Transcript 1. Biophysics of the Nervous System

BIOPHYSICS OF THE NERVOUS SYSTEM
Prof. Dr. Metin TULGAR
A General View to
the Nerveous System
There are billions of cells in the nervous system.
Of course, it is essential to know the nerve cells
to understand the underlying construction and
mechanisms of the system.
But, to avoid missing the actual whole system,
better to start with a general view.
We must be aware of the forest first, before we see only one tree.
Its duties:



Take care of the body,
Protection of the body,
Functions of the body.
Its product:

Performance of the body (behaviour of man)
Since it has such important responsibilities,
it is normal that it has a complicated structure.
Functional Organization of the Nervous System
the nervous system
central nervous system
peripheral nervous system
(CNS)
(PNS)
efferent pathways
afferent pathways
autonomic system
somatic system
(involuntary)
(voluntary)
“visceral motor neurons”
“musculoskeletal”
parasympathetic nerves
sympathetic nerves
Anatomy and Physiology of the Nervous System
brain
sensory
cortex
III
thalamus
spinoreticular tract
II
PNS
action potential
receptor
I
CNS
synaps
e
peripheral nerves;
interneuron
cervical – 8 pairs,
thoracic – 12 pairs,
lumbar – 5 pairs,
sacral – 5 pairs,
cocygea – 1 pairs,
in total – 31 pairs.
Nerve Cells
 Glia
 Neuron
Glias
smaller in size compared to neurons,
but they are 10 times greater in number.
Half of the brain is covered by glias.
Their functions are not exactly known; however, it is
clear that they provide constructional support for the
neurons by means of Schwan cells producing myelin.
There are two sorts of glias, in general:

astrocytes

Oligodendracytes
Glial cells help neurons stay healthy. If neurons are
dying, restoring glial cells could be the key to survival
As known, there are billions of cells in the human body,
and every single neuron has an electrical activity
as long as it is alive.
The basic difference between glias and other cells is that
the neurons, under cirtain circumstances, are able to
conduct their electrical activity to neighbouring neurons.
Consequently, neurons are considered as functional units
of the nervous system.
Glial Cell Types by Location
and Basic Function
Basic
CNS glia
PNS glia
function
Astrocyte
Satellite cell Support
Insulation,
Oligodendrocyte Schwann cell
myelination
Immune
surveillance
Microglia
and
phagocytosis
Ependymal cell
-
Creating CSF
The Neuron
composes of two morphological region:

1) soma,

2) fibre;


I) axon
II) dendrites.
soma
axon
dendrite
receptor
Somas are called as laminae in the cortex
and cerebellum of the brain, and ganglion
outside the central nervous system.
Laminas are located in the form of sheets,
ganglions in wide nodules.
These groups form grey matter in the brain
and butterfly or H-shaped forms in the
middle region of spinal cord.
In the rest of places of the central nervous
system, they form white matter.
Axon is a single fiber.
Their length depends on the location,
sometimes being longer than 1 m.
Axons conduct nerve impulses.
In the brain,
there are about 10 billions of axons,
and in the dorsal column,
more than 1 million.
An axon can be resembled to a cylindirical tube.
Intracellular fluid (axoplasm) is separated from
the extracellular fluid by a very thin membrane.
extracellular fluid
intracellular fluid (axoplasm)
membrane
In the end of axons,
there are receptors
which are bare nerve endings.
Diameters of axons: 0.5 - 20 μm
In myelinated axons;
conduction velocity is approximately
proportional to the diameter:
v~D
In the non-myelinated fibers;
with square root of the diameter:
v ~ √D
Classification of Axons
type
diameter (μm) conductivity (m/s)
A-α
12 - 20
70 - 120
A-β
5 – 12
30 – 70
A-γ
“thick myelinated” “rapidly conducting”
3–6
“thin myelinated”
15 - 30
function
somatic motor
connected to low-threshold receptors
(sensitive to light mechanical stimuli)
motor neuron connected to muscle spindles
(sensitive to cold, pinprick and needling)
A-δ
2-5
12 - 30
B
<3
3 - 15
preganglionic autonomic
C
0.3 – 1.3
0.7 – 2.3
post ganglionic autonomic
C
0.4 1.2
0.5 – 2
connected to high-threshold receptors
“slowly conducting”
(responsible for pain transmission)
Myelin
A lipid substance covering the axon along the membrane.
It is not contineuosly located, there are gaps of 1-2 μm called
Ranvier nodes in every 1-2 mm.
Functions like a kind of electrical isolator to increase capasitive
effect of the neuron, and also its conductivity.
In accordance with the equation,
XC = 1/ωC = 1 /2πfC
as the myelin gets thicker, capasitive reactance decreases.
Considering Ohm’s Law;
i = V/XC
the conductivity of axon for transmitting of nerve impulses
increases.
Dendrites
short branches along the axon.
Numerous in number.
They increase the surface of the neuron to
facilitate the communication with
neighbouring neurons.
Some neurons have dendritic contacts of up
to 60000.
Synapse
Sherrington & Lord Adrian, 1921
Nobel Price in Medicine
a very narrow gap (200 - 300 Å)
between two neurons.
provides the connection for nerve
impulses to be transmitted.
During this transmission,
active neuron sending signal is called
presynaptic neuron, and passive one
receiving signal is postsynaptic neuron.
Classification of Synapses

according to anatomical construction

according to physiological mechanism

according to effect of synaptic activity
Anatomical Classification of Synapses

1) axosomatic synaps (between axson and soma)

2) axsodendritic synaps (between axson and dendrit)

3) axoaxonic synaps (between two axons)
These are most common, and play role in the transmission
of action potentials.

4) dendrodendritic synaps (between two dendrits)
Only in the central nervous system.
Physiological Classification of Synapses
In 1930s, there have been various arguments on the synaptic
transmission mechanisms between physiologists and
pharmacologists.
Physiologists put forward that synapses transmitted electrically,
whilist pharmacologists considered chemical basis.
After improvement in physiological technics, in 1950s and 1960s,
it was understood that the underlying mechanism of the synaptic
processes is not only a single mechanism; both chemical and
electrical activities were effective (Eccles and et al.).

Chemical Synapses

Electrical Synapses
Chemical Synapses
During transmission, active neuron releases a
chemical substance called neurotransmitter onto the
surface of passive neuron.
These neurotransmitters including acetylcoline,
noradrenaline, dopamine and serotonine are stored
in the synaptic vesicles of 300 - 600 Å on the nerve
endings of presynaptic terminals.
Chemical transmission occurs in two stages:
presynatic and postsynaptic.
At presynaptic stage, a chemical transmitter is released by
presynaptic neuron; postsynaptic procedure covers the effect of
the neurotransmitter by receptors of the post synaptic neuron.
Postsynaptic mechanism is based on increase or decrease of
permeability of the membrane against one or more ion species.
Synaptic activities resulting from the increased permeability of
the membrane are more common.
There is a narrow gap of 30 nm
between pre and post synaptic neurons.
Transmission in chemical synapses is slower
than that in electrical synapses.
Electrical Synapses
In some neurons, e.g. in cerebral cortex,
there are no bubbles, and the synaptic gap is
bridged by thin fibres. For this reason,
electrical synapses are also called
bridged synapses.
A connection between cytoplasms of presynaptic and post-synaptic neurons has been
established by thin fibers.
The distance between pre and post
synaptic terminals is 20 nm (20 Ǻ);
this is less than that of chemical synaps
by 10 nm.
Transmission of electrical synapses,
that is very fast, results in synchronized
activation of a group of neuron.
Electrical synapses are effective in
stimulating of extraocular motor neurons
which are responsible for stereotypical
behaviours such as fast eye movements.
Classification of Synapses
According to Synaptic Activity
Depending on the type and effect of the
neurotransmitter released by the active neuron
during the transmission on passive neuron;
excitatory
synapses
(depolarization)

inhibitory
synapses
(hyperpolarization)

Membrane Traffic
In a neuron,
ions (Na, K, Cl, Ca) and organic substances (aminoacids,
proteins) are much more than those in sea water
and blood.
The membrane is semipermeable,
because channels are present along the
neuron.
These channels are called ionic channels.
There are two kinds of ionic channels:

open channels
non-gated channels
passive channels
provide a pathway for
ionic diffussion

Closed channels
gated channels
active channels
control of the gate depends on
the intensity of physical stimuli
at receptor level and
effect of neurotransmitters in
synaptic terminals.
Na
extracellular fluid
intracellular fluid (axoplasm)
K
open
channel
gated
channel
The behaviour of the channels to ions are selective,
but not ideally selective.
e.g. a K channel allows 1 Na ion to pass through per 12 K ions.
Permeability of the membrane against K and Cl ions is high,
but it is low against Na ions.
Permeability rates:
PK / PNa / PCl ~ 1 / 0.04 / 0.45
So, the membrane is 25 times more permeable against
K ions compared with that against Na.
The velocity of ions as they pass through the channels
are different.
Experimental sudies undertaken in the same conditions applying
1 V/cm, showed that movement speed for Na ions was 5 μm/s
and 8 μm/s for K. These results were found surprising.
Because, Na ions, which are smaller in size,
are expected to move faster.
These unexpected results were explained based on hydratation factor.
The functional sizes of more hydralized Na ions increases;
that’s why they move slower.
Active Sodium – Potasium Pump
Ionic concentrations of the extracellular and intracellular fluids are
different.
Outside the cell, concentration of Na ions are high, whilist
potasiums are more intensive in the inside.
So, Na ions tend to diffuse into the cell, as K ions want to go out.
This passive diffussion is not out of control.
If it was so, the internal and external concentrations of Na and K
ions would eventually be in balance, and
in the end ionic traffic would stop.
Such a result means that biopotentials goes to zero, thus the cell
and organism composed of the cells dies.
For the liveliness to continue, various physiological mechanisms,
particularly active methabolic Na-K pump,
control internal and external concentrations.
The action of this pump is in the opposite direction with passive
leakage currents.
Therefore, the concentrations of Na and K ions are kept at a
certain level, by sending excessive ions back.
The pump is electrical in character; it sends 3 Na ions back to the
outside of the neuron, and 2 K ion back into the neuron.
Because passive currents are equal to a few hundred times of
the currents carried by the pump, when an impulse is formed, 1 s
or more time is necessary for the ionic balance to be restored.
The Resting Membrane Potential
The difference between internal and external chemical
concentrations results in a chemical gradient across the neuron.
Because ions are charged, an electrical gradient is also formed.
As a result, an electrical potential difference across the
membrane occurs, inside the cell being more negative compared
with the outside.
+
-
60 – 70 mV
This potential difference is, in general, called membrane
potential.
As the neuron is in rest, it is called the resting membrane
potential.
When the neuron is stimulated by a physical stimuli, it is called
depolarized membrane potential.
The resting membrane potential is usually around – 90 mV,
and it rarely exceeds – 100 mV.
Ionic Balance
Mathematical analysis of ionic traffic
through the membrane has been done
to get numerical values for ionic balance.

Nernst equation

Goldman equation
Nernst Equation
In case of ionic balance, the membrane potential defined by Nernst;
RT
[iyon]o
Vm = ------- ln ----------FZ
[iyon]i
where;
R: universal gas constant (8.31 j/mol)
T: absulate temperature
t: temperature of medium in ºC
T = 273 + t
F: Faraday constant (96500 c/mol)
Z: valence value of the ion analysed
If Nernst equation is applied for K ions;
8.31 (273 + t)
[K]o
Vmk = ------------------- ln -------96500 x 1
[K]i
at room temperature,
t = 37 ºC
the ratio of external and internal concentrations of K ions,
[K]o
1
-------- = -----[K]i
20
Therefore,
8.31 (273 + 37)
1
Vmk = -------------------- ln ----96500 x 1
20
Vmk ~ - 80 mV
This result means that, if membrane potential is made – 80 mV,
K ions will be in balance, and they will not be able to move across
the mambrane.
This rule is valid in voltage clamp technique which is used for
balancing certain ions.
So, net potential electrical effect on K ions to prevent their leakage:
V*K = Vm – Vmk
If the resting membrane potential is accepted to be -60 mV, then
V*K = - 60 – (- 80) = 20 mV
This means that the electrical effect forcing K ions to move
across the membrane is to be less than 20 mV.
In a biological membrane, the Reversal
potential (also known as the Nernst
potential) of an ion is the membrane
potential at which there is no net (overall)
flow of ions from one side of the
membrane to the other.
In the case of post-synaptic neurons, the
reversal potential is the membrane
potential at which a given neurotransmitter
causes no net current flow of ions
Goldman Equation
In Nernst equation;
only external and internal chemical concentration differences are
considered.
Goldman established a more comprehensive equation
considering membrane permiabilities against ions in addition to
chemical concentration differences;
RT
PK[K]o + PNa[Na]o + PCl[Cl]i
Vm = ------- ln ------------------------------------F
PK[K]i + PNa[Na]i + PCl[Cl]o
If Goldman equation is applied to Na ions, it
becomes the same as Nernst equation for any
ion of 1 valency;
RT
[Na]o
VmNa ~ ------- ln --------F
[Na]i
By placing the relevant numerical values in this equation,
8.31 x (273 + 37)
9.1
VmNa ~ ----------------------- ln -------96500
1
VmNa ~ 58 mV
This result means that, if membrane potential is made + 58 mV,
Na ions will be in balance, and they will not be able to move
across the mambrane.
This rule is valid in voltage clamp technic which is used for
balancing certain ions.
So, net electrical effect on Na ions to prevent their leakage:
V*Na = Vm – VNa
If the resting membrane potential is accepted to be -60 mV, then
V*Na = - 60 – (58) = - 118 mV
This means that the electrical effect forcing Na ions to move
across the membrane is to be less than - 118 mV.
Electrical Parameters of the Neuron
The neuron has four electrical parameters based
on its construction and functions:

Voltage source

Current source

Resistance

Capacitance
Voltage Source of the Neuron
Seperation of charges across the membrane results in
a potential difference.
This potential difference that can be calculated by Nernst or
Goldman equations, puts forward the concept of electromotive
force (e.m.f.).
VNa = 58 mV
VK = - 80 mV
Current Source of the Neuron
The active sodium – potasium pump,
which controls the passive diffussion of ions
through the membrane working
in opposite direction, can be considered as a
current source in an electrical circuitry.
INa
IK
Resistance of the Neuron
Ions, as they diffuse through the open
channels, cause heating losses by rubbing
themselves against the walls of the channels.
Electrical equivalent of this event can be
considered as resistance.
Rna = 10 M
RK = 1 M
Capacitance of the Neuron
Capacitor, a circuit component, is formed by placing an isolator
material (dielectric) between two opposite electrical characters.
C
+
Q
V
-
The charge of a capacitor is given by the equation,
Q = V.C
where;
Q: total charge
V: potential difference
C: capacitance
In the neuron, all conditions are present for a capacitor to be formed.
There is a potential difference across the membrane,
inside of the cell being more negative compared with the outside.
The semipermiable membrane functions as a dielectric material.
Capacitance of the neuron calculated by experimental studies;
Cm = 1 μF/cm2
Under normal circumstances, the resting membrane potential for a healthy neuron;
Vm = - 60 mV
Electrical charge of the neuron resulting from its capacitive effect;
Qm = Vm.Cm = 60x10-3 V . 1x10-6 F/cm2 = 6x10-8 c/cm2
It is known that,
1 c = 6.2x1018 electron charge
So,
Qm = (6x10-8 c/cm2)(6.2x1018 charge/c) = 4.3x1011 charge/cm2
A neurons capacitance is
proportional to its
membrane surface area, so
large neurons, have larger
capacitances.
Capacitance also decreases
with the distance between
the two conducting surfaces
Membrane Model
To do mathematical analysises related to the neuron,
an electrical equivalent circuitry can be drawn using its
parameters.
RNa
ENa
RK
EK
C
IK
INa
Electrical equivalent circuit of the neuron
The equivalent circuit of the neuron can be simplified ignoring the
effects of current sources based on the active Na - K pump and
the membrane capacitance.
RNa
RK
i
ENa
EK
Simplified electrical circuit of the neuron.
By applying the second Kirchoff law;
ENa + EK + (RNa + RK) i = 0 → ENa + EK = - (RNa + RK) i
55x10-3 V + 75x10-3 V = (5x106 Ω + 0.2x106 Ω) i
i ~ 25x10-9 A ~ 25 nA
Vm = Vo – V = ENa - RNa.INa = 55x10-3 V - (5x106 Ω)(25x10-9)
= - 70x10-3 V = - 70 mV
This result is within normal limits.
Cable Theory
Cable Theory
V(x, t) is the voltage across the membrane at a
time t and a position x along the length of the
neuron, and where λ and τ are the characteristic
length and time scales on which those voltages
decay in response to a stimulus. These scales
can be determined from the resistances and
capacitances per unit length.
Biopotentials
In the nervous system; there are three potentials
called biopotentials, altogether.

Receptor potential

Synaptic potential

Action potential
Transmembrane potentials according to Theodore H.
Bullock.
Receptor Potential
Receptors in the sensory nervous system percept physical stimuli.
Receptors operate like a transducer device in technology, and
convert one energy into another kind of energy.
Every kind of physical stimuli (touch, heat, sound, light, taste, smell)
is converted into miniature electrical potentials.
These miniature potentials, called biopotentials, are transmitted by
nerves from periphery to the brain., e.g. during stretch reflex (sudden
touch) event, as a result of change in the dimension of muscle, the
resting membrane potential previously stored in the membrane is
released, and thus, mechanical energy is converted into electrical
energy.
Receptor potential is a local signal spreading passively, 1 – 2 mm,
generally 1 mm/s. To the end of the distance its amplitude decreases
up to 1/3 of its original value at starting point.
Its effect can be depolarizing or hyperpolarizing.
Synaptic Potential
Helps neuron stimulate neighbouring
neurons.
Passively spreading a local signal.
Trigger Zone
A special site of the neuron,
typically located in the entrance
which has the lowest perception threshold.
By algebraic summation of local excitatory and
inhibitory signals here,
it is decided if an action potential will be
produced or not.
Thus, trigger zone is also called decision
making point.
Action Potential
Transmission in the nervous system
is provided by action potentials.
During action potential, positively charged
ions outside the neuron suddenly (100 μs)
goes inside, and then they move outside
again with approximately same velocity.
Action potential can be divided into three phases:

Polarization

Depolarization

Repolarization
Polarization
When the membrane is in rest,
the resting membrane potential
(between - 60 mV and - 70 mV)
causes polarization.
Depolarization
For an action potential to be produced,
the resting membrane potential
should be made less more negative
by decreasing charge seperation across the membrane.
Stimulation threshold of neurons is generally
about 15-30 mV.
So, as the resting membrane potential is – 90
mV, if it is made – 50 or – 70 mV
depolarization will be achieved.
When the intensity of physical stimuli reaches a
level enough to change membrane permeability,
ionic concentration changes.
For a short while, inside the cell becomes positive,
and outside negative, the membrane potential
being 40-50 mV.
At the same time, Na and Cl ions rapidly enters
into the cell, and K ions goes outside.
This change in electrical polarity, resulting from
change in chemical concentration,
is called depolarization.
There are two kinds of gated sodium channels:
1) activation gate that is near to outside of the membrane,
2) inactivation gate which is near to inside of the membrane.
As the resting membrane potential increases from – 90 mV
to – 70 mV or – 50 mV, permeability of the membrane to Na ions
increases for 500 to 5000 times.
As a result, Na ions enters into the cell, rapidly.
In the meantime, inactivation gate is closed, it is opened 100 μs later
after opening of the activation gate.
During depolarization, the membrane potential rapidly increases in the
positive direction;
in thick myelinated fibers it becomes 40 - 50 mV,
in thin fibers and in most of the neurons of the central nervous
system, it approaches to zero, but not exceeds to positive side.
Repolarization
When the neuron is in rest,
with the increases in resting membrane potential
gated sodium channels is opening slowly.
In the meantime, inactivation gate of sodium ions is closed.
As a result,
whilist the number of sodium ions entering into the cell increase
approaches to the peak,
potasium ions going out of the neuron increases;
therefore repolarization takes place.
Restoration of Polarization
As an action potential is formed, Na ions entering into the cell and
K ions going outside return to their original state with the help of
active Na-K pump.
The energy source for this metabolic pump to operate is
adenozine trifosfate (ATP). Activation of sodium-potasium pump
is proportional to third power of the concentration of sodium.
e.g. As sodium concentration changes 2 times, the pump
becomes 8 times more active.
Heat is released as a product of chemical reactions in the relevant
energy metabolism.
For this reason, in a nerve fiber, change in heat is proportional to
metabolic velocity.
Comparison of Properties of Biopotentials
receptor potential synaptic potential
action potential
Amplitude
low
low
(100 μV – 10 mV)
high
(70 mV – 110 mV)
Pulse width
5 ms – 100 ms
5 ms – 20 ms
1 ms – 10 ms
Variation
gradually
gradually
all or none
Spread
passive
passive
active
Effect
depolarizing/
hyperpolarizing
depolarizing/
hyperpolarizing
depolarizing
Artificial Depolarization
A neuron can be depolarized by applying an external electrical
current.
In laboratory, this is achieved by using microelectrodes.
One of these electrodes is external and the other internal.
They are connected to a stimulator which supplies a current.
Therefore, the resting membrane potential is converted into
action potential.
A neuron must be healthy and
have appropriate ionic concentration
(high Na outside and high K inside)
to be able to produce action potential.
Otherwise, the action potential produced
will be of low amplitude.
During absulate refractory period (0.5 - 1 ms),
the neuron is saturated, and
its depolarization is impossible.
During 1 to 2 ms following this period known
as relative refractory period,
depolarization can only be achieved
with high intensity current,
and action potential with only low amplitude
can be produced.