The overall goal of this course
is to obtain a causal and mechanistic  understanding of brain function.
We will be taking a bottom-up approach,
and so the first thing we need to do  is to look at the components:
what makes the brain.
Like every other organ of the body, the brain is made of cells.
There are many types of brain cells,
and each performs its own function.
In order to get a causal understanding of the brain
we therefore must study cellular mechanisms.
The cell is a fundamental unit of organization of the brain.
A key defining feature of a cell is the so-called cell membrane.
It separates the inside of a cell from the outside of a cell.
When the cell membrane evolved, some three billion years ago,
presumedly its primary advantage
was to offer a stable intracellular environment
for biochemical reactions to take place
that wouldn't be affected by changes in the extracellular milieu.
As we will learn,
the brain has evolved to take exquisite advantage
of the electrical properties of the cell membrane,
and has turned this into a dedicated computational device
working on transmembrane currents
changing the electrical field across the plasma membrane.
The cell membrane is made of phospholipids,
and this is a typical example of a phospholipid.
It can be divided into two parts:
a phosphate-containing head group,
and long hydrocarbon chains.
These long hydrocarbon chains are lipophilic, non-polar,
and therefore they are hydrophobic,
they don't like to interact with water.
On the other hand,
the phosphate head group that's shown magnified here,
that links through the ester bonds to the hydrocarbon tails,
is highly polar.
It contains a phosphate group
with oxygen atoms that carry strong negative charges.
These negative charges like to interact with water,
and the head group is polar and hydrophilic.
Phospholipids have remarkable properties.
In water, they spontaneously form a variety of stable structures,
a bit like droplets of oil in water.
Of particular interest to us is the fact that phospholipids
spontaneously form planar lipid bilayers in water.
In a phospholipid bilayer, the polar head groups,
containing the phosphate group, interacts and is close
to the aqueous phase of the solution.
The lipid hydrocarbon tails join together
the two leaflets of the membrane, and form a lipophilic core
surrounded by hydrophilic edges here by the polar head group.
The phospholipid bilayer
then forms the membrane of the cell,
separating the inside and the outside.
Importantly, as we look at these static images,
it's useful to think that actually, in the living cell,
these are jiggling around and diffusing at high rates
in the two-dimensional structure of the membrane.
The most important feature of the phospholipid bilayer
is that it is only permeable to lipophilic substances
such as gases, lipids, and small non-polar molecules.
The cell membrane has very limited permeability to water
and, most importantly, the cell membrane is impermeable to ions,
that is charged atoms, and other charged molecules.
Ions are of enormous importance in all biology,
but nowhere more so, than in the context of brain function.
Ions are charged, and it this charge of the ions
that forms the basis of electrical signaling
in the nervous system.
That the cell membrane is impermeable to ions
means that there can be different concentrations of ions
on the two sides of the cell membrane.
In a typical cell there is a high concentration
of positively-charged potassium ions on the inside of a cell,
and on the outside of a cell the extracellular solution
contains high concentrations of positively-charged sodium ions
and high concentrations of negatively-charged chloride ions.
So the extracellular solution is made out of salt,
just like the salt that we use in the kitchen.
The plasma membrane is very thin.
It's about five nanometers in thickness.
And this very small distance allows the charged ions
on one side of the membrane
to interact, through electrostatic fields,
with the charged membranes
on the other side of the plasma membrane.
The fact that the ions can't move across the membrane,
but that they can interact through electrostatic forces,
means that the lipid membrane is a capacitor, it's a dielectric,
and there is electric fields that are strong across the lipid membrane.
If ions are moved from one side of the membrane
to another side of the membrane, they generate an electric field.
And the potential difference, across the plasma membrane,
is called the membrane potential.
Membrane potential is of fundamental importance to neuroscience.
That the lipid membrane
can be considered electrically as a capacitor
means that we can also apply some of the simple equations of physics
to uncover the membrane biophysics.
From physics we know that the potential of a capacitor
is equal to the charge of that capacitor divided by the capacitance.
And so by placing different amounts of charge
on the two sides of the plasma membrane
we can generate membrane potentials,
and the amount of the membrane potential
will depend upon the charge and the capacitance
of the lipid membrane.
In this first lesson
we've learned that the cell membrane
is made of a phospholipid bilayer that's impermeable to ions,
and is of about five nanometer thickness,
allowing the cell membrane
to act as an electrical capacitor.
Charges separated on the different sides of the plasma membrane
generate electric fields, a membrane potential,
and this membrane potential is of fundamental importance,
forming the basis of electrical cycling in the nervous system.
Now I'd like to be a bit more specific,
and get to some numbers, just some ballpark numbers
from back of the envelope calculations
so that you can see approximately how many ions,
how much charge is involved in generating membrane potentials
and electrical signals in biological cells.
The cell membrane has a specific capacitance
that is a capacitance per unit area
of around one microfarad per centimeter square.
The area of a cell, of a small circular cell,
with a radius of around 10 micrometers
means that the capacitance of a typical cell
is somewhere around 10 picofarad,
a number useful to bear in mind when you're thinking about
how the membrane biophysics of cells works.
Knowing the capacitance of a cell, we can now calculate
how much positive charge would need to move
from the inside of a cell to the outside of a cell
in order to generate a membrane potential of -100 mV.
The outside of a cell, by convention,
is always fixed to be at 0 mV.
So we take our standard equation:
charge is equal to the capacitance times the voltage.
We agreed that the capacitance of a typical cell
was somewhere around 10 x 10ˆ-12 farad,
and the voltage is 0.1 volts.
This gives us a charge of 10ˆ-12 coulomb,
and that is one picocoulomb.
So one picocoulomb of charge
needs to move from the inside to the outside
in order to generate a membrane potential of -100 mV.
How many ions does that correspond to?
So one picocoulomb of charge needs to move
from the inside to the outside in order to generate
a membrane potential of -100 mV.
Now the inside of a cell contains a lot of potassium ions.
And so let's wonder how many potassium ions it would take
in order to move one picocoulomb.
In order to make that calculation
we need to look at the charge on each individual potassium ion.
The potassium ions are monovalent, they carry a single charge,
and that charge is then given by e, the elementary charge:
1.6 x 10ˆ-19 coulomb.
And so in order to see how many ions is in one picocoulomb,
we take 10ˆ-12 coulomb,
and we divide it by 1.6 x 10ˆ-19,
and that gives us a number of 6 x 10ˆ6.
So six million potassium ions need to move
from the inside of a cell to the outside of a cell
in order to generate -100 mV membrane potential
in a small typical cell.
Is six million ions a lot?
Are there even six million ions inside a cell?
Well let's find out.
How many ions are there inside a cell?
A cell has a diameter of around 10 micrometers.
The volume is then around one picoliter, and in order to work out
how many mole of potassium there are inside this
we then need to know the potassium concentration
and the intracellular potassium concentration of a typical nerve cell
is sitting at around 150 millimolar.
So the number of moles of potassium inside a typical cell
is then 0.15 x 10ˆ-12,
and that is then the number of mole in a given cell.
In order to find out how many ions that is,
we'll then need to multiply this number by Avogadro's number.
And so the total number of ions, then,
is equal to the above number,
0.15 x 10ˆ-12
x Avogadro's number, 6 x 10ˆ23,
and that gives us a final number
of 10ˆ11 ions of potassium
inside an individual cell.
So we found that we needed to move six million ions
to generate the -100 mV membrane potential,
but inside a cell we have 10ˆ11 ions,
100 thousand times more than are needed
to generate the electric field.
This back of the envelope calculation
has told us a number of useful things.
Most importantly, we find that only a small fraction
of the total number of ions inside a cell
need to move across some plasma membrane
in order to generate biologically- relevant membrane potentials.
This means that electrical cycling can be extremely efficient.
You can generate large changes in membrane potential
without changing the intracellular concentrations.
As we will see in the next lessons,
the nervous system has evolved specific mechanisms
to move ions across the plasma membrane
and rapidly change membrane potential,
and this forms the underlying signals
that drive brain function and neuronal computations.