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

Abstract

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.

Machine Learning Enables Selection of Epistatic Enzyme Mutants for Stability Against Unfolding and Detrimental Aggregation

“…[7] Indeed, a concatenation of multiples indices, that is, an extended_sequence (Ext_SEQ), is evaluated as descriptor (as exemplified in Figure 1). In the most recent contribution, [16] we showed that the use of multiple physicochemical indices coupled with the implementation of the FFT, taking into account the interactions between residues of amino acids within the protein sequence, [7,17] leads to very significant improvement in the quality of models. The choice of the descriptor (i. e., combination of indices) with or without applying FFT, during the statistical modelling, is dependent of the couple protein/fitness, thereby improving the prediction of enzyme activity.…”

Novel Descriptors and Digital Signal Processing- Based Method for Protein Sequence Activity Relationship Study

“…Digital signal processing (DSP) techniques are analytic procedures, which decompose and process signals in order to reveal information embedded in them [15,16]. The signals may be continuous or discrete, as is the case for protein residues.…”

Information Theory in Molecular Evolution: From Models to Structures and Dynamics

“…A second set of articles in this issue [ 10 , 11 , 12 ] deals with the complex problem of evolutionary dynamics in protein structures and sequences. Cadet et al [ 12 ] study formal statistical properties of sequence change and show how fluctuations follow a −5/3 Kolmogorov power and behave like an incremental Brownian process. In another study, Wang et al [ 10 ] investigate members of the family of -Lactamases, enzymes involved in antibiotic resistance.…”