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.

Equilibration of the terrestrial water, nitrogen, and carbon cycles

Recent advances in biologically based ecosystem models of the coupled terrestrial, hydrological, carbon, and nutrient cycles have provided new perspectives on the terrestrial biosphere’s behavior globally, over a range of time scales. We used the terrestrial ecosystem model Century to examine relationships between carbon, nitrogen, and water dynamics. The model, run to a quasi-steady-state, shows strong correlations between carbon, water, and nitrogen fluxes that lead to equilibration of water/energy and nitrogen limitation of net primary productivity. This occurs because as the water flux increases, the potentials for carbon uptake (photosynthesis), and inputs and losses of nitrogen, all increase. As the flux of carbon increases, the amount of nitrogen that can be captured into organic matter and then recycled also increases. Because most plant-available nitrogen is derived from internal recycling, this latter process is critical to sustaining high productivity in environments where water and energy are plentiful. At steady-state, water/energy and nitrogen limitation “equilibrate,” but because the water, carbon, and nitrogen cycles have different response times, inclusion of nitrogen cycling into ecosystem models adds behavior at longer time scales than in purely biophysical models. The tight correlations among nitrogen fluxes with evapotranspiration implies that either climate change or changes to nitrogen inputs (from fertilization or air pollution) will have large and long-lived effects on both productivity and nitrogen losses through hydrological and trace gas pathways. Comprehensive analyses of the role of ecosystems in the carbon cycle must consider mechanisms that arise from the interaction of the hydrological, carbon, and nutrient cycles in ecosystems.