Experiments: how do we know
what single motors do?
Optical tweezers
 
Fgrad  12  p  E    E 2
Optical trapping
• Is simply a TM-00 (Gausian cross section)
laser beam focussed to a diffraction-limited
spot.
• Can use it to grab, and manipulate, small
dielectric objects
• Vesicles, lipid droplets, cell membranes,
small glass or plastic spheres are all small
dielectric objects
Optical trap
• Can position beads anywhere
• Easy to see motor-microtubule binding events
How much force can the motor exert:
Optical tweezers as a spring
Methods For Force calibration in
Optical Tweezers
(If interested, please see Dr.
Yonggun Jun who has just spent a
lot of time thinking about OT
calibration!!)
Equipartition Theorem
Equipartition Theorem
40
P=72 mW
P=170mW
P=260mW
x (nm)
20
0
-20
-40
0.0
0.2
0.4
0.6
Time (s)
0.8
1.0
1
10
100
1000
Histogram
Stalling Force measurements
How far can a single motor move
a cargo?
• Vesicle transport motors such as kinesin
and Myosin-V are “processive” enzymes
• Processive: go through repeated complete
enzymatic cycles, while remaining bound to
the substrate (in this case the MT or AF)
Use of Optical trap to
characterize kinesin
12
Microtubule motors are unidirectional
Single Kinesin motor moving a bead in vitro
A single motor moves ~ 1 m
Single motor bead assays: processivity
Histogram
Individual Traces
Does it take discrete steps, or move
continuously? If steps, what size?
• MT built of repeating subunits (dimers).
Each dimer is 8 nm in length
• If moves along a single protofilament,
expect steps that are some multiple of 8nm.
If lateral steps possible, could take smaller
steps.
Single-molecule driven beads move in
Single-molecule
steps
are 8[ATP],
nm at low [ATP],
load
8 nm
steps at
low
low low
load
Distance (nm)
a
8 nm
1
Time (s)
0.02
b
Power
Number
0.6
3
0.4
5
7
c
0.01
0.2
0
8
16
24
32
Distance (nm)
40
48
0.00
0.000
0.125
0.250
0.375
-1
Spatial Frequency (nm )
Extraction of Step size from displacement records
Position
Pairwise Distance
Function analysis
Step
Size ?
Time
You expect to see regular
peaks in a histogram of such
pairwise distance at multiples
of the Step size
Step Detection Techniques—individual rapid steps
Feedback
 Force Clamp
AOD
Halogen Lamp
L5
980nm IR Laser
M1
PSD
DM1
BFPC
L1
Condenser NA=1.4
XYZ Piezo-Stage
x
 High Sampling
100x Objective
NA=1.3
BFPO
L2
DM2
M2
L3
L6
L4
CCD camera
M3
Chi-squared Minimization Method
B.C. Carter, et al “A Comparison of Step-Detection Methods:
How Well Can You Do?” Biophys. J., 94(1):306-19, (2008)
18
Step Size Measurements
Kinesin
0.10
Kinesin-EXPT
Detected Steps
Position (nm)
128
112
96
80
64
48
32
16
0
-16
AOD Feedback
Normalized
Kinesin
0.05
0.00
0.0
0.1
0.2
-32
0.3
Time (sec)
Position (nm)
96
Counts (Normalized)
Kinesin Simulation
Detected Steps
112
80
64
48
32
16
0
0.0
0.1
Time (sec)
0.2
-16
0
16
Step Size (nm)
32
48
EXPT_Kinesin
Sim_+8nm only
Residual
0.15
0.10
0.05
0.00
-32
-16
0
16
32
Step Size (nm)
48
Label one head
Selvin, Science
Tracks:
Distribution of steps:
The average step-size is 17.3 ±3.3 nm; uncertanty of mean (SEM) is
0.27 nm
Three families of molecular motors
Kinesin
Myosin-V
Dynein
Cargo
Cargo
KLC
Pi
KR1
Dynactin
binding
KR2
MR2
Ca2+
Pi
KAPP
KR3
MR1
Head
(ATPase)
Stalk
2 1 c
3
6
4 5
Lever (?)
KHC
Head (ATPase)
MT binding
Processivity: porters vs rowers
Processive (porter)
Non-processive
(rower)
Images: MCRI Molecular motors group
Kinesin is Processive; Myosin II
(muscle) is not. Why?
• A processive motor doesn’t let go of the substrate (MT or
AF) so the cargo doesn’t diffuse away
• Many processive motors could get in each others way--all
bound to the filament at the same time
• A non-processive motor lets go of the filament at some
point in its enzymatic cycle. Thus, multiple motors don’t
get in each others way--not active at exactly the same time
• The ‘duty ratio’ is the ratio of (time bound to
substrate)/(complete time for enzymatic cycle)
• Duty ratio=1 for processive motor
Summary of single-molecule
experiments
Motor proteins:
 Are uni-directional, and move along straight filaments
 Exert 1-6 pN force
 Typically go ~ 1m before detaching
 Kinesin motors take 8 nm steps, Dynein takes a variety of step
sizes, Myosins take 36 nm steps
 Move between 0.1 and 2 m/s
Is this how transport functions inside cells?
How do we go from singlemolecule characterization to in vivo
function?
Herpes virus in cultured neuron
Why do cargos need multiple
motors?
Many intercellular distances are longer
than 1 micron
Motion in cells is different from
what might be expected based on
single-molecule properties
Cargos can move long distances
Maybe multiple motors?
Bead moved by multiple kinesin motors
So, multiple motors can move a
cargo long distances.
Now, lets look more carefully…
Start to build complexity in a
controlled environment, i.e. in
vitro, and understand how
motors work together
Poisson statistics: Getting down to the
single molecule limit…
•
Catch Dynein- or kinesin-coated
beads, bring in contact with MT
•
Find probability for
Binding/motion (Bind fraction)
•
Repeat at different motor:Bead
ratios
•
Plot the Bind fraction Vs
motor:Bead ratio
•
Stay where probability for
“doubles” is negligible
For single motor, use
Binding/moving fraction ≤ 0.3
Motor - polystyrene bead assays
Kinesin I: single motor
30% or less of beads bind to MTs
Run Length (Processivity)
Decay constant
± SEM :
1.46±0.16 µm
Force production
Peak center
± SEM :
4.8±0.06 pN
Poisson statistics: Getting down to the
single molecule limit…and then back to multiple motors
•
Catch motor-coated beads,
bring in contact with MT
•
Find probability for
Binding/motion (Bind fraction)
•
Repeat at different motor:Bead
ratios
•
Plot the Bind fraction Vs
motor:Bead ratio
•
Now, use concentration where
probability for “doubles” is high:
mixed population
Mixed bead population-->
How do we know how many
motors are moving a specific
bead?
What we think is going on
Bf~0.3
Bf~0.7
Bf~1.0
Increasing Kinesins per bead
Bf~1.0
Evolution of force production
with increasing kinesins per bead
Single motor
(Bf ~0.3)
1-2 motor
Mostly single motor
(Bf ~1)
Conclusion: for multiple-motor
driven transport, binding fraction
cannot tell you how many motors
engaged.
Stalling forces are additive at low
motor number; use this as a readout
of the number of instantaneously
engaged motors
Motor - polystyrene bead assays
Kinesin I: ~two motors
driving polystyrene bead
Force production
Run Length
Summary for ~2 engaged Kinesins:
* Velocities unchanged (not shown)
* Stall forces ~ additive
* Cargo travel lengths very
long, but this is not really
correct (see next)
>> Similar results for cytoplasmic dynein (see Mallik et al,
Curr. Bio, 2005)
More: see website bioweb.bio.uci.edu/sgross
Conclusion: motion in cells is
different from what might be
expected based on single-molecule
properties
We have three ‘systems’ level questions to understand:
 Cargos can move long distances
 Cargos can reverse course, move
bi-directionally
Cargo transport can be regulated
What single-molecule properties are
particularly important for how
multiple motors function together?
Cartoon of processive motion of a cargo
moved by two motors
From cartoon…
On-rate
Off-rate
Overall number of motors
Back of the envelope calculation for how
far 2 motors will go on average….
Assume single-motor processivity of 1200 nm, velocity of 800
nm/sec, on rate of 5/sec
1.
2.
3.
4.
5.
6.
7.
8.
First motor detaches at t0 . How long to rebind? T(rebind) ~ 1/Kon =1/5 sec.
Does second motor detach before first rebinds?
What is off rate? Processivity (mean travel): 1200 nm, vel 800 nm/sec
avg duration of run: 1200 nm/800 nm/sec=1.5 sec
Off rate: 1/avg duration = Koff= 1/1.5
Prob of second motor detaching is Koff*(rebinding time)=(1/1.5)*(1/5)= 0.1333
i.e. ~13% chance of failing to make it though cycle.
Adjust this to 26% (ignored second motor detaching right before first motor)
On avg make it through ~ 4 cycles.
Regulation: how?
From expression <X>= ½*(D/N)*(Kon/Koff)N-1
Kon: On-rate, i.e. rate at which single motor binds MT
Koff: Off-rate in time, i.e. rate at which single motor detaches
from MT
D=processivity, i.e. mean travel (distance) before detaching. Note
that Koff and D are NOT independent: Koff = V/D
V=Motor velocity
 can tune mean travel by altering N, Kon, or
Koff (V or D, or both).
Analytic Mean-field theory of average cargo travel
carried by two motors
p: binding rate (1/s)
e: unbinding rate (1/s)
d=v*(1/ ev/ e
Velocity: crucial initial condition
Klumpp and Lipowsky, PNAS, 2005
Experiment: established for single-motor study
Valentine et al., Nat. Cell Bio., 2006
Experiment: established for single-motor study
Valentine et al., Nat. Cell Bio., 2006
Experiment: difficult to interpret for more motors
?
Experiment: difficult to interpret for more motors
?
Experiment: difficult to interpret for more motors
?
Experiment: difficult to interpret for more motors
?
Experiment: modify surface chemistry for two-motor
Experiment: modify surface chemistry for two-motor
Position
Position
Experiment: force to further require two-motor
Time
Time
Experiment: clean one- vs. two-motor system!
d
D
Goal: Test
Strategy: reduce ATP to slow down motor
10M ATP
20M ATP
1mM ATP
Experiment: one-motor travel d
30
30
15
15
0
0
16
16
8
8
0
0
60
60
30
30
0
0.0
0.5
1.0
1.5
Velocity (m/s)
0
0
2
4
6
Travel (m)
8
10M ATP
20M ATP
1mM ATP
Experiment: two-motor travel D
16
20
8
10
0
0
20
14
10
7
0
0
12
12
6
6
0
0.0
0.5
1.0
1.5
Velocity (m/s)
0
0
2
4
6
Travel (m)
8
30
30
15
15
D
1mM ATP
1mM ATP
d
0
0
0.0 0.5 1.0 1.5 0 2 4 6 8
Velocity (m/s) Travel (m)
16
20
8
10
0
0
0.0 0.5 1.0 1.5 0 2 4 6 8
Velocity (m/s) Travel (m)
D=1.7d
Rogers et al., Phys. Chem. Chem. Phys, 2009
Velocity tunes travel distance for two-motor system
0
0
16
16
8
8
0
60
0
60
30
30
0
0
0.0 0.5 1.0 1.5 0 2 4 6 8
Velocity (m/s) Travel (m)
1mM ATP
15
16
20
8
10
0
0
20M ATP
15
D
20
14
10
7
0
10M ATP
1mM ATP
30
10M ATP
30
20M ATP
d
12
0
12
6
6
0
0
0.0 0.5 1.0 1.5 0 2 4 6 8
Velocity (m/s) Travel (m)
Motors work in small ensemble in cells
We establish velocity as a control for ensemble travel
May be particularly important, as beautiful work by Joanny
(Campas, et al, Biophys. J. , 2008) suggests a limited number of
motors (~ 9 max) can be active.
Hw #2 :
Model two kinesin motors functioning together, and then investigate
velocity effects.
In Hw #1 you developed a simulation for 1 motor. Here, stick two such
motors together. Assume initially that the motors here have the same
properties as in the previous hw.
The main goal here is to get the simulation working, and compare its
results for a few different choices of ‘on’ rates and ‘off’ rates to the
order-of-magnitude theory developed in class. How similar are the two
sets of predictions?
For a single motor with processivity of 1.2 microns, what is your
prediction for the mean travel of a cargo with two such motors,
assuming an ‘on’ rate of 2/sec or 5/sec. Do this assuming a velocity of
800 nm/sec, and a velocity of 100 nm/sec.
Velocity: the link between temporal and spatial
of individual motor unbinding from microtubule
Slower velocity buys more time for additional motor
to bind before the current bound one detaches.
(see Xu et al, Traffic, 2012)