A stochastic model for a chemical reaction network is embedded in a one-parameter family of models with species numbers and rate constants scaled by powers of the parameter. A systematic approach is developed for determining appropriate choices of the exponents that can be applied to large complex networks. When the scaling implies subnetworks have different time-scales, the subnetworks can be approximated separately providing insight into the behavior of the full network through the analysis of these lower dimensional approximations.MSC 2000 subject classifications: 60J27, 60J80, 60F17, 92C45, 80A30

Ordinary differential equations obtained as limits of Markov processes appear in many settings. They may arise by scaling large systems, or by averaging rapidly fluctuating systems, or in systems involving multiple time-scales, by a combination of the two. Motivated by models with multiple time-scales arising in systems biology, we present a general approach to proving a central limit theorem capturing the fluctuations of the original model around the deterministic limit. The central limit theorem provides a method for deriving an appropriate diffusion (Langevin) approximation.There are many proofs for theorems like these. In particular, results of both types can be proved using the martingale central limit theorem (Theorem A.1). For example, in the first case, there is typically a sequence of functions F N such that

Fibrinogen like protein 1(Fgl1) is a secreted protein with mitogenic activity on primary hepatocytes. Fgl1 is expressed in the liver and its expression is enhanced following acute liver injury. In animals with acute liver failure, administration of recombinant Fgl1 results in decreased mortality supporting the notion that Fgl1 stimulates hepatocyte proliferation and/or protects hepatocytes from injury. However, because Fgl1 is secreted and detected in the plasma, it is possible that the role of Fgl1 extends far beyond its effect on hepatocytes. In this study, we show that Fgl1 is additionally expressed in brown adipose tissue. We find that signals elaborated following liver injury also enhance the expression of Fgl1 in brown adipose tissue suggesting that there is a cross talk between the injured liver and adipose tissues. To identify extra hepatic effects, we generated Fgl1 deficient mice. These mice exhibit a phenotype suggestive of a global metabolic defect: Fgl1 null mice are heavier than wild type mates, have abnormal plasma lipid profiles, fasting hyperglycemia with enhanced gluconeogenesis and exhibit differences in white and brown adipose tissue morphology when compared to wild types. Because Fgl1 shares structural similarity to Angiopoietin like factors 2, 3, 4 and 6 which regulate lipid metabolism and energy utilization, we postulate that Fgl1 is a member of an emerging group of proteins with key roles in metabolism and liver regeneration.

ObjectivesHepatocellular carcinoma (HCC) is a common cancer with high rate of recurrence and mortality. Diverse aetiological agents and wide heterogeneity in individual tumours impede effective and personalised treatment. Tonicity-responsive enhancer-binding protein (TonEBP) is a transcriptional cofactor for the expression of proinflammatory genes. Although inflammation is intimately associated with the pathogenesis of HCC, the role of TonEBP is unknown. We aimed to identify function of TonEBP in HCC.DesignTumours with surrounding hepatic tissues were obtained from 296 patients with HCC who received completion resection. TonEBP expression was analysed by quantitative reverse transcription–quantitative real-time PCR (RT-PCR) and immunohfistochemical analyses of tissue microarrays. Mice with TonEBP haplodeficiency, and hepatocyte-specific and myeloid-specific TonEBP deletion were used along with HCC and hepatocyte cell lines.ResultsTonEBP expression is higher in tumours than in adjacent non-tumour tissues in 92.6% of patients with HCC regardless of aetiology associated. The TonEBP expression in tumours and adjacent non-tumour tissues predicts recurrence, metastasis and death in multivariate analyses. TonEBP drives the expression of cyclo-oxygenase-2 (COX-2) by stimulating the promoter. In mouse models of HCC, three common sites of TonEBP action in response to diverse aetiological agents leading to tumourigenesis and tumour growth were found: cell injury and inflammation, induction by oxidative stress and stimulation of the COX-2 promoter.ConclusionsTonEBP is a key component of the common pathway in tumourigenesis and tumour progression of HCC in response to diverse aetiological insults. TonEBP is involved in multiple steps along the pathway, rendering it an attractive therapeutic target as well as a prognostic biomarker.