Testing for spatial correlation in nonstationary binary data, with application to aberrant crypt foci in colon carcinogenesis

In an experiment to understand colon carcinogenesis, all animals were exposed to a carcinogen, with half the animals also being exposed to radiation. Spatially, we measured the existence of what are referred to as aberrant crypt foci (ACF), namely, morphologically changed colonic crypts that are known to be precursors of colon cancer development. The biological question of interest is whether the locations of these ACFs are spatially correlated: if so, this indicates that damage to the colon due to carcinogens and radiation is localized. Statistically, the data take the form of binary outcomes (corresponding to the existence of an ACF) on a regular grid. We develop score-type methods based upon the Matern and conditionally autoregressive (CAR) correlation models to test for the spatial correlation in such data, while allowing for nonstationarity. Because of a technical peculiarity of the score-type test, we also develop robust versions of the method. The methods are compared to a generalization of Moran's test for continuous outcomes, and are shown via simulation to have the potential for increased power. When applied to our data, the methods indicate the existence of spatial correlation, and hence indicate localization of damage.     

A mathematical model of actin filament turnover for fitting FRAP data

A novel mathematical model of the actin dynamics in living cells under steady-state conditions has been developed for fluorescence recovery after photobleaching (FRAP) experiments. As opposed to other FRAP fitting models, which use the average lifetime of actins in filaments and the actin turnover rate as fitting parameters, our model operates with unbiased actin association/dissociation rate constants and accounts for the filament length. The mathematical formalism is based on a system of stochastic differential equations. The derived equations were validated on synthetic theoretical data generated by a stochastic simulation algorithm adapted for the simulation of FRAP experiments. Consistent with experimental findings, the results of this work showed that (1) fluorescence recovery is a function of the average filament length, (2) the F-actin turnover and the FRAP are accelerated in the presence of actin nucleating proteins, (3) the FRAP curves may exhibit both a linear and non-linear behaviour depending on the parameters of actin polymerisation, and (4) our model resulted in more accurate parameter estimations of actin dynamics as compared with other FRAP fitting models. Additionally, we provide a computational tool that integrates the model and that can be used for interpretation of FRAP data on actin cytoskeleton.     

Global analysis of fluorescence fluctuation data

Over the last decade the number of applications of fluorescence correlation spectroscopy (FCS) has grown rapidly. Here we describe the development and application of a software package, FCS Data Processor, to analyse the acquired correlation curves. The algorithms combine strong analytical power with flexibility in use. It is possible to generate initial guesses, link and constrain fit parameters to improve the accuracy and speed of analysis. A global analysis approach, which is most effective in analysing autocorrelation curves determined from fluorescence fluctuations of complex biophysical systems, can also be implemented. The software contains a library of frequently used models that can be easily extended to include user-defined models. The use of the software is illustrated by analysis of different experimental fluorescence fluctuation data sets obtained with Rhodamine Green in aqueous solution and enhanced green fluorescent protein in vitro and in vivo.An erratum to this article can be found at Victor V. Skakun, Mark A. Hink and Anatoli V. Digris contributed equally to this work.     

Prediction of the three-dimensional structure of aflatoxin of Aspergillus flavus by homology modelling

Aflatoxins are polyketide-derived secondary metabolites produced by Aspergillus spp. The toxic effects of aflatoxins have adverse consequences for human health and agricultural economics. The aflR gene, a regulatory gene for aflatoxin biosynthesis, encodes a protein containing a zinc-finger DNA-binding motif. AFLR-Protein three-dimensional model was generated using Robetta server. The modeled AFLR-Protein was further optimization and validation using Rampage. In the simulations, we monitored the backbone atoms and the C-α-helix of the modeled protein. The low RMSD and the simulation time indicate that, as expected, the 3D structural model of AFLR-protein represents a stable folding conformation. This study paves the way for generating computer molecular models for proteins whose crystal structures are not available and which would aid in detailed molecular mechanism of inhibition of aflatoxin.     

Mapping the amino acid properties of constituent nucleoporins onto the yeast nuclear pore complex

Visualization of molecular structures aids in the understanding of structural and functional roles of biological macromolecules. Macromolecular transport between the cell nucleus and cytoplasm is facilitated by the nuclear pore complex (NPC). The ring structure of the NPC is large and contains several distinct proteins (nucleoporins) which function as a selective gate for the passage of certain molecules into and out of the nucleus. In this note we demonstrate the utility of a python code that allows direct mapping of the physiochemical properties of the constituent nucleoporins on the scaffold of the yeast NPC׳s cytoplasmic view. We expect this tool to be useful for researchers to visualize the NPC based on their physiochemical properties and how it alters when specific mutations are introduced in one or more of the nucleoporins. The code developed using Python is available freely from the authors.     

Aberrant crypt foci and semiparametric modeling of correlated binary data

Summary .   Motivated by the spatial modeling of aberrant crypt foci (ACF) in colon carcinogenesis, we consider binary data with probabilities modeled as the sum of a nonparametric mean plus a latent Gaussian spatial process that accounts for short-range dependencies. The mean is modeled in a general way using regression splines. The mean function can be viewed as a fixed effect and is estimated with a penalty for regularization. With the latent process viewed as another random effect, the model becomes a generalized linear mixed model. In our motivating data set and other applications, the sample size is too large to easily accommodate maximum likelihood or restricted maximum likelihood estimation (REML), so pairwise likelihood, a special case of composite likelihood, is used instead. We develop an asymptotic theory for models that are sufficiently general to be used in a wide variety of applications, including, but not limited to, the problem that motivated this work. The splines have penalty parameters that must converge to zero asymptotically: we derive theory for this along with a data-driven method for selecting the penalty parameter, a method that is shown in simulations to improve greatly upon standard devices, such as likelihood crossvalidation. Finally, we apply the methods to the data from our experiment ACF. We discover an unexpected location for peak formation of ACF.     

Initial guesses generation for fluorescence intensity distribution analysis

The growing number of applications of Fluorescence Intensity Distribution Analysis (FIDA) demands for new approaches in data processing, aiming at increased speed and robustness. Iterative algorithms of parameter estimation, although proven to be universal and accurate, require some initial guesses (IG) of the unknown parameters. An essential component of any data processing technology, IG become especially important in case of FIDA, since even with apparently reasonable, and physically admissible but randomly chosen IG, the iterative procedure may converge to situations where the FIDA model cannot be evaluated correctly. In the present work we introduce an approach for IG generation in FIDA experiments based on the method of moments. IG are generated for the sample parameters: brightness, concentration, and for the parameters related to experimental set-up: background, observation volume profile. A number of analytical simplifications were introduced in order to increase the accuracy and robustness of the numerical algorithms. The performance of the developed method has been tested on number of simulations and experimental data. Iterative fitting with generated IG proved to be more robust and at least five times faster than with an arbitrarily chosen IG. Applicability of the proposed method for quick estimation of brightness and concentrations is discussed.     

Simultaneous diffusion and brightness measurements and brightness profile visualization from single fluorescence fluctuation traces of GFP in living cells

Fluorescence correlation spectroscopy (FCS) and photon-counting histogram (PCH) analysis use the same experimental fluorescence intensity fluctuations, but each analytical method focuses on a different property of the signal. The time-dependent decay of the correlation of fluorescence fluctuations is measured in FCS yielding, for instance, molecular diffusion coefficients. The amplitude distribution of these fluctuations is calculated by PCH analysis yielding information about the molecular brightness of fluorescent species. Analysis of both FCS and PCH results in the molecular concentration of the sample. Using a previously described global analysis procedure we report here precise, simultaneous measurements of diffusion constants and brightness values from single fluorescence fluctuation traces of green-fluorescent protein (GFP, S65T) in the cytoplasm of Dictyostelium cells. The use of a polynomial profile in PCH analysis, describing the detected three-dimensional shape of the confocal volume, enabled us to obtain well fitting results for GFP in cells. We could visualize the polynomial profile and show its deviation from a Gaussian profile.