Chemical master versus chemical langevin for first-order reaction networks

Markov jump processes are widely used to model interacting species in circumstances where discreteness and stochasticity are relevant. Such models have been particularly successful in computational cell biology, and in this case, the interactions are typically rst-order. The Chemical Langevin Equation is a stochastic dierential equation that can be regarded as an approximation to the underlying jump process. In particular, the Chemical Langevin Equation allows simulations to be performed more eectively. In this work, we obtain expressions for the rst and second moments of the Chemical Langevin Equation for a generic rst-order reaction network. Moreover, we show that these moments exactly match those of the under-lying jump process. Hence, in terms of means, variances and correlations, the Chemical Langevin Equation is an excellent proxy for the Chemical Master Equation. Our work assumes that a unique solution exists for the Chemical Langevin Equation. We also show that the moment matching re- sult extends to the case where a gene regulation model of Raser and O'Shea (Science, 2004) is replaced by a hybrid model that mixes elements of the Master and Langevin equations. We nish with numerical experiments on a dimerization model that involves second order reactions, showing that the two regimes continue to give similar results

Mathematical and computational modelling of post-transcriptional gene relation by micro-RNA

Mathematical models and computational simulations have proved valuable in many areas of cell biology, including gene regulatory networks. When properly calibrated against experimental data, kinetic models can be used to describe how the concentrations of key species evolve over time. A reliable model allows ‘what if’ scenarios to be investigated quantitatively in silico, and also provides a means to compare competing hypotheses about the underlying biological mechanisms at work. Moreover, models at different scales of resolution can be merged into a bigger picture ‘systems’ level description. In the case where gene regulation is post-transcriptionally affected by microRNAs, biological understanding and experimental techniques have only recently matured to the extent that we can postulate and test kinetic models. In this chapter, we summarize some recent work that takes the first steps towards realistic modelling, focusing on the contributions of the authors. Using a deterministic ordinary differential equation framework, we derive models from first principles and test them for consistency with recent experimental data, including microarray and mass spectrometry measurements. We first consider typical mis-expression experiments, where the microRNA level is instantaneously boosted or depleted and thereafter remains at a fixed level. We then move on to a more general setting where the microRNA is simply treated as another species in the reaction network, with microRNA-mRNA binding forming the basis for the post-transcriptional repression. We include some speculative comments about the potential for kinetic modelling to contribute to the more widespread sequence and network based approaches in the qualitative investigation of microRNA based gene regulation. We also consider what new combinations of experimental data will be needed in order to make sense of the increased systems-level complexity introduced by microRNAs

Dinucleotide Weight Matrices for Predicting Transcription Factor Binding Sites: Generalizing the Position Weight Matrix

Background: Identifying transcription factor binding sites (TFBS) in silico is key in understanding gene regulation. TFBS are string patterns that exhibit some variability, commonly modelled as ‘‘position weight matrices’ ’ (PWMs). Though convenient, the PWM has significant limitations, in particular the assumed independence of positions within the binding motif; and predictions based on PWMs are usually not very specific to known functional sites. Analysis here on binding sites in yeast suggests that correlation of dinucleotides is not limited to near-neighbours, but can extend over considerable gaps. Methodology/Principal Findings: I describe a straightforward generalization of the PWM model, that considers frequencies of dinucleotides instead of individual nucleotides. Unlike previous efforts, this method considers all dinucleotides within an extended binding region, and does not make an attempt to determine a priori the significance of particular dinucleotide correlations. I describe how to use a ‘‘dinucleotide weight matrix’ ’ (DWM) to predict binding sites, dealing in particular with the complication that its entries are not independent probabilities. Benchmarks show, for many factors, a dramatic improvement over PWMs in precision of predicting known targets. In most cases, significant further improvement arises by extending the commonly defined ‘‘core motifs’ ’ by about 10bp on either side. Though this flanking sequence shows no strong motif at the nucleotide level, the predictive power of the dinucleotide model suggests that the ‘‘signature’ ’ in DNA sequence of protein-binding affinity extends beyond the core protein-DNA contact region

New Mechanism for Voltage Induced Charge Movement Revealed in GPCRs - Theory and Experiments

Depolarization induced charge movement associated currents, analogous to gating currents in channels, were recently demonstrated in G-protein coupled receptors (GPCRs), and were found to affect the receptor's Agonist binding Affinity, hence denoted AA-currents. Here we study, employing a combined theoretical-experimental approach, the properties of the AA-currents using the m2-muscarinic receptor (m2R) as a case study. We found that the AA-currents are characterized by a “bump”, a distinct rise followed by a slow decline, which appears both in the On and the Off responses. The cumulative features implied a directional behavior of the AA-currents. This forced us to abandon the classical chemical reaction type of models and develop instead a model that includes anisotropic processes, thus producing directionality. This model fitted well the experimental data. Our main findings are that the AA-currents include two components. One is extremely fast, , at all voltages. The other is slow, at all voltages. Surprisingly, the slow component includes a process which strongly depends on voltage and can be as fast as at . The reason that it does not affect the overall time constant of the slow component is that it carries very little charge. The two fast processes are suitable candidates to link between charge movement and agonist binding affinity under physiological conditions

Feature Selection and Classification of MAQC-II Breast Cancer and Multiple Myeloma Microarray Gene Expression Data

Microarray data has a high dimension of variables but available datasets usually have only a small number of samples, thereby making the study of such datasets interesting and challenging. In the task of analyzing microarray data for the purpose of, e.g., predicting gene-disease association, feature selection is very important because it provides a way to handle the high dimensionality by exploiting information redundancy induced by associations among genetic markers. Judicious feature selection in microarray data analysis can result in significant reduction of cost while maintaining or improving the classification or prediction accuracy of learning machines that are employed to sort out the datasets. In this paper, we propose a gene selection method called Recursive Feature Addition (RFA), which combines supervised learning and statistical similarity measures. We compare our method with the following gene selection methods

Comprehensive evaluation of differential gene expression analysis methods for RNA-seq data

A large number of computational methods have been developed for analyzing differential gene expression in RNA-seq data. We describe a comprehensive evaluation of common methods using the SEQC benchmark dataset and ENCODE data. We consider a number of key features, including normalization, accuracy of differential expression detection and differential expression analysis when one condition has no detectable expression. We find significant differences among the methods, but note that array-based methods adapted to RNA-seq data perform comparably to methods designed for RNA-seq. Our results demonstrate that increasing the number of replicate samples significantly improves detection power over increased sequencing depth

Modeling Oncogenic Signaling in Colon Tumors by Multidirectional Analyses of Microarray Data Directed for Maximization of Analytical Reliability

Clinical progression of colorectal cancers (CRC) may occur in parallel with distinctive signaling alterations. We designed multidirectional analyses integrating microarray-based data with biostatistics and bioinformatics to elucidate the signaling and metabolic alterations underlying CRC development in the adenoma-carcinoma sequence.Studies were performed on normal mucosa, adenoma, and carcinoma samples obtained during surgery or colonoscopy. Collections of cryostat sections prepared from the tissue samples were evaluated by a pathologist to control the relative cell type content. The measurements were done using Affymetrix GeneChip HG-U133plus2, and probe set data was generated using two normalization algorithms: MAS5.0 and GCRMA with least-variant set (LVS). The data was evaluated using pair-wise comparisons and data decomposition into singular value decomposition (SVD) modes. The method selected for the functional analysis used the Kolmogorov-Smirnov test. Expressional profiles obtained in 105 samples of whole tissue sections were used to establish oncogenic signaling alterations in progression of CRC, while those representing 40 microdissected specimens were used to select differences in KEGG pathways between epithelium and mucosa. Based on a consensus of the results obtained by two normalization algorithms, and two probe set sorting criteria, we identified 14 and 17 KEGG signaling and metabolic pathways that are significantly altered between normal and tumor samples and between benign and malignant tumors, respectively. Several of them were also selected from the raw microarray data of 2 recently published studies (GSE4183 and GSE8671).Although the proposed strategy is computationally complex and labor–intensive, it may reduce the number of false results