On the Propagation of Mitochondrial Mutations

Click to see the Instructions  or a brief explanation of the Modelling Technique used


ver. 1.00          Computer Model          ©2009 Ian Logan

PHASE A:    From Initial Mutational event - to - Mitochondrial Capture


     Initial event                   Nucleoid Size                   Nucleoid No.     

Capture a                          



PHASE B:    From Mitochondrial Capture - to - Heteroplasmy - to - Homoplasmy

Runs                   Mitochondrial No.                   Replications         

Generations                   Full Results                           



Instructions

This computer model ilustrates the emergence of mitochondrial mutations by considering the process as occurring in 2 distinct phases:

PHASE A: From Initial Mutational event - to - Mitochondrial Capture

To use the Computer Model, click on A: START.
The number of Initial Events and the Nucleoid Size can be varied.
After any alteration, press CLEAR and click on A: START again.

The Initial Events are to be considered as single mutations occurring in individual mtDNA molecules.
The Nucleoid Size is the count of the number of mtDNA molecules in each mitochondrial nucleoid.

The Computer Model shows that a mutation occurring in a small nucleoid can become established.
However, as the Nucleoid Size is increased, there is only a small chance of a mutation successfully 'capturing' the nucleoid.

Next, change Nucleoid to Mitochondrion and select the number of nucleoids found in each mitochondrion
Now click on A: START again.

The Computer Model shows that for the successful capture of a mitochondrion it is necessary for the number of initial events
to be high, and both the size of the nucleoid and the number of mtDNA molecules in each mitochondrion to be fairly low.


PHASE B: From Mitochondrial Capture - to - Heteroplasmy - to - Homoplasmy

This Computer Model assumes that with the 'capture' of a mitochondrion, it is possible to show how
the level of heteroplasmy varies over a number of generations; and the progression to homoplasmy might be achieved.

Clicking on B: START shows the heteroplasmy levels over a number of generation, for a specified number of trial runs.

In this phase, it is possible to alter the number of trial runs, the number of mitochondria per cell, the number
of replications that place between generations and, finally, the number of generations for which the results are calculated.

The selection of Full Results YES permits viewing of all the results, even when heteroplasmy levels fall to zero.
Whereas, selecting of Full Results NO restricts the viewing to only the trail runs that lead to homoplasmy.

The Computer Model suggests that a single 'captured' mitochondrion can lead to homoplasmy
when the number of mitochondria per cell is reasonably low.
The model also suggests that low levels of heteroplasmy can exist in a population over many generations.

Modelling Technique

This Computer Model considers the propagation of a new mutation in three separate stages.

- from an initial mutational event to the capture of a nucleoid.
- from a captured nucleoid to the the capture of a mitochondrion.
- from a captured mitochondrion to heteroplasmy and homoplasmy.

The first two stages use the same Javascript function to randomly increase or decrease the number of mutations each time the function is called.
The core of the function used is:

     for (i=1; i<=200; i++){
      if (Math.floor(1+(Math.random()* size_num)) <= muts) muts = muts + 1;
      else muts = muts - 1;
     }
I.e.
If a randomly selected number is less than, or equal to, the present number of mutations
then the number of mutations present is increased by 1, otherwise it is decreased by 1.
And, this operation is repeated until either the mutation dies out, or captures the whole nucleoid, or mitochondrion.

This routine models the natural world where a particular mtDNA molecule, or nucleoid, can become duplicated at RANDOM
and the mutated mtDNA molecules, or nucleoid, again at RANDOM, can become the dominant form.

The Javascript Math.random function is only a pseudo-random number generator, but the random number sequence produced
does appear to be sufficiently varied for the present model.

The third stage of the model uses a similar routine which at RANDOM increases or decreases the level
of heteroplasmy each time the function is called.

The present model assumes that the maturity of a nucleoid, a mitochondrion, or a cell, makes no dfference
to the propagation of a new mutation. But in any future model it may be appropriate to consider the
how these factors alter the rate at which mew mutations might appear.

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2009