Bela Novak

Sniffers, buzzers, toggles and blinkers: dynamics of regulatory and signaling pathways in the cell

The physiological responses of cells to external and internal stimuli are governed by genes and proteins interacting in complex networks whose dynamical properties are impossible to understand by intuitive reasoning alone. Recent advances by theoretical biologists have demonstrated that molecular regulatory networks can be accurately modeled in mathematical terms. These models shed light on the design principles of biological control systems and make predictions that have been verified experimentally.

The cell cycle

‘Dividing cells pass through a regular sequence of cell growth and division, known as the cell cycle’, according to a college textbook of biology published in 1983 [[1][1]], 5 years before the underlying principles of control were first laid bare during 1988, the annus mirabilis of cell cycle

Network dynamics and cell physiology

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

Functional Motifs in Biochemical Reaction Networks

The signal-response characteristics of a living cell are determined by complex networks of interacting genes, proteins, and metabolites. Understanding how cells respond to specific challenges, how these responses are contravened in diseased cells, and how to intervene pharmacologically in the decision-making processes of cells requires an accurate theory of the information-processing capabilities of macromolecular regulatory networks. Adopting an engineers approach to control systems, we ask whether realistic cellular control networks can be decomposed into simple regulatory motifs that carry out specific functions in a cell. We show that such functional motifs exist and review the experimental evidence that they control cellular responses as expected.

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 (Lahav et al., Nature Genetics, 36, 147-150, 2004). 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.

Regulation of APC/C Activity in Oocytes by a Bub1-Dependent Spindle Assembly Checkpoint

BACKGROUND Missegregation of chromosomes during meiosis in human females causes aneuploidy, including trisomy 21, and is thought also to be the major cause of age-related infertility. Most errors are thought to occur at the first meiotic division. The high frequency of errors raises questions as to whether the surveillance mechanism known as the spindle assembly checkpoint (SAC) that controls the anaphase-promoting complex or cyclosome (APC/C) operates effectively in oocytes. Experimental approaches hitherto used to inactivate the SAC in oocytes suffer from a number of drawbacks. RESULTS Bub1 protein was depleted specifically in oocytes with a Zp3-Cre transgene to delete exons 7 and 8 from a floxed BUB1(F) allele. Loss of Bub1 greatly accelerates resolution of chiasmata and extrusion of polar bodies. It also causes defective biorientation of bivalents, massive chromosome missegregation at meiosis I, and precocious loss of cohesion between sister centromeres. By using a quantitative assay for APC/C-mediated securin destruction, we show that the APC/C is activated in an exponential fashion, with activity peaking 12-13 hr after GVBD, and that this process is advanced by 5 hr in oocytes lacking Bub1. Importantly, premature chiasmata resolution does not occur in Bub1-deficient oocytes also lacking either the APC/Cs Apc2 subunit or separase. Finally, we show that Bub1s kinase domain is not required to delay APC/C activation. CONCLUSIONS We conclude that far from being absent or ineffective, the SAC largely determines the timing of APC/C and hence separase activation in oocytes, delaying it for about 5 hr.

Irreversible cell-cycle transitions are due to systems-level feedback

The irreversibility of cell-cycle transitions is commonly thought to derive from the irreversible degradation of certain regulatory proteins. We argue that irreversible transitions in the cell cycle (or in any other molecular control system) cannot be attributed to a single molecule or reaction, but that they derive from feedback signals in reaction networks. This systems-level view of irreversibility is supported by many experimental observations.

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

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

Phosphorylation network dynamics in the control of cell cycle transitions

Summary Fifteen years ago, it was proposed that the cell cycle in fission yeast can be driven by quantitative changes in the activity of a single protein kinase complex comprising a cyclin – namely cyclin B – and cyclin dependent kinase 1 (Cdk1). When its activity is low, Cdk1 triggers the onset of S phase; when its activity level exceeds a specific threshold, it promotes entry into mitosis. This model has redefined our understanding of the essential functional inputs that organize cell cycle progression, and its main principles now appear to be applicable to all eukaryotic cells. But how does a change in the activity of one kinase generate ordered progression through the cell cycle in order to separate DNA replication from mitosis? To answer this question, we must consider the biochemical processes that underlie the phosphorylation of Cdk1 substrates. In this Commentary, we discuss recent findings that have shed light on how the threshold levels of Cdk1 activity that are required for progression through each phase are determined, how an increase in Cdk activity generates directionality in the cell cycle, and why cell cycle transitions are abrupt rather than gradual. These considerations lead to a general quantitative model of cell cycle control, in which opposing kinase and phosphatase activities have an essential role in ensuring dynamic transitions.

A model of yeast cell-cycle regulation based on multisite phosphorylation

In order for the cells genome to be passed intact from one generation to the next, the events of the cell cycle (DNA replication, mitosis, cell division) must be executed in the correct order, despite the considerable molecular noise inherent in any protein‐based regulatory system residing in the small confines of a eukaryotic cell. To assess the effects of molecular fluctuations on cell‐cycle progression in budding yeast cells, we have constructed a new model of the regulation of Cln‐ and Clb‐dependent kinases, based on multisite phosphorylation of their target proteins and on positive and negative feedback loops involving the kinases themselves. To account for the significant role of noise in the transcription and translation steps of gene expression, the model includes mRNAs as well as proteins. The model equations are simulated deterministically and stochastically to reveal the bistable switching behavior on which proper cell‐cycle progression depends and to show that this behavior is robust to the level of molecular noise expected in yeast‐sized cells (∼50 fL volume). The model gives a quantitatively accurate account of the variability observed in the G1‐S transition in budding yeast, which is governed by an underlying sizer+timer control system.