Mathematical Modeling of Biological Systems, Volume I pptx

[...]... reaction scheme of Ca2+ binding to the protein with activatory and inhibitory Ca2+ binding sites (Prot2 ) is presented in Fig 2.1 The binding scheme for the other protein (Prot1 ) is the same, however, the inhibitory binding reactions are lacking The inhibition type considered is noncompetitive, so the binding affinity of Ca2+ to the inhibitory site is independent of whether or not the activatory site is... generated by direct parasite action Gerisch and Geris introduce a finite -volume spatial discretisation scheme for taxisdiffusion-reaction systems with axi-symmetry In particular, the numerical simulation of a time-dependent taxis-diffusion-reaction model of fracture healing in mice using the method of lines is considered The partial differential equation problem has an axisymmetric structure, and this is employed... calculations the rapid-equilibrium approximation is used Parameter values are given in Fig 2.2 of proteins (Fig 2.2) indicate that a selective regulation of proteins 1 and 2 is possible Sole activation of protein 1 can be achieved by a signal with an amplitude corresponding to a high activation of protein 1 in a concentration range where protein 2 is already inhibited (see binding curves in Fig 2.2) As the... Ca2+ signals has been demonstrated via protein cascades or frequencies of time-limited oscillations: A bell-shaped and separate activation of two Ca2+ -binding proteins with distinct velocities of Ca2+ -binding and dissociation is possible by applying different frequencies of the calcium signal, modelled by differential equations Essential for this phenomenon is a limited number of calcium spikes [55,... with activatory and inhibitory Ca2+ binding sites (Prot2 ) For the other protein (Prot1 ) the inhibitory binding reactions are absent K 2 and K I are the reaction-associated dissociation constants interfere directly with the binding of Mg2+ to the catalytic metal binding site of EF, thereby inhibiting catalysis [32] Therefore, we calculated with two activating and two inhibiting Ca2+ ions for protein 2... an initial transient This is due to the slower dynamics of binding and dissociation in the differential equations In particular, exponential decay of protein activity in the interspike intervals causes the smoothing effect To see the effect of the dynamics, the protein activation curves obtained by both methods of calculation are compared in Fig 2.5 Especially protein 2 is more efficiently activated... oscillations, in Fig 2.4, protein activation by an increasing frequency of spiking oscillations is also plotted (thin lines) The amplitude of simple spiking oscillations was set to 0.7 µM, corresponding to the intersection point of the two binding curves in Fig 2.2 Note that the average Ca2+ level is then even higher than the Ca2+ level in the bursting signal A simultaneous activation of both proteins is... receptors This is used to calculate the rate of production of nitric oxide (NO), which is a potent vasodilator and anti-atherogenic factor It is hypothesised that the section of endothelium adjacent to a region of recirculating flow is most at risk of developing atherosclerotic plaque, due to reduced bioavailability of NO Trenado and Strauss consider magnetic nanoparticles for in vivo applications In particular,... typical for splice sites As a promising splice-site feature, the frequencies of binding motifs in the context of exonic and intronic splice-site flanks and between the alternative and reference splice sites have been investigated It is shown that both partitions of splice sites can statistically be separated, not only by their distance to the splice signal consensus, but also via frequencies of splice... kinetics than it would be activated by a fast kinetics which could be simulated by the rapid-equilibrium approximation 2.5 Discussion A mathematical model for the decoding of regular bursting Ca2+ oscillations has been proposed, based on the binding of cytosolic Ca2+ to two distinct proteins, both cooperatively binding Ca2+ at activatory sites with different binding constants and numbers of Ca2+ ions . bioavailability of NO. Trenado and Strauss consider magnetic nanoparticles for in vivo applications. In particular, in vivo applications of biocompatible magnetic nanoparticles in a carrier liquid controlled. domains to disintegrate if effector binding is inhibited. Tracqui, et al. discuss in vitro tubulogenesis of endothelial cells. The formation of new blood vessels in vivo is a multistep process in. Byrne Centre for Mathematical Medicine School of Mathematical Sciences University of Nottingham Nottingham NG7 2RD U.K. Gerda de Vries Department of Mathematical and Statistical Sciences University of Alberta Edmonton,