Biomedical subjects
J J Tyson
Publications and source records attributed to J J Tyson.
Modeling the cell division cycle: cdc2 and cyclin interactions.
The proteins cdc2 and cyclin form a heterodimer (maturation promoting factor) that controls the major events of the cell cycle. A mathematical model for the interactions of cdc2 and cyclin is constructed. Simulation and analysis of the model show that the control system can operate in three modes: as a steady state with high maturation promoting factor activity, as a spontaneous oscillator, or as an excitable switch. We associate the steady state with metaphase arrest in unfertilized eggs, the spontaneous oscillations with rapid division cycles in early embryos, and the excitable switch with growth-controlled division cycles typical of nonembryonic cells.
Analysis of the kinetic hairpin transfer model for parvoviral DNA replication.
All linear DNA molecules face special problems in replicating their 5' ends, as DNA polymerases add nucleotides only to pre-existing strands with free 3'-OH groups. Parvoviruses, a group of small animal viruses with a linear single-stranded DNA genome, cope with this problem by having palindromic terminal sequences that can fold back on themselves to form hairpin structures essential in priming DNA replication. The 3' terminal sequence that initiates replication becomes reversed in orientation during the process, and if the palindrome is imperfect, two different, reverse-complementary terminal sequences are generated. The relative abundances of the terminal sequence orientations at each end of the DNA molecules can be measured and give information about the replication process. From such clues, we developed a "kinetic hairpin transfer model" based on differential rates of hairpin formation and inversion processes depending on the conformations of the 3' termini. Numerical studies showed that this simple idea can account for the diverse pattern of DNA distributions observed in the family Parvoviridae. In this paper, we simplify the model to a set of coupled linear first-order ordinary differential equations in order to delineate its essential properties by Perron-Frobenius theory. Secondly, we examine our assumption of linear kinetics by modeling enzyme catalysis of the component steps of the hairpin transfer process. We show that the rate-determining step of the process is the binding of initiation complex to the self-priming hairpin structures. Furthermore, we find that if the replication machinery is saturated by DNA substrate late in an infection, the differential equations become non-linear but the steady-state DNA distribution is still given by the solution of our original linear equations.
A cellular automation model of excitable media including curvature and dispersion.
Excitable media are spatially distributed systems characterized by their ability to propagate signals undamped over long distances. Wave propagation in excitable media has been modeled extensively both by continuous partial differential equations and by discrete cellular automata. Cellular automata are desirable because of their intuitive appeal and efficient digital implementation, but until now they have not served as reliable models because they have lacked two essential properties of excitable media. First, traveling waves show dispersion, that is, the speed of wave propagation into a recovering region depends on the time elapsed since the preceding wave passed through that region. Second, wave speed depends on wave front curvature: curved waves travel with normal velocities noticeably different from the plane-wave velocity. These deficiencies of cellular automation models are remedied by revising the classical rules of the excitation and recovery processes. The revised model shows curvature and dispersion effects comparable to those of continuous models, it predicts rotating spiral wave solutions in quantitative accord with the theory of continuous excitable media, and it is parameterized so that the spatial step size of the automation can be adjusted for finer resolution of traveling waves.
A kinetic hairpin transfer model for parvoviral DNA replication.
The DNAs encapsidated by parvoviruses show distinctly different patterns with respect to the ratio of plus-to-minus strands and sequence heterogeneity at the ends. A kinetic model, based on differential rates of hairpin transfer at 3' termini, is described and shown to account for all known parvoviral DNA distributions.
Effects of asymmetric division on a stochastic model of the cell division cycle.
The stochastic model of cell division formulated by Alt and Tyson is generalized to the case of imprecise binary fission. Closed-form expressions are derived for the generation-time distribution, the birth-size and division-size distributions, the beta curve, and the correlation coefficient of generation times of sister cells. The theoretical results are compared to observations of cell division statistics in a culture of fission yeast.
Cyclic AMP waves during aggregation of Dictyostelium amoebae.
During the aggregation phase of their life cycle, Dictyostelium discoideum amoebae communicate with each other by traveling waves of cyclic AMP. These waves are generated by an interplay between random diffusion of cyclic AMP in the extracellular milieu and the signal-reception/signal/relaying capabilities of individual amoebae. Kinetic properties of the enzymes, transport proteins and cell-surface receptor proteins involved in the cyclic AMP signaling system have been painstakingly worked out over the past fifteen years in many laboratories. Recently Martiel & Goldbeter (1987) incorporated this biochemical information into a unified mathematical model of communication among Dictyostelium amoebae. Numerical simulations of the mathematical model, carried out by Tyson et al. (1989), agree in quantitative detail with experimental observations of cyclic AMP traveling waves in Dictyostelium cultures. Such mathematical modeling and numerical experimentation provide a necessary link between detailed studies of the molecular control mechanism and experimental observations of the intact developmental system.
Size control of cell division.
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Sloppy size control of the cell division cycle.
In an asynchronous, exponentially proliferating cell culture there is a great deal of variability among individual cells in size at birth, size at division and generation time (= age at division). To account for this variability we assume that individual cells grow according to some given growth law and that, after reaching a minimum size, they divide with a certain probability (per unit time) which increases with increasing cell size. This model is called sloppy size control because cell division is assumed to be a random process with size-dependent probability. We derive general equations for the distribution of cell size at division, the distribution of generation time, and the correlations between generation times of closely related cells. Our theoretical results are compared in detail with experimental results (obtained by Miyata and coworkers) for cell division in fission yeast, Schizosaccharomyces pombe. The agreement between theory and experiment is superior to that found for any other simple models of the coordination of cell growth and division.
Cell growth and division: a deterministic/probabilistic model of the cell cycle.
A model of the cell cycle, incorporating a deterministic cell-size monitor and a probabilistic component, is investigated. Steady-state distributions for cell size and generation time are calculated and shown to be globally asymptotically stable. These distributions are used to calculate various statistical quantities, which are then compared to known experimental data. Finally, the results are compared to distributions calculated from a Monte-Carlo simulation of the model.
An improved data analysis method for interleukin 2 microassay.
Development of the interleukin 2(IL 2) microassay, coupled with the use of highly purified or recombinant factors has allowed a detailed examination of the mechanism of action of this important biological response modifier. However, probit analysis of the microassay data does not allow inherent error of the system to be approximated nor can units of activity be assessed for significance. A computer program was developed to analyze the validity of each regression line and to generate 95% confidence intervals around each line. This program employs analysis of variance, linear regression analysis and the parallel line assay to fix confidence intervals for each IL 2 unit value. The use of recombinant IL 2 as an immunomodulator in clinical settings warrants a more precise statistical method to evaluate normal fluctuations of this factor than currently in use. The development of such a method is presented here.
The distributions of cell size and generation time in a model of the cell cycle incorporating size control and random transitions.
A deterministic/probabilistic model of the cell division cycle is analysed mathematically and compared to experimental data and to other models of the cell cycle. The model posits a random-exiting phase of the cell cycle and a minimum-size requirement for entry into the random-exiting phase. By design, the model predicts exponential "beta-curves", which are characteristic of sister cell generation times. We show that the model predicts "alpha-curves" with exponential tails and hyperbolic-sine-like shoulders, and that these curves fit observed generation-time data excellently. We also calculate correlation coefficients for sister cells and for mother-daughter pairs. These correlation coefficients are more negative than is generally observed, which is characteristic of all size-control models and is generally attributed to some unknown positive correlation in growth rates of related cells. Next we compare theoretical size distributions with observed distributions, and we calculate the dependence of average cell mass on specific growth rate and show that this dependence agrees with a well-known relation in bacteria. In the discussion we argue that unequal division is probably not the source of stochastic fluctuations in deterministic size-control models, transition-probability models with no feedback from cell size cannot account for the rapidity with which the new, stable size distribution is established after perturbation, and Kubitschek's rate-normal model is not consistent with exponential beta-curves.
Stability of the steady-state size distribution in a model of cell growth and division.
The approach to steady-state size distribution is studied for a growing population of cells. The model incorporates cell growth at a linear rate and division into two equal daughters after a random time composed of an exponentially distributed phase and a constant deterministic phase.
Global asymptotic stability of the size distribution in probabilistic models of the cell cycle.
Probabilistic models of the cell cycle maintain that cell generation time is a random variable given by some distribution function, and that the probability of cell division per unit time is a function only of cell age (and not, for instance, of cell size). Given the probability density, f(t), for time spent in the random compartment of the cell cycle, we derive a recursion relation for psi n(x), the probability density for cell size at birth in a sample of cells in generation n. For the case of exponential growth of cells, the recursion relation has no steady-state solution. For the case of linear cell growth, we show that there exists a unique, globally asymptotically stable, steady-state birth size distribution, psi*(x). For the special case of the transition probability model, we display psi*(x) explicitly.
Analysis of Physarum proteins throughout the cell cycle by two-dimensional PAGE.
The accumulation of several hundred proteins during the nuclear division cycle of Physarum polycephalum was measured by digital image processing of silver-stained two-dimensional (2D) polyacrylamide gels. In contrast to previous studies, we have used an organism with a naturally synchronous cell cycle, so there are no uncertainties concerning synchronization artifacts or cell-sorting artifacts, and we have measured the specific amounts of each protein rather than the rate of synthesis. Since one-dimensional SDS-PAGE shows no significant fluctuations in the most abundant plasmodial proteins, we have loaded 2D gels so that proteins of low-to-moderate abundance appear in the linear range of the silver stain standard curve. Only five proteins showed reproducible, measureable fluctuations during the cell cycle. One of these proteins was tubulin. Full quantitative information was obtained by analysing the digital images of silver-stained gels by a general image processing system.
Induction of polyploid nuclei in Physarum polycephalum by cycloheximide treatment in prophase.
Macroplasmodia of the acellular slime mold Physarum polycephalum were treated with pulses of cycloheximide (10 micrograms/ml medium, for 3 h), initiated 10-20 min before metaphase in the synchronous nuclear division cycle. This treatment interfered with normal division of the nuclei, but permitted DNA synthesis in the next S phase. This interpretation is supported by measurements of the DNA content per nucleus in cycloheximide-treated cultures as compared to control cultures, which show that some nuclei after cycloheximide treatment are polyploid. By this method we can produce polyploid strains of Physarum, but the elevated nuclear DNA content is not stable, and after several months the strains have reverted to the normal diploid DNA content.
Unstable activator models for size control of the cell cycle.
The unstable activator model of Wheals & Silverman (1982) is extended to account for the delay of nuclear division in the acellular slime mold, Physarum polycephalum, that is caused by pulse treatments with inhibitors of protein synthesis. The model is solved exactly to predict the delay as a function of the half-life of the activator. The Wheals-Silverman model is found to give results comparable, but not superior, to other unstable activator models of the cell cycle.
Periodic enzyme synthesis and oscillatory repression: why is the period of oscillation close to the cell cycle time?
During exponential growth of a cell culture, some enzymes are synthesized periodically. In a synchronous culture, in which all cells undergo DNA synthesis and division more-or-less synchronously, the burst of enzyme synthesis also occurs synchronously in each cell once per division cycle. However, there are a number of interesting cases in which periodic enzyme synthesis continues in the absence of synchronous DNA replication or cell division. In all cases of periodic enzyme synthesis in asynchronous cultures, the time between bursts of enzyme synthesis, though no longer identical to the cell cycle time, is still close to the interdivision time of the growing, replicating cells. The theory of oscillatory repression looks for an explanation of this phenomenon in the periodic repression of gene transcription caused by periodic fluctuations in the concentration of the endproduct of the metabolic pathway of which the enzyme is a part. A major difficulty with this theory is that there is no obvious relationship between the periodicity of the negative feedback loop, which is determined by the kinetics of synthesis and degradation of the individual components of the feedback loop, and the periodicity of the cell cycle, which is determined by overall net synthetic rates of cellular macromolecules. Why should the period of oscillation of a repressible gene transcription system be close to the interdivision time of a population of growing cells? In this paper, I show that the relationship may be coincidental: the two fundamental periods are close to each other because they are both close to the mass-doubling time of the cell culture. That the mean interdivision time must be close to the mass-doubling time is a consequence of "balanced" growth: there is a stable size distribution of cells in a growing culture. That the period of oscillation of the negative feedback loop is also close to the mass-doubling time is shown to be a consequence of the large, nearly constant demand for endproduct and the assumed stability of the enzyme. The period of oscillation is largely attributable to the slow dilution of the stable enzyme by cell growth. For reasonable values of the parameters describing the gene-control system, I show that the enzyme must be diluted by a factor of two (approximately), that is, by the growth accomplished by one mass-doubling (nearly).