ECE 795:

Quantitative ElectrophysiologyNotes for Lecture #5Friday, October 17, 2008

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9. THE NEUROMUSCULAR JUNCTION

We will look at:

Structure of the neuromuscular junction

Evidence for the quantal nature of transmitter release

Poisson statistics for transmitter releaseThe effect of Ca++ and Mg++ on transmitter release

Post-junctional response to transmitter

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Structure of the neuromuscular junction:Studying the structure and function of the neuromuscular junction is useful for understanding:

some general principles of chemical synapses, andthe specifics of skeletal muscle activation.

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Structure of the neuromuscular junction (cont.):Motor nerve axons are normally myelinated, except at their terminals where they branch and synapse onto muscle fibers. The set of muscle fibers activated by a single motor neuron is known as a motor unit.

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Structure of the neuromuscular junction (cont.):The nerve terminal contacts the muscle fiber at an end plate.The pre- and post-synaptic membranes form a specialized “gutter”.

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Structure of the neuromuscular junction (cont.):The pre- and post-synaptic membrane formations are similar to nerve-to-nerve chemical synapses, except for the synaptic gutter.

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Structure of the neuromuscular junction (cont.):Muscle fiber end-plate potentials (EPPs) are equivalent to excitatory postsynaptic potentials (EPSPs) in neurons—note that they are always excitatory.

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Structure of the neuromuscular junction (cont.):The neuromuscular junction transmitter is acetylcholine (ACh).A model of the ACh

receptor is shown to the right.Channel opening requires binding of ACh

with both α

subunits.

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Evidence for the quantal nature of transmitter release:

In the absence of stimulation of the presynaptic nerve, miniature end-plate potentials (MEPPs) of around 0.5 mV are observed.EPPs produced by presynaptic nerve stimulation always have amplitudes that are integer multiples of the MEPP amplitude⇒ transmitter release is quantal

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Poisson statistics for transmitter release:Suppose there are n

presynaptic release sites and

that the probability of release at any site is p, where p

depends on the presynaptic

transmembrane potential and the concentration of Ca++, Mg++

and other ions.

The probability of exactly x

of n

releases is given by the binomial distribution:

where q

= 1 −

p.

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Poisson statistics for transmitter release (cont.):In the case where n

→∞, p

¿ 1 and x

¿ n, then

the binomial distribution is well approximated by the Poisson distribution:

where m

= np

is the mean release rate.

Note that the variance in the number of events (e.g., synaptic releases) for a Poisson process is equal to the mean.

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The effect of Ca++ and Mg++ on transmitter release:Decreasing the concentration of extracellular Ca++

or elevating the concentration of Mg++

has the

effect of reducing p.The reason is that the pre-junctional nerve terminal has many voltage-gated Ca++

channels, which

facililates Ca++

entry near the ACh

release sites.

It is actually binding of intracellular Ca++

to

proteins in the release site that triggers exocytosis and neurotransmitter release. Mg++

can block the

Ca++

channel, which reduces neurotransmitter

release.

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Post-junctional response to transmitter:The postsynaptic membrane has an ACh

receptor density of around 104/μm2, which is an order of magnitude greater than the density of sodium and potassium channels in squid axon.To simulate the effects of transmitter binding to the post-synaptic receptor, a parallel- conductance model can be created where a mixed potassium, sodium and chloride channel is opened when ACh

binds to the

receptor.

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Post-junctional response to transmitter (cont.):For the frog neuromuscular junction:

gCl ≈ 0

gNa/gK

≈ 1.29

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Post-junctional response to transmitter (cont.):The synaptic membrane model can be simplified to a single ionic current with conductance gs

and reversal potential Es

. Since Es

> Er

, the synapse is excitatory.

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10. SKELETAL MUSCLE

We will look at:

Muscle structure

Muscle biomechanics

Muscle electro-chemical function

EMG measurement and interpretation

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Muscle structureOrganization:– skeletal muscle is

made up of muscle fibers

– each fiber is a single cell

– the contraction of a fiber is achieved by the motor proteins actin & myosin

(from Guyton and Hall, 10th

Edition)

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Fiber orientation:– muscles that undergo

large length changes or high velocities usually have long fibers running lengthwise

– muscles that undergo only small length changes but are required to produce large forces or stiffness have fibers arranged at an angle to the tendons to which they are attached

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Muscle fiber innervation:

1. Motor neuron2. Peripheral nerve3. Neuromuscular junction4. Muscle

Motor unit:A motor unit is defined as an individual motor neuron plus all the muscle fibers that are innervated by that neuron.

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Neuromuscular junction:

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Steps in muscle fiber contraction1. Motor neuron action potential2. Action potential propagation along motor axon

(myelinated fiber)3. Transmission of acetylcholine (ACh) at

neuromuscular junctions (synapses)4. Action potential generation in muscle fiber5. Release of Ca2+

from sarcoplasmic reticulum

initiates attractive forces between actin & myosin filaments, causing them to slide alongside each other ⇒ muscle contraction

6. Return of Ca2+

to sarcoplasmic reticulum,

ending muscle contraction

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Actin & myosin filament movement:

(from Guyton and Hall, 10th

Edition)

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Fiber types

1. Fast twitch– large fibers, for greater contraction strength

– extensive sarcoplasmic reticulum for rapid release of Ca2+

– large amounts of glycolytic enzymes

– less extensive blood supply

– fewer mitochondria

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2. Slow twitch– smaller fibers

– innervated by smaller nerve fibers (axons)

– more extensive blood vessel system

– more mitochondria

– large amounts of myoglobin, speeding oxygen transport

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Muscle fiber mechanics

The main factors in determining muscle fiber contractile force are:

1. Velocity of contraction

2. Length of muscle fiber (relative to its resting length)

3. Neural activation

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Force versus velocity:

where F

is the contractile force (N), v

is the contractile

velocity (lengths·s-1), and F0

, a

& b are constants.

F0

corresponds to the force when v

= 0, i.e., during an

isometric contraction.

vmax

= bF0

/a, when F

= 0.

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Force versus velocity (cont.):Often the stress value (P0

= F0

/A) is used instead of F0

, where A

is the “physiological cross sectional area” obtained by dividing the muscle volume by its length.

P0

is generally between 100 and 300 kPa, and does not depend on the metabolic fiber type (fast or slow twitch).

However, vmax

depends on the fiber type.

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Force versus fiber length:

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Force versus fiber length (cont.):

(from Guyton and Hall, 10th

Edition)

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Force versus activation:– individual motor neuron

action potentials produce a contractile force in a motor unit referred to as a “twitch”

– twitches begin to fuse as the action potential frequency increases

– above the “fusion frequency” the motor unit produces its maximum (“tetanic”) force

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Force versus activation (cont.):The total muscle force is modulated by:– the frequency of twitches in each of a

muscle’s motor units ⇒ rate coding

and

– the number of motor units being activated ⇒ recruitment

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Hill’s model:

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Muscle electro- chemical function:Each fibril is surrounded by:

a sarcoplasmic reticulum (SR), which stores Ca2+ for triggering muscle fiber contraction, andthe transverse tubules system (TTS), which ensures that action potentials propagate deep into the fiber.

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Muscle electro-chemical function (cont.):The TTS and SR are crucial for synchronized contraction of all fibrils in skeletal myocytes and mammalian cardiac myocytes.

(Song et al., Ann. N.Y. Acad. Sci. 2005).

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Muscle electro-chemical function (cont.):Organization of key channel and transporter proteins and SR structures, including the junctional SR (JSR), near the TT —

(Song et al., Ann. N.Y. Acad. Sci. 2005).

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Muscle electro-chemical function (cont.):The release of Ca2+

to trigger contraction of

fibrils is facilitated by two different types of Ca2+

channels:

1. dihydropyridine receptors (DHPRs) or L- type Ca2+

channels, and

2. ryanodine receptors (RyRs).

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Muscle electro-chemical function (cont.):L-type Ca2+ channels are voltage-gated and appear on the TT and sarcolemmal(SL) membrane. These are opened by Na+ action potentials, allowing Ca2+ to flow into the intracellular space near the JSR.Reception of Ca2+ by RyRs opens up Ca2+ channels in the JSR membrane allowing release of Ca2+ from the SR. This leads to a positive feedback loop of Ca2+ release, triggering fibril contraction.

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Measuring muscle forces– strain-gauge tendon transducers

problem: invasive

– derivation from kinematics and external forces problem: often the system of equations is indeterminate, e.g., several flexion and/or extension moments but only one moment equilibrium equation

– electromyography (EMG): problem: EMG is usually the sum of several motor unit action potentials ⇒ difficult to interpret

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EMG measurement and interpretation:

Dynamic Isometric

(Berger et al.)