Permutation, Multiscale and Modified Multiscale Entropies a Natural Complexity for Low-High Infection Level Intracellular Viral Reaction Kinetics

📝 Abstract

Viral infectious diseases, such as HIV virus growth, cause an important health concern. Study of intracellular viral processes can provide us to develop drug and understanding the drug dose to decrease the HIV virus in during growth. Kinetics Monte Carlo simulation has been done for solving Master equation about dynamics of intracellular viral reaction kinetics. Scaling relationship between equilibrium time and initial population of template has been found as power low, , where N , are the number of initial population of template species , equilibrium time, a = 163.1 , b = -0.1429 respectively. Stochastic dynamics shows that increasing initial population of template decreases the time of equilibrium. Entropy generation has been considered in low, intermediate and high infection level of intracellular viral kinetics reaction in during dynamical process. Permutation, multi scaling and modified multiscaling entropies have been calculated for three kinds of species in intracellular reaction dynamics, genome, structural protein, and template. Our result shows that presence of noise in dynamical process of intracellular reaction will change order of permutation entropy for the mentioned of three species. In addition to multiscaling entropy is computed for mentioned model and it has the following order: template > structural protein> genome. Dependency of permutation entropy result to permutation order becomes small in high infection level in intracellular viral kinetics dynamics. At short time scale in intracellular reaction dynamics, convergency of permutation entropy occurs with medium permutation order value. In the big time scale of intracellular dynamics, permutation entropy scale with permutation order n as a scaling relation .

💡 Analysis

Viral infectious diseases, such as HIV virus growth, cause an important health concern. Study of intracellular viral processes can provide us to develop drug and understanding the drug dose to decrease the HIV virus in during growth. Kinetics Monte Carlo simulation has been done for solving Master equation about dynamics of intracellular viral reaction kinetics. Scaling relationship between equilibrium time and initial population of template has been found as power low, , where N , are the number of initial population of template species , equilibrium time, a = 163.1 , b = -0.1429 respectively. Stochastic dynamics shows that increasing initial population of template decreases the time of equilibrium. Entropy generation has been considered in low, intermediate and high infection level of intracellular viral kinetics reaction in during dynamical process. Permutation, multi scaling and modified multiscaling entropies have been calculated for three kinds of species in intracellular reaction dynamics, genome, structural protein, and template. Our result shows that presence of noise in dynamical process of intracellular reaction will change order of permutation entropy for the mentioned of three species. In addition to multiscaling entropy is computed for mentioned model and it has the following order: template > structural protein> genome. Dependency of permutation entropy result to permutation order becomes small in high infection level in intracellular viral kinetics dynamics. At short time scale in intracellular reaction dynamics, convergency of permutation entropy occurs with medium permutation order value. In the big time scale of intracellular dynamics, permutation entropy scale with permutation order n as a scaling relation .

📄 Content

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Equilibrium Time, Permutation, Multiscale and Modified Multiscale Entropies for Low-High Infection Level Intracellular Viral Reaction Kinetics

Fariborz Taherkhani1, Farid Taherkhani 2*

1Department of Computer Science, University of Wisconsin-Milwaukee, Milwaukee, WI, USA

2 Departments of Chemistry Sharif University of Technology, Tehran, Iran

Corresponding Author:
faridtaherkhani@gmail.com

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Abstract Viral infectious diseases, such as HIV virus growth, cause an important health concern. Study of intracellular viral processes can provide us to develop drug and understanding the drug dose to decrease the HIV virus in during growth. Kinetics Monte Carlo simulation has been done for solving Master equation about dynamics of intracellular viral reaction kinetics. Scaling relationship between equilibrium time and initial population of template has been found as power low,

( ) b eq time f N aN  , where N ,

( ) eq time f N are the number of initial population of template species , equilibrium time, a = 163.1 , b = -0.1429 respectively. Stochastic dynamics shows that increasing initial population of template decreases the time of equilibrium. Entropy generation has been considered in low, intermediate and high infection level of intracellular viral kinetics reaction in during dynamical process. Permutation, multi scaling and modified multiscaling entropies have been calculated for three kinds of species in intracellular reaction dynamics, genome, structural protein, and template. Our result shows that presence of noise in dynamical process of intracellular reaction will change order of permutation entropy for the mentioned of three species. In addition to multiscaling entropy is computed for mentioned model and it has the following order: template > structural protein> genome. Dependency of permutation entropy result to permutation order becomes small in high infection level in intracellular viral kinetics dynamics. At short time scale in intracellular reaction dynamics, convergency of permutation entropy occurs with medium permutation order value. In the big time scale of intracellular dynamics, permutation entropy ( ) H n scale with permutation order n as a scaling relation ( ) ( =0.30) H n n  . Three different kinds of trend for low, medium and high 3

infection level observed for multiscaling entropy of template species versus scaling factor. In high infection level behavior of multiscaling entropy of template is non- monotonic however monotonic behavior of permutation entropy of template can be observed in low and very high infection level. Both multiscaling entropy and modified multiscaling entropy shows one maximum peak as a function of initial template population however permutation entropy versus initial population does not show such a peak and permutation entropy increase with initial template population monotonically.
Keyword: Permutation Entropy, Multi Scale Entropy, Kinetics Monte Carlo, Equilibrium Time, Intracellular Viral Reaction

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1. Introduction Various measures of complexity were developed to compare time series and distinguish regular, chaotic, and random variable. The main types of complexity parameter are entropies, fractal dimensions, and Lyapunov exponent[1, 2].
   Many ingenious algorithms, tricks, and recipes have been developed during the last 20 years in order to estimate complexity measures from real- world time series. Another way of complexity measure which is used for any time series (regular, chaotic, noisy) is permutation entropy[3]. During the last two decades, a number of interesting methods have been proposed to detect dynamical changes. They include, among others, recurrence plots and recurrence quantification analysis, recurrence time statistics based approaches, space- time separation plots, and their associated probability distribution, statistical test using desterilized invariant distribution in the reconstructed phase space, cross correlation sum analysis, and nonlinear cross prediction analysis[4]. Most of these methods are based on quantifying certain aspect of the nearest neighbors in phase space and as a result are computationally expensive. Recently, Bandt, and Pompe introduced the interesting concept of permutation entropy, as a complexity measure for time series analysis[3].
   Permutation entropy for analyzing of time series of heart interbeat signal has been applied for recognition healthy and heart failure people[5].
   Diseased systems, when associated with the emergence of more regular behavior, show reduced entropy values compared to the dynamics of free-running healthy systems[5]. However, certain pathologies, including cardiac arrhythmias like atrial fibrillation, are associated with highly erratic fluctuations with statistical properties resembling uncorrelated noise[6- 8]. Viruses are ideal systems for probing how

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