Neuromuscular integration
Tom Burkholder
thomas.burkholder@ap.gatech.edu
4-1029
Weber 123
http://www.ap.gatech.edu/burkholder/8813/
Learning goals
• Technical
–
–
–
–
Frog anatomy
Muscle mechanics
Force transducer
Feedback control
• Conceptual
– Muscle physiology
– Proprioceptors
– Sensorimotor integration
Develop a closed loop hybrid system to investigate some
aspect of neuromuscular control. Ideally, the structure or
parameters of the computational system will test a model of
biological control
References
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Gasser HS and Hill AV. The dynamics of muscular contraction. Proc R Soc
Lond (B) 96: 398-437, 1924.
Rack PM and Westbury DR. The effects of length and stimulus rate on
tension in the isometric cat soleus muscle. J Physiol (Lond) 204: 443-460,
1969.
Nichols TR and Houk JC. Improvement in linearity and regulation of stiffness
that results from actions of stretch reflex. J Neurophysiol 39: 119-142, 1976.
McCrea DA. Spinal circuitry of sensorimotor control of locomotion. J Physiol
533: 41-50, 2001.
Lutz GJ and Rome LC. Built for jumping: the design of the frog muscular
system. Science 263: 370-372, 1994.
Rome LC, Swank D, and Corda D. How fish power swimming. Science 261:
340-343, 1993.
Chizeck HJ, Crago PE, and Kofman LS. Robust closed-loop control of
isometric muscle force using pulsewidth modulation. IEEE Trans Biomed
Eng 35: 510-517, 1988.
Control of Motion
•
•
•
•
Phylogenic background
Motor proteins
Muscle properties
Control systems
Protista motility
• RNA Polymerase
• Mitosis
• Swimming
– Flagella
– Cilia
• Crawling
– Rolling
– Pseudopod formation
• Chemotactic
• Receptor mediated activation of myosin
Nematodes
• Large scale swimming
– Cyclical
– Force/motion phase
Muscle activation
• Specialized organs
– Sensors
– Motors
– Wiring
• Complex behavior
– Avoidance
Muscle activation
Insect Flight
• Indirect flight muscles
• Activated less than once per cycle
• Molecular kinetics
• Springlike, but positive work
• Stretch activation
Active force
1
100
0
DL (mm)
Force (mN)
A
3
5
Passive force
100 kN m -2
500
0
0.2
0
5%
Stimulation
0
100
200
300
Time (ms)
400
Applied length
50 ms
Mammalian locomotion
• Multiple limbs
• Ballistic
Muscular work during gait
• Positive work
• Passive elastic mechanisms
Daley, M. A. et al. J Exp Biol 2003;206:2941-2958
Terrestrial posture
• Support body against gravity
• Perturbation control
– External (wind)
– Internal (respiration, muscle)
• Small movements
Motor proteins
• Kinesin, dynein, myosin
• Globular head
– Filament binding & ATPase
• Cargo-carrying tail
Kinesin
Myosin
Myofilament structure
• Myosin polymers arrange motor domains to
maximize interaction with actin filament
200 nm
Structural homogeneity
• Structural order yield functional consistency
– Narrow range of sarcomere “strength”
– Minimizes intra-muscular force loss
Sliding filament theory
• Force varies in proportion to crossbridge
binding
Z I
A
I
Crossbridge cycle
• ATP driven, ratchet motion
• Mechanochemical coupling by crossbridge
elasticity
Crossbridge Cycle
Hydrolysis of ATP
energizes myosin;
moves crossbridge
ATP binding to
myosin displaces
actin
Energized myosin
binds actin
Myosin binds actin
strongly (rigor)
Release of inorganic
phosphate triggers
power stroke
Fundamental reactions
• Actin-myosin association
– Slow (20 ms)
– All or none change in force
• Power stroke
– Fast (1 ms)
– Modulatory
A rapid shortening pushes
crossbridges through the power
stroke. These crossbridges rapidly
accommodate the change and are
slowly displaced by new
crossbridges
Isotonic shortening
• Muscle can shorten against less load than it
can hold.
• Stimulate muscle
• Allow force to stabilize
Magnetic
catch
• Release against
constant load
Counterweight
Muscle
Dynamic response of muscle
• Isotonic force velocity relation
• Stretch and hold response
Vmax  v
P  P0
P0
Vmax 
v
a
1.8
1.6
1.4
100
00
Force
Force response
500
0
0.2
0
(mm)
L
D 0
1.2
Po
1.0
0.8
0.6
Force (mN)
0.4
100
200
300
Time (ms)
400
Applied length
0.2
0.0
-0.5
0
0.5
Shortening Velocity
Vmax
1
Engineering analog
• “Force-length” is like stiffness
• “Force-velocity” is like viscosity
F=kx
Force
F=Fo-bv
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0-0.5
Po
0
0.5
Shortening Velocity
Vmax
1
Phenomenological (Hill) Model
• Linear model
– Force-length spring constant
– Force-velocity viscosity
• Standard linear solid analogy
– Contractile Force-length
– Contractile Force-velocity
– Elastic elements account for dynamics
Control of activation
• Troponin/tropomyosin complex
– Bind actin
– Block myosin
– Calcium dependent
Calcium control
• Contractile dynamics are calcium dependent
• Efficient contraction requires homogeneous
calcium transients
• Sarcoplasmic reticulum
• T-Tubules
Excitation contraction coupling
•
•
•
•
•
Synaptic discharge initiates action potential
V-gated Ca2+ channels open
Ca2+ bind TnC
Force generation
Action potential
Recovery
Calcium
Force
Force summation
• Nonlinear addition of subsequent APs
Force Frequency
• Muscle & species dependent
• Myosin kinetics
• Calcium kinetics
Whole muscle organization
• Physical
–
–
–
–
Fiber
Fascicle
Muscle
Agonist
• Neural
–
–
–
–
Motor unit
Compartment
Muscle
Synergy
Motor Unit
• Alpha motorneuron
– Large (12-20 um)
– High CV (70-120 m/s)
MN
• Innervated muscle fibers
– 10-1000 fibers/neuron
– Generally proportional to axon size
– Generally of similar function
• 5-1000s per muscle
Innervated fibers
Whole muscle force modulation
• Rate
– Force-frequency
– Continuous control
• Recruitment
–
–
–
–
Select subpopulation of MU
Force sharing
Metabolic optimization
Size principle
Motor unit control
• Smooth force
generation
– Individual MUs subtetanic
– Rate & phase
variation
Electrical stimulation
• Recruitment
– Axonal input resistance
– Capacitance
• Synchrony
• Recruitment modulation
– Intensity
– Pulse width
– High frequency block