Cooperative effects in models of steady-state transport across membranes. I

Three simple models are discussed which show cooperative effects in the steady-state transport of neutral molecules across a membrane. The Bragg-Williams approximation is employed, and its limitations discussed. In this approximation to cooperative problems, the diagram method for the calculation of steady-state probabilities and fluxes can still be used. This paper is closely related to one by Blumenthal, Changeux, and Lefever, and provides the foundation for sequels on an oscillatory steady-state phase-transition model (part II) and on simple models possibly related to steady-state potassium ion transport across a nerve membrane (part III).

Flow through a collapsible tube. Experimental analysis and mathematical model

Flow through thin-wall axisymmetric tubes has long been of interest to physiologists. Analysis is complicated by the fact that such tubes will collapse when the transmural pressure (internal minus external pressure) is near zero. Because of the absence of any body of related knowledge in other sciences or engineering, previous workers have directed their efforts towards experimental studies of flow in collapsible tubes. More recently, some attention has been given towards analytical studies. Results of an extensive series of experiments show that the significant system parameter is transmural pressure. The cross-sectional area of the tube depends upon the transmural pressure, and changes in cross-section in turn affect the flow geometry. Based on experimental studies, a lumped parameter system model is proposed for the collapsible tube. The mathematical model is simulated on a hybrid computer. Experimental data were used to define the functional relationship between cross-sectional area and transmural pressure as well as the relation between the energy loss coefficient and cross-sectional area. Computer results confirm the validity of the model for both steady and transient flow conditions.