| 1. |
- Odille, Fabrice, et al.
(författare)
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On the characterization of dynamic supramolecular systems: A general mathematical association model for linear supramolecular copolymers and application on a complex two-component hydrogen-bonding system
- 2007
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Ingår i: Chemistry: A European Journal. - : Wiley. - 1521-3765 .- 0947-6539. ; 13:34, s. 9617-9636
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Tidskriftsartikel (refereegranskat)abstract
- A general mathematical model for the characterization of the dynamic (kinetically labile) association of supramolecular assemblies in solution is presented. It is an extension of the equal K (EK) model by the stringent use of linear algebra to allow for the simultaneous presence of an unlimited number of different units in the resulting assemblies. It allows for the analysis of highly complex dynamic equilibrium systems in solution, including both supramolecular homo- and copolymers without the recourse to extensive approximations, in a field in which other analytical methods are difficult. The derived mathematical methodology makes it possible to analyze dynamic systems such as supramolecular copolymers regarding for instance the degree of polymerization, the distribution of a given monomer in different copolymers as well as its position in an aggregate. It is to date the only general means to characterize weak supramolecular systems. The model was fitted to NMR dilution titration data by using the program Matlab((R)), and a detailed algorithm for the optimization of the different parameters has been developed. The methodology is applied to a case study, a hydrogen-bonded supramolecular system, salen 4+porphyrin 5. The system is formally a two-component system but in reality a three-component system. This results in a complex dynamic system in which all monomers are associated to each other by hydrogen bonding with different association constants, resulting in homo- and copolymers 4,,5,, as well as cyclic structures 6 and 7, in addition to free 4 and 5. The system was analyzed by extensive NMR dilution titrations at variable temperatures. All chemical shifts observed at different temperatures were used in the fitting to obtain the Delta H degrees and Delta S degrees values producing the best global fit. From the derived general mathematical expressions, system 4+5 could be characterized with respect to above-mentioned parameters.
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| 2. |
- Stjernqvist, Susann, et al.
(författare)
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A continuous-index hidden Markov jump process for modeling DNA copy number data
- 2009
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Ingår i: Biostatistics. - : Oxford University Press (OUP). - 1465-4644 .- 1468-4357. ; 10:4, s. 773-778
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Tidskriftsartikel (refereegranskat)abstract
- The number of copies of DNA in human cells can be measured using array comparative genomic hybridization (aCGH), which provides intensity ratios of sample to reference DNA at genomic locations corresponding to probes on a microarray. In the present paper, we devise a statistical model, based on a latent continuous-index Markov jump process, that is aimed to capture certain features of aCGH data, including probes that are unevenly long, unevenly spaced, and overlapping. The model has a continuous state space, with 1 state representing a normal copy number of 2, and the rest of the states being either amplifications or deletions. We adopt a Bayesian approach and apply Markov chain Monte Carlo (MCMC) methods for estimating the parameters and the Markov process. The model can be applied to data from both tiling bacterial artificial chromosome arrays and oligonucleotide arrays. We also compare a model with normal distributed noise to a model with t-distributed noise, showing that the latter is more robust to outliers.
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| 3. |
- Stjernqvist, Susann, et al.
(författare)
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Continuous-index hidden Markov modelling of array CGH copy number data
- 2007
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Ingår i: Bioinformatics. - : Oxford University Press (OUP). - 1367-4803 .- 1367-4811 .- 1460-2059. ; 23:8, s. 1006-1014
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Tidskriftsartikel (refereegranskat)abstract
- Motivation: In recent years, a range of techniques for analysis and segmentation of array comparative genomic hybridization (aCGH) data have been proposed. For array designs in which clones are of unequal lengths, are unevenly spaced or overlap, the discrete-index view typically adopted by such methods may be questionable or improved. Results: We describe a continuous-index hidden Markov model for aCGH data as well as a Monte Carlo EM algorithm to estimate its parameters. It is shown that for a dataset from the BT-474 cell line analysed on 32K BAC tiling microarrays, this model yields considerably better model fit in terms of lag-1 residual autocorrelations compared to a discrete-index HMM, and it is also shown how to use the model for e.g. estimation of change points on the base-pair scale and for estimation of conditional state probabilities across the genome. In addition, the model is applied to the Glioblastoma Multiforme data used in the comparative study by Lai et al. (Lai,W.R. et al. (2005) Comparative analysis of algorithms for identifying amplifications and deletions in array CGH data. Bioinformatics, 21, 3763–3370.) giving result similar to theirs but with certain features highlighted in the continuous-index setting
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| 4. |
- Stjernqvist, Susann, et al.
(författare)
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Model-integrated estimation of normal tissue contamination for cancer SNP copy number data
- 2011
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Ingår i: Cancer Informatics. - 1176-9351. ; 10, s. 159-173
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Tidskriftsartikel (refereegranskat)abstract
- SNP allelic copy number data provides intensity measurements for the two different alleles separately. We present a method that estimates the number of copies of each allele at each SNP position, using a continuous-index hidden Markov model. The method is especially suited for cancer data, since it includes the fraction of normal tissue contamination, often present when studying data from cancer tumors, into the model. The continuous-index structure takes into account the distances between the SNPs, and is thereby appropriate also when SNPs are unequally spaced. In a simulation study we show that the method performs favorably compared to previous methods even with as much as 70% normal contamination. We also provide results from applications to clinical data produced using the Affymetrix genome-wide SNP 6.0 platform.
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| 5. |
- Stjernqvist, Susann
(författare)
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Modelling Allelic and DNA Copy Number Variations using Continuous-index Hidden Markov Models
- 2010
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In human cells there are usually two copies of each chromosome, but in cancer cells abnormalities could exist. The differences consist of segments of chromosomes with an altered number of copies. There can be deletions as well as amplifications and the lengths of the segments can also vary. Localising the deviant regions is of great importance for increasing the knowledge of the disease. In this thesis the copy numbers are modelled using Hidden Markov Models (HMMs). A hidden Markov process can be described as a Markov process observed in noise; thus it consists of two different processes such that one is an unobservable Markov process, while the other is the observed process. In paper A we present a method suitable for aCGH data from tiling BAC arrays, i.e. the probes are rather long and could overlap. In addition they are of unequal lengths and unevenly spread over the genome, which makes it suitable to apply a continuous-index process. We assume the Markov model to have a discrete state space and the parameters are estimated with an MCEM algorithm. The model in paper B is a modification of the model in paper A, such that the Markov process takes values in a continuous state space. This makes the method more realistic since it can handle larger differences in the data, including systematic errors. In addition we assume some of the transition rates to be common to get a parsimonious model. We take a Bayesian approach and use reversible jump MCMC to simulate the Markov process. In paper C we present a model designed for SNP data which consists of allelic intensities for the two alleles at each SNP. We assume a discrete number of states, but keep the parsimonious approach from paper B such that some of the transition rates are common. The SNPs are point measurements but unevenly spread over the genome which motivates a continuous-index process. Further on in paper D we present an MCMC sampler, which is suitable for hidden Markov models, when taking a Bayesian approach. We alternate between updating the parameters and the trajectory, and for the latter update we present a sequential Monte Carlo method based on forward filtering-backward simulation. The method is applied on oligonucleotide copy number data with the same model as in paper B.
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