Computational analyses on the structure-function relation in ion channels

Ion channels are protein molecules, embedded in the lipid bilayer of the cell membranes. They act as powerful sensing elements switching chemicalphysical stimuli into ion-fluxes. At a glance, ion channels are water-filled pores, which can open and close in response to different stimuli (gating), and one once open select the permeating ion species (selectivity). They play a crucial role in several physiological functions, like nerve transmission, muscular contraction, and secretion. Besides, ion channels can be used in technological applications for different purpose (sensing of organic molecules, DNA sequencing). As a result, there is remarkable interest in understanding the molecular determinants of the channel functioning. Nowadays, both the functional and the structural characteristics of ion channels can be experimentally solved. The purpose of this thesis was to investigate the structure-function relation in ion channels, by computational techniques. Most of the analyses focused on the mechanisms of ion conduction, and the numerical methodologies to compute the channel conductance. The standard techniques for atomistic simulation of complex molecular systems (Molecular Dynamics) cannot be routinely used to calculate ion fluxes in membrane channels, because of the high computational resources needed. The main step forward of the PhD research activity was the development of a computational algorithm for the calculation of ion fluxes in protein channels. The algorithm - based on the electrodiffusion theory - is computational inexpensive, and was used for an extensive analysis on the molecular determinants of the channel conductance. The first record of ion-fluxes through a single protein channel dates back to 1976, and since then measuring the single channel conductance has become a standard experimental procedure. Chapter 1 introduces ion channels, and the experimental techniques used to measure the channel currents. The abundance of functional data (channel currents) does not match with an equal abundance of structural data. The bacterial potassium channel KcsA was the first selective ion channels to be experimentally solved (1998), and after KcsA the structures of four different potassium channels were revealed. These experimental data inspired a new era in ion channel modeling. Once the atomic structures of channels are known, it is possible to define mathematical models based on physical descriptions of the molecular systems. These physically based models can provide an atomic description of ion channel functioning, and predict the effect of structural changes. Chapter 2 introduces the computation methods used throughout the thesis to model ion channels functioning at the atomic level. In Chapter 3 and Chapter 4 the ion conduction through potassium channels is analyzed, by an approach based on the Poisson-Nernst-Planck electrodiffusion theory. In the electrodiffusion theory ion conduction is modeled by the drift-diffusion equations, thus describing the ion distributions by continuum functions. The numerical solver of the Poisson- Nernst-Planck equations was tested in the KcsA potassium channel (Chapter 3), and then used to analyze how the atomic structure of the intracellular vestibule of potassium channels affects the conductance (Chapter 4). As a major result, a correlation between the channel conductance and the potassium concentration in the intracellular vestibule emerged. The atomic structure of the channel modulates the potassium concentration in the vestibule, thus its conductance. This mechanism explains the phenotype of the BK potassium channels, a sub-family of potassium channels with high single channel conductance. The functional role of the intracellular vestibule is also the subject of Chapter 5, where the affinity of the potassium channels hEag1 (involved in tumour-cell proliferation) and hErg (important in the cardiac cycle) for several pharmaceutical drugs was compared. Both experimental measurements and molecular modeling were used in order to identify differences in the blocking mechanism of the two channels, which could be exploited in the synthesis of selective blockers. The experimental data pointed out the different role of residue mutations in the blockage of hEag1 and hErg, and the molecular modeling provided a possible explanation based on different binding sites in the intracellular vestibule. Modeling ion channels at the molecular levels relates the functioning of a channel to its atomic structure (Chapters 3-5), and can also be useful to predict the structure of ion channels (Chapter 6-7). In Chapter 6 the structure of the KcsA potassium channel depleted from potassium ions is analyzed by molecular dynamics simulations. Recently, a surprisingly high osmotic permeability of the KcsA channel was experimentally measured. All the available crystallographic structure of KcsA refers to a channel occupied by potassium ions. To conduct water molecules potassium ions must be expelled from KcsA. The structure of the potassium-depleted KcsA channel and the mechanism of water permeation are still unknown, and have been investigated by numerical simulations. Molecular dynamics of KcsA identified a possible atomic structure of the potassium-depleted KcsA channel, and a mechanism for water permeation. The depletion from potassium ions is an extreme situation for potassium channels, unlikely in physiological conditions. However, the simulation of such an extreme condition could help to identify the structural conformations, so the functional states, accessible to potassium ion channels. The last chapter of the thesis deals with the atomic structure of the !- Hemolysin channel. !-Hemolysin is the major determinant of the Staphylococcus Aureus toxicity, and is also the prototype channel for a possible usage in technological applications. The atomic structure of !- Hemolysin was revealed by X-Ray crystallography, but several experimental evidences suggest the presence of an alternative atomic structure. This alternative structure was predicted, combining experimental measurements of single channel currents and numerical simulations. This thesis is organized in two parts, in the first part an overview on ion channels and on the numerical methods adopted throughout the thesis is provided, while the second part describes the research projects tackled in the course of the PhD programme. The aim of the research activity was to relate the functional characteristics of ion channels to their atomic structure. In presenting the different research projects, the role of numerical simulations to analyze the structure-function relation in ion channels is highlighted.

Supramolecular hybrid organic-inorganic multicomponent architectures in solution and on surface

Supramolecular architectures can be built-up from a single molecular component (building block) to obtain a complex of organic or inorganic interactions creating a new emergent condensed phase of matter, such as gels, liquid crystals and solid crystal. Further the generation of multicomponent supramolecular hybrid architecture, a mix of organic and inorganic components, increases the complexity of the condensed aggregate with functional properties useful for important areas of research, like material science, medicine and nanotechnology. One may design a molecule storing a recognition pattern and programming a informed self-organization process enables to grow-up into a hierarchical architecture. From a molecular level to a supramolecular level, in a bottom-up fashion, it is possible to create a new emergent structure-function, where the system, as a whole, is open to its own environment to exchange energy, matter and information. “The emergent property of the whole assembly is superior to the sum of a singles parts”. In this thesis I present new architectures and functional materials built through the selfassembly of guanosine, in the absence or in the presence of a cation, in solution and on the surface. By appropriate manipulation of intermolecular non-covalent interactions the spatial (structural) and temporal (dynamic) features of these supramolecular architectures are controlled. Guanosine G7 (5',3'-di-decanoil-deoxi-guanosine) is able to interconvert reversibly between a supramolecular polymer and a discrete octameric species by dynamic cation binding and release. Guanosine G16 (2',3'-O-Isopropylidene-5'-O-decylguanosine) shows selectivity binding from a mix of different cation's nature. Remarkably, reversibility, selectivity, adaptability and serendipity are mutual features to appreciate the creativity of a molecular self-organization complex system into a multilevelscale hierarchical growth. The creativity - in general sense, the creation of a new thing, a new thinking, a new functionality or a new structure - emerges from a contamination process of different disciplines such as biology, chemistry, physics, architecture, design, philosophy and science of complexity.

Computational investigation of the Plasmodium falciparum fatty acid biosynthetic pathway toward the discovery of novel antimalarials

The structural peculiarities of a protein are related to its biological function. In the fatty acid elongation cycle, one small carrier protein shuttles and delivers the acyl intermediates from one enzyme to the other. The carrier has to recognize several enzymatic counterparts, specifically interact with each of them, and finally transiently deliver the carried substrate to the active site. Carry out such a complex game requires the players to be flexible and efficiently adapt their structure to the interacting protein or substrate. In a drug discovery effort, the structure-function relationships of a target system should be taken into account to optimistically interfere with its biological function. In this doctoral work, the essential role of structural plasticity in key steps of fatty acid biosynthesis in Plasmodium falciparum is investigated by means of molecular simulations. The key steps considered include the delivery of acyl substrates and the structural rearrangements of catalytic pockets upon ligand binding. The ground-level bases for carrier/enzyme recognition and interaction are also put forward. The structural features of the target have driven the selection of proper drug discovery tools, which captured the dynamics of biological processes and could allow the rational design of novel inhibitors. The model may be perspectively used for the identification of novel pathway-based antimalarial compounds.

Magnetic fields around radio galaxies from Faraday rotation measure analysis

The purpose of this thesis is to investigate the strength and structure of the magnetized medium surrounding radio galaxies via observations of the Faraday effect. This study is based on an analysis of the polarization properties of radio galaxies selected to have a range of morphologies (elongated tails, or lobes with small axial ratios) and to be located in a variety of environments (from rich cluster core to small group). The targets include famous objects like M84 and M87. A key aspect of this work is the combination of accurate radio imaging with high-quality X-ray data for the gas surrounding the sources. Although the focus of this thesis is primarily observational, I developed analytical models and performed two- and three-dimensional numerical simulations of magnetic fields. The steps of the thesis are: (a) to analyze new and archival observations of Faraday rotation measure (RM) across radio galaxies and (b) to interpret these and existing RM images using sophisticated two and three-dimensional Monte Carlo simulations. The approach has been to select a few bright, very extended and highly polarized radio galaxies. This is essential to have high signal-to-noise in polarization over large enough areas to allow computation of spatial statistics such as the structure function (and hence the power spectrum) of rotation measure, which requires a large number of independent measurements. New and archival Very Large Array observations of the target sources have been analyzed in combination with high-quality X-ray data from the Chandra, XMM-Newton and ROSAT satellites. The work has been carried out by making use of: 1) Analytical predictions of the RM structure functions to quantify the RM statistics and to constrain the power spectra of the RM and magnetic field. 2) Two-dimensional Monte Carlo simulations to address the effect of an incomplete sampling of RM distribution and so to determine errors for the power spectra. 3) Methods to combine measurements of RM and depolarization in order to constrain the magnetic-field power spectrum on small scales. 4) Three-dimensional models of the group/cluster environments, including different magnetic field power spectra and gas density distributions. This thesis has shown that the magnetized medium surrounding radio galaxies appears more complicated than was apparent from earlier work. Three distinct types of magnetic-field structure are identified: an isotropic component with large-scale fluctuations, plausibly associated with the intergalactic medium not affected by the presence of a radio source; a well-ordered field draped around the front ends of the radio lobes and a field with small-scale fluctuations in rims of compressed gas surrounding the inner lobes, perhaps associated with a mixing layer.

Simulation of Smart Materials

The aim of this thesis is the elucidation of structure-properties relationship of molecular semiconductors for electronic devices. This involves the use of a comprehensive set of simulation techniques, ranging from quantum-mechanical to numerical stochastic methods, and also the development of ad-hoc computational tools. In more detail, the research activity regarded two main topics: the study of electronic properties and structural behaviour of liquid crystalline (LC) materials based on functionalised oligo(p-phenyleneethynylene) (OPE), and the investigation on the electric field effect associated to OFET operation on pentacene thin film stability. In this dissertation, a novel family of substituted OPE liquid crystals with applications in stimuli-responsive materials is presented. In more detail, simulations can not only provide evidence for the characterization of the liquid crystalline phases of different OPEs, but elucidate the role of charge transfer states in donor-acceptor LCs containing an endohedral metallofullerene moiety. Such systems can be regarded as promising candidates for organic photovoltaics. Furthermore, exciton dynamics simulations are performed as a way to obtain additional information about the degree of order in OPE columnar phases. Finally, ab initio and molecular mechanics simulations are used to investigate the influence of an applied electric field on pentacene reactivity and stability. The reaction path of pentacene thermal dimerization in the presence of an external electric field is investigated; the results can be related to the fatigue effect observed in OFETs, that show significant performance degradation even in the absence of external agents. In addition to this, the effect of the gate voltage on a pentacene monolayer are simulated, and the results are then compared to X-ray diffraction measurements performed for the first time on operating OFETs.

Semi-synthetic bile acids as novel drug candidate in liver diseases: physico-chemical characterization and HPLC-ES-MS/MS methods for their quali-quantitative analysis in different experimental animal models

The physico-chemical characterization, structure-pharmacokinetic and metabolism studies of new semi synthetic analogues of natural bile acids (BAs) drug candidates have been performed. Recent studies discovered a role of BAs as agonists of FXR and TGR5 receptor, thus opening new therapeutic target for the treatment of liver diseases or metabolic disorders. Up to twenty new semisynthetic analogues have been synthesized and studied in order to find promising novel drugs candidates. In order to define the BAs structure-activity relationship, their main physico-chemical properties (solubility, detergency, lipophilicity and affinity with serum albumin) have been measured with validated analytical methodologies. Their metabolism and biodistribution has been studied in “bile fistula rat”, model where each BA is acutely administered through duodenal and femoral infusion and bile collected at different time interval allowing to define the relationship between structure and intestinal absorption and hepatic uptake ,metabolism and systemic spill-over. One of the studied analogues, 6α-ethyl-3α7α-dihydroxy-5β-cholanic acid, analogue of CDCA (INT 747, Obeticholic Acid (OCA)), recently under approval for the treatment of cholestatic liver diseases, requires additional studies to ensure its safety and lack of toxicity when administered to patients with a strong liver impairment. For this purpose, CCl4 inhalation to rat causing hepatic decompensation (cirrhosis) animal model has been developed and used to define the difference of OCA biodistribution in respect to control animals trying to define whether peripheral tissues might be also exposed as a result of toxic plasma levels of OCA, evaluating also the endogenous BAs biodistribution. An accurate and sensitive HPLC-ES-MS/MS method is developed to identify and quantify all BAs in biological matrices (bile, plasma, urine, liver, kidney, intestinal content and tissue) for which a sample pretreatment have been optimized.

Novel dual D3R/GSK-3β modulators: an innovative multitarget strategy for bipolar disorder

Among the psychiatric diseases, bipolar disorder (BD) is the sixth leading cause of disability with a prevalence up to 4 % worldwide. BD is a complex neuropsychiatric condition which alternates episodes of mania with symptoms of depression. Although the neurobiological pathways are not completely clarified, the dopamine (DA) hypothesis, recognized as the leading theory explaining the pathophysiology of the malady, states that the dramatically compromised homeostatic regulation of dopaminergic circuits leads to alternated changes in DA neurotransmission. Modulation of D2 and D3 receptors (D2/3R) through partial agonists represents the first-line therapeutic strategy for psychiatric diseases. Moreover, a deregulation of the enzyme glycogen synthase kinase-3β (GSK-3β) has been reported as peculiar feature of BD. In this scenario, the concomitant modulation of D3R and GSK-3β, by employing multitarget compounds, could offer promises to achieve an effective cure of this illness. In the light of these findings, we rationally envisaged the pharmacophoric model at the basis of the design of several D3R partial agonists, suitable to be exploited for the dual D3R/GSK-3β ligand design. Thus, synthetic efforts were addressed to develop a first set of hybrid molecules able to concurrently modulate the selected targets. For a chemical structure point of view, we employed different spacers to combine a substituted aryl-piperazine moiety, reported in previously discovered D3R modulators, with a pyrazole-based fragment, already identified in GSK-3β inhibitors. A fluorescent and a cellular functional assays were carried out to assess the activity of all synthetized compounds against GSK-3β and on D3R, respectively. Most of the derivatives proved to effectively modulate both GSK-3β and D3R with potencies in the low-µM and low-nM range, respectively. The consistent biological data allowed us to identify some lead candidates worth to be further modified with the aim to optimize their biological profile and to perform a structure-activity relationship (SAR) study.

Catalytic upgrading of carboxylic acids and esters to bio fuels and bio chemicals

The research activity was focused on the transformation of methyl propionate (MP) into methyl methacrylate (MMA), avoiding the use of formaldehyde (FAL) thanks to a one-pot strategy involving in situ methanol (MeOH) dehydrogenation over the same catalytic bed were the hydroxy-methylation/dehydration of MP with FAL occurs. The relevance of such research line is related to the availability of cheap renewable bio-glycerol from biodiesel production, from which MP can be obtained via a series of simple catalytic reactions. Moreover, the conventional MMA synthesis (Lucite process) suffers from safety issues related to the direct use of carcinogenic FAL and depends on non-renewable MP. During preliminary studies, ketonization of carboxylic acids and esters has been recognized as a detrimental reaction which hinders the selective synthesis of MMA at low temperature, together with H-transfer hydrogenation with FAL or MeOH as the H-donor at higher temperatures. Therefore, ketonization of propionic acid (PA) and MP was investigated over several catalysts (metal oxides and metal phosphates), to obtain a better understanding of the structure-activity relationship governing the reaction and to design a catalyst for MMA synthesis capable to promote the desired reaction while minimizing ketonization and H-transfer. However, ketonization possesses scientific and industrial value itself and represents a strategy for the upgrade of bio oils from fast pyrolysis of lignocellulosic materials, a robust and versatile technology capable to transform the most abundant biomass into liquid biofuels. The catalysts screening showed that ZrO2 and La2O3 are the best catalysts, while MgO possesses low ketonization activity, but still, H-transfer parasitic hydrogenation of MMA reduces its yield over all catalysts. Such study resulted in the design of Mg/Ga mixed oxides that showed enhanced dehydrogenating activity towards MeOH at low temperatures. It was found that the introduction of Ga not only minimize ketonization, but also modulates catalyst basicity reducing H-transfer hydrogenations.

Computational Investigation of the Molecular Mechanisms Regulating Nucleic Acid Processing Metalloenzymes

Polymerases and nucleases are enzymes processing DNA and RNA. They are involved in crucial processes for cell life by performing the extension and the cleavage of nucleic acid chains during genome replication and maintenance. Additionally, both enzymes are often associated to several diseases, including cancer. In order to catalyze the reaction, most of them operate via the two-metal-ion mechanism. For this, despite showing relevant differences in structure, function and catalytic properties, they share common catalytic elements, which comprise the two catalytic ions and their first-shell acidic residues. Notably, recent studies of different metalloenzymes revealed the recurrent presence of additional elements surrounding the active site, thus suggesting an extended two-metal-ion-centered architecture. However, whether these elements have a catalytic function and what is their role is still unclear. In this work, using state-of-the-art computational techniques, second- and third-shell elements are showed to act in metallonucleases favoring the substrate positioning and leaving group release. In particular, in hExo1 a transient third metal ion is recruited and positioned near the two-metal-ion site by a structurally conserved acidic residue to assist the leaving group departure. Similarly, in hFEN1 second- and third-shell Arg/Lys residues operate the phosphate steering mechanism through (i) substrate recruitment, (ii) precise cleavage localization, and (iii) leaving group release. Importantly, structural comparisons of hExo1, hFEN1 and other metallonucleases suggest that similar catalytic mechanisms may be shared by other enzymes. Overall, the results obtained provide an extended vision on parallel strategies adopted by metalloenzymes, which employ divalent metal ion or positively charged residues to ensure efficient and specific catalysis. Furthermore, these outcomes may have implications for de novo enzyme engineering and/or drug design to modulate nucleic acid processing.

Design and characterization of polymorphs and co-crystals of organic molecular semiconductors

In the last decades, organic semiconductors have attracted attention due to their possible employment in solution-processed optoelectronic and electronic devices. One of the advantages of solution processing is the possibility to process into flexible substrates at low cost. Organic molecular materials tend to form polymorphs, which can exhibit very different properties. In most cases, the control of the crystal structure is decisive to maximize the performance of the final device. Although organic electronics have progressed a lot, n-type organic semiconductors still lag behind p-type, presenting challenges such as air instability and poor solubility. NDI derivatives are promising candidates for applications in organic electronics due to their characteristics. Recently, the structure-properties relationship and the polymorphism of these molecules have gained attention. In the first part of this thesis, NDI-C6 thermal behavior was extensively explored which revealed two different behaviors depending on the annealing process. This study allowed to define the stability ranking of the NDI-C6 bulk forms and to determine the crystal structure of Form γ at 54°C. Additionally, the polymorphic and thermal behavior of thin films of NDI-C6 was also explored. It was possible to isolate pure Form α, Form β, Form γ and a new metastable Form ε. It was also possible to determine the stability ranking of the phases in thin films. OFETs were fabricated having different polymorphs as active layer, unfortunately the performance was not ideal. During the second part of this thesis, core-chlorinated NDIs with fluoroalkyl chains were studied. Initially, the focus was on the polymorphism of CF3-NDI that revealed a solvate form with a very interesting molecular arrangement suggesting the possibility to form charge transfer co-crystals. In the last part of the thesis, the synthesis and characterization of CT co-crystal with different NDI derivatives, and acceptor and as donor BTBT and ditBu-BTBT were explored.

Anticancer drug discovery using artificial intelligence: an application in pharmacological activity prediction

Hematological cancers are a heterogeneous family of diseases that can be divided into leukemias, lymphomas, and myelomas, often called “liquid tumors”. Since they cannot be surgically removable, chemotherapy represents the mainstay of their treatment. However, it still faces several challenges like drug resistance and low response rate, and the need for new anticancer agents is compelling. The drug discovery process is long-term, costly, and prone to high failure rates. With the rapid expansion of biological and chemical "big data", some computational techniques such as machine learning tools have been increasingly employed to speed up and economize the whole process. Machine learning algorithms can create complex models with the aim to determine the biological activity of compounds against several targets, based on their chemical properties. These models are defined as multi-target Quantitative Structure-Activity Relationship (mt-QSAR) and can be used to virtually screen small and large chemical libraries for the identification of new molecules with anticancer activity. The aim of my Ph.D. project was to employ machine learning techniques to build an mt-QSAR classification model for the prediction of cytotoxic drugs simultaneously active against 43 hematological cancer cell lines. For this purpose, first, I constructed a large and diversified dataset of molecules extracted from the ChEMBL database. Then, I compared the performance of different ML classification algorithms, until Random Forest was identified as the one returning the best predictions. Finally, I used different approaches to maximize the performance of the model, which achieved an accuracy of 88% by correctly classifying 93% of inactive molecules and 72% of active molecules in a validation set. This model was further applied to the virtual screening of a small dataset of molecules tested in our laboratory, where it showed 100% accuracy in correctly classifying all molecules. This result is confirmed by our previous in vitro experiments.

Cardiac functional and structural abnormalities in a mouse model of CDKL5 deficiency disorder

CDKL5 (cyclin-dependent kinase-like 5) deficiency disorder (CDD) is a rare and severe neurodevelopmental disease that mostly affects girls who are heterozygous for mutations in the X-linked CDKL5 gene. The lack of CDKL5 protein expression or function leads to the appearance of numerous clinical features, including early-onset seizures, marked hypotonia, autistic features, and severe neurodevelopmental impairment. Mouse models of CDD, Cdkl5 KO mice, exhibit several behavioral phenotypes that mimic CDD features, such as impaired learning and memory, social interaction, and motor coordination. CDD symptomatology, along with the high CDKL5 expression levels in the brain, underscores the critical role that CDKL5 plays in proper brain development and function. Nevertheless, the improvement of the clinical overview of CDD in the past few years has defined a more detailed phenotypic spectrum; this includes very common alterations in peripheral organ and tissue function, such as gastrointestinal problems, irregular breathing, hypotonia, and scoliosis, suggesting that CDKL5 deficiency compromises not only CNS function but also that of other organs/tissues. Here we report, for the first time, that a mouse model of CDD, the heterozygous Cdkl5 KO (Cdkl5 +/-) female mouse, exhibits cardiac functional and structural abnormalities. The mice also showed QTc prolongation and increased heart rate. These changes correlate with a marked decrease in parasympathetic activity to the heart and in the expression of the Scn5a and Hcn4 voltage-gated channels. Moreover, the Cdkl5 +/- heart shows typical signs of heart aging, including increased fibrosis, mitochondrial dysfunctions, and increased ROS production. Overall, our study not only contributes to the understanding of the role of CDKL5 in heart structure/function but also documents a novel preclinical phenotype for future therapeutic investigation.

Analyzing the dependence structure of microarray data: a copula–based approach

The main aim of this Ph.D. dissertation is the study of clustering dependent data by means of copula functions with particular emphasis on microarray data. Copula functions are a popular multivariate modeling tool in each field where the multivariate dependence is of great interest and their use in clustering has not been still investigated. The first part of this work contains the review of the literature of clustering methods, copula functions and microarray experiments. The attention focuses on the K–means (Hartigan, 1975; Hartigan and Wong, 1979), the hierarchical (Everitt, 1974) and the model–based (Fraley and Raftery, 1998, 1999, 2000, 2007) clustering techniques because their performance is compared. Then, the probabilistic interpretation of the Sklar’s theorem (Sklar’s, 1959), the estimation methods for copulas like the Inference for Margins (Joe and Xu, 1996) and the Archimedean and Elliptical copula families are presented. In the end, applications of clustering methods and copulas to the genetic and microarray experiments are highlighted. The second part contains the original contribution proposed. A simulation study is performed in order to evaluate the performance of the K–means and the hierarchical bottom–up clustering methods in identifying clusters according to the dependence structure of the data generating process. Different simulations are performed by varying different conditions (e.g., the kind of margins (distinct, overlapping and nested) and the value of the dependence parameter ) and the results are evaluated by means of different measures of performance. In light of the simulation results and of the limits of the two investigated clustering methods, a new clustering algorithm based on copula functions (‘CoClust’ in brief) is proposed. The basic idea, the iterative procedure of the CoClust and the description of the written R functions with their output are given. The CoClust algorithm is tested on simulated data (by varying the number of clusters, the copula models, the dependence parameter value and the degree of overlap of margins) and is compared with the performance of model–based clustering by using different measures of performance, like the percentage of well–identified number of clusters and the not rejection percentage of H0 on . It is shown that the CoClust algorithm allows to overcome all observed limits of the other investigated clustering techniques and is able to identify clusters according to the dependence structure of the data independently of the degree of overlap of margins and the strength of the dependence. The CoClust uses a criterion based on the maximized log–likelihood function of the copula and can virtually account for any possible dependence relationship between observations. Many peculiar characteristics are shown for the CoClust, e.g. its capability of identifying the true number of clusters and the fact that it does not require a starting classification. Finally, the CoClust algorithm is applied to the real microarray data of Hedenfalk et al. (2001) both to the gene expressions observed in three different cancer samples and to the columns (tumor samples) of the whole data matrix.

Computational methods for the analysis of protein structure and function

The vast majority of known proteins have not yet been experimentally characterized and little is known about their function. The design and implementation of computational tools can provide insight into the function of proteins based on their sequence, their structure, their evolutionary history and their association with other proteins. Knowledge of the three-dimensional (3D) structure of a protein can lead to a deep understanding of its mode of action and interaction, but currently the structures of <1% of sequences have been experimentally solved. For this reason, it became urgent to develop new methods that are able to computationally extract relevant information from protein sequence and structure. The starting point of my work has been the study of the properties of contacts between protein residues, since they constrain protein folding and characterize different protein structures. Prediction of residue contacts in proteins is an interesting problem whose solution may be useful in protein folding recognition and de novo design. The prediction of these contacts requires the study of the protein inter-residue distances related to the specific type of amino acid pair that are encoded in the so-called contact map. An interesting new way of analyzing those structures came out when network studies were introduced, with pivotal papers demonstrating that protein contact networks also exhibit small-world behavior. In order to highlight constraints for the prediction of protein contact maps and for applications in the field of protein structure prediction and/or reconstruction from experimentally determined contact maps, I studied to which extent the characteristic path length and clustering coefficient of the protein contacts network are values that reveal characteristic features of protein contact maps. Provided that residue contacts are known for a protein sequence, the major features of its 3D structure could be deduced by combining this knowledge with correctly predicted motifs of secondary structure. In the second part of my work I focused on a particular protein structural motif, the coiled-coil, known to mediate a variety of fundamental biological interactions. Coiled-coils are found in a variety of structural forms and in a wide range of proteins including, for example, small units such as leucine zippers that drive the dimerization of many transcription factors or more complex structures such as the family of viral proteins responsible for virus-host membrane fusion. The coiled-coil structural motif is estimated to account for 5-10% of the protein sequences in the various genomes. Given their biological importance, in my work I introduced a Hidden Markov Model (HMM) that exploits the evolutionary information derived from multiple sequence alignments, to predict coiled-coil regions and to discriminate coiled-coil sequences. The results indicate that the new HMM outperforms all the existing programs and can be adopted for the coiled-coil prediction and for large-scale genome annotation. Genome annotation is a key issue in modern computational biology, being the starting point towards the understanding of the complex processes involved in biological networks. The rapid growth in the number of protein sequences and structures available poses new fundamental problems that still deserve an interpretation. Nevertheless, these data are at the basis of the design of new strategies for tackling problems such as the prediction of protein structure and function. Experimental determination of the functions of all these proteins would be a hugely time-consuming and costly task and, in most instances, has not been carried out. As an example, currently, approximately only 20% of annotated proteins in the Homo sapiens genome have been experimentally characterized. A commonly adopted procedure for annotating protein sequences relies on the "inheritance through homology" based on the notion that similar sequences share similar functions and structures. This procedure consists in the assignment of sequences to a specific group of functionally related sequences which had been grouped through clustering techniques. The clustering procedure is based on suitable similarity rules, since predicting protein structure and function from sequence largely depends on the value of sequence identity. However, additional levels of complexity are due to multi-domain proteins, to proteins that share common domains but that do not necessarily share the same function, to the finding that different combinations of shared domains can lead to different biological roles. In the last part of this study I developed and validate a system that contributes to sequence annotation by taking advantage of a validated transfer through inheritance procedure of the molecular functions and of the structural templates. After a cross-genome comparison with the BLAST program, clusters were built on the basis of two stringent constraints on sequence identity and coverage of the alignment. The adopted measure explicity answers to the problem of multi-domain proteins annotation and allows a fine grain division of the whole set of proteomes used, that ensures cluster homogeneity in terms of sequence length. A high level of coverage of structure templates on the length of protein sequences within clusters ensures that multi-domain proteins when present can be templates for sequences of similar length. This annotation procedure includes the possibility of reliably transferring statistically validated functions and structures to sequences considering information available in the present data bases of molecular functions and structures.

Velocity structure and seismic anisotropy in the crust and upper mantle from Receiver Function analysis: three case studies in Italy

The research for this PhD project consisted in the application of the RFs analysis technique to different data-sets of teleseismic events recorded at temporary and permanent stations located in three distinct study regions: Colli Albani area, Northern Apennines and Southern Apennines. We found some velocity models to interpret the structures in these regions, which possess very different geologic and tectonics characteristics and therefore offer interesting case study to face. In the Colli Albani some of the features evidenced in the RFs are shared by all the analyzed stations: the Moho is almost flat and is located at about 23 km depth, and the presence of a relatively shallow limestone layer is a stable feature; contrariwise there are features which vary from station to station, indicating local complexities. Three seismic stations, close to the central part of the former volcanic edifice, display relevant anisotropic signatures­­­ with symmetry axes consistent with the emplacement of the magmatic chamber. Two further anisotropic layers are present at greater depth, in the lower crust and the upper mantle, respectively, with symmetry axes directions related to the evolution of the volcano complex. In Northern Apennines we defined the isotropic structure of the area, finding the depth of the Tyrrhenian (almost 25 km and flat) and Adriatic (40 km and dipping underneath the Apennines crests) Mohos. We determined a zone in which the two Mohos overlap, and identified an anisotropic body in between, involved in the subduction and going down with the Adiratic Moho. We interpreted the downgoing anisotropic layer as generated by post-subduction delamination of the top-slab layer, probably made of metamorphosed crustal rocks caught in the subduction channel and buoyantly rising toward the surface. In the Southern Apennines, we found the Moho depth for 16 seismic stations, and highlighted the presence of an anisotropic layer underneath each station, at about 15-20 km below the whole study area. The moho displays a dome-like geometry, as it is shallow (29 km) in the central part of the study area, whereas it deepens peripherally (down to 45 km); the symmetry axes of anisotropic layer, interpreted as a layer separating the upper and the lower crust, show a moho-related pattern, indicated by the foliation of the layer which is parallel to the Moho trend. Moreover, due to the exceptional seismic event occurred on April 6th next to L’Aquila town, we determined the Vs model for two station located next to the epicenter. An extremely high velocity body is found underneath AQU station at 4-10 km depth, reaching Vs of about 4 km/s, while this body is lacking underneath FAGN station. We compared the presence of this body with other recent works and found an anti-correlation between the high Vs body, the max slip patches and earthquakes distribution. The nature of this body is speculative since such high velocities are consistent with deep crust or upper mantle, but can be interpreted as a as high strength barrier of which the high Vs is a typical connotation.