Anders Løland

Effects of mRNA amplification on gene expression ratios in cDNA experiments estimated by analysis of variance

BackgroundA limiting factor of cDNA microarray technology is the need for a substantial amount of RNA per labeling reaction. Thus, 20–200 micro-grams total RNA or 0.5–2 micro-grams poly (A) RNA is typically required for monitoring gene expression. In addition, gene expression profiles from large, heterogeneous cell populations provide complex patterns from which biological data for the target cells may be difficult to extract. In this study, we chose to investigate a widely used mRNA amplification protocol that allows gene expression studies to be performed on samples with limited starting material. We present a quantitative study of the variation and noise present in our data set obtained from experiments with either amplified or non-amplified material.ResultsUsing analysis of variance (ANOVA) and multiple hypothesis testing, we estimated the impact of amplification on the preservation of gene expression ratios. Both methods showed that the gene expression ratios were not completely preserved between amplified and non-amplified material. We also compared the expression ratios between the two cell lines for the amplified material with expression ratios between the two cell lines for the non-amplified material for each gene. With the aid of multiple t-testing with a false discovery rate of 5%, we found that 10% of the genes investigated showed significantly different expression ratios.ConclusionAlthough the ratios were not fully preserved, amplification may prove to be extremely useful with respect to characterizing low expressing genes.

Limitations of mRNA amplification from small-size cell samples

BackgroundGlobal mRNA amplification has become a widely used approach to obtain gene expression profiles from limited material. An important concern is the reliable reflection of the starting material in the results obtained. This is especially important with extremely low quantities of input RNA where stochastic effects due to template dilution may be present. This aspect remains under-documented in the literature, as quantitative measures of data reliability are most often lacking. To address this issue, we examined the sensitivity levels of each transcript in 3 different cell sample sizes. ANOVA analysis was used to estimate the overall effects of reduced input RNA in our experimental design. In order to estimate the validity of decreasing sample sizes, we examined the sensitivity levels of each transcript by applying a novel model-based method, TransCount.ResultsFrom expression data, TransCount provided estimates of absolute transcript concentrations in each examined sample. The results from TransCount were used to calculate the Pearson correlation coefficient between transcript concentrations for different sample sizes. The correlations were clearly transcript copy number dependent. A critical level was observed where stochastic fluctuations became significant. The analysis allowed us to pinpoint the gene specific number of transcript templates that defined the limit of reliability with respect to number of cells from that particular source. In the sample amplifying from 1000 cells, transcripts expressed with at least 121 transcripts/cell were statistically reliable and for 250 cells, the limit was 1806 transcripts/cell. Above these thresholds, correlation between our data sets was at acceptable values for reliable interpretation.ConclusionThese results imply that the reliability of any amplification experiment must be validated empirically to justify that any gene exists in sufficient quantity in the input material. This finding has important implications for any experiment where only extremely small samples such as single cell analyses or laser captured microdissected cells are available.

Causal modeling and inference for electricity markets

How does dynamic price information flow among Northern European electricity spot prices and prices of major electricity generation fuel sources? We use time series models combined with new advances in causal inference to answer these questions. Applying our methods to weekly Nordic and German electricity prices, and oil, gas and coal prices, with German wind power and Nordic water reservoir levels as exogenous variables, we estimate a causal model for the price dynamics, both for contemporaneous and lagged relationships. In contemporaneous time, Nordic and German electricity prices are interlinked through gas prices. In the long run, electricity prices and British gas prices adjust themselves to establish the equilibrium price level, since oil, coal, continental gas and EUR/USD are found to be weakly exogenous.

Statistical rehabilitation of improper correlation matrices

The simplest way to describe the dependence for a set of financial assets is their correlation matrix. This correlation matrix can be improper when it is specified element-wise. We describe a new method for obtaining a positive definite correlation matrix starting from an improper one. The experts opinion and trust in each pairwise correlation is described by a beta distribution. Then, by combining these individual distributions, a joint distribution over the space of positive definite correlation matrices is obtained using Cholesky factorization, and its mode constitutes the new proper correlation matrix. The optimization is complemented by a visual representation of the entries that were most affected by the legalization procedure. We also sketch a Bayesian approach to the same problem.

Modeling Nord Pool's NO1 area price

The Nordic electricity spot power market (Nord Pool) is divided into several price areas. The NO1 area (southern Norway) is of particular interest. It is dominated by hydropower and has experienced large deviations from the system price. Using historical data (prices, reservoir levels and transmission congestion data), we statistically investigate the historical contributors to this price spread. The water reservoir level, followed by the Elspot capacity and Elspot net capacity utilization, are found to be the most important explanatory variables. As expected, lower capacity and more flow coincide with higher price spreads.