A Procedure for the Common Estimation of Parameters Corresponding to Several Treatment Groups

In this article we give a procedure for the common estimation of parameters corresponding to several treatment groups. Thereby we assume that the distribution functions of the groups belong to the same family and differ only in the parameter values. The procedure allows the common estimation of some of these parameters. The parameters themselves will be estimated by the maximum likelihood method; the estimators will be calculated iteratively by the Newton-Raphson method. To prove if the common estimation is possible, we propose as a suitable test the maximum likelihood ratio test. Finally we show the application of our procedure in the case of the probit analysis.     

Effects of Different PER Translational Kinetics on the Dynamics of a Core Circadian Clock Model

Living beings display self-sustained daily rhythms in multiple biological processes, which persist in the absence of external cues since they are generated by endogenous circadian clocks. The period (per) gene is a central player within the core molecular mechanism for keeping circadian time in most animals. Recently, the modulation PER translation has been reported, both in mammals and flies, suggesting that translational regulation of clock components is important for the proper clock gene expression and molecular clock performance. Because translational regulation ultimately implies changes in the kinetics of translation and, therefore, in the circadian clock dynamics, we sought to study how and to what extent the molecular clock dynamics is affected by the kinetics of PER translation. With this objective, we used a minimal mathematical model of the molecular circadian clock to qualitatively characterize the dynamical changes derived from kinetically different PER translational mechanisms. We found that the emergence of self-sustained oscillations with characteristic period, amplitude, and phase lag (time delays) between per mRNA and protein expression depends on the kinetic parameters related to PER translation. Interestingly, under certain conditions, a PER translation mechanism with saturable kinetics introduces longer time delays than a mechanism ruled by a first-order kinetics. In addition, the kinetic laws of PER translation significantly changed the sensitivity of our model to parameters related to the synthesis and degradation of per mRNA and PER degradation. Lastly, we found a set of parameters, with realistic values, for which our model reproduces some experimental results reported recently for Drosophila melanogaster and we present some predictions derived from our analysis.     

Robustness analysis and behavior discrimination in enzymatic reaction networks

Characterizing the behavior and robustness of enzymatic networks with numerous variables and unknown parameter values is a major challenge in biology, especially when some enzymes have counter-intuitive properties or switch-like behavior between activation and inhibition. In this paper, we propose new methodological and tool-supported contributions, based on the intuitive formalism of temporal logic, to express in a rigorous manner arbitrarily complex dynamical properties. Our multi-step analysis allows efficient sampling of the parameter space in order to define feasible regions in which the model exhibits imposed or experimentally observed behaviors. In a first step, an algorithmic methodology involving sensitivity analysis is conducted to determine bifurcation thresholds for a limited number of model parameters or initial conditions. In a second step, this boundary detection is supplemented by a global robustness analysis, based on quasi-Monte Carlo approach that takes into account all model parameters. We apply this method to a well-documented enzymatic reaction network describing collagen proteolysis by matrix metalloproteinase MMP2 and membrane type 1 metalloproteinase (MT1-MMP) in the presence of tissue inhibitor of metalloproteinase TIMP2. For this model, our method provides an extended analysis and quantification of network robustness toward paradoxical TIMP2 switching activity between activation or inhibition of MMP2 production. Further implication of our approach is illustrated by demonstrating and analyzing the possible existence of oscillatory behaviors when considering an extended open configuration of the enzymatic network. Notably, we construct bifurcation diagrams that specify key parameters values controlling the co-existence of stable steady and non-steady oscillatory proteolytic dynamics.     

Estimating parameters for generalized mass action models using constraint propagation

As modern molecular biology moves towards the analysis of biological systems as opposed to their individual components, the need for appropriate mathematical and computational techniques for understanding the dynamics and structure of such systems is becoming more pressing. For example, the modeling of biochemical systems using ordinary differential equations (ODEs) based on high-throughput, time-dense profiles is becoming more common-place, which is necessitating the development of improved techniques to estimate model parameters from such data. Due to the high dimensionality of this estimation problem, straight-forward optimization strategies rarely produce correct parameter values, and hence current methods tend to utilize genetic/evolutionary algorithms to perform non-linear parameter fitting. Here, we describe a completely deterministic approach, which is based on interval analysis. This allows us to examine entire sets of parameters, and thus to exhaust the global search within a finite number of steps. In particular, we show how our method may be applied to a generic class of ODEs used for modeling biochemical systems called Generalized Mass Action Models (GMAs). In addition, we show that for GMAs our method is amenable to the technique in interval arithmetic called constraint propagation, which allows great improvement of its efficiency. To illustrate the applicability of our method we apply it to some networks of biochemical reactions appearing in the literature, showing in particular that, in addition to estimating system parameters in the absence of noise, our method may also be used to recover the topology of these networks.     

Genetic correlational analysis of glycogen synthase kinase-3 beta and prepulse inhibition in inbred mice

In humans, GSK-3β activity is diminished in schizophrenic patients as is prepulse inhibition of the startle response (PPI). We performed a genetic correlational analysis between published PPI values and frontal cortex GSK-3 activity analyzed in our laboratory in 10 inbred mouse strains. This methodology could indicate relevant parameters for study in an animal model. Indeed, we obtained significant correlations between the enzyme's activity and PPI measured by two different methods. This may indicate that investigation of the genetics of GSK-3β regulation holds promise for understanding some of the biochemical underpinnings of schizophrenia.     

An unbiased sensitivity analysis reveals important parameters controlling periodicity of circadian clock

To assess the importance of model parameters in kinetic models, sensitivity analysis is generally employed to provide key measures. However, it is quite often that no information is available for a significant number of parameters in biochemical models. Therefore, the results of sensitivity analysis that heavily rely on the accuracy of parameters are largely ambiguous. In this study, we propose a computational approach to determine the relative importance of parameters controlling the performance of the circadian clock in Drosophila. While previous attempts to sensitivity analysis largely depend on the knowledge of model parameters which are generally unknown, our study depicts a consistent picture of sensitivity assessment for a large number of parameters, even when the values of these parameters are not available in vivo. The resulting parametric sensitivity analysis suggests that PER/TIM negative loop is critical to maintain the stable periodicity of the circadian clock, which is consistent to the previously experimental and computational findings. Furthermore, our analysis generates a rich hypothesis of important parameters in the circadian clock that can be further tested experimentally. This approach can also be extended to assess the sensitivity of parameters in any biochemical system where a large number of parameters have unknown values. Biotechnol. Bioeng. 2010; 105: 250–259. © 2009 Wiley Periodicals, Inc.     

Mechanics of the mitral valve

Alterations in mitral valve mechanics are classical indicators of valvular heart disease, such as mitral valve prolapse, mitral regurgitation, and mitral stenosis. Computational modeling is a powerful technique to quantify these alterations, to explore mitral valve physiology and pathology, and to classify the impact of novel treatment strategies. The selection of the appropriate constitutive model and the choice of its material parameters are paramount to the success of these models. However, the in vivo parameters values for these models are unknown. Here, we identify the in vivo material parameters for three common hyperelastic models for mitral valve tissue, an isotropic one and two anisotropic ones, using an inverse finite element approach. We demonstrate that the two anisotropic models provide an excellent fit to the in vivo data, with local displacement errors in the sub-millimeter range. In a complementary sensitivity analysis, we show that the identified parameter values are highly sensitive to prestrain, with some parameters varying up to four orders of magnitude. For the coupled anisotropic model, the stiffness varied from 119,021 kPa at 0 % prestrain via 36 kPa at 30 % prestrain to 9 kPa at 60 % prestrain. These results may, at least in part, explain the discrepancy between previously reported ex vivo and in vivo measurements of mitral leaflet stiffness. We believe that our study provides valuable guidelines for modeling mitral valve mechanics, selecting appropriate constitutive models, and choosing physiologically meaningful parameter values. Future studies will be necessary to experimentally and computationally investigate prestrain, to verify its existence, to quantify its magnitude, and to clarify its role in mitral valve mechanics.     

Estimation and identification issues in the promotion time cure model when the same covariates influence long‐ and short‐term survival

The promotion time cure model is a survival model acknowledging that an unidentified proportion of subjects will never experience the event of interest whatever the duration of the follow‐up. We focus our interest on the challenges raised by the strong posterior correlation between some of the regression parameters when the same covariates influence long‐ and short‐term survival. Then, the regression parameters of shared covariates are strongly correlated with, in addition, identification issues when the maximum follow‐up duration is insufficiently long to identify the cured fraction. We investigate how, despite this, plausible values for these parameters can be obtained in a computationally efficient way. The theoretical properties of our strategy will be investigated by simulation and illustrated on clinical data. Practical recommendations will also be made for the analysis of survival data known to include an unidentified cured fraction.     

Response to “Critical Assessment of the Evidence for Striped Nanoparticles”

Stirling et al., (10.1371/journal.pone.0108482) presented an analysis on some of our publications on the formation of stripe-like domains on mixed-ligand coated gold nanoparticles. The authors shed doubts on some of our results however no valid argument is provided against what we have shown since our first publication: scanning tunneling microscopy (STM) images of striped nanoparticles show stripe-like domains that are independent of imaging parameters and in particular of imaging speed. We have consistently ruled out the presence of artifacts by comparing sets of images acquired at different tip speeds, finding invariance of the stipe-like domains. Stirling and co-workers incorrectly analyzed this key control, using a different microscope and imaging conditions that do not compare to ours. We show here data proving that our approach is rigorous. Furthermore, we never solely relied on image analysis to draw our conclusions; we have always used the chemical nature of the particles to assess the veracity of our images. Stirling et al. do not provide any justification for the spacing of the features that we find on nanoparticles: ~1 nm for mixed ligand particles and ~ 0.5 nm for homoligand particles. Hence our two central arguments remain unmodified: independence from imaging parameters and dependence on ligand shell chemical composition. The paper report observations on our STM images; none is a sufficient condition to prove that our images are artifacts. We thoroughly addressed issues related to STM artifacts throughout our microscopy work. Stirling et al. provide guidelines for what they consider good STM images of nanoparticles, such images are indeed present in our literature. They conclude that the evidences we provided to date are insufficient, this is a departure from one of the authors’ previous article which concluded that our images were composed of artifacts. Given that four independent laboratories have reproduced our measurements and that no scientifically rigorous argument is presented to invalidate our STM images, and also given that Stirling et al. do not contest the quality of our recent STM images, we re-affirm that specific binary mixture of ligands spontaneously form features in their ligand shell that we describe as stripe-like domains ~1 nm in width.     

Growth and secular trend in school-children from Cento, Ferrara, Italy

Growth parameters were surveyed in a sample of 296 Italian children, 6-9 years old, from Cento (Ferrara, Emilia-Romagna). The comparison with children from the same town measured in 1974-75 show changes in some parameters, suggesting an ongoing secular trend. To better understand the observed weight increase and the sex difference, we also evaluated body composition and motricity. The analysis of the present sample is a preliminary part of a longitudinal study dealing with modifications of body composition and motor capacity induced by growth. In our sample the children are growing according to the Italian reference standard. The females present weight, height and Body Mass Index (BMI) values comparable to the 50th centile, while the males present higher values of weight, skinfold thicknesses and BMI. Sex differences in the motor performance were noted. A methodological comparison of obesity assessments based on BMI and percentage of body fat (%F) shows similar conclusions but somewhat different results.     

Thermal unfolding of soybean peroxidase. Appropriate high denaturant concentrations induce cooperativity allowing the correct measurement of thermodynamic parameters

We have earlier reported that both guanidine hydrochloride (GdnHCl)-induced and heat-induced unfolding of seed coat soybean peroxidase (SBP), monitored by far UV CD, show single step transition. However, although GdnHCl-induced unfolding follows a two-state pathway, the heat-induced denaturation proceeds through intermediates as indicated by the very low cooperativity of transition. In the former case, analysis of the data based on the two-state model gives true thermodynamic parameters, whereas underestimated values are obtained in the latter case. Available complex equations also cannot be applied for the analysis of the thermal unfolding of SBP due to the absence of separate transitions for the intermediates. In the present study, we report a method to obtain true thermodynamic parameters from thermal transition curves of SBP using the two-state model. When SBP is subjected to thermal unfolding at high GdnHCl concentrations (5.8-6.9 M), cooperative behavior is observed, which allowed the analysis by the two-state model to determine their thermodynamic parameters. We then obtained the thermodynamic parameters in the absence of GdnHCl by extrapolating the graph of linear dependence of DeltaH(m) on T(m) to the T(m) corresponding to 0 m GdnHCl. Another key point for checking the validity of our method was the fact that the unfolded state of SBP generated by either heat or GdnHCl is the same by which we could cross-check our results with that obtained from GdnHCl unfolding. Having obtained the true thermodynamic parameters, we report a detailed thermodynamic study of SBP. Further we address the effect of heme in the thermal unfolding mechanism of SBP.     

Serum chemistry of the minke whale from the northeastern Atlantic

Serum samples were collected from 42 harpooned minke whales (Balaenoptera acutorostrata) during commercial whaling off the coast of northern Norway (1997 and 1998) and analyzed for serum chemistry parameters in order to find clinical reference values for the northeastern Atlantic stock of this species. Mean and median values, as well as standard deviation and 90% central range, are presented for 28 different serum chemistry parameters. Lipemia is a common finding in marine mammals such as the minke whale, and chemical analysis of lipemic serum samples may produce artifacts. We found statistically significant elevated values of total protein, globulin, aspartate aminotransferase (AST), alanine aminotransferase (ALT), sodium and chloride in strongly-lipemic compared to non-lipemic samples, all which may be artifacts due to interference of lipids with the methods used for analysis. In addition, we found significantly elevated levels of creatin kinase, lactate dehydrogenase (LDH), urea, uric acid and triglycerides, as well as a decrease in creatinine in the strongly lipemic samples. Reanalyzing serum samples after twelve mo storage at -20 C (n = 13) revealed reduction in the serum concentration of the enzymes ALT (42%), alkaline phosphatase (ALP; 10%), LDH (19%), gamma glutamyl transferase (17%) and amylase (11%), as well as for triglycerides (9%) and non-esterified fatty acids (16%). It is crucial that serum chemistry analysis is performed without delay after sampling. Possible changes in the values of some parameters due to the presence of high amounts of lipids or long term storage of samples must be considered when interpreting results from serum chemistry analysis in these animals.     

Effect of delay in a Lotka-Volterra type predator-prey model with a transmissible disease in the predator species

We consider a system of delay differential equations modeling the predator-prey ecoepidemic dynamics with a transmissible disease in the predator population. The time lag in the delay terms represents the predator gestation period. We analyze essential mathematical features of the proposed model such as local and global stability and in addition study the bifurcations arising in some selected situations. Threshold values for a few parameters determining the feasibility and stability conditions of some equilibria are discovered and similarly a threshold is identified for the disease to die out. The parameter thresholds under which the system admits a Hopf bifurcation are investigated both in the presence of zero and non-zero time lag. Numerical simulations support our theoretical analysis.     

Comparisons of predictive values of binary medical diagnostic tests for paired designs

Positive and negative predictive values of a diagnostic test are key clinically relevant measures of test accuracy. Surprisingly, statistical methods for comparing tests with regard to these parameters have not been available for the most common study design in which each test is applied to each study individual. In this paper, we propose a statistic for comparing the predictive values of two diagnostic tests using this paired study design. The proposed statistic is a score statistic derived from a marginal regression model and bears some relation to McNemar's statistic. As McNemar's statistic can be used to compare sensitivities and specificities of diagnostic tests, parameters that condition on disease status, our statistic can be considered as an analog of McNemar's test for the problem of comparing predictive values, parameters that condition on test outcome. We report on the results of a simulation study designed to examine the properties of this test under a variety of conditions. The method is illustrated with data from a study of methods for diagnosis of coronary artery disease.     

蛋白质序列的混合特征值对折叠速率的影响

鉴于蛋白质折叠速率预测对研究其蛋白质功能的重要性,许多的科研工作者都开始对影响蛋白质折叠速率的因素进行研究。各种预测参数和方法被提出。利用蛋白质编码序列的不同特征参数,不同的二级结构及不同的折叠类的蛋白质对折叠速率的不同影响,我们选取蛋白质编码序列的新的特征值,即选取蛋白质序列的LZ复杂度,等电点等特征值。然后把这些特征值与20种氨基酸的属性αc、Cα、K0、Pβ、Ra、ΔASA、PI、ΔGhD、Nm、LZ、Mu、El融合,建立多元线性回归模型,并利用回归模型计算了13个全α类蛋白质、18个全β类蛋白质、13个混合类蛋白质和39个未分类蛋白质的ln（kf）与预测值之间的相关系数分别达到0.89、0.93、0.98、0.86。在Jack-knife方法的验证下发现在不同的结构中混合特征值与相应折叠速率有很好的相关性。结果表明,在蛋白质折叠过程中,蛋白质序列的LZ复杂度、等电点等特征值可能影响蛋白质的折叠速率及其结构。     

On the Fractal Geometry of DNA by the Binary Image Analysis

The multifractal analysis of binary images of DNA is studied in order to define a methodological approach to the classification of DNA sequences. This method is based on the computation of some multifractality parameters on a suitable binary image of DNA, which takes into account the nucleotide distribution. The binary image of DNA is obtained by a dot-plot (recurrence plot) of the indicator matrix. The fractal geometry of these images is characterized by fractal dimension (FD), lacunarity, and succolarity. These parameters are compared with some other coefficients such as complexity and Shannon information entropy. It will be shown that the complexity parameters are more or less equivalent to FD, while the parameters of multifractality have different values in the sense that sequences with higher FD might have lower lacunarity and/or succolarity. In particular, the genome of Drosophila melanogaster has been considered by focusing on the chromosome 3r, which shows the highest fractality with a corresponding higher level of complexity. We will single out some results on the nucleotide distribution in 3r with respect to complexity and fractality. In particular, we will show that sequences with higher FD also have a higher frequency distribution of guanine, while low FD is characterized by the higher presence of adenine.     

An allometric method for the projection of eelgrass leaf biomass production rates

We demonstrate that an allometric model for eelgrass leaf-growth rates can be derived from data on leaf architecture and growth form. Using this construct, we produced indirect assessments of growth rates of leaves that we call projections, which can be easily obtained in terms of allometric parameters and proxy values for leaf area, expressed as the product of leaf length and width. These projections of leaf-growth rates displayed a high level of correspondence with values observed in our data, as well as with other sets of reference data. A comparison with growth rates obtained by using the plastochrone index method showed that our model provides more accurate estimations while using a simpler methodology. Our results also show that whenever allometric parameters for the scaling of eelgrass leaf dry weight in terms of leaf area are available, the proposed model provides an accurate, cost-effective and non-destructive alternative to assessments based on traditional or plastochrone methods.     

Disorder in nerve myelin: Phasing the higher order reflections by means of the diffuse scatter

Disorder in the stacking of membrane layers in nerve myelin has an important effect on the X-ray diffraction pattern. In a previous report we found broadening of the Bragg reflections and diffuse intensity between them. A model for the disorder was presented to account for these effects, and some of the model parameters were evaluated by analysis of the X-ray diffraction pattern in the region of Bragg reflections 1 to 6, where the phasing is well established. In this paper, we present further data and derive a more complete and precise set of values for the parameters. Then, assuming these values, all possible combinations of phases for reflections 7 to 15 are used to calculate the corresponding diffraction patterns for comparison with observation. The 20 best fitting phase combinations are considered in detail. Sixteen of these are eliminated, leaving four possible combinations which differ only in the phases for orders 8 and 15.Electron density profiles computed using the four possible phase combinations are not very different from one another. All four profiles show a markedly higher electron density in the extracellular half of the membrane bilayer than in the cytoplasmic half. Our calculations indicate that the cytoplasmic half can be accounted for entirely by myelin lipids, including cholesterol. However, an unreasonably high proportion of cholesterol would be needed to account for the extracellular half of the bilayer, and we tentatively conclude that an appreciable part of the myelin protein is inserted into this half of the bilayer.Analytical methods used by other investigators are considered in light of our experimental observations and model predictions in order to reconcile conflicting results. Failure to account properly for diffuse intensity arising from the disorder makes previous determinations of myelin membrane structure at moderate resolution questionable.     

Joint inference of the distribution of fitness effects of deleterious mutations and population demography based on nucleotide polymorphism frequencies

The distribution of fitness effects of new mutations (DFE) is important for addressing several questions in genetics, including the nature of quantitative variation and the evolutionary fate of small populations. Properties of the DFE can be inferred by comparing the distributions of the frequencies of segregating nucleotide polymorphisms at selected and neutral sites in a population sample, but demographic changes alter the spectrum of allele frequencies at both neutral and selected sites, so can bias estimates of the DFE if not accounted for. We have developed a maximum-likelihood approach, based on the expected allele-frequency distribution generated by transition matrix methods, to estimate parameters of the DFE while simultaneously estimating parameters of a demographic model that allows a population size change at some time in the past. We tested the method using simulations and found that it accurately recovers simulated parameter values, even if the simulated demography differs substantially from that assumed in our analysis. We use our method to estimate parameters of the DFE for amino acid-changing mutations in humans and Drosophila melanogaster. For a model of unconditionally deleterious mutations, with effects sampled from a gamma distribution, the mean estimate for the distribution shape parameter is approximately 0.2 for human populations, which implies that the DFE is strongly leptokurtic. For Drosophila populations, we estimate that the shape parameter is approximately 0.35. Differences in the shape of the distribution and the mean selection coefficient between humans and Drosophila result in significantly more strongly deleterious mutations in Drosophila than in humans, and, conversely, nearly neutral mutations are significantly less frequent.     

A mathematical model for chronic myelogenous leukemia (CML) and T cell interaction

In this paper, we propose and analyse a mathematical model for chronic myelogenous leukemia (CML), a cancer of the blood. We model the interaction between naive T cells, effector T cells, and CML cancer cells in the body, using a system of ordinary differential equations which gives rates of change of the three cell populations. One of the difficulties in modeling CML is the scarcity of experimental data which can be used to estimate parameters values. To compensate for the resulting uncertainties, we use Latin hypercube sampling (LHS) on large ranges of possible parameter values in our analysis. A major goal of this work is the determination of parameters which play a critical role in remission or clearance of the cancer in the model. Our analysis examines 12 parameters, and identifies two of these, the growth and death rates of CML, as critical to the outcome of the system. Our results indicate that the most promising research avenues for treatments of CML should be those that affect these two significant parameters (CML growth and death rates), while altering the other parameters should have little effect on the outcome.