Systems biology of cellular rhythms.

Rhythms abound in biological systems, particularly at the cellular level where they originate from the feedback loops present in regulatory networks. Cellular rhythms can be investigated both by experimental and modeling approaches, and thus represent a prototypic field of research for systems biology. They have also become a major topic in synthetic biology. We review advances in the study of cellular rhythms of biochemical rather than electrical origin by considering a variety of oscillatory processes such as Ca++ oscillations, circadian rhythms, the segmentation clock, oscillations in p53 and NF-κB, synthetic oscillators, and the oscillatory dynamics of cyclin-dependent kinases driving the cell cycle. Finally we discuss the coupling between cellular rhythms and their robustness with respect to molecular noise.

Adult liver transplantation at UCL: update 2002.

The authors present the results of a single centre study of 587 liver transplants performed in 522 adults during the period 1984-2002. Results have improved significantly over time due to better pre-, peri- and post-transplant care. One, five, ten and fifteen year actuarial survivals for the whole patient group are 81.2; 69.8; 58.9 and 51.2%. The high incidence of de novo tumors (12.3%), of cardiovascular diseases (7.5%) and of end-stage renal function (3.6%) should be further incentives to tailor the immunosuppression to the individual patient and to direct the attention of the transplant physician to the long-term quality of life of the liver recipient.

[Deterministic and stochastic models for circadian rhythms]. / Modèles déterministes et stochastiques pour les rythmes circadiens.

Circadian rhythms, characterized by a period of about 24h, are generated in nearly all living organisms by the negative autoregulation of clock gene expression. Deterministic models based on this genetic regulation account for circadian oscillations in constant environmental conditions (e.g., in constant darkness) and for entrainment of these rhythms by light-dark cycles. When the number of clock mRNA and protein molecules is low, it is necessary to resort to stochastic simulations to assess the influence of molecular noise on circadian oscillations. Indeed, it is possible that the autoregulatory mechanism of gene expression might not produce stable rhythms due to fluctuations if the number of molecules involved in the clock mechanism remains too low. We have compared the deterministic and stochastic approaches for a model based on the negative autoregulation of a clock gene. We show by means of stochastic simulations that robust circadian oscillations can already occur when the maximum number of mRNA and protein molecules is of the order of a few tens or hundreds, respectively. Furthermore, the results indicate that the cooperativity characterizing the repression of the transcription process strenghtens the robustness of circadian rhythms and that entrainment by light-dark cycles stabilizes the phase of the oscillations.

Deterministic versus stochastic models for circadian rhythms.

Circadian rhythms which occur with a period close to 24 h in nearly all living organisms originate from the negative autoregulation of gene expression.Deterministic models based on genetic regulatory processes account for theoccurrence of circadian rhythms in constant environmental conditions (e.g.constant darkness), for entrainment of these rhythms by light-dark cycles, and for their phase-shifting by light pulses. At low numbers of protein and mRNA molecules, it becomes necessary to resort to stochastic simulations to assess the influence of molecular noise on circadian oscillations. We address the effect of molecular noise by considering two stochastic versions of a core model for circadian rhythms. The deterministic version of this core modelwas previously proposed for circadian oscillations of the PER protein in Drosophila and of the FRQ protein in Neurospora. In the first, non-developed version of the stochastic model, we introduce molecular noise without decomposing the deterministic mechanism into detailed reaction steps while in the second, developed version we carry out such a detailed decomposition. Numerical simulations of the two stochastic versions of the model are performed by means of the Gillespie method. We compare the predictions of the deterministic approach with those of the two stochastic models, with respect both to sustained oscillations of the limit cycle type and to the influence of the proximity of a bifurcation point beyond which the system evolves to a stable steady state. The results indicate that robust circadian oscillations can occur even when the numbers of mRNA and nuclear protein involved in the oscillatory mechanism are reduced to a few tens orhundreds, respectively. The non-developed and developed versions of the stochastic model yield largely similar results and provide good agreement with the predictions of the deterministic model for circadian rhythms.

A model for a network of phosphorylation-dephosphorylation cycles displaying the dynamics of dominoes and clocks.

We consider a model for a network of phosphorylation-dephosphorylation cycles coupled through forward and backward regulatory interactions, such that a protein phosphorylated in a given cycle activates the phosphorylation of a protein by a kinase in the next cycle as well as the dephosphorylation of a protein by a phosphatase in a preceding cycle. The network is cyclically organized in such a way that the protein phosphorylated in the last cycle activates the kinase in the first cycle. We study the dynamics of the network in the presence of both forward and backward coupling, in conditions where a threshold exists in each cycle in the amount of protein phosphorylated as a function of the ratio of kinase to phosphatase maximum rates. We show that this system can display sustained (limit-cycle) oscillations in which each cycle in the pathway is successively turned on and off, in a sequence resembling the fall of a series of dominoes. The model thus provides an example of a biochemical system displaying the dynamics of dominoes and clocks (Murray & Kirschner, 1989). It also shows that a continuum of clock waveforms exists of which the fall of dominoes represents a limit. When the cycles in the network are linked through only forward (positive) coupling, bistability is observed, while in the presence of only backward (negative) coupling, the system can display multistability or oscillations, depending on the number of cycles in the network. Inhibition or activation of any kinase or phosphatase in the network immediately stops the oscillations by bringing the system into a stable steady state; oscillations resume when the initial value of the kinase or phosphatase rate is restored. The progression of the system on the limit cycle can thus be temporarily halted as long as an inhibitor is present, much as when a domino is held in place. These results suggest that the eukaryotic cell cycle, governed by a network of phosphorylation-dephosphorylation reactions in which the negative control of cyclin-dependent kinases plays a prominent role, behaves as a limit-cycle oscillator impeded in the presence of inhibitors. We contrast the case where the sequence of domino-like transitions constitutes the clock with the case where the sequence of transitions is passively coupled to a biochemical oscillator operating as an independent clock.

Modeling the differential fitness of cyanobacterial strains whose circadian oscillators have different free-running periods: comparing the mutual inhibition and substrate depletion hypotheses.

In a recent experimental study, Ouyang et al. (1998, Proc. Natl. Acad. Sci. U.S.A.95, 8660-8664) have shown that, in direct competition, cyanobacterial strains whose circadian clocks have free-running periods (FRPs) which match the period of an imposed light/dark (LD) cycle exclude strains whose FRPs are out of resonance with the LD cycle. These differences in competitive fitness are observed despite the lack of measurable differences in monoculture growth rates between the strains. Here we show that the experimental results are consistent with a mathematical model in which cells rhythmically produce a metabolic inhibitor to which they display a sensitivity modulated by their circadian rhythm. We argue that models in which there is a circadian modulation of nutrient uptake kinetics cannot account for the results of these experiments. We discuss possible experiments to further characterize this phenomenon. The experimental protocol we propose can be used to distinguish between mutual inhibition and substrate depletion as underlying causes of the competitive advantage of circadian resonance.

Theoretical models for circadian rhythms in Neurospora and Drosophila.

We examine theoretical models proposed for the molecular mechanism of circadian rhythms in Drosophila. The models are based on the negative feedback exerted by a complex between the PER and TIM proteins on the expression of the per and tim genes. We show that a similar model can account for circadian oscillations in Neurospora, where the protein FRQ negatively regulates the expression of the frq gene. The effect of light on the circadian rhythms is included by considering that it elicits a rise in the rate of TIM degradation in Drosophila, whereas in Neurospora it enhances the rate of frq transcription. The models account for the occurrence of sustained circadian oscillations in continuous darkness in Drosophila and Neurospora. Numerical simulations further indicate that the periodic forcing of circadian oscillations by light-dark cycles can result either in the entrainment to the external periodicity or in aperiodic oscillations (i.e. chaos), depending on the magnitude of the periodic changes in the light-controlled parameter.

Alternating oscillations and chaos in a model of two coupled biochemical oscillators driving successive phases of the cell cycle.

The animal cell cycle is controlled by the periodic variation of two cyclin-dependent protein kinases, cdk1 and cdk2, which govern the entry into the M (mitosis) and S (DNA replication) phases, respectively. The ordered progression between these phases is achieved thanks to the existence of checkpoint mechanisms based on mutual inhibition of these processes. Here we study a simple theoretical model for oscillations in cdk1 and cdk2 activity, involving mutual inhibition of the two oscillators. Each minimal oscillator is described by a three-variable cascade involving a cdk, together with the associated cyclin and cyclin-degrading enzyme. The dynamics of this skeleton model of coupled oscillators is determined as a function of the strength of their mutual inhibition. The most common mode of dynamic behavior, obtained under conditions of strong mutual inhibition, is that of alternating oscillations in cdk1 and cdk2, which correspond to the physiological situation of the ordered recurrence of the M and S phases. In addition, for weaker inhibition we obtain evidence for a variety of dynamic phenomena such as complex periodic oscillations, chaos, and the coexistence between multiple periodic or chaotic attractors. We discuss the conditions of occurrence of these various modes of oscillatory behavior, as well as their possible physiological significance.

Limit cycle models for circadian rhythms based on transcriptional regulation in Drosophila and Neurospora.

We examine theoretical models for circadian oscillations based on transcriptional regulation in Drosophila and Neurospora. For Drosophila, the molecular model is based on the negative feedback exerted on the expression of the per and tim genes by the complex formed between the PER and TIM proteins. For Neurospora, similarly, the model relies on the feedback exerted on the expression of the frq gene by its protein product FRQ. In both models, sustained rhythmic variations in protein and mRNA levels occur in continuous darkness, in the form of limit cycle oscillations. The effect of light on circadian rhythms is taken into account in the models by considering that it triggers degradation of the TIM protein in Drosophila, and frq transcription in Neurospora. When incorporating the control exerted by light at the molecular level, we show that the models can account for the entrainment of circadian rhythms by light-dark cycles and for the damping of the oscillations in constant light, though such damping occurs more readily in the Drosophila model. The models account for the phase shifts induced by light pulses and allow the construction of phase response curves. These compare well with experimental results obtained in Drosophila. The model for Drosophila shows that when applied at the appropriate phase, light pulses of appropriate duration and magnitude can permanently or transiently suppress circadian rhythmicity. We investigate the effects of the magnitude of light-induced changes on oscillatory behavior. Finally, we discuss the common and distinctive features of circadian oscillations in the two organisms.

The effect of peritoneal dialysis with and without aprotinin on acute experimental pancreatitis in rats.

Acute pancreatitis was induced in 139 Wistar rats by injection of trypsin in the common bilio-pancreatic duct. Peritoneal dialysis was performed in 93 rats. In some of these rats, aprotinin (250,000 UI/L) was added to the lavage fluid. Macroscopically, we noted the amount of steatonecrosis, pulmonary congestion and pleural effusion produced. The pancreatic and pulmonary lesions were studied microscopically. The effect of peritoneal dialysis with and without aprotinin on the survival rate was evaluated. Survival curves were established for the different groups of rats i.e. the non-treated group and the two groups of dialysed rats (with and without aprotinin). Peritoneal dialysis reduces the amount of steatonecrosis and the incidence of pulmonary complications of trypsin-induced pancreatitis in rats, but does not influence the pancreatic lesions. Peritoneal dialysis significantly improves the early survival rate. Addition of aprotinin to the dialysis fluid reduces the total mortality rate.