Tumor necrosis factor (TNF)-mediated kinase cascades: Bifurcation of Nuclear Factor-κB and c-jun N-terminal kinase (JNK/SAPK) pathways at TNF receptor-associated factor 2

TNF-induced activation of the transcription factor NF-κB and the c-jun N-terminal kinase (JNK/SAPK) requires TNF receptor-associated factor 2 (TRAF2). The NF-κB-inducing kinase (NIK) associates with TRAF2 and mediates TNF activation of NF-κB. Herein we show that NIK interacts with additional members of the TRAF family and that this interaction requires the conserved “WKI” motif within the TRAF domain. We also investigated the role of NIK in JNK activation by TNF. Whereas overexpression of NIK potently induced NF-κB activation, it failed to stimulate JNK activation. A kinase-inactive mutant of NIK was a dominant negative inhibitor of NF-κB activation but did not suppress TNF- or TRAF2-induced JNK activation. Thus, TRAF2 is the bifurcation point of two kinase cascades leading to activation of NF-κB and JNK, respectively.

Stretching single-domain proteins: Phase diagram and kinetics of force-induced unfolding

Single-molecule force spectroscopy reveals unfolding of domains in titin on stretching. We provide a theoretical framework for these experiments by computing the phase diagrams for force-induced unfolding of single-domain proteins using lattice models. The results show that two-state folders (at zero force) unravel cooperatively, whereas stretching of non-two-state folders occurs through intermediates. The stretching rates of individual molecules show great variations reflecting the heterogeneity of force-induced unfolding pathways. The approach to the stretched state occurs in a stepwise “quantized” manner. Unfolding dynamics and forces required to stretch proteins depend sensitively on topology. The unfolding rates increase exponentially with force f till an optimum value, which is determined by the barrier to unfolding when f = 0. A mapping of these results to proteins shows qualitative agreement with force-induced unfolding of Ig-like domains in titin. We show that single-molecule force spectroscopy can be used to map the folding free energy landscape of proteins in the absence of denaturants.

“Coarse” stability and bifurcation analysis using time-steppers: A reaction-diffusion example

Evolutionary, pattern forming partial differential equations (PDEs) are often derived as limiting descriptions of microscopic, kinetic theory-based models of molecular processes (e.g., reaction and diffusion). The PDE dynamic behavior can be probed through direct simulation (time integration) or, more systematically, through stability/bifurcation calculations; time-stepper-based approaches, like the Recursive Projection Method [Shroff, G. M. & Keller, H. B. (1993) SIAM J. Numer. Anal. 30, 1099–1120] provide an attractive framework for the latter. We demonstrate an adaptation of this approach that allows for a direct, effective (“coarse”) bifurcation analysis of microscopic, kinetic-based models; this is illustrated through a comparative study of the FitzHugh-Nagumo PDE and of a corresponding Lattice–Boltzmann model.