Drop-shape analysis of receptor-ligand binding at the oil/water interface

Drop-shape analysis was used to study the binding of streptavidin to biotin at the interface between water and a pendant chloroform droplet. Polyethylene oxide molecules were synthesized with a hydrophobic tail at one end of the molecule and a hydroxyl or biotin group at the other end. The interfacial tension of the water/chloroform interface was measured before and after addition of these amphiphiles to the chloroform phase and before and after addition of streptavidin to the aqueous phase. The hydroxyl-terminated amphiphiles eliminate nonspecific adsorption of the streptavidin to the interface, while streptavidin binds irreversibly to the biotin-terminated molecules. Molecular interactions within this bound layer were studied by measuring changes in the interfacial pressure as the layer is contracted and expanded by changing the volume of the chloroform droplet. A picture of the interfacial structure was obtained from quantitative comparisons between the experimental results and a molecular theory of protein binding to tethered ligands. These comparisons suggest that protein binding is controlled by the extension of the PEO tethers away from the interface.     

Unit Interval Orders of Open and Closed Intervals

A poset P = (X, ?) is a unit OC interval order if there exists a representation that assigns an open or closed real interval I(x) of unit length to each x ∈ P so that x ? y in P precisely when each point of I (x) is less than each point in I (y). In this paper we give a forbidden poset characterization of the class of unit OC interval orders and an efficient algorithm for recognizing the class. The algorithm takes a poset P as input and either produces a representation or returns a forbidden poset induced in P.     

Fractional weak discrepancy and interval orders

The fractional weak discrepancywd_F(P) of a poset P=(V,?) was introduced in [A. Shuchat, R. Shull, A. Trenk, The fractional weak discrepancy of a partially ordered set, Discrete Applied Mathematics 155 (2007) 2227-2235] as the minimum nonnegative k for which there exists a function satisfying (i) if a?b then f(a)+1≤f(b) and (ii) if a∥b then |f(a)−f(b)|≤k. In this paper we generalize results in [A. Shuchat, R. Shull, A. Trenk, Range of the fractional weak discrepancy function, ORDER 23 (2006) 51-63; A. Shuchat, R. Shull, A. Trenk, Fractional weak discrepancy of posets and certain forbidden configurations, in: S.J. Brams, W.V. Gehrlein, F.S. Roberts (Eds.), The Mathematics of Preference, Choice, and Order: Essays in Honor of Peter C. Fishburn, Springer, New York, 2009, pp. 291-302] on the range of the wd_F function for semiorders (interval orders with no induced ) to interval orders with no , where n≥3. In particular, we prove that the range for such posets P is the set of rationals that can be written as r/s, where 0≤s−1≤r<(n−2)s. If wd_F(P)=r/s and P has an optimal forcing cycle C with and , then r≤(n−2)(s−1). Moreover when s≥2, for each r satisfying s−1≤r≤(n−2)(s−1) there is an interval order having such an optimal forcing cycle and containing no.