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Lecture # 14: Biological Actuators II
electro-mechanical coupling
Ca 2+
Ca 2+
Ca 2+ Ca 2+
ATPase
Ca 2+
Ca 2+
Ca 2+
diffusion
sarcoplasmic reticulum
muscle
force
motor neuron spike
How are muscles controlled?
individual
muscle
fiber
(muscle cell)
motor units
(=motor pools)
motor unit =
one motor neuron and all the
muscle fibers it controls
Two means of control:
synapse
spinal
chord
motor
neurons
muscle
nerve
(=many
neurons)
1) Recruitment
activate increasing number
of motor units
2) Frequency
drive each motor unit at
higher frequency
Measuring muscle properties
1) isometric conditions
‘twitch’
Measure
force
fast
onset
Slow
offset
force
stim
delay (~ 1 ms)
stimulate
nerve
peak
isometric
force
set
length
force
stim
tetanus
summation
tetanic
frequency
Measuring muscle properties
1) isometric conditions
measure peak tetanic force as
a function of resting length:
with
stimulus
F0
3) measure
force
2) stimulate
at tetanus
passive
properties
(J-shaped)
length
1) set
length
~ resting
length
F0
active
properties
length
Measuring muscle properties
2) isotonic conditions
3) measure
length
fulcrum
2) remove
stop
pull against load
with constant
velocity
mass
1) stimulate
to tetanus
low force
force
set by
mass
shortening
length
high force
force
stim
remove
stop
Measuring muscle properties
2) isotonic conditions
shortening
peak isometric
F0
Power
= force x velocity
Force, F
pull against load
with constant
velocity
length
Vmax
force
stim
remove stop
Force-Velocity equation
is well fit by Hill EQ:
velocity that
maximizes
power
Velocity, V
(F – a) (V + b) = (F0 + a) b
a = constant with units of force
b = constant with units of velocity
contracting
against inertia
Measuring muscle properties
extensor
stress
3) work loop conditions
flexor
strain
3) measure
force
strain
(length)
stress
(force)
stim
2) stimulate
In phase
1) oscillate
muscle
Measuring muscle properties
3) work loop technique
RK Jospehson
strain
(DL/L)
stress
(F/A)
Measuring muscle properties
3) work loop conditions
Muscle do not have to work as motors to function.
slope = stiffness
stress
changing
activation
phase
strain
diversity of muscle function
direct vs indirect flight muscle
electro-mechanical coupling
Ca 2+
Ca 2+
Ca 2+ Ca 2+
ATPase
Ca 2+
Ca 2+
Ca 2+
diffusion
sarcoplasmic reticulum
muscle
force
motor neuron spike
high frequency
d u d u d
~1000
wing beat
frequency
low frequency
force in
downstroke
muscle
down up
~10
gnat
locust
size
down up
down up
synchronous muscle
sarcoplasmic
reticulum
Bob Josephson
asynchronous muscle
(beetles)
(ants, bees, wasps)
(flies)
after Dudley, 2000
synchronous vs. asynchronous muscle
synchronous (locust)
wing
motion
stimulated
passive
muscle
spikes
asynchronous (beetle)
wing
motion
muscle
spikes
Josephson, 2000
Stretch
Activation
stimulated
passive
How do flies regulate power?
Lehmann & Dickinson, 1997
variation
in power
Lehmann & Dickinson, 1997
Sheffy Gordon
mann & Dickinson, 1997
Ca2+ regulation hypothesis
Flight
power muscle control
high
spike rate
Low Ca2+
muscle
length
motor
neuron
High Ca2+
low
spike rate