First Passage and Cooperativity of Queuing Kinetics

We model the kinetics of ligand-receptor systems, where multiple ligands may bind and unbind to the receptor, either randomly or in a specific order. Equilibrium occupation and first occurrence of complete filling of the receptor are determined and compared. At equilibrium, receptors that bind ligands sequentially are more likely to be saturated than those that bind in random order. Surprisingly however, for low cooperativity, the random process first reaches full occupancy faster than the sequential one. This is true {\it except} near a critical binding energy where a 'kinetic trap' arises and the random process dramatically slows down when the number of binding sites $N\geq 8$. These results demonstrate the subtle interplay between cooperativity and sequentiality for a wide class of kinetic phenomena, including chemical binding, nucleation, and assembly line strategies.Comment: 5pp, 5 figure

Modelling chemistry and biology after implantation of a drug-eluting stent. Part I: Drug transport

Drug-eluting stents have been used widely to prevent restenosis of arteries following percutaneous balloon angioplasty. Mathematical modelling plays an important role in optimising the design of these stents to maximise their efficiency. When designing a drug-eluting stent system, we expect to have a sufficient amount of drug being released into the artery wall for a sufficient period to prevent restenosis. In this paper, a simple model is considered to provide an elementary description of drug release into artery tissue from an implanted stent. From the model, we identified a parameter regime to optimise the system when preparing the polymer coating. The model provides some useful order of magnitude estimates for the key quantities of interest. From the model, we can identify the time scales over which the drug traverses the artery wall and empties from the polymer coating, as well as obtain approximate formulae for the total amount of drug in the artery tissue and the fraction of drug that has released from the polymer. The model was evaluated by comparing to in-vivo experimental data and good agreement was found

Stochastic theory of ligand migration in biomolecules.

When ligand binding to proteins involves the presence of more than one ligand inside a given biomolecule, linear deterministic rate equations become useless. A stochastic approach, however, permits a treatment of the migration and binding of small molecules to proteins even at high ligand concentrations. An appropriate linear master equation and its analytic solution are given. As an example, the binding of carbon monoxide to myoglobin at partial pressures from 1 to 10(3) bars (0.1 to 100 MPa) is treated

A REFLECTIVITY AND EXAFS STUDY OF LAYERED STRUCTURES

By combining the total reflection of x-rays incident on a sample at grazing angles and fluorescent detection of the EXAFS signal, it is possible, in principle, to examine the interfacial and bulk regions of layered structures. In this paper we first describe a simple sample positioner that permits a rapid, precise aliment of the sample. It is driven by stepper motors controlled by an microcomputer and permits an angular step of 0.07 mrad. A reflectivity curve can be obtained with it in less than one minute. Using this apparatus good agreement is obtained between experiment and theory for the angular dependence of the reflectivity of a multilayer film of Si/Cu/Au deposited on fused quartz. We also report structural results as a function of depth obtained via fluorescent reflection EXAFS for Ni epitaxially grown on the (100) face of a Fe single crystal