Acetylcholine is a neurotransmitter that is used by neurons that innervate muscles and also in the parasympathetic nervous system, which broadly is the calming part of the nervous system. (The activating part of the nervous system, responsible for the fight-or-flight response is called the sympathetic nervous system.) In cholinergic synapses, acetylcholine is released into the synapse, it binds to receptors on the post-synaptic cell to activate it (causing ion channels to open and the post-synaptic cell to depolarize), and then it is broken down in the synaptic cleft by an enzyme called acetylcholinesterase. This enzyme is the target of the poisonous nerve gas sarin, which inactivates it and causes the neurons/muscles to continually fire. This kills you because you cant breathe. It is also the target of a drug called tacrine that is used to treat Alzheimers disease. Tacrine is a non-competitive inhibitor of the enzyme and has only mild effects of prolonging activation of the post-synaptic cell. Heres a diagram of the system. a) Lets model neurotransmitter release simply, just as a jump in acetylcholine concentration in the synapse to 100 uM at time = 0 (uM is micromolar). The receptors on the postsynaptic cell have to work fast, since the nerves may be triggering at 100 times per second. Lets set: kon = 100 uM-1 s-1 1 koff = 1000 s-1 Simulate the binding of acetylcholine to the receptors on the post-synaptic cell. Use BME_201_Exam1_LR_code.m, which is modified version of code from HW2. You will need to edit this code to make it work. Convert the rates above to inverse msec, which makes things easier (1000 s-1 is 1 msec-1). Do the same in the code and simulate for 1 msec. Change axes accordingly. Clean up comments in code, put your name at the top, put it in a Word document and turn it in with the plot below. Q1: Generate a plot of the fraction of receptors on the post-synaptic cell with acetylcholine bound. Label axes including units, title it, and include your name in the title. Include code below your plot. Q2: What is the Kd of the receptors for acetylcholine? Q3: How long does it take for 50% of the receptors to be occupied with ligand (use Data Tips tool on your plot)? b) Now lets model breakdown of acetylcholine in the synapse by acetylcholinesterase. In this section we will treat the ligand-receptor interaction as an equilibrium use the fractional occupancy equation and dont worry about the on- and off-rates you used above. This will save computational time. Also, run simulation in msec instead of seconds and make sure you use the correct units. Our acetylcholinesterase enzyme has: kcat = 25,000 s-1 = 25 msec-1 This is a very high rate, by the way, nearly at the biochemical limit. Lets assume for now that the enzyme has an infinitely high affinity for the substrate (Km = 0), so Vel = Vmax = kcat*Etot under all conditions. Q4: Analytically (no simulations needed), what enzyme concentration would be needed for the acetylcholinesterase to fall to 1 uM in 5 msec? Now run a simulation of acetylcholine degradation from the 100 uM starting point. Use an enzyme concentration: Etot = 1 uM Simulate the ligand-receptor binding fraction (using the fractional occupancy equation), and simulate the enzyme velocity using the Michaelis-Menten equation with: Km = 10 uM Start with the code BME_201_Exam1_MM_Code.m given. Simulate for 10 msec. Q5: Generate a plot of the acetylcholine concentration in the synaptic cleft versus time over 10 msec. Label axes with units, title it, and include your name in the title. Q6: How long does it take for the acetylcholine concentration to fall to 1 uM when the enzyme has this Km? 2 Q7: Generate a plot of the fraction of receptors on the post-synaptic cell with acetylcholine bound (fractional occupancy). Label axes including units, title it, and include your name in the title. Below the plot, include the code that you used for Q5 and Q7. Q8: How long does it take to get to only 1% of receptors occupied? c) Lets explore how inhibitors work. First lets look at a therapeutic inhibitor, tacrine, that elongates the activation time a bit to increase excitability of these cells. Tacrine is a noncompetitive inhibitor that reduces the Vmax without changing the Km. If a therapeutic dose decreases Vmax by half (it decreases the effective Etot by 2 to 0.5 uM), how does this affect the activation of the post-synaptic cell? Q9: Generate a plot of the fraction of receptors on the post-synaptic cell with acetylcholine bound in presence of tacrine. Label axes, title it, and include your name in the title. If needed, increase simulation time to 20 msec. Q10: How long does it take to get to only 1% of receptors occupied? d) What if we made a competitive inhibitor that had no effect on Vmax but instead it increased Km of the acetylcholinesterase by a factor of two (decreased its apparent affinity)? Lets call this drug thinkclear and see how well it works. Set Etot back to 1 uM and set Km to 20 uM. Q11: Generate a plot of the fraction of receptors on the post-synaptic cell with acetylcholine bound in presence of thinkclear. Label axes, title it, and include your name in the title. Q12: How long does it take to get to only 1% of receptors occupied? Q13: Which drug would you choose if you wanted to increase excitability by elongating the post-synaptic cell activation? e) Now lets look at sarin nerve gas. This is a suicide inhibitor that destroys the function of the enzyme. Lets imagine that you are poisoned with sarin and 99% of your acetylcholesterase is destroyed. Lets look at how your neurons would work. Reset Km to 10 uM, keep kcat at 25 msec-1, and change Etot to 0.01 uM. Extend the simulation duration to 100 msec in this case. Q14: Generate a plot of the fraction of receptors on the post-synaptic cell with acetylcholine bound in presence of sarin. Label axes, title it, and include your name in the title. 3 Q15: What percent of receptors are still occupied after 100 msec? Q16: Acetylcholine triggers muscles in your lungs to contract. Why do you think you cant breathe any more when youve been exposed to sarin gas?
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