THE NATURE OF THE FACTORS WHICH DETERMINE THE SEQUENCE OF GROWTH-CYCLES AND ITS RELATIONSHIP TO THE DIFFERENTIATION OF TISSUES

1. It has previously been shown by the author and many others that growth, in animals and plants, is an autocatalysed process. In animals it is usual to find that growth occurs in several superimposed autocatalytic cycles. In many cases, in plants and animals, especially if the cycle is one which occupies a large proportion of the growing period, it is found that the velocity-constant of the autocatalysed monomolecular formula falls off as growth proceeds, at first rapidly and later more slowly. 2. It has previously been shown by the author that the fall of the velocity-constant of growth, in the white mouse, is directly proportional to the fall of the nucleo-cytoplasmic ratio, determined by the chemical method of Le Breton and Schaeffer. If we assume this relationship to be generally applicable to the growth of animals and plants, then the following additional conclusions may be deduced, without calling in the aid of any other assumption:— 3. The increase of cytoplasm in any given cycle of growth is proportional to the concurrent increase of nuclear material. 4. The growth of cytoplasm takes place in accordance with a monomolecular formula in which the velocity-constant varies directly as the mass of the nucleus. If we superadd to these facts and deductions the hypothesis that each growth-cycle represents the growth of a separate group of cells within the animal, then the additional conclusions follow:— 5. That the cells which participate in the growth composing any cycle have initially lower nucleo-cytoplasmic ratios than the cells which participated in the preceding cycles. 6. That cells of large nucleo-cytoplasmic ratios in a multicellular animal inhibit the growth of cells which possess smaller ratios. 7. These conclusions collectively imply that the nucleus plays a predominant role in determining the development of the cell in which it resides.     

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 VISUAL INTENSITY DISCRIMINATION OF THE HONEY BEE

1. Bees respond by a characteristic reflex to a movement in their visual field. By confining the field to a series of parallel stripes of different brightness it is possible to determine at any brightness of one of the two stripe systems the brightness of the second at which the bee will first respond to a displacement of the field. Thus intensity discrimination can be determined. 2. The discriminating power of the bee''s eye varies with illumination in much the same way that it does for the human eye. The discrimination is poor at low illumination; as the intensity of illumination increases the discrimination increases and seems to reach a constant level at high illuminations. 3. The probable error of See PDF for Equation decreases with increasing I exactly in the same way as does See PDF for Equation itself. The logarithm of the probable error of ΔI is a rectilinear function of log I for all but the very lowest intensities. Such relationships show that the measurements exhibit an internal self-consistency which is beyond accident. 4. A comparison of the efficiency of the bee''s eye with that of the human eye shows that the range over which the human eye can perceive and discriminate different brightnesses is very much greater than for the bee''s eye. When the discrimination power of the human eye has reached almost a constant maximal level the bee''s discrimination is still very poor, and at an illumination where as well the discrimination power of the human eye and the bee''s eye are at their best, the intensity discrimination of the bee is twenty times worse than in the human eye.     

THE FUNCTION OF THE BRAIN IN LOCOMOTION OF THE POLYCLAD WORM,YUNGIA AURANTIACA

Coordinated swimming movements in Yungia are not dependent upon the presence of the brain. The neuromuscular mechanism necessary for spontaneous movement and swimming is complete in the body of the animal apart from the brain. Normally this mechanism is set in motion by sensory stimulation arriving by way of the brain. The latter is a region of low threshold and acts as an amplifier by sending the impulses into a great number of channels. When the head is cut off these connections with the sensorium are broken, consequently peripheral stimulation does not have its usual effect. If, however, the motor nerves are stimulated directly as by mechanical stimulation of the median anterior region, then swimming movements result. Also if the threshold of the entire nervous mechanism is lowered by phenol or by an increase in the ion ratios See PDF for Equation and See PDF for Equation then again peripheral stimulation throws the neuromuscular mechanism into activity and swimming movements result.     

THE RATE OF GROWTH OF THE DOMESTIC FOWL

This paper points out the fact that the growth period of the domestic fowl is analogous to that of the mammal, being composed of three, or perhaps four, cycles; two of these cycles are postembryonic with maxima at about 8 and 18 weeks varying somewhat with the breed and two or at least one, are embryonic with maxima at 11 to 12 and 15 to 16 days of age. Hatching occurs during the first part of the second or third cycle resembling in this respect the guinea pig rather than the mouse. The velocity curves of each of these cycles are similar to and can be represented by the equation of an autocatalytic monomolecular reaction.     

NUMERICAL LAW OF REGRESSION OF CERTAIN SECONDARY SEX CHARACTERS

The discrepancy in the relative variation of C and of θ led us to examine more closely the velocity of regression at the beginning in all the cases. At a given point of the curve, the velocity is furnished by the differential quotient of the length with reference to the time: See PDF for Equation At the beginning of regression, that is to say, at the time 0 See PDF for Equation We have tabulated the corresponding numerical values in the various instances: See PDF for Structure Although there is not absolute equality among the figures of the last column, one cannot fail to be struck by the fact that there is very little difference; in all instances they diverge much less than those of the first two columns, in which the variation is from 0.5 to 4.75 and from 1.95 to 12.0. We must admit, therefore, within rather wide limits, the constancy of the product of the time of regression and the constant C, whether the castration is intrapuberal or post-puberal. Geometrically, this result is represented by the constancy of the angle of the ordinate and the tangent to the parabola at the point of departure of the regression curve. Furthermore, it follows that the numerical law is represented not only by a parabola, but more exactly by segments of homothetic parabolas—an unexpected generalization, which gives a remarkable unity to the law with which it is concerned.     

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 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 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     

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.     

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.     

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 KINETICS OF EXOSMOSIS OF WATER FROM LIVING CELLS

1. The rate of exosmosis of water was studied in unfertilized Arbacia eggs, in order to bring out possible differences between the kinetics of exosmosis and endosmosis. 2. Exosmosis, like endosmosis, is found to follow the equation See PDF for Equation, in which a is the total volume of water that will leave the cell before osmotic equilibrium is attained, x is the volume that has already left the cell at time t, and k is the velocity constant. 3. The velocity constants of the two processes are equal, provided the salt concentration of the medium is the same. 4. The temperature characteristic of exosmosis, as of endomosis, is high. 5. It is concluded that the kinetics of exosmosis and endosmosis of water in these cells are identical, the only difference in the processes being in the direction of the driving force of osmotic pressure.     

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.     

A SIMPLE TIME WEIGHT RELATION OBSERVED IN WELL NOURISHED RATS

The equation See PDF for Equation fits the growth of well nourished rats from weaning on. The general properties of the equation, and particularly its relation with the law of relative growth, are discussed.     

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.     

THE INFLUENCE OF X-RAYS ON THE PROPERTIES OF BLOOD

When rabbits are exposed to x-radiation as described, there results a definite change in the See PDF for Equation ratio of their plasma. This change is evidently one which defines a state of uncompensated alkali excess. The time required for a maximum change in the chemical reaction is the same as that required for a maximum change in the decrease of leucocytes. Sodium bicarbonate injected into the peritoneal cavity is followed by results identical with those observed following exposure to x-rays. The maximum changes occur in a shorter time following bicarbonate injection, but the relation between chemical and morphological changes are the same. We consider this analogy to be an important one in that it is suggestive of a relationship between the effect of salt and the effect of x-rays.     

THE PHOTOTROPIC EXCITATION OF LIMAX

The photic orientation of Limax creeping geotropically upon a vertical plate is such that the phototropic vector determining the angular deflection β from the vertical path is proportional to log I. This is proved by the fact that with horizontal illumination tan β is directly proportional to log I; with non-horizontal light rays from a small source the ratio See PDF for Equation is directly proportional to log I (where A = the angle between light rays and the path of orientation), the vector diagram of the field of excitation being in this case not a right-angled triangle.     

THE EFFECT OF RADIO-ACTIVE RADIATIONS AND X-RAYS ON ENZYMES : I. THE EFFECT OF RADIATIONS FROM RADIUM EMANATION ON SOLUTIONS OF TRYPSIN.

A quantitative study has been made of the radiochemical decomposition of trypsin by the radiations from radium emanation. The following equation accounts quantitatively for the experimental results presented. See PDF for Equation It follows from this that the amount of trypsin decomposed by the radiations from radium emanation depends on the concentration of trypsin present and is proportional to the quantity of emanation expressed in millicuries and to the time of irradiation expressed in hours. It would seem that it is the active or undissociated trypsin that is affected. Evidence has been found which suggests that the beta radiations produce the decomposition observed for which the above statement holds. Qualitative evidence has been found which suggests that x-rays, gamma rays, and beta rays produce identical effects in dilute trypsin solutions.