Theoretical Perspectives on Protein Folding

Understanding how monomeric proteins fold under in vitro conditions is crucial to describing their functions in the cellular context. Significant advances both in theory and experiments have resulted in a conceptual framework for describing the folding mechanisms of globular proteins. The experimental data and theoretical methods have revealed the multifaceted character of proteins. Proteins exhibit universal features that can be determined using only the number of amino acid residues (N) and polymer concepts. The sizes of proteins in the denatured and folded states, cooperativity of the folding transition, dispersions in the melting temperatures at the residue level, and time scales of folding are to a large extent determined by N. The consequences of finite N especially on how individual residues order upon folding depends on the topology of the folded states. Such intricate details can be predicted using the Molecular Transfer Model that combines simulations with measured transfer free energies of protein building blocks from water to the desired concentration of the denaturant. By watching one molecule fold at a time, using single molecule methods, the validity of the theoretically anticipated heterogeneity in the folding routes, and the N-dependent time scales for the three stages in the approach to the native state have been established. Despite the successes of theory, of which only a few examples are documented here, we conclude that much remains to be done to solve the "protein folding problem" in the broadest sense.Comment: 48 pages, 9 figure

Nonlinear Supply Contracts, Foreclosure, and Exclusive Dealing

We examine the incentives for market foreclosure when two upstream firms contract with a retail monopolist. We find that if nonlinear supply contracts are feasible, an exclusive dealing arrangement offers an upstream firm no advantage it would not have had without the arrangement. If a fully integratred (horizontally and vertically) firm would sell only one product, an upstream firm can foreclose its rival with a nonlinear supply contract and achieve the same profit it would receive if it required exclusive dealing. If a fully integrated firm would sell both products, the feasibility of nonlinear supply contracts renders it unprofitable to foreclose, with or without exclusive dealing.Center for Research on Economic and Social Theory, Department of Economics, University of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/100893/1/ECON344.pd

The Welfare Effects of Forbidding Discriminatory Discounts: A Ssecondary Line Analysis of Robinson-Patman

We examine the welfare effects of forbidding price discrimination in intermediate goods markets when firms can bargain over terms of their nonlinear supply contracts. In particular, our focus is on secondary line injury to competition under three interpretations of what it means to forbid price discrimination. We find that in each case, forbidding discriminatory discounts renders retailer bargaining power useless in mitigating manufacturer market power. As a result, all retailers end up paying higher input prices, and all retail prices rise. We show by example that the welfare loss can be substantial.Center for Research on Economic and Social Theory, Department of Economics, University of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/100958/1/ECON402.pd

Non-linear Contracts, Foreclosure, and Executive Dealing

This paper examines the nature of upstream rivalry in non-linear supply contracts with and without exclusive dealing. We find that foreclosure can occur without exclusive dealing, if economies of scale are sufficiently large, as well as with exclusive dealing. Surprisingly, however, it is the retailer and not the upstream firms who benefit. This formalizes the view that exclusive dealing will not be initiated by supplier because retailer compensation is too steep. It also implies that anticompetitive foreclosure is more likely to occur when downstream firms have bargaining power.Center for Research on Economic and Social Theory, Department of Economics, University of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/100895/1/ECON346.pd

Hydrodynamic mean field solutions of 1D exclusion processes with spatially varying hopping rates

We analyze the open boundary partially asymmetric exclusion process with smoothly varying internal hopping rates in the infinite-size, mean field limit. The mean field equations for particle densities are written in terms of Ricatti equations with the steady-state current $J$ as a parameter. These equations are solved both analytically and numerically. Upon imposing the boundary conditions set by the injection and extraction rates, the currents $J$ are found self-consistently. We find a number of cases where analytic solutions can be found exactly or approximated. Results for $J$ from asymptotic analyses for slowly varying hopping rates agree extremely well with those from extensive Monte Carlo simulations, suggesting that mean field currents asymptotically approach the exact currents in the hydrodynamic limit, as the hopping rates vary slowly over the lattice. If the forward hopping rate is greater than or less than the backward hopping rate throughout the entire chain, the three standard steady-state phases are preserved. Our analysis reveals the sensitivity of the current to the relative phase between the forward and backward hopping rate functions.Comment: 12 pages, 4 figure

Chickasaws: The Unconquerable People

The Chickasaw Indians were Mississippi’s second largest Indian group after the Choctaws. Before the United States government forced their removal in the 1830s, the Chickasaw resided in north Mississippi with their villages centered between the headwaters of the Yazoo and Tombigbee rivers around present-day Tupelo. They also claimed lands covering present-day western Tennessee. Their population numbers fluctuated over the 18th century between 2,000 to 5,000 people

The Conqueror Meets the Unconquered: Negotiating Cultural Boundaries on the Post-Revolutionary Southern Frontier

On December 26, 1785, A group of 127 bedraggled Choctaw Indians arrived at Hopewell, Andrew Pickens's home on the Keowee River in South Carolina. They had trekked for over two months and traveled hundreds of miles from their central Mississippi homeland to represent the Choctaw people in a meeting with representatives of the United States government. Several days of negotiations resulted in the first treaty between these two powers. This encounter in the southern backcountry (which was the second in a series of three consecutive meetings at Hopewell during the winter of 1785-1786 between the U.S. and the Cherokees, Choctaws, and Chickasaws, respectively) reveals several issues vital to an understanding of intercultural relations in the post-Revolutionary War South.

Making the Mississippi River Over Again: The Development of River Control in Mississippi

When Mark Twain wrote those words in the 1870s the United States government was just beginning to forge a massive river control system on the Mississippi River. The post-Civil War period witnessed an explosion in levees, wing-dams, dikes, jetties, and other constructions. This colossal project along more than 2,300 miles of the river continues to this day. It has had a major impact on the economy and the natural environment of the State of Mississippi and the Mississippi River Valley