The use of compressive sensing and peak detection in the reconstruction of microtubules length time series in the process of dynamic instability. (1st October 2015)

• Record Type: Journal Article
• Authors: Mahrooghy, Majid; Yarahmadian, Shantia; Menon, Vineetha; Rezania, Vahid; Tuszynski, Jack A.
• Is Part Of: Computers in biology and medicine. Volume 65(2015)
• Page Start: 25
• Page End: 33
• Publication Date: 2015-10-01
• Subjects: Microtubules -- Compressed sensing -- Wavelet -- Dynamic instability; Medicine -- Data processing -- Periodicals; Biology -- Data processing -- Periodicals; 610.285
• DOI: 10.1016/j.compbiomed.2015.07.014
• Languages: English
• ISSNs: 0010-4825

Abstract

Abstract: Microtubules (MTs) are intra-cellular cylindrical protein filaments. They exhibit a unique phenomenon of stochastic growth and shrinkage, called dynamic instability. In this paper, we introduce a theoretical framework for applying Compressive Sensing (CS) to the sampled data of the microtubule length in the process of dynamic instability. To reduce data density and reconstruct the original signal with relatively low sampling rates, we have applied CS to experimental MT lament length time series modeled as a Dichotomous Markov Noise (DMN). The results show that using CS along with the wavelet transform significantly reduces the recovery errors comparing in the absence of wavelet transform, especially in the low and the medium sampling rates. In a sampling rate ranging from 0.2 to 0.5, the Root-Mean-Squared Error (RMSE) decreases by approximately 3 times and between 0.5 and 1, RMSE is small. We also apply a peak detection technique to the wavelet coefficients to detect and closely approximate the growth and shrinkage of MTs for computing the essential dynamic instability parameters, i.e., transition frequencies and specially growth and shrinkage rates. The results show that using compressed sensing along with the peak detection technique and wavelet transform in sampling rates reduces the recovery errors for the parameters. Abstract : Highlights: We use the Compressed Sensing (CS) technique for the reconstruction of the microtubule (MT) filament length and estimation of the MT characteristic parameters based on minimum sampling measurements. CS method along with the wavelet transform significantly reduces the recovery errors. We apply a peak detection technique to the wavelet coefficients to approximate the growth and shrinkage rate of MTs for computing the essential dynamic instability parameters.