User:Andy Maloney/Notebook/Lab Notebook of Andy Maloney/2009/09/23/Thoughts on the simulation

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So to follow along with the notation Larry made, I looked at a couple of things about the reaction of kinesin walking. Larry's notation is to use a */* where the first * is the foot in the trailing position and the second star is the foot in the leading position. With that said, I can't remember exactly but I think we came up with the "normal" process as being the following. [math]\mu[/math] stands for microtubule and [math]\mathbf{\phi}[/math] means a foot with no nucleotide bound to it. A foot is bound to the microtubule if the notation has a [math]\mu[/math] in it, like this [math]\mu\cdot[/math]ATP.

[math] \overbrace{\mu\cdot\text{ADP}}^1/\overbrace{\mu\cdot\phi}^2\leftrightarrow\overbrace{\text{ADP}}^1/\overbrace{\mu\cdot\phi}^2\leftrightarrow\overbrace{\mu\cdot\phi}^2/\overbrace{\text{ADP}}^1\leftrightarrow\overbrace{\mu\cdot\text{ATP}}^2/\overbrace{\text{ADP}}^1\leftrightarrow [/math]

[math] \leftrightarrow\overbrace{\mu\cdot\text{ATP}}^2/\overbrace{\mu\cdot\text{ADP}}^1\leftrightarrow\overbrace{\mu\cdot\text{ATP}}^2/\overbrace{\mu\cdot\phi}^1\leftrightarrow\overbrace{\mu\cdot\text{ADP}\cdot\text{P}_i}^2/\overbrace{\mu\cdot\phi}^1\leftrightarrow\overbrace{\mu\cdot\text{ADP}}^2/\overbrace{\mu\cdot\phi}^1 [/math]

So what I did was to take this above equation and separate it into the the front foot and back foot equations. I've labeled the equation so it is easy to see which foot I'm calling 1 and which one is called 2. There is no particular reason for my labeling. So, just looking at the chemical reaction for the foot labeled as 1, we see that,

[math] \mu\cdot\text{ADP}\leftrightarrow\text{ADP}\leftrightarrow\text{ADP}\leftrightarrow\text{ADP}\leftrightarrow\mu\cdot\text{ADP}\leftrightarrow\mu\cdot\phi\leftrightarrow\mu\cdot\phi\leftrightarrow\mu\cdot\phi [/math]

For the second foot I have,

[math] \mu\cdot\phi\leftrightarrow\mu\cdot\phi\leftrightarrow\mu\cdot\phi\leftrightarrow\mu\cdot\text{ATP}\leftrightarrow\mu\cdot\text{ATP}\leftrightarrow\mu\cdot\text{ATP}\leftrightarrow\mu\cdot\text{ADP}\cdot\text{P}_i\leftrightarrow\mu\cdot\text{ADP} [/math]

Of course the cycle is cyclic and so the front foot becomes the back foot. So, in reality there is only one equation with differentiations of where a foot is relative to what I deem is the starting position. With that said, the following is a description of one motor domain using one ATP molecule.

[math] \overbrace{\mu\cdot\text{ADP}}^{\text{behind}}\leftrightarrow\overbrace{\text{ADP}}^{\text{behind}}\leftrightarrow\overbrace{\text{ADP}}^{\text{ahead}}\leftrightarrow\overbrace{\text{ADP}}^{\text{ahead}}\leftrightarrow\overbrace{\mu\cdot\text{ADP}}^{\text{ahead}}\leftrightarrow\overbrace{\mu\cdot\phi}^{\text{ahead}}\leftrightarrow\overbrace{\mu\cdot\phi}^{\text{ahead}}\leftrightarrow\overbrace{\mu\cdot\phi}^{\text{ahead}}\leftrightarrow\overbrace{\mu\cdot\phi}^{\text{ahead}}\leftrightarrow\overbrace{\mu\cdot\phi}^{\text{behind}}\leftrightarrow [/math]

[math] \leftrightarrow\overbrace{\mu\cdot\text{ATP}}^{\text{behind}}\leftrightarrow\overbrace{\mu\cdot\text{ATP}}^{\text{behind}}\leftrightarrow\overbrace{\mu\cdot\text{ATP}}^{\text{behind}}\leftrightarrow\overbrace{\mu\cdot\text{ADP}\cdot\text{P}_1}^{\text{behind}}\leftrightarrow\overbrace{\mu\cdot\text{ADP}}^{\text{behind}} [/math]

Somethings to note here are:

  • A motor domain has a bunch of states where there is no nucleotide in it.
  • Transitions of motor domains going in front and behind each other only occur when there is no ATP involved.
    • This of course is dependent on our model. Since Larry wants to take into consideration the diffusion of a motor domain going from a behind position to a forward position. I say this because it could be that once a motor domain that has a bound ADP leaves the microtubule, this causes the forward foot to bind ATP quickly and thus causing a power stroke to occur.