M.W.J.M. Musters

Mathematical modeling confirms the length-dependency of telomere shortening

Telomeres, the ends of chromosomes, shorten with each cell division in human somatic cells, because of the end-replication problem, C-strand processing and oxidative damage. On the other hand, the reverse transcriptase telomerase can add back telomeric repeats at the telomere ends. It has been suggested that once telomeres have reached a critical length, cells cease proliferation, also known as senescence. Evidence is accumulating that telomere shortening and subsequent senescence might play a crucial role in life-threatening diseases. So far, mathematical models described telomere shortening as an autonomous process, where the loss per cell division does not depend on the telomere length itself. In this study, published measurements of telomere distributions in human fibroblasts and human endothelial cells were used to show that telomeres shorten in a length-dependent fashion. Thereafter, a mathematical model of telomere attrition was composed, in which a shortening factor and an autonomous loss were incorporated. It was assumed that the percentage of senescence was related to the percentage of telomeres below a critical length. The model was compared with published data of telomere length and senescence of human endothelial cells using the maximum likelihood method. This enabled the estimation of physiologically important parameters and confirmed the length-dependency of telomere shortening.

Qualitative analysis of nonlinear biochemical networks with piecewise-affine functions

Nonlinearities and the lack of accurate quantitative information considerably hamper modeling and system analysis of biochemical networks. Here we propose a procedure for qualitative mathematical analysis of piecewise-affine (PWA) approximations of these networks. First the biochemical model size was reduced with quasi-steady state approaches by taking a priori information into account. Second, a conversion of a nonlinear model into a PWA approximation and subsequent qualitative analysis of this model was performed. This resulted in different sets of transition graphs that depend on the parameter values, which enables reduction of the parameter search space.

Analysis of the transforming growth factor-/spl beta//sub 1/ pathway and extracellular matrix formation as a hybrid system

It is generally accepted that aging of the vascular system plays an important role in cardiovascular disease (CVD). Recent experimental findings have indicated the involvement of the cytokine transforming growth factor-/spl beta//sub 1/ (TGF-/spl beta//sub 1/) in these vascular aging processes. This cytokine is, after binding to a cell receptor, associated with numerous cellular processes, including formation of the extracellular matrix (ECM, the biomolecular network that surrounds the cell). We implemented TGF-/spl beta//sub 1/ signaling and its effect on ECM formation with piecewise-linear differential equations (PLDEs), which have several advantageous properties over traditional continuous modeling. Aging of the system was simulated as a reduction in cell sensitivity for TGF-/spl beta//sub 1/. The model predicted a disturbed ECM balance during aging, which corresponds well to findings from the literature. The outcome of this hybrid approach was satisfactory and, therefore, we will continue modeling of various aging-related pathways with PLDEs in future research.