Logistic regression with Markov chains as covariates

The tobacco-specific nitrosamine 4-(methylnitrosamino)-1-(3-pyridyl)-1-butanone (NNK) is an obvious carcinogen for lung cancer. Since CBMN (Cytokinesis-blocked micronucleus) has been found to be extremely sensitive to NNK-induced genetic damage, it is a potential important factor to predict the lung cancer risk. However, the association between lung cancer and NNK-induced genetic damage measured by CBMN assay has not been rigorously examined. ^ This research develops a methodology to model the chromosomal changes under NNK-induced genetic damage in a logistic regression framework in order to predict the occurrence of lung cancer. Since these chromosomal changes were usually not observed very long due to laboratory cost and time, a resampling technique was applied to generate the Markov chain of the normal and the damaged cell for each individual. A joint likelihood between the resampled Markov chains and the logistic regression model including transition probabilities of this chain as covariates was established. The Maximum likelihood estimation was applied to carry on the statistical test for comparison. The ability of this approach to increase discriminating power to predict lung cancer was compared to a baseline "non-genetic" model. ^ Our method offered an option to understand the association between the dynamic cell information and lung cancer. Our study indicated the extent of DNA damage/non-damage using the CBMN assay provides critical information that impacts public health studies of lung cancer risk. This novel statistical method could simultaneously estimate the process of DNA damage/non-damage and its relationship with lung cancer for each individual.^

Evaluating statistical methods used to estimate the number of postsynaptic receptors.

Calcium levels in spines play a significant role in determining the sign and magnitude of synaptic plasticity. The magnitude of calcium influx into spines is highly dependent on influx through N-methyl D-aspartate (NMDA) receptors, and therefore depends on the number of postsynaptic NMDA receptors in each spine. We have calculated previously how the number of postsynaptic NMDA receptors determines the mean and variance of calcium transients in the postsynaptic density, and how this alters the shape of plasticity curves. However, the number of postsynaptic NMDA receptors in the postsynaptic density is not well known. Anatomical methods for estimating the number of NMDA receptors produce estimates that are very different than those produced by physiological techniques. The physiological techniques are based on the statistics of synaptic transmission and it is difficult to experimentally estimate their precision. In this paper we use stochastic simulations in order to test the validity of a physiological estimation technique based on failure analysis. We find that the method is likely to underestimate the number of postsynaptic NMDA receptors, explain the source of the error, and re-derive a more precise estimation technique. We also show that the original failure analysis as well as our improved formulas are not robust to small estimation errors in key parameters.

Concept, design and implementation of a cardiovascular gene-centric 50 k SNP array for large-scale genomic association studies.

A wealth of genetic associations for cardiovascular and metabolic phenotypes in humans has been accumulating over the last decade, in particular a large number of loci derived from recent genome wide association studies (GWAS). True complex disease-associated loci often exert modest effects, so their delineation currently requires integration of diverse phenotypic data from large studies to ensure robust meta-analyses. We have designed a gene-centric 50 K single nucleotide polymorphism (SNP) array to assess potentially relevant loci across a range of cardiovascular, metabolic and inflammatory syndromes. The array utilizes a "cosmopolitan" tagging approach to capture the genetic diversity across approximately 2,000 loci in populations represented in the HapMap and SeattleSNPs projects. The array content is informed by GWAS of vascular and inflammatory disease, expression quantitative trait loci implicated in atherosclerosis, pathway based approaches and comprehensive literature searching. The custom flexibility of the array platform facilitated interrogation of loci at differing stringencies, according to a gene prioritization strategy that allows saturation of high priority loci with a greater density of markers than the existing GWAS tools, particularly in African HapMap samples. We also demonstrate that the IBC array can be used to complement GWAS, increasing coverage in high priority CVD-related loci across all major HapMap populations. DNA from over 200,000 extensively phenotyped individuals will be genotyped with this array with a significant portion of the generated data being released into the academic domain facilitating in silico replication attempts, analyses of rare variants and cross-cohort meta-analyses in diverse populations. These datasets will also facilitate more robust secondary analyses, such as explorations with alternative genetic models, epistasis and gene-environment interactions.

Population genetics of VNTR loci and their applications in evolutionary studies

Variable number of tandem repeats (VNTR) are genetic loci at which short sequence motifs are found repeated different numbers of times among chromosomes. To explore the potential utility of VNTR loci in evolutionary studies, I have conducted a series of studies to address the following questions: (1) What are the population genetic properties of these loci? (2) What are the mutational mechanisms of repeat number change at these loci? (3) Can DNA profiles be used to measure the relatedness between a pair of individuals? (4) Can DNA fingerprint be used to measure the relatedness between populations in evolutionary studies? (5) Can microsatellite and short tandem repeat (STR) loci which mutate stepwisely be used in evolutionary analyses?^ A large number of VNTR loci typed in many populations were studied by means of statistical methods developed recently. The results of this work indicate that there is no significant departure from Hardy-Weinberg expectation (HWE) at VNTR loci in most of the human populations examined, and the departure from HWE in some VNTR loci are not solely caused by the presence of population sub-structure.^ A statistical procedure is developed to investigate the mutational mechanisms of VNTR loci by studying the allele frequency distributions of these loci. Comparisons of frequency distribution data on several hundreds VNTR loci with the predictions of two mutation models demonstrated that there are differences among VNTR loci grouped by repeat unit sizes.^ By extending the ITO method, I derived the distribution of the number of shared bands between individuals with any kinship relationship. A maximum likelihood estimation procedure is proposed to estimate the relatedness between individuals from the observed number of shared bands between them.^ It was believed that classical measures of genetic distance are not applicable to analysis of DNA fingerprints which reveal many minisatellite loci simultaneously in the genome, because the information regarding underlying alleles and loci is not available. I proposed a new measure of genetic distance based on band sharing between individuals that is applicable to DNA fingerprint data.^ To address the concern that microsatellite and STR loci may not be useful for evolutionary studies because of the convergent nature of their mutation mechanisms, by a theoretical study as well as by computer simulation, I conclude that the possible bias caused by the convergent mutations can be corrected, and a novel measure of genetic distance that makes the correction is suggested. In summary, I conclude that hypervariable VNTR loci are useful in evolutionary studies of closely related populations or species, especially in the study of human evolution and the history of geographic dispersal of Homo sapiens. (Abstract shortened by UMI.) ^

Models of DNA sequence evolution

Models of DNA sequence evolution and methods for estimating evolutionary distances are needed for studying the rate and pattern of molecular evolution and for inferring the evolutionary relationships of organisms or genes. In this dissertation, several new models and methods are developed.^ The rate variation among nucleotide sites: To obtain unbiased estimates of evolutionary distances, the rate heterogeneity among nucleotide sites of a gene should be considered. Commonly, it is assumed that the substitution rate varies among sites according to a gamma distribution (gamma model) or, more generally, an invariant+gamma model which includes some invariable sites. A maximum likelihood (ML) approach was developed for estimating the shape parameter of the gamma distribution $(\alpha)$ and/or the proportion of invariable sites $(\theta).$ Computer simulation showed that (1) under the gamma model, $\alpha$ can be well estimated from 3 or 4 sequences if the sequence length is long; and (2) the distance estimate is unbiased and robust against violations of the assumptions of the invariant+gamma model.^ However, this ML method requires a huge amount of computational time and is useful only for less than 6 sequences. Therefore, I developed a fast method for estimating $\alpha,$ which is easy to implement and requires no knowledge of tree. A computer program was developed for estimating $\alpha$ and evolutionary distances, which can handle the number of sequences as large as 30.^ Evolutionary distances under the stationary, time-reversible (SR) model: The SR model is a general model of nucleotide substitution, which assumes (i) stationary nucleotide frequencies and (ii) time-reversibility. It can be extended to SRV model which allows rate variation among sites. I developed a method for estimating the distance under the SR or SRV model, as well as the variance-covariance matrix of distances. Computer simulation showed that the SR method is better than a simpler method when the sequence length $L>1,000$ bp and is robust against deviations from time-reversibility. As expected, when the rate varies among sites, the SRV method is much better than the SR method.^ The evolutionary distances under nonstationary nucleotide frequencies: The statistical properties of the paralinear and LogDet distances under nonstationary nucleotide frequencies were studied. First, I developed formulas for correcting the estimation biases of the paralinear and LogDet distances. The performances of these formulas and the formulas for sampling variances were examined by computer simulation. Second, I developed a method for estimating the variance-covariance matrix of the paralinear distance, so that statistical tests of phylogenies can be conducted when the nucleotide frequencies are nonstationary. Third, a new method for testing the molecular clock hypothesis was developed in the nonstationary case. ^

Induction of endoplasmic reticular stress by bortezomib: A novel therapeutic strategy for pancreatic cancer

Bortezomib (VELCADE™, formerly known as PS-341) is a selective and potent inhibitor of the proteasome that was recently FDA-approved for the treatment of multiple myeloma. Despite its success in multiple myeloma and progression into clinical trials for other malignancies, bortezomib's exact mechanism of action remains undefined. The major objective of this study was to evaluate the anticancer activity of this drug using in vitro and in vivo pancreatic cancer models and determine whether bortezomib-induced apoptosis occurs via induction of endoplasmic reticular (ER) stress. The investigation revealed that bortezomib inhibited tumor cell proliferation via abrogation of cdk activity and induced apoptosis in pancreatic cancer cell lines. I hypothesized that bortezomib-induced apoptosis was triggered by a large accumulation ubiquitin-conjugated proteins that resulted in ER stress. My data demonstrated that bortezomib induced a unique type of ER stress in that it inhibited PKR-like ER kinase (PERK) and subsequent phosphorylation of eukaryotic initiation factor 2α (eif2α), a key event in translational suppression. The combined effects of proteasome inhibition and the failure to attenuate translation resulted in an accumulation of aggregated proteins (proteotoxicity), JNK activation, cytochrome c release, caspase-3 activation, and DNA fragmentation. Bortezomib also enhanced apoptosis induced by other agents that stimulated the unfolded protein response (UPR), demonstrating that translational suppression is a critical cytoprotective mechanism during ER stress. Tumor cells attempt to survive bortezomib-induced ER stress by sequestering aggregated proteins into large structures, termed aggresomes. Since histone deacetylase 6 (HDAC6) is essential for aggresome formation, tumor cells may be sensitized to bortezomib-induced apoptosis by blocking HDAC function. My results demonstrated that HDAC inhibitors disrupted aggresome formation and synergized with bortezomib to induce apoptosis in pancreatic cancer or multiple myeloma cells in vitro and in orthotopic pancreatic tumors in vivo. Taken together, my data establish a mechanistic link between bortezomib-induced aggresome formation, ER stress, and apoptosis and identify a novel therapeutic strategy for the treatment of pancreatic cancer and other hematologic and solid malignancies. ^

Modeling Techniques for the High-Resolution Interpretation of Cryo-Electron Microscopy Reconstructions

Essential biological processes are governed by organized, dynamic interactions between multiple biomolecular systems. Complexes are thus formed to enable the biological function and get dissembled as the process is completed. Examples of such processes include the translation of the messenger RNA into protein by the ribosome, the folding of proteins by chaperonins or the entry of viruses in host cells. Understanding these fundamental processes by characterizing the molecular mechanisms that enable then, would allow the (better) design of therapies and drugs. Such molecular mechanisms may be revealed trough the structural elucidation of the biomolecular assemblies at the core of these processes. Various experimental techniques may be applied to investigate the molecular architecture of biomolecular assemblies. High-resolution techniques, such as X-ray crystallography, may solve the atomic structure of the system, but are typically constrained to biomolecules of reduced flexibility and dimensions. In particular, X-ray crystallography requires the sample to form a three dimensional (3D) crystal lattice which is technically di‑cult, if not impossible, to obtain, especially for large, dynamic systems. Often these techniques solve the structure of the different constituent components within the assembly, but encounter difficulties when investigating the entire system. On the other hand, imaging techniques, such as cryo-electron microscopy (cryo-EM), are able to depict large systems in near-native environment, without requiring the formation of crystals. The structures solved by cryo-EM cover a wide range of resolutions, from very low level of detail where only the overall shape of the system is visible, to high-resolution that approach, but not yet reach, atomic level of detail. In this dissertation, several modeling methods are introduced to either integrate cryo-EM datasets with structural data from X-ray crystallography, or to directly interpret the cryo-EM reconstruction. Such computational techniques were developed with the goal of creating an atomic model for the cryo-EM data. The low-resolution reconstructions lack the level of detail to permit a direct atomic interpretation, i.e. one cannot reliably locate the atoms or amino-acid residues within the structure obtained by cryo-EM. Thereby one needs to consider additional information, for example, structural data from other sources such as X-ray crystallography, in order to enable such a high-resolution interpretation. Modeling techniques are thus developed to integrate the structural data from the different biophysical sources, examples including the work described in the manuscript I and II of this dissertation. At intermediate and high-resolution, cryo-EM reconstructions depict consistent 3D folds such as tubular features which in general correspond to alpha-helices. Such features can be annotated and later on used to build the atomic model of the system, see manuscript III as alternative. Three manuscripts are presented as part of the PhD dissertation, each introducing a computational technique that facilitates the interpretation of cryo-EM reconstructions. The first manuscript is an application paper that describes a heuristics to generate the atomic model for the protein envelope of the Rift Valley fever virus. The second manuscript introduces the evolutionary tabu search strategies to enable the integration of multiple component atomic structures with the cryo-EM map of their assembly. Finally, the third manuscript develops further the latter technique and apply it to annotate consistent 3D patterns in intermediate-resolution cryo-EM reconstructions. The first manuscript, titled An assembly model for Rift Valley fever virus, was submitted for publication in the Journal of Molecular Biology. The cryo-EM structure of the Rift Valley fever virus was previously solved at 27Å-resolution by Dr. Freiberg and collaborators. Such reconstruction shows the overall shape of the virus envelope, yet the reduced level of detail prevents the direct atomic interpretation. High-resolution structures are not yet available for the entire virus nor for the two different component glycoproteins that form its envelope. However, homology models may be generated for these glycoproteins based on similar structures that are available at atomic resolutions. The manuscript presents the steps required to identify an atomic model of the entire virus envelope, based on the low-resolution cryo-EM map of the envelope and the homology models of the two glycoproteins. Starting with the results of the exhaustive search to place the two glycoproteins, the model is built iterative by running multiple multi-body refinements to hierarchically generate models for the different regions of the envelope. The generated atomic model is supported by prior knowledge regarding virus biology and contains valuable information about the molecular architecture of the system. It provides the basis for further investigations seeking to reveal different processes in which the virus is involved such as assembly or fusion. The second manuscript was recently published in the of Journal of Structural Biology (doi:10.1016/j.jsb.2009.12.028) under the title Evolutionary tabu search strategies for the simultaneous registration of multiple atomic structures in cryo-EM reconstructions. This manuscript introduces the evolutionary tabu search strategies applied to enable a multi-body registration. This technique is a hybrid approach that combines a genetic algorithm with a tabu search strategy to promote the proper exploration of the high-dimensional search space. Similar to the Rift Valley fever virus, it is common that the structure of a large multi-component assembly is available at low-resolution from cryo-EM, while high-resolution structures are solved for the different components but lack for the entire system. Evolutionary tabu search strategies enable the building of an atomic model for the entire system by considering simultaneously the different components. Such registration indirectly introduces spatial constrains as all components need to be placed within the assembly, enabling the proper docked in the low-resolution map of the entire assembly. Along with the method description, the manuscript covers the validation, presenting the benefit of the technique in both synthetic and experimental test cases. Such approach successfully docked multiple components up to resolutions of 40Å. The third manuscript is entitled Evolutionary Bidirectional Expansion for the Annotation of Alpha Helices in Electron Cryo-Microscopy Reconstructions and was submitted for publication in the Journal of Structural Biology. The modeling approach described in this manuscript applies the evolutionary tabu search strategies in combination with the bidirectional expansion to annotate secondary structure elements in intermediate resolution cryo-EM reconstructions. In particular, secondary structure elements such as alpha helices show consistent patterns in cryo-EM data, and are visible as rod-like patterns of high density. The evolutionary tabu search strategy is applied to identify the placement of the different alpha helices, while the bidirectional expansion characterizes their length and curvature. The manuscript presents the validation of the approach at resolutions ranging between 6 and 14Å, a level of detail where alpha helices are visible. Up to resolution of 12 Å, the method measures sensitivities between 70-100% as estimated in experimental test cases, i.e. 70-100% of the alpha-helices were correctly predicted in an automatic manner in the experimental data. The three manuscripts presented in this PhD dissertation cover different computation methods for the integration and interpretation of cryo-EM reconstructions. The methods were developed in the molecular modeling software Sculptor (http://sculptor.biomachina.org) and are available for the scientific community interested in the multi-resolution modeling of cryo-EM data. The work spans a wide range of resolution covering multi-body refinement and registration at low-resolution along with annotation of consistent patterns at high-resolution. Such methods are essential for the modeling of cryo-EM data, and may be applied in other fields where similar spatial problems are encountered, such as medical imaging.