Hypoxia-inducible factor (HIF) network:insights from mathematical models

Oxygen is a crucial molecule for cellular function. When oxygen demand exceeds supply, the oxygen sensing pathway centred on the hypoxia inducible factor (HIF) is switched on and promotes adaptation to hypoxia by up-regulating genes involved in angiogenesis, erythropoiesis and glycolysis. The regulation of HIF is tightly modulated through intricate regulatory mechanisms. Notably, its protein stability is controlled by the oxygen sensing prolyl hydroxylase domain (PHD) enzymes and its transcriptional activity is controlled by the asparaginyl hydroxylase FIH (factor inhibiting HIF-1).To probe the complexity of hypoxia-induced HIF signalling, efforts in mathematical modelling of the pathway have been underway for around a decade. In this paper, we review the existing mathematical models developed to describe and explain specific behaviours of the HIF pathway and how they have contributed new insights into our understanding of the network. Topics for modelling included the switch-like response to decreased oxygen gradient, the role of micro environmental factors, the regulation by FIH and the temporal dynamics of the HIF response. We will also discuss the technical aspects, extent and limitations of these models. Recently, HIF pathway has been implicated in other disease contexts such as hypoxic inflammation and cancer through crosstalking with pathways like NF?B and mTOR. We will examine how future mathematical modelling and simulation of interlinked networks can aid in understanding HIF behaviour in complex pathophysiological situations. Ultimately this would allow the identification of new pharmacological targets in different disease settings.

Dynamic models of exchange rate dependence using option prices and historical returns

Models for the conditional joint distribution of the U.S. Dollar/Japanese Yen and Euro/Japanese Yen exchange rates, from November 2001 until June 2007, are evaluated and compared. The conditional dependency is allowed to vary across time, as a function of either historical returns or a combination of past return data and option-implied dependence estimates. Using prices of currency options that are available in the public domain, risk-neutral dependency expectations are extracted through a copula repre- sentation of the bivariate risk-neutral density. For this purpose, we employ either the one-parameter \Normal" or a two-parameter \Gumbel Mixture" specification. The latter provides forward-looking information regarding the overall degree of covariation, as well as, the level and direction of asymmetric dependence. Specifications that include option-based measures in their information set are found to outperform, in-sample and out-of-sample, models that rely solely on historical returns.