Viva Presentation

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Viva Presentation

• Gregor Kiddie

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Contents

• Aim of PhD.
• Neuronal Structure and Growth.
• Modelling Neurite Growth.
• 1st Year Project.
• Plan of further study.

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The Grand Aim

• The aim of the PhD is to explore the underlying
  biophysical mechanisms that form the
  characteristic morphologies of different neuronal
  types.

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Neuronal Structure and Growth

• Neurons are much specialised structures designed
  for information transfer, storage and processing.
• The neuron can be separated up into three
  distinct segments, the Soma, the Axon, and the
  Dendritic arbor.
• The Soma is the centre of the cell, where all
  growth originates, and much of the information
  processing is performed.
• The Axon, is a thin tube like structure capable
  of travelling from micrometers to meters. It
  carries electrical signals from the Soma before
  terminating upon a synapse when it meets a
  dendrite.
• The elements of the dendritic arbor will be
  looked at in more detail.

Cell Organisation (From Junek 2003)
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Neuronal Structure and Growth(2)

• The Cytoskeleton
• The cytoskeleton of the growth cone is there for
  several reasons. It adds mechanical strength to a
  structure, keeping its shape, and also helps
  drive and guide the structures movement.
• The cytoskeleton is deformable and can create
  filopodia to promote movement and guidance.
• The strength of the cytoskeleton is also
  important to the promotion of branching within
  the neurite.

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Neuronal Structure and Growth(3)

• The Growth Cone
• The growth cone is a structure at the terminal of
  a dendrite that acts as driving force for
  guidance, and plays an acting role in the growth
  of the neurite.
• It can process external cues from the environment
  and turn this into useful action in terms of
  guidance, and its structure, pulling the tip of
  the dendrite along, or in separate directions,
  can promote either growth or branching.
• The growth cone has a caterpillar track style
  movement. Its dendritic spikes are very
  important to the anchoring and movement of the
  growth cone.

The growth cone (From Hely, Thesis)
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Neuronal Structure and Growth(4)

• Filopodia
• Filopodia are small actin filament bundles
  extruding from the tip of the growth cone.
• These filopodia grow and retract at a tremendous
  rate, testing the current environment
  continuously, picking up guidance cues from the
  environment.
• Once the filopodia reach full length, they adhere
  themselves to the substrate, producing tension
  within the growth cone for a while.

Filopodia Tension (From Li et al, 1995)
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Neuronal Structure and Growth(5)

• Synapse Formation
• The effect synapse formation has upon growth has
  yet to be decided.
• That synapse formation stunts growth in a
  particular dendrite, and that synapse formation
  promotes growth in a particular dendrite are both
  considered.
• There is sufficient proof that a dendrite forming
  a synapse at its terminal slows its growth while
  promoting further growth in other parts of the
  arbor.
• This has been explained by a stop growing
  signal, or more appropriately, the release of a
  chemical inhibiting the transport of tubulin
  along that particular branch.

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Neuronal Structure and Growth(6)

• Growth Cone Guidance
• As the neurite grow, it does not grow in a
  straight line, the substrate is a full
  three-dimensional area, filled with environmental
  clues for growth into the area.
• The growth cone is guided primarily by filopodia,
  which extrude from the tip of the growth cone.
• These filopodia test the surrounding environment
  and are attracted to chemicals such laminin or
  thrombospondin 1 (TSP-1), but repelled by
  chemicals such as chondroitin sulphate.
• This can mean that the growth cone is pulled in a
  different direction, and guidance is therefore
  achieved.

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Neuronal Structure and Growth(7)

• Calcium
• Calcium is the mainstay of much of the growth and
  branching inside the neurite.
• Certain models use only the levels of calcium in
  the neurite to determine outgrowth, but its
  interaction goes deeper than that.
• Calcium regulates the rate in which MAP-2 binds,
  unbinds and phosphorylates.
• Calcium is an effecter of change, rather the be
  all and end all of growth.

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Neuronal Structure and Growth(8)

• Tubulin
• Tubulin is a chemical that forms the skeletal
  innards of the dendrite.
• Tubulin is produced in the soma and is actively
  transported through the length of the dendrite,
  until it reaches the terminal, or growth cone.
• When the tubulin reaches the terminal area, it is
  bundled together to form a thick rod like
  structure through the middle of the dendrite.
• The rate of this addition and bundling is
  regulated by MAP-2, which also regulates the
  debundling and subtraction of tubulin from this
  rod.
• Branching within the terminal area can be
  facilitated by the destabilisation of the
  microtubules.

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Neuronal Structure and Growth(9)

• MAP-2
• MAP is a collection of chemicals known as,
  Microtubulin Associated Proteins.
• The main purpose of MAP-2 in the growing neurite
  is to facilitate growth and branching.
• MAP-2 dictates these factors by the way in which
  it affects microtubulin.
• Dephosphorylated MAP-2 favours growth as it
  promotes the bundling of microtubulin, creating
  long tubules and forcing the neurite to create
  more space by becoming longer.
• Phosphorylated MAP-2 is more likely to create
  branching conditions as the tubules binding is
  relaxed, are spaced further apart and are
  therefore easier to be forced apart.

MAP-2 (From Hely, Thesis)
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Neuronal Structure and Growth(10)

• Summary
• The main building block of the brain is the
  neuron .
• The neuron can be split into three distinct
  parts, the soma, axon, and dendrites.
• The dendrites can be further broken down into the
  growth cone and it composing parts, the internal
  chemical balances, and the cytoskeleton.
• Each of these areas plays an important role in
  the growth and functioning of a neurite.
• Accurately modelling the growth of a neuron
  therefore requires a knowledge and understanding
  of these components.

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Modelling Neurite Growth

• Compartmental Modelling
• Compartmental modelling is a technique usually
  more associated with modelling electrical
  properties of neurons than chemical modelling.
• The main problem with trying to model something
  such as a neuron, is that there are few
  constants, it is constantly in a state of flux.
• Chemicals, much like electrical signals, move
  through the neuron, flowing and diffusing.
• A model, especially if it is to be transferred to
  a computer simulation, must be precisely aware of
  how much of everything there is at a particular
  point in a structure.

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Modelling Neurite Growth

• Compartmental Modelling
• example
• This represents a cell body, and one of its
  growing dendrites.
• With the levels of substance at a particular
  point flowing and changing at every moment, few
  methods would allow a simulation to track the
  amount of substance.
• The neurite has been segmented up into
  compartments.
• Each of these compartments contains an amount of
  substance that a simulation can track, and the
  rates at which the substance flows and diffuses
  through the neurite can be tracked and modelled.
• This means an accurate model can be made from the
  example.

From Kiddie (1st year Report)
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1st Year Project

• The aim of the 1st year project was twofold.
• Firstly, to create a computer simulation of a
  current model.
• Secondly, to create an initial paper model
  incorporating several elements.

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1st Year Project

• The chosen current model was Graham, and Van
  Ooyens tubulin model.
• This was chosen due to its use of a desired
  chemical, and its compartmental model, which
  included a simple simulated growth cone.
• It fixes the size of the terminal compartment,
  and elongates the preceding compartment.
• When the compartment reaches 2dx, it is split
  into two compartments.

Compartmental Model (From Graham van Ooyen CNS
2000)
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1st Year Project

• Tim Hely produced a model featuring MAP-2 as in
  integral part.
• Hely used four differential equations to control
  the rates of change in each of the compartments.
• The two dynamic variables of the model were
  calcium (Ca) and unbound MAP-2 (MAP-2u).
• These variables directly controlled the
  concentration of dephosphorylated MAP-2 which was
  bound to microtubules (MAP-2b), or bound and then
  phosphorylated by CaMKII (MAP-2p).
• Tubulin, and CaMKII are not explicitly modelled,
  it is assumed that there is always enough of
  these substances for what is required.

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1st Year Project

• The Equation for Calcium diffusion influx
  decay
• The equation for Unbound MAP-2 diffusion
  production rate to/from MAP-2b decay
• The equation for Bound MAP-2 rate to/from MAP-2u
  de/phosphorylation to/from MAP-2p decay
• The equation for Phosphorylated MAP-2
  de/phosphorylation to/from MAP-2b - decay

Equations (From Hely, Thesis)
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1st Year Project

• F is set by levels of calcium in the compartment.
• G is also set by the levels of calcium in the
  compartment.
• Elongation is handled with this equation.
• The probability of branching is calculated with
  this formula.

Equations (From Hely, Thesis)
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1st Year Project

• Both models contained certain elements that were
  desirable in a combined model, tubulin from the
  Graham van Ooyen model, Calcium and MAP-2 from
  Helys.
• There were three sets of equations, a set for
  each of the three chemicals, with the set for
  MAP-2 being larger thanks to tracking bound, and
  phosphorylated MAP-2 as well as bound MAP-2.

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1st Year Project

• The calcium equations followed a simple format of
  Influx(-) Diffusion-Decay.
• The tubulin equations followed the same pattern
  with the addition of an active transport term.
• The MAP-2 equations are all interdependent and
  are governed by conversion rates (Uunbound,
  Bbound, Pbound phosphorylated)

Equations (From Kiddie 1st Year Report)
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1st Year Project

• Again, F, and G are coefficients set by the level
  of calcium in the compartment.
• The elongation is now affected by the amount of
  tubulin in the compartment.
• The branching probability is still based upon the
  relationship between phosphorylated and bound
  MAP-2.

Equations (From Kiddie 1st Year Report)
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1st Year Project

• The computer simulation of the Graham van Ooyen
  models was initially created in Java.
• However it was ported to MATLAB.
• This generated a delay due to an unfamiliarity
  with MATLAB.

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An alternative approach

• An approach formulated by McLean and Graham.
• A fixed multi compartmental model.
• The amount of compartments remains static
  regardless of length.
• Numerically superior, but has inherent problems.
  As the compartments move as the neurite grows,
  features such as synapse formation would be hard
  to include.

Fixed Compartments (From Kiddie, Brain Research
Summer School 2003)
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Plan of further Study

• Creating Neurite Model.
• Continue reading subject matter for greater
  understanding of current techniques, and data.
• Refine model to be more biologically plausible as
  well as more accurate.
• Add to current model
• True Growth Cone
• Filopodia
• Proper Cytoskeleton
• Tubulin structures
• directional cues

• Computer simulation tools
• Add better integration techniques to current
  simulation
• Test the computer model against the PDE solution
  created by McLean and Graham.
• Convert the neurite model created (left) to the
  computer simulation, with relevant testing.
• Keep simulation of model up to date with any
  changes in the paper model.

Realistic goals
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Thank you for listening

• Questions?