Mathematical modeling of intracellular signaling pathways

Dynamic modeling and simulation of signal transduction pathways is an important topic in systems biology and is obtaining growing attention from researchers with experimental or theoretical background. Here we review attempts to analyze and model specific signaling systems. We review the structure of recurrent building blocks of signaling pathways and their integration into more comprehensive models, which enables the understanding of complex cellular processes. The variety of mechanisms found and modeling techniques used are illustrated with models of different signaling pathways. Focusing on the close interplay between experimental investigation of pathways and the mathematical representations of cellular dynamics, we discuss challenges and perspectives that emerge in studies of signaling systems

Structural and magnetic investigations on Ni2MnAl

Ferromagnetic alloys undergoing thermoelastic martensitic transformations have recently become very attractive owing to the possibility of inducing giant deformations by rotating martensitic domains with an externally applied magnetic field. It is expected that ferromagnetic alloys with the Heusler stucture may exhibit a strong magnetoelastic coupling resulting in potentially interesting magneto-mechanical properties. In this paper we present preliminary results on structural and magnetic studies on Ni2MnAl. It is shown that in this material the magnetic properties strongly depend on the heat treatment, chiefly because of the difficulty in achieving a complete L21 order

Precursor phenomena in a quenched and aged Ni52_{52}Ti48_{48} shape memory alloy

We measured the electrical resistivity R(T) and specific heat C$_{\rm p}$(T) between room temperature (RT) and 4.2 K as well as the microstructure by transmission electron microscopy (TEM) of a Ni$_{52}$Ti$_{48}$ SMA quenched from 1000°C (B2-Phase range) to RT and then annealed for 1h at $\rm T=380^\circ$C, 550°C and 650°C. In the “as quenched” and the “650°C annealed” state no martensitic transformations (MT's) occur. The diffraction pattems show faint reflections originating from coherent Ni$_4$Ti$_3$, precipitates in an early state of formation. Additional reflections of the type 1/2 $$, 1/2$$ and 1/3 $$result from various lattice displacement waves, which are precursors of the MT's to the B19' and R-phase, respectively. Indeed, high resolution TEM micrographs of the [001] zone of the “as quenched” sample reveal transverse 1/2$$ $$ lattice displacement waves, precursors of the B19' martensite. The coherent Ni$_4$Ti$_3$ precipitates, homogeneously distributed on a small length scale, hinder the MT's in the “as quenched” and the “650°C annealed” state, and thus only the precursors appear. When annealed at $\rm T=380^\circ$C, however, coherent Ni$_4$Ti$_3$ precipitates with a length of 10 nm are clearly visible in TEM. These precipitates trigger the MT from the B2 to the R-phase on cooling, as evidenced also by anomalies in R(T) and C$_{\rm p}$(T). Annealing at $\rm T= 550^\circ$C leads to the well known two step MT's from the B2 to the R-phase and then into the B19'-phase. These martensitic transitions are clearly seen as additional peaks in the specific heat and anomalies in the resistance, while the “as quenched” and 650°C annealed samples show weak features in R(T) and C$_{\rm p}$(T)

Microstructure of quenched Ni-rich Ni-Ti shape memory alloys

Microstructural investigations with transmission electron microscopy were carried out on quenched Ni-Ti alloys with 52 and 54.5 at% Ni. For the Ni52Ti48 specimen long time exposed diffraction patterns of a single grain show besides the expected reflections of the B2-phase, two sets of extra reflections in different zones. The first type of spots is explained by lattice displacement waves, which are regarded as precursors of the martensitic Ni-Ti phases, B19' and R-phase, respectively. The second set of reflection with more diffuse intensity than the other reflections is related to Ni4Ti3 precipitates in an early state of formation. For the Ni-richer Ni54.5Ti45.5 alloy only Ni4Ti3 precipitates in an early state of formation are found but no precursors of the B19' - and R-phase

In-situ TEM cooling/heating experiments on deformed NiTi shape memory single crystals

In the present study we report about the influence of dislocations on martensitic transformations in NiTi single crystals. Microstructural investigations are performed on Ni50.4Ti49.6 (at.%) single crystals using in-situ cooling and heating transmission electron microscopy (TEM). Solution heat-treated Ni50.4Ti49.6 single crystals were oriented by electron backscatter diffraction (EBSD) and compressed in [111] B2-direction to different strain levels. DSC measurements on undeformed and deformed material states reveal a two step transformation from B2 to R-phase and then from R-phase to B19´ confirmed by TEM. The analysis of the dislocation structure of a 3.3% compressed single crystal shows that mainly screw dislocations with [001] type burgers vectors are present. During cooling, the martensitic R-phase grows homogeneously. On further cooling in some regions a burst like growth of B19'-neddles can be observed in addition to B19'-regions that nucleate and grow promoted by the stress-fields of dislocations. Dislocation analysis after back transformation suggests that dislocations form as a result of the martensitic transformation

3D FIB/SEM study of Ni4Ti3 precipitates in Ni-Ti alloys with different thermal-mechanical histories

The three-dimensional size, morphology and distribution of Ni4Ti3 precipitates growing in binary Ni-rich Ni-Ti alloys have been investigated via a slice & view procedure in a Dual-Beam FIB/SEM system, in order to better understand their influence on the B2 to B19’ martensitic transformation. In the present work, both a stress-free Ni50.8Ti49.2 alloy with all four variants of precipitates and a compressed Ni51Ti49 alloy with aligned precipitates in one family were studied. The Ni4Ti3 precipitates reach a volume fraction of 9.6% in the reconstructed region of the stressfree alloy and 4.3% in the compressed one. In both cases, the mean volume, specific surface area, sphericity and aspect ratio of the precipitates are calculated and the Pair Distribution Functions of the precipitates are obtained. It is shown that most precipitates in the stress-free sample grow larger and have a more lenticular shape, while those in the compressed sample are more cylindrical. Deviations from these ideal shapes reveal internal steps in the stress-free sample and lamellae formation in the compressed one