Transition-state structure as a unifying basis in protein-folding mechanisms: Contact order, chain topology, stability, and the extended nucleus mechanism

I attempt to reconcile apparently conflicting factors and mechanisms that have been proposed to determine the rate constant for two-state folding of small proteins, on the basis of general features of the structures of transition states. Φ-Value analysis implies a transition state for folding that resembles an expanded and distorted native structure, which is built around an extended nucleus. The nucleus is composed predominantly of elements of partly or well-formed native secondary structure that are stabilized by local and long-range tertiary interactions. These long-range interactions give rise to connecting loops, frequently containing the native loops that are poorly structured. I derive an equation that relates differences in the contact order of a protein to changes in the length of linking loops, which, in turn, is directly related to the unfavorable free energy of the loops in the transition state. Kinetic data on loop extension mutants of CI2 and α-spectrin SH3 domain fit the equation qualitatively. The rate of folding depends primarily on the interactions that directly stabilize the nucleus, especially those in native-like secondary structure and those resulting from the entropy loss from the connecting loops, which vary with contact order. This partitioning of energy accounts for the success of some algorithms that predict folding rates, because they use these principles either explicitly or implicitly. The extended nucleus model thus unifies the observations of rate depending on both stability and topology.

Characterization of residual structure in the thermally denatured state of barnase by simulation and experiment: Description of the folding pathway

Residual structure in the denatured state of a protein may contain clues about the early events in folding. We have simulated by molecular dynamics the denatured state of barnase, which has been studied by NMR spectroscopy. An ensemble of 104 structures was generated after 2 ns of unfolding and following for a further 2 ns. The ensemble was heterogeneous, but there was nonrandom, residual structure with persistent interactions. Helical structure in the C-terminal portion of helix α1 (residues 13–17) and in helix α2 as well as a turn and nonnative hydrophobic clustering between β3 and β4 were observed, consistent with NMR data. In addition, there were tertiary contacts between residues in α1 and the C-terminal portion of the β-sheet. The simulated structures allow the rudimentary NMR data to be fleshed out. The consistency between simulation and experiment inspires confidence in the methods. A description of the folding pathway of barnase from the denatured to the native state can be constructed by combining the simulation with experimental data from φ value analysis and NMR.

Submillisecond events in protein folding.

The pathway of protein folding is now being analyzed at the resolution of individual residues by kinetic measurements on suitably engineered mutants. The kinetic methods generally employed for studying folding are typically limited to the time range of > or = 1 ms because the folding of denatured proteins is usually initiated by mixing them with buffers that favor folding, and the dead time of rapid mixing experiments is about a millisecond. We now show that the study of protein folding may be extended to the microsecond time region by using temperature-jump measurements on the cold-unfolded state of a suitable protein. We are able to detect early events in the folding of mutants of barstar, the polypeptide inhibitor of barnase. A preliminary characterization of the fast phase from spectroscopic and phi-value analysis indicates that it is a transition between two relatively solvent-exposed states with little consolidation of structure.

An economic analysis of unilateral refusals to license intellectual property

The intellectual property laws in the United States provide the owners of intellectual property with discretion to license the right to use that property or to make or sell products that embody the intellectual property. However, the antitrust laws constrain the use of property, including intellectual property, by a firm with market power and may place limitations on the licensing of intellectual property. This paper focuses on one aspect of antitrust law, the so-called “essential facilities doctrine,” which may impose a duty upon firms controlling an “essential facility” to make that facility available to their rivals. In the intellectual property context, an obligation to make property available is equivalent to a requirement for compulsory licensing. Compulsory licensing may embrace the requirement that the owner of software permit access to the underlying code so that others can develop compatible application programs. Compulsory licensing may undermine incentives for research and development by reducing the value of an innovation to the inventor. This paper shows that compulsory licensing also may reduce economic efficiency in the short run by facilitating the entry of inefficient producers and by promoting licensing arrangements that result in higher prices.