SYNERESIS AND SWELLING OF GELATIN

1. When solid blocks of isoelectric gelatin are placed in cold distilled water or dilute buffer of pH 4.7, only those of a gelatin content of more than 10 per cent swell, while those of a lower gelatin content not only do not swell but actually lose water. 2. The final quantity of water lost by blocks of dilute gelatin is the same whether the block is immersed in a large volume of water or whether syneresis has been initiated in the gel through mechanical forces such as shaking, pressure, etc., even in the absence of any outside liquid, thus showing that syneresis is identical with the process of negative swelling of dilute gels when placed in cold water, and may be used as a convenient term for it. 3. Acid- or alkali-containing gels give rise to greater syneresis than isoelectric gels, after the acid or alkali has been removed by dialysis. 4. Salt-containing gels show greater syneresis than salt-free gels of the same pH, after the salt has been washed away. 5. The acid and alkali and also the salt effect on syneresis of gels disappears at a gelatin concentration above 8 per cent. 6. The striking similarity in the behavior of gels with respect to syneresis and of gelatin solutions with respect to viscosity suggests the probability that both are due to the same mechanism, namely the mechanism of hydration of the micellæ in gelatin by means of osmosis as brought about either by diffusible ions, as in the presence of acid or alkali, or by the soluble gelatin present in the micellæ. The greater the pressures that caused swelling of the micellæ while the gelatin was in the sol state, the greater is the loss of water from the gels when the pressures are removed. 7. A quantitative study of the loss of water by dilute gels of various gelatin content shows that the same laws which have been found by Northrop to hold for the swelling of gels of high concentrations apply also to the process of losing water by dilute gels, i.e. to the process of syneresis. The general behavior is well represented by the equations: See PDF for Equation and See PDF for Equation where P ₁ = osmotic pressure of the soluble gelatin in the gel, P ₂ = stress on the micellæ in the gelatin solution before setting, K_e = bulk modulus of elasticity, V_o = volume of water per gram of dry gelatin at setting and V_e = volume of water per gram of gelatin at equilibrium.     

THE KINETICS OF OSMOTIC SWELLING IN LIVING CELLS

The rate of swelling of unfertilized sea urchin eggs in hypotonic sea water was investigated. Analysis of curves leads to the following conclusions. 1. The rate of swelling follows the equation, See PDF for Equation where V _eq., V ₀, and V_t stand for volume at equilibrium, at first instant, and at time t, respectively, the other symbols having their usual significance. This equation is found to hold over a wide range of temperatures and osmotic pressures. This relation is the one expected in a diffusion process. 2. The rate of swelling is found to have a high temperature coefficient (Q ₁₀ = 2 to 3, or µ = 13,000 to 19,000). This deviation from the usual effect of temperature on diffusion processes is thought to be associated with changes in cell permeability to water. The possible influence of changes in viscosity is discussed. 3. The lower the osmotic pressure of the solution, the longer it takes for swelling of the cell. Thus at 15° in 80 per cent sea water, the velocity constant has a value of 0.072, in 20 per cent sea water, of 0.006.     

HYDRATION OF GELATIN IN SOLUTION

1. It was shown that the high viscosity of gelatin solutions as well as the character of the osmotic pressure-concentration curves indicates that gelatin is hydrated even at temperatures as high as 50°C. 2. The degree of hydration of gelatin was determined by means of viscosity measurements through the application of the formula See PDF for Equation. 3. When the concentration of gelatin was corrected for the volume of water of hydration as obtained from the viscosity measurements, the relation between the osmotic pressure of various concentrations of gelatin and the corrected concentrations became linear, thus making it possible to determine the apparent molecular weight of gelatin through the application of van''t Hoff''s law. The molecular weight of gelatin at 35°C. proved to be 61,500. 4. A study was made of the mechanism of hydration of gelatin and it was shown that the experimental data agree with the theory that the hydration of gelatin is a pure osmotic pressure phenomenon brought about by the presence in gelatin of a number of insoluble micellæ containing a definite amount of a soluble ingredient of gelatin. As long as there is a difference in the osmotic pressure between the inside of the micellæ and the outside gelatin solution the micellæ swell until an equilibrium is established at which the osmotic pressure inside of the micellæ is balanced by the total osmotic pressure of the gelatin solution and by the elasticity pressure of the micellæ. 5. On addition of HCl to isoelectric gelatin the total activity of ions inside of the micellæ is greater than in the outside solution due to a greater concentration of protein in the micellæ. This brings about a further swelling of the micellæ until a Donnan equilibrium is established in the ion distribution accompanied by an equilibrium in the osmotic pressure. Through the application of the theory developed here it was possible actually to calculate the osmotic pressure difference between the inside of the micellæ and the outside solution which was brought about by the difference in the ion distribution. 6. According to the same theory the effect of pH on viscosity of gelatin should diminish with increase in concentration of gelatin, since the difference in the concentration of the protein inside and outside of the micellæ also decreases. This was confirmed experimentally. At concentrations above 8 gm. per 100 gm. of H₂O there is very little difference in the viscosity of gelatin of various pH as compared with that of isoelectric gelatin.     

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.     

AMPHOTERIC COLLOIDS : III. CHEMICAL BASIS OF THE INFLUENCE OF ACID UPON THE PHYSICAL PROPERTIES OF GELATIN.

1. The method of removing the excess of hydrobromic acid after it has had a chance to react chemically with gelatin has permitted us to measure the amount of Br in combination with the gelatin. It is shown that the curves representing the amount of bromine bound by the gelatin are approximately parallel with the curves for the osmotic pressure, the viscosity, and swelling of the gelatin solution. This proves that the curves for osmotic pressure are an unequivocal function of the number of gelatin bromide molecules formed under the influence of the acid. The cc. of 0.01 N Br in combination with 0.25 gm, of gelatin we call the bromine number. 2. The explanation of this influence of the acid on the physical properties of gelatin is based on the fact that gelatin is an amphoteric electrolyte, which at its isoelectric point is but sparingly soluble in water, while its transformation into a salt with a univalent anion like gelatin Br makes it soluble. The curve for the bromine number thus becomes at the same time the numerical expression for the number of gelatin molecules rendered soluble, and hence the curve for osmotic pressure must of necessity be parallel to the curve for the bromine number. 3. Volumetric analysis shows that gelatin treated previously with HBr is free from Br at the isoelectric point as well as on the more alkaline side from the isoelectric point (pH ≧ 4.7) of gelatin. This is in harmony with the fact that gelatin (like any other amphoteric electrolyte) can dissociate on the alkaline side of its isoelectric point only as an anion. On the more acid side from the isoelectric point gelatin is found to be in combination with Br and the Br number rises with the pH. 4. When we titrate gelatin, treated previously with HBr but possessing a pH = 4,7, with NaOH we find that 25 cc. of a 1 per cent solution of isoelectric gelatin require about 5.25 to 5.5 cc. of 0.01 N NaOH for neutralization (with phenolphthalein as an indicator). This value which was found invariably is therefore a constant which we designate as "NaOH (isoelectric)." When we titrate 0.25 gm. of gelatin previously treated with HBr but possessing a pH < 4.7 more than 5.5 cc. of 0.01 N NaOH are required for neutralization. We will designate this value of NaOH as "(NaOH)_n," where n represents the value of pH. If we designate the bromine number for the same pH as "Br_n" then we can show that the following equation is generally true: (NaOH)_n = NaOH (isoelectric) + Br_n. In other words, titration with NaOH of gelatin (previously treated with HBr) and being on the acid side of its isoelectric point results in the neutralization of the pure gelatin (NaOH isoelectric) with NaOH and besides in the neutralization of the HBr in combination with the gelatin. This HBr is set free as soon as through the addition of the NaOH the pH of the gelatin solution becomes equal to 4.7. 5. A comparison between the pH values and the bromine numbers found shows that over 90 per cent of the bromine or HBr found was in our experiments in combination with the gelatin.     

STUDIES IN THE PHYSICAL CHEMISTRY OF THE PROTEINS : VI. THE ACTIVITY COEFFICIENTS OF THE IONS IN CERTAIN OXYHEMOGLOBIN SOLUTIONS.

1. The solvent action of a neutral salt upon a protein, oxyhemoglobin, has been found identical to the solvent action of a neutral salt upon a bi-bivalent or uni-quadrivalent compound. 2. The solubility of oxyhemoglobin in phosphate solutions of varying ionic strength has been defined by the equation: log See PDF for Equation in which µ is the ionic strength, and S ₀ is the solubility in the absence of salt. 3. The values of S ₀ have been calculated to be 12.2, 11.2, and 13.1 gm. per liter respectively at pH 6.4, 6.6, and 6.8. 4. The relatively great solubility of oxyhemoglobin in water has been ascribed to the strong affinity constants for acid and base of certain groups in oxyhemoglobin. 5. The small change in the solubility of oxyhemoglobin effected by neutral salts suggests that but few such groups are dissociated in oxyhemoglobin in the state in which it crystallizes near its isoelectric point. 6. Certain of the other properties of oxyhemoglobin, such as its low viscosity, are considered in the light of its molecular weight and its valence type.     

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     

THE SWELLING OF ISOELECTRIC GELATIN IN WATER : II. KINETICS.

It has been assumed that gelatin consists of a network of an insoluble material enclosing a solution of a more soluble material. The swelling of gelatin is therefore primarily an osmotic phenomena in that the water tends to diffuse in owing to the osmotic pressure of the soluble material. This osmotic pressure is opposed by the elasticity of the insoluble constituent, and equilibrium results when these two pressures are equal. The rate of the entrance of water should then obey Poiseuille''s law, provided the variable terms are expressed as functions of the volume. Equations have been derived in this way which agree quite well with the experimental curves and which predict the proper relation between the size and shape of the block and the rate of swelling. They lead to a value for the rate of flow of water through gelatin which has been checked by direct measurement. The mechanism assumed predicts that at a higher temperature and under conditions such that the water has to pass through collodion before reaching the gelatin, the experiment should follow the same course as that of osmosis discussed previously. This was also found to be the case. The slow secondary increase in swelling is ascribed to fatigue of the elastic properties of the gelatin. The rate of this secondary swelling should therefore be independent of the size of the block, in contrast to the rate of primary swelling which is inversely proportional to the size. It can further be shown that this secondary swelling should be proportional to the square root of the time, and also that with large blocks at higher temperatures the entire swelling should be of this secondary type. These predictions have also been found to be true.     

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.     

OSMOTIC PROPERTIES OF THE EGG CELLS OF THE OYSTER (OSTREA VIRGINICA)

Investigations of the osmotic properties of oyster eggs by a diffraction method for measuring volumes have led to the following conclusions: 1. The product of cell volume and osmotic pressure is approximately constant, if allowance is made for osmotically inactive cell contents (law of Boyle-van''t Hoff). The space occupied by osmotically inactive averages 44 per cent of cell volume. 2. Volume changes over a wide range of pressures are reversible, indicating that the semipermeability of the cell during such changes remains intact. 3. The kinetics of endosmosis and of exosmosis are described by the equation, See PDF for Equation, where dV is rate of volume change; S, surface area of cell, (P-P_e), the difference in osmotic pressure between cell interior and medium, and K, the permeability of the cell to water. 4. Permeability to water during endosmosis is 0.6µ³ of water per minute, per square micron of cell surface, per atmosphere of pressure. The value of permeability for exosmosis is closely the same; in this respect the egg cell of the oyster appears to be a more perfect osmometer than the other marine cells which have been studied. Permeability to water computed by the equation given above is in good agreement with computations by the entirely different method devised by Jacobs. 5. Permeability to diethylene glycol averages 27.2, and to glycerol 20.7. These values express the number of mols x 10^–15 which enter per minute through each square micron of cell surface at a concentration difference of 1 mol per liter and a temperature of 22.5°C. 6. Values for permeability to water and to the solutes tested are considerably higher for the oyster egg than for other forms of marine eggs previously examined. 7. The oyster egg because of its high degree of permeability is a natural osmometer particularly suitable for the study of the less readily penetrating solutes.     

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 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     

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.     

AMPHOTERIC COLLOIDS : IV. THE INFLUENCE OF THE VALENCY OF CATIONS UPON THE PHYSICAL PROPERTIES OF GELATIN.

1. A method is given by which the amount of equivalents of metal in combination with 1 gm. of a 1 per cent gelatin solution previously treated with an alkali can be ascertained when the excess of alkali is washed away and the pH is determined. The curves of metal equivalent in combination with 1 gm. of gelatin previously treated with different concentrations of LiOH, NaOH, KOH, NH₄OH, Ca(OH)₂, and Ba(OH)₂ were ascertained and plotted as ordinates, with the pH of the solution as abscissæ, and were found to be identical. This proves that twice as many univalent as bivalent cations combine with the same mass of gelatin, as was to be expected. 2. The osmotic pressure of 1 per cent solutions of metal gelatinates with univalent and bivalent cation was measured. The curves for the osmotic pressure of 1 per cent solution of gelatin salts of Li, Na, K, and NH₄ were found to be identical when plotted for pH as abscissæ, tending towards the same maximum of a pressure of about 325 mm. of the gelatin solution (for pH about 7.9). The corresponding curves for Ca and Ba gelatinate were also found to be identical but different from the preceding ones, tending towards a maximum pressure of about 125 mm. for pH about 7.0 or above. The ratio of maxi mal osmotic pressure for the two groups of gelatin salts is therefore about as 1:3 after the necessary corrections have been made. 3. When the conductivities of these solutions are plotted as ordinates against the pH as abscissæ, the curves for the conductivities of Li, Na, Ca, and Ba gelatinate are almost identical (for the same pH), while the curves for the conductivities of K and NH₄ gelatinate are only little higher. 4. The curves for the viscosity and swelling of Ba (or Ca) and Na gelatinate are approximately parallel to those for osmotic pressure. 5. The practical identity or close proximity of the conductivities of metal gelatinates with univalent and bivalent metal excludes the possibility that the differences observed in the osmotic pressure, viscosity, and swelling between metal gelatinates with univalent and bivalent metal are determined by differences in the degree of ionization (and a possible hydratation of the protein ions). 6. Another, as yet tentative, explanation is suggested.     

THE COLLOIDAL BEHAVIOR OF PROTEINS

1. It is well known that neutral salts depress the osmotic pressure, swelling, and viscosity of protein-acid salts. Measurements of the P.D. between gelatin chloride solutions contained in a collodion bag and an outside aqueous solution show that the salt depresses the P.D. in the same proportion as it depresses the osmotic pressure of the gelatin chloride solution. 2. Measurements of the hydrogen ion concentration inside the gelatin chloride solution and in the outside aqueous solution show that the difference in pH of the two solutions allows us to calculate the P.D. quantitatively on the basis of the Nernst formula See PDF for Equation if we assume that the P.D. is due to a difference in the hydrogen ion concentration on the two sides of the membrane. 3. This difference in pH inside minus pH outside solution seems to be the consequence of the Donnan membrane equilibrium, which only supposes that one of the ions in solution cannot diffuse through the membrane. It is immaterial for this equilibrium whether the non-diffusible ion is a crystalloid or a colloid. 4. When acid is added to isoelectric gelatin the osmotic pressure rises at first with increasing hydrogen ion concentration, reaches a maximum at pH 3.5, and then falls again with further fall of the pH. It is shown that the P.D. of the gelatin chloride solution shows the same variation with the pH (except that it reaches its maximum at pH of about 3.9) and that the P.D. can be calculated from the difference of pH inside minus pH outside on the basis of Nernst''s formula. 5. It was found in preceding papers that the osmotic pressure of gelatin sulfate solutions is only about one-half of that of gelatin chloride or gelatin phosphate solutions of the same pH and the same concentration of originally isoelectric gelatin; and that the osmotic pressure of gelatin oxalate solutions is almost but not quite the same as that of the gelatin chloride solutions of the same pH and concentration of originally isoelectric gelatin. It was found that the curves for the values for P.D. of these four gelatin salts are parallel to the curves of their osmotic pressure and that the values for pH inside minus pH outside multiplied by 58 give approximately the millivolts of these P.D. In this preliminary note only the influence of the concentration of the hydrogen ions on the P.D. has been taken into consideration. In the fuller paper, which is to follow, the possible influence of the concentration of the anions on this quantity will have to be discussed.     

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."     

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 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.     

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.     

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.