The analysis of cell kinetics using cohort fraction labelled mitosis (COFLM) curves

A method has been developed to determine the cell cycle kinetics for a quiescent population of cells which are stimulated to undergo a single transit of the division cycle. The method, known as the cohort of fraction labelled mitoses (COFLM), requires no knowledge of the proliferative fraction. The probability statements of the model were formulated and then compared by an iterative fitting procedure to experimental data to obtain estimates of the model parameters. Best fit model responses show good agreement with a set of experimental data.     

Analysis of fluorescence decay curves by means of the Laplace transformation.

A computational procedure is described for the analysis of fluorescence decay data convolved with a lamp flash of finite width. The computer program calculates the ratio of the Laplace transforms of the decay and the lamp flash for different values of s to give the transforms of the impulse response for each value of s. These are set equal to the analytical Laplace transforms of the decay law involved. Solution of the nonlinear simultaneous equations yields the desired decay parameters. The method can be modified to analyze data that contains a component due to scattered light and can also provide essential information regarding transit time changes of the photomultiplier with changes in emission wavelength. The method was tested by the analysis of real and simulated data. The accuracy of the analysis depends on the degree of correlation among the parameters.     

THE TECHNIQUE OF LABELLED MITOSES: ANALYSIS BY AUTOMATIC CURVE-FITTING

An improved method is described for the analysis of data obtained by the technique of labelled mitoses. It is a development of the method described by Barrett (1966) in which theoretical curves are computed on the basis of a model which assumes that the phases G¹, S and G² are described by independent log-normal distributions; the analysis consists in finding a form of this model which gives a labelled mitoses curve which is the best fit to the available data. This fitting procedure has now been made automatic. No comprehensive indication of the goodness of fit can be given, although in the analysis of over fifty sets of data the method appears to have worked well.
A supplementary computer program is described which, on the basis of three separate assumed modes of cell loss, calculates the form of the age distributions and theoretical continuous labelling curves. This allows growth fraction to be calculated in a way which takes account of the distribution of phase durations and the non-rectangular age distributions of expanding cell populations. It also gives an opportunity to study the implications of continuous labelling data as regards the mode of cell loss.
A comparison is made between the present method of labelled mitoses curve analysis and the empirical rules which have often been used.     

THE KINETICS OF GRANULOSA CELLS IN DEVELOPING FOLLICLES IN THE MOUSE OVARY

This investigation describes the kinetics of the granulosa cells in medium-sized follicles type 3b, 4 and 5a in ovaries of 28-day-old Bagg mice. the method of labelling with ³H-thymidine followed by high resolution autoradiography is used in the experimental work, which consist of determining percentage labelled mitosis (PLM-) and continuous labelling (CL-) curves. In order to analyse the data by computer two alternative hypotheses A and B are set up. Both include the assumptions of no cell loss, exponential growth and a resting compartment Q. In hypothesis A cells from Q re-enter the mitotic cycle via the normal DNA-synthesis compartment S_p. Hypothesis B includes beside compartment S_p a special DNA-synthesis compartment S_q where only cells from Q are synthesizing DNA, and these cells re-enter the mitotic cycle via the G₂ compartment. the mean transit time in S_q is considered to be longer than the mean transit time in S_q. On the basis of the hypothesis mathematical expressions for the PLM- and CL-curves are obtained, and by means of a computer the theoretical curves are fitted to the experimental values: thereby all relevant cell kinetical parameters are estimated. Hypothesis B seems to give the best fit between the theoretical and experimental curves. the estimated parameters are: mean cycle times, μ_c= (56.1 hr, 56.1 hr and 22.3 hr for type 3b, 4 and 5a respectively), doubling times, T _D= (96.4 hr, 118.6 hr and 59.1 hr) and the proportion of cells in Q, p _Q = (0.60, 0.71 and 0.69).     

稳定同位素质量平衡混合模型的性能评估

稳定同位素技术可以用于消费者营养溯源,以确定多种营养来源对消费者营养的贡献比重。因此,稳定同位素质量平衡混合模型已经是消费者营养溯源分析的必要方法之一。通常使用贝叶斯混合模型来估计不同营养来源的贡献;此类模型提供了每个营养来源对消费者的贡献比例的概率分布特征。然而,混合模型拟合结果的好坏,及其与实际生态学理论的匹配水平,是模型性能的重要评价内容。例如,模型在不能很好地解析营养来源贡献时,仍将返回默认先验结果,给模型解释带来困难。为直接避免同位素构建消费者营养溯源分析中的诸多技术问题,文章将综述在拟合和评估贝叶斯混合模型时遵循的最佳实践。因此,文章基于实测的同位素数据集(蒙古鲌Culter mongolicus mongolicus同位素数据集),通过识别消费者营养功能类群特征、改变营养来源先验信息特征,构建系列贝叶斯模型;通过比较模型总体性能、实测值与预测值差异,及先验信息和后验信息差异等多种模型性能评价方法,来描述模型性能评价的方法和过程。通过这些方法的综合运用,将进一步提高消费者营养溯源准确性,为更深刻地认识食物网规律提供科学支撑。     

THE DISCRETE–TIME KINETIC MODEL ANALYSIS OF DNA CONTENT DISTRIBUTIONS IN EXPERIMENTAL TUMOUR CELLS

A method was developed to analyse and characterize FMF measurements of DNA content distribution, utilizing the discrete time kinetic (DTK) model for cell kinetics analysis. The DTK model determines the time sequence of the cell age distribution during the proliferation of a tumor cell population and simulates the distribution pattern of the DNA content of cells in each age compartment of the cell cycle. The cells in one age compartment are distributed and spread into several compartments of the DNA content distribution to allow for different rates of DNA synthesis and instrument dispersion effects. It is assumed that the DNA content of cells in each age compartment has a Gaussian distribution. Thus, for a given cell age distribution the DNA content distribution depends on two parameters of the cells in each age compartment: the average DNA content and its coefficient of variation. As the DTK model generates the best fit DNA content distribution to the FMF measurement data, it enables one to estimate specific values of these two parameters in each stage of the cell cycle and to determine the fraction of cells in each cycle phase. The method was utilized to fit FMF measurements of DNA content distributions and to analyse their relationship to the cell kinetic parameters, namely cell loss rate, cell cycle times and growth fraction of exponentially growing Chinese hamster ovary cells in vitro and, also, with a wide range of coefficients of variation, of the L1210 ascites tumour during the growth period.     

时间分辨荧光光谱测量结果的一种数据处理改进方法

在综合矩方法和拉普拉斯变换方法原理的基础上,本文报道一种时间相关单光子计数测出的荧光衰变动力学曲线的数据处理的改进方法.此方法使我们能在花费时间较少的条件下得出和用最小二乘法拟合相比拟的准确分析结果.这一方法的优点已被用于分析香豆素102+DCM和香豆素102+PBBO激光染料乙醇溶液的双指数荧光衰变过程的结果所证实,此外,本文也讨论了仪器时间漂移校正及拉普拉斯变换的数据截取问题.     

Cluster analysis of dynamic parameters of gene expression

Cluster analysis has proven to be a valuable statistical method for analyzing whole genome expression data. Although clustering methods have great utility, they do represent a lower level statistical analysis that is not directly tied to a specific model. To extend such methods and to allow for more sophisticated lines of inference, we use cluster analysis in conjunction with a specific model of gene expression dynamics. This model provides phenomenological dynamic parameters on both linear and non-linear responses of the system. This analysis determines the parameters of two different transition matrices (linear and nonlinear) that describe the influence of one gene expression level on another. Using yeast cell cycle microarray data as test set, we calculated the transition matrices and used these dynamic parameters as a metric for cluster analysis. Hierarchical cluster analysis of this transition matrix reveals how a set of genes influence the expression of other genes activated during different cell cycle phases. Most strikingly, genes in different stages of cell cycle preferentially activate or inactivate genes in other stages of cell cycle, and this relationship can be readily visualized in a two-way clustering image. The observation is prior to any knowledge of the chronological characteristics of the cell cycle process. This method shows the utility of using model parameters as a metric in cluster analysis.     

THE APPLICATION OF AGE RESPONSE FUNCTIONS TO THE OPTIMIZATION OF TREATMENT SCHEDULES

A computer-based technique is described for calculating the survival of normal and malignant cell populations during and after chemotherapy or radiotherapy. For exponentially growing cells, cell sensitivity as a function of the position in the cell cycle (age response function) is considered and survival calculated by means of a method discussed previously (Hahn, 1966; Hahn & Kallman, 1967). It is shown how the age response function is obtained from experimental data. Two examples of the application of the computer-based technique are given. As one example, the technique is used to 'optimize' the scheduling of fractionated irradiations to differentially kill one cell line over another using as a basis for optimization differences in their age response functions. the second example illustrates the use of the technique to determine the relative advantage of different chemotherapy protocols. Here the survival of cycling and noncycling bone marrow stem cells, and resistant and sensitive malignant cells, is calculated. It is suggested that the technique may have direct relevance for the chemotherapy of some leukemias.     

Parameter identification of the calvin photosynthesis cycle

Summary This article is concerned with the determination of kinetic parameters of the Calvin photosynthesis cycle which is described by seventeen nonlinear ordinary differential equations. It is shown that the task requires dynamic data for several sets of initial conditions. The numerical technique is based upon an algorithm for non-linear optimization and Gear's numerical integration scheme for stiff systems of differential equations. The sensitivity of the parameters to noise in the data is tested with a method adapted from Rosenbrook and Storey. A preliminary set of parameters has been obtained from a preliminary set of experimental data. The numerical methods are then tested with synthetic data derived from these parameters. The mathematical model and the results obtained in the simulation are used as an aid in designing new experiments.     

AN EVALUATION OF ERYTHROPOIESIS IN THE YOUNG RAT

Estimates of the cell population kinetic parameters have been obtained for the erythroid cells of the young growing rat using the technique of labelled mitoses and these results have been analysed by a computer programme. The phases of the cell cycle for the proliferating cells have been shown to be of shorter duration than generally reported. Together with the differential cell count and initial labelling index these data have enabled estimates of the growth fraction, birthrate, flow rate, number of divisions and transit time to be determined for each compartment.     

Cell proliferation kinetics of six xenografted human cervix carcinomas: comparison of autoradiography and bromodeoxyuridine labelling methods

Cell kinetic and histologic parameters of six xenografted tumours with volume doubling times ranging from 6 to 43 d were investigated in order to obtain kinetic information on a panel of tumours to be used in radiobiological studies. The six tumours covered a range of histologies and their DNA indices varied from 2.7 to 1.4. The length of the cell cycle (Tc), potential doubling time (Tpot) and labelling index (LI) were determined by continuous labelling with [3H]TdR and autoradiography in three tumours, Tc varied from 30 to 40 h. Determinations of the length of the S phase (Ts) were found to be less reliable by this method. Data on Ts and LI were also determined in all six tumours using bromodeoxyuridine (Brd) labelling and the single sample method: values of Tpot were slightly longer than those obtained via the autoradiographic method. In addition, multiple samples were taken after BrdU labelling. Tc was determined by fitting the data obtained from mid-S, mid-G2 and mid-G1 windows to curves described by a damped oscillator. Data obtained via the mid-S window were found to be most reliable. Generally, cell cycle times obtained by the BrdU method were longer than those observed with the autoradiographic method. Differences between the two methods could be explained by inaccuracies in the determination of Ts, LI and Tc and differences in the experimental approach. We consider the BrdU labelling method to be a suitable alternative for the time-consuming autoradiography, if data on Ts or Tpot are sufficient. Due to difficulties in the reproducibility of the immunofluorescence staining and asynchronization of cells approximately 10 h after labelling, the method of windows analysis was affected by similar problems to those observed in interpretation of percentage labelled mitosis (PLM) curves. However, the method may serve as an alternative to determine cell cycle times in vitro and, if improved technically, in vivo. Careful comparison of the data obtained from mid-S, mid-G1 and mid-G2 windows may increase the reliability of the determination of cell kinetic parameters.     

ANALYSIS OF THE KINETICS OF GRANULOSA CELL POPULATIONS IN THE MOUSE OVARY

The kinetics of granulosa cell populations in two types of follicles in ovaries of 28-day-old Bagg mice are investigated. The analysis includes estimations of mean values and standard deviations of the transit times (T_G1, T_S, T_G2 and T_C), the doubling time T_D, and the proliferative fraction p. First the percentage of labelled mitosis curve (PLM-curve) and the continuous labelling curve (CL-curve) are estimated. Then a hypothesis concerning the cell kinetics of the granulosa cells in the two follicle types is set up. The normal distribution is chosen to simulate the probability density functions of the transit times. On the basis of the hypothesis mathematical expressions for the PLM- and CL-curves are worked out. By fitting the calculated PLM-curve to the experimental one it is possible to estimate mean values and standard deviations of T_G1, T_S>, and T_G2. As a test of the hypothesis the CL-curve is calculated by means of the estimated parameter values and compared to the experimental one. The calculated PLM- and CL-curves are found to be in good agreement with the experimental data as far as both follicle types are concerned. It is concluded that the method is a useful procedure. The choice of a normal distribution does not imply a significant limitation of the method in these investigations. Moreover it is concluded that the hypothesis is plausible. This means, e.g., that the proliferative fraction is unity in the two follicle types and that there is no cell loss from the cell systems.     

NEW METHODS OF CELL CYCLE ANALYSIS BASED ON THE SELECTIVE TAGGING OF CELLS EITHER AT THE BEGINNING OR END OF S PHASE

New techniques for cell cycle analysis are presented. Using HeLa cells, methods are described for the selection of a narrow window or cohort of lightly [³H]-labeled cells located either at the very beginning or the very end of S phase. The cohort cells are tagged by a labeling procedure which entails alternating pulses of high and low levels of [³H]thymidine and are identified autoradiographically. Additional methods are described for following the progress of cohort cells through the cell cycle. Theoretically, with the methods described, it should be possible to follow the ‘early S cohort’ cells as they exit from S phase, as they enter and exit M and as they enter the subsequent S phase. This would allow a determination of S, S + G₂, S + G₂+ M and T. It should theoretically be possible to follow ‘late S cohort’ cells in a similar manner, allowing a determination of G₂, G₂+ M and G₂+ M + G₁. To test these predictions, several experiments are presented in which the progress of the two cohorts is monitored. The best data were obtained from the mitotic curves of cohort cells. For each of the cohorts, values were obtained for the time required for peak concentration of cells in mitosis, the coefficients of variation and of skew. The curve of cohort cells passing through mitosis is shown to fit a log-normal curve better than a normal curve. In addition, the mitotic curves are used to estimate the length of M and to estimate the loss of cohort synchrony. Other uses of these methods are discussed.     

CELL CYCLE DURATION IN THE MERISTEM OF NEPHROLEPIS BISERRATA STOLONS: THE ROLE OF THE APICAL CELL

The stolons of Nephrolepis biserrata (sw.) Schott are thin axes that grow rapidly (from 2 to 4 mm per day) in the controlled conditions applied. In the cylindro-conical meristem, three histological zones are defined. Cell cycle duration was determined for each zone by autoradiographic methods after incorporation of tritiated thymidine and confirmed by the colchicine-induced metaphase-accumulation technique. The apical cell and its derivatives (Zone 1) are mitotically more active (cell cycle duration: 80 hr) than the cells of the subapical zones (2 and 3), where cell cycle lengths are 142 hr and 95 hr respectively. These data, compared to previous results, give evidence for the main role played by the relative rate of division of the apical cell compared to that of lateral cells in the organization and the shape of the meristem of pteridophytes. Moreover, the apical cell appears to be unique in having a differentiated cytological aspect not usually associated with an intensely proliferating cell.     

ANALYSIS OF THE GROWTH KINETICS OF A HUMAN LYMPHOMA CELL LINE

The growth kinetics of an established human lymphoma cell line were analyzed by a variety of techniques utilizing various cell inocula (5 x 10⁴ - 5 x 10⁵ cells) dispensed into 60 mm diameter dishes. Techniques included pulse-labeled mitosis (PLM), continuous labeling with ³H-TdR, time-lapse photography (TLP), cell counts by electronic particle counter, and DNA histography obtained by pulse cytophotometry (PCP). There were no significant differences among values determined for any kinetic parameters as a function of cell concentration. the average doubling time of exponentially growing cells, regardless of cell inoculum, was 44.1 hr. the generation time determined by PLM was 31.1 hr with a SD of 4.7 hr. Transit times for each stage were: T_G1= 10.6 hr, T_s= 9.9 hr, T_G2= 9.9 hr, and T_m= 0.7 hr. Repeated experiments using continuous labeling with ³H-TdR demonstrated a T_G2 of 6.3 hr. the longer value determined by PLM is possibly due to the technical manipulations of this procedure which may delay pulse-labeled cells from resuming cell cycle transit. Hence, values for cell cycle stages were recalculated to give T_G1= 14.1 hr, T_s= 9.9 hr, T_G2 = 6.3 hr, and T_m= 0.7 hr. These results were used to compute the size of each cell cycle stage compartment pool and corresponded very closely to values defined directly by PCP. TLP analysis considered only cells that produced colonies of at least thirty-two cells. Generation times ranged from 8 to 89 hr and showed a positive skewness. the average value measured for 330 divisions was 34.5 hr with a SD of 13.2 hr. Thus, the variance predicted by curve fitting of the PLM data did not correlate with that defined by time-lapse photography nor did it encompass the range in generation times observed directly by TLP. There was a positive correlation between sister-sister cell generation times (+0.66) but no relation was noted for mother-daughter values.