Modeling the cell cycle: why do certain circuits oscillate?

Computational modeling and the theory of nonlinear dynamical systems allow one to not simply describe the events of the cell cycle, but also to understand why these events occur, just as the theory of gravitation allows one to understand why cannonballs fly in parabolic arcs. The simplest examples of the eukaryotic cell cycle operate like autonomous oscillators. Here, we present the basic theory of oscillatory biochemical circuits in the context of the Xenopus embryonic cell cycle. We examine Boolean models, delay differential equation models, and especially ordinary differential equation (ODE) models. For ODE models, we explore what it takes to get oscillations out of two simple types of circuits (negative feedback loops and coupled positive and negative feedback loops). Finally, we review the procedures of linear stability analysis, which allow one to determine whether a given ODE model and a particular set of kinetic parameters will produce oscillations.     

USP2a protein deubiquitinates and stabilizes the circadian protein CRY1 in response to inflammatory signals

The mammalian circadian clock coordinates various physiological activities with environmental cues to achieve optimal adaptation. The clock manifests oscillations of key clock proteins, which are under dynamic control at multiple post-translational levels. As a major post-translational regulator, the ubiquitination-dependent proteasome degradation system is counterbalanced by a large group of deubiquitin proteases with distinct substrate preference. Until now, whether deubiquitination by ubiquitin-specific proteases can regulate the clock protein stability and circadian pathways remains largely unclear. The mammalian clock protein, cryptochrome 1 (CRY1), is degraded via the FBXL3-mediated ubiquitination pathway, suggesting that it is also likely to be targeted by the deubiquitination pathway. Here, we identified that USP2a, a circadian-controlled deubiquitinating enzyme, interacts with CRY1 and enhances its protein stability via deubiquitination upon serum shock. Depletion of Usp2a by shRNA greatly enhances the ubiquitination of CRY1 and dampens the oscillation amplitude of the CRY1 protein during a circadian cycle. By stabilizing the CRY1 protein, USP2a represses the Per2 promoter activity as well as the endogenous Per2 gene expression. We also demonstrated that USP2a-dependent deubiquitination and stabilization of the CRY1 protein occur in the mouse liver. Interestingly, the pro-inflammatory cytokine, TNF-α, increases the CRY1 protein level and inhibits circadian gene expression in a USP2a-dependent fashion. Therefore, USP2a potentially mediates circadian disruption by suppressing the CRY1 degradation during inflammation.     

Cyclic Negative Feedback Systems: What is the Chance of Oscillation?

Many biological oscillators have a cyclic structure consisting of negative feedback loops. In this paper, we analyze the impact that the addition of a positive or a negative self-feedback loop has on the oscillatory behavior of the three negative feedback oscillators proposed by Tsai et al. (Science 231:126–129, 2008) where, in contrast with numerous oscillator models, the interactions between elements occur via the modulation of the degradation rates. Through analytical and computational studies we show that an additional self-feedback affects the oscillatory behavior. In the high-cooperativity limit, i.e., for large Hill coefficients, we derive exact analytical conditions for oscillations and show that the relative location between the dissociation constants of the Hill functions and the ratio of kinetic parameters determines the possibility of oscillatory activities. We compute analytically the probability of oscillations for the three models and show that the smallest domain of periodic behavior is obtained for the negative-plus-negative feedback system whereas the additional positive self-feedback loop does not modify significantly the chance to oscillate. We numerically investigate to what extent the properties obtained in the sharp situation applied in the smooth case. Results suggest that a switch-like coupling behavior, a time-scale separation, and a repressilator-type architecture with an even number of elements facilitate the emergence of sustained oscillations in biological systems. An additional positive self-feedback loop produces robustness and adaptability whereas an additional negative self-feedback loop reduces the chance to oscillate.     

Positive Feedback Promotes Oscillations in Negative Feedback Loops

A simple three-component negative feedback loop is a recurring motif in biochemical oscillators. This motif oscillates as it has the three necessary ingredients for oscillations: a three-step delay, negative feedback, and nonlinearity in the loop. However, to oscillate, this motif under the common Goodwin formulation requires a high degree of cooperativity (a measure of nonlinearity) in the feedback that is biologically “unlikely.” Moreover, this recurring negative feedback motif is commonly observed augmented by positive feedback interactions. Here we show that these positive feedback interactions promote oscillation at lower degrees of cooperativity, and we can thus unify several common kinetic mechanisms that facilitate oscillations, such as self-activation and Michaelis-Menten degradation. The positive feedback loops are most beneficial when acting on the shortest lived component, where they function by balancing the lifetimes of the different components. The benefits of multiple positive feedback interactions are cumulative for a majority of situations considered, when benefits are measured by the reduction in the cooperativity required to oscillate. These positive feedback motifs also allow oscillations with longer periods than that determined by the lifetimes of the components alone. We can therefore conjecture that these positive feedback loops have evolved to facilitate oscillations at lower, kinetically achievable, degrees of cooperativity. Finally, we discuss the implications of our conclusions on the mammalian molecular clock, a system modeled extensively based on the three-component negative feedback loop.     

The COP9 signalosome: an alternative lid for the 26S proteasome?

Two groups have recently reported ubiquitin-deconjugating activities associated with the COP9 signalosome (CSN). Together with a previously identified deneddylation activity, CSN now appears to possess biochemical activities towards the cullin-containing ubiquitin ligases (e.g. deneddylation) and ubiquitinated protein substrates in the proteasome-mediated degradation processes (e.g. deubiquitination). Here, we discuss how these findings support a central role for CSN in ubiquitination of substrate proteins and their proteolysis     

Design principles of biochemical oscillators

Cellular rhythms are generated by complex interactions among genes, proteins and metabolites. They are used to control every aspect of cell physiology, from signalling, motility and development to growth, division and death. We consider specific examples of oscillatory processes and discuss four general requirements for biochemical oscillations: negative feedback, time delay, sufficient 'nonlinearity' of the reaction kinetics and proper balancing of the timescales of opposing chemical reactions. Positive feedback is one mechanism to delay the negative-feedback signal. Biological oscillators can be classified according to the topology of the positive- and negative-feedback loops in the underlying regulatory mechanism.     

Modelling receptor-controlled intracellular calcium oscillators.

This paper presents mathematical models for the hepatocyte calcium oscillator which follow the concepts in a class of informal models developed to account for the striking dependence on the receptor type of several features of the calcium oscillations, in particular the shape and duration of the free calcium transients. The essence of these models is that the transients should be timed by a build-up of activated GTP-binding proteins, which, combined with positive feedback processes and perhaps with cooperative effects, leads to a sudden activation of phospholipase C (PLC), followed by negative feedback processes which switch off the calcium rise and lead to a fall in free calcium back to resting levels. These models predict pulsatile oscillations in inositol (1,4,5)P3 as well as in free calcium. We show that receptor-controlled intracellular calcium oscillators involving an unknown positive feedback pathway onto PLC and negative feedback from protein kinase C (PKC) onto G-proteins and receptors, or negative feedback by stimulation of GTPase activity can simulate many of the features of observed intracellular calcium oscillations. These oscillators exhibit a dependence of frequency on agonist concentration and a dependence of transient duration on receptor and G-protein type. We also show that a PLC-dependent GTPase activating factor (GAF) could provide explanations for some otherwise puzzling features of intracellular calcium oscillations.     

Stochastic Models of Gene Expression with Delayed Degradation

In many biochemical reactions occurring in living cells, number of various molecules might be low which results in significant stochastic fluctuations. In addition, most reactions are not instantaneous, there exist natural time delays in the evolution of cell states. It is a challenge to develop a systematic and rigorous treatment of stochastic dynamics with time delays and to investigate combined effects of stochasticity and delays in concrete models.We propose a new methodology to deal with time delays in biological systems and apply it to simple models of gene expression with delayed degradation. We show that time delay of protein degradation does not cause oscillations as it was recently argued. It follows from our rigorous analysis that one should look for different mechanisms responsible for oscillations observed in biological experiments.We develop a systematic analytical treatment of stochastic models of time delays. Specifically we take into account that some reactions, for example degradation, are consuming, that is: once molecules start to degrade they cannot be part in other degradation processes.We introduce an auxiliary stochastic process and calculate analytically the variance and the autocorrelation function of the number of protein molecules in stationary states in basic models of delayed protein degradation.     

Loss of HAUSP-mediated deubiquitination contributes to DNA damage-induced destabilization of Hdmx and Hdm2

The p53 tumor suppressor protein has a major role in protecting the integrity of the genome. In unstressed cells, p53 is maintained at low levels by the ubiquitin-proteasome pathway. A balance between ubiquitin ligase activity (Hdm2, COP1, and Pirh2) and the ubiquitin protease activity of the Herpes virus-associated ubiquitin-specific protease (HAUSP) determines the half-life of p53. HAUSP also modulates p53 stability indirectly by deubiquitination and stabilization of Hdm2. The Hdmx protein affects p53 stability as well through its interaction with and regulation of Hdm2. Vice versa, Hdmx is a target for Hdm2-mediated ubiquitination and degradation. Here, we show that HAUSP also interacts with Hdmx, resulting in its direct deubiquitination and stabilization. HAUSP activity is required to maintain normal Hdmx protein levels. Therefore, the balance between HAUSP and Hdm2 activity determines Hdmx protein stability. Importantly, impaired deubiquitination of Hdmx/Hdm2 by HAUSP contributes to the DNA damage-induced degradation of Hdmx and transient instability of Hdm2.     

The role of ubiquitination and deubiquitination in the regulation of cell junctions

Maintenance of cell junctions plays a crucial role in the regulation of cellular functions including cell proliferation, permeability, and cell death. Disruption of cell junctions is implicated in a variety of human disorders, such as inflammatory diseases and cancers. Understanding molecular regulation of cell junctions is important for development of therapeutic strategies for intervention of human diseases. Ubiquitination is an important type of post-translational modification that primarily regulates endogenous protein stability, receptor internalization, enzyme activity, and protein-protein interactions. Ubiquitination is tightly regulated by ubiquitin E3 ligases and can be reversed by deubiquitinating enzymes. Recent studies have been focusing on investigating the effect of protein stability in the regulation of cell-cell junctions. Ubiquitination and degradation of cadherins, claudins, and their interacting proteins are implicated in epithelial and endothelial barrier disruption. Recent studies have revealed that ubiquitination is involved in regulation of Rho GTPases’ biological activities. Taken together these studies, ubiquitination plays a critical role in modulating cell junctions and motility. In this review, we will discuss the effects of ubiquitination and deubiquitination on protein stability and expression of key proteins in the cell-cell junctions, including junction proteins, their interacting proteins, and small Rho GTPases. We provide an overview of protein stability in modulation of epithelial and endothelial barrier integrity and introduce potential future search directions to better understand the effects of ubiquitination on human disorders caused by dysfunction of cell junctions.     

USP19 modulates autophagy and antiviral immune responses by deubiquitinating Beclin‐1

Autophagy, mediated by a number of autophagy‐related (ATG) proteins, plays an important role in the bulk degradation of cellular constituents. Beclin‐1 (also known as Atg6 in yeast) is a core protein essential for autophagic initiation and other biological processes. The activity of Beclin‐1 is tightly regulated by multiple post‐translational modifications, including ubiquitination, yet the molecular mechanism underpinning its reversible deubiquitination remains poorly defined. Here, we identified ubiquitin‐specific protease 19 (USP19) as a positive regulator of autophagy, but a negative regulator of type I interferon (IFN) signaling. USP19 stabilizes Beclin‐1 by removing the K11‐linked ubiquitin chains of Beclin‐1 at lysine 437. Moreover, we found that USP19 negatively regulates type I IFN signaling pathway, by blocking RIG‐I‐MAVS interaction in a Beclin‐1‐dependent manner. Depletion of either USP19 or Beclin‐1 inhibits autophagic flux and promotes type I IFN signaling as well as cellular antiviral immunity. Our findings reveal novel dual functions of the USP19‐Beclin‐1 axis by balancing autophagy and the production of type I IFNs.     

Deubiquitination Step in the Endocytic Pathway of Yeast Plasma Membrane Proteins: Crucial Role of Doa4p Ubiquitin Isopeptidase

The Fur4p uracil permease, like most yeast plasma membrane proteins, undergoes ubiquitin-dependent endocytosis and is then targeted to the vacuole (equivalent to the mammalian lysosome) for degradation. The cell surface ubiquitination of Fur4p is mediated by the essential Rsp5p ubiquitin ligase. Ubiquitination of Fur4p occurs on two target lysines, which receive two ubiquitin moieties linked through ubiquitin Lys63, a type of linkage (termed UbK63) different from that involved in proteasome recognition. We report that pep4 cells deficient for vacuolar protease activities accumulate vacuolar unubiquitinated Fur4p. In contrast, pep4 cells lacking the Doa4p ubiquitin isopeptidase accumulate ubiquitin-conjugated Fur4p. These data suggest that Fur4p undergoes Doa4p-dependent deubiquitination prior to vacuolar degradation. Compared to pep4 cells, pep4 doa4 cells have huge amounts of membrane-bound ubiquitin conjugates. This indicates that Doa4p plays a general role in the deubiquitination of membrane-bound proteins, as suggested by reports describing the suppression of some doa4 phenotypes in endocytosis and vacuolar protein sorting mutants. Some of the small ubiquitin-linked peptides that are a hallmark of Doa4 deficiency are not present in rsp5 mutant cells or after overproduction of a variant ubiquitin modified at Lys 63 (UbK63R). These data suggest that the corresponding peptides are degradation products of Rsp5p substrates and probably of ubiquitin conjugates carrying UbK63 linkages. Doa4p thus appears to be involved in the deubiquitination of endocytosed plasma membrane proteins, some of them carrying UbK63 linkages.     

Targeting ubiquitin specific protease 7 in cancer: A deubiquitinase with great prospects

Deubiquitinase (DUB)‐mediated cleavage of ubiquitin chain balances ubiquitination and deubiquitination for determining protein fate. USP7 is one of the best characterized DUBs and functionally important. Numerous proteins have been identified as potential substrates and binding partners of USP7; those play crucial roles in diverse array of cellular and biological processes including tumour suppression, cell cycle, DNA repair, chromatin remodelling, and epigenetic regulation. This review aims at summarizing the current knowledge of this wide association of USP7 with many cellular processes that enlightens the possibility of abnormal USP7 activity in promoting oncogenesis and the importance of identification of specific inhibitors.     

Oscillations and temporal signalling in cells

The development of new techniques to quantitatively measure gene expression in cells has shed light on a number of systems that display oscillations in protein concentration. Here we review the different mechanisms which can produce oscillations in gene expression or protein concentration using a framework of simple mathematical models. We focus on three eukaryotic genetic regulatory networks which show 'ultradian' oscillations, with a time period of the order of hours, and involve, respectively, proteins important for development (Hes1), apoptosis (p53) and immune response (NF-kappaB). We argue that underlying all three is a common design consisting of a negative feedback loop with time delay which is responsible for the oscillatory behaviour.