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PubMed1988

Informational parameters of nucleic acid and molecular evolution.

From the point of view of information theory, a statistical analysis of 2000 nucleic acid sequences (732 coding regions and 1177 non-coding regions) is given. The sequences are grouped into 20 categories. The probability-order-difference (POD) matrix is defined which is used to analyse the evolutionary distance of any two categories of sequences. The informational parameters D1, D2 and X = (1 + D1/D2)-1 and F are calculated for each sequence and averaged in each category. The statistical dependence of these parameters on molecular evolution is discussed. It is found that [X] is a good statistical quantity which describes the vocabulary compositions as well as the grammatical constructions of the genetic language. From the statistical analysis it is shown that [X] may play an important role in investigating the evolutionary level of nucleic acid molecules.

Base Sequence↗

PubMed1995

Unrooted genealogical tree probabilities in the infinitely-many-sites model.

The infinitely-many-sites process is often used to model the sequence variability observed in samples of DNA sequences. Despite its popularity, the sampling theory of the process is rather poorly understood. We describe the tree structure underlying the model and show how this may be used to compute the probability of a sample of sequences. We show how to produce the unrooted genealogy from a set of sites in which the ancestral labeling is unknown and from this the corresponding rooted genealogies. We derive recursions for the probability of the configuration of sequences (equivalently, of trees) in both the rooted and unrooted cases. We give a computational method based on Monte Carlo recursion that provides approximates to sampling probabilities for samples of any size. Among several applications, this algorithm may be used to find maximum likelihood estimators of the substitution rate, both when the ancestral labeling of sites is known and when it is unknown.

Biological Evolution↗

PubMed2000

Typical error versus limits of agreement.

We have shown that the SEM (typical error) and LOA are very similar when defined at the same level of abstraction. The calculation of these sample statistics does not depend on sample size, but the precision of their estimate for the population parameter does. Only the latter concept involves the t-statistic. They do differ in the type of measurement error that is described (true score error versus test-retest error) and the coverage probability of the reference interval (0.6 versus 0.95). Bland and Altman and Atdinson and Nevill have promoted the citation of either the SEM or the LOA to help researchers in their discussion of the impact of error to real uses of the measurement tol. What is vital in this discussion is the researcher having a thorough understanding of the underlying theory behind the measurement error statistic(s) that is/are employed, especially the definition of error and the coverage probability that is selected. Such issues have been built into the title of the 95% LOA statistic, and are also an inherent part of SEM. Whilst the concept of typical error appears to be easy to understand and teach, this is only because the underlying theory and definition of what the statistic actually represents is not communicated. Only if all researchers adopt one single statistic (e.g. typical error) for measurement error is it remotely possible to push underlying theory into the background, since there would be a baseline of comparison for all. Because this scenario is highly unlikely, it is important that any measurement error statistic is well defined and understood by researchers.

Confidence Intervals↗

PubMed2006

Density functional theory study of vibronic structure of the first absorption Qx band in free-base porphin.

Harmonic vibrational frequencies and vibronic intensities in the first S(0)-->S(1) (pipi( *)) absorption band of free-base porphin (H(2) P) are investigated by hybrid density functional theory (DFT) with the standard B3LYP functional. The S(0)-S(1) transition probability is calculated using time-dependent DFT with account of Franck-Condon (FC) and Herzberg-Teller (HT) contributions to the electric-dipole transition moments including displacements along all 108 vibrational modes. Two weak wide bands observed in the gas phase absorption spectra of the H(2) P molecule at 626 and 576 nm are interpreted as the 0-0 band of the X(1) A(g)-->1B(3u) transition and the 0-1 band with largest contributions from the nu(10)(a(g))=1610 cm(-1) and nu(19)(b(1g))=1600 cm(-1) modes, respectively, in agreement with previous tentative assignments. Both bands are induced by the HT mechanism, while the FC contributions are negligible. A number of fine structure bands, including combination of two vibrational quanta, are obtained and compared with available spectra from supersonic jet and Shpolskij matrices. Both absorption and fluorescence spectra are interpreted on ground of the linear coupling model and a good fulfillment of the mirror-symmetry rule.

Chemical Phenomena↗

PubMed1991

The dynamics of gene amplification described as a multitype compartmental model and as a branching process.

The present work is aimed at developing the mathematical tools by which the dynamics of gene amplification (GA) can be described in detail. Some discrete compartmental models of GA by disproportionate replication and a general model for other putative GA mechanisms are presented and analyzed. The dynamical distribution of gene copy number in the cell population is calculated with the loss of cells taken either as constant or as copy-number-dependent. Our analysis shows that for a one-copy GA process with constant loss of cells, the relative frequency of single-gene-copy cells (sensitive cells) converges to zero, with the rate of convergence depending on the amplification probability. In contrast, for a one-copy GA process with copy-number-dependent loss of cells, the relative frequency of single-copy cells is bounded, implying a bounded compartment of many-gene-copy cells. Using branching processes theory we calculate the dynamical distribution of the single-gene-copy compartment as well as its extinction probability. Our models are used for estimating treatment prognosis as affected by drug resistance due to GA, showing significant differences in prognosis resulting from small changes in drug dose.

Animals↗

PubMed2005

Distribution of the largest aftershocks in branching models of triggered seismicity: theory of the universal Båth law.

Using the epidemic-type aftershock sequence (ETAS) branching model of triggered seismicity, we apply the formalism of generating probability functions to calculate exactly the average difference between the magnitude of a mainshock and the magnitude of its largest aftershock over all generations. This average magnitude difference is found empirically to be independent of the mainshock magnitude and equal to 1.2, a universal behavior known as Båth's law. Our theory shows that Båth's law holds only sufficiently close to the critical regime of the ETAS branching process. Allowing for error bars +/- 0.1 for Båth's constant value around 1.2, our exact analytical treatment of Båth's law provides new constraints on the productivity exponent alpha and the branching ratio n: 0.9 approximately < alpha < or =1. We propose a method for measuring alpha based on the predicted renormalization of the Gutenberg-Richter distribution of the magnitudes of the largest aftershock. We also introduce the "second Båth law for foreshocks:" the probability that a main earthquake turns out to be the foreshock does not depend on its magnitude rho.

Journal Article↗

PubMed1975

Comments of Holmquist's theory for paleogenetics: the effect of multiple hits on nucleotide differences between homologous DNA's.

The notion of the probability of back mutation is introduced and the method of probability generating functions is used in order to simplify and unify the Holmquist's (1972) investigation of the effect of multiple hits on nucleotide differences between homologous DNAs. We obtain explicit expressions for the distribution of the number of hit nucleotide sites, the number of altered sites, and the number of differences between two homologous DNAs, as functions of the total number of hits. For the case where the hit rate is a known function of time, we derive a formula for extending these results as functions of time.

Base Sequence↗

PubMed2003

MDFT account of decision making under time pressure.

In this paper, decision making under time pressure for multiattribute choice alternatives in a risky environment is investigated. A model, multiattribute decision field theory (MDFT), is introduced that describes both the dynamic and the stochastic nature of decision making and accounts for the observed changes in choice probabilities, including preference reversals as a function of time limit. An experiment in which five different time limits were imposed on the decision maker is presented to test the predictions of the model. It is shown that MDFT is able to account for the complex decision behavior observed in the data. Furthermore, MDFT is compared with the predictions of decision field theory (Busemeyer & Townsend, 1993; Roe, Busemeyer, & Townsend, 2001).

Adult↗

PubMed2006

Caloric restriction increases longevity substantially only when the reaction norm is steep.

Evolutionary theory leads to the general expectation that dietary restriction will often result in increased survival probabilities, and thus increased lifespan. The reaction norm is a basic tool of evolutionary analysis that quantifies the relationship between environmental parameters and functional characters, including reproduction and longevity. In rodents, the reaction norm connecting adult longevity to caloric intake is fairly steep; small changes in intake lead to large changes in longevity. If this strong quantitative relationship were evolutionarily conserved among all mammals, then the prospects for a substantial increase in human lifespan from caloric restriction would be very good. In theory, however, reaction norms are expected to evolve for fitness related characters such as reproduction and survival. It has been shown experimentally in Drosophila that dietary reaction norms readily evolve in the laboratory, suggesting that they can do so among mammals as well, particularly over the millions of years since contemporary rodents and primates last shared a common ancestor. Our previous work crudely estimates that the dietary reaction norms of rodents and humans have diverged substantially, with a very flat dietary reaction norm for human longevity. These general principles and our specific results suggest that the benefits from human caloric restriction would be minor.

Adaptation, Physiological↗

PubMed2005

Recent developments in the kinetic theory of nucleation.

A review of recent progress in the kinetics of nucleation is presented. In the conventional approach to the kinetic theory of nucleation, it is necessary to know the free energy of formation of a new-phase particle as a function of its independent variables at least for near-critical particles. Thus the conventional kinetic theory of nucleation is based on the thermodynamics of the process. The thermodynamics of nucleation can be examined by using various approaches, such as the capillarity approximation, density functional theory, and molecular simulation, each of which has its own advantages and drawbacks. Relatively recently a new approach to the kinetics of nucleation was proposed [Ruckenstein E, Nowakowski B. J Colloid Interface Sci 1990;137:583; Nowakowski B, Ruckenstein E. J Chem Phys 1991;94:8487], which is based on molecular interactions and does not employ the traditional thermodynamics, thus avoiding such a controversial notion as the surface tension of tiny clusters involved in nucleation. In the new kinetic theory the rate of emission of molecules by a new-phase particle is determined with the help of a mean first passage time analysis. This time is calculated by solving the single-molecule master equation for the probability distribution function of a surface layer molecule moving in a potential field created by the rest of the cluster. The new theory was developed for both liquid-to-solid and vapor-to-liquid phase transitions. In the former case the single-molecule master equation is the Fokker-Planck equation in the phase space which can be reduced to the Smoluchowski equation owing to the hierarchy of characteristic time scales. In the latter case, the starting master equation is a Fokker-Planck equation for the probability distribution function of a surface layer molecule with respect to both its energy and phase coordinates. Unlike the case of liquid-to-solid nucleation, this Fokker-Planck equation cannot be reduced to the Smoluchowski equation, but the hierarchy of time scales does allow one to reduce it to the Fokker-Plank equation in the energy space. The new theory provides an equation for the critical radius of a new-phase particle which in the limit of large clusters (low supersaturations) yields the Kelvin equation and hence an expression for the macroscopic surface tension. The theory was illustrated with numerical calculations for a molecular pair interaction potential combining the dispersive attraction with the hard-sphere repulsion. The results for the liquid-to-solid nucleation clearly show that at given supersaturation the nucleation rate depends on the cluster structure (for three cluster structures considered-amorphous, fcc, and icosahedral). For both the liquid-to-solid and vapor-to-liquid nucleation, the predictions of the theory are consistent with the results of classical nucleation theory (CNT) in the limit of large critical clusters (low supersaturations). For small critical clusters the new theory provides higher nucleation rates than CNT. This can be accounted for by the fact that CNT uses the macroscopic interfacial tension which presumably overpredicts the surface tension of small clusters, and hence underpredicts nucleation rates.

Kinetics↗

PubMed1977

Psychological differentiation, event uncertainty, and heart rate.

Psychological differentiation and uncertainty about receiving a painful noise were examined for their effects on heart rate during the anticipatory, impact and recovery phases of the tone presentation. Psychologically differentiated and nondifferentiated subjects were randomly assigned to three event uncertainty conditions (5 percent, 50 percent, 95 percent probability of noise). Subjects were informed of the probability of receiving the noise, as well as the time of occurrence as indicated by a sequentially numbered visual display. Subjects received the noise on the second of the experiment's two trials. Cognitive style and event uncertainty interacted during the anticipatory phase--i.e., differentiated subjects showed a monotonic increase in heart rate with increasing probability of receiving the noise that represents preparation for instrumental activity. Results are consistent with the theory that meaningful personality-stress relationships may be obtained when examining stimulus-oriented dispositions.

Acoustic Stimulation↗

PubMed2002

Pressure amorphization through displacive disorder.

After classifying amorphous materials according to their topology, we review a recently proposed theory of pressure amorphization (PA) that arises from some degree of displacive disorder while retaining a crystalline topology. That theory is based on the notion that one or more branches of the phonon spectrum become soft and flat with increasing pressure and is illustrated by a simple model that possesses the range of features displayed by many of the materials which undergo PA with displacive disorder. We report the results of Langevin simulations of the simple model which show how the probability of amorphization increases with the number of unit cells in the system and support our theory. We comment on how to generalize the model for the study of real systems.

Journal Article↗

PubMedDate not supplied

[Membrane probability profile construction based on amino acids sequences multiple alignment].

Prediction of membrane segments in sequences of membrane proteins is well known and important problem. Accuracy of the solution of this problem by methods that don't use homology search in additional data bank can be improved. There is a lack of testing data in this area because of small amount of real structures of membrane proteins. In this work, we create a testing set of structural alignments of membrane proteins, in which positioning of the membrane segments reflects agreement of known 3D-structures of proteins in the alignment. We propose a method for predicting position of membrane segments in multiple alignment based on forward-backward algorithm from HMM theory. This method not only allows to predict positions of membrane segments but also forms probability membrane profile, which can be used in multiple alignment methods that take into account secondary structure information about sequences. Method is implemented in computer program available on the World-Wide Web site http://bioinf.fbb.msu.ru/fwdbck/. Proposed method provides results better than MEMSAT method, which is nearly only tool for prediction of membrane segments in multiple alignments without additional homology search.

Animals↗

PubMed2005

Exact and resampling probability values for measures of categorical variation and consensus.

When analyzing categorical data, it is often important to assess the magnitude of variation, or consensus, among observations in unordered categories. Utilizing the theory of partitions, exact solutions for five commonly used measures of categorical variation are presented. When the number of partitions is very large, resampling methods provide close approximations to exact probability values.

Algorithms↗

PubMedDate not supplied

Mental models and probabilistic thinking.

This paper outlines the theory of reasoning based on mental models, and then shows how this theory might be extended to deal with probabilistic thinking. The same explanatory framework accommodates deduction and induction: there are both deductive and inductive inferences that yield probabilistic conclusions. The framework yields a theoretical conception of strength of inference, that is, a theory of what the strength of an inference is objectively: it equals the proportion of possible states of affairs consistent with the premises in which the conclusion is true, that is, the probability that the conclusion is true given that the premises are true. Since there are infinitely many possible states of affairs consistent with any set of premises, the paper then characterizes how individuals estimate the strength of an argument. They construct mental models, which each correspond to an infinite set of possibilities (or, in some cases, a finite set of infinite sets of possibilities). The construction of models is guided by knowledge and beliefs, including lay conceptions of such matters as the "law of large numbers". The paper illustrates how this theory can account for phenomena of probabilistic reasoning.

Humans↗

PubMed2005

Influence of supercoiling on the disruption of dsDNA.

We propose that supercoiling energizes double-stranded DNA (dsDNA) so as to facilitate thermal fluctuations to an unzipped state. We support this with a model of two elastic rods coupled via forces that represent base-pair interactions. Supercoiling is shown to lead to a distention of base pairs over a short span of dsDNA. This enhances the thermal probability for their disruption. The localized region of distention is analogous to a soliton. Our theory permits the development of an analogy between the unzipping transition and a second-order phase transition, for which the possibility of a new set of critical exponents is identified.

Base Composition↗

PubMed2006

Mechanics-based statistics of failure risk of quasibrittle structures and size effect on safety factors.

In mechanical design as well as protection from various natural hazards, one must ensure an extremely low failure probability such as 10(-6). How to achieve that goal is adequately understood only for the limiting cases of brittle or ductile structures. Here we present a theory to do that for the transitional class of quasibrittle structures, having brittle constituents and characterized by nonnegligible size of material inhomogeneities. We show that the probability distribution of strength of the representative volume element of material is governed by the Maxwell-Boltzmann distribution of atomic energies and the stress dependence of activation energy barriers; that it is statistically modeled by a hierarchy of series and parallel couplings; and that it consists of a broad Gaussian core having a grafted far-left power-law tail with zero threshold and amplitude depending on temperature and load duration. With increasing structure size, the Gaussian core shrinks and Weibull tail expands according to the weakest-link model for a finite chain of representative volume elements. The model captures experimentally observed deviations of the strength distribution from Weibull distribution and of the mean strength scaling law from a power law. These deviations can be exploited for verification and calibration. The proposed theory will increase the safety of concrete structures, composite parts of aircraft or ships, microelectronic components, microelectromechanical systems, prosthetic devices, etc. It also will improve protection against hazards such as landslides, avalanches, ice breaks, and rock or soil failures.

Journal Article↗

PubMed1977

Acquisition of the covalent quaternary structure of an immunoglobulin G molecule. Theoretical reoxidation models.

A theoretical format suitable for analyzing diverse complex kinetic systems where reaction pathways may exhibit cooperativity, is developed to account for the in vitro kinetics of air reoxidation of a human IgGlkappa immunoglobulin, in which the four interchain disulfide bonds have been reduced (Sears, D.W., et al. (1977), Biochemistry 16 (preceding paper in this issue)). The equations relate experimentally determined concentrations of the reactants, product, and macroscopic intermediates to the probability of occurrence of any of 12 distinct microscopic states. The concentrations of the macroscopic species--light chains (L), heavy chains (H), covalently associated intermediates HL, H2, H2L, and product H2L2--are also explicitly related to an observable function of those concentrations, the sulfhydryl titer, r. Since values of r can be calculated for any microscopic state of the system, the theory is in principle capable of a complete description of the experimental reaction course. In practice, limited experimental information precludes a unique solution of the equations at present, and it was not judged worthwhile to attempt curve fitting or approximation of probability terms with adjustable parameters of unknown physical significance. Certain special cases of the theory are, however, readily and exactly solved. These include models in which reoxidation is a random process and others in which the probabilities for inter-HL and inter-HH bond formation are different but independent of one another. The experimental results in the case of the IgGlkappa studied here clearly depart form the predicted behavior in either of these models. The initial probability for formation of a bond between a heavy and light chain is 1.5 to 2 times greater than for a bond between heavy chains. From the fact that this ratio changes as the reaction proceeds, and from the pattern of variation in concentration of intermediates during the reaction, it is concluded that the reoxidation process is not random, and that the bonds do not form independently, exhibiting instead kinetic cooperativity. The results are discussed in terms of assembly pathways in this and related systems. A novel feature of the theory is that it eliminates time as an explicit variable in the treatment of the kinetic process. This makes it especially useful for discerning whether the formation of one bond influences the reaction probability of another in a system where several similar or intrinsically identical reactions occur, and where kinetic order is difficult to establish. While the theory here is formulated in terms of the reoxidation reactions, it is, for example, equally applicable to the reduction process described (Sears, D.W., et al. (1977b), Biochemistry 16 (following paper in this issue)).

Disulfides↗