  Recent studies has revealed that Microtubules (MTs) exhibit three transition
states of growth, shrinkage and pause. In this paper, we first introduce a
three states random evolution model as a framework for studying MTs dynamics in
three transition states of growth, pause and shrinkage. Then, we introduce a
non-traditional stack run encoding scheme with 5 symbols for detecting
transition states as well as to encode MT experimental data. The peak detection
is carried out in the wavelet domain to effectively detect these three
transition states. One of the added advantages of including peak information
while encoding being that it enables to detect the peaks efficiently and
encodes them simultaneously in the wavelet domain without having the need to do
further processing after the decoding stage. Experimental results show that
using this form of non-traditional stack run encoding has better compression
and reconstruction performance as opposed to traditional stack run encoding and
run length encoding schemes. Parameters for MTs modeled in the three states are
estimated and is shown to closely approximate original MT data for lower
compression rates. As the compression rate increases, we may end up throwing
away details that are required to detect transition states of MTs. Thus,
choosing the right compression rate is a trade-off between admissible level of
error in signal reconstruction, its parameter estimation and considerable rate
of compression of MT data.
