The molecular biology of Euglena gracilis. XV. Recovery from centrifugation-induced stratification

The contents of Euglena gracilis cells can be separated in vivo by ultracentrifugation. Within the unbroken cell, each set of components forms a distinct layer according to their respective densities. The degree of segregation increases with both the g-force and the time of centrifugation, up to a maximum at 100,000 x g for 1 h, when six distinct strata can be observed. When returned to normal growth conditions, essentially all the cells return to the normal state and growth pattern. Greater g-forces or longer exposures do not alter the observable strata, but the ability of the cells to recover is diminished. Smaller g-forces result in less separation of cellular contents and all cells recover, even after 18 h of exposure. Euglena cells stratified at 100,000 x g for 1 h were returned to normal growth conditions; recovery was followed microscopically and by the rate of utilization of oxygen as well as that of the single carbon source. The cells recovered their normal state within 1 to 2 h, which is only a tenth of the normal doubling time. The mechanism for this recovery involves a natural process of change in cell shape caused by contraction and relaxation of the pellicle, a cell surface structure.     

Responses to hypergravity in proliferation of Paramecium tetraurelia

It has been reported that Paramecium proliferates faster when cultured under microgravity in orbit, and slower when cultured under hypergravity. This shows that the proliferation rate of Paramecium affected by gravity. The effect of gravity on Paramecium proliferation has been argued to be direct in a paper with an axenic culture under hypergravity. To clear up uncertainties with regard to the effect of gravity, Paramecium tetraurelia was cultured axenically under hypergravity (20 x g) and the time course of the proliferation was investigated quantitatively by a new non-invasive method, laser-beam optical slice, for measuring the cell density. This method includes optical slicing a part of the culture and computer-aided counting of cells in the sliced volume. The effects of hypergravity were assessed by comparing the kinetic parameters of proliferation that were obtained through a numerical analysis based on the logistic growth equation. Cells grown under 20 x g conditions had a significantly lower proliferation rate, and had a lower population density at the stationary phase. The lowered proliferation rate continued as long as cells were exposed to hypergravity (> one month). Hypergravity reduced the cell size of Paramecium. The long and short axes of the cell became shorter at 20 x g than those of control cells, which indicates a decrease in volume of the cell grown under hypergravity and is consistent with the reported increase in cell volume under microgravity. The reduced proliferation rate implies changes in biological time defined by fission age. In fact the length of autogamy immaturity decreased by measure of clock time, whereas it remained unchanged by measure of fission age.     

A model with 'growth retardation' for the kinetic heterogeneity of tumour cell populations

In the present paper we propose a continuous cell population model based on Shackney's idea of growth retardation. Cells are characterized by two state variables: the cell maturity x, 0 < or = x < or = 1, and a state variable T that identifies the rate of maturation along cell cycle. During their life span, cells can change T at random by jump transitions to T values corresponding to slower maturation rates, while at each jump the maturity x is conserved. Both the time evolution of the population and the exponential stationary solution are numerically computed. The distribution of the cell cycle transit time in asynchronous exponential growth is investigated by Monte Carlo simulation. An approximated formula for the distribution of cell cycle time is also provided.     

Stress relaxation property of the cell wall and auxin-induced cell elongation

A stress-relaxation method has been developed to measure the mechanical property of the plant cell wall, as a physically defined terms. In the method, the stress relaxation property of the cell wall is simulated with a Maxwell viscoelastic model whose character is represented by four parameters; the minimum relaxation time, To, the relaxation rate, b, the maximum relaxation time, Tm and the residual stress, c. Thus, the mechanical property of the cell wall is represented by the four parameters. Physical and physiological meanings of the parameters are discussed. Auxin effects on the parameters were also studied. The cell elongation is simply thought to be extension of the cell wall under a force. The extension of the cell wall can be simulated by the mechanical property of the cell wall. However, the calculated extension was found to be incomparable to the real cell growth, indicating that there has to be other factors limiting the rate of cell growth. Major factors governing cell growth are discussed to be the cell wall mechanical property, the osmotic potential and water movement in the apoplast. A possibility to predict cell expansion with the three factors was discussed and a novel equation representing cell growth was obtained: $$1/R = 1/R_w + 1/R_p $$ whereR is the rate of cell elongation,R _w is the rate of cell wall extension due to the osmotic pressure andR _p is the rate of cell elongation determined by water conductivity.     

Modeling genome evolution with a diffusion approximation of a birth-and-death process

MOTIVATION: In our previous studies, we developed discrete-space birth, death and innovation models (BDIMs) of genome evolution. These models explain the origin of the characteristic Pareto distribution of paralogous gene family sizes in genomes, and model parameters that provide for the evolution of these distributions within a realistic time frame have been identified. However, extracting the temporal dynamics of genome evolution from discrete-space BDIM was not technically feasible. We were interested in obtaining dynamic portraits of the genome evolution process by developing a diffusion approximation of BDIM. RESULTS: The diffusion version of BDIM belongs to a class of continuous-state models whose dynamics is described by the Fokker-Plank equation and the stationary solution could be any specified Pareto function. The diffusion models have time-dependent solutions of a special kind, namely, generalized self-similar solutions, which describe the transition from one stationary distribution of the system to another; this provides for the possibility of examining the temporal dynamics of genome evolution. Analysis of the generalized self-similar solutions of the diffusion BDIM reveals a biphasic curve of genome growth in which the initial, relatively short, self-accelerating phase is followed by a prolonged phase of slow deceleration. This evolutionary dynamics was observed both when genome growth started from zero and proceeded via innovation (a potential model of primordial evolution), and when evolution proceeded from one stationary state to another. In biological terms, this regime of evolution can be tentatively interpreted as a punctuated-equilibrium-like phenomenon whereby evolutionary transitions are accompanied by rapid gene amplification and innovation, followed by slow relaxation to a new stationary state.     

Kinetorheological aspects of biorheology

The relationship between stress and strain is the rheological equation of state. In the case of sophisticated systems such as biological tissue, this is rarely a simple relationship. The relationship is seen to be even more complex when it is recalled that in most living tissues, the tissue is not in chemical equilibrium, but is at best in some controlled steady state. At worst, it is undergoing major fluctuations or transitions because the chemical reactions or fluxes are altering the system. It is shown, in particular, that in addition to the changes in composition, the effective rheological relaxation times of the system are shortened due to contributions deriving from the reaction rate constants. These and other points are illustrated by considering a process of irreversible monomolecular degradation of a large macromolecular species.     

Kinetic analysis of the growth of Chlorella vulgaris

The energy of the total transmitted light was subtracted from that of the incident light in a culture vessel and the difference was divided by the weight of cells. The value thus obtained was defined as the amount, E(x), of light energy absorbed per unit cell weight per unit time.Batch and continuous cultures of Chlorella vulgaris were carried out at 30 degrees C in the pH range of 6.4-6.7 while restricting illumination. Next the specific growth rate, mu, in the batch culture and the fixed dilution rate, D, in the continuous culture were plotted against E(x). The results showed that the relation between D and E(x) can be expressed in a Michaelis-Menten equation, where the maximal specific growth rate is 0.24 h (-1) and the saturation constant is 6.58 kcal/g . h.Cell concentration calculated by substituting the apparent concentration, X(e), of incubated cells and the apparent maintenance constant, M(e), for this equation agreed with that observed in almost all growth phases. Furthermore, from the change of chlorophyll productivity and the relationship between D and E(x) expressed in this equation, it is assumed that E(x) involves the light energy directly utilized in photosynthesis in the cells and that which is converted into, e.g., heat. This equation also indicated that a maximum in the growth yield existed. Then the growth yield of 0.029 g/kcal obtained at the incident light of 1.46 or 2.63 cal/cm(2) . h was maximum (maximal conversion efficiency of light energy, 15.6%).These results indicate that this method of deriving the equation for the growth rate from this study is a useful procedure for obtaining bioengineering findings.     

A cytokinetic model for heterogeneous mammalian cell populations. I. Cell growth and cell death

A general model is proposed for describing the growth behavior of mammalian cell populations, which features:(a) a cell cycle time distribution function with properties such that mean and variance increase with increasing population size; (b) maturation age and maturation rate functions which constrain the maturational pathways of individual cells; and (c) a death rate function, where cell death is construed as irreparable damage to a cell's reproductive apparatus. The biological implications of the model are discussed, and methods for relating the model to real cell systems by means of commonly used experimental techniques are described. The model is compared with earlier models.     

The ferrous iron oxidation kinetics of Thiobacillus ferrooxidans in batch cultures

The ferrous iron oxidation kinetics of Thiobacillus ferrooxidans in batch cultures was examined, using on-line off-gas analyses to measure the oxygen and carbon dioxide consumption rates continuously. A cell suspension from continuous cultures at steady state was used as the inoculum. It was observed that a dynamic phase occurred in the initial phase of the experiment. In this phase the bacterial ferrous iron oxidation and growth were uncoupled. After about 16 h the bacteria were adapted and achieved a pseudo-steady state, in which the specific growth rate and oxygen consumption rate were coupled and their relationship was described by the Pirt equation. In pseudo-steady state, the growth and oxidation kinetics were accurately described by the rate equation for competitive product inhibition. Bacterial substrate consumption is regarded as the primary process, which is described by the equation for competitive product inhibition. Subsequently the kinetic equation for the specific growth rate, μ, is derived by applying the Pirt equation for bacterial substrate consumption and growth. The maximum specific growth rate, μ _max, measured in the batch culture agrees with the dilution rate at which washout occurs in continuous cultures. The maximum oxygen consumption rate, q _O2,max, of the cell suspension in the batch culture was determined by respiration measurements in a biological oxygen monitor at excess ferrous iron, and showed changes of up to 20% during the course of the experiment. The kinetic constants determined in the batch culture slightly differ from those in continuous cultures, such that, at equal ferric to ferrous iron concentration ratios, biomass-specific rates are up to 1.3 times higher in continuous cultures. Received: 8 February 1999 / Accepted: 17 February 1999     

Management of individual body weight growth of infant squirrel monkey (Saimiri sciureus) in indoor breeding colony

We biometrically analyzed the body weight growth data of new-born squirrel monkeys, obtained during the nursing period from 0 to 12 weeks of age. Body weight (y in grams) could be expressed as a function of birth weight (a in grams) and age (x in weeks) by the following equation: y = a + b x, where b indicates growth rate. This equation corresponded significantly with actual growth curves (R2 = 0.96). The frequency distribution of b values was demonstrated to be abnormal distribution. This value was used to judge whether the body weight growth of each monkey was normal or abnormal. The lower control limit (LCL) was calculated by using a linear equation with the b value of 9.07 (M-1.25 x S.D.) and each birth weight. For the monkeys whose body weight was above the LCL during the first three weeks after birth, it was determined whether the frequency of weighings could be reduced from 13 to 7. Using the same animals, no significant difference was detected between the b value estimated from 13 measurements and that estimated from 7 measurements. Thus, from the standpoint of management's policy to save labor, the frequency of weighings could be reduced. A new daily routine has been established in our primate center to save labor by reducing the number of body weighings of the many infant monkeys. In the new program, newborn monkeys whose body weight is above the LCL are weighed only 7 times during the nursing period of 12 weeks, while those whose weight is below the LCL are weighed 8 to 13 times.     

Mathematical description of stress relaxation of bovine femoral cortical bone

In 1993 we proposed an empirical formula for describing the relaxation modulus of cortical bone based on the results of stress relaxation experiments performed for 1 x 10(5) sec: [E(t) = E0{A exp[ -(t/tau1)beta] + (1 - A) exp(-t/tau2)}, (0 < A, beta <1 and tau1 < tau2) where E0 is the initial value of the relaxation modulus, A is the portion of the first term, tau1 and tau2 are characteristic relaxation times, and beta is a shape factor [Sasaki et al., J. Biomechanics 26 (1993), 1369]. Although the relaxation properties of bone under various external conditions were described well by the above equation, recent experimental results have indicated some limitations in its application. In order to construct an empirical formula for the relaxation modulus of cortical bone that has a high degree of completeness, stress relaxation experiments were performed for 6 x 10(5) seconds. The second term in the equation was determined as an apparently linear portion in a log E(t) vs t plot at t>1 x 10(4) sec. The same plot for experiments performed for 6 x 10(5) seconds revealed that the linear portion corresponding to the second term was in fact a curve with a large radius of curvature. On the basis of this fact, we proposed a second improved empirical equation E(t) = E0{A exp [ -(t/tau1)beta] + (1 - A) exp[-(t/tau2)gamma]}, (0相似文献   

Regulatory control and the costs and benefits of biochemical noise

Experiments in recent years have vividly demonstrated that gene expression can be highly stochastic. How protein concentration fluctuations affect the growth rate of a population of cells is, however, a wide-open question. We present a mathematical model that makes it possible to quantify the effect of protein concentration fluctuations on the growth rate of a population of genetically identical cells. The model predicts that the population's growth rate depends on how the growth rate of a single cell varies with protein concentration, the variance of the protein concentration fluctuations, and the correlation time of these fluctuations. The model also predicts that when the average concentration of a protein is close to the value that maximizes the growth rate, fluctuations in its concentration always reduce the growth rate. However, when the average protein concentration deviates sufficiently from the optimal level, fluctuations can enhance the growth rate of the population, even when the growth rate of a cell depends linearly on the protein concentration. The model also shows that the ensemble or population average of a quantity, such as the average protein expression level or its variance, is in general not equal to its time average as obtained from tracing a single cell and its descendants. We apply our model to perform a cost-benefit analysis of gene regulatory control. Our analysis predicts that the optimal expression level of a gene regulatory protein is determined by the trade-off between the cost of synthesizing the regulatory protein and the benefit of minimizing the fluctuations in the expression of its target gene. We discuss possible experiments that could test our predictions.     

The dynamics of continuous microbial culture described by cell age distribution and concentration of one substrate

A mathematical model has been considered in which the known equation of McKendrick and Von Foerster for cell age distribution is combined with that for substrate concentration. The dependence of cell division rate on cell age has been taken as a step function. The interrelation between culture parameters describing the substrate consumption and cell division has been found. The shape of cell age distribution as well as the values of substrate and cell concentrations in steady and transient states have been investigated. Stationary regimes at the initial culture state synchronized by ages have been found to be established as damped oscillations and age waves. Under definite conditions the transition from one steady growth regime to another includes sharp single-time age synchronization of the culture.     

Kinetics of Growth of Individual Cells of Escherichia coli and Azotobacter agilis

Escherichia coli and Azotobacter agilis were grown in minimal media until a steady state was established. The distribution of cell size was determined electronically. From the equation of Collins and Richmond, the growth rate of individual cells was computed as a function of size. The main features of the growth of individual E. coli and A. agilis cells revealed by this work were: the specific growth rate decreased at the time of division, and both the absolute and specific growth rates increased between divisions. The frequency function of interdivision times was computed and was found to be positively skewed with a coefficient of variation of approximately 0.3. The results supported the hypothesis of Koch and Schaechter that the size of an individual cell at division is highly regulated.     

Quantification of cell size distribution as applied to the growth of Corynebacterium glutamicum

It is known that the cell size is related to the physiological state of a cell. Therefore, cell size distribution directly reflects the average physiological properties of the cell culture. Cell size distribution can be enumerated by image analysis, flow cytometry and coulter counter. In this study, image analysis was used to characterize the cell size distribution during the growth of Corynebacterium glutamicum and was further analyzed by a distribution function. The parameters of the distribution function indicate the mean value and spread of the distribution. Analysis demonstrated that the maximum specific growth rate was higher (0.67h(-1)) for the growth obtained through serial dilution of seed as compared to growth from a normal seed culture (0.53h(-1)). This was due to a greater percentage of the cell population being in the state of division for the growth through serial dilution in the mid-log phase. The measurement of the cell size distribution demonstrated that the average cell size decreased during the course of growth. The distribution function was also used to enumerate the average specific growth rate of both the conditions of the culture. The demonstrated methodology can be used to predict an average growth property of a cell culture.     

Microbial growth dynamics on the basis of individual budgets

The popular theories for microbial dynamics by Monod, Pirt and Droop are shown to be special cases of a model for individual budgets, in which growth and maintenance are on the expense of reserve materials. The dynamics of reserve materials is a first order process with a relaxation time proportional to cell length; maintenance is proportional to cell volume, and uptake, which depends hyperbolically on substrate density, is proportional to cell volume as well. Because of the latter, population dynamics depends on the behaviour of the individuals in a simple way, such that the cell volume distribution has no quantitative effect.When uptake is proportional to the surface area of the cell, which is realistic from a physical point of view, the relation between the individual level and the population one becomes more complicated and the cell size and shape distribution affects population dynamics. It is shown how the changing shape of rods modifies uptake and, consequently, growth.The concept of energy conductance, defined as the ratio, of the maximum surface area specific uptake and the volume specific energy reserve has been introduced in the analysis of microbial dynamics. The first tentative results indicate that the value for E. coli is close to the mean value for a wide variety of animals.Properties of the model for cell suspension at constant substrate densities are analyzed and tested against a variety of experimental data from the literature on both the individual and the population level.     

Theoretical analysis of thermal damage in biological tissues caused by laser irradiation

A bioheat transfer approach is proposed to study thermal damage in biological tissues caused by laser radiation. The laser light propagation in the tissue is first solved by using a robust seven-flux model in cylindrical coordinate system. The resulting spatial distribution of the absorbed laser energy is incorporated into the bioheat transfer equation for solving temperature response. Thermal damage to the tissue is assessed by the extent of denatured protein using a rate process equation. It is found that for the tissue studied, a significant protein denaturation process would take place when temperature exceeds about 53 degrees C. The effects of laser power, exposure time and beam size as well as the tissue absorption and scattering coefficients on the thermal damage process are examined and discussed. The laser conditions that cause irreversible damage to the tissue are also identified.     

An algorithmic approach to constructing the on-line estimation system for the specific growth rate

The objective of this article is to propose an algorithm for the on-line estimation of the specific growth rate in a batch or a fed-batch fermentation process. The algorithm shows the practical procedure for the estimation method utilizing the macroscopic balance and the extended Kalman filter. A number of studies of the on line estimation have been presented. However, there are few studies discussing about the selection of the observed variables and for the tuning of some parameters of the extended Kalman filter, such as covariance matrix and initial values of the state.The beginning of this article is devoted to explain the selection of the observed variable. This information is very important in terms of the practical know-how for using technique. It is discovered that the condition number is a practically useful and valid criterion for number is a practically useful and valid criterion for choosing the variable to be observed.Next, when the extended Kalman filter in applied to the online estimation of the specific growth rate, which is directly unmeasurable, criteria for judging the validity of the estimated value from the observed data are proposed. Based on the proposed criterial, the system equation of the specific growth rate is selected and initial value of the state variable and covariance matrix of the system noises are adjusted. From many experiments, it is certified that the specific growth rate in the batch or fed -batch fermentation can be estimated accurately by means of the algorithm proposed here. In these experiments, that is, when the cell concentration is measured directly, the extended Kalman filter using the convariance matrix with a constant element can estimate more accurately values of the specific growth rate than the adaptive extended Kalman filter does.     

Effect of Cell Density on Thermotaxis of Paramecium1

ABSTRACT. The swiftness of thermotaxis of Paramecium caudatum has been investigated for various populations of organisms by measuring the transient spatial distribution of the gathering process of organisms that are transferred to a temperature-gradient cell from the culture medium. The dispersion obtained from the spatial distribution for each population is found to decrease linearly with time and finally reach a steady state value. The gathering rate determined by the slope of the dispersion strongly depends on population; it increases with population.