Workshop 1: Control of Cell Growth, Division and Death

(September 29,2003 - October 3,2003 )

Organizers


Baltazar Aguda
Genetics and Genomics, Boston University

The cell cycle is the sequence of events by which a growing cell replicates all its components and divides them between two daughter cells, so that each daughter receives all the information and machinery necessary to repeat the process. Because cell proliferation underlies all biological growth, development, and reproduction, an understanding of the molecular machinery controlling cell growth and division is a fundamental goal of cell biology. In the past 15 years, there has been an explosion of information about: (1) the genes and proteins that regulate DNA replication, mitosis and cell division (the cell cycle "engine"), and (2) the signal transduction pathways that control the "accelerators and brakes" of the engine. Everyone now agrees that this regulatory network is so complex that rigorous mathematical modeling will be required to understand the intricate relationships among its components, and to derive the observed behavior of proliferating cells to the underlying regulatory system. The purposes of the first workshop of this quarter are to summarize current knowledge about the molecular controls of cell division, to examine the state-of-the-art in computational modeling of these controls, to open a fruitful dialogue between experimental cell biologists and theoreticians, to define the next set of problems to be attacked by mathematical modeling, and to recruit a new generation of collaborative experimentalists and theoreticians to the problem.

The workshop will focus on the cell cycle engine and signal transduction pathways in mammalian cells to set the stage for the next workshop, which will address issues of cancer biology (tumorigenesis, angiogenesis, chemotherapy, drug resistance). The first 2 days will address the mammalian cell cycle engine, as sketched out in a molecular wiring diagram published by Kohn in Molec Biol Cell (10:2703-2734, 1999). Speakers will address the following issues:

  • Cyclin-dependent kinases and their partners (cyclins A, B, ...),
  • Cyclin-dependent kinase inhibitors (p15, p21, p27),
  • Regulation of cell cycle genes expression,
  • Cell cycle checkpoints,
  • Computational models.

 

Days 3-5 will focus on the network of signal transduction pathways surrounding the cell cycle engine, as described in a recent review by Hanahan and Weinberg in Cell (100: 57-70, 2000):

  • Growth signals (MAP kinase pathway -> cyclin D and pRb),
  • Antigrowth signals (TGFb -> Smads -> p15, p21, p27),
  • Cell adhesion signals and anoikis (Integrins, Cadherins),
  • Survival factors (e.g., IGF1 -> P13K -> NF-kB, FGF -> MEK),
  • Cell suicide signals (intrinsic and extrinsic pathways of apoptosis),
  • Immortalization (telomerase dynamics),
  • Genetic instability (p53 and DNA damage checkpoint).

 

The mathematical tools that are expected to contribute strongly to these questions are:

  • Dynamical systems theory
  • Bifurcation theory
  • Multiple time scales
  • Parameter estimation
  • Robust control
  • Stochastic differential equations
  • Graph theoretic methods

 

The workshop will bring together experimental cell biologists, theoretical biologists, mathematicians, and computer scientists who are all interested in problems of cell growth, division, and death.

Accepted Speakers

Baltazar Aguda
Genetics and Genomics, Boston University
Rengul Cetin-Atalay
Molecular Biology & Genetics, Bilkent University
Stephen Cooper
Microbiology and Immunology, University of Michigan
Paul Dent
Radiation Oncology, Virginia Common Wealth Center
Marty Feinberg
Chemical Engineering & Mathematics, The Ohio State University
Boris Kholodenko
Pathology and Cell Biology, Thomas Jefferson Univ., JAH
Andre Levchenko
Whitaker Inst for Biomed Eng, Johns Hopkins University
Tomasz Lipniacki
Department of Statistics, Rice University
Bela Novak
Agricultural Chemical Technology, Budapest Univ. of Technology
Mandri Obeyesekere
Unit 237, Biomathematics, University of Texas M. D. Anderson Cancer Center
Joseph Pomerening
Molecular Pharmacology, Stanford University
Jill Sible
Department of Biology, Virginia Polytechnic Institute and State University
Jaroslav Stark
Department of Mathematics, Imperial College London
Dennis Thron
John Tyson
Department of Biology, Virginia Polytechnic Institute and State University
Jean Wang
Biological Sciences, University of California, San Diego
Monday, September 29, 2003
Time Session
09:30 AM
10:30 AM
John Tyson - Modeling the Cell Cycle Engine and Checkpoints in Yeast Cells

The physiology of a cell is largely determined by complex networks of interacting proteins. For example, eukaryotic cell division is regulated by an underlying cell cycle engine that is known in great detail. The basic molecular mechanisms controlling DNA replication, mitosis and cell division are highly conserved among eukaryotes, with homologous proteins functioning in both yeast and humans. To understand the dynamics of such a complicated control system requires sophisticated theoretical and computational tools. Our approach is to decompose the cell cycle engine into "modules" that are responsible for the characteristic transitions of the cell cycle (G1/S, G2/M and meta/anaphase) and to analyse these modules by standard tools of dynamical system theory (phase plane techniques, stability analysis, bifurcation theory etc.). We will show that some of the modules (G1/S and G2/M) are based on antagonistic relationships between cell cycle regulators. As a consequence of this antagonism, these modules operate as switches with different turning-on and turning-off points, a phenomenon called hysteresis. In contrast, the mitotic module, which is based on a negative feedback loop, operates as an oscillator. We will also describe how to assemble G1/S-, G2/M- and meta/anaphase-modules into a comprehensive model of the eukaryotic cell cycle, using yeast cells as an example. With this comprehensive model, we will also discuss the mechanisms by which cell cycle checkpoint pathways stabilise cell cycle states and inhibit the transitions that drive cell cycle progression.

11:00 AM
12:00 PM
Bela Novak - Modeling Cell Growth, Division and Morphology in Fission Yeast

Because of its regular shape and excellent genetics, fission yeast is a convenient organism to study cellular morphogenesis. Genetic analysis has identified a host of proteins that regulate shape changes during the cell cycle. Most of these proteins interact with either the microtubular or actin cytoskeleton of the cell. In this lecture, we present a simple model for fission yeast morphogenesis based on an interplay between the two cytoskeletal systems. An essential assumption of the model is that actin polymerisation is a self-reinforcing (autocatalytic) process: F-actin promotes its own formation from G-actin subunits via regulatory molecules. Since the diffusion coefficient of F-actin is much smaller than the diffusion coefficient for its substrate, G-actin, our model is a version of the well-known, Turing pattern-formation mechanism: local self-enhancement and long range inhibition. Microtubules stimulate actin polymerisation in the model by delivering a component of the autocatalytic actin assembly feedback loop. We show that the model captures all the characteristic features of polarised growth in fission yeast during normal mitotic cycle. We also show that all the major classes of morphogenetic mutants (orb and tea) are natural outcomes of the model.

02:00 PM
03:00 PM
Jill Sible - Cell Cycle Controls in Frog Eggs and Embryos: Molecular Mechanisms and Mathematical Models

Cell-free extracts derived from the eggs of the South African clawed frog, Xenopus laevis, provide a biochemically tractable and relatively simple system in which to investigate fundamental cell cycle control mechanisms. By pairing mathematical modeling with experimental cell biology, we have demonstrated that entry into and exit from mitosis in egg extracts is driven by hysteresis. We are building upon these studies to determine the mechanisms that regulate cell cycle arrest at checkpoints in response to damaged and unreplicated DNA. In addition to studying basic cell cycle controls in egg extracts, we utilize intact Xenopus embryos to investigate the remodeling cell cycles of early development. In particular, we have built a preliminary mathematical model of the cyclin E/Cdk2 developmental timer that regulates the midblastula transition during early development. We believe that close collaboration between computational biologists and experimental cell biologists provides a powerful new approach for investigating the most challenging questions about the molecular network that regulates the eukaryotic cell cycle.

Tuesday, September 30, 2003
Time Session
09:00 AM
10:00 AM
Joseph Pomerening - Hysteresis and Bistability in Cdc2 Activation: Constructing a Cell Cycle Oscillator

In the early embryonic cell cycle, Cdc2-cyclin B functions like an autonomous oscillator, whose robust biochemical rhythm continues even when DNA replication or mitosis is blocked (Hara et al., 1980). At the core of the oscillator is a negative feedback loop; cyclins accumulate and produce active mitotic Cdc2-cyclin B (Evans et al., 1983; Murray and Kirschner, 1989); Cdc2 activates the anaphase-promoting complex (APC); the APC then promotes cyclin degradation and resets Cdc2 to its inactive, interphase state. Cdc2 regulation also involves positive feedback (Masui and Markert, 1971), with active Cdc2-cyclin B stimulating its activator Cdc25 (Izumi et al., 1992; Kumagai and Dunphy, 1992; Hoffmann et al., 1993) and inactivating its inhibitors Wee1 and Myt1 (Tang et al., 1993; McGowan and Russell, 1995; Mueller et al., 1995). Under the proper circumstances, these positive feedback loops could function as a bistable trigger for mitosis (Novak and Tyson, 1993; Thron, 1996), and oscillators with bistable triggers might be especially relevant to biological applications such as cell cycle regulation (Goldbeter, 2002; McMillen et al., 2002; Vilar et al., 2002). Therefore, we examined whether Cdc2 activation is bistable. We confirm that the response of Cdc2 to non-degradable cyclin B is temporally abrupt and switch-like, as would be expected if Cdc2 activation were bistable. We also show that Cdc2 activation exhibits hysteresis, a property of bistable systems with particular relevance to biochemical oscillators. These findings help establish the basic systems-level logic of the mitotic oscillator.


Bibliography



  1. Evans, T., Rosenthal, E., Youngblom, J., Distel, D., & Hunt, T. (1983). Cyclin: A protein specified by maternal mRNA in sea urchin eggs that is destroyed at each cleavage division. 33, 389-396.

  2. Goldbeter, A. (2002). Computational approaches to cellular rhythms. Nature, 420(6912), 238-45.

  3. Hara, K., Tydeman, P., & Kirschner, M. (1980). A cytoplasmic clock with the same period as the division cycle in Xenopus eggs. Proc Natl Acad Sci U S A, 77(1), 462-6.

  4. Hoffmann, I., Clarke, P., Marcote, M., Karsenti, E., & Draetta, G. (1993). Phosphorylation and activation of human cdc25-C by cdc2-cyclin B and its involvement in the self-amplification of MPF at mitosis. EMBO J., 12, 53-63.

  5. Izumi, T., Walker, D., & Maller, J. (1992). Periodic changes in phosphorylation of the Xenopus cdc25 phosphatase regulate its activity. Mol Biol Cell., 3(8), 927-39.

  6. Kumagai, A. & Dunphy, W. G. (1992). Regulation of the cdc25 protein during the cell cycle in Xenopus extracts. Cell. 70(1), 139-51.

  7. Masui, Y. & Markert, C. (1971). Cytoplasmic control of nuclear behavior during meiotic maturation of frog oocytes. J Exp Zool., 177, 129-146.

  8. McGowan, C. & Russell, P. (1995). Cell cycle regulation of human WEE1. EMBO J., 14(10), 2166-75.

  9. McMillen, D., Kopell, N., Hasty, J., & Collins, J. (2002). Synchronizing genetic relaxation oscillators by intercell signaling. Proc Natl Acad Sci U S A., 99(2), 679-84.

  10. Mueller, P., Coleman, T., & Dunphy, W. (1995). Cell cycle regulation of a Xenopus Wee1-like kinase. 6, 119-134.

  11. Murray, A. & Kirschner, M. (1989). Cyclin synthesis drives the early embryonic cell cycle. Nature, 339, 275-280.

  12. Novak, B. & Tyson, J. (1993). Numerical analysis of a comprehensive model of M-phase control in Xenopus oocyte extracts and intact embryos. J Cell Sci., 106(Pt 4), 1153-68.

  13. Tang, Z., Coleman, T., & Dunphy, W. (1993). Two distinct mechanisms for negative regulation of the Wee1 protein kinase. EMBO J., 12(9), 3427-36.

  14. Thron, C. (1996). A model for a bistable biochemical trigger of mitosis. Biophys Chem., 57(2-3), 239-51.

  15. Vilar, J., Kueh, H., Barkai, N., & Leibler, S. (2002). Mechanisms of noise-resistance in genetic oscillators. Proc Natl Acad Sci U S A., 99(9), 5988-92.

10:30 AM
11:30 AM
Mandri Obeyesekere - Mathematical Model for Cell Cycle Regulation and Cancer

A mathematical model of the kinetics of a few regulatory proteins will be presented. This model, restricted to the dynamics during the DNA synthesis phase (S-phase) and mitosis (M-phase) of the cell cycle, incorporates the activities of the major cyclin-cdks (cell division kinases), i.e., cyclin A/cdk2, cyclin A/cdk1 and cyclin B/cdk1. It also embeds the interactions by cdc25c, p53, and P21. Numerical solutions of this mathematical model that reproduces well-known experimental results will be discussed; namely, cell arrest due to DNA damage and cell proliferation in p53 null cells. Based on mathematical analysis of the underlying ODE system, different end point behaviors will be discussed. How the model, along with the mathematical analysis, can help cancer research will be presented.

02:00 PM
03:00 PM
Dennis Thron - On Stability Analysis of the Bistable Biochemical Switches in the Cell Cycle

As presently conceived, the cell cycle is quite different from most other biological oscillators, in that it has a sequence of phases and can be arrested at any of several points, e.g. the so-called "checkpoints." Analysis of cell cycle control therefore tends to focus on the presumed bistable biochemical switching at the arrest points (1-3), rather than on a Hopf bifurcation. For this discussion it will be assumed that bistable biochemical switching requires two nonzero stable steady states or attractors, with a saddle point produced by some form of positive feedback which must be strong enough, in terms of reaction order, to overcome the damping tendencies that are always present in chemical systems. Switching out of a stable steady state can occur by saddle-node bifurcation, or in unusual cases by homoclinic loop bifurcation followed by subcritical Hopf bifurcation. Switching out of a periodic orbit to a particular checkpoint (or to G0 phase, apoptosis, or differentiation) can occur by homoclinic loop bifurcation. Possible biochemical mechanisms for saddle-node bifurcation will be discussed for several cell cycle checkpoints, with particular attention to (a) reaction order requirements for effective positive feedback, and (b) biochemical kinetic questions that call for further experimental investigation.



  1. Thron, C. D. (1996). A model for a bistable trigger of mitosis. Biophys. Chem., 57, 239-251.

  2. Thron, C. D. (1998). Cell cycle checkpoints in the overall dynamics of cell cycle control. In M. A. Horn, G. Simonett, & G. F. Webb (Eds.), Mathematical Models in Medical and Health Science (pp. 369-380). Nashville, TN: Vanderbilt University Press.

  3. Thron, C. D. (1999). Mathematical analysis of binary activation of a cell cycle kinase which down-regulates its own inhibitor. Biophys. Chem., 79, 95-106.

Wednesday, October 1, 2003
Time Session
09:00 AM
10:00 AM
Marty Feinberg - Biochemical Reaction Network Structure and the Capacity for Switch-Like Behavior

There are two themes, stated with varying degrees of certainty, that seem to be recurrent in discussions of how the cell cycle might be understood: The first is that the underlying biochemical machinery is so complex that only a suitably sensible "systems" model, taken with sensible analysis, will serve to indicate how the cell cycle works and how it might be controlled. The second is the supposition that the machinery has embedded within it crucial biochemical switches that might have their origin in bistable behavior, construed in the dynamical systems sense. (See [1] for an example of ambitious experimental work aimed investigating the role of bistability in cell cycle progress.) The problem for modelers of the cell cycle (and for cellular processes generally) quickly becomes apparent: (i) Models - even of small biochemical "modules" - that reflect the underlying chemistry with reasonable fidelity will be inherently complex. (ii) At least at outset, parameter values (e.g., reaction rate constants) will be known poorly, if at all. Thus, in the normal evolution of an intricate biochemical model, it becomes important to understand the qualitative capacity of its components, working in concert, to admit particular phenomena (e.g, bistability) without a priori commitment to specified parameter values or even to ranges of parameter values. Moreover, it becomes important to do this in the context of considerable complexity. Chemical reaction network theory has as its goal the development of powerful but readily implementable tools for connecting complex reaction network structure to the qualitative capacity for certain phenomena (in particular, bistability). The theory goes back at least to the 1970s [2]. It has not been specific to biology, but, for reasons already stated, there is now growing interest in biological applications [3]. Very recent work has, in fact, been dedicated specifically to biochemical networks driven by enzyme-catalyzed reactions. In particular, it is now known that there are remarkable and quite subtle connections between properties of reaction diagrams of the kind that biochemists normally draw and the capacity for biochemical switching. Our aim in this talk will be to explain, for an audience unfamiliar with chemical reaction network theory, those tools that have recently become available.



  1. Cross, F. R., Archambault, V., Miller, M., & Klovstad, M. (2002). Testing a mathematical model of the yeast cell cycle. Mol. Biol. Cell, 13, 52-70.

  2. For some early results, see M. Feinberg, Lectures on Chemical Reaction Networks, University of Wisconsin Mathematics Research Center, 1979, available at http://www.che.eng.ohio-state.edu/~feinberg/LecturesOnReactionNetworks/

  3. Bailey, James E. (2001). Complex biology with no parameters. Nature Biotechnology, 19, 503-504.

10:30 AM
11:30 AM
Rengul Cetin-Atalay - Cancer Cell Signaling Database with PATIKA

Human genome, which contain at least 28 000 genes, is expected to create a much more complex network, composed of hundreds and thousands of different molecules and factors. The exact map knowledge of this network is very important since it will potentially explain the mechanisms of life processes as well as disease conditions. Such knowledge will also serve as a key for further biomedical applications such as development of new drugs and diagnostic approaches.


There are already significant amount of work on pathway modeling and pathway databases (DIP KEGG, EcoCyc, BRENDA, WIT, BIND, TRANSPATH). However the data colleted on cellular networks can be best represented by integrated pathway editing environment, which provides all of the previously described functionality, including editing, visualization, storing and retrieval, basic simulation, in a single solution. Such a tool can integrate fragmented and incomplete data on cellular pathways in a single knowledge base and must have a graphical or user-friendly interface.


We have recently developed a pathway database tool PATIKA (Pathway Analysis Tool for Integration and Knowledge Acquisition, Demir E. et al. Bioinformatics 18 996-1003, 2002, http://www.patika.org) that can be used for rapid knowledge acquisition providing an integrated single source for pathway information. PATIKA aims to provide an integrated pathway-editing environment with a well-defined ontology, powerful querying and analysis options, and a dynamic visualization of any given subgraph of database.


We are currently constructing an interactive cancer cell database, which will allow storing, visualizing and analyzing cellular signaling pathways. PATIKA based cancer cell signaling database can provide a single source for cancer related pathway information that may allow micro array data analysis and provide well thought-out explanations to the high throughput data. Moreover, various data gathered on the cancer cell signaling, its subsequent analysis, and the consequently synthesized information can be used for disease gene identification, drug design and toxicity.

02:00 PM
03:00 PM
Stephen Cooper - The Continuum Model: Regulation of the Mammalian Cell Cycle is Related to a Continuous Accumulation Process and Not Dependent on Phase-Specific Cascades of Gene Expression

The Continuum Model of the eukaryotic cell cycle proposes that the principal, fundamental, and ultimate control of the cell cycle is a continuous accumulation process occurring in all phases of the cell cycle. The Continuum Model proposes that there are no G1-phase specific events (1), that there is no G1-phase restriction point controlling passage through the G1 phase (2), and that the G0 phase-a postulated phase into which cells have been proposed to enter when conditions for growth are not favorable-is an anthropomorphic construct that has no existence and no biological meaning (1-5). The Continuum Model proposes that there are no events unique to the G1 phase; processes occurring in the G1 phase occur in the other phases as well (1, 6). Events unique to the S- and G2/M-phases can and do occur; these events are superimposed upon the continuous regulatory process or processes occurring throughout the cell cycle. The Continuum Model explains the well-known variability of G1 phase duration, as well as the existence of G1-less cells (7, 8). The Continuum Model prompted experiments defining, identifying, and explaining artifacts that led to the widely-accepted proposal of G1-phase dependent Rb protein phosphorylation (6, 9). These experiments supported the Continuum Model prediction of no G1-phase Rb phosphorylation. The Continuum Model led to a reexamination and reinterpretation of the microarray data on G1-phase specific gene expression as studied using microarrays (10-12). The Continuum Model proposes that whole-culture synchronization, the dominant and near-prevalent approach to cell-cycle analysis, cannot synchronize cells at all (1, 13-17). Time-lapse studies have supported the Continuum Model prediction that whole-culture, non-selective methods of "synchronization" cannot synchronize cells (13). The widespread and near-universal use of whole-culture synchronization methods-methods that neither synchronize cells nor avoid unwanted and deviant perturbations-have led to the current view of the cell cycle with myriad proposed variations in gene expression occurring during G1 phase. The Continuum Model does not postulate any metabolic switches during the G1 phase when certain genes are turned on leading to the initiation of subsequent events such as S phase. No metabolic cascade with G1-phase specific gene expression regulates the cell cycle. Rather, the continuous accumulation of material leads to initiation of S phase, the subsequent passage through S phase, and then mitosis and cytokinesis. Theoretical, mathematical, and formal studies and analyses of cell cycle control should always consider problems with data based on questionable experimental approaches, particularly experiments using whole-culture synchronization.



  1. Cooper, S. (2000). The continuum model and G1-control of the mammalian cell cycle. Prog Cell Cycle Res., 4, 27-39.

  2. Cooper, S. (2003). Reappraisal of Serum Starvation, the Restriction Point, G0, and G1-phase Arrest Points. FASEB J, 17, 333-340.

  3. Cooper, S. (2003). How the change from FLM to FACS affected our understanding of the G1 phase of the cell cycle. Cell Cycle, 2, 157-159.

  4. Cooper, S. (1998). On the proposal of a G0 phase and the restriction point. FASEB J, 12, 367-373.

  5. Cooper, S. (1987).On G0 and cell cycle controls. Bioessays, 7, 220-223.

  6. Cooper, S., & Shayman, J.A. (2001). Revisiting retinoblastoma protein phosphorylation during the mammalian cell cycle. Cell Mol Life Sci, 58, 580-595.

  7. Cooper, S. (1979). A unifying model for the G1 period in prokaryotes and eukaryotes. Nature, 280, 17-19.

  8. Cooper, S. (1998). On the interpretation of the shortening of the G1-phase by overexpression of cyclins in mammalian cells. Exp Cell Res, 238, 110-115.

  9. Cooper, S., Yu, C., & Shayman, J.A. (1999). Phosphorylation-dephosphorylation of retinoblastoma protein not necessary for passage through the mammalian cell division cycle. IUBMB Life, 48, 225-230.

  10. Cooper, S. (2002).Cell cycle analysis and microarrays. Trends in Genetics, 18, 289-290.

  11. Shedden, K., & Cooper, S. (2002). Analysis of cell-cycle-specific gene expression in human cells as determined by microarrays and double-thymidine block synchronization. Proc Natl Acad Sci USA, 99, 4379-4384.

  12. Shedden, K., & Cooper, S. (2002).Analysis of cell-cycle-specific gene exresssion in Saccharomyces cerevisiae as determined by Microarrays and Multiple synchronization methods. Nuc Acids Res, 30, 2920-2929.

  13. Cooper, S. (2002). Reappraisal of G1-phase arrest and synchronization by lovastatin. Cell Biol Int, 26, 715-727.

  14. Cooper, S. (2002). Minimally Disturbed, Multi-Cycle, and Reproducible Synchrony using a Eukaryotic "Baby Machine". Bioessays, 24, 499-501.

  15. Cooper, S. (2003). Rethinking Synchronization of mammalian cells for cell-cycle analysis. Cell Mol Life Sci, 6, 1099-1106.

  16. Cooper, S. (2003).On the Persistence of Forcing Synchronization Methodology. Manuscript submitted for publication.

  17. Cooper, S. (1998). Mammalian cells are not synchronized in G1-phase by starvation or inhibition: considerations of the fundamental concept of G1-phase synchronization. Cell Prolif, 31, 9-16.


(Many of the cited references can be read directly at www.umich.edu/~cooper; just click on the appropriate article title. The experimental data supporting the Continuum Model are described in more detail in these references.)

Thursday, October 2, 2003
Time Session
09:00 AM
10:00 AM
Baltazar Aguda - The Links and Controls of the Initiation of the Cell Cycle and of Apoptosis

I will talk about a proposed integration and modular organization of the complex regulatory networks involved in the mammalian cell cycle, apoptosis, and related intracellular signaling cascades. A common node linking the cell cycle and apoptosis permits the possibility of coordinate control between the initiation of these two cellular processes. From this node, pathways emanate that lead to the activation of cyclin-dependent kinases (in the cell cycle) and caspases (in apoptosis). Some computer simulations have been carried out to demonstrate that the proposed network architecture and certain module-module interactions can account for the experimentally observed sequence of cellular events (quiescence, cell cycle, and apoptosis) as the transcriptional activities of E2F-1 and c-Myc are increased. Despite the lack of quantitative kinetic data on most of the pathways, it is demonstrated that there can be meaningful conclusions regarding system stability that arise from the topology of the network. It is shown that only cycles in the 'qualitative network' graph determine stability. Thus, several positive and negative feedback loops are identified from a literature review of the major pathways involved in the initiation of the cell cycle and of apoptosis. Some relevant experimental results carried out in my laboratory on human chronic myeloid leukemic cells will be presented.

10:30 AM
11:30 AM
Jaroslav Stark - Divide or Die: Coupling Proliferation and Apoptosis

Control of both proliferation and cell death is essential to the maintenance of homeostasis. The signalling path-ways of these two processes are closely coupled. As a result, for example, it is often the case that dormant cells are less susceptible to apoptosis than ones that are in cycle. This talk will explore the consequences of such cou-pling on the homeostasis of a population of cells. In particular, we will present a model of T-cell memory that depends on apoptosis mediated by Fas-FasL binding. Unlike most homeostasis models, which rely on a nonlinear growth term, the nonlinearity appears in the death term. By treating dormant and cycling subpopulations separately, we are able to investigate the effects of coupling apoptosis to the cell cycle. When this is done, it turns out that a small subpopulation of active cells can control the size of a much larger population. We extend the model to incorporate an increased rate of division amongst some cells, for instance due to HIV infection. Paradoxically, this can lead to a decline in cell numbers, and may help to explain the high death rate of uninfected T-cells that has been observed during HIV infection.

02:00 PM
03:00 PM
Jean Wang - Regulation of Cell Proliferation, Differentiation and Apoptosis by DNA Damage

In eukaryotic cells, DNA lesions trigger several conserved cell cycle checkpoints to prevent replication and segregation of damaged genome and to promote repair. In mammalian cells, the DNA damage-signaling network generates additional biological outputs, including the inhibition of differentiation, the activation of apoptosis and the induction of premature senescence. The cell cycle checkpoints and the inhibition of differentiation are reversible, allowing the resumption of proliferation and differentiation after the lesions are repaired. Apoptosis and premature senescence are irreversible, resulting from the accumulation of irreparable DNA lesions.


We have identified the Abl tyrosine kinase to be a regulator of differentiation and apoptosis in response to DNA damage. The nuclear Abl kinase is activated by a variety of DNA lesions. In myoblasts, exposure to MMS (an alkylating agent) or low dose cisplatin (a cross-linking agent) causes a reversible inhibition of myogenic differentiation in an Abl-dependent mechanism. DNA damage-induced differentiation checkpoint is also dependent on the transcription factor p73, which is a downstream effector of Abl. The Abl-p73 pathway also activates apoptosis in response to cisplatin and other DNA lesions. These findings suggest differentiation and apoptosis are a continuum of response to DNA damage. Factors that modulate the amplitude or duration of output from the Abl-p73 pathway are therefore likely to control the biological outcome following DNA damage.


We have identified a few factors that modulate the Abl kinase activity. Two of these factors, in particular, are known to regulate cell proliferation, differentiation and apoptosis. The first is the retinoblastoma tumor suppressor protein, RB, which inhibits Abl kinase. The second is cell adhesion, which activates Abl kinase. RB is well known for its ability to block cell cycle progression. This, however, is not the only function of RB. More importantly, RB promotes terminal differentiation and inhibits apoptosis. Thus, RB antagonizes Abl's ability to inhibit differentiation and activate apoptosis. Regarding cell adhesion, we have found that DNA damage does not activate Abl kinase in detached fibroblasts. Thus, Abl can integrate adhesion and damage signals to regulate differentiation and apoptosis.


The Abl-p73 pathway not only transduces cell adhesion and DNA damage signals, it also plays a role in transducing the apoptotic signal from death receptors, e.g., those activated by TNF and TRAIL. Thus, Abl-p73 participates in the activation of apoptosis induced by intrinsic (DNA damage) and extrinsic (death receptors) pathways. This is in contrast to p53, which is only required to activate the intrinsic pathway of apoptosis. At present, we do not fully understand the specific functions of p53 and p73, which are two related members of the p53-family of transcription factors. Our work with RB, Abl-p73 and p53 has suggested that each of these regulators can be assigned to a binary of biological output. RB inhibits proliferation and apoptosis; Abl-p73 inhibits differentiation and activates apoptosis; p53 inhibits proliferation and activates apoptosis. In fact, many transcription regulators can be assigned binary outputs. For example, Myc stimulates proliferation and apoptosis. E2F-1 stimulates proliferation and apoptosis. NF-kB stimulates proliferation and inhibits apoptosis. MyoD inhibits proliferation and apoptosis. Understanding the hierarchical order among these units of binary output in response to perturbations in cellular physiology will be a challenge of the future.

Friday, October 3, 2003
Time Session
09:00 AM
10:00 AM
Tomasz Lipniacki - Mathematical Model of NF-kappaB Regulatory Module

The two-feedback-loop regulatory module of NF-kappaB signaling pathway is modeled by means of ordinary differential equations. The constructed model involves two-compartment kinetics of the activators IkappaB kinase (IKK) and NF-kappaB, the inhibitors A20 and IkappaBalpha, and their complexes. In resting cells the unphosphorylated IkappaBalpha binds to NF-kappaB and sequesters it in an inactive form in the cytoplasm. In response to extracellular signals such as TNF or IL-1, IKK is transformed from its neutral form (IKKn) into its active form (IKKa), a form capable of phosphorylating IkappaBalpha leading to IkappaBalpha degradation. Degradation of IkappaBalpha releases the main activator NF-kappaB, which then enters the nucleus and triggers transcription of the inhibitors and numerous other genes. The newly synthesized IkappaBalpha leads NF-kappaB out of the nucleus and sequesters it in the cytoplasm, while A20 inhibits IKK by easing its transformation into the inactive form (IKKi), a form different from IKKn, no longer capable of phosphorylating IkappaBalpha. After parameter fitting, the proposed model is able to properly reproduce time behavior of all variables for which the data now is available: nuclear NF-kappaB, cytoplasmic IkappaBalpha, A20 and IkappaBalpha mRNA transcripts, IKK and IKK catalytic activity in both wild-type and A20-deficient cells. The model allows detailed analysis of kinetics of the involved proteins and their complexes and gives the predictions of the possible responses of whole kinetics to the change in the level of a given activator or inhibitor.

10:30 AM
11:30 AM
Paul Dent - Regulation of Signaling Pathways by Radiation and Drugs: Free Radicals and Autocrine Growth Factors

Within the last 15 years, multiple new signal transduction pathways within cells have been discovered. Many of these pathways belong to what is now termed "the mitogen activated protein kinase (MAPK) superfamily." These pathways have been linked to the growth factor-mediated regulation of diverse cellular events such as proliferation, senescence, differentiation and apoptosis. Based on currently available data, exposure of cells to chemotherapeutic drugs or ionizing radiation, as well as a variety of other cellular stresses, induces simultaneous compensatory activation of multiple MAPK pathways. These signals play critical roles in controlling cell survival and re-population effects following cell stress, in a cell-type-dependent manner. Some of the signaling pathways activated are those normally activated by mitogens, such as the "classical" MAPK (also known as the ERK) pathway and the PI3 kinase / AKT pathway. Other MAPK pathways activated include those downstream of death receptors and pro-caspases, and DNA-damage signals, including the JNK and p38 MAPK pathways. Generally, enhanced ERK and PI3 kinase / AKT activity has been linked to the inhibition of pro-apoptotic caspase molecules whereas JNK and p38 signaling have been linked to enhanced caspase activity or activation. The balance of signals between each kinase pathway can thus determine the fate of a cell. The basal expression and stress-induced release of autocrine growth factor ligands such as TGF alpha and TNF alpha following cell stress has recently been mathematically modelled, and these factors can also enhance the secondary responses of MAPK pathways in cells, and consequently, of bystander cells. Thus the ability of stresses to activate MAPK and PI3 kinase signaling pathways may depend on the expression of multiple growth factor receptors and autocrine factors, which will also control cell fate.

02:00 PM
03:00 PM
Boris Kholodenko - Modular and Mechanistic Analyses of Cellular Networks: Can We Navigate Through Molecular Jungles?

The deciphering of the genome has generated a list of the macromolecular parts of living cells. A challenge for systems biology is to understand how this "genetics parts" list gives raise to a space and time varying cellular behavior resulting from dynamic interactions within cellular signaling, metabolic, and gene networks. Advances in high-throughput genomics and proteomics analyses have enabled the acquisition of large data sets on the gene expression levels and activities of signaling proteins. However, these data do not reveal interactions between components of cellular networks. Recently, a novel strategy to infer the topology and the strength of network connections using steady-state responses to perturbations was proposed [1]. Here we extend this method by analyzing time-varying responses that provide more information than steady-state dependencies. Monitoring time series has an additional advantage because, in contrast with the steady-state case, not every network component has to be perturbed, although the number of independent perturbations has to be equal to the number of components.


External information received by plasma membrane receptors, such as G-protein coupled receptors and receptor tyrosine kinases is processed and encoded into complex temporal and spatial patterns of phosphorylation and topological relocation of signaling proteins. We quantify cellular signal transduction in terms of the sensitivity of a target (e.g., a transcription factor) to a signal (e.g., a growth factor or neurotransmitter). Our experimental monitoring and computational modeling of growth factor signaling revealed kinetic and molecular factors that control the time course of phosphorylation responses, such as transient versus sustained activation patterns and oscillations in protein phosphorylation state [2]. We showed how the cellular response is controlled by the membrane translocation of signaling proteins upon receptor activation. The modeling of a 4D-organization of protein phosphorylation cascades demonstrates that the spatial separation of kinases and phosphatases may cause precipitous spatial gradients of activated kinases resulting in a strong attenuation of the signal towards the nucleus [3]. The results suggest that there are additional (besides simple diffusion) molecular mechanisms that facilitate passing of signals from the plasma membrane to transcription factors in the nucleus [3]. They may involve phospho-protein trafficking within endocytic vesicles, scaffolding and active transport of signaling complexes by molecular motors. We also discuss long-range signaling within a cell, such as survival signaling in neurons. We hypothesize that ligand-independent waves of receptor activation or/and traveling waves of phosphorylated kinases emerge to spread the signals over long distances [4].


References.



  1. Kholodenko, B.N., Kiyatkin, A., Bruggeman, F.J., Sontag, E., Westerhoff, H.V., & Hoek, J.B. (2002). Untangling the wires: A strategy to trace functional interactions in signaling and gene networks. Proc Natl Acad Sci U S A., 20, 12841-12846.

  2. Moehren, G., Markevich, N., Demin, O., Kiyatkin, A., Hoek, J.B., & Kholodenko, B.N. (2002). Temperature dependence of epidermal growth factor receptor signaling can be accounted for by a kinetic model. Biochemistry, 41, 306-320.

  3. Kholodenko, B.N. (2002). Map kinase cascade signaling and endocytic trafficking: a marriage of convenience? Trends Cell Biol., 12, 173-177.

  4. Kholodenko, B.N. (2003). Four-dimensional organization of protein kinase signaling cascades: The roles of diffusion, endocytosis and molecular motors. J. Exp. Biol., 206, 2073-2082.

Name Email Affiliation
Aguda, Baltazar bdaguda@gmail.com Genetics and Genomics, Boston University
Best, Janet jbest@mbi.osu.edu Mathematics, The Ohio State University
Borisyuk, Alla borisyuk@mbi.osu.edu Mathematical Biosciences Institute, The Ohio State University
Cetin-Atalay, Rengul rengul@bilkent.edu.tr Molecular Biology & Genetics, Bilkent University
Cooper, Stephen cooper@c.imap.itd.umich.edu Microbiology and Immunology, University of Michigan
Cracium, Gheorghe craciun@math.wisc.edu Mathematical Biosciences Institute, The Ohio State University
Danthi, Sanjay danthi.1@osu.edu Staff Scientist II, Genzyme Corporation
Dent, Paul pdent@vcu.edu Radiation Oncology, Virginia Common Wealth Center
Diez, Ruth r.diezdelcorral@dundee.ac.uk Department of Mathematics, University of Dundee
Dougherty, Daniel dpdoughe@mbi.osu.edu Mathematical Biosciences Institute, The Ohio State University
Eladdadi, Amana eladda2@rpi.edu Mathematical Sciences, Rensselaer Polytechnic Institute
Feidler, Jordan feidler@mitre.org Signal Processing Center, The Mitre Corporation
Feinberg, Martin feinberg.14@osu.edu Chemical Engineering & Mathematics, The Ohio State University
French, Donald french@math.uc.edu Department of Mathematical Sciences, University of Cincinnati
Goel, Pranay goelpra@helix.nih.gov NIDDK, Indian Institute of Science Education and Research
Grzybowski, Deb grzybowski.3@osu.edu Ophthalmology & Biomedical Eng, The Ohio State University
Guo, Yixin yixin@math.drexel.edu Department of Mathematics, The Ohio State University
Gupta, Gaorav gag2007@med.cornell.edu Cell Biology, Sloan-Kettering Institute
Hu, Shelly College of Pharmacy, The Ohio State University
Kao, Lie-Jane ljkao@mbi.osu.edu Department of Industrial Engineering, Da-Yeh University
Kholodenko, Boris boris.kholodenko@mail.tju.edu Pathology and Cell Biology, Thomas Jefferson Univ., JAH
Kimmel, Marek kimmel@stat.rice.edu Department of Statistics, Rice University
Levchenko, Andre alev@jhu.edu Whitaker Inst for Biomed Eng, Johns Hopkins University
Levine, Howard halevine@iastate.edu Department of Mathematics, Iowa State University
Lim, Sook-Kyung Mathematical Biosciences Institute, The Ohio State University
Lipniacki, Tomasz tlipnia@ippt.gov.pl, Department of Statistics, Rice University
MacMillan, Hugh macmilla@csit.fsu.edu Chemistry & Biochemistry, University of California, San Diego
Matta, Ronny College of Pharmacy, The Ohio State University
Mo, Xiaokui xiaokui.mo@osumc.edu Internal Medicine, The Ohio State University
Morgan, Jeff jmorgan@math.uh.edu Department of Mathematics, University of Houston
Nie, Qing qnie@math.uci.edu Department of Mathematics, University of California, Irvine
Novak, Bela bnovak@mail.bme.hu Agricultural Chemical Technology, Budapest Univ. of Technology
Obeyesekere, Mandri mandri@odin.mdacc.tmc.edu Unit 237, Biomathematics, University of Texas M. D. Anderson Cancer Center
Paszek, Pawel ppaszek@stat.rice.edu Department of Statistics, Rice University
Pomerening, Joseph pomereni@stanford.edu Molecular Pharmacology, Stanford University
Poyatos, Juan jpoyatos@cnio.es Structural & Computational Biology, Spanish National Cancer Center (CNIO)
Rejniak, Katarzyna rejniak@mbi.osu.edu Mathematical Biosciences Institute, The Ohio State University
Sandstede, Bjorn sandsted@math.ohio-state.edu Department of Mathematics, The Ohio State University
Sible, Jill siblej@vt.edu Department of Biology, Virginia Polytechnic Institute and State University
Sneyd, James sneyd@mbi.osu.edu Mathematics, The University of Auckland
Stark, Jaroslav j.stark@imperial.ac.uk Department of Mathematics, Imperial College London
Stredney, Donald don@osc.edu Ohio Supercomputer Center, The Ohio State University
Swierniak, Andrzej Department of Automatic Control, Silesian University of Technology
Terman, David terman@math.ohio-state.edu Mathemathics Department, The Ohio State University
Thomson, Mitchell Mathematical Biosciences Institute, The Ohio State University
Thron, Dennis dennis.thron@valley.net
Tsai, Chih-Chiang tsaijc@mbi.osu.edu Department of Mathematics, National Taiwan Normal University
Tyson, John tyson@vt.edu Department of Biology, Virginia Polytechnic Institute and State University
Walsh, Colin College of Pharmacy, The Ohio State University
Wang, Jean jywang@ucsd.edu Biological Sciences, University of California, San Diego
Wechselberger, Martin wm@mbi.osu.edu Mathematical Biosciences Insitute, The Ohio State University
Wientjes, Guillaume College of Pharmacy, The Ohio State University
Wright, Geraldine wright.572@osu.edu School of Biology, Newcastle University
Xin, Yan College of Pharmacy, The Ohio State University
Yu, Bei College of Pharmacy, The Ohio State University
Zhao, Liang College of Pharmacy, The Ohio State University
The Links and Controls of the Initiation of the Cell Cycle and of Apoptosis

I will talk about a proposed integration and modular organization of the complex regulatory networks involved in the mammalian cell cycle, apoptosis, and related intracellular signaling cascades. A common node linking the cell cycle and apoptosis permits the possibility of coordinate control between the initiation of these two cellular processes. From this node, pathways emanate that lead to the activation of cyclin-dependent kinases (in the cell cycle) and caspases (in apoptosis). Some computer simulations have been carried out to demonstrate that the proposed network architecture and certain module-module interactions can account for the experimentally observed sequence of cellular events (quiescence, cell cycle, and apoptosis) as the transcriptional activities of E2F-1 and c-Myc are increased. Despite the lack of quantitative kinetic data on most of the pathways, it is demonstrated that there can be meaningful conclusions regarding system stability that arise from the topology of the network. It is shown that only cycles in the 'qualitative network' graph determine stability. Thus, several positive and negative feedback loops are identified from a literature review of the major pathways involved in the initiation of the cell cycle and of apoptosis. Some relevant experimental results carried out in my laboratory on human chronic myeloid leukemic cells will be presented.

Cancer Cell Signaling Database with PATIKA

Human genome, which contain at least 28 000 genes, is expected to create a much more complex network, composed of hundreds and thousands of different molecules and factors. The exact map knowledge of this network is very important since it will potentially explain the mechanisms of life processes as well as disease conditions. Such knowledge will also serve as a key for further biomedical applications such as development of new drugs and diagnostic approaches.


There are already significant amount of work on pathway modeling and pathway databases (DIP KEGG, EcoCyc, BRENDA, WIT, BIND, TRANSPATH). However the data colleted on cellular networks can be best represented by integrated pathway editing environment, which provides all of the previously described functionality, including editing, visualization, storing and retrieval, basic simulation, in a single solution. Such a tool can integrate fragmented and incomplete data on cellular pathways in a single knowledge base and must have a graphical or user-friendly interface.


We have recently developed a pathway database tool PATIKA (Pathway Analysis Tool for Integration and Knowledge Acquisition, Demir E. et al. Bioinformatics 18 996-1003, 2002, http://www.patika.org) that can be used for rapid knowledge acquisition providing an integrated single source for pathway information. PATIKA aims to provide an integrated pathway-editing environment with a well-defined ontology, powerful querying and analysis options, and a dynamic visualization of any given subgraph of database.


We are currently constructing an interactive cancer cell database, which will allow storing, visualizing and analyzing cellular signaling pathways. PATIKA based cancer cell signaling database can provide a single source for cancer related pathway information that may allow micro array data analysis and provide well thought-out explanations to the high throughput data. Moreover, various data gathered on the cancer cell signaling, its subsequent analysis, and the consequently synthesized information can be used for disease gene identification, drug design and toxicity.

The Continuum Model: Regulation of the Mammalian Cell Cycle is Related to a Continuous Accumulation Process and Not Dependent on Phase-Specific Cascades of Gene Expression

The Continuum Model of the eukaryotic cell cycle proposes that the principal, fundamental, and ultimate control of the cell cycle is a continuous accumulation process occurring in all phases of the cell cycle. The Continuum Model proposes that there are no G1-phase specific events (1), that there is no G1-phase restriction point controlling passage through the G1 phase (2), and that the G0 phase-a postulated phase into which cells have been proposed to enter when conditions for growth are not favorable-is an anthropomorphic construct that has no existence and no biological meaning (1-5). The Continuum Model proposes that there are no events unique to the G1 phase; processes occurring in the G1 phase occur in the other phases as well (1, 6). Events unique to the S- and G2/M-phases can and do occur; these events are superimposed upon the continuous regulatory process or processes occurring throughout the cell cycle. The Continuum Model explains the well-known variability of G1 phase duration, as well as the existence of G1-less cells (7, 8). The Continuum Model prompted experiments defining, identifying, and explaining artifacts that led to the widely-accepted proposal of G1-phase dependent Rb protein phosphorylation (6, 9). These experiments supported the Continuum Model prediction of no G1-phase Rb phosphorylation. The Continuum Model led to a reexamination and reinterpretation of the microarray data on G1-phase specific gene expression as studied using microarrays (10-12). The Continuum Model proposes that whole-culture synchronization, the dominant and near-prevalent approach to cell-cycle analysis, cannot synchronize cells at all (1, 13-17). Time-lapse studies have supported the Continuum Model prediction that whole-culture, non-selective methods of "synchronization" cannot synchronize cells (13). The widespread and near-universal use of whole-culture synchronization methods-methods that neither synchronize cells nor avoid unwanted and deviant perturbations-have led to the current view of the cell cycle with myriad proposed variations in gene expression occurring during G1 phase. The Continuum Model does not postulate any metabolic switches during the G1 phase when certain genes are turned on leading to the initiation of subsequent events such as S phase. No metabolic cascade with G1-phase specific gene expression regulates the cell cycle. Rather, the continuous accumulation of material leads to initiation of S phase, the subsequent passage through S phase, and then mitosis and cytokinesis. Theoretical, mathematical, and formal studies and analyses of cell cycle control should always consider problems with data based on questionable experimental approaches, particularly experiments using whole-culture synchronization.



  1. Cooper, S. (2000). The continuum model and G1-control of the mammalian cell cycle. Prog Cell Cycle Res., 4, 27-39.

  2. Cooper, S. (2003). Reappraisal of Serum Starvation, the Restriction Point, G0, and G1-phase Arrest Points. FASEB J, 17, 333-340.

  3. Cooper, S. (2003). How the change from FLM to FACS affected our understanding of the G1 phase of the cell cycle. Cell Cycle, 2, 157-159.

  4. Cooper, S. (1998). On the proposal of a G0 phase and the restriction point. FASEB J, 12, 367-373.

  5. Cooper, S. (1987).On G0 and cell cycle controls. Bioessays, 7, 220-223.

  6. Cooper, S., & Shayman, J.A. (2001). Revisiting retinoblastoma protein phosphorylation during the mammalian cell cycle. Cell Mol Life Sci, 58, 580-595.

  7. Cooper, S. (1979). A unifying model for the G1 period in prokaryotes and eukaryotes. Nature, 280, 17-19.

  8. Cooper, S. (1998). On the interpretation of the shortening of the G1-phase by overexpression of cyclins in mammalian cells. Exp Cell Res, 238, 110-115.

  9. Cooper, S., Yu, C., & Shayman, J.A. (1999). Phosphorylation-dephosphorylation of retinoblastoma protein not necessary for passage through the mammalian cell division cycle. IUBMB Life, 48, 225-230.

  10. Cooper, S. (2002).Cell cycle analysis and microarrays. Trends in Genetics, 18, 289-290.

  11. Shedden, K., & Cooper, S. (2002). Analysis of cell-cycle-specific gene expression in human cells as determined by microarrays and double-thymidine block synchronization. Proc Natl Acad Sci USA, 99, 4379-4384.

  12. Shedden, K., & Cooper, S. (2002).Analysis of cell-cycle-specific gene exresssion in Saccharomyces cerevisiae as determined by Microarrays and Multiple synchronization methods. Nuc Acids Res, 30, 2920-2929.

  13. Cooper, S. (2002). Reappraisal of G1-phase arrest and synchronization by lovastatin. Cell Biol Int, 26, 715-727.

  14. Cooper, S. (2002). Minimally Disturbed, Multi-Cycle, and Reproducible Synchrony using a Eukaryotic "Baby Machine". Bioessays, 24, 499-501.

  15. Cooper, S. (2003). Rethinking Synchronization of mammalian cells for cell-cycle analysis. Cell Mol Life Sci, 6, 1099-1106.

  16. Cooper, S. (2003).On the Persistence of Forcing Synchronization Methodology. Manuscript submitted for publication.

  17. Cooper, S. (1998). Mammalian cells are not synchronized in G1-phase by starvation or inhibition: considerations of the fundamental concept of G1-phase synchronization. Cell Prolif, 31, 9-16.


(Many of the cited references can be read directly at www.umich.edu/~cooper; just click on the appropriate article title. The experimental data supporting the Continuum Model are described in more detail in these references.)

Regulation of Signaling Pathways by Radiation and Drugs: Free Radicals and Autocrine Growth Factors

Within the last 15 years, multiple new signal transduction pathways within cells have been discovered. Many of these pathways belong to what is now termed "the mitogen activated protein kinase (MAPK) superfamily." These pathways have been linked to the growth factor-mediated regulation of diverse cellular events such as proliferation, senescence, differentiation and apoptosis. Based on currently available data, exposure of cells to chemotherapeutic drugs or ionizing radiation, as well as a variety of other cellular stresses, induces simultaneous compensatory activation of multiple MAPK pathways. These signals play critical roles in controlling cell survival and re-population effects following cell stress, in a cell-type-dependent manner. Some of the signaling pathways activated are those normally activated by mitogens, such as the "classical" MAPK (also known as the ERK) pathway and the PI3 kinase / AKT pathway. Other MAPK pathways activated include those downstream of death receptors and pro-caspases, and DNA-damage signals, including the JNK and p38 MAPK pathways. Generally, enhanced ERK and PI3 kinase / AKT activity has been linked to the inhibition of pro-apoptotic caspase molecules whereas JNK and p38 signaling have been linked to enhanced caspase activity or activation. The balance of signals between each kinase pathway can thus determine the fate of a cell. The basal expression and stress-induced release of autocrine growth factor ligands such as TGF alpha and TNF alpha following cell stress has recently been mathematically modelled, and these factors can also enhance the secondary responses of MAPK pathways in cells, and consequently, of bystander cells. Thus the ability of stresses to activate MAPK and PI3 kinase signaling pathways may depend on the expression of multiple growth factor receptors and autocrine factors, which will also control cell fate.

Biochemical Reaction Network Structure and the Capacity for Switch-Like Behavior

There are two themes, stated with varying degrees of certainty, that seem to be recurrent in discussions of how the cell cycle might be understood: The first is that the underlying biochemical machinery is so complex that only a suitably sensible "systems" model, taken with sensible analysis, will serve to indicate how the cell cycle works and how it might be controlled. The second is the supposition that the machinery has embedded within it crucial biochemical switches that might have their origin in bistable behavior, construed in the dynamical systems sense. (See [1] for an example of ambitious experimental work aimed investigating the role of bistability in cell cycle progress.) The problem for modelers of the cell cycle (and for cellular processes generally) quickly becomes apparent: (i) Models - even of small biochemical "modules" - that reflect the underlying chemistry with reasonable fidelity will be inherently complex. (ii) At least at outset, parameter values (e.g., reaction rate constants) will be known poorly, if at all. Thus, in the normal evolution of an intricate biochemical model, it becomes important to understand the qualitative capacity of its components, working in concert, to admit particular phenomena (e.g, bistability) without a priori commitment to specified parameter values or even to ranges of parameter values. Moreover, it becomes important to do this in the context of considerable complexity. Chemical reaction network theory has as its goal the development of powerful but readily implementable tools for connecting complex reaction network structure to the qualitative capacity for certain phenomena (in particular, bistability). The theory goes back at least to the 1970s [2]. It has not been specific to biology, but, for reasons already stated, there is now growing interest in biological applications [3]. Very recent work has, in fact, been dedicated specifically to biochemical networks driven by enzyme-catalyzed reactions. In particular, it is now known that there are remarkable and quite subtle connections between properties of reaction diagrams of the kind that biochemists normally draw and the capacity for biochemical switching. Our aim in this talk will be to explain, for an audience unfamiliar with chemical reaction network theory, those tools that have recently become available.



  1. Cross, F. R., Archambault, V., Miller, M., & Klovstad, M. (2002). Testing a mathematical model of the yeast cell cycle. Mol. Biol. Cell, 13, 52-70.

  2. For some early results, see M. Feinberg, Lectures on Chemical Reaction Networks, University of Wisconsin Mathematics Research Center, 1979, available at http://www.che.eng.ohio-state.edu/~feinberg/LecturesOnReactionNetworks/

  3. Bailey, James E. (2001). Complex biology with no parameters. Nature Biotechnology, 19, 503-504.

Modular and Mechanistic Analyses of Cellular Networks: Can We Navigate Through Molecular Jungles?

The deciphering of the genome has generated a list of the macromolecular parts of living cells. A challenge for systems biology is to understand how this "genetics parts" list gives raise to a space and time varying cellular behavior resulting from dynamic interactions within cellular signaling, metabolic, and gene networks. Advances in high-throughput genomics and proteomics analyses have enabled the acquisition of large data sets on the gene expression levels and activities of signaling proteins. However, these data do not reveal interactions between components of cellular networks. Recently, a novel strategy to infer the topology and the strength of network connections using steady-state responses to perturbations was proposed [1]. Here we extend this method by analyzing time-varying responses that provide more information than steady-state dependencies. Monitoring time series has an additional advantage because, in contrast with the steady-state case, not every network component has to be perturbed, although the number of independent perturbations has to be equal to the number of components.


External information received by plasma membrane receptors, such as G-protein coupled receptors and receptor tyrosine kinases is processed and encoded into complex temporal and spatial patterns of phosphorylation and topological relocation of signaling proteins. We quantify cellular signal transduction in terms of the sensitivity of a target (e.g., a transcription factor) to a signal (e.g., a growth factor or neurotransmitter). Our experimental monitoring and computational modeling of growth factor signaling revealed kinetic and molecular factors that control the time course of phosphorylation responses, such as transient versus sustained activation patterns and oscillations in protein phosphorylation state [2]. We showed how the cellular response is controlled by the membrane translocation of signaling proteins upon receptor activation. The modeling of a 4D-organization of protein phosphorylation cascades demonstrates that the spatial separation of kinases and phosphatases may cause precipitous spatial gradients of activated kinases resulting in a strong attenuation of the signal towards the nucleus [3]. The results suggest that there are additional (besides simple diffusion) molecular mechanisms that facilitate passing of signals from the plasma membrane to transcription factors in the nucleus [3]. They may involve phospho-protein trafficking within endocytic vesicles, scaffolding and active transport of signaling complexes by molecular motors. We also discuss long-range signaling within a cell, such as survival signaling in neurons. We hypothesize that ligand-independent waves of receptor activation or/and traveling waves of phosphorylated kinases emerge to spread the signals over long distances [4].


References.



  1. Kholodenko, B.N., Kiyatkin, A., Bruggeman, F.J., Sontag, E., Westerhoff, H.V., & Hoek, J.B. (2002). Untangling the wires: A strategy to trace functional interactions in signaling and gene networks. Proc Natl Acad Sci U S A., 20, 12841-12846.

  2. Moehren, G., Markevich, N., Demin, O., Kiyatkin, A., Hoek, J.B., & Kholodenko, B.N. (2002). Temperature dependence of epidermal growth factor receptor signaling can be accounted for by a kinetic model. Biochemistry, 41, 306-320.

  3. Kholodenko, B.N. (2002). Map kinase cascade signaling and endocytic trafficking: a marriage of convenience? Trends Cell Biol., 12, 173-177.

  4. Kholodenko, B.N. (2003). Four-dimensional organization of protein kinase signaling cascades: The roles of diffusion, endocytosis and molecular motors. J. Exp. Biol., 206, 2073-2082.

Mathematical Model of NF-kappaB Regulatory Module

The two-feedback-loop regulatory module of NF-kappaB signaling pathway is modeled by means of ordinary differential equations. The constructed model involves two-compartment kinetics of the activators IkappaB kinase (IKK) and NF-kappaB, the inhibitors A20 and IkappaBalpha, and their complexes. In resting cells the unphosphorylated IkappaBalpha binds to NF-kappaB and sequesters it in an inactive form in the cytoplasm. In response to extracellular signals such as TNF or IL-1, IKK is transformed from its neutral form (IKKn) into its active form (IKKa), a form capable of phosphorylating IkappaBalpha leading to IkappaBalpha degradation. Degradation of IkappaBalpha releases the main activator NF-kappaB, which then enters the nucleus and triggers transcription of the inhibitors and numerous other genes. The newly synthesized IkappaBalpha leads NF-kappaB out of the nucleus and sequesters it in the cytoplasm, while A20 inhibits IKK by easing its transformation into the inactive form (IKKi), a form different from IKKn, no longer capable of phosphorylating IkappaBalpha. After parameter fitting, the proposed model is able to properly reproduce time behavior of all variables for which the data now is available: nuclear NF-kappaB, cytoplasmic IkappaBalpha, A20 and IkappaBalpha mRNA transcripts, IKK and IKK catalytic activity in both wild-type and A20-deficient cells. The model allows detailed analysis of kinetics of the involved proteins and their complexes and gives the predictions of the possible responses of whole kinetics to the change in the level of a given activator or inhibitor.

Modeling Cell Growth, Division and Morphology in Fission Yeast

Because of its regular shape and excellent genetics, fission yeast is a convenient organism to study cellular morphogenesis. Genetic analysis has identified a host of proteins that regulate shape changes during the cell cycle. Most of these proteins interact with either the microtubular or actin cytoskeleton of the cell. In this lecture, we present a simple model for fission yeast morphogenesis based on an interplay between the two cytoskeletal systems. An essential assumption of the model is that actin polymerisation is a self-reinforcing (autocatalytic) process: F-actin promotes its own formation from G-actin subunits via regulatory molecules. Since the diffusion coefficient of F-actin is much smaller than the diffusion coefficient for its substrate, G-actin, our model is a version of the well-known, Turing pattern-formation mechanism: local self-enhancement and long range inhibition. Microtubules stimulate actin polymerisation in the model by delivering a component of the autocatalytic actin assembly feedback loop. We show that the model captures all the characteristic features of polarised growth in fission yeast during normal mitotic cycle. We also show that all the major classes of morphogenetic mutants (orb and tea) are natural outcomes of the model.

Mathematical Model for Cell Cycle Regulation and Cancer

A mathematical model of the kinetics of a few regulatory proteins will be presented. This model, restricted to the dynamics during the DNA synthesis phase (S-phase) and mitosis (M-phase) of the cell cycle, incorporates the activities of the major cyclin-cdks (cell division kinases), i.e., cyclin A/cdk2, cyclin A/cdk1 and cyclin B/cdk1. It also embeds the interactions by cdc25c, p53, and P21. Numerical solutions of this mathematical model that reproduces well-known experimental results will be discussed; namely, cell arrest due to DNA damage and cell proliferation in p53 null cells. Based on mathematical analysis of the underlying ODE system, different end point behaviors will be discussed. How the model, along with the mathematical analysis, can help cancer research will be presented.

Hysteresis and Bistability in Cdc2 Activation: Constructing a Cell Cycle Oscillator

In the early embryonic cell cycle, Cdc2-cyclin B functions like an autonomous oscillator, whose robust biochemical rhythm continues even when DNA replication or mitosis is blocked (Hara et al., 1980). At the core of the oscillator is a negative feedback loop; cyclins accumulate and produce active mitotic Cdc2-cyclin B (Evans et al., 1983; Murray and Kirschner, 1989); Cdc2 activates the anaphase-promoting complex (APC); the APC then promotes cyclin degradation and resets Cdc2 to its inactive, interphase state. Cdc2 regulation also involves positive feedback (Masui and Markert, 1971), with active Cdc2-cyclin B stimulating its activator Cdc25 (Izumi et al., 1992; Kumagai and Dunphy, 1992; Hoffmann et al., 1993) and inactivating its inhibitors Wee1 and Myt1 (Tang et al., 1993; McGowan and Russell, 1995; Mueller et al., 1995). Under the proper circumstances, these positive feedback loops could function as a bistable trigger for mitosis (Novak and Tyson, 1993; Thron, 1996), and oscillators with bistable triggers might be especially relevant to biological applications such as cell cycle regulation (Goldbeter, 2002; McMillen et al., 2002; Vilar et al., 2002). Therefore, we examined whether Cdc2 activation is bistable. We confirm that the response of Cdc2 to non-degradable cyclin B is temporally abrupt and switch-like, as would be expected if Cdc2 activation were bistable. We also show that Cdc2 activation exhibits hysteresis, a property of bistable systems with particular relevance to biochemical oscillators. These findings help establish the basic systems-level logic of the mitotic oscillator.


Bibliography



  1. Evans, T., Rosenthal, E., Youngblom, J., Distel, D., & Hunt, T. (1983). Cyclin: A protein specified by maternal mRNA in sea urchin eggs that is destroyed at each cleavage division. 33, 389-396.

  2. Goldbeter, A. (2002). Computational approaches to cellular rhythms. Nature, 420(6912), 238-45.

  3. Hara, K., Tydeman, P., & Kirschner, M. (1980). A cytoplasmic clock with the same period as the division cycle in Xenopus eggs. Proc Natl Acad Sci U S A, 77(1), 462-6.

  4. Hoffmann, I., Clarke, P., Marcote, M., Karsenti, E., & Draetta, G. (1993). Phosphorylation and activation of human cdc25-C by cdc2-cyclin B and its involvement in the self-amplification of MPF at mitosis. EMBO J., 12, 53-63.

  5. Izumi, T., Walker, D., & Maller, J. (1992). Periodic changes in phosphorylation of the Xenopus cdc25 phosphatase regulate its activity. Mol Biol Cell., 3(8), 927-39.

  6. Kumagai, A. & Dunphy, W. G. (1992). Regulation of the cdc25 protein during the cell cycle in Xenopus extracts. Cell. 70(1), 139-51.

  7. Masui, Y. & Markert, C. (1971). Cytoplasmic control of nuclear behavior during meiotic maturation of frog oocytes. J Exp Zool., 177, 129-146.

  8. McGowan, C. & Russell, P. (1995). Cell cycle regulation of human WEE1. EMBO J., 14(10), 2166-75.

  9. McMillen, D., Kopell, N., Hasty, J., & Collins, J. (2002). Synchronizing genetic relaxation oscillators by intercell signaling. Proc Natl Acad Sci U S A., 99(2), 679-84.

  10. Mueller, P., Coleman, T., & Dunphy, W. (1995). Cell cycle regulation of a Xenopus Wee1-like kinase. 6, 119-134.

  11. Murray, A. & Kirschner, M. (1989). Cyclin synthesis drives the early embryonic cell cycle. Nature, 339, 275-280.

  12. Novak, B. & Tyson, J. (1993). Numerical analysis of a comprehensive model of M-phase control in Xenopus oocyte extracts and intact embryos. J Cell Sci., 106(Pt 4), 1153-68.

  13. Tang, Z., Coleman, T., & Dunphy, W. (1993). Two distinct mechanisms for negative regulation of the Wee1 protein kinase. EMBO J., 12(9), 3427-36.

  14. Thron, C. (1996). A model for a bistable biochemical trigger of mitosis. Biophys Chem., 57(2-3), 239-51.

  15. Vilar, J., Kueh, H., Barkai, N., & Leibler, S. (2002). Mechanisms of noise-resistance in genetic oscillators. Proc Natl Acad Sci U S A., 99(9), 5988-92.

Cell Cycle Controls in Frog Eggs and Embryos: Molecular Mechanisms and Mathematical Models

Cell-free extracts derived from the eggs of the South African clawed frog, Xenopus laevis, provide a biochemically tractable and relatively simple system in which to investigate fundamental cell cycle control mechanisms. By pairing mathematical modeling with experimental cell biology, we have demonstrated that entry into and exit from mitosis in egg extracts is driven by hysteresis. We are building upon these studies to determine the mechanisms that regulate cell cycle arrest at checkpoints in response to damaged and unreplicated DNA. In addition to studying basic cell cycle controls in egg extracts, we utilize intact Xenopus embryos to investigate the remodeling cell cycles of early development. In particular, we have built a preliminary mathematical model of the cyclin E/Cdk2 developmental timer that regulates the midblastula transition during early development. We believe that close collaboration between computational biologists and experimental cell biologists provides a powerful new approach for investigating the most challenging questions about the molecular network that regulates the eukaryotic cell cycle.

Divide or Die: Coupling Proliferation and Apoptosis

Control of both proliferation and cell death is essential to the maintenance of homeostasis. The signalling path-ways of these two processes are closely coupled. As a result, for example, it is often the case that dormant cells are less susceptible to apoptosis than ones that are in cycle. This talk will explore the consequences of such cou-pling on the homeostasis of a population of cells. In particular, we will present a model of T-cell memory that depends on apoptosis mediated by Fas-FasL binding. Unlike most homeostasis models, which rely on a nonlinear growth term, the nonlinearity appears in the death term. By treating dormant and cycling subpopulations separately, we are able to investigate the effects of coupling apoptosis to the cell cycle. When this is done, it turns out that a small subpopulation of active cells can control the size of a much larger population. We extend the model to incorporate an increased rate of division amongst some cells, for instance due to HIV infection. Paradoxically, this can lead to a decline in cell numbers, and may help to explain the high death rate of uninfected T-cells that has been observed during HIV infection.

On Stability Analysis of the Bistable Biochemical Switches in the Cell Cycle

As presently conceived, the cell cycle is quite different from most other biological oscillators, in that it has a sequence of phases and can be arrested at any of several points, e.g. the so-called "checkpoints." Analysis of cell cycle control therefore tends to focus on the presumed bistable biochemical switching at the arrest points (1-3), rather than on a Hopf bifurcation. For this discussion it will be assumed that bistable biochemical switching requires two nonzero stable steady states or attractors, with a saddle point produced by some form of positive feedback which must be strong enough, in terms of reaction order, to overcome the damping tendencies that are always present in chemical systems. Switching out of a stable steady state can occur by saddle-node bifurcation, or in unusual cases by homoclinic loop bifurcation followed by subcritical Hopf bifurcation. Switching out of a periodic orbit to a particular checkpoint (or to G0 phase, apoptosis, or differentiation) can occur by homoclinic loop bifurcation. Possible biochemical mechanisms for saddle-node bifurcation will be discussed for several cell cycle checkpoints, with particular attention to (a) reaction order requirements for effective positive feedback, and (b) biochemical kinetic questions that call for further experimental investigation.



  1. Thron, C. D. (1996). A model for a bistable trigger of mitosis. Biophys. Chem., 57, 239-251.

  2. Thron, C. D. (1998). Cell cycle checkpoints in the overall dynamics of cell cycle control. In M. A. Horn, G. Simonett, & G. F. Webb (Eds.), Mathematical Models in Medical and Health Science (pp. 369-380). Nashville, TN: Vanderbilt University Press.

  3. Thron, C. D. (1999). Mathematical analysis of binary activation of a cell cycle kinase which down-regulates its own inhibitor. Biophys. Chem., 79, 95-106.

Modeling the Cell Cycle Engine and Checkpoints in Yeast Cells

The physiology of a cell is largely determined by complex networks of interacting proteins. For example, eukaryotic cell division is regulated by an underlying cell cycle engine that is known in great detail. The basic molecular mechanisms controlling DNA replication, mitosis and cell division are highly conserved among eukaryotes, with homologous proteins functioning in both yeast and humans. To understand the dynamics of such a complicated control system requires sophisticated theoretical and computational tools. Our approach is to decompose the cell cycle engine into "modules" that are responsible for the characteristic transitions of the cell cycle (G1/S, G2/M and meta/anaphase) and to analyse these modules by standard tools of dynamical system theory (phase plane techniques, stability analysis, bifurcation theory etc.). We will show that some of the modules (G1/S and G2/M) are based on antagonistic relationships between cell cycle regulators. As a consequence of this antagonism, these modules operate as switches with different turning-on and turning-off points, a phenomenon called hysteresis. In contrast, the mitotic module, which is based on a negative feedback loop, operates as an oscillator. We will also describe how to assemble G1/S-, G2/M- and meta/anaphase-modules into a comprehensive model of the eukaryotic cell cycle, using yeast cells as an example. With this comprehensive model, we will also discuss the mechanisms by which cell cycle checkpoint pathways stabilise cell cycle states and inhibit the transitions that drive cell cycle progression.

Regulation of Cell Proliferation, Differentiation and Apoptosis by DNA Damage

In eukaryotic cells, DNA lesions trigger several conserved cell cycle checkpoints to prevent replication and segregation of damaged genome and to promote repair. In mammalian cells, the DNA damage-signaling network generates additional biological outputs, including the inhibition of differentiation, the activation of apoptosis and the induction of premature senescence. The cell cycle checkpoints and the inhibition of differentiation are reversible, allowing the resumption of proliferation and differentiation after the lesions are repaired. Apoptosis and premature senescence are irreversible, resulting from the accumulation of irreparable DNA lesions.


We have identified the Abl tyrosine kinase to be a regulator of differentiation and apoptosis in response to DNA damage. The nuclear Abl kinase is activated by a variety of DNA lesions. In myoblasts, exposure to MMS (an alkylating agent) or low dose cisplatin (a cross-linking agent) causes a reversible inhibition of myogenic differentiation in an Abl-dependent mechanism. DNA damage-induced differentiation checkpoint is also dependent on the transcription factor p73, which is a downstream effector of Abl. The Abl-p73 pathway also activates apoptosis in response to cisplatin and other DNA lesions. These findings suggest differentiation and apoptosis are a continuum of response to DNA damage. Factors that modulate the amplitude or duration of output from the Abl-p73 pathway are therefore likely to control the biological outcome following DNA damage.


We have identified a few factors that modulate the Abl kinase activity. Two of these factors, in particular, are known to regulate cell proliferation, differentiation and apoptosis. The first is the retinoblastoma tumor suppressor protein, RB, which inhibits Abl kinase. The second is cell adhesion, which activates Abl kinase. RB is well known for its ability to block cell cycle progression. This, however, is not the only function of RB. More importantly, RB promotes terminal differentiation and inhibits apoptosis. Thus, RB antagonizes Abl's ability to inhibit differentiation and activate apoptosis. Regarding cell adhesion, we have found that DNA damage does not activate Abl kinase in detached fibroblasts. Thus, Abl can integrate adhesion and damage signals to regulate differentiation and apoptosis.


The Abl-p73 pathway not only transduces cell adhesion and DNA damage signals, it also plays a role in transducing the apoptotic signal from death receptors, e.g., those activated by TNF and TRAIL. Thus, Abl-p73 participates in the activation of apoptosis induced by intrinsic (DNA damage) and extrinsic (death receptors) pathways. This is in contrast to p53, which is only required to activate the intrinsic pathway of apoptosis. At present, we do not fully understand the specific functions of p53 and p73, which are two related members of the p53-family of transcription factors. Our work with RB, Abl-p73 and p53 has suggested that each of these regulators can be assigned to a binary of biological output. RB inhibits proliferation and apoptosis; Abl-p73 inhibits differentiation and activates apoptosis; p53 inhibits proliferation and activates apoptosis. In fact, many transcription regulators can be assigned binary outputs. For example, Myc stimulates proliferation and apoptosis. E2F-1 stimulates proliferation and apoptosis. NF-kB stimulates proliferation and inhibits apoptosis. MyoD inhibits proliferation and apoptosis. Understanding the hierarchical order among these units of binary output in response to perturbations in cellular physiology will be a challenge of the future.