Cell cycle kinetics by BrdU-Hoechst flow cytometry: an alternative to the differential metaphase labelling technique

Human lymphocyte cell cycle kinetics was studied in parallel in whole blood and in isolated lymphocyte cultures by differential metaphase labelling and by flow cytometry, employing the principle of quenching of Hoechst fluorescence by BrdU substituted DNA. The BrdU-Hoechst flow technique yields information on the kinetics of cell recruitment and cell cycle progression superior to the differential metaphase staining, since it provides data from interphase cells, including cycle compartment durations, non-cycling cell fractions and transition probabilities. The Smith and Martin model, modified to include a fraction of non-cycling cells, yields excellent correspondence to the experimental data. We show that lymphocytes isolated from Ficoll gradients respond to PHA stimulation with a 4-6 hr delay compared to whole blood cultures or to cultures with autologous serum supplementation. A detailed study of the effects of such culture supplements on lag phase duration, cell cycle compartment length, non-cycling cell fractions and transition probabilities illustrates the application and reproducibility of the flow assay. The potential of the method is further documented with two examples showing the dependence of lymphocyte proliferation on donor age and donor genotype.     

Cell cycle model for recombinant Pichia pastoris during glycerol fed-batch cultivation

A cell cycle model is proposed for methylotrophic yeast Pichia pastoris grown on glycerol during fed-batch cultivation. Morphological differentiation of cells, such as unbudded daughter cell, unbudded parent cell and budding cell, is depicted by the model. During the cyclic growth, cells in different cycling period are assumed to undergo sequential shifting dominantly. The input of the cell cycle model is the specific growth rate, which is calculated from the macrokinetic model proposed previously. The cell cycle related variables, such as the fraction of budding cells and the cell density are then simulated. Model validation is carried out with the experimental data of off-line assays.     

Cell Cycle Kinetics By Brdu-Hoechst Flow Cytometry: an Alternative to the Differential Metaphase Labelling Technique

Abstract. Human lymphocytes cell cycle kinetics was studied in parallel in whole blood and in isolated lymphocyte cultures by differential metaphase labelling and by flow cytometry, employing the principle of quenching of Hoechst fluorescence by BrdU substituted DNA. the BrdU-Hoechst flow technique yields information on the kinetics of cell recruitment and cell cycle progression superior to the differential metaphase staining, since it provides data from interphase cells, including cycle compartment durations, non-cycling cell fractions and transition probabilities. the Smith and Martin model, modified to include a fraction of non-cycling cells, yields excellent correspondence to the experimental data. We show that lymphocytes isolated from Ficoll gradients respond to PHA stimulation with a 4-6 hr delay compared to whole blood cultures or to cultures with autologous serum supplementation. A detailed study of the effects of such culture supplements on lag phase duration, cell cycle compartment length, non-cycling cell fractions and transition probabilities illustrates the application and reproducibility of the flow assay. the potential of the method is further documented with two examples showing the dependence of lymphocyte proliferation on donor age and donor genotype.     

A modification of the grain count halving method for detailed analysis of cell kinetic parameters

A modification of the conventional grain count halving (GCH) method is presented. By determining the decrease of the mean grain number of all interphase cells in addition to that of all labelled interphase cells on the same autoradiographs, the potential doubling time Tpot (or the cell production rate kp) can be obtained in one and the same experiment. Thus the modified GCH method provides not only the cycle time of the cell population studied but also the growth fraction and, with additional cytofluorometric measurements, the duration of all cycle phases. By evaluating the cell production rate and the growth fraction this method leads to more reliable cell kinetic data of experimental tumours and human tumours growing in nude mice. In contrast to other cell kinetic methods, the modified GCH method can also be applied in special cases to human tumours in vivo, since only few points of measurement are needed. A comparison of the cell kinetic results obtained by the modified GCH method with those derived from the fraction of labelled mitoses method, both applied to allotransplants of the adenocarcinoma EO 771 in nude mice, shows good agreement.     

A modification of the grain count halving method for detailed analysis of cell kinetic parameters

Abstract A modification of the conventional grain count halving (GCH) method is presented. By determining the decrease of the mean grain number of all interphase cells in addition to that of all labelled interphase cells on the same autoradiographs, the potential doubling time T _pot (or the cell production rate k _p) can be obtained in one and the same experiment. Thus the modified GCH method provides not only the cycle time of the cell population studied but also the growth fraction and, with additional cytofluorometric measurements, the duration of all cycle phases. By evaluating the cell production rate and the growth fraction this method leads to more reliable cell kinetic data of experimental tumours and human tumours growing in nude mice. In contrast to other cell kinetic methods, the modified GCH method can also be applied in special cases to human tumours in vivo , since only few points of measurement are needed. A comparison of the cell kinetic results obtained by the modified GCH method with those derived from the fraction of labelled mitoses method, both applied to allotransplants of the adenocarcinoma EO 771 in nude mice, shows good agreement.     

THE APPLICATION OF AGE DISTRIBUTION THEORY IN THE ANALYSIS OF CYTOFLUORIMETRIC DNA HISTOGRAM DATA

Age distribution theory has been employed in a model to analyse a variety of histograms of the DNA content of single cells in samples from experimental tumours growing in tissue culture. The method has produced satisfactory correspondence with the experimental data in which there was a wide variation in the proportions of cells in the intermitotic phases, and generally good agreement between the ³H-thymidine labelling index and the computed proportion in S phase. The model has the capacity to analyse data from populations which contain a proportion of non-cycling cells. However, it is concluded that reliable results for the growth fraction and also for the relative durations of the intermitotic phase times cannot be obtained for the data reported here from the DNA histograms alone. To obtain reliable estimates of the growth fraction the relative durations of the phase times must be known, and conversely, reliable estimates of the relative phase durations can only be obtained if the growth fraction is known.     

Modeling experimental time series with ordinary differential equations

Recently some methods have been presented to extract ordinary differential equations (ODE) directly from an experimental time series. Here, we introduce a new method to find an ODE which models both the short time and the long time dynamics. The experimental data are represented in a state space and the corresponding flow vectors are approximated by polynomials of the state vector components. We apply these methods both to simulated data and experimental data from human limb movements, which like many other biological systems can exhibit limit cycle dynamics. In systems with only one oscillator there is excellent agreement between the limit cycling displayed by the experimental system and the reconstructed model, even if the data are very noisy. Furthermore, we study systems of two coupled limit cycle oscillators. There, a reconstruction was only successful for data with a sufficiently long transient trajectory and relatively low noise level.     

Mathematical model of proliferative activity in epidermis of the normal skin and of the skin afflicted by psoriasis

A mathematical model of the mitotic activity of epidermis in norm and psoriasis is presented, which consists of a system of two autonomous nonlinear differential equations. A qualitative analysis of the model was done, and numerical solutions at the parameter values corresponding to these state were obtained. It was shown that, in norm, the system can exist only in one stationary equilibrium state of the "focus" type, and in psoriasis, due to an increase in the growing fraction, hyperproliferation, and enhanced migration of keratinocytes, a stable limiting cycle arises from the state of an unstable focus. The existence of two stable states (focus and the limiting cycle) is regulated by a parameter that describes the inhibition of division of maturing cells of suprabasal epidermal layers by the intrinsic tissue-specific transmitters of mitosis of G1-keilon type. The model is consistent with experimental data on the kinetics of cell proliferation in the epidermis in norm and psoriasis and the clinical course of the disease.     

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.     

A stochastic model of cell cycle desynchronization

A general branching process model is suggested to describe cell cycle desynchronization. Cell cycle phase times are modeled as random variables and a formula for the expected fraction of cells in S phase as a function of time is established. The model is compared to data from the literature and is also compared to previously suggested deterministic and stochastic models.     

A New Variant for Mathematical Analysis of Pulse Cytophotometric Data

The staining of DNA by specific fluorochromes provides a suitable method of receiving histograms in a short time by means of pulse cytometry. They represent the proliferative structure of cell populations at a high degree of statistical security. A method for quantitative determination of cell cycle phases (G_1-, S- and G₂ + M-phase) is presented which includes the fraction of cell debris in the calculation procedure. The advantages of this method are the elimination of overlapping between the fraction of debris and cell cycle phases and the quantitative determination of the fraction of cell debris offers the opportunity to get information on cytolytic potencies. Apart from the calculation of the various cell cycle phases the method provides criteria on the adaptation of mathematical analysis to primary data.     

肌球蛋白工作循环的一个新模型

分析总结关于分子马达肌球蛋白的最新研究结果,给出一个新的肌球蛋白工作循环的机械化学偶联模型.从新模型出发,用一组化学动力学方程描述肌肉中大量肌球蛋白的集体工作行为.利用动力学方程的非平衡定态解,并结合Pate和Cooke的实验结果得到了力作为变量的肌肉态方程.理论结果同热力学原理一致,与传统的肌肉收缩理论有一定区别.根据肌肉的特殊结构,对肌肉态方程做了进一步讨论.     

The mutation process of microsatellites during the polymerase chain reaction.

We build a mathematical model for the mutation process of microsatellites during polymerase chain reaction (PCR) using the theory of branching processes. Based on the model, we develop a method to estimate the mutation rate of microsatellites per PCR cycle and the probability of expansion by maximizing a quasi-likelihood of the observed data. We show by simulations that the proposed estimation method can accurately recover the relationship between the mutation rate and number of repeat units. The theoretical basis for the proposed method is also given. We apply the method to experimental data on poly-A and poly-CA repeats.     

Characteristics of the isoprenaline stimulated proliferative response of rat submaxillary gland.

A simple stochastic model has been developed to determine the cell cycle kinetics of the isoprenaline stimulated proliferative response in rat acinar cells. The response was measured experimentally, using 3H-TdR labelling of interphase cells and cumulative collections of mitotic cells with vincristine. The rise and fall of the fraction of labelled interphase cells and of metaphase cells is expressed by the product of the proliferative fraction and a difference of probability distributions. 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. The model when fitted to the combined fraction labelled interphase (FLIW) and fraction metaphase (FMWa) waves gave a mean Gis transit time of 21-2 hr, mean Gis +S transit time of 27-0 hr, and mean Gis + S + G2 transit time of 35-8 hr for a single injection of isoprenaline, where Gis is the initiation to S phase time. When successive injections of isoprenaline were given at intervals of 24 and 28 hr the corresponding values after the third injection were 12-4 hr, 20-8 hr and 25-7 hr respectively. The variance of the Gis phase dropped from 18-1 to 1-3 while the other variances remained unchanged. The estimated proliferative fraction was 0-24 after a single injection of isoprenaline, and 0.31 after three injections of the drug. Independently determined values of the proliferative fraction, obtained from repeated 3H-TdR injections, were 0-21 and 0-36 respectively.     

Growth and production modeling in hybridoma continuous cultures

Several experimental data on continuous cultures of hybridoma cells show that monoclonal antibody productivity is a decreasing function of dilution rate. It has been suggested that this unusual behavior may be due to the arrest of a fraction of cycling cells at a critical point of Phase G(1). Although this hypothesis has been recently investigated by using population balance models, mathematical analysis has been performed without accounting for the dynamics of the arrested cells properly. In this article, a more general and accurate approach is presented and new specific assumptions are introduced to characterize the arrest and the later progress through the cycle. Two different models (stochastic and deterministic) and two different critical points for the arrest (at the beginning and at the end of G(1)) are considered. The cell cycle parameters are estimated so that data predicted by the model fit those reported in the literature. In particular, the fraction of arrested cells, the cell arrest probability, and the mean cell generation time are computed as functions of the dilution rate. Results so far obtained predict that there is an optimal value of dilution rate for maximizing specific production rate of monoclonal antibody. (c) 1993 John Wiley & Sons, Inc.     

An integrative and practical evolutionary optimization for a complex, dynamic model of biological networks

Computer simulation is an important technique to capture the dynamics of biochemical networks. Numerical optimization is the key to estimate the values of kinetic parameters so that the dynamic model reproduces the behaviors of the existing experimental data. It is required to develop general strategies for the optimization of complex biochemical networks with a huge space of search parameters, under the condition that kinetic and quantitative data are hardly available. We propose an integrative and practical strategy for optimizing a complex dynamic model by using qualitative and incomplete experimental data. The key technologies are the divide and conquer method for reducing the search space, handling of multiple objective functions representing different types of biological behaviors, and design of rule-based objective functions that are suitable for qualitative and error-prone experimental data. This strategy is applied to optimizing a dynamic model of the yeast cell cycle to demonstrate the feasibility of it.     

Cell cycle progression

In this paper we consider cell cycle models for which the transition operator for the evolution of birth mass density is a simple, linear dynamical system with a stochastic perturbation. The convolution model for a birth mass distribution is presented. Density functions of birth mass and tail probabilities in n-th generation are calculated by a saddle-point approximation method. With these probabilities, representing the probability of exceeding an acceptable mass value, we have more control over pathological growth. A computer simulation is presented for cell proliferation in the age-dependent cell cycle model. The simulation takes into account the fact that the age-dependent model with a linear growth is a simple linear dynamical system with an additive stochastic perturbation. The simulated data as well as the experimental data (generation times for mouse L) are fitted by the proposed convolution model.     

The Automatic Analysis of Flm Curves

Abstract. Seven parameters of the cell cycle are extracted from experimental FLM data by computer using a completely automated, least-squares, regression analysis. the procedure is based on a model of the cell cycle with four phases, three coefficients of variation, and a Poisson process of cell progression. T _M is estimated separately, using mitoses per labeled cells over the first cycle. Beginning with raw data, the computer calculates initial estimates of the parameters, uses these estimates to generate a synthetic FLM curve, and then measures a weighted mean square deviation of fit between the data and the curve. By a process of iteration, involving a three-dimensional Newton-Raphson method for mean transit times and an orthogonal search for coefficients of variation, the measure of fit is progressively minimized. Eighteen experimental data sets have been analysed successfully. Several procedures for the evaluation of the analysis are described.     

Estimating the contribution of assembly activity to cortical dynamics from spike and population measures

The hypothesis that cortical networks employ the coordinated activity of groups of neurons, termed assemblies, to process information is debated. Results from multiple single-unit recordings are not conclusive because of the dramatic undersampling of the system. However, the local field potential (LFP) is a mesoscopic signal reflecting synchronized network activity. This raises the question whether the LFP can be employed to overcome the problem of undersampling. In a recent study in the motor cortex of the awake behaving monkey based on the locking of coincidences to the LFP we determined a lower bound for the fraction of spike coincidences originating from assembly activation. This quantity together with the locking of single spikes leads to a lower bound for the fraction of spikes originating from any assembly activity. Here we derive a statistical method to estimate the fraction of spike synchrony caused by assemblies—not its lower bound—from the spike data alone. A joint spike and LFP surrogate data model demonstrates consistency of results and the sensitivity of the method. Combining spike and LFP signals, we obtain an estimate of the fraction of spikes resulting from assemblies in the experimental data.