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Shoot apices of greenhouse-reared Picea abies seedlings undergo a sequence of age-related developmental changes before closely approaching a steady-state condition when about 140 days old. Apical dome diameter and height increase with seedling age. Thus, although the relative volume growth rate of the apical dome declines as the seedlings age, the increase in size of the mean apical dome itself is so large that the absolute volume of new tissue generated per day still increases several fold. Therefore, the observed decline in plastochron duration, decreases in relative growth rates per plastochron, increase in absolute volume growth per plastochron, and increase in tissue doubling time with increasing age are all mutually compatible. The apical dome of the mean 20-day-old plant produced about 1 10,000,u3 of tissue per plastochron of 18.5 hr, or about 140,000 ,x per day. Relative volume growth rate was about 20 % per day. At that rate about 4.4 plastochrons or 82 hr would be needed to double a unit volume of apical dome tissue. In contrast, the apical dome of the mean 140-day-old plant produced about 220,000 A of tissue per plastochron of 5.7 hr, or about 940,000 A' per day. Relative volume growth rate was about 12 % per day; consequently, about 23 plastochrons or 130 hr would be needed to double a unit volume of apical dome tissue. Further analysis indicated that an internode, newly initiated by the mean 140-day-old plant, increased in volume at the rate of 7.46 % per plastochron or 31.5 % per day for the first 10 plastochrons. Methods are presented for estimating vertical, radial, and volume growth rates at any level of the shoot apex when steady-state conditions prevail. IN THE FIRST PAPER of this series (Gregory and Romberger, 1972) we described some anatomical and ontogenetic features of the shoot apex in embryos and greenhouse-grown seedlings of Picea abies. We also derived the following equations for predicting the basal diameter of the apical dome (D) in microns, and plastochron duration (PD) in hours, relative to seedling age (A) in days: D -71.72 + 3.6120A 0.0129542A2 (1) PD24 0.4039 + 0.04750A 0.0001450A 2 In this paper we quantitatively describe and mathematically analyze additional features of the developing Picea abies shoot apex. The basic terminology is given in the first paper. The additional term "caulis" refers to the cauline component of the shoot apex; that is, the shoot apex minus the primordia. Other new terms and abbreviations are defined when first used. The rationale is best introduced by reference to radial growth as an example. Radial growth rates at the shoot apex can be determined by measuring the rate at which leaf primordia recede radially away from the longitudinal axis of the shoot. Richards (1948, 1951) described the radial expansion of the shoot apex during one plasto1Received for publication 11 October 1971. chron as the ratio between the radial distance of a primordium from the longitudinal axis of the apex to that of the next primordium to be initiated. This ratio, normally only slightly greater than unity, is the plastochron ratio or quotient (P0). The natural logarithm of PQ is the relative transverse linear or radial growth rate per plastochron (Rr). The latter relation is a consequence of the definition of the natural logarithmic function and of the so-called organic growth formula. An analogy with the mathematics of compound interest is obvious. The increase of an amount of money invested at a given interest rate, compounded at fixed intervals in time, is a joint function of the amount initially deposited, the interest rate, and time. The effective growth rate is slightly higher when, for example, compounding is done daily rather than quarterly. However, growth of an organic system is strictly analogous to the growth of funds deposited on interest only if interest is compounded continuously. These relations can be expressed more clearly in mathematical terms. If G is any linear measure of a growing system which is changing at the constant rate of R times its existing dimension at all times, and if the value of G at time zero is Go, then the value of G at time t is given by the equation

The gross growth rates of 158 soft tissue metastatic lesions of breast cancer in 54 patients seen at Ellis Fischel State Cancer Hospital were studied. The frequency distributions of both the linear diametric and exponential volumetric (doubling time) growth rates were lognormal and were analyzed statistically as such. Among the 66 untreated metastatic lesions, parasternal lymph node had the fastest growth rate, although this could be a reflection of the crudeness of the measurement method. Undifferentiated or poorly differentiated recurrent lesions in the chest wall appeared to consist of two heterogeneous groups: one group grew faster than the more differentiated cancers and the other group slower, suggesting tumor with more necrosis. This paper further documented the prevalence of lognormal distribution of events associated with human cancers.

The DNA-synthesizing capacity of single antibody-forming cells was tested by a combination of micromanipulatory and autoradiographic techniques. Rats were immunized with S. adelaide flagellin, a protein antigen known to contain significant contamination with somatic (O) antigen. Single cells from secondarily immunized rats were tested for production of anti-H and anti-O antibodies by previously described and newer techniques. Positive antibody producers were transferred onto clean dry slides by micromanipulation, and autoradiographs were performed. When rats had received tritiated thymidine 1 hour before killing, labeling of antibody-forming cells was taken to imply that the cell was preparing for further mitotic division. It was found that on the 2nd and 3rd day of a secondary response, many of the antibody-producing cells in the nodes (chiefly plasmablasts) were incorporating tritiated thymidine. At the height of the cellular response, however, at 4 and 5 days, the majority of active antibody producers (chiefly mature plasma cells) were incapable of DNA synthesis. There appeared to be an inverse relationship between the antibody-forming and DNA-synthesizing capacities of the cell population under study; as more of the cells studied formed detectable antibody, fewer of them incorporated the DNA precursor. The age of plasma cells was also studied. Animals were killed at the height of the cellular immune response, having previously received an injection of tritiated thymidine 1 to 48 hours before killing; i.e., at 63 to 110 hours after their secondary stimulus. As the interval between isotope injection and killing increased, the proportion of antibody-forming cells showing labeling increased. With an interval of 30 hours, about half the antibody-forming cells were labeled and of 48 hours, over 95 per cent were labeled. This was taken as evidence that, few, if any, antibody-forming cells found at the height of a secondary response were more than 48 hours old. On the basis of these experiments and those reported in the accompanying paper, a simplified scheme showing the development of an antibody-forming clone in the secondary response was proposed.

Peritoneal cells (PC) from normal, unimmunized mice were placed in ultra-thin monolayer cultures containing carboxymethylcellulose (CMC), sheep red blood cells (SRBC), and complement, and tested for the appearance of plaques of lysis. The behavior of PC from young male mice and from female mice that had given birth to several litters (retired breeder mice) was studied. It was found that cells from spleen, mesenteric lymph node, thymus, bone marrow, thoracic duct lymph, or Peyer's patches could not form plaques in the CMC microcultures. Also, various combinations of these cells did not lead to plaque formation. When cells from any of these sources were mixed with PC, there was either no effect or an actual inhibition of plaque formation, the plaque counts being lower than would have been expected from the number of PC present in the mixture. Optimal plaque formation by peritoneal cells was found to be dependent on an optimal cell concentration, this optimum being around 5 x 106/ml for young male mice and 0.5 x 106/ml for retired breeders. Inhibition of plaque formation was found with either supra- or suboptimal cell concentrations. The inhibition by excess cell concentration may have been a simple nutritional or nonspecific overcrowding effect, as it could also be induced by an addition of an excess of spleen or lymph node cells. The failure of more dilute PC preparations to give adequate numbers of plaques appeared to be more specific, as plaque numbers could not be restored to normal by addition of spleen cells. The suggestion was that some cell to cell interaction between PC was involved. This dependence on cell concentration was not seen with immunized spleen PFC. Plaque appearance could be specifically and reversibly suppressed by placing PC in a medium containing rabbit anti-mouse IgM serum. Anti-IgG serum had no such effect. These experiments strengthened our view, expressed in the accompanying paper, that plaque formation was due to the formation of IgM, hemolytic antibody to SRBC by the PC. Metabolic inhibitors were incorporated into monolayer cultures and had different effects with the different types of PFC used. In the case of spleen cells from mice actively immunized against SRBC 4 days before killing, actinomycin D had no effect on plaque counts and puromycin reduced plaque numbers by a factor of 2. In the case of PC from young male mice, actinomycin D in concentrations above 0.01 µg/ml caused reductions down to < 2% of control values in plaque counts, and puromycin (10 µg/ml) had a similar effect. The PC from retired breeder mice occupied an intermediate position between the two cases just discussed. A compartment of cells, equal to about one-fifth of the total normal PFC compartment, was identified as resistant to high concentrations of either actinomycin D or puromycin, being similar in these respects to PFC from spleens of intentionally preimmunized mice. The mitotic poison, Colcemid, did not affect plaque counts in any situation tested. The theoretical implications of these results are briefly discussed.

Early in the course of experiments on radiotherapy of spontaneous mammary adenocarcinomas in C3H mice it was noticed that many tumors were reduced to a small size by treatment and then remained unchanged over many months. For a tumor with a doubling time of about eight days, this is a very long time. Many papers have been published in the last few years giving calculations of the tumor-lethal dose in various numbers of fractions, all of which are based on the assumption that the reproductive capacity of every tumor cell must be destroyed to cure the tumor and that regrowth will occur if a single viable cell is left. Therefore, it seemed worthwhile to examine the records on the mice to determine whether such small tumors remain a threat to survival and whether they invariably regrow if the mouse survives long enough. The records on mice receiving the same radiation therapy technic—1,000 R twice a week to 6,000 R in eighteen days—were used. The gas breathed during irradiation, however, varied. There are man...

Having developed in previous papers the mathematical connections between growth fraction and cellular losses, and between growth fraction, doubling time, initial cell population, resistance to a given therapy and the number of courses of this therapy per doubling time, the authors examine here how these parameters are connected when eradication is to be achieved. The various calculations show that resistance must be lowered by means of combinations, well beyond the theoretical limits, in order to deal with non-dividing cells and/or large initial tumor cell populations. For a given percentage of resistance, eradication is achieved only for growth fraction above a certain limit, only for tumor cell population below a certain limit, and only for a number of courses of therapy per doubling time above a certain limit. In order to meet these requirements, it appears necessary (1) to combine the available drugs without cross-resistance; (2) to give simultaneous combinations instead of sequential ones; (3) to treat as soon as possible; (4) to find out ways of lowering toxicity in order to give as many courses as possible per doubling time; (5) to incorporate in combinations drugs effective against non-dividing cells.

In earlier papers (1, 2) we reported chemically defined medium CMRL-14151 and described the preparation and use of certain macromolecular supplements, namely, α1-acid glycoprotein (orosomucoid) from the supernatant solution of Cohn's fraction V (method 6), sometimes referred to as fraction VI, of human plasma together with α2-macroglobulin from horse serum or with commercial dextran (mol wt 100,000–200,000). The latter combination (CMRL-1415-DSCV1) yielded a population doubling time of 2.5 days for newly-isolated mouse embryo cells, whereas in replicate cultures prepared with unsupplemented CMRL-1415 it was 4.33 days.Although many established cell lines have been adapted to serum-free, chemically defined media, newly-isolated mammalian cells in continuous culture require certain proteins that are usually supplied in the form of a native or dialyzed serum supplement in a suitable defined medium. The nature of these proteins and their nutritional role have not been fully elucidated. It is generally agreed t...

Haploid anuran embryos can readily be obtained by the classical methods of experimental embryology and provide a source of tissue for the initiation of haploid cell cultures. In order to exploit the obvious advantages for genetic experimentation of cell populations with a single chromosome set, we have for some time been studying cell lines initiated from haploid as well as diploid frog embryos (1). Since our initial publication in 1962, we have evaluated a number of growth media; the most useful appears to be that of Leibovitz (2) as modified for amphibian cells by Balls and Ruben (3), which we have employed since 1966. Using this medium, 3 5 lines have been initiated by passaging primary cultures. Of these, 23 have successfully been maintained in serial culture, i.e., carried through 10 or more passages. Clonal isolates have been obtained from some of these lines and passaged separately. Thus, 3 6 distinct lines are at present maintained in frozen storage or continuous culture. Our purpose in this paper is to describe how such lines are initiated, the morphological changes which the cells undergo, their chromosome constitution, and their properties as experimental material. We will consider in detail features of four lines of particular interest because of their origin or behavior.

It has been shown previously [6] that the growth of tumours with a constant doubling time may be described by an equation linking the growth fraction and cellular losses. It is shown in this paper that analysis of chemotherapeutic response of measurable tumours may lead to the quantitative evaluation of the growth fraction and of the resistant population to the drug employed. The mathematical model describing the response also allows decisions to be made about the connection between schedule and doubling time, and about the superiority of a simultaneous combination over a sequential one. The parameters employed in such a model may be measured and used by the therapist in clinical cases in order to optimize the treatment.