- Final project info
- Problem Set 4: covering Kinetics and Bifurcations
Q: For your de-dimensionalized ODEs, it seems as though both M and P degrade at a rate proportional to their own concentrations. (RateDegradationP = -P) (RateDegradationM = -M) and the rate of production is constant ( RateProductionP = 1 ). But in the problem it states that the rate of degradation of the two species is equal. That seems like a contradiction, whats going on?
- Problem Set 3: covering Fluid Flow on the Scale of a Cell A and B
Q: Question 1: How should diffusion be treated at the boundaries of the system?
- Problem Set 2: covering Molecular Motions in the Cell C
Q: In 1a, clarify the motion of the protein undergoing a power stroke with Brownian fluctuations.
- Problem Set 1: covering Molecular Motions in the Cell A and B
Q: For problem 1, what is the order of the reaction?
Q: For problem 1, do you want us to derive another concentration profile for the case where there is no chemical reaction or just discuss?
Q:For problem 1, do you want the flux of the molecule P with the chemical reaction rate or without?
Q: For problem 2, how do I do a probability distribution in three dimensions?
Problem sets are due by 5pm the day listed on the syllabus, and can be handed in in class or to either of our desks.
For late work - let us know in advance and we can work out extensions if circumstances require, otherwise each day late will be 1 point off of the grade.
Due 2/26 5pm
Student questions for PS4:
A: That degradation rate has units 1/sec. - it tells us the rate of the reactions M->nothing and P-> nothing occur, but to determine the total amount of degradation that is occurring at any point in time we must multiply that constant times the current concentration of the pertinent species. The production rate, P0, has units of concentration, so the product of P0 and the degradation rate give the production rate in units moles/sec.
Student questions for PS3:
A: Assume that there are hard boundaries, so the molecule can not diffuse out of the region that you are modeling.
Student questions for PS2:
A: The protein is moved forward by an external force a fixed distance Δx per unit time Δt. In that same unit Δt, it makes 10 random moves of the same size Δx forward or backward with equal probability. So, on average it will move forward with a velocity Δx/Δt, but sometimes it will move a touch faster or slower due to Brownian fluctuations.
A: The rate is first order. The reaction causes P to be depleted in proportion to its concentration.
A: Just discuss.
A: With the chemical reaction rate.
A: Sorry, this isn't made clear in the problem. Just look at the three dimensions separately using the 1D probability distribution Chris showed in class.