BB101 Lecture 3-4 - SM

Nerves and Communication

S. Mukherji, IIT-Bombay ([email protected])

Who Are They What brings them together?


Who Are They What brings them together?

Amyotrophic Lateral Sclerosis (ALS) aka Lou Gehrig's disease.

Muscle weakness and atrophy throughout the body due to the degeneration of the upper and lower motor neurons

Parkinson's disease aka paralysis agitans) is a degenerative disorder of the central nervous system. death of dopamine-generating cells in the substantia nigra,

most obvious symptoms are movement-related .. .. thinking and behavioral problems may arise

Alzheimer's disease (AD) is the most common form of dementia. Early stages, the most common symptom is difficulty in remembering recent events. Later confusion, irritability, aggression, mood swings, trouble with language, and long-term memory loss. Even later bodily functions are lost, ultimately leading to death


Muscle cells and Nerve cells - Specialists

The muscle cell has made contraction its specialty. Its cytoplasm is packed with organized arrays of protein filaments, including vast numbers of actin filaments and mitochondria.

The nerve cell stimulates the muscle to contract, conveying an excitatory signal to the muscle from the brain or spinal cord.

Schwann cells are specialists in the mass production of plasma membrane, which they wrap around the elongated portion of the nerve cell, laying down layer upon layer of membrane like a roll of tape, to form a myelin sheath that serves as insulation.


Features of the Nerve Cell

The nerve cell has to be extraordinarily elongated

o After all it is carrying a signal from the brain to a far off muscle.

o The main body, containing the nucleus, may lie a meter or more from the junction with the muscle.

The cytoskeleton has to be well developed so as to maintain the unusual shape of the cell and to transport materials efficiently from one end of the cell to the other.

The plasma membrane, which contains proteins that act as ion pumps and ion channels, causing a movement of ions that is equivalent to a flow of electricity.

o All cells contain such pumps and channels in their plasma membranes, however the nerve cell has exploited them in such a way that a pulse of electricity can propagate in a fraction of a second from one end of the cell to the other, conveying a signal for action.


Membrane proteins in the lipid bilayer

Ref. Quantitative Human Physiology by Joseph Feher


Ionophores and Voltage/Ligand Gated Channels



Concentrations of Na, K and Ca and resting membrane potential across muscle cell membrane

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The Nernst Equation

The Equilibrium Potential across a membrane arises from the balance between electrical forces and mechanical (i.e. diffusion) forces.

We can derive it either from the Ficks laws of diffusion or from the energetics point of view.

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For sodium ions at 37 C this translates to 61.5 mV per decade gradient.


What if there are multiple ions

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From Ficks Law with an electrical force

Goldman-Hodgkin-Katz current equation

We can derive the voltage equation from this

Nernst-Planck Electrodiffusion Equation


Goldman-Hodgkin-Katz Equation

Earlier we assumed a hypothetical membrane through which only one type of ion can pass through but life is not so simple..

o Many other ions are also present and some of them may also pass

o Membrane permeability to ions may be time varying.

An outcome of integrating the Nernst-Planck Electrodiffusion Equation gives the Goldman-Hodgkin-Katz Equation

oCliNaiK

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]Cl[P]Na[P]K[P

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Equilibrium potentials for Na, K, and Cl in a muscle cell

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Conductances to Ions

The GHK current equation describes current carried by any ion, given its concentration on two sides of a membrane and the membrane potential.

At the equilibrium potential for each ion there is no current due to that ion (reversal potential).

Following Ohms law and noting that the reversal potential is non-zero we can say that for chord conductance gi :

Similarly the slope conductance g is :

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Currents carried by K+(left) and Na+ (right) as predicted by the GHK current equation if the membrane were permeable only to K+ or to Na+

Ref. Q

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Balance of forces driving Na+ movement

Ref. Q

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Transduction and Transmission of Stimulii

Ref. Q

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Measuring the Membrane Potential and Stimulating it

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Effect of Hyperpolarizing and Depolarizing stimulii of varying intensity on the axon membrane potential, Em

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When the strength of depolarization reaches beyond a threshold it does not matter any more .. It generates an action potential.. The shape of which is approximately the same. However latency might change.


Effect of stimulus strength (above threshold) on Latency

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Once an action potential is generated, it can be seen at points away from the point of origin.. This is called propagation. At points a bit away the AP-s are indistinguishable.

Near the origin there can be certain differences that have to do with how fast Em reaches the threshold (since Em is not an exact duplicate of the stimulating potential capacitance effects)


Changes in gNa and gK during the propagated action potential as calculated by Hodgkin and Huxley

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Cl

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Hypothetical model of the voltage-gated tri-state Na+ channel

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Tetrodotoxin or TTX- binds to Na+ channels and blocks them.

Saxitoxin also has similar effects


Changes in the Na+ and K+ channels that give rise to the action potential



The appearance of the action potential at later times down the axon from the point of stimulation

Ref. Q

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Depolarization Can Spread passively

Ref. Q

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Electrotonic Spread of the Action Potential

The Hyperpolarizing or Depolarizing stimulii are not faithfully reproduced in the axon the signal is distorted due to the cable properties of the neuron.


If we pass a constant current across the membrane between any two nodes (lets say A and B), a new membrane potential is established (Em).

At some point x away from A or B, the membrane potential Ex will depend on the distance from the current source and the time since the current was turned on.

The capacitances and the resistances due to the membrane are in parallel.

where Rm is the resistance of a patch of membrane of unit area.

The axon cable can be considered to be a conductor and resistance equation holds. However the external solution has very large (undetermined) cross sectional area .. So effectively Ro is zero.

A

RR m


Currents at a unit membrane area of membrane

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radius theis where.2 Using

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Currents at a unit membrane area of membrane (2)

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through law sOhm' Using

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At steady state, when dV/dt = 0, the space constant defines the way in which voltage varies with distance


Currents at a unit membrane area of membrane (3)

At steady state, when dV/dt = 0, the space constant defines the way in which voltage varies with distance.

dV/dt = 0 can happen when a constant current has been passed through the membrane for a time long enough to charge all the capacitors. In such a case the earlier equation

i.e. the voltage falls off exponentially from the point of application

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Steady-state voltage as a function of distance from the point of injection in myelinated and unmyelinated nerve fibers

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mm

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Saltatory Conduction

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What happens if the myelin sheath degrades or is lost ?


Electrically-coupled calcium signaling


Ligand-gated ion channels


Motor Neurons

Activates skeletal muscles

Receives thousands of inputs from other cells

o Upon excitation the presynaptic cell releases a neurotransmitter that binds to the post synaptic cell and modulates ligand gated ion channels.

o Neurotransmitters can be ionotropic i.e. directly alter ion conductances or metabotropic that affect other targets which in turn affect ion conductances.

Postsynaptic potentials can be Excitatory (EPSP) or Inhibitory (IPSP)

o Excitatory may work through increasing the Ca channel conductance

o Inhibitory might work by increasing K or Cl channel conductance.

AP-s in motor neurons originate in the Axon Hillock

Motor Neurons integrate multiple inputs to initiate AP-s


Spatial and Temporal summation in a Motor Neuron


Conduction of Impulses from Nerves to Muscles

Motor Neuron 1 innervates Muscles fibers A, B and C.

Motor Neuron 2 innervates D and E.

The motor neurons can fire independently or together. In the latter case, larger force is generated.


Fig. 3.5.2. Electron Micrograph of Muscle

A Anisotropic I- Isotropic H Helles (clear) Z Zwischen (between) M - Middle


Microscopic Appearance of Muscle

A - Anisotropic I - Isotropic H - Helles (clear) Z - Zwischen (between) M - Middle


Structure of the Sarcoplasmic Reticulum around the myofibril


Structure of the neuromuscular junction


Release of acetylcholine at the neuromuscular junction


Duration of action potential, Ca transient and force in a twitch

BB101 Lecture 3-4 - SM

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