Targeted reduction of complex models with time scale hierarchy--a case study

Systems analysis of the role of bone morphogenic protein 4 in endothelial inflammation

Shear stress is an important factor in the onset and progression of atherosclerosis. High and unidirectional laminar stress is seen as protective, while low and oscillatory shear stress is considered pro-inflammatory and pro-atherogenic. The mechanosensitive response of endothelial cells is governed by a complex system of genes, proteins, and signals that operate at distinctly different time scales. We propose a dynamic mathematical model that quantitatively describes this mechanosensing system and permits novel insights into its functioning. The model, the first of its kind, is constructed within the guidelines of Biochemical Systems Theory and accounts for different time scales by means of approximated delays. Parameter values are obtained directly from biochemical observations in an ad hoc fashion. The model reflects most documented observations well and leads to a number of predictions and novel hypotheses. In particular, it demonstrates the crucial role of Bone Morphogenic Protein 4 and p47(phox)-dependent NADPH oxidases in endothelial inflammation.

What are melanocytes really doing all day long...?

Everyone knows and seems to agree that melanocytes are there to generate melanin - an intriguing, but underestimated multipurpose molecule that is capable of doing far more than providing pigment and UV protection to skin (1). What about the cell that generates melanin, then? Is this dendritic, neural crest-derived cell still serving useful (or even important) functions when no-one looks at the pigmentation of our skin and its appendages and when there is essentially no UV exposure? In other words, what do epidermal and hair follicle melanocytes do in their spare time - at night, under your bedcover? How much of the full portfolio of physiological melanocyte functions in mammalian skin has really been elucidated already? Does the presence or absence of melanocytes matter for normal epidermal and/or hair follicle functions (beyond pigmentation and UV protection), and for skin immune responses? Do melanocytes even deserve as much credit for UV protection as conventional wisdom attributes to them? In which interactions do these promiscuous cells engage with their immediate epithelial environment and who is controlling whom? What lessons might be distilled from looking at lower vertebrate melanophores and at extracutaneous melanocytes in the endeavour to reveal the 'secret identity' of melanocytes? The current Controversies feature explores these far too infrequently posed, biologically and clinically important questions. Complementing a companion viewpoint essay on malignant melanocytes (2), this critical re-examination of melanocyte biology provides a cornucopia of old, but under-appreciated concepts and novel ideas on the slowly emerging complexity of physiological melanocyte functions, and delineates important, thought-provoking questions that remain to be definitively answered by future research.

Approximation of delays in biochemical systems

In the past metabolic pathway analyses have mostly ignored the effects of time delays that may be due to processes that are slower than biochemical reactions, such as transcription, translation, translocation, and transport. We show within the framework of biochemical systems theory (BST) that delay processes can be approximated accurately by augmenting the original variables and non-linear differential equations with auxiliary variables that are defined through a system of linear ordinary differential equations. These equations are naturally embedded in the structure of S-systems and generalized mass action systems within BST and can be interpreted as linear signaling pathways or cascades. We demonstrate the approximation method with the simplest generic modules, namely single delayed steps with and without feedback inhibition. These steps are representative though, because they are easily incorporated into larger systems. We show that the dynamics of the approximated systems reflects that of the original delay systems well, as long as the systems do not operate in very close vicinity of threshold values where the systems lose stability. The accuracy of approximation furthermore depends on the selected number of auxiliary variables. In the most relevant situations where the systems operate at states away from their critical thresholds, even a few auxiliary variables lead to satisfactory approximations.