A mathematical and computational approach for integrating the major sources of cell population heterogeneity

Several approaches have been used in the past to model heterogeneity in bacterial cell populations, with each approach focusing on different source(s) of heterogeneity. However, a holistic approach that integrates all the major sources into a comprehensive framework applicable to cell populations is still lacking.In this work we present the mathematical formulation of a cell population master equation (CPME) that describes cell population dynamics and takes into account the major sources of heterogeneity, namely stochasticity in reaction, DNA-duplication, and division, as well as the random partitioning of species contents into the two daughter cells. The formulation also takes into account cell growth and respects the discrete nature of the molecular contents and cell numbers. We further develop a Monte Carlo algorithm for the simulation of the stochastic processes considered here. To benchmark our new framework, we first use it to quantify the effect of each source of heterogeneity on the intrinsic and the extrinsic phenotypic variability for the well-known two-promoter system used experimentally by Elowitz et al. (2002). We finally apply our framework to a more complicated system and demonstrate how the interplay between noisy gene expression and growth inhibition due to protein accumulation at the single cell level can result in complex behavior at the cell population level.The generality of our framework makes it suitable for studying a vast array of artificial and natural genetic networks. Using our Monte Carlo algorithm, cell population distributions can be predicted for the genetic architecture of interest, thereby quantifying the effect of stochasticity in intracellular reactions or the variability in the rate of physiological processes such as growth and division. Such in silico experiments can give insight into the behavior of cell populations and reveal the major sources contributing to cell population heterogeneity. © 2010 Elsevier Ltd

3D multi-agent models for protein release from PLGA spherical particles with complex inner morphologies

In order to better understand and predict the release of proteins from bioerodible micro- or nanospheres, it is important to know the influences of different initial factors on the release mechanisms. Often though it is difficult to assess what exactly is at the origin of a certain dissolution profile. We propose here a new class of fine-grained multi-agent models built to incorporate increasing complexity, permitting the exploration of the role of different parameters, especially that of the internal morphology of the spheres, in the exhibited release profile. This approach, based on Monte-Carlo (MC) and Cellular Automata (CA) techniques, has permitted the testing of various assumptions and hypotheses about several experimental systems of nanospheres encapsulating proteins. Results have confirmed that this modelling approach has increased the resolution over the complexity involved, opening promising perspectives for future developments, especially complementing in vitro experimentation

Sub-population analysis based on temporal features of high content images

Background: High content screening techniques are increasingly used to understand the regulation and progression of cell motility. The demand of new platforms, coupled with availability of terabytes of data has challenged the traditional technique of identifying cell populations by manual methods and resulted in development of high-dimensional analytical methods. Results: In this paper, we present sub-populations analysis of cells at the tissue level by using dynamic features of the cells. We used active contour without edges for segmentation of cells, which preserves the cell morphology, and autoregressive modeling to model cell trajectories. The sub-populations were obtained by clustering static, dynamic and a combination of both features. We were able to identify three unique sub-populations in combined clustering. Conclusion: We report a novel method to identify sub-populations using kinetic features and demonstrate that these features improve sub-population analysis at the tissue level. These advances will facilitate the application of high content screening data analysis to new and complex biological problems.Computation and Systems Biology Programme of Singapore--Massachusetts Institute of Technology Allianc

Dimensionality reduction and prediction of the protein macromolecule dissolution profile

A suitable regression model for predicting the dissolution profile of Poly (lactic-co-glycolic acid) (PLGA) micro-and nanoparticles can play a significant role in pharmaceutical/medical applications. The rate of dissolution of proteins is influenced by several factors and taking all such influencing factors into account; we have a dataset in hand with three hundred input features. Therefore, a primary approach before identifying a regression model is to reduce the dimensionality of the dataset at hand. On the one hand, we have adopted Backward Elimination Feature selection techniques for an exhaustive analysis of the predictability of each combination of features. On the other hand, several linear and non-linear feature extraction methods are used in order to extract a new set of features out of the available dataset. A comprehensive experimental analysis for the selection or extraction of features and identification of the corresponding prediction model is offered. The designed experiment and prediction models offer substantially better performance over the earlier proposed prediction models in literature for the said problem

Genetics of human hydrocephalus

Human hydrocephalus is a common medical condition that is characterized by abnormalities in the flow or resorption of cerebrospinal fluid (CSF), resulting in ventricular dilatation. Human hydrocephalus can be classified into two clinical forms, congenital and acquired. Hydrocephalus is one of the complex and multifactorial neurological disorders. A growing body of evidence indicates that genetic factors play a major role in the pathogenesis of hydrocephalus. An understanding of the genetic components and mechanism of this complex disorder may offer us significant insights into the molecular etiology of impaired brain development and an accumulation of the cerebrospinal fluid in cerebral compartments during the pathogenesis of hydrocephalus. Genetic studies in animal models have started to open the way for understanding the underlying pathology of hydrocephalus. At least 43 mutants/loci linked to hereditary hydrocephalus have been identified in animal models and humans. Up to date, 9 genes associated with hydrocephalus have been identified in animal models. In contrast, only one such gene has been identified in humans. Most of known hydrocephalus gene products are the important cytokines, growth factors or related molecules in the cellular signal pathways during early brain development. The current molecular genetic evidence from animal models indicate that in the early development stage, impaired and abnormal brain development caused by abnormal cellular signaling and functioning, all these cellular and developmental events would eventually lead to the congenital hydrocephalus. Owing to our very primitive knowledge of the genetics and molecular pathogenesis of human hydrocephalus, it is difficult to evaluate whether data gained from animal models can be extrapolated to humans. Initiation of a large population genetics study in humans will certainly provide invaluable information about the molecular and cellular etiology and the developmental mechanisms of human hydrocephalus. This review summarizes the recent findings on this issue among human and animal models, especially with reference to the molecular genetics, pathological, physiological and cellular studies, and identifies future research directions

Coal combustion: Effects of process conditions on char reactivity. Quarterly technical report No. 5, September 1, 1992--December 1, 1992

During the past quarter, we carried out a study of the kinetics of char combustion, assessed the reproducibility error of our experiments, and continued our systematic study of the effects of particle size and oxygen concentration on the reactivity of chars. The results from the kinetic study indicated that the rate expression for combustion of Illinois No. 6 chars is first order with respect to the oxygen concentration. The activation energy and the preexponential factor for this reaction were also calculated. The reproducibility error assessment shows that the average relative error increases with increasing particle size. Thus, the number of combustion runs needed for accurate measurements of the reaction rate increases with increasing particle size. For combustion in the regime of diffusional limitations, our results show the ignition temperature decreases with increasing pyrolysis heating rates, increasing coal particle size, decreasing heat treatment temperatures and increasing oxygen concentrations. The kinetic parameters (activation energy, preexponential rate factor, and order of reaction) for the combustion of Illinois No. 6 coal were determined using our thermogravimetric reactor with video microscopy imaging (TGA/VMI). In order to obtain a constant slope from the Arrhenius plot, the experiments were performed in the kinetic control regime. Our previous results demonstrated that in this regime char reactivity is independent of pyrolysis heating rate, heat treatment temperature (HTT), soak time and particle size. For this study therefore, we chose to pyrolyze and combust particles from the 28--32 mesh (500--600 {mu}m) fraction of Illinois No. 6 coal

Pyrolysis and gasification of coal at high temperatures. Quarterly progress report No. 9, September 15, 1989--December 15, 1989

Coals of different ranks will be pyrolyzed in a microscope hot-stage reactor using inert and reacting atmospheres. The macropore structure oft he produced chars will be characterized using video microscopy and digital image processing techniques to obtain pore size distributions. Comparative studies will quantify the effect of pyrolysis conditions (heating rates, final heat treatment temperatures, particle size and inert or reacting atmosphere) on the pore structure of the devolatilized chars. The devolatilized chars will be gasified in the regime of strong intraparticle diffusional limitations using O{sub 2}/N{sub 2} and O{sub 2}/H{sub 2}/N{sub 2} mixtures. Constant temperature and programmed-temperature experiments in a TGA will be used for these studies. Additional gasification experiments performed in the hot-stage reactor will be videotaped and selected images will be analyzed to obtain quantitative data on particle shrinkage and fragmentation

Coal combustion: Effect of process conditions on char reactivity. Quarterly technical report, July 1, 1994--September 30, 1994

The project will quantify the effect of the following pyrolysis conditions on the macropore structure and on the subsequent reactivity of chars: (a) pyrolysis heating rate; (b) final heat treatment temperature (HTT); (c) duration of heat treatment at HTT (or soak time); (d) pyrolysis atmosphere (N{sub 2} or O{sub 2}/N{sub 2} mixtures); (e) coal particle size (100-1,000 {mu}m in diameter); (f) sulfur-capturing additives (limestone); and (g) coal rank. Pyrolysis experiments will be carried out for three coals from the Argonne collection: (1) a high-volatile bituminous coal with high ash content (Illinois {number_sign}6), (2) a bituminous coal with low ash content (Utah Blind Canyon) and (3) a lower rank subbituminous coal (Wyodak-Anderson seam). A mathematical model was developed to study the thermal ignition of char particles. The model assumes a bimodal pores size distribution with small micropores (of the order of a few {angstrom}) and large micropores in the {mu}m size range. All the model parameters can be estimated using data obtained previously in our laboratory. We are currently testing this model to determine its validity and to investigate how char properties (porosity, particle size, macropore surface area, micropore radius) and operating conditions (temperature, oxygen concentration, flow rate) affect ignition phenomena

Coal combustion: Effect of process conditions on char reactivity. Quarterly technical report, September 1, 1991--December 1, 1991

The project will quantify the effect of the following pyrolysis conditions on the macropore structure and on the subsequent reactivity of chars: (a) pyrolysis heating rate; (b) final heat treatment temperature (HTT); (c) duration of heat treatment at HTT (or soak time); (d) pyrolysis atmosphere (N{sub 2} or O{sub 2}/N{sub 2} mixtures); (e) coal particle size (100 {endash} 1000 {mu}m in diameter); (f) sulfur-capturing additives (limestone); and (g) coal rank. Pyrolysis experiments will be carried out for three coals from the Argonne collection: (1) a high-volatile bituminous coal with high ash content (Illinois {number_sign}6), (2) a bituminous coal with low ash content (Utah Blind Canyon) and (3) a lower rank subbituminous coal (Wyodak-Anderson seam)

Coal combustion: Effects of process conditions on char reactivity

During the past quarter, we carried out a study of the kinetics of char combustion, assessed the reproducibility error of our experiments, and continued our systematic study of the effects of particle size and oxygen concentration on the reactivity of chars. The results from the kinetic study indicated that the rate expression for combustion of Illinois No. 6 chars is first order with respect to the oxygen concentration. The activation energy and the preexponential factor for this reaction were also calculated. The reproducibility error assessment shows that the average relative error increases with increasing particle size. Thus, the number of combustion runs needed for accurate measurements of the reaction rate increases with increasing particle size. For combustion in the regime of diffusional limitations, our results show the ignition temperature decreases with increasing pyrolysis heating rates, increasing coal particle size, decreasing heat treatment temperatures and increasing oxygen concentrations. The kinetic parameters (activation energy, preexponential rate factor, and order of reaction) for the combustion of Illinois No. 6 coal were determined using our thermogravimetric reactor with video microscopy imaging (TGA/VMI). In order to obtain a constant slope from the Arrhenius plot, the experiments were performed in the kinetic control regime. Our previous results demonstrated that in this regime char reactivity is independent of pyrolysis heating rate, heat treatment temperature (HTT), soak time and particle size. For this study therefore, we chose to pyrolyze and combust particles from the 28--32 mesh (500--600 [mu]m) fraction of Illinois No. 6 coal