In this paper we examine molecular stretching in the inception of uniaxial elongational flow of dilute polymer solutions. The polymer molecules are modeled as bead–spring chains with finitely extensible nonlinear elastic springs, and we use the Peterlin approximation. This work is distinguished from earlier work because we model the macromolecules with chains instead of dumbbells, and we examine the time dependence of three average quantities describing the chain conformation in unsteady flows: root-mean-square end-to-end distance, root-mean-square extensions of the individual links, and mean moment of inertia about the axis of elongation. We observe a gradual transition from the coiled equilibrium state of the chain to the stretched state after the inception of strong uniaxial elongational flow, and we describe the nature of this transition which takes place in roughly four stages: I equilibrium coil; II deformed coil; III spring stretched (‘‘locally unraveled’’); and IV unfolded chain. Inclusion of hydrodynamic interaction changes the macromolecular response quantitatively but not qualitatively.

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Vesicle formation provides a means of cellular entry for extracellular substances and for recycling of membrane constituents. Mechanisms governing the two primary endocytic pathways (i.e., caveolae- and clathrin-mediated endocytosis, as well as newly emerging vesicular pathways) have become the focus of intense investigation to improve our understanding of nutrient, hormone, and drug delivery, as well as opportunistic invasion of pathogens. In this review of endocytosis, we broadly discuss the structural and signaling proteins that compose the molecular machinery governing endocytic vesicle formation (budding, invagination, and fission from the membrane), with some regard for the specificity observed in certain cell types and species. Important biochemical functions of endocytosis and diseases caused by their disruption also are discussed, along with the structures of key components of endocytic pathways and their known mechanistic contributions. The mechanisms by which principal components of the endocytic machinery are recruited to the plasma membrane, where they interact to induce vesicle formation, are discussed, together with computational approaches used to simulate simplified versions of endocytosis with the hope of clarifying aspects of vesicle formation that may be difficult to determine experimentally. Finally, we pose several unanswered questions intended to stimulate further research interest in the cell biology and modeling of endocytosis.

One of the goals in polymer fluid dynamics is to use kinetic theory to derive a constitutive equation for a polymeric liquid starting from a molecular model, to use the constitutive equation to solve flow problems, and finally to use kinetic theory to describe molecular stretching and orientation. We illustrate this procedure by using a finitely extensible, nonlinear, elastic dumbbell with the Peterlin approximation (FENE-P dumbbell) as a crude model of a polymer molecule and then derive the constitutive equation. A number of new results for the FENE-P dumbbell are given which include an analytic expression for the elongational viscosity, numerical calculations of the stress growth after the start-up of elongational flow, and the third-order fluid constants. The technique of "model matching" is illustrated for squeezing flow between circular disks, the Weissenberg rod-climbing effect, and the torque on a rotating sphere. Conclusions can be drawn about the average extension and alignment of the dumbbell in these three flow fields. (5) where Qo is the maximum extension. Equation 4 cannot f(Q2) = H/[1 -(Q/QO)~I

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