Information Dynamics of a Nonlinear Stochastic Nanopore System

Abstract

Nanopores have become a subject of interest in the scientific community due to their potential uses in nanometer-scale laboratory and research applications, including infectious disease diagnostics and DNA sequencing. Additionally, they display behavioral similarity to molecular and cellular scale physiological processes. Recent advances in information theory have made it possible to probe the information dynamics of nonlinear stochastic dynamical systems, such as autonomously fluctuating nanopore systems, which has enhanced our understanding of the physical systems they model. We present the results of local (LER) and specific entropy rate (SER) computations from a simulation study of an autonomously fluctuating nanopore system. We learn that both metrics show increases that correspond to fluctuations in the nanopore current, indicating fundamental changes in information generation surrounding these fluctuations.of as the rate of information generation at a given time point. The specific entropy rate (SER) represents the statistical uncertainty in an as yet unobserved future, given a specific past [24]. The LER, in isolation, is a retrospective measure, and the SER is a prospective measure, and each yields distinct information about the behavior of the dynamical system.In [25], the authors use current-voltage data collected from a single, conical nanopore in contact with an ion solution to motivate a mechanistic model for the electronic behavior of the nanopore system. The pore is externally biased, but its fluctuations (openings and closings) are autonomous and result from dynamic formation and dissolution (or passage) of tiny inorganic precipitates [26,27]. They demonstrated that their mathematical model captures important properties of the observable from the nanopore system, including these fluctuations, which appear as rapid transitions between high and low conductance states in the time series. One reason this system is an ideal candidate for analysis via information dynamics is that its fluctuations may be informed by its previous states (transitions may depend on previous states, as they do in a Markov process).The structure of this paper is as follows. In Section 2, we present the definitions and estimation procedures for local and specific entropy rates. We introduce the model of the nanopore in Section 3. We then investigate the properties of the nanopore system as viewed through the lens of information dynamics in Section 4. Finally, in Section 5, we conclude by considering other potential avenues of study for this and other nanoscale systems.

Approximate Continuous Time Measures of Information Movement in Complex Extended Networks

“…A summary is given by Gilpin et al [7] "Local and specific entropy rates quantify complementary properties of a dynamical system. If we have a time series representing an observable, the local entropy rate (LER) represents the statistical surprise of seeing an already observed local future given specific past.…”

Thermodynamics and Statistical Mechanics of Small Systems

“…In [8], a stochastic model of nanopore is investigated in the framework of information dynamics, focusing on the local and specific entropy rates computed in simulations. Those metrics are put in relation with the fluctuations of the current in the nanopore.…”

Discrete Information Dynamics with Confidence via the Computational Mechanics Bootstrap: Confidence Sets and Significance Tests for Information-Dynamic Measures

“…Computational mechanics subsumes information dynamics and reveals the complete computational structure of the system via its -machine representation. Together, these two approaches comprise a toolbox for analyzing time series viewed as realizations of stochastic processes, and they have been applied to physical [ 1 , 2 , 3 ], biological [ 4 , 5 , 6 ], social [ 7 , 8 , 9 ], and engineered/artificial systems [ 10 , 11 , 12 , 13 ].…”