NEXUS/Physics 131, Fall 2020 Lab 4: Examining Motion of vesicles in Onion Cells. Lab 4: Examining Motion of vesicles in Onion Cells. Characterizing the diffusion constant and viscosity of Onion Cells. Introduction Plant cells store information, food, and waste in small bubbles called vesicles. These vesicles are transported throughout cells using a variety of mechanisms. In some cases, cells utilize processes of random motion, like diffusion. Diffusion is a low power mechanism for transport but far too slow for transporting important packages. So, cells have developed a series of complex mechanisms for directed motion. In many cells, motor proteins transport vesicles along pathways framed by cytoskeletal fiber. One such process involves vesicles being transported by myosin motors along actin filaments. Another involves kinesin motors carrying vesicles along microtubules. All of these types of motion can be observed in onion cells. Therefore, onion cells are a cheap and simple experimental subject that allows us to make several interesting observations. By looking at individual onion cells, we can make both qualitative and quantitative observations about the different types of motion. Moreover, analysis of the work required to move the vesicle, and the diffusion of vesicles can allow us to better understand the structure of onion cells, including the effective viscosity and diffusion constant inside a cell. Investigation The lower cell membrane of the skin that separates the layers of an onion is composed of a single layer of thick cells. It is relatively easy to remove this layer from an inner layer of an onion and prepare a simple slide for viewing under a microscope. The picture shown to the right gives an example of what you would see. You have been provided with a couple of videos that capture the activity of vesicles in the onion skin cells. You should see some variety in the nature of the motion among different clusters of vesicles; some will be moving along paths of seemingly directed motion, while others may be more stationary or undergoing Brownian or confined/caged motion to some extent. Try to identify different forms of motion in the video, discussing with your group to compare what you have found. First as individuals, watch those videos and focus on the different types of motion of vesicles in the cell. Identify vesicles that are moving randomly and those moving directed, and others that don’t quite fit those labels. NEXUS/Physics 131, Fall 2020 Lab 4: Examining Motion of vesicles in Onion Cells. Come back with your group and discuss your observations. What might be different mechanisms behind the different kinds of motions you observe? Why are some moving rapidly while others aren’t? What might be the difference of vesicles across the kinds of motion? This investigation consists of several parts. Each week will consist of a different part of this investigation. Week 1. Random vs Directed Motion, the math, taking data. Week 2. Building a model to describe the motion of vesicles undergoing directed motion Week 3. Determining viscosity from directed motion Week 4. Determining the diffusion constant from random motion. 1) Random vs Directed motion, the Math. In order to examine diffusion or random motion we must first determine which vesicles are undergoing random motion and which are undergoing directed. In the previous lab, you were introduced to the diffusion equation, < π 2 > = 4π·π‘ < π 2 >∝ π‘ Where r is distance, D is the diffusion constant and t is time. You should also be familiar with directed motion under constant velocity, π = π£π‘ Where r is distance, v is velocity, and t is time. For our purposes, it’s easier to rewrite this equation as, π 2 = π£ 2π‘2 π2 ∝ π‘2 Notice now that we have two possible relationships between distance and time. Either r^2 is proportional to t (in the case of random) or r^2 is proportional to t^2 (in the case of directed motion). If we can then fit one of these functional dependencies to our data, we can identify the type of motion and potentially, the type of transport. Test a fit for both random and directed motion. It’s possible to test both at once using log-log plots http://umdberg.pbworks.com/w/page/48040885/Log-log%20plots Examine the onion videos provided on ELMS. Choose vesicles that appear to be undergoing random motion. Analyze them to determine if they are quantitatively undergoing random motion. NEXUS/Physics 131, Fall 2020 Lab 4: Examining Motion of vesicles in Onion Cells. Perform a separate investigation for vesicles appearing to be undergoing directed motion. Things to think about: β Should you use Manual- or Multi-tracker? β How are you going to determine the nature of the motion (random vs directed)? β What is the certainty in your final conclusion? β Consider what else you know about these vesicles from your biological studies. 2) Building the model of viscosity from directed motion. Note: for each numbered part, write your answer down in a lab journal or a shared google document. Here are some useful parameters: β Average size of a myosin motor 'step' = 10 nm, stepping along an actin filament. β Average size of a kinesin motor 'step' = 8 nm, stepping across/along a tubulin dimer. β One 'step' for a motor is equivalent to 1 ATP hydrolyzation cycle (EATP = 23 kJ/mole, notice the units: you’ll need J/*molecule*) β For both myosin motors and kinesin, the efficiency e (work produced ÷ energy consumed) is 60%. Unlike random motion and diffusion, which have an existing model, we have to build the model describing the viscosity. Step 1: Draw a Freebody Diagram for a vesicle attached to a motor, moving with some speed through fluid. What force is driving it forward? Are there any forces pulling it back? Any forces perpendicular to the line of motion? • Using Newton’s Second law, write an equation describing the forces acting on the vesicle. (Hint: Remember viscous force, πΉπ£ππ π = 6ππππ£) β‘ Check-in with your TA before moving on. Vesicles undergoing directed motion are being moved by protein motors, either Kinesin or Myosin. In physics and engineering we use efficiency to describe machines like motors and engines. This is the ratio of the amount of work done by the motor vs the amount of energy put into the motor. In other words: π= πππ’π‘ πΈππ NEXUS/Physics 131, Fall 2020 Lab 4: Examining Motion of vesicles in Onion Cells. πΈππ comes from ATP hydrolyzation; given the energy value stated above, how much energy E is consumed by a single motor molecule to take a single step on the dimer or filament? Step 2: Derive an expression for πππ’π‘ produced in a single step in terms of the (onemolecule, one-step) input energy E, the efficiency e, the driving force created by the motor Fapp, and the step size s. Remember work = force * distance (π = πΉ ∗ π). β‘ Check-in with your TA before moving on. We don’t know and can’t measure directly the force that the motor puts on the vesicle. So, what do we do? • Refer back to your Freebody Diagram and your 2nd law equation…. if our vesicle is moving at a roughly constant velocity, what does that tell you about acceleration? Given that, what is the relationship between the driving force and the drag force? Step 3: Rewrite your expression for πππ’π‘ in terms of the drag force variables, viscosity ο, object size r, and terminal velocity v, leaving the others (E, e, s) in place. • • What can we say about the object size r ? Obviously the motor + vesicle object isn’t a sphere, but we’ll pretend it is for simplicity (we already did by using πΉπ£ππ π = 6ππππ£; this introduces a tiny discrepancy, but shouldn’t affect the result on the scale of our uncertainties); how can we determine a proper object size from our resources? Which velocity is this v ? Do you already have it somewhere? β‘ Check-in with your TA before moving on. Step 4: Rearrange your equation to solve for viscosity μ. This should be your model for the following analysis. • • Which values are constants? Which variables are held constant during the motion? Which variables are from measurement? Reframe (at least mentally…) your model equation in terms of the independent variable vs everything else. Which step size s are you going to use? Do you think these are kinesins on actin filaments or myosins on tubulin dimers? β‘ Check your final equation with your TA. NEXUS/Physics 131, Fall 2020 Lab 4: Examining Motion of vesicles in Onion Cells. 3) Determining viscosity from Directed motion. In this part of the lab, you will focus on determining the viscosity of Onion cell structures. Using the data you obtained in the first week, determine the average velocities of your motor molecules (if you haven’t already). Use this data to with your viscosity model equation to analyze the vesicles undergoing directed motion of the Onion cell and determine an estimate for the viscosity ο of the cytosol. Here are some questions for you to think about: β What specifically is it you want to calculate? β How should you handle acceleration (changes in speed OR direction) present in the tracks? β Do you need to keep track of x- and y-components? β Should your velocity algorithm rely on adjacent/subsequent position data or a “cumulative” comparison, always with the initial position? β What are the uncertainties present in your data? Were there any uncertainties present before you started, from the recording of the video that someone else did for you? β Are there any uncertainties important enough to significantly affect your resulting velocity values? β‘ Check your method with your TA. 4) Determining the diffusion constant from random motion. This week you will focus on determining the diffusion constant of Onion cell structures. Using the data you obtained in the first week, analyze the vesicles undergoing random motion for the diffusion constant D of the cytosol in the onion cell. Remember how you determined the diffusion constant in lab 3. Here are some questions for you to think about: β What specifically do you want to calculate? More specifically, what is the formula for mean-squared displacement and how does it relate the data you have taken? β do you need to keep track of components? β What are the mathematical properties of mean-squared displacement? β Do the number values that result from your algorithm have the correct properties to be <r 2> values? β What would you expect to see in an <r 2> vs time plot if the motion is truly random? β Would using log plots be a helpful alternative? β What are the uncertainties present in your data? NEXUS/Physics 131, Fall 2020 Lab 4: Examining Motion of vesicles in Onion Cells. β Were there any present before you started, from the recording of the video that someone else did for you? β Are there any uncertainties important enough to significantly affect your resulting <r 2> values? At the end of today’s lab you will turn in a full lab report. Make sure to explain clearly how you decided that (or if !) your vesicles are undergoing random or directed motion, how you developed the model to find the viscosity, and how you analyzed your data to determine viscosity and the diffusion constant.
