Computational analysis of CFSE proliferation assay

CFSE based tracking of the lymphocyte proliferation using flow cytometry is a powerful experimental technique in immunology allowing for the tracing of labelled cell populations over time in terms of the number of divisions cells undergone. Interpretation and understanding of such population data can be greatly improved through the use of mathematical modelling. We apply a heterogenous linear compartmental model, described by a system of ordinary differential equations similar to those proposed by Kendall. This model allows division number-dependent rates of cell proliferation and death and describes the rate of changes in the numbers of cells having undergone j divisions. The experimental data set that we specifically analyze specifies the following characteristics of the kinetics of PHA-induced human T lymphocyte proliferation assay in vitroL (1) the total number of live cells, (2) the total number of dead but not disintegrated cells and (3) the number of cells divided j times. Following the maximum likelihood approach for data fitting, we estimate the model parameters which, in particular, present the CTL birth- and death rate “functions”. It is the first study of CFSE labelling data which convincingly shows that the lymphocyte proliferation and death both in vitro and in vivo are division number dependent. For the first time, the confidence in the estimated parameter values is analyzed by comparing three major methods: the technique based on the variance–covariance matrix, the profile-likelihood-based approach and the bootstrap technique. We compare results and performance of these methods with respect to their robustness and computational cost. We show that for evaluating mathematical models of differing complexity the information-theoretic approach, based upon indicators measuring the information loss for a particular model (Kullback–Leibler information), provides a consistent basis. We specifically discuss methodological and computational difficulties in parameter identification with CFSE data, e.g. the loss of confidence in the parameter estimates starting around the sixth division. Overall, our study suggests that the heterogeneity inherent in cell kinetics should be explicitly incorporated into the structure of mathematical models.      

SpeciesRax: A Tool for Maximum Likelihood Species Tree Inference from Gene Family Trees under Duplication,Transfer, and Loss

Species tree inference from gene family trees is becoming increasingly popular because it can account for discordance between the species tree and the corresponding gene family trees. In particular, methods that can account for multiple-copy gene families exhibit potential to leverage paralogy as informative signal. At present, there does not exist any widely adopted inference method for this purpose. Here, we present SpeciesRax, the first maximum likelihood method that can infer a rooted species tree from a set of gene family trees and can account for gene duplication, loss, and transfer events. By explicitly modeling events by which gene trees can depart from the species tree, SpeciesRax leverages the phylogenetic rooting signal in gene trees. SpeciesRax infers species tree branch lengths in units of expected substitutions per site and branch support values via paralogy-aware quartets extracted from the gene family trees. Using both empirical and simulated data sets we show that SpeciesRax is at least as accurate as the best competing methods while being one order of magnitude faster on large data sets at the same time. We used SpeciesRax to infer a biologically plausible rooted phylogeny of the vertebrates comprising 188 species from 31,612 gene families in 1 h using 40 cores. SpeciesRax is available under GNU GPL at https://github.com/BenoitMorel/GeneRax and on BioConda.     

A Comment on Maximum Likelihood Estimation for Finite Mixtures of Distributions

Iterative numerical methods are necessary to find the maximum likelihood estimates for finite mixture distributions. This paper shows that it will often be possible to analytically reduce the number of equations that must ultimately be solved numerically. Such a reduction in dimensionality has not generally been used, or sought after, for mixture distributions. Yet such results are easily derived when each mixture component is assumed to be from the same parametric model within the exponential family.     

A Maximum Likelihood Estimator for Shape Parameters of S‐Distributions

The S‐distribution is a four‐parameter distribution that is defined in terms of a differential equation, in which the cumulative is represented as the dependent variable: The article proposes a maximum likelihood estimator for the shape parameters of this distribution.     

Local Perturbation Analysis: A Computational Tool for Biophysical Reaction-Diffusion Models

Diffusion and interaction of molecular regulators in cells is often modeled using reaction-diffusion partial differential equations. Analysis of such models and exploration of their parameter space is challenging, particularly for systems of high dimensionality. Here, we present a relatively simple and straightforward analysis, the local perturbation analysis, that reveals how parameter variations affect model behavior. This computational tool, which greatly aids exploration of the behavior of a model, exploits a structural feature common to many cellular regulatory systems: regulators are typically either bound to a membrane or freely diffusing in the interior of the cell. Using well-documented, readily available bifurcation software, the local perturbation analysis tracks the approximate early evolution of an arbitrarily large perturbation of a homogeneous steady state. In doing so, it provides a bifurcation diagram that concisely describes various regimes of the model’s behavior, reducing the need for exhaustive simulations to explore parameter space. We explain the method and provide detailed step-by-step guides to its use and application.     

Maximum Likelihood Estimation of Population Parameters

One of the most important parameters in population genetics is θ = 4N(e)μ where N(e) is the effective population size and μ is the rate of mutation per gene per generation. We study two related problems, using the maximum likelihood method and the theory of coalescence. One problem is the potential improvement of accuracy in estimating the parameter θ over existing methods and the other is the estimation of parameter λ which is the ratio of two θ's. The minimum variances of estimates of the parameter θ are derived under two idealized situations. These minimum variances serve as the lower bounds of the variances of all possible estimates of θ in practice. We then show that Watterson's estimate of θ based on the number of segregating sites is asymptotically an optimal estimate of θ. However, for a finite sample of sequences, substantial improvement over Watterson's estimate is possible when θ is large. The maximum likelihood estimate of λ = θ(1)/θ(2) is obtained and the properties of the estimate are discussed.     

CarSPred: A Computational Tool for Predicting Carbonylation Sites of Human Proteins

Protein carbonylation is one of the most pervasive oxidative stress-induced post-translational modifications (PTMs), which plays a significant role in the etiology and progression of several human diseases. It has been regarded as a biomarker of oxidative stress due to its relatively early formation and stability compared with other oxidative PTMs. Only a subset of proteins is prone to carbonylation and most carbonyl groups are formed from lysine (K), arginine (R), threonine (T) and proline (P) residues. Recent advancements in analysis of the PTM by mass spectrometry provided new insights into the mechanisms of protein carbonylation, such as protein susceptibility and exact modification sites. However, the experimental approaches to identifying carbonylation sites are costly, time-consuming and capable of processing a limited number of proteins, and there is no bioinformatics method or tool devoted to predicting carbonylation sites of human proteins so far. In the paper, a computational method is proposed to identify carbonylation sites of human proteins. The method extracted four kinds of features and combined the minimum Redundancy Maximum Relevance (mRMR) feature selection criterion with weighted support vector machine (WSVM) to achieve total accuracies of 85.72%, 85.95%, 83.92% and 85.72% for K, R, T and P carbonylation site predictions respectively using 10-fold cross-validation. The final optimal feature sets were analysed, the position-specific composition and hydrophobicity environment of flanking residues of modification sites were discussed. In addition, a software tool named CarSPred has been developed to facilitate the application of the method. Datasets and the software involved in the paper are available at https://sourceforge.net/projects/hqlstudio/files/CarSPred-1.0/.     

A Maximum Likelihood Method for Estimating Genome Length Using Genetic Linkage Data

The genetic length of a genome, in units of Morgans or centimorgans, is a fundamental characteristic of an organism. We propose a maximum likelihood method for estimating this quantity from counts of recombinants and nonrecombinants between marker locus pairs studied from a backcross linkage experiment, assuming no interference and equal chromosome lengths. This method allows the calculation of the standard deviation of the estimate and a confidence interval containing the estimate. Computer simulations have been performed to evaluate and compare the accuracy of the maximum likelihood method and a previously suggested method-of-moments estimator. Specifically, we have investigated the effects of the number of meioses, the number of marker loci, and variation in the genetic lengths of individual chromosomes on the estimate. The effect of missing data, obtained when the results of two separate linkage studies with a fraction of marker loci in common are pooled, is also investigated. The maximum likelihood estimator, in contrast to the method-of-moments estimator, is relatively insensitive to violation of the assumptions made during analysis and is the method of choice. The various methods are compared by application to partial linkage data from Xiphophorus.     

Boolean Models: Maximum Likelihood Estimation from Circular Clumps

This paper deals with the problem of making inferences on the maximum radius and the intensity of the Poisson point process associated to a Boolean Model of circular primary grains with uniformly distributed random radii. The only sample information used is observed radii of circular clumps (DUPAC, 1980). The behaviour of maximum likelihood estimation has been evaluated by means of Monte Carlo methods.     

Sparse Sampling and Maximum Likelihood Estimation for Boolean Models

A condition for practical independence of contact distribution functions in Boolean models is obtained. This result allows the authors to use maximum likelihcod methods, via sparse sampling, for estimating unknown parameters of an isotropic Boolean model. The second part of this paper is devoted to a simulation study of the proposed method. AMS classification: 60D05     

Maximum Likelihood Estimates for Binary Data with Random Effects

The purpose of this paper is to present a procedure for obtaining approximate maximum likelihood estimates for compound binary response models. The extra binomial variation is incorporated into the model by adding random effects to the fixed effects on the probit (or logit) scale. Numerical integration techniques are used to arrive at a solution of the likelihood equations. The paper also presents an illustrating numerical example based on a large toxicological data set. The computations are carried out within the GLIM statistical package.     

MyDEP: A New Computational Tool for Dielectric Modeling of Particles and Cells

Dielectrophoresis (DEP) and electrorotation (ROT) are two electrokinetic phenomena exploiting nonuniform electric fields to exert a force or torque on biological particles suspended in liquid media. They are widely used in lab-on-chip devices for the manipulation, trapping, separation, and characterization of cells, microorganisms, and other particles. The DEP force and ROT torque depend on the respective polarizabilities of the particle and medium, which in turn depend on their dielectric properties and on the field frequency. In this work, we present a new software, MyDEP, which implements several particle models based on concentric shells with adjustable dielectric properties. This tool enables the study of the variation in DEP and ROT spectra according to different parameters, such as the field frequency and medium conductivity. Such predictions of particle behavior are very useful for choosing appropriate parameters in DEP experiments. The software also enables the study of the homogenized properties of spherical or ellipsoidal multishell particles and provides a database containing published cell properties. Equivalent electrical conductivity and relative permittivity of the cell alone and in suspension can be calculated. The software also offers the ability to create graphs of the evolution of the crossover frequencies with the electric field frequency. These graphs can be directly exported from the software.     

PepBind: A Comprehensive Database and Computational Tool for Analysis of Protein-peptide Interactions

Protein–peptide interactions, where one partner is a globular protein (domain) and the other is a flexible linear peptide, are key components of cellular processes predominantly in signaling and regulatory networks, hence are prime targets for drug design. To derive the details of the protein–peptide interaction mechanism is often a cumbersome task, though it can be made easier with the availability of specific databases and tools. The Peptide Binding Protein Database (PepBind) is a curated and searchable repository of the structures, sequences and experimental observations of 3100 protein–peptide complexes. The web interface contains a computational tool, protein inter-chain interaction (PICI), for computing several types of weak or strong interactions at the protein–peptide interaction interface and visualizing the identified interactions between residues in Jmol viewer. This initial database release focuses on providing protein–peptide interface information along with structure and sequence information for protein–peptide complexes deposited in the Protein Data Bank (PDB). Structures in PepBind are classified based on their cellular activity. More than 40% of the structures in the database are found to be involved in different regulatory pathways and nearly 20% in the immune system. These data indicate the importance of protein–peptide complexes in the regulation of cellular processes. PepBind is freely accessible at http://pepbind.bicpu.edu.in/.     

Maximum Likelihood Estimation of Exponential Polynomial Rate for Poisson Data

The heterogeneous Poisson process with discretized exponential quadratic rate function is considered. Maximum likelihood estimates of the parameters of the rate function are derived for the case when the data consists of numbers of occurrences in consecutive equal time periods. A likelihood ratio test of the null hypothesis of exponential quadratic rate is presented. Its power against exponential linear rate functions is estimated using Monte Carlo simulation. The maximum likelihood method is compared with a log-linear least squares techniques. An application of the technique to the analysis of mortality rates due to congenital malformations is presented.     

Computational Approaches for RNA Structure Ensemble Deconvolution from Structure Probing Data

RNA structure probing experiments have emerged over the last decade as a straightforward way to determine the structure of RNA molecules in a number of different contexts. Although powerful, the ability of RNA to dynamically interconvert between, and to simultaneously populate, alternative structural configurations, poses a nontrivial challenge to the interpretation of data derived from these experiments. Recent efforts aimed at developing computational methods for the reconstruction of coexisting alternative RNA conformations from structure probing data are paving the way to the study of RNA structure ensembles, even in the context of living cells. In this review, we critically discuss these methods, their limitations and possible future improvements.     

QHELIX: A Computational Tool for the Improved Measurement of Inter-Helical Angles in Proteins

Knowledge about the assembled structures of the secondary elements in proteins is essential to understanding protein folding and functionality. In particular, the analysis of helix geometry is required to study helix packing with the rest of the protein and formation of super secondary structures, such as, coiled coils and helix bundles, formed by packing of two or more helices. Here we present an improved computational method, QHELIX, for the calculation of the orientation angles between helices. Since a large number of helices are known to be in curved shapes, an appropriate definition of helical axes is a prerequisite for calculating the orientation angle between helices. The present method provides a quantitative measure on the irregularity of helical shape, resulting in discriminating irregular-shaped helices from helices with an ideal geometry in a large-scale analysis of helix geometry. It is also capable of straightforwardly assigning the direction of orientation angles in a consistent way. These improvements will find applications in finding a new insight on the assembly of protein secondary structure. Electronic Supplementary Material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

A Simplified Newton Method for Computing the Factor Loadings in Maximum Likelihood Factor Analysis

A simplified Newton iteration scheme for computation of factor loadings in maximum likelihood factor analysis is described. It operates in the space of factor loadings and avoids eigenvalue problems. From this, a comparatively small computational effort results. Besides of the case of positive unique variances, also the Heywood case is considered, where some unique variances vanish. The ability of the proposed method is demonstrated in three examples, results and iteration process are compared with data given in literature.     

Propylthiouracil Tasting: Determination of Underlying Threshold Distributions using Maximum Likelihood

The ability to taste low concentrations of propylthiouracil(PROP) and related bitter compounds is heritable. The currentanalysis determines whether the distribution of PROP taste thresholdsis consistent with an additive or a dominant mode of Mendeliantransmission. To that end, the lowest concentration of PROPdetectable was determined for 1015 subjects and models of bi-or tri-modal distributions of PROP taste thresholds were tested.The model with the greatest likelihood had three distributionsand followed an additive model of PROP taste sensitivity ifthe variances associated with the distributions were assumedto be equal. However, if the taste thresholds were transformedto remove skewness, or if the variances were unequal, then three-or two-distribution models were equally likely. Resolution ofthe mode of inheritance for bitter taste perception awaits additionalfamily studies and the characterization of the molecular basisof taste perception for these bitter compounds. Chem. Senses20: 529–533, 1995.