THE KINETICS OF PENETRATION : XIV. THE PENETRATION OF IODIDE INTO VALONIA

When 0.1 M NaI is added to the sea water surrounding Valonia iodide appears in the sap, presumably entering as NaI, KI, and HI. As the rate of entrance is not affected by changes in the external pH we conclude that the rate of entrance of HI is negligible in comparison with that of NaI, whose concentration is about 10⁷ times that of HI (the entrance of KI may be neglected for reasons stated). This is in marked contrast with the behavior of sulfide which enters chiefly as H₂S. It would seem that permeability to H₂S is enormously greater than to Na₂S. Similar considerations apply to CO₂. In this respect the situation differs greatly from that found with iodide. NaI enters because its activity is greater outside than inside so that no energy need be supplied by the cell. The rate of entrance (i.e. the amount of iodide entering the sap in a given time) is proportional to the external concentration of iodide, or to the external product [N⁺]_o [I^-l_o, after a certain external concentration of iodide has been reached. At lower concentrations the rate is relatively rapid. The reasons for this are discussed. The rate of passage of NaI through protoplasm is about a million times slower than through water. As the protoplasm is mostly water we may suppose that the delay is due chiefly to the non-aqueous protoplasmic surface layers. It would seem that these must be more than one molecule thick to bring this about. There is no great difference between the rate of entrance in the dark and in the light.     

THE KINETICS OF PENETRATION : VI. SOME FACTORS AFFECTING PENETRATION

Some of the factors affecting penetration in living cells may be advantageously studied in models in which the organic salts KG and NaG diffuse from an aqueous solution A, through a non-aqueous layer B (representing the protoplasmic surface) into an aqueous solution C (representing the sap and hence called artificial sap) where they react with CO₂ to form KHCO₃ and NaHCO₃. Their relative proportions in C depend chiefly on the partition coefficients and on the diffusion constants in the non-aqueous layer. But the ratio is also affected by other variables, among which are the following: 1. Temperature, affecting diffusion constants and partition coefficients and altering the thickness of the unstirred layers by changing viscosity. 2. Viscosity (especially in the non-aqueous layers) which depends on temperature and the presence of solutes. 3. Rate of stirring, which affects the thickness of the unstirred layers and the transport of electrolyte in those that are stirred. 4. Shape and surface area of the non-aqueous layer. 5. Surface forces. 6. Reactions occurring at the outer surface such as loss of water by the electrolyte or its molecular association in the non-aqueous phase. The reverse processes will occur at the inner surface and here also combinations with acids or other substances in the "artificial sap" may occur. 7. Outward diffusion from the artificial sap. The outward movement of KHCO₃ and NaHCO₃ is small compared with the inward movement of KG and NaG when the concentrations are equal. This is because the partition coefficients³ of the bicarbonates are very low as compared with those of NaG and KG. Since CO₂ and HCO₃ ^- diffuse into A and combine with KG and NaG the inward movement of potassium and sodium falls off in proportion as the concentration of KG and NaG is lessened. 8. Movement of water into the non-aqueous phase and into the artificial sap. This may have a higher temperature coefficient than the penetration of electrolytes. 9. Variation of the partition coefficients with concentration and pH. Many of these variables may occur in living cells. (It happens that the range of variation in the ratio of potassium to sodium in the models resembles that found in Valonia.)     

THE KINETICS OF PENETRATION : IV. DIFFUSION AGAINST A GROWING POTENTIAL GRADIENT IN MODELS

In a model consisting of a non-aqueous layer (representing the protoplasm) placed between an inner, more acid, aqueous layer (representing the sap) and an outer, more alkaline, aqueous solution (representing the external solution bathing a living cell) the penetration of potassium creates an outwardly directed potential against which potassium continues to diffuse inward, thereby increasing the outward potential. This continues until the steady state is reached. The potassium sets up less potential in entering than in escaping and the net result is an outwardly directed potential. A similar process appears to take place in certain living cells.     

THE KINETICS OF PENETRATION : VIII. TEMPORARY ACCUMULATION

A model is described which throws light on the mechanism of accumulation. In the model used an external aqueous phase A is separated by a non-aqueous phase B (representing the protoplasm) from the artificial sap in C. A contains KOH and C contains HCl: they tend to mix by passing through the non-aqueous layer but much more KOH moves so that most of the KCl is formed in C, where the concentration of potassium becomes much greater than in A. This accumulation is only temporary for as the system approaches equilibrium the composition of A approaches identity with that of C, since all the substances present can pass through the non-aqueous layer. Such an approach to equilibrium may be compared to the death of the cell as the result of which accumulation disappears. During the earlier stages of the experiment potassium tends to go in as KOH and at the same time to go out as KCl. These opposing tendencies do not balance until the concentration of potassium inside becomes much greater than outside (hence potassium accumulates). The reason is that KCl, although its driving force be great, moves very slowly in B because its partition coefficient is low and in consequence its concentration gradient in B is small. This illustrates the importance of partition coefficients for penetration in models and in living cells. It also indicates that accumulation depends on the fact that permeability is greater for the ingoing compound of the accumulating substance than for the outgoing compound. Other things being equal, accumulation is increased by maintaining a low pH in C. Hence we may infer that anything which checks the production of acid in the living cell may be expected to check accumulation and growth. This model recalls the situation in Valonia and in most living cells where potassium accumulates as KCl, perhaps because it enters as KOH and forms KA in the sap (where A is an organic anion). In some plants potassium accumulates as KA but when HCl exists in the external solution it will tend to enter and displace the weaker acid HA (if this be carbonic it can readily escape): hence potassium may accumulate to a greater or less extent as KCl. Injury of the cell may produce a twofold effect, (1) increase of permeability, (2) lessened accumulation. The total amount of electrolyte taken up in a given time will be influenced by these factors and may be greater than normal in the injured cell or less, depending somewhat on the length of the interval of time chosen.     

THE KINETICS OF PENETRATION : XII. HYDROGEN SULFIDE

The rate of entrance of H₂S into cells of Valonia macrophysa has been studied and it has been shown that at any given time up to 5 minutes the rate of entrance of total sulfide (H₂S + S^-) into the sap is proportional to the concentration of molecular H₂S in the external solution. This is in marked contrast with the entrance of ammonia, where Osterhout has shown that the rate of entrance of total ammonia (NH₃ + NR₄ ⁺) does not increase in a linear way with the increase in the external concentration of NH₃, but falls off. The strong base guanidine also acts thus. It has been shown that the rate of entrance of H₂S is best explained by assuming that it enters by diffusion of molecular H₂S through the non-aqueous protoplasmic surface. It has been pointed out that the simple diffusion requires that the rate of entrance might be expected to be monomolecular. Possible causes of the failure of H₂S to follow this relationship have been discussed.     

THE KINETICS OF PENETRATION : XV. THE RESTRICTION OF THE CELLULOSE WALL

When Valonia cells are impaled on capillaries, it is in some ways equivalent to removing the comparatively inelastic cellulose wall. Under these conditions sap can migrate into a free space and it is found that on the average the rate of increase of volume of the sap is 15 times what it is in intact cells kept under comparable conditions. The rate of increase of volume is a little faster during the first few hours of the experiment, but it soon becomes approximately linear and remains so as long as the experiment is continued. The slightly faster rate at first may mean that the osmotic pressure of the sap is approaching that of the sea water (in the intact cell the sap osmotic pressure is always slightly above that of the sea water). This might result from a more rapid entrance of water than of electrolyte, as would be expected when the restriction of the cellulose wall was removed. During the linear part of the curve the osmotic concentration and the composition of the sap suffer no change, so that entrance of electrolyte must be 15 times as fast in the impaled cells as it is in the intact cells. The explanation which best accords with the facts is that in the intact cell the entrance of electrolyte tends to increase the osmotic pressure. As a consequence the protoplasm is partially dehydrated temporarily and it cannot take up more water until the cellulose wall grows so that it can enclose more volume. The dehydration of the protoplasm may have the effect of making the non-aqueous protoplasm less permeable to electrolytes by reducing the diffusion and partition coefficients on which the rate of entrance depends. In this way the cell is protected against great fluctuations in the osmotic concentration of the sap.     

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 KINETICS OF PENETRATION : III. EQUATIONS FOR THE EXCHANGE OF IONS

Equations are given for a variety of cases when ions of the same sign are exchanged between the interior of a living cell and the external solution.     

THE KINETICS OF PENETRATION : V. THE KINETICS OF A MODEL AS RELATED TO THE STEADY STATE

An organic potassium salt, KG, passes from an aqueous phase, A, through a non-aqueous layer, B, into a watery solution, C. In C it reacts with CO₂ to form KHCO₃. The ionic activity product (K) (G) in C is thus kept at such a low level that KG continues to diffuse into C after the concentration of potassium becomes greater in C than in A. Hence potassium accumulates in C, the osmotic pressure rises, and water goes in. A steady state is eventually reached in which potassium and water enter C in a constant ratio. The rate of entrance of potassium (with no water penetrating into C) may fall off in a manner approximately exponential. But water enters and may produce an exponential decrease in concentration. This suggests that the kinetics may be treated like that of two consecutive monomolecular reactions. Calculations made on this basis agree very well with the observed values. The rate of penetration appears to be proportional to the concentration gradient of KG in the non-aqueous layer and in consequence depends upon the partition coefficients which determine this gradient. Exchange of ions (passing as such through the non-aqueous layer) does not seem to play an important rôle in the entrance of potassium. The kinetics of the model may be similar to that of living cells.     

THE KINETICS OF PENETRATION : XVIII. ENTRANCE OF WATER INTO IMPALED HALICYSTIS

The rate of entrance of water into impaled cells of Halicystis Osterhoutii, Blinks and Blinks, has been determined directly by measurements of the rise of sap in a capillary for dilute sea waters (containing between 90 and 30 per cent sea water). The velocity constant remains reasonably constant down to 50 per cent sea water but it decreases markedly in lower concentrations.     

THE KINETICS OF PENETRATION : XVII. THE EXIT OF AMMONIA IN LIGHT AND DARKNESS

The exit of accumulated ammonia from the sap of Valonia macrophysa, Kütz., into normal (nearly ammonia-free) sea water, has been studied in light (alternation of daylight and darkness) and in darkness. Exit is always preceded by an induction period lasting 1 or more days. This is longer in darkness. After exit starts the rate is greater in light than in darkness. The pH of the sap drops off soon after the cells are exposed to normal sea water even before any definite decrease in the ammonia concentration of the sap has occurred. This suggests that the decrease in the pH is due to the loss of a very small amount of NH₃ or NH4OH without a corresponding gain of sodium as a base. In most cases sodium replaced the ammonia lost during exit, but there is some evidence that potassium may also replace ammonia. To account for the induction period it is suggested that other species than NH₄ X are concerned in the transport of ammonia, for example urea or amino acids.     

THE KINETICS OF PENETRATION : XVI. THE ACCUMULATION OF AMMONIA IN LIGHT AND DARKNESS

The accumulation of ammonia takes place more rapidly in light than in darkness. The accumulation appears to go on until a steady state is attained. The steady state concentration of ammonia in the sap is about twice as great in light as in darkness. Both effects are possibly due to the fact that the external pH (and hence the concentration of undissociated ammonia) outside is raised by photosynthesis. Certain "permeability constants" have been calculated. These indicate that the rate is proportional to the concentration gradient across the protoplasm of NH₄ X which is formed by the interaction of NH₃ or NH₄OH and HX, an acid elaborated in the protoplasm. The results are interpreted to mean that HX is produced only at the sap-protoplasm interface and that on the average its concentration there is about 7 times as great as at the sea water-protoplasm interface. This ratio of HX at the two surfaces also explains why the concentration of undissociated ammonia in the steady state is about 7 times as great in the sea water as in the sap. The permeability constant P'''''' appears to be greater in the dark. This is possibly associated with an increase in the concentration of HX at both interfaces, the ratio at the two surfaces, however, remaining about the same. The pH of sap has been determined by a new method which avoids the loss of gas (CO₂), an important source of error. The results indicate that the pH rises during accumulation but the extent of this rise is smaller than has hitherto been supposed. As in previous experiments, the entering ammonia displaced a practically equivalent amount of potassium from the sap and the sodium concentration remained fairly constant. It seems probable that the pH increase is due to the entrance of small amounts of NH₃ or NH₄OH in excess of the potassium lost as a base.     

THE PENETRATION OF CATIONS INTO LIVING CELLS

Direct tests of the cell sap of Nitella show that the protoplasm is normally permeable to Li, Cs, and Sr, and that penetration is more rapid in an unbalanced than in a balanced solution.     

THE KINETICS OF PENETRATION : XIX. ENTRANCE OF ELECTROLYTES AND OF WATER INTO IMPALED HALICYSTIS

When cells of Halicystis are impaled on a capillary so that space is provided into which the sap can migrate, the rate of entrance of water and of electrolyte is increased about 10-fold. In impaled Valonia cells the rate is increased about 15-fold. After a relatively rapid non-linear rate of increase of sap volume immediately after impalement (which may possibly represent the partial dissipation of the difference of the osmotic energy between intact and impaled cells) the volume increases at a linear rate, apparently indefinitely. Since the halide concentration of the sap at the end of the experiment is (within the limits of natural variation) the same as in the intact cell, we conclude that electrolyte also enters the sap about 10 times as fast as in the intact cell. As in the case of Valonia we conclude that there is a mechanism whereby in the intact cell the osmotic concentration of the sap is prevented from greatly exceeding that of the sea water. This may be associated with the state of hydration of the non-aqueous protoplasmic surfaces.     

THE CELL POPULATION KINETICS OF NEUTROPHILIC CELLS

Autoradiographic data for the entry of tritiated thymidine labelled cells into the post-proliferative neutrophilic cell compartments following a single injection of isotope have been analysed in terms of two cell kinetic models which differ in the assumed relationships between cell maturation and division. Comparisons with the experimental data were made in an attempt to assess the validities of the models, and kinetic parameters for the compartments of recognizable neutrophilic cells were estimated. Control mechanisms which have been proposed for the granulocyte system are discussed in terms of the kinetic models which were chosen in their determination. Although it was not possible to make a clear choice between the proposed models, preference was established for a random model which did not involve cell loss.     

KINETICS OF PENETRATION : VII. MOLECULAR VERSUS IONIC TRANSPORT

In some living cells the order of penetration of certain cations corresponds to that of their mobilities in water. This has led to the idea that electrolytes pass chiefly as ions through the protoplasmic surface in which the order of ionic mobilities is supposed to correspond to that found in water. If this correspondence could be demonstrated it would not prove that electrolytes pass chiefly as ions through the protoplasmic surface for such a correspondence could exist if the movement were mostly in molecular form. This is clearly shown in the models here described. In these the protoplasmic surface is represented by a non-aqueous layer interposed between two aqueous phases, one representing the external solution, the other the cell sap. The order of penetration through the non-aqueous layer is Cs > Rb > K > Na > Li. This will be recognized as the order of ionic mobilities in water. Nevertheless the movement is mostly in molecular form in the nonaqueous layer (which is used in the model to represent the protoplasmic surface) since the salts are very weak electrolytes in this layer. The chief reason for this order of penetration lies in the fact that the partition coefficients exhibit the same order, that of cesium being greatest and that of lithium smallest. The partition coefficients largely control the rate of entrance since they determine the concentration gradient in the non-aqueous layer which in turn controls the process of penetration. The relative molecular mobilities (diffusion constants) in the non-aqueous layer do not differ greatly. The ionic mobilities are not known (except for K⁺ and Na⁺) but they are of negligible importance, since the movement in the non-aqueous layer is largely in molecular form. They may follow the same order as in water, in accordance with Walden''s rule. Ammonium appears to enter faster than its partition coefficient would lead us to expect, which may be due to rapid penetration of NH₃. This recalls the apparent rapid penetration of ammonium in living cells which has also been explained as due to the rapid penetration of NH₃. Both observation and calculation indicate that the rate of penetration is not directly proportional to the partition coefficient but increases somewhat less rapidly. Many of these considerations doubtless apply to living cells.     

KINETICS OF THE SWELLING OF CELLS AND TISSUES

The rate of swelling of Arbacia eggs in dilute sea water, studied by Lillie and by Lucke and McCutcheon, may be expressed by the formulæ derived for the rate of increase in volume of a solution enclosed in a collodion sac. The rate of swelling of slices of carrot in distilled water, measured by Stiles and Jørgensen, may be expressed by the equation derived previously for the swelling of similarly shaped blocks of gelatin.     

THE KINETICS OF PENETRATION : XX. EFFECT OF pH AND OF LIGHT ON ABSORPTION IN IMPALED HALICYSTIS

The rate of entrance of electrolyte and of water into impaled cells of Halicystis Osterhoutii is unaffected by raising the pH of the sea water to 9.2 or lowering it to 7.0. It is quite possible that sodium enters by combining with an organic acid HX produced by the protoplasm. If the pK'' of this acid is sufficiently low the change in external pH would not produce much effect on the rate of entrance of sodium. The rate of entrance of electrolytes is affected by light. In normal light (i.e. natural succession of daylight and darkness) the rate is about twice as great as in darkness.     

尼罗罗非鱼成熟卵结构及精子入卵早期的电镜观察

用扫描电镜观察尼罗罗非鱼(Tilopia nilotica)成熟卵卵膜孔结构和精子入卵的早期情况,用透射电镜观察成熟卵皮质,可见卵膜孔包括前庭和精孔管两部分,前庭壁及壳膜外表面上有许多小孔洞,精孔管壁呈阶梯状。卵膜孔下的卵皮质是一凹陷区,这一区域存在着皮质小泡。本实验见到5种形态的皮质小泡,其中大的皮质小泡靠近质膜。     

ANALYSIS OF THE PROLIFERATION KINETICS OF BURKITT'S LYMPHOMA CELLS

The in vitro proliferation kinetics of a cell line derived from a patient with American Burkitt's lymphoma were investigated at three different growth phases: lag (day 1), exponential (day 3) and plateau (day 5). The growth curve, labeling and mitotic indices, percentage labeled mitosis (PLM) curves and DNA content distributions were determined. The data obtained have been analysed by the previously developed discrete-time kinetic (DTK) model by which a time course of DNA distributions during a 10-day growth period was characterized in terms of other cell kinetic parameters. The mean cell cycle times, initially estimated from PLM curves on days 1, 3 and 5, were further analysed by the DTK model of DNA distributions and subsequently the mean cell cycle times with respect to DNA distributions during the entire growth period were determined. The doubling times were 39·6, 31·2 and 67·2 hr, respectively, at days 1, 3 and 5. The mean cell cycle time increased from 23·0 to 37·7 hr from day 3 to day 5 mainly due to an elongation of the G₁ and G₂ phases. A slight increase in the cell loss rate from 0·0077 to 0·0081 fraction/hr was accompanied by a decrease in the cell production rate from 0·0299 to 0·0184 fraction/hr. This calculated cell loss rate correlated significantly with the number of dead cells determined by trypan blue exclusion. Analysis of the number of dead cells in relation to the cell cycle stage revealed that a majority of cell death occurred in G₁ (r= 0·908; P < 0·0001). There was a good correlation between the in vitro proliferation kinetics at plateau phase of this Burkitt's lymphoma derived cell line and the in vivo proliferation kinetics of African Burkitt's lymphoma (Iversen et al., 1974), suggesting the potential utility of information obtained by in vitro kinetic studies.