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Motor Olympics

This problem is an invitation to the annual IronGeek event. Teams can try to make the strongest muscle motors or the most efficient muscle motors by optimizing the design of an idealized myosin 2 - actin system.

What it describes

This model describes a greatly simplified version of the may that muscles work at the microscopic level. The most important features are being kept so you can see how the motor actually functions. As opposed to the other motor problem on this week's homework, the motor has one end clamped and pulls on a filament that is moving past it, doing work. We are interested in the amount of power that it can generate.

To Install

You'll need to have the gnu C compiler installed, which you probably do if you've managed to run the simulations up to now. You have to determine if you have a 32 or 64 bit version of python installed. Try typing "python --version" in a terminal to determine this.

 

If you're on windows 10 using the windows linux subsystem,  and python 2, you need to  additionally install:

sudo apt-get install g++-multilib

Unzip hw8/1head/1head.zip. Then if you have 32 bit python, type:

 make

If you're on 64 bit (which you most likely are), type instead:

 make BITS=""

If all goes well (you might see some warnings though), you should now be able to run my.py in python or ipython.

The Model

The model is quite similar to the other myosin motor problem on this homework, except for two things. First one end is clamped. This motor is not suppose to walk, just pull things along. So it has one end tethered to one spot. The other end will associate and disassociate from an actin filament. This filament has binding sites that are periodically arranged, and moves at some fixed velocity. As with the other motor problem, there are quite a few parameters that describe the system and they are the same as in this problem. You can look there to find out how it works. One difference is there is a separation in height, the "Height" parameter, that is the vertical distance between the tether point and the actin filament.

The major difference between this problem and myosin V, is in the way the way that we analyze this system. The program calculates the average force, f, exerted on the actin filament. This force is exerted in the x-direction. The filament is going at a velocity v. This means that power is being produced by the system.

  • 1. How much power is being produced on average in terms of f and v?

By varying the velocity, v, of the actin filament, you'll see a different average force f. What does the shape of this curve look like?

  • 2. You can try to do two things with this motor. Get the greatest force out of it, or get the greatest power. In both cases, try to optimize parameters. You should find that the design of the motors for both cases is quite different. Explain what differences you find and why. You are also allowed to change the rates of binding and unbinding.
  • 3 You might also want to get the greatest efficiency out of a motor. Would a motor that is optimized for greatest force, give maximum efficiency?
  • 4. What do these differences in what you're optimizing for, e.g. maximum force versus maximum power, tell you about why you see so many different types of biological motors. Do different kinds of biological motors appear to be optimized to do different things?
  • 5 Describe how this model might be modified to do photo-mechanical conversion. How does the operation of it depend on light intensity?