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The Anthropocene is characterized by the strengthening of planetary-scale interactions between the biophysical Earth system (ES) and human societies. This increasing social-ecological entanglement poses new challenges for studying possible future World-Earth system (WES) trajectories and World-Earth resilience defined as the capacity of the system to absorb and regenerate from anthropogenic stresses such as greenhouse gas emissions and land-use changes. The WES is currently in a non-equilibrium transitional regime of the early Anthropocene with arguably no plausible possibilities of remaining in Holocene-like conditions while sheltering up to 10 billion humans without risk of undermining the resilience of the ES. We develop a framework within which to conceptualize World-Earth resilience to examine this risk. Because conventional ball-and-cup type notions of resilience are hampered by the rapid and open-ended social, cultural, economic and technological evolution of human societies, we focus on the notion of ‘pathway resilience’, i.e. the relative number of paths that allow the WES to move from the currently occupied transitional states towards a safe and just operating space in the Anthropocene. We formalize this conceptualization mathematically and provide a foundation to explore how interactions between ES resilience (biophysical processes) and World system (WS) resilience (social processes) impact pathway resilience. Our analysis shows the critical importance of building ES resilience to reach a safe and just operating space. We also illustrate the importance of WS dynamics by showing how perceptions of fairness coupled with regional inequality affects pathway resilience. The framework provides a starting point for the analysis of World-Earth resilience that can be extended to more complex model settings as well as the development of quantitative planetary-scale resilience indicators to guide sustainable development in a stabilized ES.

Quantitative description of how proteins fold under experimental conditions remains a challenging problem. Experiments often use urea and guanidinium chloride to study folding whereas the natural variable in simulations is temperature. To bridge the gap, we use the molecular transfer model that combines measured denaturant-dependent transfer free energies for the peptide group and amino acid residues, and a coarse-grained Cα-side chain model for polypeptide chains to simulate the folding of src SH3 domain. Stability of the native state decreases linearly as [C] (the concentration of guanidinium chloride) increases with the slope, m, that is in excellent agreement with experiments. Remarkably, the calculated folding rate at [C] = 0 is only 16-fold larger than the measured value. Most importantly ln kobs (kobs is the sum of folding and unfolding rates) as a function of [C] has the characteristic V (chevron) shape. In every folding trajectory, the times for reaching the native state, interactions stabilizing all the substructures, and global collapse coincide. The value of mf/m (mf is the slope of the folding arm of the chevron plot) is identical to the fraction of buried solvent accessible surface area in the structures of the transition state ensemble. In the dominant transition state, which does not vary significantly at low [C], the core of the protein and certain loops are structured. Besides solving the long-standing problem of computing the chevron plot, our work lays the foundation for incorporating denaturant effects in a physically transparent manner either in all-atom or coarse-grained simulations. [ABSTRACT FROM AUTHOR]