Brain's Explained

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Neuroplasticity part 2 - Spike timing dependant plasticity

Spike timing dependant plasticity:

However it has become apparent that the neuroplasticity may be more complicated than Hebbian plasticity. In particular timing plays a very important role.

This new form of plasticity is called spike timing dependant plasticity (STDP)

Language of STDP

Action potentials in the presynaptic cell cause synaptic potentials in the post synaptic cells.

These can be excitatory or inhibitory:

·         Excitatory post synaptic potential – EPSP

·         Inhibitory post synaptic potential – IPSP

Usually a single synapse induces a sub-threshold potential,

When many (hundreds) combine they cause a depolarisation.

• Strengthening of a synapse is known as:  - Long term potentiation

The EPSP evoked by the presynaptic cell on that synapse will be greater. This is what we mean by increasing the synaptic strength. LTP increases the EPSP. This potentiation only occurs at those synapses which where stimulated.

• The weakening of synaptic strengths is known as -  Long term depression.

The EPSP will be smaller, This is what we mean when we say a synapse is weakened. LTD decreases the EPSP

Temporal specificity:

What determines whether a synapse will undergo LTP or LTD? it’s all a matter of timing.

• If the presynaptic neurone fires before the post synaptic neurone within the preceding 20ms – long term potentiation occurs.

• If the presynaptic neurone fires after the post synaptic neurone, within the following 20ms  – Long term depression occurs.

There is a critical window for synaptic plasticity, with the peak time for changes to synaptic strengths being in 20 seconds before and after an action potential.

We can then alter the initial Hebbian hypothesis to include the new findings;

If the presynaptic neurone fires within a window of 20ms before the postsynaptic window the synapse will be strengthened (LTP), however if the presynaptic neurone fires within a window of 20ms after the postsynaptic neurone, the synapse will be weakened.

Associativity:

Although the key time window for effective synaptic modification is 20ms, in certain circumstances the window can be increased to up to 40 milliseconds.

This is due to associativity.

Some weak synaptic inputs that cause only small EPSPs will not lead to LTP,

However if these arrive close in time to a larger input, both these synapses will show LTP.

This means that weak inputs that are not normally able to modify synapses, do cause synaptic strengthening if associated with another strong input.

This is what is meant by associativity

Cellular mechanism of neuroplasticity:

The cellular mechanism can vary depending in which area of the brain the memory is stored and which type of memory is being encoded. The classic and most widely studied type is that in the hippocampus and is thought to the basis for long-term memory, which we will discuss now.

Glutamate receptors:

Glutamate is released from the presynaptic neurone.

Glutamate activates glutamate receptors.

There are two particularly important glutamate receptors,

• AMPA receptor
• NDMA receptor

The AMPA receptor is permeable to K⁺ and Na⁺ and it is this inward flux through the AMPA receptor which depolarises the cell.

The NDMA receptors in contrast are blocked by magnesium at negative voltages, and therefore do not significantly contribute to the postsynaptic depolarisation of the cell. However once the cell is depolarised the magnesium is displaced, and ions then flow through the NDMA receptor. Importantly the NDMA receptor also allows calcium to flow through.

It is the nature of the calcium current which causes Spike timing dependant plasticity.

Calcium current and timing:

If the presynaptic neurone fires first:

It becomes depolarised and release glutamate

The glutamate binds to AMPA receptors causing it to depolarise,

At the same time it and binds NDMA receptors,

as the cell is depolarised it causes a large calcium influx.

If the post synaptic neurone fires first.

It becomes depolarised.

As it is repolarising the presynaptic neurone fires, and releases glutamate.

 glutamate binds to the NDMA receptors, but Because the cell is repolarising it is at a lower voltage,

This means fewer NDMA can open.

This leads to a more moderate calcium influx.

• A large calcium influx leads to LTP
• A small calcium influx leads to LTD

Recycling of AMPA receptors:

In the cell, AMPA receptors are constantly being recycled.

New ones are undergoing exocytosis onto the perisynaptic sites where they then migrate the post synaptic areas. Receptors at the post synaptic areas are migrating to perisynaptic sites where they undergo endocytosis and are brought back into the cell.

Endosomes inside the post synaptic neurone are thought to contain a pool of AMPA receptors.

A large calcium influx increases the number of AMPA receptors:

A calcium influx large enough to cross a critical threshold will activate calcium dependant kinases, most importantly CaMKII.

These kinases alter the recycling of AMPA receptors, in particular they increase the exocytosis of them.

This increases the number of AMPA receptors on the post synaptic terminal.

They also change the structure of the AMPA receptors to make them more permeable.

This means when this synapse is triggered again, more AMPA receptors are there to open, more current flows through and the EPSP is increased.

A small calcium influx decreases the number of AMPA receptors

A more moderate calcium influx does not cross the critical threshold to activate calcium dependant kinases, and instead it only activates protein phosphatases.

These again alter the recycling of AMPA receptors, but in the opposite way.

They increase the endocytosis of AMPA receptors, decreasing the number of them at the post synaptic terminal.

Phosphatases, also de phosphorylate receptors and make them less permeable.

This means when the synapse is triggered again, fewer receptors are there to open, less current flows through and the EPSP is decreased.

In Summary. the plasticity is our brain is all due to the timing of synaptic potentials.

is the pre synaptic neurone fires before the post synaptic neurone, the synapse will be strengthened

if the post synaptic neurone fires before the pre synaptic neurone, the synapse will be weakened.

This all due to the nature of the calcium influx, a large influx increases the number of AMPA receptors, leading to LTP and a small influx decreases the number of AMPA receptors, leading to LTP.

How the brain manages such temporal precision will become apparent in the next entry, on neuronal oscillations.

Sources:

Mu-ming Poo Part 1: The Cellular Basis of Learning and Memory. http://www.ibioseminars.org

Hebb, D.O. (1949). The organization of behaviour. New York: Wiley & Sons

Postsynaptic protein phosphorylation and LTP. Soderling TR, Derkach VA. Trends Neurosci. 2000 Feb;23(2):75-80.

Synaptic Plasticity: Multiple Forms, Functions, and Mechanisms. Ami Citri. Robert C Malenka. Neuropsychopharmacology (2008) 33, 18–41

Paul C. Bressloff, lectures in mathematical neuroscience http://www.neurosecurity.com/articles/PCMI/Lect5.pdf

(date accessed 28/10/2012)

Note:

It is important to note that the neuroplasticity coverd here is that of STDP in the hippocampus. But there are other types of synaptic plasticity, acting with different mechanism and at different timescales, to perform different functions. The nature of neuroplasticity itself is very plastic! a phenomena known as metaplasticity.

Neuroplasticity part 1 - Introduction to neuroplasticity:

Throughout our lives we are shaped by our experiences. They not only change our behaviour but even how we think.These psychological changes are the result of corresponding physical changes in the connections between the neurones in our brains.

We have a view that the structure of our brain is fixed, but the function of our brain is to interpret the environment, discover relationships and change our behaviour accordingly. Our brain is not a static organ and indeed to function properly it needs to be dynamic and changing on every level.

This changing and shaping of the connections in our brain is known as neuroplasticity.

Hebbian plasticity:

The first person to notice this “plastic” nature of the brain was the Canadian psychologist Donald Hebb.

In his book the organization of behaviour, he wrote his now classic Hebb’s postulate:

“When an axon of cell A is near enough to excite a cell B and repeatedly or persistently takes part in firing it, some growth process of metabolic change takes place in one or both cells such that’s As efficiency as one of the cell firing B in increased”

Simply put;

When two neurones fire at the same time, the connections between them are strengthened, and thus they become more likely to fire again together in the future.

When two neurones repeatedly fire in an uncoordinated manner, the connections between them weaken, and they are more likely to act independently in the future.

This can be simplified to the mantra:

• ·         Cells that fire together, wire together.
• ·         Cells that fire apart, wire apart.

These plastic mechanisms form the basis of the brains ability to change in the face of the environment, to learn and remember.

Plasticity, memory and learning:

But how do these plastic changes form the basis of learning and memory?

The type of learning plasticity has been applied to most is classical conditioning.

The most famous example of classical conditioning is Pavlov’s dogs,

a stimulus (food) which produced a response (salivation), was paired with a stimulus that did not produce a response (bell.)

After multiple exposures, the bell produced the same response (salivation) even without the presence of the original stimulus (the food)

the similarities with Hebb’s postulate are easily seen.

The neurones responsible for the bell and the neurones responsible for the salivation were repeatedly activated at the same time, this strengthened the synaptic connections between them, and so in the future they were activated together.

When we learn something, a set of neurones are triggered and become connected. This now connected “assembly” of cells persists, and if this set of neurones is triggered again, we will re-experience the event as a memory.

The theoretical memory trace In the brain is known as an Engram

The relationship between cell assemblies and memory was initially investigated by Karl Lashley.

He taught a rat to complete a maze, then destroyed a different part of the cortex each time, and would see which area affected the maze memory.

                                                             

The only relationship he found was that the number of errors made was directly proportion to the amount of cortex destroyed.

	Lashley concluded that memory is equally distributed in all cortical areas, through these interconnected cell assemblies*.

Storing information in assemblies like this can also explain another phenomenon of memory, how only a partial cue can trigger the reactivation of a whole memory, for example how a small detail, such as a familiar smell can cause to us relive a detailed memory.

Activation of a single part of the assembly will reverberate through all its connections, activating other cells encoded at the same time.

                                                                                                                                                                         

 Now can see very basically how the brains ability to change itself and alter its connections, enable it to learn meaningful relationships and store this learnt knowledge as memories, in the form of cell assemblies, which may be activated again upon presentation of only part of a familiar experience.

Sources:

Mu-ming Poo Part 1: The Cellular Basis of Learning and Memory. http://www.ibioseminars.org

Hebb, D.O. (1949). The organization of behaviour. New York: Wiley & Sons

The Brain that changes itself: Dr Norman Doidge,

The method of pawlow in animal psychology. Robert M. Yerkes and Sergius Morgulis (1909).Harvard University. First published in The Psychological Bulletin, 6, 257-273.

The neurobiology of consolidations, or, how stable is the engram? Dudai Y. Annu Rev. Psychol. 2004;55:51-86.

Studies of cerebral function in learning IX. Mass action in relation to the number of elements in the problem to be learned^† Lashely and wiley 1933. The Journal of Comparative Neurology. Volume 57, Issue 1, pages 3–55, February 1933

*”we now know that Lashely’s experiment did not distinguish between memory or motor areas, and so the rats impairment in the maze may not be due to memory impairment but instead the impairment of its motor functions. The current view is that memory is indeed distributed by not, but not equally. Some areas such as the hippocampus paly a particularly crucial role, which we will discuss later.”

Understanding the Nernst equation

Understanding the Nernst equation:

The Nernst equation can seem arbitrary and complicated however conceptually it is quite simple. Learning where the equation comes from can be greatly helpful in understanding and remembering it.

Membrane potential:

Nerve cells have a potential difference between the voltage inside the cell, and the voltage outside the cell.

As the barrier allowing this difference is the cell membrane, it is called the membrane potential.

 It is given the symbol:  V_m

 It is calculated by simply working out the difference between the voltage inside and the voltage outside.

o   Vm = membrane potential

o   Vin = voltage inside the cell

o   Vout = voltage outside the cell

Maintaining a membrane potential:

The membrane potential is maintained by 3 principle ions;

•  Potassium (K+)
•  Chlorine (Cl-)
• Sodium (Na+) 

At the resting potential:

• Higher concentration f K+ inside cell
• Higher concentration of Na+ and Cl- outside cell

This is largely produced by the sodium potassium pump (Na+/K+ ATPase),

Which pumps two 3 sodium ions out for every 2 potassium ions pumped in

However the membrane also contains sodium and potassium leakage channels which allow ions to move freely across the membrane.

Two opposing forces:

This means there are two forces affecting the movement of ions across the membrane:

• The difference in concentration (diffusion gradient)
• The difference in potential (electrostatic gradient)

Ions want to move down their concentration gradient, away from areas where they are in high concentration.

And

Ions want to move down their electrochemical gradient, away from areas high in the same charge.

For example:

• Potassium is found in greater concentration in the cell, therefore it wants to move down its concentration gradient across the membrane and outside the cell. 

• However as it is a positive ion it also wants to move away from areas of high positive charge, and so wants to move inside of the cell where it is more negative.

 

The membrane potential at which electrostatic forces equal the action of diffusion for a particular ion is known as the:

 Nernst equilibrium

Deriving the equation:

As we have seen the Nernst equation needs to model the opposing actions of the concentrating gradient, and the electrochemical gradient.

• [C] (x)is the concentration of an ion, at position (x) along the membrane
• [V](x) is the potential at some point along the membrane, (x)

Flicks law of diffusion:

Flicks law of diffusion allows us to model the diffusive flux.

“flux” means the number of molecules flowing through a certain area in a certain time.

o   C = concentration difference

o   X = distance to diffuse

o   D = diffusion constant

For example, Calculate the flux of oxygen across a membrane segment with area 2x10 ^-6m²,  if the concentration on the right hand side of the membrane is 4mL/L and on the left side is 2mL/L. molecular diffusion constant for oxygen = 3x10^-5

 

• The difference in concentration = 2ml/l (4 – 2)
• Molecular diffusion constant for oxygen = 3x10^-5
• Length of membrane = 2x10 ^-6m

So:                  

= 30 molecules/sec  

Ohms law:

We can model the electrostatic flux with a similar equation: using a version of ohms law.

μ = motility  

z = valence of ion, eg +1, +2

[C] = concentration

[v] = potential difference

X = distance, length of membrane.

Total flux:

Therefore the full movement of ions can be models by the sum of the equations:

The diffusion constant in flicks equation can be model more accurately and related to the motility through Einstein’s relation;

K  = Boltzmann constant

t = temperature

q = charge

u = motility

Thus we can replace D and change the equation to:

From molecules to moles:

As we have seen this equation will give the diffusive flux in molecules.

However often in science it is more useful to use moles, and we change the equation to reflect this.

We can do this simply by taking some of our constants, which are in terms of molecules and multiplying them by Avogadro’s number (6.022 x 10²³ the number of molecules in a mol)

·         The Boltzmann constant (K) is related to the energy of a particular particle, we can simply times it by Avogadro’s number to work in term of moles.

                K x Avogadro’s constant = R

               This number is called the gas constant, and given the symbol R.

        So;  to work in terms of moles instead of particles, we simply need to replace the Boltzmann         constant with the gas constant.

          

·         We must also do a similar thing to the electrostatic aspect of the equation.

Currently we are working with the charge of an individual electron.

Again we can times this by Avogadro’s number to work in terms of moles

               q x Avogadro’s constant = F

                F is the charge of a mole of electrons, and is known the faraday constrant.

        So; again to work in terms of moles instead of particles, we simply need to replace the individual charge with Faradays constant.

   

So we can ultimately write the molar form of the equation:

From Flux to charge:

Flux is the flow of molecules, and current is the flow of charge.

So by simply multiplying the flux, by the total charge of all the ions we can work out the current going through the membrane.

The total charge per mol of electrons will simply by faradays constant (F) multiplied by the valence of the ions (z)

So if we multiply the whole equation by Fz, we can see the current through the membrane is:

This simplifies to the famous Nernst equation:

Although we have missed out a lot of the maths here, we can see that the Nernst equation is equal to the equilibrium potential.

·         This potential is a balance between the diffusion flux and the electrostatic flux

·         Both are dependent upon the concentration of ions inside and outside the cell,

·         Both can accurately be model using molar constants related to

o   The energy each particle has to diffuse (RT)

o  The charge acting on each particle (zF)