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John J Tyson

Publications and source records attributed to John J Tyson.

At least 19 recordsLinked to original sources
PubMed2007

A proposal for robust temperature compensation of circadian rhythms.

The internal circadian rhythms of cells and organisms coordinate their physiological properties to the prevailing 24-h cycle of light and dark on earth. The mechanisms generating circadian rhythms have four defining characteristics: they oscillate endogenously with period close to 24 h, entrain to external signals, suffer phase shifts by aberrant pulses of light or temperature, and compensate for changes in temperature over a range of 10 degrees C or more. Most theoretical descriptions of circadian rhythms propose that the underlying mechanism generates a stable limit cycle oscillation (in constant darkness or dim light), because limit cycles quite naturally possess the first three defining properties of circadian rhythms. On the other hand, the period of a limit cycle oscillator is typically very sensitive to kinetic rate constants, which increase markedly with temperature. Temperature compensation is therefore not a general property of limit cycle oscillations but must be imposed by some delicate balance of temperature dependent effects. However, "delicate balances" are unlikely to be robust to mutations. On the other hand, if circadian rhythms arise from a mechanism that concentrates sensitivity into a few rate constants, then the "balancing act" is likely to be more robust and evolvable. We propose a switch-like mechanism for circadian rhythms that concentrates period sensitivity in just two parameters, by forcing the system to alternate between a stable steady state and a stable limit cycle.

Circadian Rhythm↗
PubMed2007

Mathematical modeling as a tool for investigating cell cycle control networks.

Although not a traditional experimental "method," mathematical modeling can provide a powerful approach for investigating complex cell signaling networks, such as those that regulate the eukaryotic cell division cycle. We describe here one modeling approach based on expressing the rates of biochemical reactions in terms of nonlinear ordinary differential equations. We discuss the steps and challenges in assigning numerical values to model parameters and the importance of experimental testing of a mathematical model. We illustrate this approach throughout with the simple and well-characterized example of mitotic cell cycles in frog egg extracts. To facilitate new modeling efforts, we describe several publicly available modeling environments, each with a collection of integrated programs for mathematical modeling. This review is intended to justify the place of mathematical modeling as a standard method for studying molecular regulatory networks and to guide the non-expert to initiate modeling projects in order to gain a systems-level perspective for complex control systems.

Animals↗
PubMed2006

Synchronization of eukaryotic cells by periodic forcing.

We study a cell population described by a minimal mathematical model of the eukaryotic cell cycle subject to periodic forcing that simultaneously perturbs the dynamics of the cell cycle engine and cell growth, and we show that the population can be synchronized in a mode-locked regime. By simplifying the model to two variables, for the phase of cell cycle progression and the mass of the cell, we calculate the Lyapunov exponents to obtain the parameter window for synchronization. We also discuss the effects of intrinsic mitotic fluctuations, asymmetric division, and weak mutual coupling on the pace of synchronization.

Biomechanical Phenomena↗
PubMed2006

Analysis of a generic model of eukaryotic cell-cycle regulation.

We propose a protein interaction network for the regulation of DNA synthesis and mitosis that emphasizes the universality of the regulatory system among eukaryotic cells. The idiosyncrasies of cell cycle regulation in particular organisms can be attributed, we claim, to specific settings of rate constants in the dynamic network of chemical reactions. The values of these rate constants are determined ultimately by the genetic makeup of an organism. To support these claims, we convert the reaction mechanism into a set of governing kinetic equations and provide parameter values (specific to budding yeast, fission yeast, frog eggs, and mammalian cells) that account for many curious features of cell cycle regulation in these organisms. Using one-parameter bifurcation diagrams, we show how overall cell growth drives progression through the cell cycle, how cell-size homeostasis can be achieved by two different strategies, and how mutations remodel bifurcation diagrams and create unusual cell-division phenotypes. The relation between gene dosage and phenotype can be summarized compactly in two-parameter bifurcation diagrams. Our approach provides a theoretical framework in which to understand both the universality and particularity of cell cycle regulation, and to construct, in modular fashion, increasingly complex models of the networks controlling cell growth and division.

Cell Cycle↗
PubMed2006

Cell cycle control in bacteria and yeast: a case of convergent evolution?

Superficially similar traits in phylogenetically unrelated species often result from adaptation to common selection pressures. Examples of convergent evolution are known at the levels of whole organisms, organ systems, gene networks and specific proteins. The phenotypic properties of living things, on the other hand, are determined in large part by complex networks of interacting proteins. Here we present a mathematical model of the network of proteins that controls DNA synthesis and cell division in the alpha-proteobacterium, Caulobacter crescentus. By comparing the protein regulatory circuits for cell reproduction in Caulobacter with that in budding yeast (Saccharomyces cerevisiae), we suggest that convergent evolution may have created similar molecular reaction networks in order to accomplish the same purpose of coordinating DNA synthesis to cell division. Although the genes and proteins involved in cell cycle regulation in prokaryotes and eukaryotes are very different and (apparently) phylogenetically unrelated, they seem to be wired together in similar regulatory networks, which coordinate cell cycle events by identical dynamical principles.

Biological Evolution↗
PubMed2006

Periodic forcing of a mathematical model of the eukaryotic cell cycle.

In a differential equation model of the molecular network governing cell growth and division, cell cycle phases and transitions through checkpoints are associated with certain bifurcations of the underlying vector field. If the cell cycle is driven by another rhythmic process, interactions between forcing and bifurcations lead to emergent orbits and oscillations. In this paper, by varying the amplitude and frequency of forcing of the synthesis rates of regulatory proteins and the mass growth rate in a minimal model of the eukaryotic cell cycle, we study changes of the probability distributions of interdivision time and mass at division. By computing numerically the Lyapunov exponent of the model, we show that the splitting of probability distributions is associated with mode-locked solutions. We also introduce a simple, integrate-and-fire model to analyze mode locking in the cell cycle.

Journal Article↗
PubMed2005

Rewiring the exit from mitosis.

The mitotic cell cycle can be described as an alternation between two states. During mitosis, MPF (mitosis promoting factor) is high and keeps inactive its numerous molecular antagonists. In interphase, MPF is inactivated, and the antagonists prevail. The transition between the two states is ensured by 'helper' molecules that favor one state over the other. It has long been assumed that active MPF (a dimer of cyclin B and cyclin-dependent kinase 1) induces exit from mitosis by activating APC:Cdc20, a ubiquitin ligase responsible for cyclin B degradation. The molecular details have not been fully worked out yet, but recent results show that MPF and the ubiquitin ligase are not involved in a simple negative feedback loop. While it is proven that MPF activates APC, new data suggest that MPF inhibits Cdc20, i.e., that MPF and Cdc20 are antagonists. We introduce this new idea into a published model for cell cycle regulation in Xenopus laevis, and study its dynamical behavior. We show that the new wiring permits oscillations with a simpler and smaller network than previously envisaged and that the antagonism between MPF and Cdc20 suggests a new interpretation of the spindle checkpoint.

Anaphase-Promoting Complex-Cyclosome↗
PubMed2005

Steady states and oscillations in the p53/Mdm2 network.

p53 is activated in response to events compromising the genetic integrity of a cell. Recent data show that p53 activity does not increase steadily with genetic damage but rather fluctuates in an oscillatory fashion. Theoretical studies suggest that oscillations can arise from a combination of positive and negative feedbacks or from a long negative feedback loop alone. Both negative and positive feedbacks are present in the p53/Mdm2 network, but it is not known what roles they play in the oscillatory response to DNA damage. We developed a mathematical model of p53 oscillations based on positive and negative feedbacks in the p53/Mdm2 network. According to the model, the system reacts to DNA damage by moving from a stable steady state into a region of stable limit cycles. Oscillations in the model are born with large amplitude, which guarantees an all-or-none response to damage. As p53 oscillates, damage is repaired and the system moves back to a stable steady state with low p53 activity. The model reproduces experimental data in quantitative detail. We suggest new experiments for dissecting the contributions of negative and positive feedbacks to the generation of oscillations.

Animals↗
PubMed2005

Parameter estimation for a mathematical model of the cell cycle in frog eggs.

Parameter values for a kinetic model of the nuclear replication-division cycle in frog eggs are estimated by fitting solutions of the kinetic equations (nonlinear ordinary differential equations) to a suite of experimental observations. A set of optimal parameter values is found by minimizing an objective function defined as the orthogonal distance between the data and the model. The differential equations are solved by LSODAR and the objective function is minimized by ODRPACK. The optimal parameter values are close to the "guesstimates" of the modelers who first studied this problem. These tools are sufficiently general to attack more complicated problems, where guesstimation is impractical or unreliable.

Animals↗
PubMed2004

A model for restriction point control of the mammalian cell cycle.

Inhibition of protein synthesis by cycloheximide blocks subsequent division of a mammalian cell, but only if the cell is exposed to the drug before the "restriction point" (i.e. within the first several hours after birth). If exposed to cycloheximide after the restriction point, a cell proceeds with DNA synthesis, mitosis and cell division and halts in the next cell cycle. If cycloheximide is later removed from the culture medium, treated cells will return to the division cycle, showing a complex pattern of division times post-treatment, as first measured by Zetterberg and colleagues. We simulate these physiological responses of mammalian cells to transient inhibition of growth, using a set of nonlinear differential equations based on a realistic model of the molecular events underlying progression through the cell cycle. The model relies on our earlier work on the regulation of cyclin-dependent protein kinases during the cell division cycle of yeast. The yeast model is supplemented with equations describing the effects of retinoblastoma protein on cell growth and the synthesis of cyclins A and E, and with a primitive representation of the signaling pathway that controls synthesis of cyclin D.

Animals↗
PubMed2004

Turbulence near cyclic fold bifurcations in birhythmic media.

We show that at the onset of a cyclic fold bifurcation, a birhythmic medium composed of glycolytic oscillators displays turbulent dynamics. By computing the largest Lyapunov exponent, the spatial correlation function, and the average transient lifetime, we classify it as weak turbulence of a transient nature. Virtual heterogeneities generating unstable fast oscillations account for the transient turbulence. In the presence of a wave number instability, unstable oscillations can be reinjected, leading to stationary turbulence. We also find similar turbulence in a cell cycle model. These findings suggest that weak turbulence may be universal in biochemical birhythmic media exhibiting cyclic fold bifurcations.

Biophysical Phenomena↗
PubMed2004

the JigCell model builder and run manager.

SUMMARY: We describe the JigCell Model Builder (JCMB), a tool for creating biochemical reaction network models. JCMB is designed for ease of use and its interface uses the standard spreadsheet metaphor. The JigCell Run Manager (JCRM) is a tool for organizing the large collections of simulation runs typically required by reaction network modeling activities. AVAILABILITY: JCMB and JCRM are part of the JigCell suite available at http://jigcell.biol.vt.edu.

Animals↗
PubMed2004

Integrative analysis of cell cycle control in budding yeast.

The adaptive responses of a living cell to internal and external signals are controlled by networks of proteins whose interactions are so complex that the functional integration of the network cannot be comprehended by intuitive reasoning alone. Mathematical modeling, based on biochemical rate equations, provides a rigorous and reliable tool for unraveling the complexities of molecular regulatory networks. The budding yeast cell cycle is a challenging test case for this approach, because the control system is known in exquisite detail and its function is constrained by the phenotypic properties of >100 genetically engineered strains. We show that a mathematical model built on a consensus picture of this control system is largely successful in explaining the phenotypes of mutants described so far. A few inconsistencies between the model and experiments indicate aspects of the mechanism that require revision. In addition, the model allows one to frame and critique hypotheses about how the division cycle is regulated in wild-type and mutant cells, to predict the phenotypes of new mutant combinations, and to estimate the effective values of biochemical rate constants that are difficult to measure directly in vivo.

Cell Cycle↗
PubMed2004

Cycling without the cyclosome: modeling a yeast strain lacking the APC.

The construction of viable Saccharomyces cerevisiae strains that lack the anaphase promoting complex (APC) was recently reported. The normally lethal deletions of APC genes were suppressed by the double deletion of the PDS1 and CLB5 genes in conjunction with the insertion of multiple copies of the SIC1 gene controlled by its endogenous promoter. It was proposed that cyclic expression and degradation of Sic1 results in oscillations of Clb/CDK activity necessary for the cell cycle. We have used an updated version of a mathematical model of the yeast cell cycle to model strains that lack the APC. With a few modifications, the model accurately simulates the viability of Apc- strains, as well as the phenotypes of 27 other previously characterized strains. We discuss a few minor inconsistencies between the model and experiment, and how these may inform future revisions to the model.

Anaphase-Promoting Complex-Cyclosome↗