The thermodynamics and statistical mechanics of protein folding

The physics of self-organization and complexity is manifested on a variety of biological scales, from large ecosystems to the molecular level. Protein molecules exhibit characteristics of complex systems in terms of their structure, dynamics, and function. Proteins have the extraordinary ability to fold to a specific functional three-dimensional shape, starting from a random coil, in a biologically relevant time. How they accomplish this is one of the secrets of life. In this work, theoretical research into understanding this remarkable behavior is discussed. Thermodynamic and statistical mechanical tools are used in order to investigate the protein folding dynamics and stability. Theoretical analyses of the results from computer simulation of the dynamics of a four-helix bundle show that the excluded volume entropic effects are very important in protein dynamics and crucial for protein stability. The dramatic effects of changing the size of sidechains imply that a strategic placement of amino acid residues with a particular size may be an important consideration in protein engineering. Another investigation deals with modeling protein structural transitions as a phase transition. Using finite size scaling theory, the nature of unfolding transition of a four-helix bundle protein was investigated and critical exponents for the transition were calculated for various hydrophobic strengths in the core. It is found that the order of the transition changes from first to higher order as the strength of the hydrophobic interaction in the core region is significantly increased. Finally, a detailed kinetic and thermodynamic analysis was carried out in a model two-helix bundle. The connection between the structural free-energy landscape and folding kinetics was quantified. I show how simple protein engineering, by changing the hydropathy of a small number of amino acids, can enhance protein folding by significantly changing the free energy landscape so that kinetic traps are removed. The results have general applicability in protein engineering as well as understanding the underlying physical mechanisms of protein folding. ^

Regional processes in mangrove ecosystems: spatial scaling relationships, biomass, and turnover rates following catastrophic disturbance

Physiological processes and local-scale structural dynamics of mangroves are relatively well studied. Regional-scale processes, however, are not as well understood. Here we provide long-term data on trends in structure and forest turnover at a large scale, following hurricane damage in mangrove ecosystems of South Florida, U.S.A. Twelve mangrove vegetation plots were monitored at periodic intervals, between October 1992 and March 2005. Mangrove forests of this region are defined by a −1.5 scaling relationship between mean stem diameter and stem density, mirroring self-thinning theory for mono-specific stands. This relationship is reflected in tree size frequency scaling exponents which, through time, have exhibited trends toward a community average that is indicative of full spatial resource utilization. These trends, together with an asymptotic standing biomass accumulation, indicate that coastal mangrove ecosystems do adhere to size-structured organizing principles as described for upland tree communities. Regenerative dynamics are different between areas inside and outside of the primary wind-path of Hurricane Andrew which occurred in 1992. Forest dynamic turnover rates, however, are steady through time. This suggests that ecological, more-so than structural factors, control forest productivity. In agreement, the relative mean rate of biomass growth exhibits an inverse relationship with the seasonal range of porewater salinities. The ecosystem average in forest scaling relationships may provide a useful investigative tool of mangrove community biomass relationships, as well as offer a robust indicator of general ecosystem health for use in mangrove forest ecosystem management and restoration.

Does the Pareto Distribution of Hurricane Damage Inherit its Fat Tail from a Zipf Distribution of Assets at Hazard?

Tropical Cyclones are a continuing threat to life and property. Willoughby (2012) found that a Pareto (power-law) cumulative distribution fitted to the most damaging 10% of US hurricane seasons fit their impacts well. Here, we find that damage follows a Pareto distribution because the assets at hazard follow a Zipf distribution, which can be thought of as a Pareto distribution with exponent 1. The Z-CAT model is an idealized hurricane catastrophe model that represents a coastline where populated places with Zipf- distributed assets are randomly scattered and damaged by virtual hurricanes with sizes and intensities generated through a Monte-Carlo process. Results produce realistic Pareto exponents. The ability of the Z-CAT model to simulate different climate scenarios allowed testing of sensitivities to Maximum Potential Intensity, landfall rates and building structure vulnerability. The Z-CAT model results demonstrate that a statistical significant difference in damage is found when only changes in the parameters create a doubling of damage.