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BMEN 3310 – Human Systems

LAB MANUAL FOR LAB #3

Diffusion and osmosis

Dr. Shi

Goals: The goal of this lab is to use Matlab to make a model to simulate diffusion and osmosis.

Instructions: Read the lab manual in its entirety before attending your lab and bring a copy of it with you.

UNIVERSITY OF NORTH TEXAS

Fall 2023

BACKGROUND

Function of the Cell Membrane

Impermeable: nothing passes.

Permeable: everything passes.

Semi-permeable: small molecules pass but large molecules cannot pass.

Selectively permeable: only certain small and large molecules can pass.

Osmotic Pressure

Hypertonic: more solutes, less solvents.

Isotonic: equal solute/solvent concentration

Hypotonic: less solutes, more solvents

Tonicity: describes cell volume

Equations

Factors that affect Diffusion

Osmolarity vs Tonicity

PROCEDURE

Membrane Diffusion Model

Recall we discussed diffusion of substances across cell membranes in class. This can be done via passive diffusion (i.e., purely based on the concentration gradient, all other factors being equal) or via facilitated diffusion (i.e., where additional factors play a role in the movement of substances). Your tasks for this portion of the lab are the following:

Using MATLAB to create a general script to predict the rates of diffusion across the cell membrane for any substance. For this, it would be a good idea to use the version of the equation with membrane permeability (P) and area (i.e., flux J = number of moles/times = P*A*concentration difference). In the script, describe the version of the equation that you used, including what each term does and the units of each term (flux, permeability, etc). (10 points)

Under normal (healthy) circumstances, the concentration of carbon dioxide in the blood for humans is 30 mM/L. Using your script, estimate the concentration of carbon dioxide inside a spherical cell of diameter 7 μm. Note that a typical membrane thickness is 4 nm. Assume that it takes 5 seconds for the concentration outside the cell to reach 30 mM/L. Use the chart in Figure 1 and assume a reasonable membrane permeability for carbon dioxide. (20 points) clue: n=c*v

Figure 1: Membrane permeabilities for different substances [1]

Modify your script such that it can span across concentration of carbon dioxide inside the cell and plot the behavior of time taken for different interior concentrations to diffuse out. Is there a trend? Describe what is happening in physical terms. Plot at least 10 different interior concentrations spanning an order of magnitude (20 points)

Osmosis Model

Recall we discussed that the net diffusion of water across a cell membrane is called osmosis. A typical range of osmolarity of cells and extracellular fluid which is in osmotic equilibrium is 300 mOsm (i.e., both inside and outside the cell). Based on addition or removal of solutes, a cell will swell or shrink to maintain this level or osmolarity. Thus, your tasks are the following:

Create a script in MATLAB to relate the osmolarity to cell volume. Similar to the previous exercise, your code should include information about all the terms and the units used. Also include information about the molecular weights of typical physiological ions such as sodium, potassium, chlorine and calcium (10 points)

Assume a cell with an internal osmolarity of 300 mOsm/L (i.e., typical physiological scenario) and whose radius is 10 microns in a 7 nL solution also at 300 mOsm/L. To this, a 4 nL, 3% NaCl solution by weight is added. Assuming that NaCl is impermeable (i.e., sodium and chlorine does not enter the cell), calculate the change in volume of the cell to adjust to the osmolarity change due to addition of NaCl (20 points)

Using a modified version of your script, estimate the concentration of saline that should be added to obtain no volume change of the cell (10 points)

Vary the range of osmolarity and plot the change of cell volume vs. osmolarity. How does the curve look? Explain the curve in physical and conceptual terms (10 points)

Grading Rubric

The final report should include:

Your script (with comments)

Solved problems

Plots (where applicable)

Explanation of the results

Make sure to follow the lab format

RESULTS

Attach screenshots of your graphs. Please explain in your own words what is happening.

QUESTIONS AND ANALYSIS

What type of permeability is the cell membrane? Why? (cite your source)

What factors affect diffusion and permeability?

What is the Overton rule? How is this rule used in diffusion and permeability? (cite your source)

What is the relationship between osmolarity and tonicity?

CONCLUSIONS

Please write one conclusion paragraph on what you have learned during this lab session. Aside from the technical conclusion aspect you need to answer the following questions in the conclusion section:

1. What was the goal of this lab?

2. How did you approach the problem? (a summary of the simulation set up – about two sentences)

3. What was the main result?

4. How can you improve the process?

References

Philips, R. M. & R. (n.d.). What is the permeability of the cell membrane? Cell biology by the numbers What is the permeability of the cell membrane Comments. http://book.bionumbers.org/what-is-the-permeability-of-the-cell-membrane/

Lab Report Format

All labs must follow the following format:

1-inch margins, 1.15 line spacing, size 12 font, Times New Roman

Must include:

Cover Page

Lab title, date, name(s)

Introduction:

1-2 paragraphs

Introduce the background for the problem

Introduce the problem

Methods:

What did you do to solve the problem

Any calculations, analysis done

Summarize the full process of how you got the results

Results:

Put any graphs, figures, and tables of the results

All figures, tables, and graphs should be labeled and numbered

Include titles and axis labels for your graphs

Conclusion:

Summarize the results

Do they make sense?

Appendix

Matlab code (if any)

Copy and paste it, no pictures

******LAB FORMAT EXAMPLE BELOW******

Lab #: Title

BMEN 3310.XXX

Date

Name(s)

Introduction

This section of the laboratory introduces the background for the problem and then introduces the problem. This section should be from 1-2 paragraphs to provide enough background information using the information provided in the lecture or laboratory section.

Methods

In this section you summarize how you solved the problem, show any calculations and analysis done.

Results

Show your results using any graphs, figures, and tables. Examples of how to label a table and a graph are below.

Table 1: Average Velocity Results – Car A vs Car B.

Figure 1: Plot of cos(x)

Conclusion:

Summarize the results and relate them back to the problem.

Appendix

The code for figure 1 is below:

clear all

clc

close all

x = linspace(0,10,200);

y = cos(2*x);

figure(1)

plot(x,y)

title(‘Plot of cos(x)’)

xlabel(‘x’)

ylabel(‘cos(2x)’)

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