Dielectric relaxation in biological materials

The study of dielectric properties concerns storage and dissipation of electric and magnetic energy in materials. Dielectrics are important in order to explain various phenomena in Solid-State Physics and in Physics of Biological Materials. Indeed, during the last two centuries, many scientists have tried to explain and model the dielectric relaxation. Starting from the Kohlrausch model and passing through the ideal Debye one, they arrived at more com- plex models that try to explain the experimentally observed distributions of relaxation times, including the classical (Cole-Cole, Davidson-Cole and Havriliak-Negami) and the more recent ones (Hilfer, Jonscher, Weron, etc.). The purpose of this thesis is to discuss a variety of models carrying out the analysis both in the frequency and in the time domain. Particular attention is devoted to the three classical models, that are studied using a transcendental function known as Mittag-Leffler function. We highlight that one of the most important properties of this function, its complete monotonicity, is an essential property for the physical acceptability and realizability of the models. Lo studio delle proprietà dielettriche riguarda l’immagazzinamento e la dissipazione di energia elettrica e magnetica nei materiali. I dielettrici sono importanti al fine di spiegare vari fenomeni nell’ambito della Fisica dello Stato Solido e della Fisica dei Materiali Biologici. Infatti, durante i due secoli passati, molti scienziati hanno tentato di spiegare e modellizzare il rilassamento dielettrico. A partire dal modello di Kohlrausch e passando attraverso quello ideale di Debye, sono giunti a modelli più complessi che tentano di spiegare la distribuzione osservata sperimentalmente di tempi di rilassamento, tra i quali modelli abbiamo quelli classici (Cole-Cole, Davidson-Cole e Havriliak-Negami) e quelli più recenti (Hilfer, Jonscher, Weron, etc.). L’obiettivo di questa tesi è discutere vari modelli, conducendo l’analisi sia nel dominio delle frequenze sia in quello dei tempi. Particolare attenzione è rivolta ai tre modelli classici, i quali sono studiati utilizzando una funzione trascendente nota come funzione di Mittag-Leffler. Evidenziamo come una delle più importanti proprietà di questa funzione, la sua completa monotonia, è una proprietà essenziale per l’accettabilità fisica e la realizzabilità dei modelli.

Numerical model of the human cornea based on stromal microstructure: identification of mechanical properties for two age groups

The optical quality of the human eye mainly depends on the refractive performance of the cornea. The shape of the cornea is a mechanical balance between intraocular pressure and tissue intrinsic stiffness. Several surgical procedures in ophthalmology alter the biomechanics of the cornea to provoke local or global curvature changes for vision correction. Legitimated by the large number of surgical interventions performed every day, the demand for a deeper understanding of corneal biomechanics is rising to improve the safety of procedures and medical devices. The aim of our work is to propose a numerical model of corneal biomechanics, based on the stromal microstructure. Our novel anisotropic constitutive material law features a probabilistic weighting approach to model collagen fiber distribution as observed on human cornea by Xray scattering analysis (Aghamohammadzadeh et. al., Structure, February 2004). Furthermore, collagen cross-linking was explicitly included in the strain energy function. Results showed that the proposed model is able to successfully reproduce both inflation and extensiometry experimental data (Elsheikh et. al., Curr Eye Res, 2007; Elsheikh et. al., Exp Eye Res, May 2008). In addition, the mechanical properties calculated for patients of different age groups (Group A: 65-79 years; Group B: 80-95 years) demonstrate an increased collagen cross-linking, and a decrease in collagen fiber elasticity from younger to older specimen. These findings correspond to what is known about maturing fibrous biological tissue. Since the presented model can handle different loading situations and includes the anisotropic distribution of collagen fibers, it has the potential to simulate clinical procedures involving nonsymmetrical tissue interventions. In the future, such mechanical model can be used to improve surgical planning and the design of next generation ophthalmic devices.

Coupling biomechanics to a cellular level model: An approach to patient-specific image driven multi-scale and multi-physics tumor simulation

Modeling of tumor growth has been performed according to various approaches addressing different biocomplexity levels and spatiotemporal scales. Mathematical treatments range from partial differential equation based diffusion models to rule-based cellular level simulators, aiming at both improving our quantitative understanding of the underlying biological processes and, in the mid- and long term, constructing reliable multi-scale predictive platforms to support patient-individualized treatment planning and optimization. The aim of this paper is to establish a multi-scale and multi-physics approach to tumor modeling taking into account both the cellular and the macroscopic mechanical level. Therefore, an already developed biomodel of clinical tumor growth and response to treatment is self-consistently coupled with a biomechanical model. Results are presented for the free growth case of the imageable component of an initially point-like glioblastoma multiforme tumor. The composite model leads to significant tumor shape corrections that are achieved through the utilization of environmental pressure information and the application of biomechanical principles. Using the ratio of smallest to largest moment of inertia of the tumor material to quantify the effect of our coupled approach, we have found a tumor shape correction of 20\% by coupling biomechanics to the cellular simulator as compared to a cellular simulation without preferred growth directions. We conclude that the integration of the two models provides additional morphological insight into realistic tumor growth behavior. Therefore, it might be used for the development of an advanced oncosimulator focusing on tumor types for which morphology plays an important role in surgical and/or radio-therapeutic treatment planning.

A BAYESIAN HIERARCHICAL MODEL FOR CONSTRAINED DISTRIBUTED LAG FUNCTIONS: ESTIMATING THE TIME COURSE OF HOSPITALIZATION ASSOCIATED WITH AIR POLLUTION EXPOSURE

Numerous time series studies have provided strong evidence of an association between increased levels of ambient air pollution and increased levels of hospital admissions, typically at 0, 1, or 2 days after an air pollution episode. An important research aim is to extend existing statistical models so that a more detailed understanding of the time course of hospitalization after exposure to air pollution can be obtained. Information about this time course, combined with prior knowledge about biological mechanisms, could provide the basis for hypotheses concerning the mechanism by which air pollution causes disease. Previous studies have identified two important methodological questions: (1) How can we estimate the shape of the distributed lag between increased air pollution exposure and increased mortality or morbidity? and (2) How should we estimate the cumulative population health risk from short-term exposure to air pollution? Distributed lag models are appropriate tools for estimating air pollution health effects that may be spread over several days. However, estimation for distributed lag models in air pollution and health applications is hampered by the substantial noise in the data and the inherently weak signal that is the target of investigation. We introduce an hierarchical Bayesian distributed lag model that incorporates prior information about the time course of pollution effects and combines information across multiple locations. The model has a connection to penalized spline smoothing using a special type of penalty matrix. We apply the model to estimating the distributed lag between exposure to particulate matter air pollution and hospitalization for cardiovascular and respiratory disease using data from a large United States air pollution and hospitalization database of Medicare enrollees in 94 counties covering the years 1999-2002.

Functional and structural characterization of the first prokaryotic member of the L-amino acid transporter (LAT) family: a model for APC transporters

We have identified YkbA from Bacillus subtilis as a novel member of the L-amino acid transporter (LAT) family of amino acid transporters. The protein is approximately 30% identical in amino acid sequence to the light subunits of human heteromeric amino acid transporters. Purified His-tagged YkbA from Escherichia coli membranes reconstituted in proteoliposomes exhibited sodium-independent, obligatory exchange activity for L-serine and L-threonine and also for aromatic amino acids, albeit with less activity. Thus, we propose that YkbA be renamed SteT (Ser/Thr exchanger transporter). Kinetic analysis supports a sequential mechanism of exchange for SteT. Freeze-fracture analysis of purified, functionally active SteT in proteoliposomes, together with blue native polyacrylamide gel electrophoresis and transmission electron microscopy of detergent-solubilized purified SteT, suggest that the transporter exists in a monomeric form. Freeze-fracture analysis showed spherical particles with a diameter of 7.4 nm. Transmission electron microscopy revealed elliptical particles (diameters 6 x 7 nm) with a distinct central depression. To our knowledge, this is the first functional characterization of a prokaryotic member of the LAT family and the first structural data on an APC (amino acids, polyamines, and choline for organocations) transporter. SteT represents an excellent model to study the molecular architecture of the light subunits of heteromeric amino acid transporters and other APC transporters.

IDENTIFICATION OF GENES CONTROLLING BIOLOGICAL PROCESSES AND PATHWAYS THROUGH STATISTICAL ANALYSIS AND NETWORK RECONSTRUCTION

The developmental processes and functions of an organism are controlled by the genes and the proteins that are derived from these genes. The identification of key genes and the reconstruction of gene networks can provide a model to help us understand the regulatory mechanisms for the initiation and progression of biological processes or functional abnormalities (e.g. diseases) in living organisms. In this dissertation, I have developed statistical methods to identify the genes and transcription factors (TFs) involved in biological processes, constructed their regulatory networks, and also evaluated some existing association methods to find robust methods for coexpression analyses. Two kinds of data sets were used for this work: genotype data and gene expression microarray data. On the basis of these data sets, this dissertation has two major parts, together forming six chapters. The first part deals with developing association methods for rare variants using genotype data (chapter 4 and 5). The second part deals with developing and/or evaluating statistical methods to identify genes and TFs involved in biological processes, and construction of their regulatory networks using gene expression data (chapter 2, 3, and 6). For the first part, I have developed two methods to find the groupwise association of rare variants with given diseases or traits. The first method is based on kernel machine learning and can be applied to both quantitative as well as qualitative traits. Simulation results showed that the proposed method has improved power over the existing weighted sum method (WS) in most settings. The second method uses multiple phenotypes to select a few top significant genes. It then finds the association of each gene with each phenotype while controlling the population stratification by adjusting the data for ancestry using principal components. This method was applied to GAW 17 data and was able to find several disease risk genes. For the second part, I have worked on three problems. First problem involved evaluation of eight gene association methods. A very comprehensive comparison of these methods with further analysis clearly demonstrates the distinct and common performance of these eight gene association methods. For the second problem, an algorithm named the bottom-up graphical Gaussian model was developed to identify the TFs that regulate pathway genes and reconstruct their hierarchical regulatory networks. This algorithm has produced very significant results and it is the first report to produce such hierarchical networks for these pathways. The third problem dealt with developing another algorithm called the top-down graphical Gaussian model that identifies the network governed by a specific TF. The network produced by the algorithm is proven to be of very high accuracy.

Making epothilones fluoresce: design, synthesis, and biological characterization of a fluorescent N12-aza-epothilone (azathilone)

A green fluorescent 12-aza-epothilone (azathilone) derivative has been prepared through the attachment of the 4-nitro-2,1,3-benzoxadiazole (NBD) fluorophore to the 12-nitrogen atom of the azamacrolide core structure. While less potent than natural epothilones or different N12-acylated azathilone derivatives, NBD-azathilone (3) promotes tubulin assembly, inhibits cancer cell proliferation in vitro and arrests the cell cycle at the G2/M transition. Most significantly, the binding of 3 to cellular microtubules (MTs) could be directly visualized by confocal fluorescence microscopy. Based on competition binding experiments with laulimalide-stabilized MTs in vitro, the N12-Boc substituted azathilone 1, Epo A, and NBD-azathilone (3) all interact with the same tubulin-binding site. Computational studies provided a structural model of the complexes between beta-tubulin and 1 or 3, respectively, in which the NBD moiety of 3 or the BOC moiety of 1 directly and specifically contribute to MT binding. Collectively, these data demonstrate that the cellular effects of 3 and, by inference, also of other azathilones are the result of their interactions with the cellular MT network.

XML for Model Specification in Neuroscience

One of the main roles of the Neural Open Markup Language, NeuroML, is to facilitate cooperation in building, simulating, testing and publishing models of channels, neurons and networks of neurons. MorphML, which was developed as a common format for exchange of neural morphology data, is distributed as part of NeuroML but can be used as a stand-alone application. In this collection of tutorials and workshop summary, we provide an overview of these XML schemas and provide examples of their use in down-stream applications. We also summarize plans for the further development of XML specifications for modeling channels, channel distributions, and network connectivity.

VR Based Visualization and Exploration of Plant Biological Data

This paper investigates the use of virtual reality (VR) technologies to facilitate the analysis of plant biological data in distinctive steps in the application pipeline. Reconstructed three-dimensional biological models (primary polygonal models) transferred to a virtual environment support scientists' collaborative exploration of biological datasets so that they obtain accurate analysis results and uncover information hidden in the data. Examples of the use of virtual reality in practice are provided and a complementary user study was performed.

Zebrafish (Danio rerio) as a model organism for investigating endocrine disruption

Endocrine-disrupting compounds (EDCs) are widespread in the aquatic environment and can cause alterations in development, physiological homeostasis and health of vertebrates. Zebrafish, Danio rerio, has been suggested as a model species to identify targets as well as modes of EDC action. In fact, zebrafish has been found useful in EDC screening, in EDC effects assessment and in studying targets and mechanisms of EDC action. Since many of the environmental EDCs interfere with the sex steroid system of vertebrates, most EDC studies with zebrafish addressed disruption of sexual differentiation and reproduction. However, other targets of EDCs action must not be overlooked. For using a species as a toxicological model, a good knowledge of the biological traits of this species is a pre-requisite for the rational design of test protocols and endpoints as well as for the interpretation and extrapolation of the toxicological findings. Due to the genomic resources available for zebrafish and the long experience with zebrafish in toxicity testing, it is easily possible to establish molecular endpoints for EDC effects assessment. Additionally, the zebrafish model offers a number of technical advantages including ease and cost of maintenance, rapid development, high fecundity, optical transparency of embryos supporting phenotypic screening, existence of many mutant strains, or amenability for both forward and reverse genetics. To date, the zebrafish has been mainly used to identify molecular targets of EDC action and to determine effect thresholds, while the potential of this model species to study immediate and delayed physiological consequences of molecular interactions has been instrumentalized only partly. One factor that may limit the exploitation of this potential is the still rather fragmentary knowledge of basic biological and endocrine traits of zebrafish. Information on species-specific features in endocrine processes and biological properties, however, need to be considered in establishing EDC test protocols using zebrafish, in extrapolating findings from zebrafish to other vertebrate species, and in understanding how EDC-induced gene expression changes translate into disease.

Zebrafish (Danio rerio) neuromast: promising biological endpoint linking developmental and toxicological studies

Aquatic toxicology is facing the challenge to assess the impact of complex mixtures of compounds on diverse biological endpoints. So far, ecotoxicology focuses mainly on apical endpoints such as growth, lethality and reproduction, but does not consider sublethal toxic effects that may indirectly cause ecological effects. One such sublethal effect is toxicant-induced impairment of neurosensory functions which will affect important behavioural traits of exposed organisms. Here, we critically review the mechanosensory lateral line (LL) system of zebrafish as a model to screen for chemical effects on neurosensory function of fish in particular and vertebrates in general. The LL system consists of so-called neuromasts, composed of centrally located sensory hair cells, and surrounding supporting cells. The function of neuromasts is the detection of water movements that is essential for the fish's ability to detect prey, to escape predator, to socially interact or to show rheotactic behaviour. Recent advances in the study of these organs provided researchers with a broad area of molecular tools for easy and rapid detection of neuromasts dysfunction and/or disturbed development. Further, genes involved in neuromasts differentiation have been identified using auditory/mechanosensory mutants and morphants. A number of environmental toxicants including metals and pharmaceuticals have been shown to affect neuromasts development and/or function. The use of the LL organ for toxicological studies offers the advantage to integrate the available profound knowledge on developmental biology of the neuromasts with the study of chemical toxicity. This combination may provide a powerful tool in environmental risk assessment.

Using state variables to model the response of tumour cells to radiation and heat: a novel multi-hit-repair approach

In order to overcome the limitations of the linear-quadratic model and include synergistic effects of heat and radiation, a novel radiobiological model is proposed. The model is based on a chain of cell populations which are characterized by the number of radiation induced damages (hits). Cells can shift downward along the chain by collecting hits and upward by a repair process. The repair process is governed by a repair probability which depends upon state variables used for a simplistic description of the impact of heat and radiation upon repair proteins. Based on the parameters used, populations up to 4-5 hits are relevant for the calculation of the survival. The model describes intuitively the mathematical behaviour of apoptotic and nonapoptotic cell death. Linear-quadratic-linear behaviour of the logarithmic cell survival, fractionation, and (with one exception) the dose rate dependencies are described correctly. The model covers the time gap dependence of the synergistic cell killing due to combined application of heat and radiation, but further validation of the proposed approach based on experimental data is needed. However, the model offers a work bench for testing different biological concepts of damage induction, repair, and statistical approaches for calculating the variables of state.

Dynamics of a minimal model of interlocked positive and negative feedback loops of transcriptional regulation by cAMP-response element binding proteins.

cAMP-response element binding (CREB) proteins are involved in transcriptional regulation in a number of cellular processes (e.g., neural plasticity and circadian rhythms). The CREB family contains activators and repressors that may interact through positive and negative feedback loops. These loops can be generated by auto- and cross-regulation of expression of CREB proteins, via CRE elements in or near their genes. Experiments suggest that such feedback loops may operate in several systems (e.g., Aplysia and rat). To understand the functional implications of such feedback loops, which are interlocked via cross-regulation of transcription, a minimal model with a positive and negative loop was developed and investigated using bifurcation analysis. Bifurcation analysis revealed diverse nonlinear dynamics (e.g., bistability and oscillations). The stability of steady states or oscillations could be changed by time delays in the synthesis of the activator (CREB1) or the repressor (CREB2). Investigation of stochastic fluctuations due to small numbers of molecules of CREB1 and CREB2 revealed a bimodal distribution of CREB molecules in the bistability region. The robustness of the stable HIGH and LOW states of CREB expression to stochastic noise differs, and a critical number of molecules was required to sustain the HIGH state for days or longer. Increasing positive feedback or decreasing negative feedback also increased the lifetime of the HIGH state, and persistence of this state may correlate with long-term memory formation. A critical number of molecules was also required to sustain robust oscillations of CREB expression. If a steady state was near a deterministic Hopf bifurcation point, stochastic resonance could induce oscillations. This comparative analysis of deterministic and stochastic dynamics not only provides insights into the possible dynamics of CREB regulatory motifs, but also demonstrates a framework for understanding other regulatory processes with similar network architecture.