Currently, there exist several methods for finding roots of polynomial functions. From elementary processes such as the quadratic formula and the Rational Root Theorem to calculus-based ideas, choosing an appropriate means of solving often depends on the conditions of the given polynomial. This report will explore several solving methods and discuss their advantages as well as their limitations. / text

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The Major Intrinsic Proteins are represented in all forms of life; plants, animals, bacteria and recently archaebacteria have all been shown to express at least one member of this superfamily of integral membrane proteins. We have overexpressed the E. coli aquaglyceroporin, glycerol facilitator (GlpF), to use as a model for studying membrane protein structure, folding and stability. Understanding membrane protein folding, stability, and dynamics is required for a molecular explanation of membrane protein function and for the development of interventions for the hundreds of membrane protein folding diseases. X-ray analysis of GlpF crystals shows that the protein exits as a tetramer in the crystallized state [1]. However, preparations of stable aqueous detergent solutions of GlpF in its native oligomeric state have been difficult to make; the protein readily unfolds and forms non-specific aggregates in many detergents. Here, I report the study of the structure and stability of the glycerol facilitator in several detergent solutions by blue native and sodium dodecyl sulphate polyacrylamide gel electrophoresis, circular dichroism, and fluorescence. For the first time, stable protein tetramers were prepared in two different detergent solutions (dodecyl maltoside (DDM) and lyso-myristoyl phosphatidylcholine (LMPC)) at neutral pH. Thermal unfolding experiments show that the protein is slightly more stable in LMPC than in DDM and that the thermal stability of the helical core at 95oC is slightly greater in the former detergent. In addition, tertiary structure unfolds before quaternary and secondary structures in LMPC whereas unfolding is more cooperative in DDM. The high stability of the protein is also evident from the unfolding half-life of 8 days in 8 M urea suggesting that hydrophobic interactions contribute to the stability. The GlpF tetramers are less resistant to acidic conditions; LMPC-solubilized GlpF shows loss of tertiary and quaternary structure by pH 6, while in DDM the tertiary structure is lost by pH 5, however the tetramer remains mostly intact at pH 4. The implications of thermal and chemical stress on the stability of the detergent-solubilized protein and its in vivo folding are discussed.

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