Enrico Carlon

Modeling background intensity in DNA microarrays

DNA microarrays are devices that are able, in principle, to detect and quantify the presence of specific nucleic acid sequences in complex biological mixtures. The measurement consists in detecting fluorescence signals from several spots on the microarray surface onto which different probe sequences are grafted. One of the problems of the data analysis is that the signal contains a noisy background component due to non-specific binding. This paper presents a physical model for background estimation in Affymetrix Genechips. It combines two different approaches. The first is based on the sequence composition, specifically its sequence dependent hybridization affinity. The second is based on the strong correlation of intensities from locations which are the physical neighbors of a specific spot on the chip. Both effects are incorporated in a background functional which contains 24 free parameters, fixed by minimization on a training data set. In all data analyzed the sequence specific parameters, obtained by minimization, are found to strongly correlate with empirically determined stacking free energies for RNA/DNA hybridization in solution. Moreover, there is an overall agreement with experimental background data and we show that the physicsbased model proposed in this paper performs on average better than purely statistical approaches for background calculations. The model thus provides an interesting alternative method for background subtraction schemes in Affymetrix Genechips.

Reparametrizing the loop entropy weights: effect on DNA melting curves.

Recent advances in the understanding of the melting behavior of double-stranded DNA with statistical mechanics methods lead to improved estimates of the weight factors for the dissociation events of the chains, in particular for interior loop melting. So far, in the modeling of DNA melting, the entropy of denaturated loops has been estimated from the number of configurations of a closed self-avoiding walk. It is well understood now that a loop embedded in a chain is characterized by a loop closure exponent c which is higher than that of an isolated loop. Here we report an analysis of DNA melting curves for sequences of a broad range of lengths (from 10 to 10(6) base pairs) calculated with a program based on the algorithms underlying MELTSIM. Using the embedded loop exponent we find that the cooperativity parameter is one order of magnitude bigger than current estimates. We argue that in the melting region the double helix persistence length is greatly reduced compared to its room temperature value, so that the use of the embedded loop closure exponent for real DNA sequences is justified.

Physico-chemical foundations underpinning microarray and next-generation sequencing experiments

Hybridization of nucleic acids on solid surfaces is a key process involved in high-throughput technologies such as microarrays and, in some cases, next-generation sequencing (NGS). A physical understanding of the hybridization process helps to determine the accuracy of these technologies. The goal of a widespread research program is to develop reliable transformations between the raw signals reported by the technologies and individual molecular concentrations from an ensemble of nucleic acids. This research has inputs from many areas, from bioinformatics and biostatistics, to theoretical and experimental biochemistry and biophysics, to computer simulations. A group of leading researchers met in Ploen Germany in 2011 to discuss present knowledge and limitations of our physico-chemical understanding of high-throughput nucleic acid technologies. This meeting inspired us to write this summary, which provides an overview of the state-of-the-art approaches based on physico-chemical foundation to modeling of the nucleic acids hybridization process on solid surfaces. In addition, practical application of current knowledge is emphasized.

Density matrix renormalization group and reaction-diffusion processes

Abstract:The density matrix renormalization group ( DMRG) is applied to some one-dimensional reaction-diffusion models in the vicinity of and at their critical point. The stochastic time evolution for these models is given in terms of a non-symmetric “quantum Hamiltonian”, which is diagonalized using the DMRG method for open chains of moderate lengths (up to about 60 sites). The numerical diagonalization methods for non-symmetric matrices are reviewed. Different choices for an appropriate density matrix in the non-symmetric DMRG are discussed. Accurate estimates of the steady-state critical points and exponents can then be found from finite-size scaling through standard finite-lattice extrapolation methods. This is exemplified by studying the leading relaxation time and the density profiles of diffusion-annihilation and of a branching-fusing model in the directed percolation universality class.

Critical properties of the reaction-diffusion model 2A-->3A, 2A-->0.

The steady-state phase diagram of the one-dimensional reaction-diffusion model 2A-->3A, 2A-->0 is studied through the non-Hermitian density matrix renormalization group. In the absence of single-particle diffusion the model reduces to the pair-contact process, which has a phase transition in the universality class of directed percolation (DP) and an infinite number of absorbing steady states. When single-particle diffusion is added, the number of absorbing steady states is reduced to 2 and the model no longer shows DP critical behavior. The exponents theta=nu(parallel)/nu(perpendicular) and beta/nu(perpendicular) are calculated numerically. The value of beta/nu(perpendicular) is close to the value of the parity conserving universality class, in spite of the absence of local conservation laws.

Thermodynamic Behavior of Short Oligonucleotides in Microarray Hybridizations Can Be Described Using Gibbs Free Energy in a Nearest-Neighbor Model

While designing oligonucleotide-based microarrays, cross-hybridization between surface-bound oligos and non-intended labeled targets is probably the most difficult parameter to predict. Although literature describes rules-of-thumb concerning oligo length, overall similarity, and continuous stretches, the final behavior is difficult to predict. The aim of this study was to investigate the effect of well-defined mismatches on hybridization specificity using CodeLink Activated Slides and to study quantitatively the relation between hybridization intensity and Gibbs free energy (DeltaG), taking the mismatches into account. Our data clearly showed a correlation between the hybridization intensity and DeltaG of the oligos over 3 orders of magnitude for the hybridization intensity, which could be described by the Langmuir model. As DeltaG was calculated according to the nearest-neighbor model, using values related to DNA hybridizations in solution, this study clearly shows that target-probe hybridizations on microarrays with a three-dimensional coating are in quantitative agreement with the corresponding reaction in solution. These results can be interesting for some practical applications. The correlation between intensity and DeltaG can be used in quality control of microarray hybridizations by designing probes and corresponding RNA spikes with a range of DeltaG values. Furthermore, this correlation might be of use to fine-tune oligonucleotide design algorithms in a way to improve the prediction of the influence of mismatching targets on microarray hybridizations.

Breakdown of thermodynamic equilibrium for DNA hybridization in microarrays

Test experiments of hybridization in DNA microarrays show systematic deviations from the equilibrium isotherms. We argue that these deviations are due to the presence of a partially hybridized long-lived state, which we include in a kinetic model. Experiments confirm the model predictions for the intensity vs free-energy behavior. The existence of slow relaxation phenomena has important consequences for the specificity of microarrays as devices for the detection of a target sequence from a complex mixture of nucleic acids.

Exons, Introns, and DNA Thermodynamics

The genes of eukaryotes are characterized by protein coding fragments, the exons, interrupted by introns, i.e., stretches of DNA which do not carry useful information for protein synthesis. We have analyzed the melting behavior of randomly selected human cDNA sequences obtained from genomic DNA by removing all introns. A clear correspondence is observed between exons and melting domains. This finding may provide new insights into the physical mechanisms underlying the evolution of genes.

Inverse Langmuir method for oligonucleotide microarray analysis.

BackgroundAn algorithm for the analysis of Affymetrix Genechips is presented. This algorithm, referred to as the Inverse Langmuir Method (ILM), estimates the binding of transcripts to complementary probes using DNA/RNA hybridization free energies, and the hybridization between partially complementary transcripts in solution using RNA/RNA free energies. The balance between these two competing reactions allows for the translation of background-subtracted intensities into transcript concentrations.ResultsTo validate the ILM, it is applied to publicly available microarray data from a multi-lab comparison study. Here, microarray experiments are performed on samples which deviate only in few genes. The log2 fold change between these two samples, as obtained from RT-PCR experiments, agrees well with the log2 fold change as obtained with the ILM, indicating that the ILM determines changes in the expression level accurately. We also show that the ILM allows for the identification of outlying probes, as it yields independent concentration estimates per probe.ConclusionThe ILM is robust and offers an interesting alternative to purely statistical algorithms for microarray data analysis.

Reptation in the Rubinstein-Duke model: The influence of end-reptons dynamics

We investigate the Rubinstein–Duke model for polymer reptation by means of density-matrix renormalization group techniques both in the absence and presence of a driving field. In the former case the renewal time τ and the diffusion coefficient D are calculated for chains up to N=150 reptons and their scaling behavior in N is analyzed. Both quantities scale as powers of N:τ∼Nz and D∼1/Nx with the asymptotic exponents z=3 and x=2, in agreement with the reptation theory. For an intermediate range of lengths, however, the data are well fitted by some effective exponents whose values are quite sensitive to the dynamics of the end reptons. We find 2.7<z<3.3 and 1.8<x<2.1 for the range of parameters considered and we suggest how to influence the end reptons dynamics in order to bring out such a behavior. At finite and not too small driving field, we observe the onset of the so-called band inversion phenomenon according to which long polymers migrate faster than shorter ones as opposed to the small field dynamics...