The adaptive responses of a living cell to internal and external signals are controlled by networks proteins whose interactions so complex that the functional integration network cannot be comprehended intuitive reasoning alone. Mathematical modeling, based on biochemical rate equations, provides rigorous reliable tool for unraveling complexities molecular regulatory networks. budding yeast cycle is challenging test case this approach, because control system known in exquisite detail its...

Cells progressing through the cell cycle must commit irreversibly to mitosis without slipping back interphase before properly segregating their chromosomes. A mathematical model of cell-cycle progression in cell-free egg extracts from frog predicts that irreversible transitions into and out are driven by hysteresis molecular control system. Hysteresis refers toggle-like switching behavior a dynamical In model, toggle switch is created positive feedback phosphorylation reactions controlling...

The molecular machinery of cell cycle control is known in more detail for budding yeast, Saccharomyces cerevisiae, than any other eukaryotic organism. In recent years, many elegant experiments on yeast have dissected the roles cyclin molecules (Cln1–3 and Clb1–6) coordinating events DNA synthesis, bud emergence, spindle formation, nuclear division, separation. These experimental clues suggest a mechanism principal interactions controlling synthesis degradation. Using standard techniques...

The proteins cdc2 and cyclin form a heterodimer (maturation promoting factor) that controls the major events of cell cycle. A mathematical model for interactions is constructed. Simulation analysis show control system can operate in three modes: as steady state with high maturation factor activity, spontaneous oscillator, or an excitable switch. We associate metaphase arrest unfertilized eggs, oscillations rapid division cycles early embryos, switch growth-controlled typical nonembryonic cells.

Periodic expanding target patterns of chemical activity are observed in thin layers solution containing bromate, malonic acid and ferroin dilute sulfuric acid. Commonly these appear as blue (oxidized) rings propagating out from a central point into red (reduced) bulk medium. Recently, the opposite pattern has been observed: waves reduction through an oxidized We discuss both under assumption that there is heterogeneity at center pattern—most likely dust particle or scratch on glass—which...

To contribute to a deeper understanding of M-phase control in eukaryotic cells, we have constructed model based on the biochemistry promoting factor (MPF) Xenopus oocyte extracts, where there is evidence for two positive feedback loops (MPF stimulates its own production by activating Cdc25 and inhibiting Wee1) negative loop destruction indirectly ubiquitin pathway that degrades cyclin subunit). uncover full dynamical possibilities system, translate regulatory network into set differential...

Excitable media are spatially distributed systems characterized by their ability to propagate signals undamped over long distances. Wave propagation in excitable has been modeled extensively both continuous partial differential equations and discrete cellular automata. Cellular automata desirable because of intuitive appeal efficient digital implementation, but until now they have not served as reliable models lacked two essential properties media. First, traveling waves show dispersion,...

The Description for this book, When Time Breaks Down: Three-Dimensional Dynamics of Electrochemical Waves and Cardiac Arrhythmias, will be forthcoming.

p53 is activated in response to events compromising the genetic integrity of a cell. Recent data show that activity does not increase steadily with damage but rather fluctuates an oscillatory fashion (Lahav et al., Nature Genetics, 36, 147-150, 2004). Theoretical studies suggest oscillations can arise from combination positive and negative feedbacks or long feedback loop alone. Both are present p53/Mdm2 network, it known what roles they play DNA damage. We developed mathematical model based...

That chemical reactions can exhibit all of the interesting and well known behavior nonlinear oscillators is shown by collecting scattered results in literature for a simple reaction mechanism, supplementing them with some new results, analyzing single oscillator using method isoclines. Furthermore, two coupled series illustrate phenomena synchronization, multiply periodic almost-periodic oscillations, subharmonic resonance. Finally mechanism modified to form which biochemically realistic...