Wavelet-Based Compression and Peak Detection Method for the Experimentally Estimation of Microtubules Dynamic Instability Parameters Identified in Three States

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 nontraditional 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.