Individual typologic characteristics of the open-field behavior of rats

By means of ethograms record and analysis, connection has been studied between the properties of rats behaviour organization in the open field, determining the level of behaviour entropy in this test, and the speed of conditioned reflexes formation in the Skinner chamber. According to behaviour entropy level the rats are significantly divided into four groups; the lowest speed of conditioned reflexes formation in the Skinner's chamber is observed in the animals of the first (low entropy) group, the highest--in the fourth (high entropy) group. The obtained data are discussed according to Pavlov's concepts on the characteristics of the basic nervous processes, determining individual-typological characteristics of the higher nervous activity of the animal. Conclusion is made that division according to the level of behaviour entropy in the open field test may serve as a safe method of express-estimation of the animals abilities to conditioned habits formation.     

Local Renyi entropic profiles of DNA sequences

Background  

In a recent report the authors presented a new measure of continuous entropy for DNA sequences, which allows the estimation of their randomness level. The definition therein explored was based on the Rényi entropy of probability density estimation (pdf) using the Parzen's window method and applied to Chaos Game Representation/Universal Sequence Maps (CGR/USM). Subsequent work proposed a fractal pdf kernel as a more exact solution for the iterated map representation. This report extends the concepts of continuous entropy by defining DNA sequence entropic profiles using the new pdf estimations to refine the density estimation of motifs.     

Combining Experiments and Simulations Using the Maximum Entropy Principle

A key component of computational biology is to compare the results of computer modelling with experimental measurements. Despite substantial progress in the models and algorithms used in many areas of computational biology, such comparisons sometimes reveal that the computations are not in quantitative agreement with experimental data. The principle of maximum entropy is a general procedure for constructing probability distributions in the light of new data, making it a natural tool in cases when an initial model provides results that are at odds with experiments. The number of maximum entropy applications in our field has grown steadily in recent years, in areas as diverse as sequence analysis, structural modelling, and neurobiology. In this Perspectives article, we give a broad introduction to the method, in an attempt to encourage its further adoption. The general procedure is explained in the context of a simple example, after which we proceed with a real-world application in the field of molecular simulations, where the maximum entropy procedure has recently provided new insight. Given the limited accuracy of force fields, macromolecular simulations sometimes produce results that are at not in complete and quantitative accordance with experiments. A common solution to this problem is to explicitly ensure agreement between the two by perturbing the potential energy function towards the experimental data. So far, a general consensus for how such perturbations should be implemented has been lacking. Three very recent papers have explored this problem using the maximum entropy approach, providing both new theoretical and practical insights to the problem. We highlight each of these contributions in turn and conclude with a discussion on remaining challenges.     

Entropy changes associated with a nerve impulse

In this paper the problem of entropy changes in a nerve fibre when an action potential is taking place is analysed. A probability field associated with the ionic distribution in the axoplasma and the extracellular space is defined. The total variation of its entropy can be computed on the basis of Gibbs' distribution of ions in the system. The final formula deduced for the entropy variation allows computations based on experimental data for the giant axon and the myelinated fibre. It represents at the same time a derivation of Brillouin's neguentropy principle of information in the particular case of the nerve.     

Complexity and information in regular and random phyllotactic patterns.

In biology, the theory of information has been used to study the degree of order of many living systems. Different concepts of entropy have been applied to the analysis of phyllotaxis. In the present paper we will determine the degree of order of disorganized patterns by using informational entropy concepts deduced from the work of Brillouin, Shannon, and Yagil. As case studies, we will apply these concepts of entropy to the disorganized patterns found in mutants of Arabidopsis. The calculation of entropy gives a precise idea of the degree of order of a phyllotactic system.     

Concepts in protein folding.

Certain concepts and misconceptions in the field of protein folding are discussed from the viewpoint of a theoretical physicist. It is argued that there can be no protein folding code and that perceived correlations between sequence or composition and three-dimensional structure are more likely to be an artefact of a limited database than a real result. Attempts at using molecular dynamics algorithms are also likely to produce artefactual results because results depend critically on the unknown hamiltonian energy function. Correct calculations of configurational entropy are thought to be the most likely next step in understanding how and why proteins fold.     

Accurate estimation of entropy in very short physiological time series: the problem of atrial fibrillation detection in implanted ventricular devices

Entropy estimation is useful but difficult in short time series. For example, automated detection of atrial fibrillation (AF) in very short heart beat interval time series would be useful in patients with cardiac implantable electronic devices that record only from the ventricle. Such devices require efficient algorithms, and the clinical situation demands accuracy. Toward these ends, we optimized the sample entropy measure, which reports the probability that short templates will match with others within the series. We developed general methods for the rational selection of the template length m and the tolerance matching r. The major innovation was to allow r to vary so that sufficient matches are found for confident entropy estimation, with conversion of the final probability to a density by dividing by the matching region volume, 2r(m). The optimized sample entropy estimate and the mean heart beat interval each contributed to accurate detection of AF in as few as 12 heartbeats. The final algorithm, called the coefficient of sample entropy (COSEn), was developed using the canonical MIT-BIH database and validated in a new and much larger set of consecutive Holter monitor recordings from the University of Virginia. In patients over the age of 40 yr old, COSEn has high degrees of accuracy in distinguishing AF from normal sinus rhythm in 12-beat calculations performed hourly. The most common errors are atrial or ventricular ectopy, which increase entropy despite sinus rhythm, and atrial flutter, which can have low or high entropy states depending on dynamics of atrioventricular conduction.     

混交林测树因子概率分布模型的构建及应用

基于最大熵原理,针对目前对混交林测树因子概率分布模型研究的不足,提出了联合最大熵概率密度函数,该函数具有如下特点：1）函数的每一组成部分都是相互联系的最大熵函数,故可以综合混交林各主要组成树种测树因子的概率分布信息;2）函数是具有双权重的概率表达式,能体现混交林结构复杂的特点,在最大限度地利用混交林每一主要树种测树因子概率分布信息的同时,还能精确地全面反映混交林测树因子概率分布规律;3）函数的结构简洁、性能优良.用天目山自然保护区的混交林样地对混交林测树因子概率分布模型进行了应用与检验,结果表明：模型的拟合精度(R²=0.9655)与检验精度(R²=
0.9772)都较高.说明联合最大熵概率密度函数可以作为混交林测树因子概率分布模型,为全面了解混交林林分结构提供了一种可行的方法.     

Entropic benefit of a cross-link in protein association

We introduce a method to estimate the loss of configurational entropy upon insertion of a cross-link to a dimeric system. First, a clear distinction is established between the loss of entropy upon tethering and binding, two quantities that are often considered to be equivalent. By comparing the probability distribution of the center-to-center distances for untethered and cross-linked versions, we are able to calculate the loss of translational entropy upon cross-linking. The distribution function for the untethered helices is calculated from the probability that a given helix is closer to its partner than to all other helices, the "Nearest Neighbor" method. This method requires no assumptions about the nature of the solvent, and hence resolves difficulties normally associated with calculations for systems in liquids. Analysis of the restriction of angular freedom upon tethering indicates that the loss of rotational entropy is negligible. The method is applied in the context of the folding of a ten turn helical coiled coil with the tether modeled as a Gaussian chain or a flexible amino acid chain. After correcting for loop closure entropy in the docked state, we estimate the introduction of a six-residue tether in the coiled coil results in an effective concentration of the chain to be about 4 or 100 mM, depending upon whether the helices are denatured or pre-folded prior to their association. Thus, tethering results in significant stabilization for systems with millimolar or stronger dissociation constants.     

Sample entropy analysis of neonatal heart rate variability

Abnormal heart rate characteristics of reduced variability and transient decelerations are present early in the course of neonatal sepsis. To investigate the dynamics, we calculated sample entropy, a similar but less biased measure than the popular approximate entropy. Both calculate the probability that epochs of window length m that are similar within a tolerance r remain similar at the next point. We studied 89 consecutive admissions to a tertiary care neonatal intensive care unit, among whom there were 21 episodes of sepsis, and we performed numerical simulations. We addressed the fundamental issues of optimal selection of m and r and the impact of missing data. The major findings are that entropy falls before clinical signs of neonatal sepsis and that missing points are well tolerated. The major mechanism, surprisingly, is unrelated to the regularity of the data: entropy estimates inevitably fall in any record with spikes. We propose more informed selection of parameters and reexamination of studies where approximate entropy was interpreted solely as a regularity measure.     

Origin and evolution of life and intellect from the point of view of information processing]

Beginning of life and intellect on the Earth is determined by the fact that synthesis of semantic information about algorithms of chemical transformation for appointed classes of chemical compounds is not accompanied by the information synthesis, but is controlled by chance in genetic material. Genetic information as memorizing accidental choice always arises as a result of the environment interaction, when memorizing realization in the form of repeated reproduction occurs on the basis of processes radically different from those which created initial genetic chance. Such stepped synthesis of information has hierarchical character and it is described by entropy of different dimensions. Entropy is determined by conditional probabilities. Therefore as a form of life becomes complicated, the entropy is decreased within the limits of the given hierarchical step. The part of entropy depending on the number of elements of the system (cells, individuals, etc.) always increases in the memorizing process, i. e. life defines the maximum of entropy production (but not the minimum like in nature). This fact settles paradoxes of chance in Darwinism: as a result of entropy decrease within higher hierarchical step the simbiotic processes for more complex forms of life can arise with great probability. For instance, rapidity of evolution of human brain given by supplementary chance in the mechanism of fecundation under the conditions of biochemical pressure of androgenes both, on the brain development and on muscular force at the same time. Synthesis of information in the brain is determined by the same principles, but extremums of the thermo-dynamic potential (their analogues in logic) are based on an arbitrary system of axioms. As a whole life and intellect are not fluctuations pointed against entropy increases, but they arose according to spontaneous process of entropy development.     

Thermodynamic study of motor behaviour optimization

Our work is aimed at studying the optimization of a complex motor behaviour from a global perspective. First, free climbing as a sport will be briefly introduced while emphasizing in particular its psychomotor aspect called route finding. The basic question raised here is how does the optimization of a sensorimotoricity-environment system take place. The material under study is the free climber's trajectory, viewed as the signature of climbing behaviour (i.e., the spatial dimension). The concepts of learning, optimization, constraint, and degrees of freedom of a system will be discussed using the synergistic approach to the study of movement (Bernstein, 1967; Kelso, 1977). Measures of a trajectory's length and convex hull can be used to define an index whose equation resembles that of an entropy. This index is a measure of the trajectory's overall complexity. Some important concepts related to the thermodynamics of curves will also be discussed. The optimization process will be studied by examining the changes in entropy over time for a set of trajectories generated during the learning of a route (ten successive repetitions of the same climb). It will be shown that the entropy of the trajectories decreases as learning progresses, that each level of expertise has its own characteristic entropy curve, and that for the subjects tested, the mean entropy of skilled climbers is lower than that of average climbers. Basing our analysis on the concepts of degrees of freedom and constraint equations, an attempt is made to relate trajectory entropy to system entropy. Based on the postulate that trajectory entropy is equal to the difference in entropy between the unconstrained and constrained system, a model of motor optimization is proposed. This model is illustrated by an entropy graph reflecting a dynamic release process. In the light of our results, two opposing views will be examined: movement construction vs. movement emergence.     

The Path Integral Formulation of Climate Dynamics

The chaotic nature of the atmospheric dynamics has stimulated the applications of methods and ideas derived from statistical dynamics. For instance, ensemble systems are used to make weather predictions recently extensive, which are designed to sample the phase space around the initial condition. Such an approach has been shown to improve substantially the usefulness of the forecasts since it allows forecasters to issue probabilistic forecasts. These works have modified the dominant paradigm of the interpretation of the evolution of atmospheric flows (and oceanic motions to some extent) attributing more importance to the probability distribution of the variables of interest rather than to a single representation. The ensemble experiments can be considered as crude attempts to estimate the evolution of the probability distribution of the climate variables, which turn out to be the only physical quantity relevant to practice. However, little work has been done on a direct modeling of the probability evolution itself. In this paper it is shown that it is possible to write the evolution of the probability distribution as a functional integral of the same kind introduced by Feynman in quantum mechanics, using some of the methods and results developed in statistical physics. The approach allows obtaining a formal solution to the Fokker-Planck equation corresponding to the Langevin-like equation of motion with noise. The method is very general and provides a framework generalizable to red noise, as well as to delaying differential equations, and even field equations, i.e., partial differential equations with noise, for example, general circulation models with noise. These concepts will be applied to an example taken from a simple ENSO model.     

The concept of structural entropy in tissue-based diagnosis

The concept of entropy is described and its characteristics discussed as applied in tissue-based diagnosis. The concept of entropy includes at least 2 points of view--thermodynamic and informatics perspectives. Entropy can be defined by various methods: a measure of nonreversible energy or of system heterogeneity or as information content of a message. It is a statistical measure and system feature composed of macrosystems and microsystems. The structural entropy of macrosystems relies on definition of individual events and built-in microsystems. It depends on interaction of events and probability distribution (e.g., Gibbs-Boltzmann). The more generalized q-entropy involves account interaction of neighboring events. The thermodynamic concept of structural entropy can be expanded according to the theorem of Prigogine, introducing entropy flow. In biology, cells usually serve for events in the thermodynamic entropy approach. Entropy has been successfully used to describe tissue sections, nuclei and nuclear substructures such as DNA content, chromosomes and AgNORs. The concept of entropy reveals a close relationship of structural entropy and prognosis-associated diagnosis of malignancies. It is useful in prognosis-associated, tissue-based diagnosis in breast, prostate, bladder and lung cancer and is a promising expansion of image analysis in diagnostic agnosis in breast, prostate, bladder and lung cancer and is a promising expansion of image analysis in diagnostic pathology.     

A thermodynamic perspective on food webs: quantifying entropy production within detrital-based ecosystems

Because ecosystems fit so nicely the framework of a "dissipative system", a better integration of thermodynamic and ecological perspectives could benefit the quantitative analysis of ecosystems. One obstacle is that traditional food web models are solely based upon the principles of mass and energy conservation, while the theory of non-equilibrium thermodynamics principally focuses on the concept of entropy. To properly cast classical food web models within a thermodynamic framework, one requires a proper quantification of the entropy production that accompanies resource processing of the food web. Here we present such a procedure, which emphasizes a rigorous definition of thermodynamic concepts (e.g. thermodynamic gradient, disequilibrium distance, entropy production, physical environment) and their correct translation into ecological terms. Our analysis provides a generic way to assess the thermodynamic operation of a food web: all information on resource processing is condensed into a single resource processing constant. By varying this constant, one can investigate the range of possible food web behavior within a given fixed physical environment. To illustrate the concepts and methods, we apply our analysis to a very simple example ecosystem: the detrital-based food web of marine sediments. We examine whether entropy production maximization has any ecological relevance in terms of food web functioning.     

Sample entropy analysis of cervical neoplasia gene-expression signatures

Background  

We introduce Approximate Entropy as a mathematical method of analysis for microarray data. Approximate entropy is applied here as a method to classify the complex gene expression patterns resultant of a clinical sample set. Since Entropy is a measure of disorder in a system, we believe that by choosing genes which display minimum entropy in normal controls and maximum entropy in the cancerous sample set we will be able to distinguish those genes which display the greatest variability in the cancerous set. Here we describe a method of utilizing Approximate Sample Entropy (ApSE) analysis to identify genes of interest with the highest probability of producing an accurate, predictive, classification model from our data set.     

The entropic cost of protein-protein association: a case study on acetylcholinesterase binding to fasciculin-2

Protein-protein association is accompanied by a large reduction in translational and rotational (external) entropy. Based on a 15 ns molecular dynamics simulation of acetylcholinesterase (AChE) in complex with fasciculin 2 (Fas2), we estimate the loss in external entropy using quasiharmonic analysis and histogram-based approximations of the probability distribution function. The external entropy loss of AChE-Fas2 binding, ~30 cal/mol K, is found to be significantly larger than most previously characterized protein-ligand systems. However, it is less than the entropy loss estimated in an earlier study by A. V. Finkelstein and J. Janin, which was based on atomic motions in crystals.     

Rare Dissipative Transitions Punctuate the Initiation of Chemical Denaturation in Proteins

Protein unfolding dynamics are bound by their degree of entropy production, a quantity that relates the amount of heat dissipated by a nonequilibrium process to a system’s forward and time-reversed trajectories. We here explore the statistics of heat dissipation that emerge in protein molecules subjected to a chemical denaturant. Coupling large molecular dynamics datasets and Markov state models with the theory of entropy production, we demonstrate that dissipative processes can be rigorously characterized over the course of the urea-induced unfolding of the protein chymotrypsin inhibitor 2. By enumerating full entropy production probability distributions as a function of time, we first illustrate that distinct passive and dissipative regimes are present in the denaturation dynamics. Within the dissipative dynamical region, we next find that chymotrypsin inhibitor 2 is strongly driven into unfolded states in which the protein’s hydrophobic core has been penetrated by urea molecules and disintegrated. Detailed analyses reveal that urea’s interruption of key hydrophobic contacts between core residues causes many of the protein’s native structural features to dissolve.