Moments of the Boltzmann distribution for RNA secondary structures

We here present a dynamic programming algorithm which is capable of calculating arbitrary moments of the Boltzmann distribution for RNA secondary structures. We have implemented the algorithm in a program called RNA-variance and investigate the difference between the Boltzmann distribution of biological and random RNA sequences. We find that the minimum free energy structure of biological sequences has a higher probability in the Boltzmann distribution than random sequences. Moreover, we show that the free energies of biological sequences have a smaller variance than random sequences and that the minimum free energy of biological sequences is closer to the expected free energy of the rest of the structures than that of random sequences. These results suggest that biologically functional RNA sequences not only require a thermodynamically stable minimum free energy structure, but also an ensemble of structures whose free energies are close to the minimum free energy.

A genetic code Boolean structure. II. The genetic information system as a Boolean information system

A Boolean structure of the genetic code where Boolean deductions have biological and physicochemical meanings was discussed in a previous paper. Now, from these Boolean deductions we propose to define the value of amino acid information in order to consider the genetic information system as a communication system and to introduce the semantic content of information ignored by the conventional information theory. In this proposal, the value of amino acid information is proportional to the molecular weight of amino acids with a proportional constant of about 1.96 x 10(25) bits per kg. In addition to this, for the experimental estimations of the minimum energy dissipation in genetic logic operations, we present two postulates: (1) the energy Ei (i=1,2,...,20) of amino acids in the messages conveyed by proteins is proportional to the value of information, and (2) amino acids are distributed according to their energy Ei so the amino acid population in proteins follows a Boltzmann distribution. Specifically, in the genetic message carried by the DNA from the genomes of living organisms, we found that the minimum energy dissipation in genetic logic operations was close to kTLn(2) joules per bit.

Assessment of Agreement under Nonstandard Conditions Using Regression Models for Mean and Variance

The total deviation index of Lin and Lin et al. is an intuitive approach for the assessment of agreement between two methods of measurement. It assumes that the differences of the paired measurements are a random sample from a normal distribution and works essentially by constructing a probability content tolerance interval for this distribution. We generalize this approach to the case when differences may not have identical distributions -- a common scenario in applications. In particular, we use the regression approach to model the mean and the variance of differences as functions of observed values of the average of the paired measurements, and describe two methods based on asymptotic theory of maximum likelihood estimators for constructing a simultaneous probability content tolerance band. The first method uses bootstrap to approximate the critical point and the second method is an analytical approximation. Simulation shows that the first method works well for sample sizes as small as 30 and the second method is preferable for large sample sizes. We also extend the methodology for the case when the mean function is modeled using penalized splines via a mixed model representation. Two real data applications are presented.

Effect of short-term exposure to low levels of gaseous pollutants on chronic obstructive pulmonary disease hospitalizations

We examined the associations between gaseous pollutants and hospitalization for chronic obstructive pulmonary diseases (COPD) among elderly people living in Vancouver, British Columbia, Canada, a city in which ambient air pollution levels are relatively low. We regressed the logarithm of daily counts of acute COPD hospitalization during the 5-year period from 1994 to 1998 on the daily mean levels of each pollutant, after accounting for seasonal and subseasonal fluctuations, non-Poisson dispersion, and weather variables. Nitrogen dioxide and carbon monoxide were significantly associated with hospitalization for COPD, and the magnitude of effects was increased slightly with increasing days of exposure averaging, with the relative risk for a 7-day average being 1.11 (95%CI: 1.04, 1.20) and 1.08 (1.02, 1.13) for nitrogen dioxide and carbon monoxide, respectively. There was no significant association between either sulfur dioxide or ozone and COPD hospitalization. The combined relative risk for all four gaseous pollutants on COPD hospitalization was 1.21. The effects of gaseous pollutants on COPD hospitalization were not significant after adjustment for PM(10), although its inclusion did not have a marked effect on the point estimates for relative risks. Nitrogen dioxide has a significant impact on COPD hospitalization. Further studies are needed to separate the effects of single pollutants from the combined effects of the complex mixture of air pollutants in urban atmospheres.

Multipoint correlation functions for continuous-time random walk models of anomalous diffusion

Recursive relations are developed for computing the multipoint correlation functions of a particle undergoing a biased continuous-time random walk (CTRW) in an external potential. Two- and three-point correlation functions are calculated for waiting-time distributions with an anomalous power-law profile t(-alpha-1), 0 < alpha < 1, on intermediate time scales with a crossover to an exponential long time decay. Comparison of the CTRW with the Brownian harmonic oscillator model (Gaussian process) illustrates how higher-order correlation functions may be used to distinguish between dynamical models that have the same two-point correlation function.

Power laws of complex systems from extreme physical information

Many complex systems obey allometric, or power, laws y=Y x(a) . Here y > or = 0 is the measured value of some system attribute a , Y> or =0 is a constant, and x is a stochastic variable. Remarkably, for many living systems the exponent a is limited to values n/4 , n=0, +/-1, +/-2.... Here x is the mass of a randomly selected creature in the population. These quarter-power laws hold for many attributes, such as pulse rate (n=-1) . Allometry has, in the past, been theoretically justified on a case-by-case basis. An ultimate goal is to find a common cause for allometry of all types and for both living and nonliving systems. The principle I-J=extremum of extreme physical information is found to provide such a cause. It describes the flow of Fisher information J-->I from an attribute value a on the cell level to its exterior observation y . Data y are formed via a system channel function y identical to f (x,a) , with f (x,a) to be found. Extremizing the difference I-J through variation of f (x,a) results in a general allometric law f (x,a) identical to y=Y x(a) . Darwinian evolution is presumed to cause a second extremization of I-J , now with respect to the choice of a . The solution is a=n/4 , n=0,+/-1,+/-2..., defining the particular powers of biological allometry. Under special circumstances, the model predicts that such biological systems are controlled by only two distinct intracellular information sources. These sources are conjectured to be cellular DNA and cellular transmembrane ion gradients.

Complex networks emerging from fluctuating random graphs: analytic formula for the hidden variable distribution

In analogy to superstatistics, which connects Boltzmann-Gibbs statistical mechanics to its generalizations through temperature fluctuations, complex networks are constructed from fluctuating Erdös-Rényi random graphs. Using a quantum-mechanical method, the exact analytic formula for the hidden variable distribution is presented which describes the nature of the fluctuations and generates a generic degree distribution through the Poisson transformation. As an example, a static scale-free network is discussed and the corresponding hidden variable distribution is found to decay as a power law and to diverge at the origin.

The molecular changes during placental detachment

OBJECTIVES

RCAS1 is a membrane protein that plays a role in the maintenance of maternal immune tolerance during pregnancy. The work presented here demonstrates the results of RCAS1 expression in placenta in cases of placental abruption and patients with retained placental tissue during the third stage of labor.

STUDY DESIGN

The placenta tissue samples were obtained during vaginal and cesarean delivery (derived from 117 pregnancies). Pregnant women were divided into four groups according to the onset of labor and the time of placental detachment in term labors. The samples were analyzed by the Western blot method. Statistical analysis was performed using the Shapiro-Wilk procedure. The Mann-Whitney test and Student's t-test were applied to compare the differences between parametric data.

RESULTS

The average relative amount of RCAS1 observed in those patients with retained placental tissue was statistically significantly higher than in the patients with placental abruption.

CONCLUSION

The differences observed in placental RCAS1 levels confirm the participation of this protein in the inhibition of maternal immune response during gestation. The present results also indicate that RCAS1 participates in the changes in the maternal immune system that take place during parturition and reinforce its potential involvement in the mechanism of placental abruption.

Contributions of low molecule number and chromosomal positioning to stochastic gene expression

The presence of low-copy-number regulators and switch-like signal propagation in regulatory networks are expected to increase noise in cellular processes. We developed a noise amplifier that detects fluctuations in the level of low-abundance mRNAs in yeast. The observed fluctuations are not due to the low number of molecules expressed from a gene per se but originate in the random, rare events of gene activation. The frequency of these events and the correlation between stochastic expressions of genes in a single cell depend on the positioning of the genes along the chromosomes. Transcriptional regulators produced by such random expression propagate noise to their target genes.

Statistics of particle velocities in dense granular flows

We present measurements of the particle velocity distribution in the slow flow of granular material through vertical channels. The velocities of particles adjacent to the smooth, transparent front face of the channel were determined by video imaging and particle tracking. We find that the mean velocity changes sharply in shear layers near the side walls, but remains constant in a substantial core. The velocity distribution is non-Gaussian, is anisotropic, and follows a power law at large velocities. Remarkably, the distribution is identical in the shear layer and the core. We show evidence of spatially correlated motion, and propose a mechanism for the generation of fluctuational motion in the absence of shear.

Optimal design for dose response using beta distributed responses

Whenever a response is naturally confined to a finite interval (such as a visual analog scale for pain severity), the beta distribution provides a simple and flexible probability distribution to model such a response. The parameters of the distribution can then be related to covariates, such as dose, in a clinical trial through the generation of a beta regression model. In this article, we explore locally optimal designs for this class of regression models, focusing mainly on minimization of the generalized variance of maximum likelihood estimators (D-optimality). Optimal designs and sensitivity to misspecification of model parameters are examined using a candidate points searching algorithm. Although formally the model assumes that the response is continuous, it provides a parsimonious approximation for ordinal data when there is a relatively large number of categories. The resulting estimators and optimal designs are simpler and may offer more ease in interpretation than those derived from models for ordered categorical outcomes. The proposed methods are applied to data from a clinical trial.

Velocity distributions of granular gases with drag and with long-range interactions

We study velocity statistics of electrostatically driven granular gases. For two different experiments, (i) nonmagnetic particles in a viscous fluid and (ii) magnetic particles in air, the velocity distribution is non-Maxwellian, and its high-energy tail is exponential, P(upsilon) approximately exp(-/upsilon/). This behavior is consistent with the kinetic theory of driven dissipative particles. For particles immersed in a fluid, viscous damping is responsible for the exponential tail, while for magnetic particles, long-range interactions cause the exponential tail. We conclude that velocity statistics of dissipative gases are sensitive to the fluid environment and to the form of the particle interaction.

Analytical results for the statistical distribution related to a memoryless deterministic walk: dimensionality effect and mean-field models

Consider a medium characterized by N points whose coordinates are randomly generated by a uniform distribution along the edges of a unitary d-dimensional hypercube. A walker leaves from each point of this disordered medium and moves according to the deterministic rule to go to the nearest point which has not been visited in the preceding mu steps (deterministic tourist walk). Each trajectory generated by this dynamics has an initial nonperiodic part of t steps (transient) and a final periodic part of p steps (attractor). The neighborhood rank probabilities are parametrized by the normalized incomplete beta function Id= I1/4 [1/2, (d+1) /2] . The joint distribution S(N) (mu,d) (t,p) is relevant, and the marginal distributions previously studied are particular cases. We show that, for the memory-less deterministic tourist walk in the euclidean space, this distribution is Sinfinity(1,d) (t,p) = [Gamma (1+ I(-1)(d)) (t+ I(-1)(d) ) /Gamma(t+p+ I(-1)(d)) ] delta(p,2), where t=0, 1,2, ... infinity, Gamma(z) is the gamma function and delta(i,j) is the Kronecker delta. The mean-field models are the random link models, which correspond to d-->infinity, and the random map model which, even for mu=0 , presents nontrivial cycle distribution [ S(N)(0,rm) (p) proportional to p(-1) ] : S(N)(0,rm) (t,p) =Gamma(N)/ {Gamma[N+1- (t+p) ] N( t+p)}. The fundamental quantities are the number of explored points n(e)=t+p and Id. Although the obtained distributions are simple, they do not follow straightforwardly and they have been validated by numerical experiments.

New Data Base-independent, Sequence Tag-based Scoring of Peptide MS/MS Data Validates Mowse Scores, Recovers Below Threshold Data, Singles Out Modified Peptides, and Assesses the Quality of MS/MS Techniques

The Mascot score (M-score) is one of the conventional validity measures in data base identification of peptides and proteins by MS/MS data. Although tremendously useful, M-score has a number of limitations. For the same MS/MS data, M-score may change if the protein data base is expanded. A low M-value may not necessarily mean poor match but rather poor MS/MS quality. In addition M-score does not fully utilize the advantage of combined use of complementary fragmentation techniques collisionally activated dissociation (CAD) and electron capture dissociation (ECD). To address these issues, a new data base-independent scoring method (S-score) was designed that is based on the maximum length of the peptide sequence tag provided by the combined CAD and ECD data. The quality of MS/MS spectra assessed by S-score allows poor data (39% of all MS/MS spectra) to be filtered out before the data base search, speeding up the data analysis and eliminating a major source of false positive identifications. Spectra with below threshold M-scores (poor matches) but high S-scores are validated. Spectra with zero M-score (no data base match) but high S-score are classified as belonging to modified sequences. As an extension of S-score, an extremely reliable sequence tag was developed based on complementary fragments simultaneously appearing in CAD and ECD spectra. Comparison of this tag with the data base-derived sequence gives the most reliable peptide identification validation to date. The combined use of M- and S-scoring provides positive sequence identification from >25% of all MS/MS data, a 40% improvement over traditional M-scoring performed on the same Fourier transform MS instrumentation. The number of proteins reliably identified from Escherichia coli cell lysate hereby increased by 29% compared with the traditional M-score approach. Finally S-scoring provides a quantitative measure of the quality of fragmentation techniques such as the minimum abundance of the precursor ion, the MS/MS of which gives the threshold S-score value of 2.

Reliability of the long-range power-law correlations obtained from the bilateral stride intervals in asymptomatic volunteers whilst treadmill walking

Stride intervals measured during steady-state walking are irregular. These stride interval fluctuations are not random but exhibit long-range power-law correlation (alpha) such that a given stride interval is 'influenced' by earlier variations in the stride intervals. To estimate alpha, one requires a minute long sequence of right or left side stride interval data. However, to obtain a reliable alpha point estimate, the minimal stride sequence length is unknown. Additionally, it is unknown if the right and left side alpha are equivalent. In this study, the within-day and the right and left side reliabilities of alpha point estimates were examined in 23 volunteers performing three 8-min treadmill walks. In addition, eight volunteers were retested on three additional days to estimate between-day reliability. The standard error of measurement (S.E.M.) and the within- and between-day intraclass correlation (ICC) values, and their 95% confidence intervals, each calculated using the combined right and left leg 8-min alpha estimates were acceptable [0.047 (0.044-0.051); 0.914 (0.882-0.932) and 0.769 (0.689-0.815), respectively]. The left alpha (0.688 +/- 0.93) was greater than the right alpha (0.664 +/- 0.094), albeit this finding was underpowered (0.55). The alpha point estimates obtained from the full 8-min walks provided minimal S.E.M. and maximal within- and between-day ICCs. However, the minimal S.E.M. was statistically indistinguishable from the 6- and 7-min walk durations and all of the within-day and between-day ICCs were similar except for the 3- and 8-min between-day ICCs. This study suggests that data from four 3 min, three 6 min or two 8 min walk duration trials provide reliable alpha point estimates from a short series of short treadmill walks.

Note in statistical treatment of medical and pharmaceutical data

This study highlights the essential concept in the statistical treatment of medical and pharmaceutical data. To explain the concept, artificial data generated using random numbers was analyzed, and the importance of the confidence interval and distribution of data was shown. Sole use of the standard deviation (SD) is not considered appropriate from the viewpoint of clinical treatment, because many oversights occur. It was shown by considering the confidence interval that such oversights rarely occur, and the safety level is increased. Moreover, the probability of the occurrence of outliers from the average can be calculated by the distribution of data. Thus, pharmacokinetic data for humans were examined. The results for the human data also support the importance of the confidence interval and the distribution of differences between groups.

Determination of orientation distribution function of anisotropic paramagnetic species by analysis of ESR spectra angular dependence

A method has been developed to determine orientation distribution function (ODF) of anisotropic paramagnetic species by analysis of the angular dependence of the ESR spectra. The method is based on computational spectra simulation. The ODF is represented as an expansion in terms of orthonormal functions. The expansion coefficients are determined through minimization of discrepancies between simulated spectra and experimental ones. By means of the suggested method we have determined the orientation distribution functions for radical probe 2,2,6,6-tetramethyl-4-ol-piperidinooxyl in 4-n-amyl-4'-cyanobiphenyl aligned by magnetic field and 2-septadecyl-2,3,4,5,5-pentamethylimidazolidine in polyethylene stretched films. In each case, thermal evolution of the ODF has been investigated.

[The validity of the Willis Law for taxonomy]

Different explanations of Willis' law are discussed. The common view on the observed relationship between species and genus frequencies suggests that Willis' rule is artifact of two independent processes. However, actual data on similarity of the diversity patterns in different taxa contradicts with this of view and show that there are intrinsic laws regulating biological diversity. The analysis of statistical parameters of diagnostic keys reveals that distribution of differential features according to the frequency of their usage appeas to be ranked. Considering taxon size as extensional characteristic and the set of differential features as intensional characteristic one can conclude that nature of disctribution is identical in both cases. Existed data indicates that biological diversity is self-organizated and self-ordered. It allow to reconsider the conception of Natural system which could be considered as fractal with the properties of the whole composed of parts (taxa) similar by their properties to each other and to the whole. The lowest parts, units of Natural system are taxa of generic rank, their characteristics is subjected to the Willis' rule.

A Markov chain model for animal estrous cycling data

Estrous cycling data contain sequences of characters (e.g., DPEMD). Each sequence represents an animal's estrous cycle, with each character indicating the daily estrous cycle stage. Changes in the estrous cycle pattern, which is determined by estrous stage lengths, can provide information on adverse events. Stage lengths are not directly observable. However interval censored lengths for all but the first and the last stages in a sequence can be extracted from the data. We propose a Markov chain model to approximate the estrous cycling process. The transition probabilities from one stage to another can be derived by conditioning on stage lengths. Assuming Weibull distribution for stage lengths, with the second Weibull parameter depending upon treatment effects and animal-specific random effects, regression models on censored stage lengths are fitted. A Bayesian approach is used for inference on dose effects. The analysis is implemented with MCMC method in WinBUGS. An estrous cycling data set from a National Toxicology Program study is analyzed as an example.

Analysis of biological motors via multidimensional fractionation: a strategy

Past strategies for the analysis of ATP-fueled motors include single-motor analysis. Single-motor analysis bypasses limitations caused by motor asynchrony during the traditional ensemble averaging analysis. The present communication describes revised ensemble averaging analysis that also can bypass asynchrony-derived limitations. This revised analysis makes measurements of one motor variable dependent on the others. One example is nondenaturing gel electrophoresis with more than one dimension. Each dimension measures one of the motor variables. This multidimensional procedure is used to obtain the values of "conformational" motor variables as a function of a "clock" motor variable. In theory, the cycle of the motor can be analyzed from a single multidimensional analysis of a collection of asynchronous motors sampled at only one time. That is to say, motor asynchrony becomes an asset, rather than a liability.

Bias-corrected maximum likelihood estimator of the negative binomial dispersion parameter

We derive a first-order bias-corrected maximum likelihood estimator for the negative binomial dispersion parameter. This estimator is compared, in terms of bias and efficiency, with the maximum likelihood estimator investigated by Piegorsch (1990, Biometrics46, 863-867), the moment and the maximum extended quasi-likelihood estimators investigated by Clark and Perry (1989, Biometrics45, 309-316), and a double-extended quasi-likelihood estimator. The bias-corrected maximum likelihood estimator has superior bias and efficiency properties in most instances. For ease of comparison we give results for the two-parameter negative binomial model. However, an example involving negative binomial regression is given.

A stochastic model to analyze clonal data on multi-type cell populations

This article presents a stochastic model designed to analyze experimental data on the development of cell clones composed of two (or more) distinct types of cells. The proposed model is an extension of the traditional multi-type Bellman-Harris branching stochastic process allowing for nonidentical time-to-transformation distributions defined for different cell types. A simulated pseudo likelihood method has been developed for the parametric statistical inference from experimental data on cell clones under the proposed model. The method uses simulation-based approximations of the means and the variance-covariance matrices of cell counts. The proposed estimator for the vector of unknown parameters is strongly consistent and asymptotically normal under mild regularity conditions, while its variance-covariance matrix is estimated by the parametric bootstrap. A Monte Carlo Wald test is proposed for the test of hypotheses. Finite sample properties of the estimator have been studied by computer simulations. The model and associated methods of parametric inference have been applied to the analysis of proliferation and differentiation of cultured O-2A progenitor cells that play a key role in the development of the central nervous system. It follows from this analysis that the time to division of the progenitor cell and the time to its differentiation (into an oligodendrocyte) are not identically distributed. This biological finding suggests that a molecular event determining the type of cell transformation is more likely to occur at the start rather than at the end of the mitotic cycle.

Reproducibility of heart rate variability, blood pressure variability and baroreceptor sensitivity during rest and head-up tilt

OBJECTIVE

Previous studies have indicated moderate-to-poor reproducibility of heart rate variability (HRV) but the reproducibility of blood pressure variability (BPV) and spectral measures of baroreceptor sensitivity (BRS) are not well established.

METHODS

We measured normal-to-normal heart beat (RR) interval and finger blood pressure (Finapres) in 14 healthy individuals on three different days. The protocol was 1 h of supine rest and 1 h of 60-degree head-up tilt. Time-series of consecutive 300-s segments as well as 1024-s segments of RR intervals and systolic, diastolic and mean blood pressures were extracted for the assessment of day-to-day and short-term reproducibility. Power spectrum analysis (Fourier) and transfer function analysis was performed. Reproducibility was assessed using the coefficient of variation (CV). The reproducibility of the mean RR interval, mean systolic, diastolic and mean blood pressure was good (CV<10 %). However, there was only moderate-to-poor reproducibility of the spectral parameters of HRV (CV range 18-36%) and BPV (16-44%) and moderate reproducibility of BRS (14-20%).

CONCLUSION

Spectral estimates of BRS had only moderate reproducibility although it was better than the spectral estimates of HRV and BPV.