Biomedical subjects

J J Tyson

Publications and source records attributed to J J Tyson.

At least 19 recordsLinked to original sources

PubMed2006

Computer evaluation of network dynamics models with application to cell cycle control in budding yeast.

Cellular processes are governed by complex networks of interacting genes and proteins. Theoretical molecular biologists attempt to describe these processes via mathematical models by writing biochemical reaction equations. Modellers are building increasingly larger and complex mathematical models to describe these cellular processes, making model evaluation a time consuming and difficult task. The authors describe an automatable process for model evaluation and a software system that implements this process. The software is adaptable to many types of models and is freely available along with all needed data files. The cell cycle control system for budding yeast is known in fine detail and constrained by more than 100 phenotypic observations in mutant strains. As an example, the authors apply their process to a model of cell cycle control in budding yeast containing dozens of regulatory equations and explaining nearly all of the known mutant phenotypes.

Cell Cycle↗

PubMed2005

Globally optimised parameters for a model of mitotic control in frog egg extracts.

DNA synthesis and nuclear division in the developing frog egg are controlled by fluctuations in the activity of M-phase promoting factor (MPF). The biochemical mechanism of MPF regulation is most easily studied in cytoplasmic extracts of frog eggs, for which careful experimental studies of the kinetics of phosphorylation and dephosphorylation of MPF and its regulators have been made. In 1998 Marlovits et al. used these data sets to estimate the kinetic rate constants in a mathematical model of the control system originally proposed by Novak & Tyson. In a recent publication, we showed that a gradient-based optimisation algorithm finds a locally optimal parameter set quite close to the 'Marlovits' estimates. In this paper, we combine global and local optimisation strategies to show that the 'refined Marlovits' parameter set, with one minor but significant modification to the Novak & Tyson equations, is the unique, best-fitting solution to the parameter estimation problem.

Animals↗

PubMed2003

Modelling the controls of the eukaryotic cell cycle.

The eukaryotic cell-division cycle is regulated by three modules that control G(1)/S, G(2)/M and meta/anaphase transitions. By using mathematical modelling, we show the dynamic characteristics of these individual modules and we also assemble them together into a comprehensive model of the eukaryotic cell-division cycle. With this comprehensive model, we also discuss the mechanisms by which different checkpoint pathways stabilize different cell-cycle states and inhibit the transitions that drive cell-cycle progression.

Cell Cycle↗

PubMed2001

A stochastic, molecular model of the fission yeast cell cycle: role of the nucleocytoplasmic ratio in cycle time regulation.

We propose a stochastic version of a recently published, deterministic model of the molecular mechanism regulating the mitotic cell cycle of fission yeast, Schizosaccharomyces pombe. Stochasticity is introduced in two ways: (i) by considering the known asymmetry of cell division, which produces daughter cells of slightly different sizes; and (ii) by assuming that the nuclear volumes of the two newborn cells may also differ. In this model, the accumulation of cyclins in the nucleus is proportional to the ratio of cytoplasmic to nuclear volumes. We have simulated the cell-cycle statistics of populations of wild-type cells and of wee1(-) mutant cells. Our results are consistent with well known experimental observations.

Algorithms↗

PubMed2001

Regulation of the eukaryotic cell cycle: molecular antagonism, hysteresis, and irreversible transitions.

In recent years, molecular biologists have uncovered a wealth of information about the proteins controlling cell growth and division in eukaryotes. The regulatory system is so complex that it defies understanding by verbal arguments alone. Quantitative tools are necessary to probe reliably into the details of cell cycle control. To this end, we convert hypothetical molecular mechanisms into sets of nonlinear ordinary differential equations and use standard analytical and numerical methods to study their solutions. First, we present a simple model of the antagonistic interactions between cyclin-dependent kinases and the anaphase promoting complex, which shows how progress through the cell cycle can be thought of as irreversible transitions (Start and Finish) between two stable states (G1 and S-G2-M) of the regulatory system. Then we add new pieces to the "puzzle" until we obtain reasonable models of the control systems in yeast cells, frog eggs, and cultured mammalian cells.

Anaphase↗

PubMed2001

Network dynamics and cell physiology.

Complex assemblies of interacting proteins carry out most of the interesting jobs in a cell, such as metabolism, DNA synthesis, movement and information processing. These physiological properties play out as a subtle molecular dance, choreographed by underlying regulatory networks. To understand this dance, a new breed of theoretical molecular biologists reproduces these networks in computers and in the mathematical language of dynamical systems.

CDC2 Protein Kinase↗

PubMed2000

Modeling the fission yeast cell cycle: quantized cycle times in wee1- cdc25Delta mutant cells.

A detailed mathematical model for the fission yeast mitotic cycle is developed based on positive and negative feedback loops by which Cdc13/Cdc2 kinase activates and inactivates itself. Positive feedbacks are created by Cdc13/Cdc2-dependent phosphorylation of specific substrates: inactivating its negative regulators (Rum1, Ste9 and Wee1/Mik1) and activating its positive regulator (Cdc25). A slow negative feedback loop is turned on during mitosis by activation of Slp1/anaphase-promoting complex (APC), which indirectly re-activates the negative regulators, leading to a drop in Cdc13/Cdc2 activity and exit from mitosis. The model explains how fission yeast cells can exit mitosis in the absence of Ste9 (Cdc13 degradation) and Rum1 (an inhibitor of Cdc13/Cdc2). We also show that, if the positive feedback loops accelerating the G(2)/M transition (through Wee1 and Cdc25) are weak, then cells can reset back to G(2) from early stages of mitosis by premature activation of the negative feedback loop. This resetting can happen more than once, resulting in a quantized distribution of cycle times, as observed experimentally in wee1(-) cdc25Delta mutant cells. Our quantitative description of these quantized cycles demonstrates the utility of mathematical modeling, because these cycles cannot be understood by intuitive arguments alone.

CDC2 Protein Kinase↗

PubMed2000

Mathematical model for early development of the sea urchin embryo.

In Xenopus and Drosophila, the nucleocytoplasmic ratio controls many aspects of cell-cycle remodeling during the transitory period that leads from fast and synchronous cell divisions of early development to the slow, carefully regulated growth and divisions of somatic cells. After the fifth cleavage in sea urchin embryos, there are four populations of differently sized blastomeres, whose interdivision times are inversely related to size. The inverse relation suggests nucleocytoplasmic control of cell division during sea urchin development as well. To investigate this possibility, we developed a mathematical model based on molecular interactions underlying early embryonic cell-cycle control. Introducing the nucleocytoplasmic ratio explicitly into the molecular mechanism, we are able to reproduce many physiological features of sea urchin development.

Animals↗

PubMed2000

Kinetic analysis of a molecular model of the budding yeast cell cycle.

The molecular machinery of cell cycle control is known in more detail for budding yeast, Saccharomyces cerevisiae, than for any other eukaryotic organism. In recent years, many elegant experiments on budding yeast have dissected the roles of cyclin molecules (Cln1-3 and Clb1-6) in coordinating the events of DNA synthesis, bud emergence, spindle formation, nuclear division, and cell separation. These experimental clues suggest a mechanism for the principal molecular interactions controlling cyclin synthesis and degradation. Using standard techniques of biochemical kinetics, we convert the mechanism into a set of differential equations, which describe the time courses of three major classes of cyclin-dependent kinase activities. Model in hand, we examine the molecular events controlling "Start" (the commitment step to a new round of chromosome replication, bud formation, and mitosis) and "Finish" (the transition from metaphase to anaphase, when sister chromatids are pulled apart and the bud separates from the mother cell) in wild-type cells and 50 mutants. The model accounts for many details of the physiology, biochemistry, and genetics of cell cycle control in budding yeast.

Cell Cycle↗

PubMed1999

Finishing the cell cycle.

The eukaryotic cell division cycle consists of two characteristic states: G1, when replication origins of chromosomes are in a pre-replicative state, and S/G2/M, when they are in a post-replicative state (Nasmyth, 1995). Using straightforward biochemical kinetics, we show that these two states can be created by antagonistic interactions between cyclin-dependent kinases (Cdk) and their foes: the cyclin-degradation machinery (APC) and a stoichiometric inhibitor (CKI). Irreversible transitions between these two self-maintaining steady states drive progress through the cell cycle: at "Start" a cell leaves the G1 state and commences chromosome replication, and at "Finish" the cell separates the products of replication to the incipient daughter cells and re-enters G1. We propose that a protein-phosphatase, by up-regulating the APC and by stabilizing the CKI, plays an essential role at Finish. The phosphatase acts in parallel pathways; hence, cells can leave mitosis in the absence of cyclin degradation or in the absence of the CKI.

Animals↗

PubMed1999

Models of cell cycle control in eukaryotes.

The molecular mechanisms of cell cycle control are now known in enough detail to warrant mathematical modeling by kinetic equations. Despite the repetitive nature of the cell division cycle, the most appropriate models emphasize steady-state solutions rather than limit cycle oscillations, because cells progress toward division by passing a series of checkpoints (steady states).

Cell Cycle↗

PubMed1998

Model scenarios for evolution of the eukaryotic cell cycle.

Progress through the division cycle of present day eukaryotic cells is controlled by a complex network consisting of (i) cyclin-dependent kinases (CDKs) and their associated cyclins, (ii) kinases and phosphatases that regulate CDK activity, and (iii) stoichiometric inhibitors that sequester cyclin-CDK dimers. Presumably regulation of cell division in the earliest ancestors of eukaryotes was a considerably simpler affair. Nasmyth (1995) recently proposed a mechanism for control of a putative, primordial, eukaryotic cell cycle, based on antagonistic interactions between a cyclin-CDK and the anaphase promoting complex (APC) that labels the cyclin subunit for proteolysis. We recast this idea in mathematical form and show that the model exhibits hysteretic behaviour between alternative steady states: a Gl-like state (APC on, CDK activity low, DNA unreplicated and replication complexes assembled) and an S/M-like state (APC off, CDK activity high, DNA replicated and replication complexes disassembled). In our model, the transition from G1 to S/M ('Start') is driven by cell growth, and the reverse transition ('Finish') is driven by completion of DNA synthesis and proper alignment of chromosomes on the metaphase plate. This simple and effective mechanism for coupling growth and division and for accurately copying and partitioning a genome consisting of numerous chromosomes, each with multiple origins of replication, could represent the core of the eukaryotic cell cycle. Furthermore, we show how other controls could be added to this core and speculate on the reasons why stoichiometric inhibitors and CDK inhibitory phosphorylation might have been appended to the primitive alternation between cyclin accumulation and degradation.

Animals↗

PubMed1998

Modeling M-phase control in Xenopus oocyte extracts: the surveillance mechanism for unreplicated DNA.

Alternating phases of DNA synthesis and mitosis, during the first 12 cell divisions of frog embryos, are driven by autonomous cytoplasmic oscillations of M-phase promoting factor (MPF). Cell-free extracts of frog eggs provide a convenient preparation for studying the molecular machinery that generates MPF oscillations and the surveillance mechanism that normally prevents entry into mitosis until chromosomal DNA is fully replicated. Early experiments suggested that unreplicated DNA blocks MPF activity by inducing phosphorylation of a crucial tyrosine residue, but recent evidence implicates a stoichiometric inhibitor (an MPF binding protein) as the 'braking' agent. Using a realistic mathematical model of the mitotic control system in frog egg extracts, we suggest that both tyrosine phosphorylation and a stoichiometric inhibitors are involved in the block of MPF by unreplicated DNA. Both pathways operate by raising the cyclin threshold for MPF activation. As a bonus, in the process of analyzing these experiments, we obtain more direct and reliable estimates of the rate constants in the model.

Animals↗

PubMed1998

Mathematical model of the fission yeast cell cycle with checkpoint controls at the G1/S, G2/M and metaphase/anaphase transitions.

All events of the fission yeast cell cycle can be orchestrated by fluctuations of a single cyclin-dependent protein kinase, the Cdc13/Cdc2 heterodimer. The G1/S transition is controlled by interactions of Cdc13/Cdc2 and its stoichiometric inhibitor, Rum1. The G2/M transition is regulated by a kinase-phosphatase pair, Wee1 and Cdc25, which determine the phosphorylation state of the Tyr-15 residue of Cdc2. The meta/anaphase transition is controlled by interactions between Cdc13/Cdc2 and the anaphase promoting complex, which labels Cdc13 subunits for proteolysis. We construct a mathematical model of fission yeast growth and division that encompasses all three crucial checkpoint controls. By numerical simulations we show that the model is consistent with a broad selection of cell cycle mutants, and we predict the phenotypes of several multiple-mutant strains that have not yet been constructed.

Anaphase↗

PubMed1997

Modeling the control of DNA replication in fission yeast.

A central event in the eukaryotic cell cycle is the decision to commence DNA replication (S phase). Strict controls normally operate to prevent repeated rounds of DNA replication without intervening mitoses ("endoreplication") or initiation of mitosis before DNA is fully replicated ("mitotic catastrophe"). Some of the genetic interactions involved in these controls have recently been identified in yeast. From this evidence we propose a molecular mechanism of "Start" control in Schizosaccharomyces pombe. Using established principles of biochemical kinetics, we compare the properties of this model in detail with the observed behavior of various mutant strains of fission yeast: wee1(-) (size control at Start), cdc13Delta and rum1(OP) (endoreplication), and wee1(-) rum1Delta (rapid division cycles of diminishing cell size). We discuss essential features of the mechanism that are responsible for characteristic properties of Start control in fission yeast, to expose our proposal to crucial experimental tests.

DNA Replication↗

PubMed1997

A proposal for temperature compensation of the circadian rhythm in Drosophila based on dimerization of the per protein.

Recently Goldbeter suggested an interesting model of circadian rhythms based on feedback inhibition by the PER protein on its own rate of transcription. In his model, the long delay necessary for generating 24 h periodicity is associated with slow phosphorylations of PER protein in the cytoplasm, assuming that only highly phosphorylated forms of PER are able to enter the nucleus and there interfere with transcription of the per gene. By casting this molecular mechanism in mathematical form, Goldbeter showed that it is consistent with many known features of circadian oscillations in PER abundance. However, he did not address one of the most important characteristics of the circadian rhythm: the near constancy of the 24 h period over a broad temperature range. Huang, Curtin, and Rosbash have recently suggested that dimerization of the PER protein is involved in temperature compensation of the circadian rhythm in Drosophila, because in mutant flies lacking the PER dimerization domain, the period is strongly dependent on temperature. We incorporate this idea into Goldbeter's model by introducing parallel pathways of phosphorylation of PER monomers and dimers. We assume that both monomers and dimers can be transported into the nucleus as long as at least one PER subunit is multiply phosphorylated. Temperature compensation in our model arises from opposing effects of temperature (T) on the rate of association of PER monomers and the rate of nuclear import of PER protein. In mutant flies, when PER subunits cannot dimerize, the period of the oscillation increases with T, so we assume that the rate constant for nuclear import is a decreasing function of T. To compensate for this effect in wild-type flies, we assume that the rate of association of PER subunits is an increasing function of T. The mathematical model reveals the relationship between these opposing tendencies that must be satisfied to achieve effective temperature compensation.

Animals↗

PubMed1996

Chemical kinetic theory: understanding cell-cycle regulation.

Progress of a cell through its reproductive cycle of DNA synthesis and division is governed by a complex network of biochemical reactions controlling the activities of both M-phase- and S-phase-promoting factors. Standard chemical kinetic theory provides a disciplined method for expressing the molecular biologists' diagrams and intuition in precise mathematical form, so that qualitative and quantitative implications of our 'working models' can be derived and compared with experiment.

Animals↗

PubMed1995

Checkpoints in the cell cycle from a modeler's perspective.

The cell division cycle is a complex process by which cells grow and divide into two viable daughter cells. So that mistakes are not made in this crucial replication process, cells stop at one or more "checkpoints" in the cycle to query their internal state and external conditions, before proceeding to the next stage of the cycle. In this paper we study some simple mathematical models of cell cycle arrest in G1 ("Start") and G2. Our models help to relate the molecular mechanisms of these checkpoints with physiological properties of the cell cycle.

Animals↗