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Phys 139 single-molecule experiment
创建日期：2024-08-28 18:01:38
所属分类：物理Physical
标签： Phys 139
single-molecule experiment

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Phys 139


2.  Consider a single-molecule experiment in which kinesin is hindered by an applied force f by attaching the motor to a plastic bead, and manip- ulating the bead using an optical trap. Recall that, in the Bell model, a chemical rate involving motion by a distance δ in the opposite direction of applied force is slowed according to k(f) = k(f = 0) exp(-f δ/T); inversely, a rate involving motion in the same direction as the applied force is sped up by k(f) = k(f = 0) exp(+f δ/T).

Analyze the efect of force on the Michaelis-Menten parameters, v max and KM, in the kinesin velocity versus  [ATP] curve, in the presence of a hindering load force f.  Particularly, determine if each parameter increases or decreases with force if we assume (1) Kinesin steps forward a distanced = 8 nm upon ATP binding, with no motion upon catalysis; or  (2)  Kinesin  steps  forward  by  d  =  8  nm  upon  catalysis,  with  no motion upon ATP binding.  Compare your prediction to experiment by  analyzing  the  data  used  in  Fig.   16.34(a)  in  the  text  (an  excel spreadsheet with this data has been uploaded in the modules).  Does either model work? What does this mean for motor activity?

3.  In class, we worked out the probability distribution of step numbers, N , for a motor protein after a ?xed time, τ , i.e.  P (Njτ ).  Here, the goal is to work out, and apply, the probability distribution of times to arrive at a ?xed step number, P (τ jN).

(a)  Assume that each step involves a single rate-determining reac- tion, with rate k.  To take 2 steps in time τ is proportional to the probability of taking 1 step in time t, , multiplied by the proba- bility to take a second step in time τ - t, , and integrated over all choices oft,  (this sort of integral is called a convolution).  Use this to ?nd P (τ j2).

(b)  Extend  the  argument  from  the  previous  part  to  ?nd  P (τjN). This can be done by iteratively working out the distributions for N  =  3, 4, . . . and detecting the pattern.   Alternatively,  it hap- pens to be the case that convolutions can be quickly carried out through multiplication of Fourier (or Laplace) transforms; if you feel con?dent in your transform mathematics, you could try this approach.

(c)  Calculate the time-domain randomness involved with taking N steps, assuming that each step involves either 1 reaction per step, or 2 sub-reactions (of equal rate k).  Note that the time domain randomness is de?ned as

where τ1  is the mean time to take one step.

4.  PBoC  16.2.   Best to do this after the previous problem.   Note that  Myosin V walks along actin in a manner similar to kinesin walking  along a microtubule, and analogous to human walking (i.e. it has two  ‘feet’ each connected to ‘legs’, and it walks along actin with an alter-  nating left-right stepping pattern), and that the ‘light chain domain’ is the proper name for the part of the protein corresponding to the  ‘leg’ .

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