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Non-Linear Dynamics Analysis of Protein Sequences. Application to CYP450

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PEACCEL, Protein Engineering Accelerator, 6 square Albin Cachot, box 42, 75013 Paris, France
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LSE laboratory, EPITA, Paris 94276, France
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Learning Intelligence Signal Processing Group, Department of Computer Science, Boston University, Boston, MA 02215, USA
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LE2P-Energy Lab, Laboratory of Energy, Electronics and Processes EA 4079, Faculty of Sciences and Technology, University of La Reunion, 97444 St Denis CEDEX, France
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Author to whom correspondence should be addressed.
Entropy 2019, 21(9), 852; https://doi.org/10.3390/e21090852
Received: 30 June 2019 / Revised: 19 August 2019 / Accepted: 29 August 2019 / Published: 31 August 2019
The nature of changes involved in crossed-sequence scale and inner-sequence scale is very challenging in protein biology. This study is a new attempt to assess with a phenomenological approach the non-stationary and nonlinear fluctuation of changes encountered in protein sequence. We have computed fluctuations from an encoded amino acid index dataset using cumulative sum technique and extracted the departure from the linear trend found in each protein sequence. For inner-sequence analysis, we found that the fluctuations of changes statistically follow a −5/3 Kolmogorov power and behave like an incremental Brownian process. The pattern of the changes in the inner sequence seems to be monofractal in essence and to be bounded between Hurst exponent [1/3,1/2] range, which respectively corresponds to the Kolmogorov and Brownian monofractal process. In addition, the changes in the inner sequence exhibit moderate complexity and chaos, which seems to be coherent with the monofractal and stochastic process highlighted previously in the study. The crossed-sequence changes analysis was achieved using an external parameter, which is the activity available for each protein sequence, and some results obtained for the inner sequence, specifically the drift and Kolmogorov complexity spectrum. We found a significant linear relationship between activity changes and drift changes, and also between activity and Kolmogorov complexity. An analysis of the mean square displacement of trajectories in the bivariate space (drift, activity) and (Kolmogorov complexity spectrum, activity) seems to present a superdiffusive law with a 1.6 power law value. View Full-Text
Keywords: power law; Brownian process; Kolmogorov complexity; entropy; chaos; monofractal; non-linear; cumulative sum; sequence analysis; protein engineering power law; Brownian process; Kolmogorov complexity; entropy; chaos; monofractal; non-linear; cumulative sum; sequence analysis; protein engineering
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Cadet, X.F.; Dehak, R.; Chin, S.P.; Bessafi, M. Non-Linear Dynamics Analysis of Protein Sequences. Application to CYP450. Entropy 2019, 21, 852.

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