The rate of protein synthesis calculated from the rate of turnover of N was 10 mg. N per kilo per hour in the adult and 18 to 27 mg. N per kilo per hour in the infants, with one exception which showed a higher rate of 52 mg. N per kilo per hour. The size of the metabolic pool of N per kilo in non-growing infants was about the same as that in the adult (0.4 to 0.5 gm.) but it was somewhat larger in growing infants (0.5 to 0.8 gm.).     

Gas chromatography-mass spectrometry determination of [15N]ammonia enrichment in blood and urine

A rapid gas chromatography-mass spectrometry method for [¹⁵N]ammonia analysis is deseribed which is based on the formation of [¹⁵N]glutamic acid from ammonia and analysis of isotopic abundance in the N-trifluoroacetyl-n-butylester glutamate derivative. Mean recovery of [¹⁵N]ammonia added to either plasma or urine was greater than 99% with a relative standard deviation of less than 10%. The method can be applied to the determination of extremely low levels of ammonia through an isotope dilution technique. The [¹⁵N]ammonia abundance of blood and urine was determined in an adult following on oral dose (500 mg) of ¹⁵NH₄Cl. A peak isotopic abundance of 13 atoms% excess was reached by 30 min. Urinary excretion of [¹⁵N]ammonia during the first 4 h after administration of the isotope amounted to 4.1% of the isotope administered.     

Transient Phases of the Isometric Tetanus in Frog's Striated Muscle

In an isometric tetanus in frog's sartorius muscle tension approaches the plateau exponentially with rate constant α. α a depends on sarcomere length, s, and temperature, T, according to the Arrhenius equation See PDF for Equation for temperatures between 1 and 20°C and for sarcomere lengths 2.0–2.8 µm. The energy of activation, E, does not vary significantly with s; E = 13.9 ± 2.4 kcal/mole. A(s) decreases monotonically with s; A(2.1 µm) is about three times greater than A(2.8 µm). Late in relaxation active tension approaches zero exponentially with rate constant r. r decreases exponentially with increasing duration of tetanus, D, from r₀ in a twitch to r_∞ for large D. The rate constant for decrease of r with D increases with s and with T. r₀ and r_∞ obey the Arrhenius equation and decrease with increasing s.     

EFFECTS OF LOW NITROGEN LEVELS AND VARIOUS NITROGEN SOURCES ON GROWTH AND WHORL DEVELOPMENT IN ACETABULARIA (CHLOROPHYTA)1

Nitrate, ammonia, urea, and glycine were compared as nitrogen sources for Acetabularia mediterranea. Cells grew normally in media containing nitrate or urea, while cells did not grow at all when the same amount of N was supplied as ammonium ion. The utilization of glycine remains questionable. Cells in medium without added N (NDM) increased in length and some formed reproductive caps. The whorls of vegetative cells showed considerable hypertrophy in NDM and in glycine. This hypertrophy was due to the elongation of only the first-(a₁) and second- (a₂) order articles. When cut, the basal portion of cells without added N regenerated new apices with whorls. The development of these whorls was inversely proportional to the NO₂ concentration. Analyses showed that the intracellular nitrogen pool in young cells and regenerating bases was very small, about 1/10 of that of fully grown cells. Therefore we suggest that trace amounts of N contaminants in the medium supported growth and development, the uptake of which was facilitated by the hypertrophied whorls, under N-limited conditions.     

Disposition of intraperitoneally injected calcium-45 in suckling rats

The time course of the concentration of radiocalcium was studied in the serum, skeleton, pelt, muscles, and pooled internal organs of 10-day-old rats. Within 10 hours of injection, the specific activity of the tissue groups exceeded the specific activity of the serum and remained above it during the period studied (120 hours). Chemical and autoradiographic analyses showed how rapidly most of the injected Ca⁴⁵ found its way into the skeleton. A model was constructed with the assumption that the skeleton constitutes an essentially irreversible reservoir for the tracer in a multicompartment system in which the blood is the central or feeding compartment. The rate of transfer of the tracer from the soft tissue compartments to the serum was calculated from the equation See PDF for Equation in which C = concentration in serum (expressed as a series of exponential terms) C' = concentration in a given soft tissue Substitution in the integrated form of this equation yielded equations which had the major properties of the empirical equations fitted to the experimental points. The relative order of transfer constants (k'_–1) was: organs ≥ pelt > muscle.     

Tracer priming in human protein turnover studies with [15N]glycine

Sixty-three studies in healthy normal volunteers (n = 29), malnourished cancer (n = 8) or non-cancer patients (n = 9), and postoperative radical cystectomy patients (n = 17) were conducted to evaluate the primed constant infusion labeling technique for the estimation of whole-body protein turnover under a variety of dietary conditions. [15N]Glycine was used as the tracer with a prime to infusion ratio of 1300 to 3300 min and a continuous-infusion rate of 0.11 to 0.33 micrograms 15N . kg-1 . min-1 for 24 to 36 hr. The isotopic steady-state enrichment was reached in all subjects both in urinary urea and ammonia between 10 and 26 hr (mean 18 +/- 2). During protein calorie fasting the attainment of isotopic steady state is much quicker (10 to 18 hr) with a primed constant infusion than with a constant infusion alone (approximately 38 hr). A P/I ratio greater or less than 1800 (min) usually resulted in a delay of plateau attainment without affecting the protein turnover values. Reliable estimates of protein kinetics in humans can be made in clinical conditions with a 26-hr infusion of glycine at the rate of 0.28 microgram 15N . kg-1 . min-1 with a P/I ratio of 1800 min, collecting six urine samples every 2 hr from 16 hr and analyzing for both urinary urea and ammonia enrichments.     

THE EFFECT OF RADIOACTIVE RADIATIONS AND X-RAYS ON ENZYMES : IV. THE EFFECT OF RADIATIONS FROM RADIUM EMANATION ON SOLUTIONS OF INVERTASE.

The radiochemical inactivation of invertase by beta radiation from the radioactive products in equilibrium with radium emanation can be explained quantitatively on the same basis as that of trypsin and pepsin previously reported; namely, the rate of change in the logarithm of the concentration of the active enzyme with respect to the variable, W, is constant, under the conditions of irradiation described, when the volume of solution exposed is constant. When, within the limits stated in this paper, this volume (V) is varied, the rate of radiochemical change is inversely proportional to V; i.e., See PDF for Equation