# BP205 Molecular Dynamics of the Cell

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### Assignments

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.

• Final project info

• Midterm
• Due 2/26 5pm

• Problem Set 4: covering Kinetics and Bifurcations
• Due 2/10
Student questions for PS4:

• 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?

• 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.

• Problem Set 3: covering Fluid Flow on the Scale of a Cell A and B
• Due 2/3
Student questions for PS3:

• Q: Question 1: How should diffusion be treated at the boundaries of the system?

• A: Assume that there are hard boundaries, so the molecule can not diffuse out of the region that you are modeling.

• Problem Set 2: covering Molecular Motions in the Cell C
• Due 1/27
Student questions for PS2:

• Q: In 1a, clarify the motion of the protein undergoing a power stroke with Brownian fluctuations.

• 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.

• Problem Set 1: covering Molecular Motions in the Cell A and B
• (PS 1 Solutions)
Coordinate files for problem 2: t0.txt and tf.txt
Due 1/20
Student questions for PS1:

• Q: For problem 1, what is the order of the reaction?

• A: The rate is first order. The reaction causes P to be depleted in proportion to its concentration.

• 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?

• A: Just discuss.

• Q:For problem 1, do you want the flux of the molecule P with the chemical reaction rate or without?

• A: With the chemical reaction rate.

• Q: For problem 2, how do I do a probability distribution in three dimensions?

• 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.