Chaotic dynamics in biological information processing: A heuristic outline

Summary A given but otherwise random environmental time series impinging on the input of a certain biological processor passes through with overwhelming probability practically undetected. A very small percentage of environmental stimuli, though, is ?captured? by the processor's nonlinear dissipative operator asinitial conditions, that is, assolutions of the processor's dissipative dynamics. The processor, then, is in such cases instrumental in compressing or abstracting those stimuli, thereby making the external world to collapse from a previous regime of a ?pure state? of suspended animation onto a set of stable eigenfunctions or ?categories?—chaotic strange attractors. The characteristics of this cognitive set depend on the operator involved and the hierarchical level where the abstraction takes place. In this paper we model the physics of such a cognitive process and the role that the thalamo-cortical pacemaker of the (human) brain plays in both stimulating the individual attractors and permutating them on a time division multiplexing basis. A synthesis of the Markovian processes taking place within each individual attractor-memory and the Markovian or semi-Markovian process involving the intermittent jumping among the different attractor-memories are discussed.

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Riassunto Una data ma casuale serie temporale ambientale che influisce sull'immissione di un determinato processore biologico passa con schiacciante probabilità praticamente inosservata. Una piccolissima percentuale di stimoli ambientali, tuttavia, è catturata dall'operatore dissipativo non lineare del processore comecondizioni iniziali, cioè comesoluzioni della dinamica dissipativa del processore. Il processore è quindi, in tali casi, strumentale nel comprimere o estrarre quegli stimoli, facendo perciò collassare il mondo esterno da un precedente regime di ?stato puro? ad animazione sospesa ad un gruppo di autofunzioni stabili o ?categorie?—attrattori caotici strani. Le caratteristiche di questo gruppo cognitivo dipendono dall'operatore coinvolto e dal livello gerarchico in cui l'estrazione ha luogo. In questo lavoro si modella la fisica di tale processo cognitivo e il ruolo che lo stimolatore talamo-corticale del cervello (umano) ha sia nello stimolare gli attrattori individuali che nel permutarli su una base che manda segnali multiplex a divisione temporale. Si discute una sintesi dei processi markoviani che hanno luogo all'interno di ogni attrattore-memoria individuale e il processo markoviano o semimarkoviano che interessa il salto intermittente tra i diversi attrattori-memoria.

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Резюме Временная последовательность на входе некоторого биологического процессора может иметь практически недетектируемую вероятность. Очень небольшой процент стимулов окружающей среды ?захватывается? нелинейным диссипативным оператором процессора как начальные условия, т.е. представляется как решение диссипативпой динамики процессора. Затем процессор обрабатывает внешние стимулы, вынуждая внешний мир коллапсировать из предыдущего режима ?чистого состояния? приостановленного оживления в систему собственных функций или ?категорий?. Характеристики зтой познавательной системы зависят от используемого оператора и иерархического уровня, на котором происходит абстрагирование. В зтой статье мы моделируем физику такого познавательного процесса. Обсуждается синтез марковских процессов, происходящий внутри отдельного злемента ?атрактор-память?, и марковский или полумарковский процесс, включающий пережежающиеся прыжки между различными злементами ?атракторпамять?.

     

Asymptotic Information-Theoretic Detection of Dynamical Organization in Complex Systems

The identification of emergent structures in complex dynamical systems is a formidable challenge. We propose a computationally efficient methodology to address such a challenge, based on modeling the state of the system as a set of random variables. Specifically, we present a sieving algorithm to navigate the huge space of all subsets of variables and compare them in terms of a simple index that can be computed without resorting to simulations. We obtain such a simple index by studying the asymptotic distribution of an information-theoretic measure of coordination among variables, when there is no coordination at all, which allows us to fairly compare subsets of variables having different cardinalities. We show that increasing the number of observations allows the identification of larger and larger subsets. As an example of relevant application, we make use of a paradigmatic case regarding the identification of groups in autocatalytic sets of reactions, a chemical situation related to the origin of life problem.     

Structural dissimilarity sampling with dynamically self‐guiding selection

Structural dissimilarity sampling (SDS) has been proposed as an enhanced conformational sampling method for reproducing the structural transitions of a given protein. SDS consists of cycles of two steps: (1) Selections of initial structures with structural dissimilarities by referring to a measure. (2) Conformational resampling by restarting short‐time molecular dynamics (MD) simulations from the initial structures. In the present study, an efficient measure is proposed as a dynamically self‐guiding selection to accelerate the structural transitions from a reactant state to a product state as an extension to the original SDS. In the extended SDS, the inner product (IP ) between the reactant and the snapshots generated by short‐time MD simulations are evaluated and ranked according to the IP s at every cycle. Then, the snapshots with low IP s are selected as initial structures for the short‐time MD simulations. This scheme enables one to choose dissimilar and distant initial structures from the reactant, and thus the initial structures dynamically head towards the product, promoting structural transitions from the reactant. To confirm the conformational sampling efficiency, the extended SDS was applied to maltodextrin binding protein (MBP), and we successfully reproduced the structural transition from the open to closed states with submicrosecond‐order simulation times. However, a conventional long‐time MD simulation failed to reproduce the same structural transition. We also compared the performance with that obtained by the ordinary SDS and other sampling techniques that have been developed by us to characterize the possible utility of the extended SDS for actual applications. © 2017 Wiley Periodicals, Inc.     

The new physics of ultrathin elastic conoids

Summary Despite centuries of intense effort amongst mathematicians, and a huge literature in this field, there has previously never been a generally valid mathematical model of ultrathin elastic ?shells? (actually surfaces) of revolution. This survey paper presents the first theoretical framework capable of unifying, into a single coherent body of knowledge, a diversity of shapes associated with elastic bows, car bumper-bars, molluscan shells, even flower-buds and pine-cones. It becomes apparent why conventional analysis enjoys limited success when approximating elastic cones to perturbedcylinders anddiscs. Also the paper provides a theoretical basis for analysing the wrinkling of compressed engineering structures. These successes, the new unification and the simplicity of relevant theory which maynever in principle be capable of working in this context.     

Stochastic resonance and transient bimodality

Summary The phenomenon of stochastic resonance is predicted in a monostable system displaying transient bimodality during the evolution. The signal-to-noise ratio as a function of the noise intensity calculated within the rate equation theory with many simplifying assumptions exhibits a promising peak. The numerical simulations are also reported. Paper presented at the International Workshop ?Fluctuations in Physics and Biology: Stochastic Resonance, Signal Processing and Related Phenomena?, Elba, 5–10 June 1994.     

Stochastic resonance in threshold devices

Summary We consider the transmission of a periodic signal by noisy threshold devices. A general expression for the input-output characteristic is developed and applied to two particular threshold devices. It is shown that the amplitude of the signal output shows in the subthreshold regime a maximum as a function of the noise strength—the fingerprint of stochastic resonance. Paper presented at the International Workshop ?Fluctuations in Physics and Biology: Stochastic Resonance, Signal Processing and Related Phenomena?, Elba 5–10 June 1994.     

Elasticity theory of a twisted stack of plates

We present an elastic model of B-form DNA as a stack of thin, rigid plates or base pairs that are not permitted to deform. The symmetry of DNA and the constraint of plate rigidity limit the number of bulk elastic constants contributing to a macroscopic elasticity theory of DNA to four. We derive an effective twist-stretch energy in terms of the macroscopic stretch along and relative excess twist about the DNA molecular axis. In addition to the bulk stretch and twist moduli found previously, we obtain a twist-stretch modulus with the following remarkable properties: 1) it vanishes when the radius of the helical curve following the geometric center of each plate is zero, 2) it vanishes with the elastic constant K₂₃ that couples compression normal to the plates to a shear strain, if the plates are perpendicular to the molecular axis, and 3) it is nonzero if the plates are tilted relative to the molecular axis. This implies that a laminated helical structure carved out of an isotropic elastic medium will not twist in response to a stretching force, but an isotropic material will twist if it is bent into the shape of a helix. Received: 4 July 1997 / Received in final form: 16 October 1997 / Accepted: 21 October 1997     

Nucleotide composition effects on the long-range correlations in human genes

We use the wavelet transform to investigate the fractal scaling properties of coding and noncoding human DNA sequences. We find that the strength of the long-range correlations observed in the introns increases with the guanine-cytosine (GC) content, while coding sequences show no such correlations at any GC content. However, we demonstrate that long-range correlations can be detected when the coding sequences are undersampled by retaining the third base of each codon only. This strongly suggests that the observed correlations are not likely to be due to insertion-deletion mechanisms. We comment about the origin of these correlations in terms of putative dynamical processes that could produce the isochore structure of the human genome. Received: 18 August 1997 / Accepted: 29 October 1997     

Information value and information content in the evolutionary strategy of the genetic code

Summary In previous papers we defined the information value of a genetic code as a measure of its efficiency in the utilization of the information stored in the DNA molecule. Here the genetic codes which have been proposed to be intermediate steps in evolution are analysed in terms of information theory. The results show that evolution follows an optimization strategy between increasing the information content and decreasing the information value,i.e. in each evolutionary step the average information value per unitary information content decreases and at the same time the probability of nonsense mutations goes down as the code evolves. To speed up publication, the authors of this paper have agreed to not recive the proofs for correction.