BIM 162 hw 8

BIM 162 hw 8 - BIM 162 Homework 08 Due date: Thursday,...

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- 1 - Problem 1 (Fill in the blanks. Use additional paper if needed.) Aim: We'd like to design, and understand the behavior of, a vesicular drug-delivery capsule that can be activated osmotically. The design is based on a biologically inert compound "ABC" that can be split into three individual parts in response to an external trigger: external trigger ABC A B C   . (1) For simplicity, we assume that the effective concentration of the drug itself will be so small that it can be neglected in all osmotic balances. Design: Assuming that we can prepare a uniform suspension of vesicles, we choose to produce capsules with a surface area of 100 μ m 2 . (For comparison, the typical surface area of a human red blood cell is 140 μ m 2 .) Our vesicle preparation initially gives spherical vesicles that are filled with, and surrounded by, the ABC solution. The spherical geometry is not ideal because such vesicles lack the freedom to change their shape and may lyse prematurely. Therefore, we will gently shrink the vesicles until their volume is 80% of the volume of a sphere (at the given, constant surface area). This volume reduction is achieved by leaving the container open to the air (in a clean environment) and letting water evaporate. Since the vesicle membrane is permeable to water (but not to the ABC compound), osmotic balance causes water to be removed from the vesicles at about the same slow rate at which it evaporates from the container. The goal is to obtain vesicles that have the desired volume when the osmolarity of the suspension reaches the physiological value of ~300 mOsm . (We continually monitor the osmolarity using an osmometer. "Osm" here denotes "osmolar concentration", i.e., the number of moles of osmotically active particles per volume.) a. In order to achieve this goal: What osmolarity must the solution have that initially is used to prepare the (spherical) vesicles? Include in your answer the value of the desired, final vesicle volume. (see next page; explain steps) Hints: The answer to the first question can be found from the stationary solution of the differential equation of water transport across the vesicle membrane: 2 in ex 0 ,H O osm,0 osm,0 d d m V V VA P C C tV  
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BIM 162 hw 8 - BIM 162 Homework 08 Due date: Thursday,...

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