A mathematical view of biological complexity

This essay is a trial on giving some mathematical ideas about the concept of biological complexity, trying to explore four different attributes considered to be essential to characterize a complex system in a biological context: decomposition, heterogeneous assembly, self-organization, and adequacy. It is a theoretical and speculative approach, opening some possibilities to further numerical and experimental work, illustrated by references to several researches that applied the concepts presented here. (C) 2008 Elsevier B.V. All rights reserved.

Impact of cholesterol on ABC and SLC transporters expression and function and its role in disposition variability to lipid-lowering drugs

This report focuses on the effects of cholesterol on the expression and function of the ATP-binding cassette (ABCB1, ABCG2 and ABCC2) and solute-linked carrier (SLCO1B1 and SLCO2B1) drug transporters with a particular focus on the potential impact of cholesterol on lipid-lowering drug disposition. Statins are the most active agents in the treatment of hypercholesterolemia. However, considerable interindividual variation exists in the response to statin therapy. Therefore, it would be huge progress if factors were identified that reliably differentiate between responders and nonresponders. Many studies have suggested that plasma lipid concentrations can affect drug disposition of compounds, such as ciclosporin and amphotericin B. Both compounds are able to affect the expression and function of ABC transporters. Although still speculative, these effects might be owing to the regulation of drug transporters by plasma cholesterol levels. Studies with normo- and hyper-cholesterolemic individuals, before and after atorvastatin treatment, have demonstrated that plasma cholesterol levels are correlated with drug transporter expression, as well as being related to atorvastatin`s cholesterol-lowering effect. The mechanism influencing the correlation between cholesterol levels and the expression and function of drug transporters remains unclear. Some studies provide strong evidence that nuclear receptors, such as the pregnane X receptor and the constitutive androstane receptor, mediate this effect. In the near future, pharmacogenomic studies with individuals in a pathological state should be performed in order to identify whether high plasma cholesterol levels might be a factor contributing to interindividual oral drug bioavailability.

STABILITY ANALYSIS WITH APPLICATIONS OF A TWO-DIMENSIONAL DYNAMICAL SYSTEM ARISING FROM A STOCHASTIC MODEL FOR AN ASSET MARKET

We analyze the stability properties of equilibrium solutions and periodicity of orbits in a two-dimensional dynamical system whose orbits mimic the evolution of the price of an asset and the excess demand for that asset. The construction of the system is grounded upon a heterogeneous interacting agent model for a single risky asset market. An advantage of this construction procedure is that the resulting dynamical system becomes a macroscopic market model which mirrors the market quantities and qualities that would typically be taken into account solely at the microscopic level of modeling. The system`s parameters correspond to: (a) the proportion of speculators in a market; (b) the traders` speculative trend; (c) the degree of heterogeneity of idiosyncratic evaluations of the market agents with respect to the asset`s fundamental value; and (d) the strength of the feedback of the population excess demand on the asset price update increment. This correspondence allows us to employ our results in order to infer plausible causes for the emergence of price and demand fluctuations in a real asset market. The employment of dynamical systems for studying evolution of stochastic models of socio-economic phenomena is quite usual in the area of heterogeneous interacting agent models. However, in the vast majority of the cases present in the literature, these dynamical systems are one-dimensional. Our work is among the few in the area that construct and study analytically a two-dimensional dynamical system and apply it for explanation of socio-economic phenomena.