Hi @2022CSBCPSONSummerUndergraduateFellows,
The Zoom recording for today's lecture has been posted on the [Curriculum](https://www.synapse.org/#!Synapse:syn29616137/wiki/617441) page.
The answers for Module 5 are as follows (from Jay):
>What is the equilibrium bound clutch number?
>ANS: That will be k1/(k1+k-1)*A0 = 68.2 (65-70 will be ok)
>
>What is the half time of this reaction (nc_bound(time_half) = 0.5*nc_bound_final)?
>ANS: that will be 0.63s (0.6-0.7 will be ok)
>
>What is the approximate frequency for clutches to unbound (unbound_freq)?
>ANS: 6.7 (5-10 will be fine)
>
>What is the mean module force (mforce_mean)?
>ANS: 21pN (20-22 will be fine)
If you have questions, please post here, email the [mentors](mailto:CSBCPSONminiDREAMMentors@synapse.org), or email Jay [directly](mailto:houxx149@umn.edu).
Lastly, in case it helps, I wanted to share how I worked through the first 2 questions as someone who is new to this topic (and honestly had a hard time with it!). Here's my code from the first Challenge Question chunk (line 169). This isn't necessarily the best way, just the way that worked for me. If you approached it differently, please share!
```
# Challenge Question
# I used the calculated number of bound clutches
# (clutchbCalc - the red line in the above plot) for this,
# since it is simpler than the stochastic model
# First, look at the last few values of clutchbCalc
# to see where it ends up stabilized - looks like 68.2
tail(clutchbCalc, 20)
# so
nc_bound_final <- 68.2
# The half-time is the time it takes to get to half this number
# (nc_bound_final / 2 = 34.1)
# So first create a matrix of bound clutches (clutchbCalc)
# at each timepoint (timeArray)
combined_matrix <- cbind(timeArray, clutchbCalc)
# Then get the times when number of bound clutches
# is close to 34.1
combined_matrix[clutchbCalc >= 34 & clutchbCalc <= 34.2]
# so
time_half <- 0.63
```
Created by Pierrette Lo lopierra @2022CSBCPSONSummerUndergraduateFellows - see more detailed answers from Jay below. (Note that the ranges for correct answers have also been broadened.)
**Exercise 1: clutch dynamics**
Challenge Questions:
* What do you observe? **Answer:** The stochastic simulation fits well with analytical solution
* What is the equilibrium bound clutch number (nc_bound_final)? **Answer:** That will be k1/(k1+k-1)*A0 = 68.2 (60-75 will be ok)
* What is the half time of this reaction (nc_bound(time_half) = 0.5*nc_bound_final)? **Answer:** That will be 0.63s (0.6-0.7 will be ok)
Bonus:
* How will kon, koff, clutchNum affect simulation results? **Answer:** Higher kon, higher equilibrium bond clutch number. higher koff, lower equilibrium bond clutch number. higher kon+koff, shorter the half time. higher clutch Num, higher equilibrium bond clutch number.
* Why stochastic simulation results fluctuate with time? What are the benefits from this behavior? **Answer:** Because stochastic simulation makes the binding and unbinding happen every time steps, so there can not be a constant bound clutch number. Stochastic simulation is more similar to the reality, so it can capture more realistic biological behaviors.
* What is the biological behavior represented by this exercise? **Answer:** When cells adhere to the substrate, they will form focal adhesion, which is the accumulation of adhesion molecules as clutches. Therefore, if there is no other forces, this exercise represent the cell adhesion.
**Exercise 2: F-actin flow stretching clutches**
Challenge Questions:
* What do you observe? **Answer:** We should see bound clutch number fluctuates with time, so does force.
* What is the approximate frequency for clutches to unbound (unbound_freq)? **Answer:** 6.7 (5-10 will be fine)
* What is the mean module force (mforce_mean)? **Answer:** 21pN (15-25 will be fine)
Bonus:
* How will kon, koff, clutchNum, clutchK, actinFlow affect simulation results? **Answer:**
* higher kon, clutch will not unbound totally, higher mean force
* higher koff, higher clutch unbound frequency, lower mean force
* higher clutchNum, clutch will not unbound totally, higher mean force
* higher clutchK, higher clutch unbound frequency, higher mean force
* higher actinFlow, higher clutch unbound frequency
* Is module force = clutch bound number $\times$ clutchK? If not, why? **Answer:** No, module force = sum (clutch_dx $\times$ clutchK)
* What is the biological behavior represented by this exercise? **Answer:** When there is a F-actin flow due to myosin contraction, F-actin will stretch the clutches, force them to unbind from the substrate, and hence the retraction of protrusions