Solid-state synthesis and mechanical unfolding of polymers of T4 lysozyme

Recent advances in single molecule manipulation methods offer a novel approach to investigating the protein folding problem. These studies usually are done on molecules that are naturally organized as linear arrays of globular domains. To extend these techniques to study proteins that normally exist as monomers, we have developed a method of synthesizing polymers of protein molecules in the solid state. By introducing cysteines at locations where bacteriophage T4 lysozyme molecules contact each other in a crystal and taking advantage of the alignment provided by the lattice, we have obtained polymers of defined polarity up to 25 molecules long that retain enzymatic activity. These polymers then were manipulated mechanically by using a modified scanning force microscope to characterize the force-induced reversible unfolding of the individual lysozyme molecules. This approach should be general and adaptable to many other proteins with known crystal structures. For T4 lysozyme, the force required to unfold the monomers was 64 ± 16 pN at the pulling speed used. Refolding occurred within 1 sec of relaxation with an efficiency close to 100%. Analysis of the force versus extension curves suggests that the mechanical unfolding transition follows a two-state model. The unfolding forces determined in 1 M guanidine hydrochloride indicate that in these conditions the activation barrier for unfolding is reduced by 2 kcal/mol.

Flows of knowledge from universities and federal laboratories: Modeling the flow of patent citations over time and across institutional and geographic boundaries

The extent to which new technological knowledge flows across institutional and national boundaries is a question of great importance for public policy and the modeling of economic growth. In this paper we develop a model of the process generating subsequent citations to patents as a lens for viewing knowledge diffusion. We find that the probability of patent citation over time after a patent is granted fits well to a double-exponential function that can be interpreted as the mixture of diffusion and obsolescense functions. The results indicate that diffusion is geographically localized. Controlling for other factors, within-country citations are more numerous and come more quickly than those that cross country boundaries.